GALILAEUS
Galilaeus
Lyncaeus
,
HIS
SYSTEME
OF
THE
WORLD
.
The
First
Dialogue
.
INTERLOCVTORS
.
SALVIATUS
,
SAGREDUS
,
and
SIMPLICIUS
.
SALVIATUS
.
IT
was
our
yesterdayes
resolution
,
and
agreement
,
that
we
should
to
day
discourse
the
most
distinctly
,
and
particularly
we
could
possible
,
of
the
natural
reasons
,
and
their
efficacy
that
have
been
hitherto
alledged
on
the
one
or
other
part
,
by
the
maintainers
of
the
Positions
,
Aristotelian
,
and
Ptolomaique
;
Copernicus
reputeth
the
Earth
a
Globe
like
to
a
Planet
.
and
by
the
followers
of
the
Copernican
Systeme
:
And
because
Copernicus
placing
the
Earth
among
the
moveable
Bodies
of
Heaven
,
comes
to
constitute
a
Globe
for
the
fame
like
to
a
Planet
;
it
would
be
good
that
we
began
our
disputation
with
the
examination
of
what
,
and
how
great
the
energy
of
the
Peripateticks
arguments
is
,
when
they
demonstrate
,
that
this
Hypothesis
is
impossible
:
Since
that
it
is
necessary
to
introduce
in
Nature
,
Coelestial
substances
that
are
in
alterable
and
Elementary
that
be
alterable
,
art
necessary
in
the
opinion
of
Aristotle
.
substances
different
betwixt
themselves
,
that
is
,
the
Coelestial
,
and
Elementary
;
that
impassible
and
immortal
,
this
alterable
and
corruptible
.
Which
argument
Aristotle
handleth
in
his
book
De
Coelo
,
insinuating
it
first
,
by
some
discourses
dependent
on
certain
general
assumptions
,
and
afterwards
confirming
it
with
experiments
and
perticular
demonstrations
:
following
the
same
method
,
I
will
propound
,
and
freely
speak
my
judgement
,
submitting
my self
to
your
censure
,
and
particularly
to
Simplicius
,
a
Stout
Champion
and
contender
for
the
Aristotelian
Doctrine
.
And
the
first
Step
of
the
Peripatetick
arguments
is
that
,
Aristotle
maketh
the
World
perfect
,
because
it
hath
the
threefold
demension
.
where
Aristotle
proveth
the
integrity
and
perfection
of
the
World
,
telling
us
,
that
it
is
not
a
simple
line
,
nor
a
bare
superficies
,
but
a
body
adorned
with
Longitude
,
Latitude
,
and
Profundity
;
and
because
there
are
no
more
dimensions
but
these
three
;
The
World
having
them
,
hath
all
,
and
having
all
,
is
to
be
concluded
perfect
.
And
again
,
that
by
simple
length
,
that
magnitude
is
constituted
,
which
is
called
a
Line
,
to
which
adding
breadth
,
there
is
framed
the
Superficies
,
and
yet
further
adding
the
altitude
or
profoundity
,
there
results
the
Body
,
and
after
these
three
dimensions
there
is
no
passing
farther
,
so
that
in
these
three
the
integrity
,
and
to
so
speak
,
totality
is
terminated
,
which
I
might
but
with
justice
have
required
Aristotle
to
have
proved
to
me
by
necessary
consequences
,
the
rather
in
regard
he
was
able
to
do
it
very
plainly
,
and
speedily
.
SIMPL.
What
say
you
to
the
excellent
demonstrations
in
the
2.
3.
and
4.
Texts
,
Aristotles
demonstrations
▪
to
prove
the
dimensions
to
be
three
and
no
more
.
after
the
definition
of
Continual
?
have
you
it
not
first
there
proved
,
that
there
is
no
more
but
three
dimensions
,
for
that
those
three
are
all
things
,
and
that
they
are
every
where
?
And
is
not
this
confirmed
by
the
Doctrine
and
Authority
of
the
Pythagorians
,
The
number
three
celebrated
amongst
the
Pythagorians
who
say
that
all
things
are
determined
by
three
,
beginning
,
middle
,
and
end
,
which
is
the
number
of
All
?
And
where
leave
you
that
reason
,
namely
,
that
as
it
were
by
the
law
of
Nature
,
this
number
is
used
in
the
sacrifices
of
the
Gods
?
And
why
being
so
dictated
by
nature
,
do
we
atribute
to
those
things
that
are
three
,
and
not
to
lesse
,
the
title
of
all
?
why
of
two
is
it
said
both
,
and
not
all
,
unless
they
be
three
?
And
all
this
Doctrine
you
have
in
the
second
Text.
Afterwards
in
the
third
,
Ad
pleniorem
scientiam
,
Omne
,
Totum
&
Perfectum
.
we
read
that
All
,
the
Whole
,
and
Perfect
,
are
formally
one
and
the
same
;
and
that
therefore
onely
the
Body
,
amongst
magnitudes
is
perfect
:
because
it
is
determined
by
three
,
which
is
All
,
and
being
divisible
three
manner
of
waies
,
it
is
every
way
divisible
;
but
of
the
others
,
some
are
dividible
in
one
manner
,
and
some
in
two
,
because
according
to
the
number
affixed
,
they
have
their
division
and
continuity
,
and
thus
one
magnitude
is
continuate
one
way
,
Or
Solid
.
another
two
,
a
third
,
namely
the
Body
,
every
way
.
Moreover
in
the
fourth
Text
;
doth
he
not
after
some
other
Doctrines
,
prove
it
by
another
demonstration
?
Scilicet
,
That
no
transition
is
made
but
according
to
some
defect
(
and
so
there
is
a
transition
or
passing
from
the
line
to
the
superficies
,
because
the
line
is
defective
in
breadth
)
and
that
it
is
impossible
for
the
perfect
to
want
any
thing
,
it
being
every
way
so
;
therefore
there
is
no
transition
from
the
Solid
or
Body
to
any
other
magnitude
.
Now
think
you
not
that
by
all
these
places
he
hath
sufficiently
proved
,
how
that
there
's
no
going
beyond
the
three
dimensions
,
Length
,
Breadth
,
and
Thickness
,
and
that
therefore
the
body
or
solid
,
which
hath
them
all
,
is
perfect
?
SALV
.
To
tell
you
true
,
I
think
not
my self
bound
by
all
these
reasons
to
grant
any
more
but
onely
this
,
That
that
which
hath
beginning
,
middle
,
and
end
,
may
,
and
ought
to
be
called
perfect
:
But
that
then
,
because
beginning
,
middle
,
and
end
,
are
Three
,
the
number
Three
is
a
perfect
number
,
and
hath
a
faculty
of
conferring
Perfection
on
those
things
that
have
the
same
,
I
find
no
inducement
to
grant
;
neither
do
I
understand
,
nor
believe
that
,
for
example
,
of
feet
,
the
number
three
is
more
perfect
then
four
or
two
,
nor
do
I
conceive
the
number
four
to
be
any
imperfection
to
the
Elements
:
and
that
they
would
be
more
perfect
if
they
were
three
.
Better
therefore
it
had
been
to
have
left
these
subtleties
to
the
Rhetoricians
,
and
to
have
proved
his
intent
,
by
necessary
demonstration
;
for
so
it
behoves
to
do
in
demonstrative
sciences
.
SIMPL.
You
seem
to
scorn
these
reasons
,
and
yet
it
is
all
the
Doctrine
of
the
Pythagorians
,
who
attribute
so
much
to
numbers
;
and
you
that
be
a
Mathematician
,
and
believe
many
opinions
in
the
Pythagorick
Philosophy
,
seem
now
to
contemn
their
Mysteries
.
SALV
.
That
the
Pythagorians
had
the
science
of
numbers
in
high
esteem
,
and
that
Plato
himself
admired
humane
understanding
,
Plato
held
that
humane
understanding
partook
of
divinity
,
because
it
understood
numbers
.
and
thought
that
it
pertook
of
Divinity
,
for
that
it
understood
the
nature
of
numbers
,
I
know
very
well
,
nor
should
I
be
far
from
being
of
the
same
opinion
:
But
that
the
Mysteries
for
which
Pythagoras
and
his
sect
,
had
the
Science
of
numbers
in
such
veneration
,
are
the
follies
that
abound
in
the
mouths
and
writings
of
the
vulgar
,
The
Mystery
of
Pythagorick
numbers
fabulous
.
I
no
waies
credit
:
but
rather
because
I
know
that
they
,
to
the
end
admirable
things
might
not
be
exposed
to
the
contempt
,
and
scorne
of
the
vulgar
,
censured
as
sacrilegious
,
the
publishing
of
the
abstruce
properties
of
Numbers
,
De
Papyrio
p●aetextato
,
Gellius
1.
2.
3.
and
incommensurable
and
irrational
quantities
,
by
them
investigated
;
and
divulged
,
that
he
who
discovered
them
,
was
tormented
in
the
other
World
:
I
believe
that
some
one
of
them
to
deter
the
common
sort
,
and
free
himself
from
their
inquisitiveness
,
told
them
that
the
mysteries
of
numbers
were
those
trifles
,
which
afterwards
did
so
spread
amongst
the
vulgar
;
and
this
with
a
discretion
and
subtlety
resembling
that
of
the
prudent
young
man
,
that
to
be
freed
from
the
importunity
of
his
inquisitive
Mother
or
Wife
,
I
know
not
whether
,
who
pressed
him
to
impart
the
secrets
of
the
Senate
,
contrived
that
story
,
which
afterwards
brought
her
and
many
other
women
to
be
derided
and
laught
at
by
the
same
Senate
.
SIMPL.
I
will
not
be
of
the
number
of
those
who
are
over
curious
about
the
Pythagorick
mysteries
;
but
adhering
to
the
point
in
hand
;
I
reply
,
that
the
reasons
produced
by
Aristotle
to
prove
the
dimensions
to
be
no
more
than
three
,
seem
to
me
concludent
,
and
I
believe
,
That
had
there
been
any
more
evident
demonstrations
thereof
,
Aristotle
would
not
have
omitted
them
.
SAGR.
Put
in
at
least
,
if
he
had
known
,
or
remembred
any
more
.
But
you
Salviatus
would
do
me
a
great
pleasure
to
alledge
unto
me
some
arguments
that
may
be
evident
,
and
clear
enough
for
me
to
comprehend
.
SALV
.
I
will
;
and
they
shall
be
such
as
are
not
onely
to
be
apprehended
by
you
,
but
even
by
Simplicius
himself
:
nor
onely
to
be
comprehended
,
but
are
also
already
known
,
although
haply
unobserved
;
and
for
the
more
easie
understanding
thereof
,
we
will
take
this
Pen
and
Ink
,
which
I
see
already
prepared
for
such
occasions
,
A
Geometrical
demonstration
of
the
triple
dimension
.
and
describe
a
few
figures
.
And
first
we
will
note
[
Fig.
1.
at
the
end
of
this
Dialog.
]
these
two
points
AB
,
and
draw
from
the
one
to
the
other
the
curved
lines
,
ACB
,
and
ADB
,
and
the
right
line
AB
,
I
demand
of
you
which
of
them
,
in
your
mind
,
is
that
which
determines
the
distance
between
the
terms
AB
,
&
why
?
SAGR.
I
should
say
the
right
line
,
and
not
the
crooked
,
as
well
because
the
right
is
shorter
,
as
because
it
is
one
,
sole
,
and
determinate
,
whereas
the
others
are
infinit
,
unequal
,
and
longer
;
and
my
determination
is
grounded
upon
that
,
That
it
is
one
,
and
certain
.
SALV
.
We
have
then
the
right
line
to
determine
the
length
between
the
two
terms
;
let
us
add
another
right
line
and
parallel
to
AB
,
which
let
be
CD
,
[
Fig.
2.
]
so
that
there
is
put
between
them
a
superficies
,
of
which
I
desire
you
to
assign
me
the
breadth
,
therefore
departing
from
the
point
A
,
tell
me
how
,
and
which
way
you
will
go
,
to
end
in
the
line
CD
,
and
so
to
point
me
out
the
breadth
comprehended
between
those
lines
;
let
me
know
whether
you
will
terminate
it
according
to
the
quantity
of
the
curved
line
AE
,
or
the
right
line
AF
,
or
any
other
.
SIMPL.
According
to
the
right
AF
,
and
not
according
to
the
crooked
,
that
being
already
excluded
from
such
an
use
.
SAGR.
But
I
would
take
neither
of
them
,
seeing
the
right
line
AF
runs
obliquely
;
But
would
draw
a
line
,
perpendicular
to
C
D
,
for
this
should
seem
to
me
the
shortest
,
and
the
properest
of
infinite
that
are
greater
,
and
unequal
to
one
another
,
which
may
be
produced
from
the
term
A
to
any
other
part
of
the
opposite
line
CD
.
SALV
.
Your
choice
,
and
the
reason
you
bring
for
it
in
my
judgment
is
most
excellent
;
so
that
by
this
time
we
have
proved
that
the
first
dimension
is
determined
by
a
right
line
,
the
second
namely
the
breadth
with
another
line
right
also
,
and
not
onely
right
,
but
withall
,
at
right-angles
to
the
other
that
determineth
the
length
,
and
thus
we
have
the
two
dimensions
of
length
and
breadth
,
definite
and
certain
.
But
were
you
to
bound
or
terminate
a
height
,
as
for
example
,
how
high
this
Roof
is
from
the
pavement
,
that
we
tread
on
,
being
that
from
any
point
in
the
Roof
,
we
may
draw
infinite
lines
,
both
curved
,
and
right
,
and
all
of
diverse
lengths
to
infinite
points
of
the
pavement
,
which
of
all
these
lines
would
you
make
use
of
?
SAGR.
I
would
fasten
a
line
to
the
Seeling
,
and
with
a
plummet
that
should
hang
at
it
,
would
let
it
freely
distend
it self
till
it
should
reach
well
near
to
the
pavement
,
and
the
length
of
such
a
thread
being
the
streightest
and
shortest
of
all
the
lines
,
that
could
possibly
be
drawn
from
the
same
point
to
the
pavement
,
I
would
say
was
the
true
height
of
this
Room
.
SALV
.
Very
well
,
And
when
from
the
point
noted
in
the
pavement
by
this
pendent
thread
(
taking
the
pavement
to
be
levell
and
not
declining
)
you
should
produce
two
other
right
lines
,
one
for
the
length
,
and
the
other
for
the
breadth
of
the
superficies
of
the
said
pavement
,
what
angles
should
they
make
with
the
said
thread
?
SAGR.
They
would
doubtless
meet
at
right
angles
,
the
said
lines
falling
perpendicular
,
and
the
pavement
being
very
plain
and
levell
.
SALV
.
Therefore
if
you
assign
any
point
,
for
the
term
from
whence
to
begin
your
measure
;
and
from
thence
do
draw
a
right
line
,
as
the
terminator
of
the
first
measure
,
namely
of
the
length
,
it
will
follow
of
necessity
,
that
that
which
is
to
design
out
the
largeness
or
breadth
,
toucheth
the
first
at
right-angles
,
and
that
that
which
is
to
denote
the
altitude
,
which
is
the
third
dimension
,
going
from
the
same
point
formeth
also
with
the
other
two
,
not
oblique
but
right
angles
,
and
thus
by
the
three
perpendiculars
,
as
by
three
lines
,
one
,
certain
,
and
as
short
as
is
possible
,
you
have
the
three
dimensions
AB
length
,
AC
breadth
,
and
AD
height
;
and
because
,
clear
it
is
,
that
there
cannot
concurre
any
more
lines
in
the
said
point
,
so
as
to
make
therewith
right-angles
,
and
the
dimensions
ought
to
be
determined
by
the
sole
right
lines
,
which
make
between
themselves
right-angles
;
therefore
the
dimensions
are
no
more
but
three
,
and
that
which
hath
three
hath
all
,
and
that
which
hath
all
,
is
divisible
on
all
sides
,
and
that
which
is
so
,
is
perfect
,
&c.
SIMPL.
And
who
saith
that
I
cannot
draw
other
lines
?
why
may
not
I
protract
another
line
underneath
,
unto
the
point
A
,
that
may
be
perpendicular
to
the
rest
?
SALV
.
You
can
doubtless
,
at
one
and
the
same
point
,
make
no
more
than
three
right
lines
concurre
,
that
constitute
right
angles
between
themselves
.
SAGR.
I
see
what
Simplicius
means
,
namely
,
that
should
the
said
DA
be
prolonged
downward
,
then
by
that
means
there
might
be
drawn
two
others
,
but
they
would
be
the
same
with
the
first
three
,
differing
onely
in
this
,
that
whereas
now
they
onely
touch
,
then
they
would
intersect
,
but
not
produce
new
dimensions
.
SIMPL.
I
will
not
say
that
this
your
argument
may
not
be
concludent
;
In
physical
proofs
●e●metrical
exactness
is
not
necessary
.
but
yet
this
I
say
with
Aristotle
,
that
in
things
natural
it
is
not
alwaies
necessary
,
to
bring
Mathematical
demonstrations
.
SAGR.
Grant
that
it
were
so
where
such
proofs
cannot
be
had
,
yet
if
this
case
admit
of
them
,
why
do
not
you
use
them
?
But
it
would
be
good
we
spent
no
more
words
on
this
particular
,
for
I
think
that
Salviatus
will
yield
,
both
to
Aristotle
,
and
you
,
without
farther
demonstration
,
that
the
World
is
a
body
,
and
perfect
,
yea
most
perfect
,
as
being
the
greatest
work
of
God
.
SALV
.
So
really
it
is
,
therefore
leaving
the
general
contemplation
of
the
whole
,
Parts
of
the
world
are
two
,
according
to
Aristotle
,
Coelestial
and
Elementary
contrary
to
one
another
.
let
us
descend
to
the
consideration
of
its
parts
,
which
Aristotle
,
in
his
first
division
,
makes
two
,
and
they
very
different
and
almost
contrary
to
one
another
;
namely
the
Coelestial
,
and
Elementary
:
that
ingenerable
,
incorruptible
,
unalterable
,
unpassible
,
&c.
and
this
exposed
to
a
continual
alteration
,
mutation
,
&c.
Which
difference
,
as
from
its
original
principle
,
he
derives
from
the
diversity
of
local
motions
,
and
in
this
method
he
proceeds
.
Leaving
the
sensible
,
if
I
may
so
speak
,
and
retiring
into
the
Ideal
world
,
he
begins
Architectonically
to
consider
that
nature
being
the
principle
of
motion
,
Local
motion
of
three
kinds
,
right
,
circular
,
&
mixt
.
it
followeth
that
natural
bodies
be
indued
with
local
motion
.
Next
he
declares
local
motion
to
be
of
three
kinds
,
namely
,
circular
,
right
,
and
mixt
of
right
and
circular
:
and
the
two
first
he
calleth
simple
,
Circular
,
and
streight
motions
are
simple
,
as
proceeding
by
simple
lines
.
for
that
of
all
lines
the
circular
,
and
right
are
onely
simple
;
and
here
somewhat
restraining
himself
,
he
defineth
anew
,
of
simple
motions
,
one
to
be
circular
,
namely
that
which
is
made
about
the
medium
,
and
the
other
namely
the
right
,
upwards
,
and
downwards
;
upwards
,
that
which
moveth
from
the
medium
;
downwards
,
that
which
goeth
towards
the
medium
.
And
from
hence
he
infers
,
as
he
may
by
and
necessary
consequence
,
Ad
medium
,
à
〈◊〉
,
&
circa
medium
.
that
all
simple
motions
are
confined
to
these
three
kinds
,
namely
,
to
the
medium
,
from
the
medium
,
and
about
the
medium
;
the
which
corresponds
saith
he
,
with
what
hath
been
said
before
of
a
body
,
that
it
also
is
perfected
by
three
things
,
and
so
is
its
motion
.
Having
confirmed
these
motions
,
he
proceeds
saying
,
that
of
natural
bodies
some
being
simple
,
and
some
composed
of
them
(
and
he
calleth
simple
bodies
those
,
that
have
a
principle
of
motion
from
nature
,
as
the
Fire
and
Earth
)
it
follows
that
simple
motions
belong
to
simple
bodies
,
and
mixt
to
the
compound
;
yet
in
such
sort
,
that
the
compounded
incline
to
the
part
predominant
in
the
composition
.
SAGR.
Pray
you
hold
a
little
Salviatus
,
for
I
find
so
many
doubts
to
spring
up
on
all
sides
in
this
discourse
,
that
I
shall
be
constrained
,
either
to
communicate
them
if
I
would
attentively
hearken
to
what
you
shall
add
,
or
to
take
off
my
attention
from
the
things
spoken
,
if
I
would
remember
objections
.
SALV
.
I
will
very
willingly
stay
,
for
that
I
also
run
the
same
hazard
,
and
am
ready
at
every
step
to
lose
my self
whilst
I
sail
between
Rocks
,
and
boisterous
Waves
,
that
make
me
,
as
they
say
,
to
lose
my
Compass
;
therefore
before
I
make
them
more
,
propound
your
difficulties
.
SAGR.
You
and
Aristotle
together
would
at
first
take
me
a
little
out
of
the
sensible
World
,
The
definition
of
Nature
,
either
imperfect
,
or
unseasonable
,
produced
by
Aristotle
.
to
tell
me
of
the
Architecture
,
wherewith
it
ought
to
be
fabricated
;
and
very
appositly
begin
to
tell
me
,
that
a
natural
body
is
by
nature
moveable
,
nature
being
(
as
elsewhere
it
is
defined
)
the
principle
of
motion
.
But
here
I
am
somewhat
doubtfull
why
Aristotle
said
not
that
of
natural
bodies
,
some
are
moveable
by
nature
,
and
others
immoveable
,
for
that
in
the
definition
,
nature
is
said
to
be
the
principle
of
Motion
,
and
Rest
;
for
if
natural
bodies
have
all
a
principle
of
motion
,
either
he
might
have
omitted
the
mention
of
Rest
,
in
the
definition
of
nature
:
or
not
have
introduced
such
a
definition
in
this
place
.
Next
,
as
to
the
declaration
of
what
Aristotle
intends
by
simple
motions
,
and
how
by
Spaces
he
determines
them
,
calling
those
simple
,
that
are
made
by
simple
lines
,
which
are
onely
the
right
,
and
circular
,
The
Helix
about
the
Cylinder
may
be
said
to
be
a
simple
line
.
I
entertain
it
willingly
;
nor
do
I
desire
to
tenter
the
instance
of
the
Helix
,
about
the
Cylinder
;
which
in
that
it
is
in
every
part
like
to
it self
,
might
seemingly
be
numbred
among
simple
lines
.
But
herein
I
cannot
concurre
,
that
he
should
so
restrain
simple
motions
(
whilst
he
seems
to
go
about
to
repeat
the
same
definition
in
other
words
)
as
to
call
one
of
them
the
motion
about
the
medium
,
the
others
Sursum
&
Deorsum
,
namely
upwards
and
downward
;
which
terms
are
not
to
be
used
,
out
of
the
World
fabricated
,
but
imply
it
not
onely
made
,
but
already
inhabited
by
us
;
for
if
the
right
motion
be
simple
,
by
the
simplicity
of
the
right
line
,
and
if
the
simple
motion
be
natural
,
it
is
made
on
every
side
,
to
wit
,
upwards
,
downwards
,
backwards
,
forwards
,
to
the
right
,
to
the
left
,
and
if
any
other
way
can
be
imagined
,
provided
it
be
straight
,
it
shall
agree
to
any
simple
natural
body
;
or
if
not
so
,
then
the
supposion
of
Aristotle
is
defective
.
Aristotle
accommodates
the
rules
of
Architecture
to
the
frame
of
the
World
,
and
not
the
frame
to
the
rules
.
It
appears
moreover
that
Aristotle
hinteth
but
one
circular
motion
alone
to
be
in
the
World
,
and
consequently
but
one
onely
Center
,
to
which
alone
the
motions
of
upwards
and
downwards
,
refer
.
All
which
are
apparent
proofs
,
that
Aristotles
aim
is
,
to
make
white
black
,
and
to
accommodate
Architecture
to
the
building
,
and
not
to
modle
the
building
according
to
the
precepts
of
Arthitecture
:
for
if
I
should
say
that
Nature
in
Universal
may
have
a
thousand
Circular
Motions
,
and
by
consequence
a
thousand
Centers
,
there
would
be
also
a
thousand
motions
upwards
,
and
downwards
.
Again
he
makes
as
hath
been
said
,
a
simple
motion
,
and
a
mixt
motion
,
calling
simple
,
the
circular
and
right
;
and
mixt
,
the
compound
of
them
two
:
of
natural
bodies
he
calls
some
simple
(
namely
those
that
have
a
natural
principle
to
simple
motion
)
and
others
compound
:
and
simple
motions
he
attributes
to
simple
bodies
,
and
the
compounded
to
the
compound
;
but
by
compound
motion
he
doth
no
longer
understand
the
mixt
of
right
and
circular
,
which
may
be
in
the
World
;
but
introduceth
a
mixt
motion
as
impossible
,
as
it
is
impossible
to
mixe
opposite
motions
made
in
the
same
right
line
,
so
as
to
produce
from
them
a
motion
partly
upwards
,
partly
downwards
;
and
,
to
moderate
such
an
absurdity
,
Right
motion
sometimes
simple
,
and
sometimes
mixt
according
to
Arist.
and
impossibility
,
he
asserts
that
such
mixt
bodies
move
according
to
the
simple
part
predominant
:
which
necessitates
others
to
say
,
that
even
the
motion
made
by
the
same
right
line
is
sometimes
simple
,
and
sometimes
also
compound
:
so
that
the
simplicity
of
the
motion
,
is
no
longer
dependent
onely
on
the
simplicity
of
the
line
.
SIMPL.
How
?
Is
it
not
difference
sufficient
,
that
the
simple
and
absolute
are
more
swift
than
that
which
proceeds
from
predominion
?
and
how
much
faster
doth
a
piece
of
pure
Earth
descend
,
than
a
piece
of
Wood
?
SAGR.
Well
,
Simplicius
;
But
put
case
the
simplicity
for
this
cause
was
changed
,
besides
that
there
would
be
a
hundred
thousand
mixt
motions
,
you
would
not
be
able
to
determine
the
simple
;
nay
farther
,
if
the
greater
or
lesse
velocity
be
able
to
alter
the
simplicity
of
the
motion
,
no
simple
body
should
move
with
a
simple
motion
;
since
that
in
all
natural
right
motions
,
the
velocity
is
ever
encreasing
,
and
by
consequence
still
changing
the
simplicity
,
which
as
it
is
simplicity
,
ought
of
consequence
to
be
immutable
,
and
that
which
more
importeth
,
you
charge
Aristotle
with
another
thing
,
that
in
the
definition
of
motions
compounded
,
he
hath
not
made
mention
of
tardity
nor
velocity
,
which
you
now
insert
for
a
necessary
and
essential
point
.
Again
you
can
draw
no
advantage
from
this
rule
,
for
that
there
will
be
amongst
the
mixt
bodies
some
,
(
and
that
not
a
few
)
that
will
move
swiftly
,
and
others
more
slowly
than
the
simple
;
as
for
example
,
Lead
,
and
Wood
,
in
comparison
of
earth
;
and
therefore
amongst
these
motions
,
which
call
you
the
simple
,
and
which
the
mixt
?
SIMPL.
I
would
call
that
simple
motion
,
which
is
made
by
a
simple
body
,
and
mixt
,
that
of
a
compound
body
.
SAGR.
Very
well
,
and
yet
Simplicius
a
little
before
you
said
,
that
the
simple
,
and
compound
motions
,
discovered
which
were
mixt
,
and
which
were
simple
bodies
;
now
you
will
have
me
by
simple
and
mixt
bodies
,
come
to
know
which
is
the
simple
,
and
which
is
the
compound
motion
:
an
excellent
way
to
keep
us
ignorant
,
both
of
motions
and
bodies
.
Moreover
,
you
have
also
a
little
above
declared
,
how
that
a
greater
velocity
did
not
suffice
,
but
you
seek
a
third
condition
for
the
definement
of
simple
motion
,
for
which
Aristotle
contented
himself
with
one
alone
,
namely
,
of
the
simplicity
of
the
Space
,
or
Medium
:
But
now
according
to
you
,
the
simple
motion
,
shall
be
that
which
is
made
upon
a
simple
line
,
with
a
certain
determinate
velocity
,
by
a
body
simply
moveable
.
Now
be
it
as
you
please
,
and
let
us
return
to
Aristotle
,
who
defineth
the
mixt
motion
to
be
that
compounded
of
the
right
,
and
circular
,
but
produceth
not
any
body
,
which
naturally
moveth
with
such
a
motion
.
SALV
.
I
come
again
to
Aristotle
,
who
having
very
well
,
and
Methodically
begun
his
discourse
,
but
having
a
greater
aim
to
rest
at
,
and
hit
a
marke
,
predesigned
in
his
minde
,
then
that
to
which
his
method
lead
him
,
digressing
from
the
purpose
,
he
comes
to
assert
,
as
a
thing
known
and
manifest
,
that
as
to
the
motions
directly
upwards
or
downwards
,
they
naturally
agree
to
Fire
,
and
Earth
;
and
that
therefore
it
is
necessary
,
that
besides
these
bodies
,
which
are
neer
unto
us
,
there
must
be
in
nature
another
,
to
which
the
circular
motion
may
agree
:
which
shall
be
so
much
the
more
excellent
by
how
much
the
circular
motion
is
more
perfect
,
then
the
streight
,
but
how
much
more
pefect
that
is
than
this
,
he
determines
from
the
greatness
of
the
circular
lines
perfection
above
the
right
line
;
The
circular
line
perfect
,
according
to
Aristotle
,
and
but
the
right
imperfect
,
and
why
.
calling
that
perfect
,
and
this
imperfect
;
imperfect
,
because
if
infinite
it
wanteth
a
termination
,
and
end
:
and
if
it
be
finite
,
there
is
yet
something
beyond
which
it
may
be
prolonged
.
This
is
the
basis
,
ground
work
,
and
master-stone
of
all
the
Fabrick
of
the
Aristotelian
World
,
upon
which
they
superstruct
all
their
other
properties
,
of
neither
heavy
nor
light
,
of
ingenerable
incorruptible
,
exemption
from
all
motions
,
some
onely
the
local
,
&c.
And
all
these
passions
he
affirmeth
to
be
proper
to
a
simple
body
that
is
moved
circularly
;
and
the
contrary
qualities
of
gravity
,
levity
,
corruptibility
,
&c.
he
assigns
to
bodies
naturally
moveable
in
a
streight
line
,
for
that
if
we
have
already
discovered
defects
in
the
foundation
,
we
may
rationally
question
what
soever
may
farther
built
thereon
.
I
deny
not
,
that
this
which
Aristotle
hitherto
hath
introduced
,
with
a
general
discourse
dependent
upon
universal
primary
principles
,
hath
been
since
in
process
of
time
,
re-inforced
with
particular
reasons
,
and
experiments
;
all
which
it
would
be
necessary
distinctly
to
consider
and
weigh
;
but
because
what
hath
been
said
hitherto
presents
to
such
as
consider
the
same
many
and
no
small
difficulties
,
(
and
yet
it
would
be
necessary
,
that
the
primary
principles
and
fundamentals
,
were
certain
,
firm
,
and
established
,
that
so
they
might
with
more
confidence
be
built
upon
)
it
would
not
be
amiss
,
before
we
farther
multiply
doubts
,
to
see
if
haply
(
as
I
conjecture
)
betaking
our selves
to
other
waies
,
we
may
not
light
upon
a
more
direct
and
secure
method
;
and
with
better
considered
principles
of
Architecture
lay
our
primary
fundamentals
.
Therefore
suspending
for
the
present
the
method
of
Aristotle
,
(
which
we
will
re-assume
again
in
its
proper
place
,
and
particularly
examine
;
The
world
is
supposed
by
the
Author
to
be
perfectly
ordinate
.
)
I
say
,
that
in
the
things
hitherto
affirmed
by
him
,
I
agree
with
him
,
and
admit
that
the
World
is
a
body
enjoying
all
dimensions
,
and
therefore
most
perfect
;
and
I
add
,
that
as
such
,
it
is
necessarily
most
ordinate
,
that
is
,
having
parts
between
themselves
,
with
exquisite
and
most
perfect
order
disposed
;
which
assumption
I
think
is
not
to
be
denied
,
neither
by
you
or
any
other
.
SIMPL.
Who
can
deny
it
?
the
first
particular
(
of
the
worlds
dimensions
)
is
taken
from
Aristotle
himself
,
and
its
denomination
of
ordinate
seems
onely
to
be
assumed
from
the
order
which
it
most
exactly
keeps
.
SALV
.
This
principle
then
established
,
Streight
motion
impossible
in
the
world
exactly
ordinate
.
one
may
immediately
conclude
,
that
if
the
entire
parts
of
the
World
should
be
by
their
nature
moveable
,
it
is
impossible
that
their
motions
should
be
right
,
or
other
than
circular
;
and
the
reason
is
sufficiently
easie
,
and
manifest
;
for
that
whatsoever
moveth
with
a
right
motion
,
changeth
place
;
and
continuing
to
move
,
doth
by
degrees
more
and
more
remove
from
the
term
from
whence
it
departed
,
and
from
all
the
places
thorow
which
it
successively
passed
;
and
if
such
motion
naturally
suited
with
it
,
then
it
was
not
at
the
beginning
in
its
proper
place
;
and
so
the
parts
of
the
World
were
not
disposed
with
perfect
order
.
But
we
suppose
them
to
be
perfectly
ordinate
,
therefore
as
such
,
it
is
impossible
that
they
should
by
nature
change
place
,
and
consequently
move
in
a
right
motion
.
Right
motion
nature
infinite
.
Again
,
the
right
motion
being
by
nature
infinite
,
for
that
the
right
line
is
infinite
and
indeterminate
,
it
is
impossible
that
any
moveable
can
have
a
natural
principle
of
moving
in
a
right
line
;
Motion
by
a
right
line
naturally
impossible
.
namely
toward
the
place
whither
it
is
impossible
to
arrive
,
there
being
no
prae-finite
term
;
Nature
attempts
not
things
impossible
to
be
effected
.
and
nature
,
as
Aristotle
himself
saith
well
,
never
attempts
to
do
that
which
can
never
be
done
,
nor
essaies
to
move
whither
it
is
impossible
to
arrive
.
And
if
any
one
should
yet
object
,
that
albeit
the
right
line
,
and
consequently
the
motion
by
it
is
producible
in
infinitum
,
that
is
to
say
,
is
interminate
;
yet
nevertheless
Nature
,
as
one
may
say
,
arbitrarily
hath
assigned
them
some
terms
,
and
given
natural
instincts
to
its
natural
bodies
to
move
unto
the
same
;
I
will
reply
,
that
this
might
perhaps
be
fabled
to
have
come
to
pass
in
the
first
Chaos
▪
Right
motion
might
perhaps
be
in
th●
first
Chaos
.
where
indistinct
matters
confusedly
and
inordinately
wandered
;
to
regulate
which
,
Right
motion
is
commodious
to
range
in
order
,
things
out
of
order
.
Nature
very
appositely
made
use
of
right
motions
,
by
which
,
like
as
the
well-constituted
,
moving
,
disorder
themselves
,
so
were
they
which
were
before
depravedly
disposed
by
this
motion
ranged
in
order
:
but
after
their
exquisite
distribution
and
collocation
,
it
is
impossible
that
there
should
remain
natural
inclinations
in
them
of
longer
moving
in
a
right
motion
,
from
which
now
would
ensue
their
removal
from
their
proper
and
natural
place
,
that
is
to
say
,
their
disordination
;
we
may
therefore
say
that
the
right
motion
serves
to
conduct
the
matter
to
erect
the
work
;
but
once
erected
,
that
it
is
to
rest
immoveable
,
or
if
moveable
,
Mundane
bodies
moved
in
the
beginning
in
a
right
line
,
and
afterwards
circularly
,
according
to
Plato
.
to
move
it self
onely
circularly
.
Unless
we
will
say
with
Plato
,
that
these
mundane
bodies
,
after
they
had
been
made
and
finished
,
were
for
a
certain
time
moved
by
their
Maker
,
in
a
right
motion
,
but
that
after
their
attainment
to
certain
and
determinate
places
,
they
were
revolved
one
by
one
in
Spheres
,
passing
from
the
right
to
the
circular
motion
,
wherein
they
have
been
ever
since
kept
and
maintained
.
A
sublime
conceipt
,
and
worthy
indeed
of
Plato
:
upon
which
,
I
remember
to
have
heard
our
common
friend
the
[
](A61244-e5390-b)*
*
Thus
doth
he
cover●ly
and
modestly
stile
himselfe
throughout
this
work
.
Lyncean
Academick
discourse
in
this
manner
,
if
I
have
not
forgot
it
.
Every
body
for
any
reason
constituted
in
a
state
of
rest
,
but
which
is
by
nature
moveable
,
being
set
at
liberty
doth
move
;
A
moveable
being
in
a
state
of
rest
,
shall
not
move
unless
it
have
an
inclination
to
some
particular
place
.
provided
withal
,
that
it
have
an
inclination
to
some
particular
place
;
for
should
it
stand
indifferently
affected
to
all
,
it
would
remain
in
its
rest
,
not
having
greater
inducement
to
move
one
way
than
another
.
From
the
having
of
this
inclination
necessarily
proceeds
,
The
moveable
accelerates
its
motion
,
going
towards
the
place
whither
it
hath
an
inclination
.
that
it
in
its
moving
shall
continually
increase
its
acceleration
,
and
beginning
with
a
most
slow
motion
,
it
shall
not
acquire
any
degree
of
velocity
,
before
it
shall
have
passed
thorow
all
the
degrees
of
less
velocity
,
or
greater
tardity
:
for
passing
from
the
state
of
quiet
(
which
is
the
infinite
degree
of
tardity
of
motion
)
there
is
no
reason
by
which
it
should
enter
into
such
a
determinate
degree
of
velocity
,
The
moveable
passing
from
rest
,
goeth
thorow
all
the
degrees
of
tardity
.
before
it
shall
have
entred
into
a
less
,
and
into
yet
a
less
,
before
it
entred
into
that
:
but
rather
it
stands
with
reason
,
to
pass
first
by
those
degrees
nearest
to
that
from
which
it
departed
,
and
from
those
to
the
more
remote
;
Rest
the
infinite
degree
of
tardity
.
but
the
degree
from
whence
the
moveable
began
to
move
,
is
that
of
extreme
tardity
,
namely
of
rest
.
Now
this
acceleration
of
motion
is
never
made
,
The
moveable
doth
not
accelerate
,
save
only
as
it
approacheth
nearer
to
us
term
.
but
when
the
moveable
in
moving
acquireth
it
;
nor
is
its
acquist
other
than
an
approaching
to
the
place
desired
,
to
wit
,
whither
its
natural
inclination
attracts
it
,
and
thither
it
tendeth
by
the
shortest
way
;
namely
,
by
a
right
line
.
We
may
upon
good
grounds
therefore
say
,
That
Nature
,
to
confer
upon
a
moveable
first
constituted
in
rest
a
determinate
velocity
,
useth
to
make
it
move
according
to
a
certain
time
and
space
with
a
right
motion
.
Nature
,
to
introduce
in
the
moveable
a
certain
degree
of
velocity
,
made
it
move
in
a
right
line
.
This
presupposed
,
let
us
imagine
God
to
have
created
the
Orb
v.
g.
of
Jupiter
,
on
which
he
had
determined
to
confer
such
a
certain
velocity
,
which
it
ought
afterwards
to
retain
perpetually
uniform
;
we
may
with
Plato
say
,
that
he
gave
it
at
the
beginning
a
right
and
accelerate
motion
,
and
that
it
afterwards
being
arrived
to
that
intended
degree
of
velocity
,
Vniform
velocity
convenient
to
the
circular
motion
.
he
converted
its
right
,
into
a
circular
motion
,
the
velocity
of
which
came
afterwards
naturally
to
be
uniform
.
SAGR.
I
hearken
to
this
Discourse
with
great
delight
;
and
I
believe
the
content
I
take
therein
will
be
greater
,
when
you
have
satisfied
me
in
a
doubt
:
that
is
,
(
which
I
do
not
very
well
comprehend
)
how
it
of
necessity
ensues
,
that
a
moveable
departing
from
its
rest
,
Betwixt
rest
,
and
any
assigned
degree
of
velocity
,
infinite
degrees
of
less
velocity
interpose
.
and
entring
into
a
motion
to
which
it
had
a
natural
inclination
,
it
passeth
thorow
all
the
precedent
degrees
of
tardity
,
comprehended
between
any
assigned
degree
of
velocity
,
and
the
state
of
rest
,
which
degrees
are
infinite
?
so
that
Nature
was
not
able
to
confer
them
upon
the
body
of
Jupiter
,
his
circular
motion
being
instantly
created
with
such
and
such
velocity
.
SALV
.
I
neither
did
,
Nature
doth
not
immediately
confer
a
determinate
degree
of
velocity
,
howbeit
she
could
.
nor
dare
say
,
that
it
was
impossible
for
God
or
Nature
to
confer
that
velocity
which
you
speak
of
,
immediately
;
but
this
I
say
,
that
de
facto
she
did
not
do
it
;
so
that
the
doing
it
would
be
a
work
extra-natural
,
and
by
consequence
miraculous
SAGR.
Then
you
believe
,
that
a
stone
leaving
its
rest
,
and
entring
into
its
natural
motion
towards
the
centre
of
the
Earth
,
passeth
thorow
all
the
degrees
of
tardity
inferiour
to
any
degree
of
velocity
?
SALV
.
I
do
believe
it
,
nay
am
certain
of
it
;
and
so
certain
,
that
I
am
able
to
make
you
also
very
well
satisfied
with
the
truth
thereof
.
SAGR.
Though
by
all
this
daies
discourse
I
should
gain
no
more
but
such
a
knowledge
,
I
should
think
my
time
very
well
bestowed
.
SALV
.
By
what
I
collect
from
our
discourse
,
a
great
part
of
your
scruple
lieth
in
that
it
should
in
a
time
,
and
that
very
short
,
pass
thorow
those
infinite
degrees
of
tardity
precedent
to
any
velocity
,
acquired
by
the
moveable
in
that
time
:
and
therefore
before
we
go
any
farther
,
I
will
seek
to
remove
this
difficulty
,
which
shall
be
an
easie
task
;
for
I
reply
,
that
the
moveable
passeth
by
the
aforesaid
degrees
,
The
moveable
departing
from
rest
passeth
thorow
all
degrees
of
velocity
without
staying
in
any
.
but
the
passage
is
made
without
staying
in
any
of
them
;
so
that
the
passage
requiring
but
one
sole
instant
of
time
,
and
every
small
time
containing
infinite
instants
,
we
shall
not
want
enough
of
them
to
assign
its
own
to
each
of
the
infinite
degrees
of
tardity
;
although
the
time
were
never
so
short
.
SAGR.
Hither
to
I
apprehend
you
;
nevertheless
it
is
very
much
that
that
Ball
shot
from
a
Cannon
(
for
such
I
conceive
the
cadent
moveable
)
which
yet
we
see
to
fall
with
such
a
precipice
,
that
in
less
than
ten
pulses
it
will
pass
two
hundred
yards
of
altitude
;
should
in
its
motion
be
〈…〉
joyned
with
so
small
a
degree
of
velocity
,
that
,
should
〈…〉
to
have
moved
at
that
rate
without
farther
〈…〉
it
would
not
have
past
the
same
in
a
day
.
SALV
.
You
may
say
,
nor
〈…〉
,
nor
in
ten
,
no
nor
in
a
thousand
;
as
I
will
endeavour
〈…〉
you
,
and
also
happily
without
your
contradiction
,
to
some
〈◊〉
simple
questions
that
I
will
propound
to
you
.
Therefore
tell
me
if
you
make
any
question
of
granting
that
,
that
that
ball
in
descending
goeth
increasing
its
impetus
and
velocity
.
SAGR.
I
am
most
certain
it
doth
.
SALV
.
And
if
I
should
say
that
the
impetus
acquired
in
any
place
of
its
motion
,
is
so
much
,
that
it
would
suffice
to
re-carry
it
to
that
place
from
which
it
came
,
would
you
grant
it
?
SAGR.
I
should
consent
to
it
without
contradiction
,
provided
alwaies
,
that
it
might
imploy
without
impediment
its
whole
impetus
in
that
sole
work
of
re-conducting
it self
,
or
another
equal
to
it
,
to
that
self-same
height
as
it
would
do
,
The
ponderous
mover
descending
acquireth
impetus
sufficient
to
recarry
it
to
the
like
height
.
in
case
the
Earth
were
bored
thorow
the
centre
,
and
the
Bullet
fell
a
thousand
yards
from
the
said
centre
,
for
I
verily
believe
it
would
pass
beyond
the
centre
,
ascending
as
much
as
it
had
descended
;
and
this
I
see
plainly
in
the
experiment
of
a
plummet
hanging
at
a
line
,
which
removed
from
the
perpendicular
,
which
is
its
state
of
rest
,
and
afterwards
let
go
,
falleth
towards
the
said
perpendicular
,
and
goes
as
far
beyond
it
;
or
onely
so
much
less
,
as
the
opposition
of
the
air
,
and
line
,
or
other
accidents
have
hindred
it
.
The
like
I
see
in
the
water
,
which
descending
thorow
a
pipe
,
re-mounts
as
much
as
it
had
descended
.
SALV
.
You
argue
very
well
.
And
for
that
I
know
you
will
not
scruple
to
grant
that
the
acquist
of
the
impetus
is
by
means
of
the
receding
from
the
term
whence
the
moveable
departed
,
and
its
approach
to
the
centre
,
whither
it
motion
tendeth
;
will
you
stick
to
yeeld
,
that
two
equal
moveables
,
though
descending
by
divers
lines
,
without
any
impediment
,
acquire
equal
impetus
,
provided
that
the
approaches
to
the
centre
be
equal
?
SAGR.
I
do
not
very
well
understand
the
question
.
SALV
.
I
will
express
it
better
by
drawing
a
Figure
:
therefore
I
will
suppose
the
line
AB
[
in
Fig.
3.
]
parallel
to
the
Horizon
,
and
upon
the
point
B
,
I
will
erect
a
perpendicular
BC
;
and
after
that
I
adde
this
slaunt
line
CA.
Understanding
now
the
line
CA
to
be
an
inclining
plain
exquisitely
polished
,
and
hard
,
upon
which
descendeth
a
ball
perfectly
round
and
of
very
hard
matter
,
and
such
another
I
suppose
freely
to
descend
by
the
perpendicular
CB
:
will
you
now
confess
that
the
impetus
of
that
which
descends
by
the
plain
CA
,
being
arrived
to
the
point
A
,
may
be
equal
to
the
impetus
acquired
by
the
other
in
the
point
B
,
after
the
descent
by
the
perpendicular
CB
?
SAGR.
I
resolutely
believe
so
:
The
impetuosity
of
moveables
equally
approaching
to
the
centre
,
are
equal
.
for
in
effect
they
have
both
the
same
proximity
to
the
centre
,
and
by
that
,
which
I
have
already
granted
,
their
impetuosities
would
be
equally
sufficient
to
re-carry
them
to
the
same
height
.
SALV
.
Tell
me
now
what
you
believe
the
same
ball
would
do
put
upon
the
Horizontal
plane
AB
?
SAGR.
It
would
lie
still
,
Vpon
an
horizontall
plane
the
moveable
lieth
still
.
the
said
plane
having
no
declination
.
SALV
.
But
on
the
inclining
plane
CA
it
would
descend
,
but
with
a
gentler
motion
than
by
the
perpendicular
CB
?
SAGR.
I
may
confidently
answer
in
the
affirmative
,
it
seeming
to
me
necessary
that
the
motion
by
the
perpendicular
CB
should
be
more
swift
,
than
by
the
inclining
plane
CA
;
yet
nevertheless
,
if
this
be
,
how
can
the
Cadent
by
the
inclination
arrived
to
the
point
A
,
have
as
much
impetus
,
that
is
,
the
same
degree
of
velocity
,
that
the
Cadent
by
the
perpendicular
shall
have
in
the
point
B
?
these
two
Propositions
seem
contradictory
.
SALV
.
Then
you
would
think
it
much
more
false
,
The
velocity
by
the
inclining
plane
equal
to
the
velocity
by
the
perpendicular
,
and
the
motion
by
the
perpendicular
swifter
than
by
the
inclination
.
should
I
say
,
that
the
velocity
of
the
Cadents
by
the
perpendicular
,
and
inclination
,
are
absolutely
equal
:
and
yet
this
is
a
Proposition
most
true
,
as
is
also
this
that
the
Cadent
moveth
more
swiftly
by
the
perpendicular
,
than
by
the
inclination
.
SAGR.
These
Propositions
to
my
ears
sound
very
harsh
:
and
I
believe
to
yours
Simplicius
?
SIMPL.
I
have
the
same
sense
of
them
.
SALV
.
I
conceit
you
jest
with
me
,
pretending
not
to
comprehend
what
you
know
better
than
my self
:
therefore
tell
me
Simplicius
,
when
you
imagine
a
moveable
more
swift
than
another
,
what
conceit
do
you
fancy
in
your
mind
?
SIMPL.
I
fancie
one
to
pass
in
the
same
time
a
greater
space
than
the
other
,
or
to
move
equal
spaces
,
but
in
lesser
time
.
SALV
.
Very
well
:
and
for
moveables
equally
swift
,
what
's
your
conceit
of
them
?
SIMPL.
I
fancie
that
they
pass
equal
spaces
in
equal
times
.
SALV
.
And
have
you
no
other
conceit
thereof
than
this
?
SIMPL.
This
I
think
to
be
the
proper
definition
of
equal
motions
.
SAGR.
We
will
add
moreover
this
other
:
Velocities
are
said
to
be
equal
,
when
the
spaces
passed
are
proportionate
to
their
time
.
and
call
that
equal
velocity
,
when
the
spaces
passed
have
the
same
proportion
,
as
the
times
wherein
they
are
past
,
and
it
is
a
more
universal
definition
.
SALV
.
It
is
so
:
for
it
comprehendeth
the
equal
spaces
past
in
equal
times
,
and
also
the
unequal
past
in
times
unequal
,
but
proportionate
to
those
spaces
.
Take
now
the
same
Figure
,
and
applying
the
conceipt
that
you
had
of
the
more
hastie
motion
,
tell
me
why
you
think
the
velocity
of
the
Cadent
by
CB
,
is
greater
than
the
velocity
of
the
Descendent
by
CA
?
SIMPL.
I
think
so
;
because
in
the
same
time
that
the
Cadent
shall
pass
all
CB
,
the
Descendent
shall
pass
in
CA
,
a
part
less
than
CB.
SALV
.
True
;
and
thus
it
is
proved
,
that
the
moveable
moves
more
swiftly
by
the
perpendicular
,
than
by
the
inclination
.
Now
consider
,
if
in
this
same
Figure
one
may
any
way
evince
the
other
conceipt
,
and
finde
that
the
moveables
were
equally
swift
by
both
the
lines
CA
and
CB.
SIMPL.
I
see
no
such
thing
;
nay
rather
it
seems
to
contradict
what
was
said
before
.
SALV
.
And
what
say
you
,
Sagredus
?
I
would
not
teach
you
what
you
knew
before
,
and
that
of
which
but
just
now
you
produced
me
the
definition
.
SAGR.
The
definition
I
gave
you
,
was
,
that
moveables
may
be
called
equally
swift
,
when
the
spaces
passed
are
proportional
to
the
times
in
which
they
passed
;
therefore
to
apply
the
definition
to
the
present
case
,
it
will
be
requisite
,
that
the
time
of
descent
by
CA
,
to
the
time
of
falling
by
CB
,
should
have
the
same
proportion
that
the
line
CA
hath
to
the
line
CB
;
but
I
understand
not
how
that
can
be
,
for
that
the
motion
by
CB
is
swifter
than
by
CA.
SALV
.
And
yet
you
must
of
necessity
know
it
.
Tell
me
a
little
,
do
not
these
motions
go
continually
accelerating
?
SAGR.
They
do
;
but
more
in
the
perpendicular
than
in
the
inclination
.
SALV
.
But
this
acceleration
in
the
perpendicular
,
is
it
yet
notwithstanding
such
in
comparison
of
that
of
the
inclined
,
that
two
equal
parts
being
taken
in
any
place
of
the
said
perpendicular
and
inclining
lines
,
the
motion
in
the
parts
of
the
perpendicular
is
alwaies
more
swift
,
than
in
the
part
of
the
inclination
?
SAGR.
I
say
not
so
:
but
I
could
take
a
space
in
the
inclination
,
in
which
the
velocity
shall
be
far
greater
than
in
the
like
space
taken
in
the
perpendicular
;
and
this
shall
be
,
if
the
space
in
the
perpendicular
should
be
taken
near
to
the
end
C
,
and
in
the
inclination
,
far
from
it
.
SALV
.
You
see
then
,
that
the
Proposition
which
saith
,
that
the
motion
by
the
perpendicular
is
more
swift
than
by
the
inclination
,
holds
not
true
universally
,
but
onely
of
the
motions
,
which
begin
from
the
extremity
,
namely
from
the
point
of
rest
:
without
which
restriction
,
the
Proposition
would
be
so
deficient
,
that
its
very
direct
contrary
might
be
true
;
namely
,
that
the
motion
in
the
inclining
plane
is
swifter
than
in
the
perpendicular
:
for
it
is
certain
,
that
in
the
said
inclination
,
we
may
take
a
space
past
by
the
moveable
in
less
time
,
than
the
like
space
past
in
the
perpendicular
.
Now
because
the
motion
in
the
inclination
is
in
some
places
more
,
in
some
less
,
than
in
the
perpendicular
;
therefore
in
some
places
of
the
inclination
,
the
time
of
motion
of
the
moveable
,
shall
have
a
greater
proportion
to
the
time
of
the
motion
of
the
moveable
,
by
some
places
of
the
perpendicular
,
than
the
space
passed
,
to
the
space
passed
:
and
in
other
places
,
the
proportion
of
the
time
to
the
time
,
shall
be
less
than
that
of
the
space
to
the
space
.
As
for
example
:
two
moveables
departing
from
their
quiescence
,
namely
,
from
the
point
C
,
one
by
the
perpendicular
CB
,
[
in
Fig.
4.
]
and
the
other
by
the
inclination
CA
,
in
the
time
that
,
in
the
perpendicular
,
the
moveable
shall
have
past
all
CB
,
the
other
shall
have
past
CT
lesser
.
And
therefore
the
time
by
CT
,
to
the
time
by
CB
(
which
is
equal
)
shall
have
a
greater
proportion
than
the
line
CT
to
CB
,
being
that
the
same
to
the
less
,
hath
a
greater
proportion
than
to
the
greater
.
And
on
the
contrary
,
if
in
CA
,
prolonged
as
much
as
is
requisite
,
one
should
take
a
part
equal
to
CB
,
but
past
in
a
shorter
time
;
the
time
in
the
inclination
shall
have
a
less
proportion
to
the
time
in
the
perpendicular
,
than
the
space
to
the
space
.
If
therefore
in
the
inclination
and
perpendicular
,
we
may
suppose
such
spaces
and
velocities
,
that
the
proportion
between
the
said
spaces
be
greater
and
less
than
the
proportion
of
the
times
;
we
may
easily
grant
,
that
there
are
also
spaces
,
by
which
the
times
of
the
motions
retain
the
same
proportion
as
the
spaces
.
SAGR.
I
am
already
freed
from
my
greatest
doubt
,
and
conceive
that
to
be
not
onely
possible
,
but
necessary
,
which
I
but
now
thought
a
contradiction
:
but
nevertheless
I
understand
not
as
yet
,
that
this
whereof
we
now
are
speaking
,
is
one
of
these
possible
or
necessary
cases
;
so
as
that
it
should
be
true
,
that
the
time
of
descent
by
CA
,
to
the
time
of
the
fall
by
CB
,
hath
the
same
proportion
that
the
line
CA
hath
to
CB
;
whence
it
may
without
contradiction
be
affirmed
,
that
the
velocity
by
the
inclination
CA
,
and
by
the
perpendicular
CB
,
are
equal
.
SALV
.
Content
your self
for
this
time
,
that
I
have
removed
your
incredulity
;
but
for
the
knowledge
of
this
,
expect
it
at
some
other
time
,
namely
,
when
you
shall
see
the
matters
concerning
local
motion
demonstrated
by
our
Academick
;
at
which
time
you
shall
find
it
proved
,
that
in
the
time
that
the
one
moveable
falls
all
the
space
CB
,
the
other
descendeth
by
CA
as
far
as
the
point
T
,
in
which
falls
the
perpendicular
drawn
from
the
point
B
:
and
to
find
where
the
same
Cadent
by
the
perpendicular
would
be
when
the
other
arriveth
at
the
point
A
,
draw
from
A
the
perpendicular
unto
CA
,
continuing
it
,
and
CB
unto
the
interfection
,
and
that
shall
be
the
point
sought
.
Whereby
you
see
how
it
is
true
,
that
the
motion
by
CB
is
swifter
than
by
the
inclination
CA
(
supposing
the
term
C
for
the
beginning
of
the
motions
compared
)
because
the
line
CB
is
greater
than
CT
,
and
the
other
from
C
unto
the
intersection
of
the
perpendicular
drawn
from
A
,
unto
the
line
CA
,
is
greater
than
CA
,
and
therefore
the
motion
by
it
is
swifter
than
by
CA.
But
when
we
compare
the
motion
made
by
all
CA
,
not
with
all
the
motion
made
in
the
same
time
by
the
perpendicular
continued
,
but
with
that
made
in
part
of
the
time
,
by
the
sole
part
CB
,
it
hinders
not
,
that
the
motion
by
CA
,
continuing
to
descend
beyond
,
may
arrive
to
A
in
such
a
time
as
is
in
proportion
to
the
other
time
,
as
the
line
CA
is
to
the
line
CB.
Now
returning
to
our
first
purpose
;
which
was
to
shew
,
that
the
grave
moveable
leaving
its
quiescence
,
passeth
descending
by
all
the
degrees
of
tardity
,
precedent
to
any
whatsoever
degree
of
velocity
that
it
acquireth
,
re-assuming
the
same
Figure
which
we
used
before
,
let
us
remember
that
we
did
agree
,
that
the
Descendent
by
the
inclination
CA
,
and
the
Cadent
by
the
perpendicular
CB
,
were
found
to
have
acquired
equal
degrees
of
velocity
in
the
terms
B
and
A
:
now
to
proceed
,
I
suppose
you
will
not
scruple
to
grant
,
that
upon
another
plane
less
steep
than
AC
;
as
for
example
,
AD
[
in
Fig.
5.
]
the
motion
of
the
descendent
would
be
yet
more
flow
than
in
the
plane
AC
.
So
that
it
is
not
any
whit
dubitable
,
but
that
there
may
be
planes
so
little
elevated
above
the
Horizon
AB
,
that
the
moveable
,
namely
the
same
ball
,
in
any
the
longest
time
may
reach
the
point
A
,
which
being
to
move
by
the
plane
AB
,
an
infinite
time
would
not
suffice
:
and
the
motion
is
made
always
more
slowly
,
by
how
much
the
declination
is
less
.
It
must
be
therefore
confest
,
that
there
may
be
a
point
taken
upon
the
term
B
,
so
near
to
the
said
B
,
that
drawing
from
thence
to
the
point
A
a
plane
,
the
ball
would
not
pass
it
in
a
whole
year
.
It
is
requisite
next
for
you
to
know
,
that
the
impetus
,
namely
the
degree
of
velocity
the
ball
is
found
to
have
acquired
when
it
arriveth
at
the
point
A
,
is
such
,
that
should
it
continue
to
move
with
this
self-same
degree
uniformly
,
that
is
to
say
,
without
accelerating
or
retarding
;
in
as
much
more
time
as
it
was
in
coming
by
the
inclining
plane
,
it
would
pass
double
the
space
of
the
plane
inclined
:
namely
(
for
example
)
if
the
ball
had
past
the
plane
DA
in
an
hour
,
continuing
to
move
uniformly
with
that
degree
of
velocity
which
it
is
found
to
have
in
its
arriving
at
the
term
A
,
it
shall
pass
in
an
hour
a
space
double
the
length
DA
;
and
because
(
as
we
have
said
)
the
degrees
of
velocity
acquired
in
the
points
B
and
A
,
by
the
moveables
that
depart
from
any
point
taken
in
the
perpendicular
CB
,
and
that
descend
,
the
one
by
the
inclined
plane
,
the
other
by
the
said
perpendicular
,
are
always
equal
:
therefore
the
cadent
by
the
perpendicular
may
depart
from
a
term
so
near
to
B
,
that
the
degree
of
velocity
acquired
in
B
,
would
not
suffice
(
still
maintaining
the
same
)
to
conduct
the
moveable
by
a
space
double
the
length
of
the
plane
inclined
in
a
year
,
nor
in
ten
,
no
nor
in
a
hundred
.
We
may
therefore
conclude
,
that
if
it
be
true
,
that
according
to
the
ordinary
course
of
nature
a
moveable
,
all
external
and
accidental
impediments
removed
,
moves
upon
an
inclining
plane
with
greater
and
greater
tardity
,
according
as
the
inclination
shall
be
less
;
so
that
in
the
end
the
tardity
comes
to
be
infinite
,
which
is
,
when
the
inclination
concludeth
in
,
and
joyneth
to
the
horizontal
plane
;
and
if
it
be
true
likewise
,
that
the
degree
of
velocity
acquired
in
some
point
of
the
inclined
plane
,
is
equal
to
that
degree
of
velocity
which
is
found
to
be
in
the
moveable
that
descends
by
the
perpendicular
,
in
the
point
cut
by
a
parallel
to
the
Horizon
,
which
passeth
by
that
point
of
the
inclining
plane
;
it
must
of
necessity
be
granted
,
that
the
cadent
departing
from
rest
,
passeth
thorow
all
the
infinite
degrees
of
tardity
,
and
that
consequently
,
to
acquire
a
determinate
degree
of
velocity
,
it
is
necessary
that
it
move
first
by
right
lines
,
descending
by
a
short
or
long
space
,
according
as
the
velocity
to
be
acquired
,
ought
to
be
either
less
or
greater
,
and
according
as
the
plane
on
which
it
descendeth
is
more
or
less
inclined
;
so
that
a
plane
may
be
given
with
so
small
inclination
,
that
to
acquire
in
it
the
assigned
degree
of
velocity
,
it
must
first
move
in
a
very
great
space
,
and
take
a
very
long
time
;
whereupon
in
the
horizontal
plane
,
any
how
little
soever
velocity
,
would
never
be
naturally
acquired
,
since
that
the
moveable
in
this
case
will
never
move
:
but
the
motion
by
the
horizontal
line
,
The
circular
motion
is
never
acquired
naturally
,
without
right
motion
precede
it
.
Circular
motion
perpetually
uniform
.
which
is
neither
declined
or
inclined
,
is
a
circular
motion
about
the
centre
:
therefore
the
circular
motion
is
never
acquired
naturally
,
without
the
right
motion
precede
it
;
but
being
once
acquired
,
it
will
continue
perpetually
with
uniform
velocity
.
I
could
with
other
discourses
evince
and
demonstrate
the
same
truth
,
but
I
will
not
by
so
great
a
digression
interrupt
our
principal
argument
:
but
rather
will
return
to
it
upon
some
other
occasion
;
especially
since
we
not
assumed
the
same
,
not
to
serve
for
a
necessary
demonstration
,
but
to
adorn
a
Platonick
Conceit
;
to
which
I
will
add
another
particular
observation
of
our
Academick
,
which
hath
in
it
something
of
admirable
.
Let
us
suppose
amongst
the
decrees
of
the
divine
Architect
,
a
purpose
of
creating
in
the
World
these
Globes
,
which
we
behold
continually
moving
round
,
and
of
assigning
the
centre
of
their
conversions
;
and
that
in
it
he
had
placed
the
Sun
immoveable
,
and
had
afterwards
made
all
the
said
Globes
in
the
same
place
,
and
with
the
intended
inclinations
of
moving
towards
the
Centre
,
till
they
had
acquired
those
degrees
of
velocity
,
which
at
first
seemed
good
to
the
same
Divine
Minde
;
the
which
being
acquired
,
we
lastly
suppose
that
they
were
turned
round
,
each
in
his
Sphere
retaining
the
said
acquired
velocity
:
it
is
now
demanded
,
in
what
altitude
and
distance
from
the
Sun
the
place
was
where
the
said
Orbs
were
primarily
created
;
and
whether
it
be
possible
that
they
might
all
be
created
in
the
same
place
?
To
make
this
investigation
,
we
must
take
from
the
most
skilfull
Astronomers
the
magnitude
of
the
Spheres
in
which
the
Planets
revolve
,
and
likewise
the
time
of
their
revolutions
:
from
which
two
cognitions
is
gathered
how
much
(
for
example
)
Jupiter
is
swifter
than
Saturne
;
and
being
found
(
as
indeed
it
is
)
that
Jupiter
moves
more
swiftly
,
it
is
requisite
,
that
departing
from
the
same
altitude
,
Jupiter
be
descended
more
than
Saturne
,
as
we
really
know
it
is
,
its
Orbe
being
inferiour
to
that
of
Saturne
.
But
by
proceeding
forwards
,
from
the
proportions
of
the
two
velocities
of
Jupiter
and
Saturne
,
and
from
the
distance
between
their
Orbs
,
and
from
the
proportion
of
acceleration
of
natural
motion
,
one
may
finde
in
what
altitude
and
distance
from
the
centre
of
their
revolutions
,
The
magnitude
of
the
Orbs
,
and
the
velocity
of
the
motion
of
the
Planets
,
answer
proportionably
,
as
if
descended
from
the
same
place
.
was
the
place
from
whence
they
first
departed
.
This
found
out
,
and
agreed
upon
,
it
is
to
be
sought
,
whether
Mars
descending
from
thence
to
his
Orb
,
the
magnitude
of
the
Orb
,
and
the
velocity
of
the
motion
,
agree
with
that
which
is
found
by
calculation
;
and
let
the
like
be
done
of
the
Earth
,
of
Venus
,
and
of
Mercury
;
the
greatness
of
which
Spheres
,
and
the
velocity
of
their
motions
,
agree
so
nearly
to
what
computation
gives
,
that
it
is
very
admirable
.
SAGR.
I
have
hearkened
to
this
conceit
with
extreme
delight
;
and
,
but
that
I
believe
the
making
of
these
calculations
truly
would
be
a
long
and
painfull
task
,
and
perhaps
too
hard
for
me
to
comprehend
,
I
would
make
a
trial
of
them
.
SALV
.
The
operation
indeed
is
long
and
difficult
;
nor
could
I
be
certain
to
finde
it
so
readily
;
therefore
we
shall
refer
it
to
another
time
,
and
for
the
present
we
will
return
to
our
first
proposal
,
going
on
there
where
we
made
digression
;
which
,
if
I
well
remember
,
was
about
the
proving
the
motion
by
a
right
line
of
no
use
,
in
the
ordinate
parts
of
the
World
;
and
we
did
proceed
to
say
,
that
it
was
not
so
in
circular
motions
,
of
which
that
which
is
made
by
the
moveable
in
it self
,
Finite
and
terminate
circular
motions
disorder
not
the
parts
of
the
World
.
still
retains
it
in
the
same
place
,
and
that
which
carrieth
the
moveable
by
the
circumference
of
a
circle
about
its
fixed
centre
,
neither
puts
it self
,
nor
those
about
it
in
disorder
;
for
that
such
a
motion
primarily
is
finite
and
terminate
(
though
not
yet
finished
and
determined
)
but
there
is
no
point
in
the
circumference
,
In
the
circular
motion
,
every
point
in
the
circumference
is
the
begining
and
end
.
that
is
not
the
first
and
last
term
in
the
circulation
;
and
continuing
it
in
the
circumference
assigned
it
,
it
leaveth
all
the
rest
,
within
and
without
that
,
free
for
the
use
of
others
,
without
ever
impeding
or
disordering
them
.
This
being
a
motion
that
makes
the
moveable
continually
leave
,
and
continually
arrive
at
the
end
;
Circular
motion
onely
is
uniform
.
it
alone
therefore
can
primarily
be
uniform
;
for
that
acceleration
of
motion
is
made
in
the
moveable
,
when
it
goeth
towards
the
term
,
to
which
it
hath
inclination
;
and
the
retardation
happens
by
the
repugnance
that
it
hath
to
leave
and
part
from
the
same
term
;
and
because
in
circular
motion
,
the
moveable
continually
leaves
the
natural
term
,
and
continually
moveth
towards
the
same
,
therefor
,
in
it
,
the
repugnance
and
inclination
are
always
of
equal
force
:
from
which
equality
results
a
velocity
,
neither
retarded
nor
accelerated
,
i.
e.
an
uniformity
in
motion
.
From
this
conformity
,
and
from
the
being
terminate
,
Circular
motion
may
be
continued
perpetually
.
may
follow
the
perpetual
continuation
by
successively
reiterating
the
circulations
;
which
in
an
undeterminated
line
,
and
in
a
motion
continually
retarded
or
accelerated
,
cannot
naturally
be
.
Right
motion
cannot
naturally
be
perpetual
.
I
say
,
naturally
;
because
the
right
motion
which
is
retarded
,
is
the
violent
,
which
cannot
be
perpetual
;
and
the
accelerate
arriveth
necessarily
at
the
term
,
if
one
there
be
;
and
if
there
be
none
,
it
cannot
be
moved
to
it
,
because
nature
moves
not
whether
it
is
impossible
to
attain
.
I
conclude
therefore
,
that
the
circular
motion
can
onely
naturally
consist
with
natural
bodies
,
parts
of
the
universe
,
and
constituted
in
an
excellent
disposure
;
and
that
the
right
,
at
the
most
that
can
be
said
for
it
,
is
assigned
by
nature
to
its
bodies
,
Right
motion
assigned
to
natural
bodies
,
to
reduce
them
to
perfect
order
,
when
removed
from
their
places
.
and
their
parts
,
at
such
time
as
they
shall
be
out
of
their
proper
places
,
constituted
in
a
depraved
disposition
,
and
for
that
cause
needing
to
be
redu●●d
by
the
shortest
way
to
their
natural
state
.
Hence
,
me
thinks
,
it
may
rationally
be
concluded
,
that
for
maintenance
of
perfect
order
amongst
the
parts
of
the
World
,
it
is
necessary
to
say
,
that
moveables
are
moveable
onely
circularly
;
and
if
there
be
any
that
move
not
circularly
,
Rest
onely
,
and
circular
motion
are
apt
to
conserve
order
.
these
of
necessity
are
immoveable
:
there
being
nothing
but
rest
and
circular
motion
apt
to
the
conservation
of
order
.
And
I
do
not
a
little
wonder
with
my self
,
that
Aristotle
,
who
held
that
the
Terrestrial
globe
was
placed
in
the
centre
of
the
World
,
and
there
remained
immoveable
,
should
not
say
,
that
of
natural
bodies
some
are
moveable
by
nature
,
and
others
immoveable
;
especially
having
before
defined
Nature
,
to
be
the
principle
of
Motion
and
Rest.
SIMPL.
Aristotle
,
though
of
a
very
perspicacious
wit
,
would
not
strain
it
further
than
needed
:
Sensible
experiments
are
to
be
preferred
before
humane
argumentations
.
holding
in
all
his
argumentations
,
that
sensible
experiments
were
to
be
preferred
before
any
reasons
founded
upon
strength
of
wit
,
and
said
those
which
should
deny
the
testimony
of
sense
deserved
to
be
punished
with
the
loss
of
that
sense
;
He
who
denies
sense
,
deserves
to
be
deprived
of
it
.
Sense
sheweth
that
things
grave
move
to
the
medium
,
and
the
light
to
the
concave
.
now
who
is
so
blind
,
that
sees
not
the
parts
of
the
Earth
and
Water
to
move
,
as
being
grave
,
naturally
downwards
,
namely
;
towards
the
centre
of
the
Universe
,
assigned
by
nature
her self
for
the
end
and
term
of
right
motion
deorsùm
;
and
doth
not
likewise
see
the
Fire
and
Air
to
move
right
upwards
towards
the
Concave
of
the
Lunar
Orb
,
as
to
the
natural
end
of
motion
sursùm
?
And
this
being
so
manifestly
seen
,
and
we
being
certain
,
that
eadem
est
ratio
totius
&
partium
,
why
may
we
not
assert
it
for
a
true
and
manifest
proposition
,
that
the
natural
motion
of
the
Earth
is
the
right
motion
ad
medium
,
and
that
of
the
Fire
,
the
right
à
medio
?
SALV
.
The
most
that
you
can
pretend
from
this
your
Discourse
,
were
it
granted
to
be
true
,
is
that
,
like
as
the
parts
of
the
Earth
removed
from
the
whole
,
namely
,
from
the
place
where
they
naturally
rest
,
that
is
in
short
reduced
to
a
depraved
and
disordered
disposure
,
return
to
their
place
spontaneously
,
and
therefore
naturally
in
a
right
motion
,
(
it
being
granted
,
that
eadem
sit
ratio
totius
&
partium
)
so
it
may
be
inferred
,
that
the
Terrestrial
Globe
removed
violently
from
the
place
assigned
it
by
nature
,
It
is
questionable
whether
descending
weights
move
in
a
right
line
.
it
would
return
by
a
right
line
.
This
,
as
I
have
said
,
is
the
most
that
can
be
granted
you
,
and
that
onely
for
want
of
examination
;
but
he
that
shall
with
exactness
revise
these
things
,
will
first
deny
,
that
the
parts
of
the
Earth
,
in
returning
to
its
whole
,
move
in
a
right
line
,
and
not
by
a
circular
or
mixt
;
and
really
you
would
have
enough
to
do
to
demonstrate
the
contrary
,
as
you
shall
plainly
see
in
the
answers
to
the
particular
reasons
and
experiments
alledged
by
Ptolomey
and
Aristotle
.
Secondly
,
If
another
should
say
that
the
parts
of
the
Earth
,
go
not
in
their
motion
towards
the
Centre
of
the
World
,
but
to
unite
with
its
Whole
,
and
that
for
that
reason
they
naturally
incline
towards
the
centre
of
the
Terrestrial
Globe
,
by
which
inclination
they
conspire
to
form
and
preserve
it
,
what
other
All
,
or
what
other
Centre
would
you
find
for
the
World
,
The
Earth
sperical
by
the
conspiration
of
its
parts
to
its
Centre
.
to
which
the
whole
Terrene
Globe
,
being
thence
removed
,
would
seek
to
return
,
that
so
the
reason
of
the
Whole
might
be
like
to
that
of
its
parts
?
It
may
be
added
,
That
neither
Aristotle
,
nor
you
can
ever
prove
,
that
the
Earth
de
facto
is
in
the
centre
of
the
Universe
;
but
if
any
Centre
may
be
assigned
to
the
Universe
,
The
Sun
more
probably
in
the
centre
of
the
Vniverse
,
than
the
Earth
.
we
shall
rather
find
the
Sun
placed
in
it
,
as
by
the
sequel
you
shall
understand
.
Now
,
like
as
from
the
consentaneous
conspiration
of
all
the
parts
of
the
Earth
to
form
its
whole
,
doth
follow
,
that
they
with
equal
inclination
concurr
thither
from
all
parts
;
Natural
inclination
of
the
parts
of
all
the
globes
of
the
World
to
go
to
their
centre
.
and
to
unite
themselves
as
much
as
is
possible
together
,
they
there
spherically
adapt
themselves
;
why
may
we
not
believe
that
the
Sun
,
Moon
,
and
other
mundane
Bodies
,
be
also
of
a
round
figure
,
not
by
other
than
a
concordant
instinct
,
and
natural
concourse
of
all
the
parts
composing
them
?
Of
which
,
if
any
,
at
any
time
,
by
any
violence
were
separated
from
the
whole
,
is
it
not
reasonable
to
think
,
that
they
would
spontaneously
and
by
natural
instinct
return
?
and
in
this
manner
to
infer
,
that
the
right
motion
agreeth
with
all
mundane
bodies
alike
.
SIMPL.
Certainly
,
if
you
in
this
manner
deny
not
onely
the
Principles
of
Sciences
,
but
manifest
Experience
,
and
the
Senses
themselves
,
you
can
never
be
convinced
or
removed
from
any
opinion
which
you
once
conceit
,
therefore
I
will
choose
rather
to
be
silent
(
for
,
contra
negantes
principia
non
est
disputandum
)
than
contend
with
you
.
And
insisting
on
the
things
alledged
by
you
even
now
(
since
you
question
so
much
as
whether
grave
moveables
have
a
right
motion
or
no
)
how
can
you
ever
rationally
deny
,
The
right
motion
of
grave
bodies
manifest
to
sense
.
that
the
parts
of
the
Earth
;
or
,
if
you
will
,
that
ponderous
matters
descend
towards
the
Centre
,
with
a
right
motion
;
whenas
,
if
from
a
very
high
Tower
,
whose
walls
are
very
upright
and
perpendicular
,
you
let
them
fall
,
they
shall
descend
gliding
and
sliding
by
the
Tower
to
the
Earth
,
exactly
in
that
very
place
where
a
plummet
would
fall
,
being
hanged
by
a
line
fastned
above
,
just
there
,
whence
the
said
weights
were
let
fall
?
is
not
this
a
more
than
evident
argument
of
the
motions
being
right
,
and
towards
the
Centre
?
Arguments
of
Aristotle
,
to
prove
that
grave
bodies
move
with
an
inclination
to
arrive
at
the
centre
of
the
Vniverse
.
In
the
second
place
you
call
in
doubt
,
whether
the
parts
of
the
Earth
are
moved
,
as
Aristotle
affirms
,
towards
the
Centre
of
the
World
;
as
if
he
had
not
rationally
demonstrated
it
by
contrary
motions
,
whilst
he
thus
argueth
;
The
motion
of
heavie
bodies
is
contrary
to
that
of
the
light
:
but
the
motion
of
the
light
is
manifest
to
be
directly
upwards
,
namely
,
towards
the
circumference
of
the
World
,
therefore
the
motion
of
the
heavie
is
directly
towards
the
Centre
of
the
World
:
and
it
happens
per
accidens
,
Heavie
bodies
move
towards
the
centre
of
the
Earth
per
accidens
.
that
it
be
towards
the
centre
of
the
Earth
,
for
that
this
striveth
to
be
united
to
that
.
The
seeking
in
the
next
place
,
what
a
part
of
the
Globe
of
the
Sun
or
Moon
would
do
,
were
it
separated
from
its
whole
,
is
vanity
;
because
that
thereby
that
is
sought
,
To
seek
what
would
follow
upon
an
impossibility
,
is
folly
.
which
would
be
the
consequence
of
an
impossibility
;
in
regard
that
,
as
Aristotle
also
demonstrates
,
the
coelestial
bodies
are
impassible
,
impenetrable
,
and
infrangible
;
so
that
such
a
case
can
never
happen
:
Coelestial
bodies
neither
heavie
nor
light
,
according
to
Aristotle
.
and
though
it
should
,
and
that
the
separated
part
should
return
to
its
whole
,
it
would
not
return
as
grave
or
light
,
for
that
the
same
Aristotle
proveth
,
that
the
Coelestial
Bodies
are
neither
heavie
nor
light
.
SALV
.
With
what
reason
I
doubt
,
whether
grave
bodies
move
by
a
right
and
perpendicular
line
,
you
shall
hear
,
as
I
said
before
,
when
I
shall
examine
this
particular
argument
.
Touching
the
second
point
,
I
wonder
that
you
should
need
to
discover
the
Paralogism
of
Aristotle
,
being
of
it self
so
manifest
;
and
that
you
perceive
not
,
that
Aristotle
supposeth
that
which
is
in
question
:
therefore
take
notice
.
SIMPL.
Pray
Salviatus
speak
with
more
respect
of
Aristotle
:
for
who
can
you
ever
perswade
,
that
he
who
was
the
first
,
only
,
and
admirable
explainer
of
the
Syllogistick
forms
of
demonstration
,
Aristotle
cannot
equivocate
,
being
the
inventer
of
Logick
.
of
Elenchs
,
of
the
manner
of
discovering
Sophisms
,
Paralogisms
,
and
in
short
,
of
all
the
parts
of
Logick
,
should
afterwards
so
notoriously
equivocate
in
imposing
that
for
known
,
which
is
in
question
?
It
would
be
better
,
my
Masters
,
first
perfectly
to
understand
him
,
and
then
to
try
,
if
you
have
a
minde
,
to
oppose
him
.
SALV
.
Simplicius
,
we
are
here
familiarly
discoursing
among
our selves
,
to
investigate
some
truth
;
I
shall
not
be
displeased
that
you
discover
my
errors
;
and
if
I
do
not
follow
the
mind
of
Aristotle
,
freely
reprehend
me
,
and
I
shall
take
it
in
good
part
.
Onely
give
me
leave
to
expound
my
doubts
,
and
to
reply
something
to
your
last
words
,
telling
you
,
that
Logick
,
as
it
is
well
understood
,
is
the
Organe
with
which
we
philosophate
;
but
as
it
may
be
possible
,
that
an
Artist
may
be
excellent
in
making
Organs
,
but
unlearned
in
playing
on
them
,
thus
he
might
be
a
great
Logician
,
but
unexpert
in
making
use
of
Logick
;
like
as
we
have
many
that
theorically
understand
the
whole
Art
of
Poetry
,
and
yet
are
unfortunate
in
composing
but
meer
four
Verses
;
others
enjoy
all
the
precepts
of
Vinci
[
](A61244-e8110-b)*
*
A
famous
Italian
Painter
.
,
and
yet
know
not
how
to
paint
a
Stoole
.
The
playing
on
the
Organs
is
not
taught
by
them
who
know
how
to
make
Organs
,
but
by
him
that
knows
how
to
play
on
them
:
Poetry
is
learnt
by
continual
reading
of
Poets
:
Limning
is
learnt
by
continual
painting
and
designing
:
Demonstration
from
the
reading
of
Books
full
of
demonstrations
,
which
are
the
Mathematical
onely
,
and
not
the
Logical
.
Now
returning
to
our
purpose
,
I
say
,
that
that
which
Aristotle
seeth
of
the
motion
of
light
bodies
,
is
the
departing
of
the
Fire
from
any
part
of
the
Superficies
of
the
Terrestrial
Globe
,
and
directly
retreating
from
it
,
mounting
upwards
;
and
this
indeed
is
to
move
towards
a
circumference
greater
than
that
of
the
Earth
;
yea
,
the
same
Aristotle
makes
it
to
move
to
the
concave
of
the
Moon
,
but
that
this
circumference
is
that
of
the
World
,
or
concentrick
to
it
,
so
that
to
move
towards
this
,
is
a
moving
towards
that
of
the
World
,
that
he
cannot
affirm
,
unless
he
supposeth
,
That
the
Centre
of
the
Earth
,
Paralogism
of
Aristotle
,
in
proving
the
Earth
to
be
in
the
Centre
of
the
World
.
from
which
we
see
these
light
ascendent
bodies
to
depart
,
be
the
same
with
the
Centre
of
the
World
;
which
is
as
much
as
to
say
,
that
the
terrestrial
Globe
is
constituted
in
the
midst
of
the
World
:
which
is
yet
that
of
which
we
were
in
doubt
,
and
which
Aristotle
intended
to
prove
.
And
do
you
say
that
this
is
not
a
manifest
Paralogism
?
The
Paralogisme
of
Aristotle
another
way
discovered
.
SAGR.
This
Argument
of
Aristotle
appeared
to
me
deficient
also
,
and
non-concludent
for
another
respect
;
though
it
were
granted
,
that
that
Circumference
,
to
which
the
Fire
directly
moveth
,
be
that
which
includeth
the
World
:
for
that
in
a
circle
,
not
onely
the
centre
,
but
any
other
point
being
taken
,
every
moveable
which
departing
thence
,
shall
move
in
a
right
line
,
and
towards
any
whatsoever
part
,
shall
without
any
doubt
go
towards
the
circumference
,
and
continuing
the
motion
,
shall
also
arrive
thither
;
so
that
we
may
truly
say
,
that
it
moveth
towards
the
circumference
:
but
yet
it
doth
not
follow
,
that
that
which
moveth
by
the
same
line
with
a
contrary
motion
,
would
go
towards
the
centre
,
unless
when
the
point
taken
were
the
centre
it self
,
or
that
the
motion
were
made
by
that
onely
line
,
which
produced
from
the
point
assigned
,
passeth
thorow
the
centre
.
So
that
to
say
,
that
Fire
moving
in
a
right
line
,
goeth
towards
the
circumference
of
the
World
,
therefore
the
parts
of
the
Earth
which
by
the
same
lines
move
with
a
contrary
motion
,
go
towards
the
centre
of
the
World
,
concludeth
not
,
unless
then
when
it
is
presupposed
,
that
the
lines
of
the
Fire
prolonged
pass
by
the
centre
of
the
World
;
and
because
we
know
certainly
of
them
,
that
they
pass
by
the
centre
of
the
Terrestrial
Globe
(
being
perpendicular
to
its
superficies
,
and
not
inclined
)
therefore
to
conclude
,
it
must
be
supposed
,
that
the
centre
of
the
Earth
is
the
same
with
the
centre
of
the
World
;
or
at
least
,
that
the
parts
of
the
Fire
and
Earth
descend
not
,
save
onely
by
one
sole
line
which
passeth
by
the
centre
of
the
World
.
Which
nevertheless
is
false
,
and
repugnant
to
experience
,
which
sheweth
us
,
that
the
parts
of
Fire
,
not
by
one
line
onely
,
but
by
infinite
,
produced
from
the
centre
of
the
Earth
towards
all
the
parts
of
the
World
,
ascend
always
by
lines
perpendicular
to
the
Superficies
of
the
Terrestrial
Globe
.
SALV
.
You
do
very
ingeniously
lead
Aristotle
to
the
same
inconvenience
,
Sagredus
,
shewing
his
manifest
equivoke
;
but
withal
you
add
another
inconsistency
.
We
see
the
Earth
to
be
spherical
,
and
therefore
are
certain
that
it
hath
its
centre
,
to
which
we
see
all
its
parts
are
moved
;
for
so
we
must
say
,
whilst
their
motions
are
all
perpendicular
to
the
Superficies
of
the
Earth
;
we
mean
,
that
as
they
move
to
the
centre
of
the
Earth
,
they
move
to
their
Whole
,
and
to
their
Universal
Mother
:
and
we
are
still
farther
so
free
,
that
we
will
suffer
our selves
to
be
perswaded
,
that
their
natural
instinct
is
,
Grave
bodies
may
more
rationally
be
affirmed
to
tend
to
the
Centre
of
the
Earth
,
than
of
the
Vniverse
.
not
to
go
towards
the
centre
of
the
Earth
,
but
towards
that
of
the
Universe
;
which
we
know
not
where
to
find
,
or
whether
it
be
or
no
;
and
were
it
granted
to
be
,
it
is
but
an
imaginary
point
,
and
a
nothing
without
any
quality
.
As
to
what
Simplicius
said
last
,
that
the
contending
whether
the
parts
of
the
Sun
,
Moon
,
or
other
coelestial
Body
,
separated
from
their
Whole
,
should
naturally
return
to
it
,
is
a
vanity
,
for
that
the
case
is
impossible
;
it
being
clear
by
the
Demonstrations
of
Aristotle
,
that
the
coelestial
Bodies
are
impassible
,
The
conditions
and
attributes
which
differ
the
coelestial
bodies
from
Elementary
,
depend
on
the
motions
assigned
them
by
Arist.
impenetrable
,
unpartable
,
&c.
I
answer
,
that
none
of
the
conditions
,
whereby
Aristotle
distinguisheth
the
Coelestial
Bodies
from
Elementary
,
hath
other
foundation
than
what
he
deduceth
from
the
diversity
of
the
natural
motion
of
those
and
these
;
insomuch
that
it
being
denied
,
that
the
circular
motion
is
peculiar
to
Coelestial
Bodies
,
and
affirmed
,
that
it
is
agreeable
to
all
Bodies
naturally
moveable
,
it
is
behoofull
upon
necessary
consequence
to
say
,
either
that
the
attributes
of
generable
,
or
ingenerable
,
alterable
,
or
unalterable
,
partable
,
or
unpartable
,
&c.
equally
and
commonly
agree
with
all
worldly
bodies
,
namely
,
as
well
to
the
Coelestial
as
to
the
Elementary
;
or
that
Aristotle
hath
badly
and
erroneously
deduced
those
from
the
circular
motion
,
which
he
hath
assigned
to
Coelestial
Bodies
.
SIMPL.
This
manner
of
argumentation
tends
to
the
subversion
of
all
Natural
Philosophy
,
and
to
the
disorder
and
subversion
of
Heaven
and
Earth
,
and
the
whole
Universe
;
but
I
believe
the
Fundamentals
of
the
Peripateticks
are
such
,
that
we
need
not
fear
that
new
Sciences
can
be
erected
upon
their
ruines
.
SALV
.
Take
no
thought
in
this
place
for
Heaven
or
the
Earth
,
neither
fear
their
subversion
,
or
the
ruine
of
Philosophy
.
As
to
Heaven
,
your
fears
are
vain
for
that
which
you
your self
hold
unalterable
and
impassible
;
as
for
the
Earth
,
we
strive
to
enoble
and
perfect
it
,
whilst
we
make
it
like
to
the
Coelestial
Bodies
,
and
as
it
were
place
it
in
Heaven
,
whence
your
Philosophers
have
exiled
it
.
The
disputes
and
contradictions
of
Philosophers
may
conduce
to
the
benefit
of
Philosophy
.
Philosophy
it self
cannot
but
receive
benefit
from
our
Disputes
,
for
if
our
conceptions
prove
true
,
new
Discoveries
will
be
made
;
if
false
,
the
first
Doctrine
will
be
more
confirmed
.
Rather
bestow
your
care
upon
some
Philosophers
,
and
help
and
defend
them
;
for
as
to
the
Science
it self
,
it
cannot
but
improve
.
And
that
we
may
return
to
our
purpose
,
be
pleased
freely
to
produce
what
presents
it self
to
you
in
confirmation
of
that
great
difference
which
Aristotle
puts
between
the
Coelestial
Bodies
,
and
the
Elementary
parts
of
the
World
,
in
making
those
ingenerable
,
incorruptible
,
unalterable
,
&c.
and
this
corruptible
,
alterable
,
&c.
SIMPL.
I
see
not
yet
any
need
that
Aristotle
hath
of
help
,
standing
as
he
doth
stoutly
and
strongly
on
his
feet
;
yea
not
being
yet
assaulted
,
much
less
foiled
by
you
.
And
what
ward
will
you
choose
in
this
combate
for
this
first
blow
?
Aristotles
discourse
to
prove
the
incorruptibility
of
Heaven
.
Aristotle
writeth
,
that
whatever
is
generated
,
is
made
out
of
a
contrary
in
some
subject
,
and
likewise
is
corrupted
in
some
certain
subject
from
a
contrary
into
a
contrary
;
Generation
&
corruption
is
onely
amongst
contraries
,
according
to
Arist.
so
that
(
observe
)
corruption
and
generation
is
never
but
onely
in
contraries
;
If
therefore
to
a
Coelestial
Body
no
contrary
can
be
assigned
,
for
that
to
the
circular
motion
no
other
motion
is
contrary
,
To
the
circular
motion
no
other
motion
is
contrary
.
then
Nature
hath
done
very
well
to
make
that
exempt
from
contraries
,
which
was
to
be
ingenerable
and
incorruptible
,
This
fundamental
first
confirmed
,
it
immediately
followeth
of
consequence
,
that
it
is
inaugmentable
,
inalterable
,
Heaven
an
habitation
for
the
immortal
Gods
.
impassible
,
and
finally
eternal
,
and
a
proportionate
habitation
to
the
immortal
Deities
,
conformable
to
the
opinion
even
of
all
men
that
have
any
conceit
of
the
Gods
.
He
afterwards
confirmeth
the
same
by
sense
;
Immutability
of
Heaven
evident
to
sense
.
in
regard
,
that
in
all
times
past
,
according
to
memory
or
tradition
,
we
see
nothing
removed
,
according
to
the
whole
outward
Heaven
,
nor
any
of
its
proper
parts
.
He
proveth
that
the
circular
motion
hath
no
contrary
.
Next
,
as
to
the
circular
motion
,
that
no
other
is
contrary
to
it
,
Aristotle
proveth
many
ways
;
but
without
reciting
them
all
,
it
is
sufficiently
demonstrated
,
since
simple
motions
are
but
three
,
to
the
medium
,
from
the
medium
,
and
about
the
medium
,
of
which
the
two
right
,
sursum
and
deorsum
,
are
manifestly
contrary
;
and
because
one
onely
hath
onely
one
for
contrary
,
therefore
there
rests
no
other
motion
which
may
be
contrary
to
the
circular
.
You
see
the
subtle
and
most
concluding
discourse
of
Aristotle
,
whereby
he
proveth
the
incorruptibility
of
Heaven
.
SALV
.
This
is
nothing
more
,
save
the
pure
progress
of
Aristotle
,
by
me
hinted
before
;
wherein
,
besides
that
I
affirm
,
that
the
motion
which
you
attribute
to
the
Coelestial
Bodies
agreeth
also
to
the
Earth
,
its
illation
proves
nothing
.
I
tell
you
therefore
,
that
that
circular
motion
which
you
assign
to
Coelestial
Bodies
,
suiteth
also
to
the
Earth
,
from
which
,
supposing
that
the
rest
of
your
discourse
were
concludent
,
will
follow
one
of
these
three
things
,
as
I
told
you
a
little
before
,
and
shall
repeat
;
namely
,
either
that
the
Earth
it self
is
also
ingenerable
,
and
incorruptible
,
as
the
Coelestial
bodies
;
or
that
the
Coelestial
bodies
are
,
like
as
the
Elementary
generable
,
alterable
&c.
or
that
this
difference
of
motion
hath
nothing
to
do
with
Generation
and
Corruption
.
The
discourse
of
Aristotle
,
and
yours
also
contain
many
Propositions
not
to
be
lightly
admitted
,
and
the
better
to
examine
them
,
it
will
be
convenient
to
reduce
them
to
the
most
abstracted
and
distinct
that
can
be
possible
;
and
excuse
me
Sagredus
,
if
haply
with
some
tediousness
you
hear
me
oft
repeat
the
same
things
,
and
fancie
that
you
see
me
reassume
my
argument
in
the
publick
circle
of
Disputations
.
You
say
Generation
and
Corruption
are
onely
made
where
there
are
contraries
;
contraries
are
onely
amongst
simple
natural
bodies
,
moveable
with
contrary
motions
;
contrary
motions
are
onely
those
which
are
made
by
a
right
line
between
contrary
terms
;
and
these
are
onely
two
,
that
is
to
say
,
from
the
medium
,
and
towards
the
medium
;
and
such
motions
belong
to
no
other
natural
bodies
,
but
to
the
Earth
,
the
Fire
,
and
the
other
two
Elements
:
therefore
Generation
and
Corruption
is
onely
amongst
the
Elements
.
And
because
the
third
simple
motion
,
namely
,
the
circular
about
the
medium
,
hath
no
contrary
,
(
for
that
the
other
two
are
contraries
,
and
one
onely
,
hath
but
onely
one
contrary
)
therefore
that
natural
body
with
which
such
motion
agreeth
,
wants
a
contrary
;
and
having
no
contrary
is
ingenerable
and
incorruptible
,
&c.
Because
where
there
is
no
contrariety
,
there
is
no
generation
or
corruption
,
&c.
But
such
motion
agreeth
onely
with
the
Coelestial
bodies
;
therefore
onely
these
are
ingenerable
,
It
s
easier
to
prove
the
Earth
to
move
,
than
that
corruption
is
made
by
contraries
.
incorruptible
,
&c.
And
to
begin
,
I
think
it
a
more
easie
thing
,
and
sooner
done
to
resolve
,
whether
the
Earth
(
a
most
vast
Body
,
and
for
its
vicinity
to
us
,
most
tractable
)
moveth
with
a
speedy
motion
,
such
as
its
revolution
about
its
own
axis
in
twenty
four
hours
would
be
,
than
it
is
to
understand
and
resolve
,
whether
Generation
and
Corruption
ariseth
from
contrariety
,
or
else
whether
there
be
such
things
as
generation
,
corruption
and
contrariety
in
nature
.
And
if
you
,
Simplicius
,
can
tell
me
what
method
Nature
observes
in
working
,
when
she
in
a
very
short
time
begets
an
infinite
number
of
flies
from
a
little
vapour
of
the
Must
of
wine
,
and
can
shew
me
which
are
there
the
contraries
you
speak
of
,
what
it
is
that
corrupteth
,
and
how
;
I
should
think
you
would
do
more
than
I
can
;
for
I
profess
I
cannot
comprehend
these
things
.
Besides
,
I
would
very
gladly
understand
how
,
and
why
these
corruptive
contraries
are
so
favourable
to
Daws
,
and
so
cruel
to
Doves
;
so
indulgent
to
Stags
,
and
so
hasty
to
Horses
,
that
they
do
grant
to
them
many
more
years
of
life
,
that
is
,
of
incorruptibility
,
than
weeks
to
these
.
Peaches
and
Olives
are
planted
in
the
same
soil
,
exposed
to
the
same
heat
and
cold
,
to
the
same
wind
and
rains
,
and
,
in
a
word
,
to
the
same
contrarieties
;
and
yet
those
decay
in
a
short
time
,
and
these
live
many
hundred
years
.
Furthermore
,
I
never
was
thorowly
satisfied
about
this
substantial
transmutation
(
still
keeping
within
pure
natural
bounds
)
whereby
a
matter
becometh
so
transform'd
,
that
it
should
be
necessarily
said
to
be
destroy'd
,
so
that
nothing
remaineth
of
its
first
being
,
and
that
another
body
quite
differing
there-from
should
be
thence
produced
;
Bare
transposition
of
parts
may
represent
bodies
under
diverse
asp●cts
.
and
if
I
fancy
to
my self
a
body
under
one
aspect
,
and
by
and
by
under
another
very
different
,
I
cannot
think
it
impossible
but
that
it
may
happen
by
a
simple
transposition
of
parts
,
without
corrupting
or
ingendring
any
thing
a-new
;
for
we
see
such
kinds
of
Metamorphoses
dayly
:
so
that
to
return
to
my
purpose
,
I
answer
you
,
that
inasmuch
as
you
go
about
to
perswade
me
that
the
Earth
can
not
move
circularly
by
way
of
corruptibility
and
generability
,
you
have
undertook
a
much
harder
task
than
I
,
that
with
arguments
more
difficult
indeed
,
but
no
less
concluding
,
will
prove
the
contrary
.
SAGR.
Pardon
me
,
Salviatus
,
if
I
interrupt
your
discourse
,
which
,
as
it
delights
me
much
,
for
that
I
also
am
gravel'd
with
the
same
doubts
;
so
I
fear
that
you
can
never
conclude
the
same
,
without
altogether
digressing
from
your
chief
design
:
therefore
if
it
be
permitted
to
proceed
in
our
first
argument
,
I
should
think
that
it
were
convenient
to
remit
this
question
of
generation
and
corruption
to
another
distinct
and
single
conference
;
as
also
,
if
it
shall
please
you
and
Simplicius
,
we
may
do
by
other
particular
questions
which
may
fall
in
the
way
of
our
discourse
;
which
I
will
keep
in
my
mind
to
propose
,
and
exactly
discuss
them
some
other
time
.
Now
as
for
the
present
,
since
you
say
,
that
if
Aristotle
deny
circular
motion
to
the
Earth
in
common
with
other
bodies
Coelestial
,
it
thence
will
follow
,
that
the
same
which
befalleth
the
Earth
,
as
to
its
being
generable
,
alterable
,
&c.
will
hold
also
of
Heaven
,
let
us
enquire
no
further
if
there
be
such
things
in
nature
,
as
generation
and
corruption
,
or
not
;
but
let
us
return
to
enquire
what
the
Globe
of
the
Earth
doth
.
SIMPL.
I
cannot
suffer
my
ears
to
hear
it
question'd
,
whether
generation
and
corruption
be
in
rerum
naturâ
,
it
being
a
thing
which
we
have
continually
before
our
eyes
,
By
denying
Principles
in
the
Sciences
,
any
Paradox
may
be
maintained
.
and
whereof
Aristotle
hath
written
two
whole
Books
.
But
if
you
go
about
to
deny
the
Principles
of
Sciences
,
and
question
things
most
manifest
,
who
knows
not
,
but
that
you
may
prove
what
you
will
,
and
maintain
any
Paradox
?
And
if
you
do
not
dayly
see
herbs
,
plants
,
animals
to
generate
and
corrupt
,
what
is
it
that
you
do
see
?
Also
,
do
you
not
continually
behold
contrarieties
contend
together
,
and
the
Earth
change
into
Water
,
the
Water
turn
to
Air
,
the
Air
into
Fire
,
and
again
the
Air
to
condense
into
Clouds
,
Rains
,
Hails
and
Storms
?
SAGR.
Yes
,
we
see
these
things
indeed
,
and
therefore
will
grant
you
the
discourse
of
Aristotle
,
as
to
this
part
of
generation
and
corruption
made
by
contraries
;
but
if
I
shall
conclude
by
virtue
of
the
same
propositions
which
are
granted
to
Aristotle
,
that
the
Coelestial
bodies
themselves
are
also
generable
and
corruptible
,
aswell
as
the
Elementary
,
what
will
you
say
then
?
SIMPL.
I
will
say
you
have
done
that
which
is
impossible
to
be
done
.
SAGR.
Go
to
;
tell
me
,
Simplicius
,
are
not
these
affections
contrary
to
one
another
?
SIMPL.
Which
?
SAGR.
Why
these
;
Alterable
,
unalterable
;
passible
,
[
](A61244-e9210-b)*
*
Or
,
Impatible
.
impassible
;
generable
,
ingenerable
;
corruptible
,
incorruptible
?
SIMPL.
They
are
most
contrary
.
SAGR.
Well
then
,
if
this
be
true
,
and
it
be
also
granted
,
that
Coelestial
Bodies
are
ingenerable
and
incorruptible
;
I
prove
that
of
necessity
Coelestial
Bodies
must
be
generable
and
corruptible
.
SIMPL.
This
must
needs
be
a
Sophism
.
SAGR.
Hear
my
Argument
,
Coelestial
Bodies
are
generable
and
corruptible
,
because
they
are
ingenerable
and
incorruptible
.
and
then
censure
and
resolve
it
.
Coelestial
Bodies
,
for
that
they
are
ingenerable
and
incorruptible
,
have
in
Nature
their
contraries
,
which
are
those
Bodies
that
be
generable
and
corruptible
;
but
where
there
is
contrariety
,
there
is
also
generation
and
corruption
;
therefore
Coelestial
Bodies
are
generable
and
corruptible
.
SIMPL.
Did
I
not
say
it
could
be
no
other
than
a
Sophism
?
This
is
one
of
those
forked
Arguments
called
Soritae
:
The
forked
Syllogism
cal'd
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
.
like
that
of
the
Cretan
,
who
said
that
all
Cretans
were
lyars
;
but
he
as
being
a
Cretan
,
had
told
a
lye
,
in
saying
that
the
Cretans
were
lyars
;
it
followed
therefore
,
that
the
Cretans
were
no
lyars
,
and
consequently
that
he
,
as
being
a
Cretan
,
had
spoke
truth
:
And
yet
in
saying
the
Cretans
were
lyars
,
he
had
said
true
,
and
comprehending
himself
as
a
Cretan
,
he
must
consequently
be
a
lyar
.
And
thus
in
these
kinds
of
Sophisms
a
man
may
dwell
to
eternity
,
and
never
come
to
any
conclusion
.
SAGR.
You
have
hitherto
censured
it
,
it
remaineth
now
that
you
answer
it
,
shewing
the
fallacie
.
SIMPL.
As
to
the
resolving
of
it
,
and
finding
out
its
fallacie
,
do
you
not
in
the
first
place
see
a
manifest
contradiction
in
it
?
Coelestial
Bodies
are
ingenerable
and
incorruptible
;
Ergo
,
Coelestial
Bodies
are
generable
and
corruptible
.
Amongst
Coelestial
Bodies
there
is
no
contrariety
.
And
again
,
the
contrariety
is
not
betwixt
the
Coelestial
Bodies
,
but
betwixt
the
Elements
,
which
have
the
contrariety
of
the
Motions
,
sursùm
and
deorsùm
,
and
of
levity
and
gravity
;
But
the
Heavens
which
move
circularly
,
to
which
motion
no
other
motion
is
contrary
,
want
contrariety
,
and
therefore
they
are
incorruptible
.
SAGR.
Fair
and
softly
,
Simplicius
;
this
contrariety
whereby
you
say
some
simple
Bodies
become
corruptible
,
resides
it
in
the
same
Body
which
is
corrupted
,
or
else
hath
it
relation
to
some
other
?
I
say
,
if
,
for
example
,
humidity
by
which
a
piece
of
Earth
is
corrupted
,
resides
it
in
the
same
Earth
or
in
some
other
bodie
,
which
must
either
be
the
Air
or
Water
?
I
believe
you
will
grant
,
that
like
as
the
Motions
upwards
and
downwards
,
and
gravity
and
levity
,
which
you
make
the
first
contraries
,
cannot
be
in
the
same
Subject
,
so
neither
can
moist
and
dry
,
hot
and
cold
:
you
must
therefore
consequently
acknowledg
that
when
a
bodie
corrupteth
,
Contraries
which
are
the
causes
of
corruption
,
reside
not
in
the
same
body
that
corrupteth
▪
it
is
occasioned
by
some
quality
residing
in
another
contrary
to
its
own
:
therefore
to
make
the
Coelestial
Body
become
corruptible
,
it
sufficeth
that
there
are
in
Nature
,
bodies
that
have
a
contrariety
to
that
Coelestial
body
;
and
such
are
the
Elements
,
if
it
be
true
that
corruptibility
be
contrary
to
incorruptibility
.
SIMPL.
This
sufficeth
not
,
Sir
;
The
Elements
alter
and
corrupt
,
because
they
are
intermixed
,
and
are
joyn'd
to
one
another
,
and
so
may
exercise
their
contrariety
;
Coelestial
Bodies
touch
,
but
are
not
touched
by
the
Elements
.
but
Coelestial
bodies
are
separated
from
the
Elements
,
by
which
they
are
not
so
much
as
toucht
,
though
indeed
they
have
an
influence
upon
the
Elements
.
It
is
requisite
,
if
you
will
prove
generation
and
corruption
in
Coelestial
bodies
,
that
you
shew
,
that
there
resides
contrarieties
between
them
.
SAGR.
See
how
I
will
find
those
contrarieties
between
them
.
The
first
fountain
from
whence
you
derive
the
contrariety
of
the
Elements
,
is
the
contrariety
of
their
motions
upwards
and
downwards
:
it
therefore
is
necessary
that
those
Principles
be
in
like
manner
contraries
to
each
other
,
Gravity
&
levity
,
rarity
and
density
,
are
contrary
qualities
.
upon
which
those
motions
depend
:
and
because
that
is
moveable
upwards
by
lightness
,
and
this
downwards
by
gravity
,
it
is
necessary
that
lightness
and
gravity
are
contrary
to
each
other
:
no
less
are
we
to
believe
those
other
Principles
to
be
contraries
,
which
are
the
causes
that
this
is
heavy
,
and
that
light
:
but
by
your
own
confession
,
levity
and
gravity
follow
as
consequents
of
rarity
and
density
;
therefore
rarity
and
density
shall
be
contraries
:
The
stars
infinitely
surpass
the
substance
of
the
rest
of
Heaven
in
density
.
the
which
conditions
or
affections
are
so
amply
found
in
Coelestial
bodies
,
that
you
esteem
the
stars
to
be
onely
more
dense
parts
of
their
Heaven
:
and
if
this
be
so
,
it
followeth
that
the
density
of
the
stars
exceeds
that
of
the
rest
of
Heaven
,
by
almost
infinite
degrees
:
which
is
manifest
,
in
that
Heaven
is
infinitely
transparent
,
and
the
stars
extremely
opacous
;
and
for
that
there
are
there
above
no
other
qualities
,
but
more
and
less
density
and
rarity
,
which
may
be
causes
of
the
greater
or
less
transparency
.
There
being
then
such
contrariety
between
the
Coelestial
bodies
,
it
is
necessary
that
they
also
be
generable
and
corruptible
,
in
the
same
manner
as
the
Elementary
bodies
are
;
or
else
that
contrariety
is
not
the
cause
of
corruptibility
,
Rarity
&
density
in
Coelestial
bodies
,
is
different
from
the
rarity
&
density
of
the
elements
.
&c.
SIMPL.
There
is
no
necessity
either
of
one
or
the
other
,
for
that
density
and
rarity
in
Coelestial
bodies
,
are
not
contraries
to
each
other
,
as
in
Elementary
bodies
;
for
that
they
depend
not
on
the
primary
qualities
,
cold
and
heat
,
which
are
contraries
;
but
on
the
more
or
less
matter
in
proportion
to
quantity
:
now
much
and
little
,
speak
onely
a
relative
opposition
,
that
is
,
the
least
of
oppositions
,
and
which
hath
nothing
to
do
with
generation
and
corruption
.
SAGR.
Therefore
affirming
,
that
density
and
rarity
,
which
amongst
the
Elements
should
be
the
cause
of
gravity
and
levity
,
which
may
be
the
causes
of
contrary
motions
sursum
and
deors●●m
,
on
which
,
again
,
dependeth
the
contrarieties
for
generation
and
corruption
;
it
sufficeth
not
that
they
be
those
densnesses
and
rarenesses
which
under
the
same
quantity
,
or
(
if
you
will
)
mass
contain
much
or
little
matter
,
but
it
is
necessary
that
they
be
densnesses
and
rarenesses
caused
by
the
primary
qualities
,
hot
and
cold
,
otherwise
they
would
operate
nothing
at
all
:
but
if
this
be
so
,
Aristotle
defective
in
assigning
the
causes
why
the
elements
are
generable
&
corruptible
.
Aristotle
hath
deceived
us
,
for
that
he
should
have
told
it
us
at
first
,
and
so
have
left
written
that
those
simple
bodies
are
generable
and
corruptible
,
that
are
moveable
with
simple
motions
upwards
and
downwards
,
dependent
on
levity
and
gravity
,
caused
by
rarity
and
density
,
made
by
much
or
little
matter
,
by
reason
of
heat
and
cold
;
and
not
to
have
staid
at
the
simple
motion
sursum
and
deorsùm
:
for
I
assure
you
that
to
the
making
of
bodies
heavy
or
light
,
whereby
they
come
to
be
moved
with
contrary
motions
,
any
kind
of
density
and
rarity
sufficeth
,
whether
it
proceed
from
heat
and
cold
,
or
what
else
you
please
;
for
heat
and
cold
have
nothing
to
do
in
this
affair
:
and
you
shall
upon
experiment
find
,
that
a
red
iron
,
which
you
must
grant
to
have
heat
,
weigheth
as
much
,
and
moves
in
the
same
manner
as
when
it
is
cold
.
But
to
overpass
this
also
,
how
know
you
but
that
Coelestial
rarity
and
density
depend
on
heat
and
cold
?
SIMPL.
I
know
it
,
because
those
qualities
are
not
amongst
Coelestial
bodies
,
which
are
neither
hot
nor
cold
.
SALV
.
I
see
we
are
again
going
about
to
engulph
our selves
in
a
bottomless
ocean
,
where
there
is
no
getting
to
shore
;
for
this
is
a
Navigation
without
Compass
,
Stars
,
or
Rudder
:
so
that
it
will
follow
either
that
we
be
forced
to
pass
from
Shelf
to
Shelf
,
or
run
on
ground
,
or
to
sail
continually
in
danger
of
being
lost
.
Therefore
,
if
according
to
your
advice
we
shall
proceed
in
our
main
design
,
we
must
of
necessity
for
the
present
overpass
this
general
consideration
,
whether
direct
motion
be
necessary
in
Nature
,
and
agree
with
some
bodies
;
and
come
to
the
particular
demonstrations
,
observations
and
experiments
;
propounding
in
the
first
place
all
those
that
have
been
hitherto
alledged
by
Aristotle
,
Ptolomey
,
and
others
,
to
prove
the
stability
of
the
Earth
,
endeavouring
in
the
next
place
to
answer
them
:
and
producing
in
the
last
place
,
those
,
by
which
others
may
be
perswaded
,
that
the
Earth
is
no
less
than
the
Moon
,
or
any
other
Planet
to
be
numbered
amongst
natural
bodies
that
move
circularly
.
SAGR.
I
shall
the
more
willingly
incline
to
this
,
in
that
I
am
better
satisfied
with
your
Architectonical
and
general
discourse
,
than
with
that
of
Aristotle
,
for
yours
convinceth
me
without
the
least
scruple
,
and
the
other
at
every
step
crosseth
my
way
with
some
block
.
And
I
see
no
reason
why
Simplicius
should
not
be
presently
satisfied
with
the
Argument
you
alledg
,
to
prove
that
there
can
be
no
such
thing
in
nature
as
a
motion
by
a
right
line
,
if
we
do
but
presuppose
that
the
parts
of
the
Universe
are
disposed
in
an
excellent
constitution
and
perfect
order
.
SALV
.
Stay
a
little
,
good
Sagredus
,
for
just
now
a
way
comes
into
my
mind
,
how
I
may
give
Simplicius
satisfaction
,
provided
that
he
will
not
be
so
strictly
wedded
to
every
expression
of
Aristotle
,
as
to
hold
it
heresie
to
recede
in
any
thing
from
him
.
Nor
is
there
any
question
to
be
made
,
but
that
if
we
grant
the
excellent
disposition
and
perfect
order
of
the
parts
of
the
Universe
,
as
to
local
scituation
,
that
then
there
is
no
other
but
the
circular
motion
,
and
rest
;
for
as
to
the
motion
by
a
right
line
,
I
see
not
how
it
can
be
of
use
for
any
thing
,
but
to
reduce
to
their
natural
constitution
,
some
integral
bodies
,
that
by
some
accident
were
remov'd
and
separated
from
their
whole
,
as
we
said
above
.
Let
us
now
consider
the
whole
Terrestrial
Globe
,
and
enquire
the
best
we
can
,
whether
it
,
and
the
other
Mundane
bodies
are
to
conserve
themselves
in
their
perfect
and
natural
disposition
.
It
is
necessary
to
say
,
〈◊〉
that
it
rests
and
keeps
perpetually
immoveable
in
its
place
;
or
else
that
continuing
always
in
its
place
,
it
revolves
in
its
self
;
or
that
it
turneth
about
a
Centre
,
moving
by
the
circumference
of
a
circle
.
Arist.
&
Ptolomey
make
the
Terrestrial
Globe
immoveable
.
Of
which
accidents
,
both
Aristotle
and
Ptolomey
,
and
all
their
followers
say
,
that
it
hath
ever
observed
,
and
shall
continually
keep
the
first
,
that
is
,
a
perpetual
rest
in
the
same
place
.
It
is
better
to
say
,
that
the
Terrestrial
Globe
naturally
resteth
,
than
that
it
moveth
directly
downwards
.
Now
,
why
,
I
pray
you
,
ought
they
not
to
have
said
,
that
its
natural
affection
is
to
rest
immoveable
,
rather
than
to
make
natural
unto
it
the
motion
[
](A61244-e10170-b)*
*
The
word
is
,
all'
ingiù
,
which
the
Latine
version
rendreth
sursùm
,
which
is
quite
contrary
to
the
Authors
sense
.
downwards
,
with
which
motion
it
never
did
or
shall
move
?
And
as
to
the
motion
by
a
right
line
,
they
must
grant
us
that
Nature
maketh
use
of
it
to
reduce
the
small
parts
of
the
Earth
,
Water
,
Air
,
Fire
,
and
every
other
integral
Mundane
body
to
their
Whole
,
when
any
of
them
by
chance
are
separated
,
and
so
transported
out
of
their
proper
place
;
if
also
haply
,
some
circular
motion
might
not
be
found
to
be
more
convenient
to
make
this
restitution
.
In
my
judgment
,
this
primary
position
answers
much
better
,
even
according
to
Aristotles
own
method
,
to
all
the
other
consequences
,
than
to
attribute
the
straight
motion
to
be
an
intrinsick
and
natural
principle
of
the
Elements
.
Which
is
manifest
,
for
that
if
I
aske
the
Peripatetick
,
if
,
being
of
opinion
that
Coelestial
bodies
are
incorruptibe
and
eternal
,
he
believeth
that
the
Terrestial
Globe
is
not
so
,
but
corruptible
and
mortal
,
so
that
there
shall
come
a
time
,
when
the
Sun
and
Moon
and
other
Stars
,
continuing
their
beings
and
operations
,
the
Earth
shall
not
be
found
in
the
World
,
but
shall
with
the
rest
of
the
Elements
be
destroyed
and
annihilated
,
I
am
certain
that
he
would
answer
me
,
no
:
therefore
generation
and
corruption
is
in
the
parts
and
not
in
the
whole
;
Right
Motion
with
more
reason
attributed
to
the
parts
,
than
to
the
whole
Elements
.
and
in
the
parts
very
small
and
superficial
,
which
are
,
as
it
were
,
incensible
in
comparison
of
the
whole
masse
.
And
because
Aristotle
deduceth
generation
and
corruption
from
the
contrariety
of
streight
motions
,
let
us
remit
such
motions
to
the
parts
,
which
onely
change
and
decay
,
and
to
the
whole
Globe
and
Sphere
of
the
Elements
,
let
us
ascribe
either
the
circular
motion
,
or
a
perpetual
consistance
in
its
proper
place
:
the
only
affections
apt
for
perpetuation
,
and
maintaining
of
perfect
order
.
This
which
is
spoken
of
the
Earth
,
may
be
said
with
the
same
reason
of
Fire
,
and
of
the
greatest
part
of
the
Air
;
to
which
Elements
,
The
Peripateticks
improperly
assign
those
motions
to
the
Elements
for
Natural
,
with
which
they
never
were
moved
,
and
those
for
Preternatural
with
which
they
alwayes
are
moved
.
the
Peripateticks
are
forced
to
ascribe
for
intrinsical
and
natural
,
a
motion
wherewith
they
were
never
yet
moved
,
nor
never
shall
be
;
and
to
call
that
motion
preternatural
to
them
,
wherewith
,
if
they
move
at
all
,
they
do
and
ever
shall
move
.
This
I
say
,
because
they
assign
to
the
Air
and
Fire
the
motion
upwards
,
wherewith
those
Elements
were
never
moved
,
but
only
some
parts
of
them
,
and
those
were
so
moved
onely
in
order
to
the
recovery
of
their
perfect
constitution
,
when
they
were
out
of
their
natural
places
;
and
on
the
contrary
they
call
the
circular
motion
preternatural
to
them
,
though
they
are
thereby
incessantly
moved
:
forgeting
,
as
it
seemeth
,
what
Aristotle
oft
inculcateth
,
that
nothing
violent
can
be
permanent
.
SIMPL.
To
all
these
we
have
very
pertinent
answers
,
Sensible
experiments
to
be
preferred
to
humane
Arguments
.
which
I
for
this
time
omit
,
that
we
may
come
to
the
more
particular
reasons
,
and
sensible
experiments
,
which
ought
in
conclusion
to
be
opposed
,
as
Aristotle
saith
well
,
to
whatever
humane
reason
can
present
us
with
.
SAGR.
What
hath
been
spoken
hitherto
,
serves
to
clear
up
unto
us
which
of
the
two
general
discourses
carrieth
with
it
most
of
probability
,
I
mean
that
of
Aristotle
,
which
would
perswade
us
,
that
the
sublunary
bodies
are
by
nature
generable
,
and
corruptible
,
&c.
and
therefore
most
different
from
the
essence
of
Coelestial
bodies
,
which
are
impassible
,
ingenerable
,
incorruptible
,
&c.
drawn
from
the
diversity
of
simple
motions
;
or
else
this
of
Salviatus
,
who
supposing
the
integral
parts
of
the
World
to
be
disposed
in
a
perfect
constitution
,
excludes
by
necessary
consequence
the
right
or
straight
motion
of
simple
natural
bodies
,
as
being
of
no
use
in
nature
,
and
esteems
the
Earth
it self
also
to
be
one
of
the
Coelestial
bodies
adorn'd
with
all
the
prerogatives
that
agree
with
them
;
which
last
discourse
is
hitherto
much
more
likely
,
in
my
judgment
,
than
that
other
.
Therefore
resolve
,
Simplicius
,
to
produce
all
the
particular
reasons
,
experiments
and
observations
,
as
well
Natural
as
Astronomical
,
that
may
serve
to
perswade
us
that
the
Earth
differeth
from
the
Coelestial
bodies
,
is
immoveable
,
and
situated
in
the
Centre
of
the
World
,
and
what
ever
else
excludes
its
moving
like
to
the
Planets
,
as
Jupiter
or
the
Moon
,
&c.
And
Salviatus
will
be
pleased
to
be
so
civil
as
to
answer
to
them
one
by
one
.
SIMPL.
See
here
for
a
begining
,
two
most
convincing
Arguments
to
demonstrate
the
Earth
to
be
most
different
from
the
Coelestial
bodies
.
First
,
the
bodies
that
are
generable
,
corruptible
,
alterable
,
&c.
are
quite
different
from
those
that
are
ingenerable
,
incorruptible
,
unalterable
,
&c.
But
the
Earth
is
generable
,
corruptible
,
alterable
,
&c.
and
the
Coelestial
bodies
ingenerable
,
incorruptible
,
unalterable
,
&c.
Therefore
the
Earth
is
quite
different
from
the
Coelestial
bodies
.
SAGR.
By
your
first
Argument
you
spread
the
Table
with
the
same
Viands
,
which
but
just
now
with
much
adoe
were
voided
.
SIMPL.
Hold
a
little
,
Sir
,
and
take
the
rest
along
with
you
,
and
then
tell
me
if
this
be
not
different
from
what
you
had
before
.
In
the
former
,
the
Minor
was
proved
à
priori
,
&
now
you
see
it
proved
à
posteriori
:
Judg
then
if
it
be
the
same
.
I
prove
the
Minor
,
therefore
(
the
Major
being
most
manifest
)
by
sensible
experience
,
which
〈…〉
that
in
the
Earth
there
are
made
continual
generations
,
corruptions
,
alterations
,
&c.
which
neither
our
senses
,
nor
the
traditions
or
memories
of
our
Ancestors
,
ever
saw
an
instance
of
in
Heaven
;
therefore
Heaven
is
unalterable
,
&c.
and
the
Earth
alterable
,
Heaven
immutable
,
because
there
never
was
any
mutation
seen
in
it
.
&c.
and
therefore
different
from
Heaven
.
I
take
my
second
Argument
from
a
principal
and
essential
accident
,
and
it
is
this
.
That
body
which
is
by
its
nature
obscure
and
deprived
of
light
,
Bodies
naturally
lucid
,
are
different
from
those
which
are
by
nature
obscure
.
is
divers
from
the
luminous
and
shining
bodies
;
but
the
Earth
is
obscure
and
void
of
light
,
and
the
Coelestial
bodies
splendid
,
and
full
of
light
;
Ergo
,
&c.
Answer
to
these
Arguments
first
,
that
we
may
not
heap
up
too
many
,
and
then
I
will
alledge
others
.
SALV
.
As
to
the
first
,
the
stresse
whereof
you
lay
upon
experience
,
I
desire
that
you
would
a
little
more
distinctly
produce
me
the
alteration
which
you
see
made
in
the
Earth
,
and
not
in
Heaven
;
upon
which
you
call
the
Earth
alterable
,
and
the
Heavens
not
so
.
SIMPL.
I
see
in
the
Earth
,
plants
and
animals
continually
generating
and
decaying
;
winds
,
rains
,
tempests
,
storms
arising
;
and
in
a
word
,
the
aspect
of
the
Earth
to
be
perpetually
metamorphosing
;
none
of
which
mutations
are
to
be
discern'd
in
the
Coelestial
bodies
;
the
constitution
and
figuration
of
which
is
most
punctually
conformable
to
that
they
ever
were
time
out
of
mind
;
without
the
generation
of
any
thing
that
is
new
,
or
corruption
of
any
thing
that
was
old
.
SALV
.
But
if
you
content
your self
with
these
visible
,
or
to
say
better
,
seen
experiments
,
you
must
consequently
account
China
and
America
Coelestial
bodies
,
for
doubtlesse
you
never
be
held
in
them
these
alterations
which
you
see
here
in
Italy
,
and
that
therefore
according
to
your
apprehension
they
are
inalterable
.
SIMPL.
Though
I
never
did
see
these
alterations
sensibly
in
those
places
,
the
relations
of
them
are
not
to
be
questioned
;
besides
that
,
cum
eadem
sit
ratio
totius
,
&
partium
,
those
Countreys
being
a
part
of
the
Earth
,
as
well
as
ours
,
they
must
of
necessity
be
alterable
as
these
are
.
SALV
.
And
why
have
you
not
,
without
being
put
to
believe
other
mens
relations
,
examined
and
observed
those
alterations
with
your
own
eyes
?
SIMPL.
Because
those
places
,
besides
that
they
are
not
exposed
to
our
eyes
,
are
so
remote
,
that
our
sight
cannot
reach
to
comprehend
therein
such
like
mutations
.
SALV
.
See
now
,
how
you
have
unawares
discovered
the
fallacy
of
your
Argument
;
for
,
if
you
say
that
the
alterations
that
are
seen
on
the
Earth
neer
at
hand
,
cannot
,
by
reason
of
the
too
great
distance
,
be
seen
in
America
,
much
lesse
can
you
see
them
in
the
Moon
,
which
is
so
many
hundred
times
more
remote
:
And
if
you
believe
the
alterations
in
Mexico
upon
the
report
of
those
that
come
from
thence
,
what
intelligence
have
you
from
the
Moon
,
to
assure
you
that
there
is
no
such
alterations
in
it
?
Therefore
,
from
your
not
seeing
any
alterations
in
Heaven
,
whereas
,
if
there
were
any
such
,
you
could
not
see
them
by
reason
of
their
too
great
distance
,
and
from
your
not
having
intelligence
thereof
,
in
regard
that
it
cannot
be
had
,
you
ought
not
to
argue
,
that
there
are
no
such
alterations
;
howbeit
,
from
the
seeing
and
observing
of
them
on
Earth
,
you
well
argue
that
therein
such
there
are
.
SIMPL.
I
will
shew
so
great
mutations
that
have
befaln
on
the
Earth
;
that
if
any
such
had
happened
in
the
Moon
,
they
might
very
well
have
been
observed
here
below
.
The
Mediterranian
Sea
made
by
the
separation
of
Abila
and
Calpen
.
We
find
in
very
antient
records
,
that
heretofore
at
the
Streights
of
Gibraltar
,
the
two
great
Mountains
Abila
,
and
Calpen
,
were
continued
together
by
certain
other
lesse
Mountains
,
which
there
gave
check
to
the
Ocean
:
but
those
Hills
,
being
by
some
cause
or
other
separated
,
and
a
way
being
opened
for
the
Sea
to
break
in
,
it
made
such
an
inundation
,
that
it
gave
occasion
to
the
calling
of
it
since
the
Mid-land
Sea
:
the
greatness
whereof
considered
,
and
the
divers
aspects
the
surfaces
of
the
Water
and
Earth
then
made
,
had
it
been
beheld
afar
off
,
there
is
no
doubt
but
so
great
a
change
might
have
been
discerned
by
one
that
was
then
in
the
Moon
;
as
also
to
us
inhabitants
of
the
Earth
,
the
like
alterations
would
be
perceived
in
the
Moon
;
but
we
find
not
in
antiquity
,
that
ever
there
was
such
a
thing
seen
;
therefore
we
have
no
cause
to
say
,
that
any
of
the
Coelestial
bodies
are
alterable
,
&c.
SALV
.
That
so
great
alterations
have
hapned
in
the
Moon
,
I
dare
not
say
,
but
for
all
that
,
I
am
not
yet
certain
but
that
such
changes
might
occur
;
and
because
such
a
mutation
could
onely
represent
unto
us
some
kind
of
variation
between
the
more
clear
,
and
more
obscure
parts
of
the
Moon
,
I
know
not
whether
we
have
had
on
Earth
observant
Selenographers
,
who
have
for
any
considerable
number
of
years
,
instructed
us
with
so
exact
Selenography
,
as
that
we
should
confidently
conclude
,
that
there
hath
no
such
change
hapned
in
the
face
of
the
Moon
;
of
the
figuration
of
which
I
find
no
more
particular
description
,
than
the
saying
of
some
,
that
it
represents
an
humane
face
;
of
others
,
that
it
is
like
the
muzle
of
a
Lyon
;
and
of
others
,
that
it
is
Cain
with
a
bundle
of
thorns
on
his
back
:
therefore
,
to
say
Heaven
is
unalterable
,
because
that
in
the
Moon
,
or
other
Coelestial
bodies
,
no
such
alterations
are
seen
,
as
discover
themselves
on
Earth
,
is
a
bad
illation
,
and
concludeth
nothing
.
SAGR.
And
there
is
another
odd
kind
of
scruple
in
this
Argument
of
Simplicius
,
running
in
my
mind
,
which
I
would
gladly
have
answered
;
therefore
I
demand
of
him
,
whether
the
Earth
before
the
Mediterranian
inundation
was
generable
and
corruptible
,
or
else
began
then
so
to
be
?
SIMPL.
It
was
doubtless
generable
and
corruptible
also
before
that
time
;
but
that
was
so
vast
a
mutation
,
that
it
might
have
been
observed
as
far
as
the
Moon
.
SAGR.
Go
to
;
if
the
Earth
was
generable
and
corruptible
before
that
Inundation
,
why
may
not
the
Moon
be
so
likewise
without
such
a
change
?
Or
why
should
that
be
necessary
in
the
Moon
,
which
importeth
nothing
on
Earth
?
SALV
.
It
is
a
shrewd
question
:
But
I
am
doubtfull
that
Simplicius
a
little
altereth
the
Text
of
Aristotle
,
and
the
other
Peripateticks
,
who
say
,
they
hold
the
Heavens
unalterable
,
for
that
they
see
therein
no
one
star
generate
or
corrupt
,
which
is
probably
a
less
part
of
Heaven
,
than
a
City
is
of
the
Earth
,
and
yet
innumerable
of
these
have
been
destroyed
,
so
as
that
no
mark
of
them
hath
remain'd
.
SAGR.
I
verily
believed
otherwise
,
and
conceited
that
Simplicius
dissembled
this
exposition
of
the
Text
,
that
he
might
not
charge
his
Master
and
Consectators
,
with
a
notion
more
absurd
than
the
former
.
And
what
a
folly
it
is
to
say
the
Coelestial
part
is
unalterable
,
because
no
stars
do
generate
or
corrupt
therein
?
What
then
?
hath
any
one
seen
a
Terrestrial
Globe
corrupt
,
and
another
regenerate
in
its
place
?
And
yet
is
it
not
on
all
hands
granted
by
Philosophers
,
that
there
are
very
few
stars
in
Heaven
less
than
the
Earth
,
It
s
no
less
impossible
for
a
star
to
corrupt
,
than
for
the
whole
Terrestrial
Globe
.
but
very
many
that
are
much
bigger
?
So
that
for
a
star
in
Heaven
to
corrupt
,
would
be
no
less
than
if
the
whole
Terrestrial
Globe
should
be
destroy'd
.
Therefore
,
if
for
the
true
proof
of
generation
and
corruption
in
the
Universe
,
it
be
necessary
that
so
vast
bodies
as
a
star
,
must
corrupt
and
regenerate
,
you
may
satisfie
your self
and
cease
your
opinion
;
for
I
assure
you
,
that
you
shall
never
see
the
Terrestrial
Globe
or
any
other
integral
body
of
the
World
,
to
corrupt
or
decay
so
,
that
having
been
beheld
by
us
for
so
many
years
past
,
they
should
so
dissolve
,
as
not
to
leave
any
footsteps
of
them
.
SALV
.
But
to
give
Simplicius
yet
fuller
satisfaction
,
and
to
reclaim
him
,
Aristotle
would
change
his
opinion
,
did
he
see
the
novelties
of
our
age
.
if
possible
,
from
his
error
;
I
affirm
,
that
we
have
in
our
age
new
accidents
and
observations
,
and
such
,
that
I
question
not
in
the
least
,
but
if
Aristotle
were
now
alive
,
they
would
make
him
change
his
opinion
;
which
may
be
easily
collected
from
the
very
manner
of
his
discoursing
:
For
when
he
writeth
that
he
esteemeth
the
Heavens
inalterable
,
&c.
because
no
new
thing
was
seen
to
be
begot
therein
,
or
any
old
to
be
dissolved
,
he
seems
implicitely
to
hint
unto
us
,
that
when
he
should
see
any
such
accident
,
he
would
hold
the
contrary
:
and
〈◊〉
,
as
indeed
it
is
meet
,
sensible
experiments
to
natural
reason
:
for
had
he
not
made
any
reckoning
of
the
senses
,
he
would
not
then
from
the
not
seeing
of
any
sensible
mutation
,
have
argued
immutability
.
SIMPL.
Aristotle
deduceth
his
principal
Argument
à
priori
,
shewing
the
necessity
of
the
inalterability
of
Heaven
by
natural
,
manifest
and
clear
principles
;
and
then
stablisheth
the
same
à
posteriori
,
by
sense
,
and
the
traditions
of
the
antients
.
SALV
.
This
you
speak
of
is
the
Method
he
hath
observed
in
delivering
his
Doctrine
,
but
I
do
not
bethink
it
yet
to
be
that
wherewith
he
invented
it
;
for
I
do
believe
for
certain
,
that
he
first
procured
by
help
of
the
senses
,
such
experiments
and
observations
as
he
could
,
The
certainty
of
the
conclusion
helpeth
by
a
resolutive
method
to
find
the
demonstration
.
to
assure
him
as
much
as
it
was
possible
,
of
the
conclusion
,
and
that
he
afterwards
sought
out
the
means
how
to
demonstrate
it
:
For
this
is
the
usual
course
in
demonstrative
Sciences
,
and
the
reason
thereof
is
,
because
when
the
conclusion
is
true
,
by
help
of
resolutive
Method
,
one
may
hit
upon
some
proposition
before
demonstrated
,
or
come
to
some
principle
known
per
se
;
but
if
the
conclusion
be
false
,
a
man
may
proceed
in
infinitum
,
and
never
meet
with
any
truth
already
known
;
but
very
oft
he
shall
meet
with
some
impossibility
or
manifest
absurdity
Pythagoras
offered
an
Hecatomb
for
a
Geometrical
demonstration
which
he
found
.
Nor
need
you
question
but
that
Pythagoras
along
time
before
he
found
the
demonstration
for
which
he
offered
the
Hecatomb
,
had
been
certain
,
that
the
square
of
the
side
subtending
the
right
angle
in
a
rectangle
triangle
,
was
equal
to
the
square
of
the
other
two
sides
:
and
the
certainty
of
the
conclusion
conduced
not
a
little
to
the
investigating
of
the
demonstration
,
understanding
me
alwayes
to
mean
in
demonstrative
Sciences
.
But
what
ever
was
the
method
of
Aristotle
,
and
whether
his
arguing
à
priori
preceded
sense
à
posteriori
,
or
the
contrary
;
it
sufficeth
that
the
same
Aristotle
preferreth
(
as
hath
been
oft
said
)
sensible
experiments
before
all
discourses
;
besides
,
as
to
the
Arguments
à
priori
their
force
hath
been
already
examined
.
Now
returning
to
my
purposed
matter
,
I
say
,
that
the
things
in
our
times
discovered
in
the
Heavens
,
are
,
and
have
been
such
,
that
they
may
give
absolute
satisfaction
to
all
Philosophers
;
forasmuch
as
in
the
particular
bodies
,
and
in
the
universal
expansion
of
Heaven
,
there
have
been
,
and
are
continually
,
seen
just
such
accidents
as
we
call
generations
and
corruptions
,
being
that
excellent
Astronomers
have
observed
many
Comets
generated
and
dissolved
in
parts
higher
than
the
Lunar
Orb
,
besides
the
two
new
Stars
,
Anno
1572
,
New
stars
discovered
in
Heaven
.
and
Anno
1604
,
without
contradiction
much
higher
than
all
the
Planets
;
and
in
the
face
of
the
Sun
it self
,
by
help
of
the
Telescope
,
Spots
generate
and
dissolve
in
the
face
of
the
Sun
.
certain
dense
and
obscure
substances
,
in
semblance
very
like
to
the
foggs
about
the
Earth
,
are
seen
to
be
produced
and
dissolved
;
and
many
of
these
are
so
vast
,
that
they
far
exceed
not
only
the
Mediterranian
Streight
,
but
all
Affrica
and
Asia
also
.
Solar
spots
are
bigger
than
all
Asia
and
Affrick
.
Now
if
Aristotle
had
seen
these
things
,
what
think
you
he
would
have
said
,
and
done
Simplicius
?
SIMPL.
I
know
not
what
Aristotle
would
have
done
or
said
,
that
was
the
great
Master
of
all
the
Sciences
,
but
yet
I
know
in
part
,
what
his
Sectators
do
and
say
,
and
ought
to
do
and
say
,
unlesse
they
would
deprive
themselves
of
their
guide
,
leader
,
and
Prince
in
Philosophy
.
As
to
the
Comets
,
are
not
those
Modern
Astronomers
,
who
would
make
them
Coelestial
,
convinced
by
the
[
](A61244-e11730-b)*
*
Astronomers
confuted
by
Anti-Tycho
.
Anti-Tycho
,
yea
,
and
overcome
with
their
own
weapons
,
I
mean
by
way
of
Paralaxes
and
Calculations
,
every
way
tryed
,
concluding
at
the
last
in
favour
of
Aristotle
,
that
they
are
all
Elementary
?
And
this
being
overthrown
,
which
was
as
it
were
their
foundation
,
have
these
Novellists
any
thing
more
wherewith
to
maintain
their
assertion
?
SALV
.
Hold
a
little
,
good
Simplicius
,
this
modern
Author
,
what
saith
he
to
the
new
Stars
,
Anno
1572
,
and
1604
,
and
to
the
Solar
spots
?
for
as
to
the
Comets
,
I
for
my
own
particular
little
care
to
make
them
generated
under
or
above
the
Moon
;
nor
did
I
ever
put
much
stresse
on
the
loquacity
of
Tycho
;
nor
am
I
hard
to
believe
that
their
matter
is
Elementary
,
and
that
they
may
elevate
(
sublimate
)
themselves
at
their
pleasure
,
without
meeting
with
any
obstacle
from
the
impenetrability
of
the
Peripatetick
Heaven
,
which
I
hold
to
be
far
more
thin
,
yielding
,
and
subtil
than
our
Air
;
and
as
to
the
calculations
of
the
Parallaxes
,
first
,
the
uncertainty
whether
Comets
are
subject
to
such
accidents
,
and
next
,
the
inconstancy
of
the
observations
,
upon
which
the
computations
are
made
,
make
me
equally
suspect
both
those
opinions
:
Anti-Tycho
wresteth
Astronomical
observations
to
his
own
purpose
.
and
the
rather
,
for
that
I
see
him
you
call
Anti-Tycho
,
sometimes
stretch
to
his
purpose
,
or
else
reject
those
observations
which
interfere
with
his
design
.
SIMPL.
As
to
the
new
Stars
,
Anti-Tycho
extricates
himself
finely
in
three
or
four
words
;
saying
,
That
those
modern
new
Stars
are
no
certain
parts
of
the
Coelestial
bodies
,
and
that
the
adversaries
,
if
they
will
prove
alteration
and
generation
in
those
superior
bodies
,
must
shew
some
mutations
that
have
been
made
in
the
Stars
described
so
many
ages
past
,
of
which
there
is
no
doubt
but
that
they
be
Coelestial
bodies
,
which
they
can
never
be
able
to
do
:
Next
,
as
to
those
matters
which
some
affirm
,
to
generate
and
dissipate
in
the
face
of
the
Sun
,
he
makes
no
mention
thereof
;
wherefore
I
conclude
,
that
he
believed
them
fictious
,
or
the
illusions
of
the
Tube
,
or
at
most
,
some
petty
effects
caused
by
the
Air
,
and
in
brief
,
any
thing
rather
than
matters
Coelestial
.
SALV
.
But
you
,
Simplicius
,
what
answer
could
you
give
to
the
opposition
of
these
importunate
spots
which
are
started
up
to
disturb
the
Heavens
,
and
more
than
that
,
the
Peripatetick
Philosophy
?
It
cannot
be
but
that
you
,
who
are
so
resolute
a
Champion
of
it
,
have
found
some
reply
or
solution
for
the
same
,
of
which
you
ought
not
to
deprive
us
.
SIMPL.
I
have
heard
sundry
opinions
about
this
particular
.
One
saith
:
They
are
Stars
which
in
their
proper
Orbs
,
Sundry
opinions
touching
the
Solar
spots
.
like
as
Venus
and
Mercury
,
revolve
about
the
Sun
,
and
in
passing
under
it
,
represent
themselves
to
us
obscure
;
and
for
that
they
are
many
,
they
oft
happen
to
aggregate
their
parts
together
,
and
afterwards
seperate
again
.
Others
believe
them
to
be
äerial
impressions
;
others
,
the
illusions
of
the
chrystals
;
and
others
,
other
things
:
But
I
incline
to
think
,
yea
am
verily
perswaded
,
That
they
are
an
aggregate
of
many
several
opacous
bodies
,
as
it
were
casually
concurrent
among
themselves
.
And
therefore
we
often
see
,
that
in
one
of
those
spots
one
may
number
ten
or
more
such
small
bodies
,
which
are
of
irregular
figures
,
and
seem
to
us
like
flakes
of
snow
,
or
flocks
of
wooll
,
or
moaths
flying
:
they
vary
fire
amongst
themselves
,
and
one
while
sever
,
another
while
meet
,
and
most
of
all
beneath
the
Sun
,
about
which
,
as
about
their
Centre
,
they
continually
move
.
But
yet
,
must
we
not
therefore
grant
,
that
they
are
generated
or
dissolved
,
but
that
at
sometimes
they
are
hid
behind
the
body
of
the
Sun
,
and
at
other
times
,
though
remote
from
it
,
yet
are
they
not
seen
for
the
vicinity
of
the
immeasurable
light
of
the
Sun
;
in
regard
that
in
the
eccentrick
Orb
of
the
Sun
,
there
is
constituted
,
as
it
were
,
an
Onion
,
composed
of
many
folds
one
within
another
,
each
of
which
,
being
[
](A61244-e12030-b)*
*
The
Original
saith
[
tempestata
si
muove
]
which
the
Latine
Translation
,
(
mistaking
Tempestata
,
a
word
in
Heraldry
,
for
Tempestato
,
)
rendereth
[
incitata
movetur
]
which
signifieth
a
violent
transportmeut
,
as
in
a
storm
,
that
of
a
Ship
.
studded
with
certain
small
spots
,
doth
move
;
and
albeit
their
motion
at
first
seemeth
inconstant
and
irregular
,
yet
neverthelesse
,
it
is
said
at
last
,
to
be
observed
that
the
very
same
spots
,
as
before
,
do
within
a
determinate
time
return
again
.
This
seemeth
to
me
the
fittest
answer
that
hath
been
found
to
assigne
a
reason
of
that
same
appearance
,
and
withal
to
maintain
the
incorruptability
and
ingenerability
of
the
Heavens
;
and
if
this
doth
not
suffice
;
there
wants
not
more
elevated
wits
,
which
will
give
you
other
more
convincing
.
SALV
.
If
this
of
which
we
dispute
,
were
some
point
of
Law
,
or
other
part
of
the
Studies
called
Humanity
,
In
natural
Sciences
,
the
art
of
Oratory
is
of
no
force
.
wherein
there
is
neither
truth
nor
falshood
,
if
we
will
give
sufficient
credit
to
the
acutenesse
of
the
wit
,
readinesse
of
answers
,
and
the
general
practice
of
Writers
,
then
he
who
most
aboundeth
in
these
,
makes
his
reason
more
probable
and
plausible
;
but
in
Natural
Sciences
,
the
conclusions
of
which
are
true
and
necessary
,
and
wherewith
the
judgment
of
men
hath
nothing
to
do
,
one
is
to
be
more
cautious
how
he
goeth
abou●
to
maintain
any
thing
that
is
false
;
for
a
man
but
of
an
ordinary
wit
,
if
it
be
his
good
fortune
to
be
of
the
right
side
,
may
lay
a
thousand
Demosthenes
and
a
thousand
Aristotles
at
his
feet
.
Therefore
reject
those
hopes
and
conceits
,
wherewith
you
flatter
your self
,
that
there
can
be
any
men
so
much
more
learned
,
read
,
and
versed
in
Authors
,
than
we
,
that
in
despite
of
nature
,
they
should
be
able
to
make
that
become
true
,
which
is
false
.
And
seeing
that
of
all
the
opinions
that
have
been
hitherto
alledged
touching
the
essence
of
these
Solar
spots
,
this
instanced
in
by
you
,
is
in
your
judgment
the
truest
,
it
followeth
(
if
this
be
so
)
that
all
the
rest
are
false
;
and
to
deliver
you
from
this
also
,
which
doubtlesse
is
a
most
false
Chimaera
,
over-passing
infinite
other
improbabilities
that
are
therein
,
An
Argument
that
necessarily
proveth
the
Solar
spots
to
generate
and
dissolve
.
I
shall
propose
against
it
onely
two
experiments
;
one
is
,
that
many
of
those
spots
are
seen
to
arise
in
the
midst
of
the
Solar
ring
,
and
many
likewise
to
dissolve
and
vanish
at
a
great
distance
from
the
circumference
of
the
Sun
;
a
necessary
Argument
that
they
generate
and
dissolve
;
for
if
without
generating
or
corrrupting
,
they
should
appear
there
by
onely
local
motion
,
they
would
all
be
seen
to
enter
,
A
conclusive
demonstration
,
that
the
spots
are
contiguous
to
the
body
of
the
Sun
.
and
pass
out
by
extreme
circumference
.
The
other
observation
to
such
as
are
not
situate
in
the
lowest
degree
of
ignorance
in
Perspective
,
by
the
mutation
of
the
appearing
figures
,
and
by
the
apparent
mutations
of
the
velocity
of
motion
is
necessarily
concluding
,
that
the
spots
are
contiguous
to
the
body
of
the
Sun
,
and
that
touching
its
superficies
,
they
move
either
with
it
or
upon
it
,
and
that
they
in
no
wise
move
in
circles
remote
from
the
same
.
The
motion
of
the
spots
towards
the
circumference
of
the
Sun
appears
slow
.
The
motion
proves
it
,
which
towards
the
circumference
of
the
Solar
Circle
,
appeareth
very
slow
,
and
towards
the
midst
,
more
swift
;
the
figures
of
the
spots
confirmeth
it
,
The
figure
of
the
spots
appears
narrow
towards
the
circumference
of
the
Suns
discus
,
&
why
.
which
towards
the
circumference
appear
exceeding
narrow
in
comparison
of
that
which
they
seem
to
be
in
the
parts
nearer
the
middle
;
and
this
because
in
the
midst
they
are
seen
in
their
full
luster
,
and
as
they
truly
be
;
and
towards
the
circumference
by
reason
of
the
convexity
of
the
globous
superficies
,
they
seem
more
compress'd
:
And
both
these
diminutions
of
figure
and
motion
,
to
such
as
know
how
to
observe
and
calculate
them
exactly
,
precisely
answer
to
that
which
should
appear
,
the
spots
being
contiguous
to
the
Sun
,
and
differ
irreconcileably
from
a
motion
in
circles
remote
,
though
but
for
smal
intervalls
from
the
body
of
the
Sun
;
as
hath
been
diffusely
demonstrated
by
our
[
](A61244-e12210-b)*
*
Under
this
word
Friend
,
as
also
that
of
Academick
,
&
Common
Friend
,
Galilaeus
modestly
conceals
himself
throughout
these
Dialogues
.
Friend
,
in
his
Letters
about
the
Solar
spots
,
to
Marcus
Velserus
.
It
may
be
gathered
from
the
same
mutation
of
figure
,
that
none
of
them
are
stars
,
or
other
bodies
of
spherical
figure
;
for
that
amongst
all
figures
the
sphere
never
appeareth
compressed
,
nor
can
ever
be
represented
but
onely
perfectly
round
;
and
thus
in
case
any
particular
spot
were
a
round
body
,
as
all
the
stars
are
held
to
be
,
the
said
roundness
would
as
well
appear
in
the
midst
of
the
Solar
ring
,
as
when
the
spot
is
near
the
extreme
:
whereas
,
it
s
so
great
compression
,
and
shewing
its
self
so
small
towards
the
extreme
,
and
contrariwise
,
spatious
and
large
towards
the
middle
,
assureth
us
,
The
Solar
spots
are
not
spherical
,
but
flat
like
thin
plates
.
that
these
spots
are
flat
plates
of
small
thickness
or
depth
,
in
comparison
of
their
length
and
breadth
.
Lastly
,
whereas
you
say
that
the
spots
after
their
determinate
periods
are
observed
to
return
to
their
former
aspect
,
believe
it
not
,
Simplicius
,
for
he
that
told
you
so
,
will
deceive
you
;
and
that
I
speak
the
truth
,
you
may
observe
them
to
be
hid
in
the
face
of
the
Sun
far
from
the
circumference
;
nor
hath
your
Observator
told
you
a
word
of
that
compression
,
which
necessarily
argueth
them
to
be
contiguous
to
the
Sun
.
That
which
he
tells
you
of
the
return
of
the
said
spots
,
is
nothing
else
but
what
is
read
in
the
forementioned
Letters
,
namely
,
that
some
of
them
may
sometimes
so
happen
that
are
of
so
long
a
duration
,
that
they
cannot
be
dissipated
by
one
sole
conversion
about
the
Sun
,
which
is
accomplished
in
less
than
a
moneth
.
SIMPL.
I
,
for
my
part
,
have
not
made
either
so
long
,
or
so
exact
observations
,
as
to
enable
me
to
boast
my self
Master
of
the
Quod
est
of
this
matter
:
but
I
will
more
accurately
consider
the
same
,
and
make
tryal
my self
for
my
own
satisfaction
,
whether
I
can
reconcile
that
which
experience
shews
us
,
with
that
which
Aristotle
teacheth
us
;
for
it
's
a
certain
Maxim
,
that
two
Truths
cannot
be
contrary
to
one
another
.
SALV
.
If
you
would
reconcile
that
which
sense
shewed
you
,
with
the
solider
Doctrines
of
Aristotle
,
One
cannot
(
saith
Aristotle
)
speak
confidently
of
Heaven
,
by
reason
of
its
great
distance
.
you
will
find
no
great
difficulty
in
the
undertaking
;
and
that
so
it
is
,
doth
not
Aristotle
say
,
that
one
cannot
treat
confidently
of
the
things
of
Heaven
,
by
reason
of
their
great
remoteness
?
SIMPL.
He
expresly
saith
so
.
SALV
.
And
doth
he
not
likewise
affirm
,
Aristotle
prefers
sense
before
ratiocination
.
that
we
ought
to
prefer
that
which
sense
demonstrates
,
before
all
Arguments
,
though
in
appearance
never
so
well
grounded
?
and
saith
he
not
this
without
the
least
doubt
or
haesitation
?
SIMPL.
He
doth
so
.
SALV
.
Why
then
,
the
second
of
these
propositions
,
which
are
both
the
doctrine
of
Aristotle
,
It
s
a
doctrine
more
agreeing
with
Aristotle
,
to
say
the
Heavens
are
alterable
,
than
that
which
affirms
them
inalterable
.
that
saith
,
that
sense
is
to
take
place
of
Logick
,
is
a
doctrine
much
more
solid
and
undoubted
,
than
that
other
which
holdeth
the
Heavens
to
be
unalterable
;
and
therefore
you
shall
argue
more
Aristotelically
,
saying
,
the
Heavens
are
alterable
,
for
that
so
my
sense
telleth
me
,
than
if
you
should
say
,
the
Heavens
are
ualterable
,
for
that
Logick
so
perswaded
Aristotle
.
We
may
by
help
of
the
Telescope
discourse
better
of
coelestical
matters
,
than
Aristot.
himself
.
Furthermore
,
we
may
discourse
of
Coelestial
matters
much
better
than
Aristotle
;
because
,
he
confessing
the
knowledg
thereof
to
be
difficult
to
him
,
by
reason
of
their
remoteness
from
the
senses
,
he
thereby
acknowledgeth
,
that
one
to
whom
the
senses
can
better
represent
the
same
,
may
philosophate
upon
them
with
more
certainty
.
Now
we
by
help
of
the
Telescope
,
are
brought
thirty
or
forty
times
nearer
to
the
Heavens
,
than
ever
Aristotle
came
;
so
that
we
may
discover
in
them
an
hundred
things
,
which
he
could
not
see
,
and
amongst
the
rest
,
these
spots
in
the
Sun
,
which
were
to
him
absolutely
invisible
;
therefore
we
may
discourse
of
the
Heavens
and
Sun
,
with
more
certainty
than
Aristolte
.
SAGR.
I
see
into
the
heart
of
Simplicius
,
and
know
that
he
is
much
moved
at
the
strength
of
these
so
convincing
Arguments
;
but
on
the
other
side
,
when
he
considereth
the
great
authority
which
Aristotle
hath
won
with
all
men
,
and
remembreth
the
great
number
of
famous
Interpreters
,
which
have
made
it
their
business
to
explain
his
sense
;
and
seeth
other
Sciences
,
so
necessary
and
profitable
to
the
publick
,
to
build
a
great
part
of
their
esteem
and
reputation
on
the
credit
of
Aristotle
he
is
much
puzzled
and
perplexed
:
The
Declamation●
of
Simplicius
.
and
methinks
I
hear
him
say
,
To
whom
then
should
we
repair
for
the
decision
of
our
controversies
,
if
Aristotle
were
removed
from
the
chair
?
What
other
Author
should
we
follow
in
the
Schools
,
Academies
and
Studies
?
What
Philosopher
hath
writ
all
the
parts
of
Natural
Philosophy
,
and
that
so
methodically
without
omitting
so
much
as
one
single
conclusion
?
Shall
we
then
overthrow
that
Fabrick
under
which
so
many
passengers
find
shelter
?
Shall
we
destroy
that
Asylum
,
that
Prytaneum
,
wherein
so
many
Students
meet
with
commodious
harbour
,
where
without
exposing
themselves
to
the
injuries
of
the
air
,
with
the
onely
turning
over
of
a
few
leaves
,
one
may
learn
all
the
secrets
of
Nature
?
Shall
we
dismantle
that
fort
in
which
we
are
safe
from
all
hostile
assaults
?
But
I
pitie
him
no
more
than
I
do
that
Gentleman
who
with
great
expence
of
time
and
treasure
,
and
the
help
of
many
hundred
artists
,
erects
a
very
sumptuous
Pallace
,
and
afterwards
beholds
it
ready
to
fall
,
by
reason
of
the
bad
foundation
;
but
being
extremely
unwilling
to
see
the
Walls
stript
which
are
adorned
with
so
many
beautifull
Pictures
;
or
to
suffer
the
columns
to
fall
,
that
uphold
the
stately
Galleries
;
or
the
gilded
roofs
,
chimney-pieces
,
the
freizes
,
the
cornishes
of
marble
,
with
so
much
cost
erected
,
to
be
ruined
;
goeth
about
with
girders
,
props
,
shoars
,
butterasses
,
to
prevent
their
subversion
.
SALV
.
But
alass
,
Simplicius
as
yet
fears
no
such
fall
,
and
I
would
undertake
to
secure
him
from
that
mischief
at
a
far
less
charge
.
Peripatetick
Philosophy
unchangeable
.
There
is
no
danger
that
so
great
a
multitude
of
subtle
and
wise
Philosophers
,
should
suffer
themselves
to
be
Hector'd
by
one
or
two
,
who
make
a
little
blustering
;
nay
,
they
will
rather
,
without
ever
turning
the
points
of
their
pens
against
them
,
by
their
silence
onely
render
them
the
object
of
universal
scorn
and
contempt
.
It
is
a
fond
conceit
for
any
one
to
think
to
introduce
new
Philosophy
,
by
reproving
this
or
that
Author
:
it
will
be
first
necessary
to
new-mold
the
brains
of
men
,
and
make
them
apt
to
distinguish
truth
from
falshood
.
A
thing
which
onely
God
can
do
.
But
from
one
discourse
to
another
whither
are
we
stray'd
?
your
memory
must
help
to
guide
me
into
the
way
again
.
SIMPL.
I
remember
very
well
where
we
left
.
We
were
upon
the
answer
of
Anti-Tycho
,
to
the
objections
against
the
immutability
of
the
Heavens
,
among
which
you
inserted
this
of
the
Solar
spots
,
not
spoke
of
by
him
;
and
I
believe
you
intended
to
examine
his
answer
to
the
instance
of
the
New
Stars
.
SALV
.
Now
I
remember
the
rest
,
and
to
proceed
,
Methinks
there
are
some
things
in
the
answer
to
Anti-Tycho
,
worthy
of
reprehension
.
And
first
,
if
the
two
New
Stars
,
which
he
can
do
no
less
than
place
in
the
uppermost
parts
of
the
Heavens
,
and
which
were
of
a
long
duration
,
but
finally
vanished
,
give
him
no
obstruction
in
maintaining
the
inalterability
of
Heaven
,
in
that
they
were
not
certain
parts
thereof
,
nor
mutations
made
in
the
antient
Stars
,
why
doth
he
set
himself
so
vigorously
and
earnestly
against
the
Comets
,
to
banish
them
by
all
ways
from
the
Coelestial
Regions
?
Was
it
not
enough
that
he
could
say
of
them
the
same
which
he
spoke
of
the
New
stars
?
to
wit
,
that
in
regard
they
were
no
certain
parts
of
Heaven
,
nor
mutations
made
in
any
of
the
Stars
,
they
could
no
wise
prejudice
either
Heaven
,
or
the
Doctrine
of
Aristotle
?
Secondly
,
I
am
not
very
well
satisfied
of
his
meaning
;
when
he
saith
that
the
alterations
that
should
be
granted
to
be
made
in
the
Stars
,
would
be
destructive
to
the
prerogative
of
Heaven
;
namely
,
its
incorruptibility
,
&c.
and
this
,
because
the
Stars
are
Coelestial
substances
,
as
is
manifest
by
the
consent
of
every
one
;
and
yet
is
nothing
troubled
that
the
same
alterations
should
be
made
[
](A61244-e12920-b)*
*
Extra
Stellas
.
without
the
Stars
in
the
rest
of
the
Coelestial
expansion
.
Doth
he
think
that
Heaven
is
no
Coelestial
substance
?
I
,
for
my
part
,
did
believe
that
the
Stars
were
called
Coelestial
bodies
,
by
reason
that
they
were
in
Heaven
,
or
for
that
they
were
made
of
the
substance
of
Heaven
;
and
yet
I
thought
that
Heaven
was
more
Coelestial
than
they
;
in
like
sort
,
as
nothing
can
be
said
to
be
more
Terrestrial
,
or
more
fiery
than
the
Earth
or
Fire
themselves
.
And
again
,
in
that
he
never
made
any
mention
of
the
Solar
spots
,
which
have
been
evidently
demonstrated
to
be
produced
,
and
dissolved
,
and
to
be
neer
the
Sun
,
and
to
turn
either
with
,
or
about
the
same
,
I
have
reason
to
think
that
this
Author
probably
did
write
more
for
others
pleasure
,
than
for
his
own
satisfaction
;
and
this
I
affirm
,
forasmuch
as
he
having
shewn
himself
to
be
skilful
in
the
Mathematicks
,
it
is
impossible
but
that
he
should
have
been
convinced
by
Demonstrations
,
that
those
substances
are
of
necessity
contiguous
with
the
body
of
the
Sun
,
and
are
so
great
generations
and
corruptions
,
that
none
comparable
to
them
,
ever
happen
in
the
Earth
:
And
if
such
,
so
many
,
and
so
frequent
be
made
in
the
very
Globe
of
the
Sun
,
which
may
with
reason
be
held
one
of
the
noblest
parts
of
Heaven
,
what
should
make
us
think
that
others
may
not
happen
in
the
other
Orbs.
SAGR.
I
cannot
without
great
admiration
,
Generability
and
alteration
is
a
greater
perfection
in
the
Worlds
bodies
than
the
contrary
qualities
.
nay
more
,
denial
of
my
understanding
,
hear
it
to
be
attributed
to
natural
bodies
,
for
a
great
honour
and
perfection
that
they
are
[
](A61244-e12970-b)*
*
Impatible
.
impassible
,
immutable
,
inalterable
,
&c.
And
on
the
contrary
,
to
hear
it
to
be
esteemed
a
great
imperfection
to
be
alterable
,
generable
,
mutable
,
&c.
The
Earth
very
noble
,
by
reason
of
the
many
mutations
made
therein
.
It
is
my
opinion
that
the
Earth
is
very
noble
and
admirable
,
by
reason
of
so
many
and
so
different
alterations
,
mutations
,
generations
,
&c.
which
are
incessantly
made
therein
;
and
if
without
being
subject
to
any
alteration
,
it
had
been
all
one
vast
heap
of
sand
,
or
a
masse
of
Jasper
,
or
that
in
the
time
of
the
Deluge
,
the
waters
freezing
which
covered
it
,
it
had
continued
an
immense
Globe
of
Christal
,
The
Earth
unprofitable
and
full
of
idlenesse
,
its
alterations
taken
away
wherein
nothing
had
ever
grown
,
altered
,
or
changed
,
I
should
have
esteemed
it
a
lump
of
no
benefit
to
the
World
,
full
of
idlenesse
,
and
in
a
word
superfluous
,
and
as
if
it
had
never
been
in
nature
;
and
should
make
the
same
difference
in
it
,
as
between
a
living
and
dead
creature
:
The
like
I
say
of
the
Moon
,
Jupiter
,
and
all
the
other
Globes
of
the
World
.
But
the
more
I
dive
into
the
consideration
of
the
vanity
of
popular
discourses
,
the
more
empty
and
simple
I
find
them
.
And
what
greater
folly
can
there
be
imagined
,
than
to
call
Jems
,
Silver
and
Gold
pretious
;
and
Earth
and
dirt
vile
?
The
Earth
more
noble
than
Gold
and
Jewels
.
For
do
not
these
persons
consider
,
that
if
there
should
be
as
great
a
scarcity
of
Earth
,
as
there
is
of
Jewels
and
pretious
metals
,
there
would
be
no
Prince
,
but
would
gladly
give
a
heap
of
Diamonds
and
Rubies
,
and
many
Wedges
of
Gold
,
to
purchase
onely
so
much
Earth
as
should
suffice
to
plant
a
Gessemine
in
a
little
pot
,
or
to
set
therein
a
China
Orange
,
that
he
might
see
it
sprout
,
grow
up
,
and
bring
forth
so
goodly
leaves
,
so
odiriferous
flowers
,
Scarcity
and
plenty
enhanse
and
debase
the
price
of
things
.
and
so
delicate
fruit
?
It
is
therefore
scarcity
and
plenty
that
make
things
esteemed
and
contemned
by
the
vulgar
;
who
will
say
that
same
is
a
most
beautiful
Diamond
,
for
that
it
resembleth
a
cleer
water
,
and
yet
will
not
part
with
it
for
ten
Tun
of
water
:
Incorruptibility
esteemed
by
the
vulgar
out
of
their
fear
of
death
.
These
men
that
so
extol
incorruptibility
,
inalterability
,
&c.
speak
thus
I
believe
out
of
the
great
desire
they
have
to
live
long
,
and
for
fear
of
death
;
not
considering
,
that
if
men
had
been
immortal
,
they
should
have
had
nothing
to
do
in
the
World
.
The
disparagers
of
corruptibility
deserve
to
be
turned
into
Statua's
.
These
deserve
to
meet
with
a
Medusa's
head
,
that
would
transform
them
into
Statues
of
Dimond
and
Jasper
,
that
so
they
might
become
more
perfect
than
they
are
.
SALV
.
And
it
may
be
such
a
Metamorphosis
would
not
be
altogether
unprofitable
to
them
;
for
I
am
of
opinion
that
it
is
better
not
to
discourse
at
all
,
than
to
argue
erroniously
.
SIMPL.
There
is
not
the
least
question
to
be
made
,
but
that
the
Earth
is
much
more
perfect
,
being
as
it
is
alterable
,
mutable
,
&c.
than
if
it
had
been
a
masse
of
stone
;
yea
although
it
were
one
entire
Diamond
,
The
Coelestial
bodies
designed
to
serve
the
Earth
,
need
no
more
but
motion
and
light
.
most
hard
and
impassile
.
But
look
how
much
these
qualifications
enoble
the
Earth
,
they
render
the
Heavenly
bodies
again
on
the
other
side
so
much
the
more
imperfect
,
in
which
,
such
conditions
would
be
superfluous
;
in
regard
that
the
Coelestial
bodies
,
namely
,
the
Sun
,
Moon
,
and
the
other
Stars
,
which
are
ordained
for
no
other
use
but
to
serve
the
Earth
,
need
no
other
qualities
for
attaining
of
that
end
,
save
onely
those
of
light
and
motion
.
SAGR.
How
?
Will
you
affirm
that
nature
hath
produced
and
designed
so
many
vast
perfect
and
noble
Coelestial
bodies
,
impassible
,
immortal
,
and
divine
,
to
no
other
use
but
to
serve
the
passible
,
frail
,
and
mortal
Earth
?
to
serve
that
which
you
call
the
drosse
of
the
World
,
and
sink
of
all
uncleannesse
?
To
what
purpose
were
the
Coelestial
bodies
made
immortal
,
&c.
to
serve
a
frail
,
&c.
Take
away
this
subserviency
to
the
Earth
,
and
the
innumerable
multitude
of
Coelestial
bodies
become
wholly
unuseful
,
Celestial
bodies
want
an
interchangeable
operation
upon
each
other
.
and
superfluous
,
since
they
neither
have
nor
can
have
any
mutual
operation
betwixt
themselves
;
because
they
are
all
unalterable
,
immutable
,
impassible
:
For
if
,
for
Example
,
the
Moon
be
impassible
,
what
influence
can
the
Sun
or
any
other
Star
have
upon
her
?
it
would
doubtlesse
have
far
lesse
effect
upon
her
,
than
that
of
one
who
would
with
his
looks
or
imagination
,
lignifie
a
piece
of
Gold
.
Moreover
,
it
seemeth
to
me
,
that
whilst
the
Coelestial
bodies
concurre
to
the
generation
and
alteration
of
the
Earth
,
they
themselves
are
also
of
necessity
alterable
;
for
otherwise
I
cannot
understand
how
the
application
of
the
Sun
or
Moon
to
the
Earth
,
to
effect
production
,
should
be
any
other
than
to
lay
a
marble
Statue
by
a
Womans
side
,
and
from
that
conjunction
to
expect
children
.
SIMPL.
Corruptibility
,
Alterability
,
&c.
are
not
in
the
whole
Terrestrial
Globe
,
but
in
some
of
its
parts
.
alteration
,
mutation
,
&c.
are
not
in
the
whole
Terrestrial
Globe
,
which
as
to
its
whole
,
is
no
lesse
eternal
than
the
Sun
or
Moon
,
but
it
is
generable
and
corruptible
as
to
its
external
parts
;
but
yet
it
is
also
true
that
likewise
in
them
generation
and
corruption
are
perpetual
,
and
as
such
require
the
heavenly
eternal
operations
;
and
therefore
it
is
necessary
that
the
Coelestial
bodies
be
eternal
.
SAGR.
All
this
is
right
;
but
if
the
corruptibility
of
the
superficial
parts
of
the
Earth
be
nowise
prejudicial
to
the
eternity
of
its
whole
Globe
,
yea
,
if
their
being
generable
,
corruptible
,
alterable
,
&c.
gain
them
great
ornament
and
perfection
;
why
cannot
,
Coelestial
bodies
alterable
in
their
outward
parts
.
and
ought
not
you
to
admit
alteration
,
generation
,
&c.
likewise
in
the
external
parts
of
the
Coelestial
Globes
,
adding
to
them
ornament
,
without
taking
from
them
perfection
,
or
bereaving
them
of
action
;
yea
rather
encreasing
their
effects
,
by
granting
not
onely
that
they
all
operate
on
the
Earth
,
but
that
they
mutually
operate
upon
each
other
,
and
the
Earth
also
upon
them
all
?
SIMPL.
This
cannot
be
,
because
the
generations
,
mutations
,
&c.
which
we
should
suppose
v.
g.
in
the
Moon
;
would
be
vain
and
uselesse
,
&
natura
nihil
frustra
facit
.
SAGR.
And
why
should
they
be
vain
and
uselesse
?
SIMPL.
Because
we
cleerly
see
,
The
generations
&
mutations
happening
in
the
Earth
,
are
all
for
the
good
of
Man
.
and
feel
with
our
hands
,
that
all
generations
,
corruptions
,
&c.
made
in
the
Earth
,
are
all
either
mediately
or
immediately
directed
to
the
use
,
convenience
,
and
benefit
of
man
;
for
the
use
of
man
are
horses
brought
forth
,
for
the
feeding
of
horses
,
the
Earth
produceth
grasse
,
and
the
Clouds
water
it
;
for
the
use
and
nourishment
of
man
,
herbs
,
corn
,
fruits
,
beasts
,
birds
,
fishes
,
are
brought
forth
;
and
in
sum
,
if
we
should
one
by
one
dilligently
examine
and
resolve
all
these
things
,
we
should
find
the
end
to
which
they
are
all
directed
,
to
be
the
necessity
,
use
,
convenience
,
and
delight
of
man
.
Now
of
what
use
could
the
generations
which
we
suppose
to
be
made
in
the
Moon
or
other
Planets
,
ever
be
to
mankind
?
unlesse
you
should
say
that
there
were
also
men
in
the
Moon
,
that
might
enjoy
the
benefit
thereof
;
a
conceit
either
fabulous
or
impious
.
SAGR.
That
in
the
Moon
or
other
Planets
,
The
Moon
hath
no
generatings
of
things
,
like
as
we
have
,
nor
is
it
inhabited
by
men
.
there
are
generated
either
herbs
,
or
plants
,
or
animals
,
like
to
ours
,
or
that
there
are
rains
,
winds
,
or
thunders
there
,
as
about
the
Earth
,
I
neither
know
,
nor
believe
,
and
much
lesse
,
that
it
is
inhabited
by
men
:
but
yet
I
understand
not
,
because
there
are
not
generated
things
like
to
ours
,
that
therefore
it
necessarily
followeth
,
that
no
alteration
is
wrought
therein
,
or
that
there
may
not
be
other
things
that
change
,
In
the
Moon
may
be
a
generation
of
things
different
from
ours
.
generate
,
and
dissolve
,
which
are
not
onely
different
from
ours
,
but
exceedingly
beyond
our
imagination
,
and
in
a
word
,
not
to
be
thought
of
by
us
.
And
if
,
as
I
am
certain
,
that
one
born
and
brought
up
in
a
spatious
Forrest
,
amongst
beasts
and
birds
,
and
that
hath
no
knowledg
at
all
of
the
Element
of
Water
,
He
that
had
not
heard
of
the
Element
of
Water
,
could
never
fancy
to
himself
Ships
and
Fishes
.
could
never
come
to
imagine
another
World
to
be
in
Nature
,
different
from
the
Eatth
,
full
of
living
creatures
,
which
without
legs
or
wings
swiftly
move
,
and
not
upon
the
surface
onely
,
as
beasts
do
upon
the
Earth
,
but
in
the
very
bowels
thereof
;
and
not
onely
move
,
but
also
stay
themselves
and
cease
to
move
at
their
pleasure
,
which
birds
cannot
do
in
the
air
;
and
that
moreover
men
live
therein
,
and
build
Palaces
and
Cities
,
and
have
so
great
convenience
in
travailing
,
that
without
the
least
trouble
,
they
can
go
with
their
Family
,
House
,
and
whole
Cities
,
to
places
far
remote
,
like
as
I
say
,
I
am
certain
,
such
a
person
,
though
of
never
so
piercing
an
imagination
,
could
never
fancy
to
himself
Fishes
,
the
Ocean
,
Ships
,
Fleets
,
Armado's
at
Sea
;
thus
,
and
much
more
easily
,
may
it
happn
,
that
in
the
Moon
,
remote
from
us
by
so
great
a
space
,
and
of
a
substance
perchance
very
different
from
the
Earth
,
there
may
be
matters
,
and
operations
,
not
only
wide
off
,
but
altogether
beyond
all
our
imaginations
,
as
being
such
as
have
no
resemblance
to
ours
,
and
therefore
wholly
inexcogitable
,
in
regard
,
that
what
we
imagine
to
our selves
,
must
necessarily
be
either
a
thing
already
seen
,
or
a
composition
of
things
,
or
parts
of
things
seen
at
another
time
;
for
such
are
the
Chimaera's
.
Centaurs
,
&c.
SALV
.
I
have
very
often
let
my
fancy
ruminate
upon
these
speculations
,
and
in
the
end
,
have
thought
that
I
had
found
some
things
that
neither
are
nor
can
be
in
the
Moon
;
but
yet
I
have
not
found
therein
any
of
those
which
I
believe
are
,
and
may
be
there
,
save
onely
in
a
very
general
acceptation
,
namely
,
things
that
adorn
it
by
operating
,
moving
and
living
;
and
perhaps
in
a
way
very
different
from
ours
;
There
may
be
substances
in
the
Moon
very
different
from
ours
.
beholding
and
admiring
the
greatness
and
beauty
of
the
World
,
and
of
its
Maker
and
Ruler
,
and
with
continual
Encomiums
singing
his
prayses
;
and
in
summe
(
which
is
that
which
I
intend
)
doing
what
sacred
Writers
so
frequently
affirm
,
to
wit
,
all
the
creatures
making
it
their
perpetual
imployment
to
laud
God
.
SAGR.
These
are
the
things
,
which
speaking
in
general
terms
,
may
be
there
;
but
I
would
gladly
hear
you
instance
in
such
as
you
believe
neither
are
nor
can
be
there
;
which
perchance
may
be
more
particularly
named
.
SALV
.
Take
notice
Sagredus
that
this
will
be
the
third
time
that
we
have
unawares
by
running
from
one
thing
to
another
,
lost
our
principal
subject
;
and
if
we
continue
these
digressions
,
it
will
be
long
ere
we
come
to
a
conclusion
of
our
discourse
;
therefore
I
should
judg
it
better
to
remit
this
,
as
also
such
other
points
,
to
be
decided
on
a
particular
occasion
.
SAGR.
Since
we
are
now
got
into
the
Moon
,
if
you
please
,
let
us
dispatch
such
things
as
concern
her
,
that
so
we
be
not
forced
to
such
another
tedious
journey
.
SALV
.
It
shall
be
as
you
would
have
it
.
And
to
begin
with
things
more
general
,
I
believe
that
the
Lunar
Globe
is
far
different
from
the
Terrestrial
,
though
in
some
things
they
agree
.
I
will
recount
first
their
resemblances
,
and
next
their
differences
.
The
Moon
is
manifestly
like
to
the
Earth
in
figure
,
The
First
resemblance
between
the
Moon
and
Earth
;
which
is
that
of
figure
;
is
proved
by
the
manner
of
being
illuminated
by
the
Sun
.
which
undoubtedly
is
spherical
,
as
may
be
necessarily
concluded
from
the
aspect
of
its
surface
,
which
is
perfectly
Orbicular
,
and
the
manner
of
its
receiving
the
light
of
the
Sun
,
from
which
,
if
its
surface
were
flat
,
it
would
come
to
be
all
in
one
and
the
same
time
illuminated
,
and
likewise
again
in
another
instant
of
time
obscured
,
and
not
those
parts
first
,
which
are
situate
towards
the
Sun
,
and
the
rest
successively
,
so
that
in
its
opposition
,
and
not
till
then
,
its
whole
apparent
circumference
is
enlightned
;
which
would
happen
quite
contrary
,
if
the
visible
surface
were
concave
;
namely
,
the
illumination
would
begin
from
the
parts
opposite
or
averse
to
the
Sun
.
The
Second
conformity
is
the
Moons
being
opacous
as
the
Earth
.
Secondly
she
is
as
the
Earth
,
in
her self
obscure
and
opacous
,
by
which
opacity
it
is
enabled
to
receive
,
and
reflect
the
light
of
the
Sun
;
〈…〉
Moon
is
〈◊〉
and
〈…〉
as
the
Earth
.
which
were
it
not
so
,
it
could
not
do
.
Thirdly
,
I
hold
its
matter
to
be
most
dense
and
solid
as
the
Earth
is
,
which
I
clearly
argue
from
the
unevenness
of
its
superficies
in
most
places
,
by
means
of
the
many
eminencies
and
cavities
discovered
therein
by
help
of
the
Telescope
:
of
which
eminencies
there
are
many
all
over
it
,
directly
resembling
our
most
sharp
and
craggy
mountains
,
of
which
you
shall
there
perceive
some
extend
and
run
in
ledges
of
an
hundred
miles
long
;
others
are
contracted
into
rounder
forms
;
and
there
are
also
many
craggy
,
solitary
,
steep
and
cliffy
rocks
.
But
that
of
which
there
are
frequentest
appearances
,
are
certain
Banks
(
I
use
this
word
,
because
I
cannot
thing
of
another
that
better
expresseth
them
)
pretty
high
raised
,
which
environ
and
inclose
fields
of
several
bignesses
,
and
from
sundry
figures
,
but
for
the
most
part
circular
;
many
of
which
have
in
the
midst
a
mount
raised
pretty
high
,
and
some
few
are
replenished
with
a
matter
somewhat
obscure
,
to
wit
,
like
to
the
great
spots
discerned
by
the
bare
eye
,
and
these
are
of
the
greatest
magnitude
;
the
number
moreover
of
those
that
are
lesser
and
lesser
is
very
great
,
and
yet
almost
all
circular
.
Fourthly
,
Fourthly
,
The
Moon
is
distinguished
into
two
different
parts
for
clarity
and
obscurity
,
as
the
Terrestrial
Globe
into
Sea
and
Land
.
The
surface
of
the
Sea
would
shew
at
a
distance
more
obscure
than
that
of
the
Earth
.
like
as
the
surface
of
our
Globe
is
distinguished
into
two
principal
parts
,
namely
,
into
the
Terrestrial
and
Aquatick
:
so
in
the
Lunar
surface
we
discern
a
great
distinction
of
some
great
fields
more
resplendant
,
and
some
less
:
whose
aspect
makes
me
believe
,
that
that
of
the
Earth
would
seem
very
like
it
,
beheld
by
any
one
from
the
Moon
,
or
any
other
the
like
distance
,
to
be
illuminated
by
the
Sun
:
and
the
surface
of
the
sea
would
appear
more
obscure
,
and
that
of
the
Earth
more
bright
.
Fifthly
,
like
as
we
from
the
Earth
behold
the
Moon
,
one
while
all
illuminated
,
another
while
half
;
Fiftly
,
Mutation
of
figures
in
the
Earth
,
like
to
those
of
the
Moon
,
and
made
with
the
same
periods
.
sometimes
more
,
sometimes
less
;
sometimes
horned
,
sometimes
wholly
invisibly
;
namely
,
when
its
just
under
the
Sun
beams
;
so
that
the
parts
which
look
towards
the
Earth
are
dark
:
Thus
in
every
respect
,
one
standing
in
the
Moon
would
see
the
illumination
of
the
Earths
surface
by
the
Sun
,
with
the
same
periods
to
an
hair
,
and
under
the
same
changes
of
figures
.
Sixtly
,
—
SAGR.
Stay
a
little
,
Salviatus
;
That
the
illumination
of
the
Earth
,
as
to
the
several
figures
,
would
represent
it self
to
a
person
placed
in
the
Moon
,
like
in
all
things
to
that
which
we
discover
in
the
Moon
,
I
understand
very
well
,
but
yet
I
cannot
conceive
how
it
shall
appear
to
be
done
in
the
same
period
;
seeing
that
that
which
the
Suns
illumination
doth
in
the
Lunar
superficies
in
a
month
,
it
doth
in
the
Terrestrial
in
twenty
four
hours
.
SALV
.
It
s
true
,
the
effect
of
the
Sun
about
the
illuminating
these
two
bodies
,
and
replenishing
with
its
splendor
their
whole
surfaces
,
is
dispatch'd
in
the
Earth
in
a
Natural
day
,
and
in
the
Moon
in
a
Month
;
but
the
variation
of
the
figures
in
which
the
illuminated
parts
of
the
Terrestrial
superficies
appear
beheld
from
the
Moon
,
depends
not
on
this
alone
,
but
on
the
divers
aspects
which
the
Moon
is
still
changing
with
the
Sun
;
so
that
,
if
for
instance
,
the
Moon
punctually
followed
the
motion
of
the
Sun
,
and
stood
,
for
example
,
always
in
a
direct
line
between
it
and
the
Earth
,
in
that
aspect
which
we
call
Conjunction
,
it
looking
always
to
the
same
Hemisphere
of
the
Earth
which
the
Sun
looks
unto
,
she
would
behold
the
same
all
light
:
as
on
the
contrary
,
if
it
should
always
stay
in
Opposition
to
the
Sun
,
it
would
never
behold
the
Earth
,
of
which
the
dark
part
would
be
continually
turn'd
towards
the
Moon
,
and
therefore
invisible
.
But
when
the
Moon
is
in
Quadrature
of
the
Sun
,
that
half
of
the
Terrestrial
Hemisphere
exposed
to
the
sight
of
the
Moon
which
is
towards
the
Sun
,
is
luminous
;
and
the
other
towards
the
contrary
is
obscure
:
and
therefore
the
illuminated
part
of
the
Earth
would
represent
it self
to
the
Moon
in
a
semi-circular
figure
.
SAGR.
I
clearly
perceive
all
this
,
and
understand
very
well
,
that
the
Moon
departing
from
its
Opposition
to
the
Sun
,
where
it
saw
no
part
of
the
illumination
of
the
Terrestrial
superficies
,
and
approaching
day
by
day
nearer
the
Sun
,
she
begins
by
little
and
little
to
discover
some
part
of
the
face
of
the
illuminated
Earth
;
and
that
which
appeareth
of
it
shall
resemble
a
thin
sickle
,
in
regard
the
figure
of
the
Earth
is
round
:
and
the
Moon
thus
acquiring
by
its
motion
day
by
day
greater
proximity
to
the
Sun
,
successively
discovers
more
and
more
of
the
Terrestrial
Hemisphere
enlightned
,
so
that
at
the
Quadrature
there
is
just
half
of
it
visible
,
insomuch
that
we
may
see
the
other
part
of
her
:
continuing
next
to
proceed
towards
the
Conjunction
,
it
successively
discovers
more
and
more
of
its
surface
to
be
illuminated
,
and
in
fine
,
at
the
time
of
Conjunction
seeth
the
whole
Hemisphere
enlightned
.
And
in
short
,
I
very
well
conceive
,
that
what
befalls
the
Inhabitants
of
the
Earth
,
in
beholding
the
changes
of
the
Moon
,
would
happen
to
him
that
from
the
Moon
should
observe
the
Earth
;
but
in
a
contrary
order
,
namely
,
that
when
the
Moon
is
to
us
at
her
full
,
and
in
Opposition
to
the
Sun
,
then
the
Earth
would
be
in
Conjunction
with
the
Sun
,
and
wholly
obscure
and
invisible
;
on
the
contrary
,
that
position
which
is
to
us
a
Conjunction
of
the
Moon
with
the
Sun
,
and
for
that
cause
a
Moon
silent
and
unseen
,
would
be
there
an
Opposition
of
the
Earth
to
the
Sun
,
and
,
to
so
speak
,
Full
Earth
,
to
wit
,
all
enlightned
.
And
lastly
,
look
what
part
of
the
Lunar
surface
appears
to
us
from
time
to
time
illuminated
,
so
much
of
the
Earth
in
the
same
time
shall
you
behold
from
the
Moon
to
be
obscured
:
and
look
how
much
of
the
Moon
is
to
us
deprived
of
light
,
so
much
of
the
Earth
is
to
the
Moon
illuminated
.
In
one
thing
yet
these
mutual
operations
in
my
judgment
seem
to
differ
,
and
it
is
,
that
it
being
supposed
,
and
not
granted
,
that
some
one
being
placed
in
the
Moon
to
observe
the
Earth
,
he
would
every
day
see
the
whole
Terrestrial
superficies
,
by
means
of
the
Moons
going
about
the
Earth
in
twenty
four
or
twenty
five
hours
;
but
we
never
see
but
half
of
the
Moon
,
since
it
revolves
not
in
it self
,
as
it
must
do
to
be
seen
in
every
part
of
it
.
SALV
.
So
that
this
,
befals
not
contrarily
,
namely
,
that
her
revolving
in
her self
,
is
the
cause
that
we
see
not
the
other
half
of
her
,
for
so
it
would
be
necessary
it
should
be
,
if
she
had
the
Epicycle
.
But
what
other
difference
have
you
behind
,
to
exchange
for
this
which
you
have
named
?
SAGR.
Let
me
see
;
Well
for
the
present
I
cannot
think
of
any
other
.
SALV
.
And
what
if
the
Earth
(
as
you
have
well
noted
)
seeth
no
more
than
half
All
the
Earth
seeth
half
onely
of
the
Moon
,
&
the
half
onely
of
the
Moon
seeth
all
the
Earth
.
the
Moon
,
whereas
from
the
Moon
one
may
see
all
the
Earth
;
and
on
the
contrary
,
all
the
Earth
seeth
the
Moon
,
and
but
onely
half
of
it
seeth
the
Earth
?
For
the
inhabitants
,
to
so
speak
,
of
the
superior
Hemisphere
of
the
Moon
,
which
is
to
us
invisible
,
are
deprived
of
the
sight
of
the
Earth
:
and
these
haply
are
the
Anti●thones
.
But
here
I
remember
a
particular
accident
,
newly
observed
by
our
Academian
,
From
the
Earth
we
see
more
than
half
the
Lunar
Globe
.
in
the
Moon
,
from
whch
are
gathered
two
necessary
consequences
;
one
is
,
that
we
see
somewhat
more
than
half
of
the
Moon
;
and
the
other
is
,
that
the
motion
of
the
Moon
hath
exact
concentricity
with
the
Earth
:
and
thus
he
finds
the
Phoenomenon
and
observation
.
When
the
Moon
hath
a
correspondence
and
natural
sympathy
with
the
Earth
,
towards
which
it
hath
its
aspect
in
such
a
determinate
part
,
it
is
necessary
that
the
right
line
which
conjoyns
their
centers
,
do
passe
ever
by
the
same
point
of
the
Moons
superficies
;
so
that
,
who
so
shall
from
the
center
of
the
Earth
behold
the
same
,
shall
alwayes
see
the
same
Discus
or
Face
of
the
Moon
punctually
determined
by
one
and
the
same
circumference
;
But
if
a
man
be
placed
upon
the
Terrestrial
surface
,
the
ray
which
from
his
eye
passeth
to
the
centre
of
the
Lunar
Globe
,
will
not
pass
by
the
same
point
of
its
superficies
,
by
which
the
line
passeth
that
is
drawn
from
the
centre
of
the
Earth
to
that
of
the
Moon
,
save
onely
when
it
is
vertical
to
him
:
but
the
Moon
being
placed
in
the
East
,
or
in
the
West
,
the
point
of
incidence
of
the
visual
ray
,
is
higher
than
that
of
the
line
which
conjoyns
the
centres
;
and
therefore
the
observer
may
discern
some
part
of
the
Lunar
Hemisphere
towards
the
upper
circumference
,
and
alike
part
of
the
other
is
invisible
:
they
are
discernable
and
undiscernable
,
in
respect
of
the
Hemisphere
beheld
from
the
true
centre
of
the
Earth
:
and
because
the
part
of
the
Moons
circumference
,
which
is
superiour
in
its
rising
,
is
nethermost
in
its
setting
;
therefore
the
difference
of
the
said
superiour
and
inferiour
our
parts
must
needs
be
very
observable
;
certain
spots
and
other
notable
things
in
those
parts
,
being
one
while
discernable
,
and
another
while
not
.
A
like
variation
may
also
be
observed
towards
the
North
and
South
extremities
of
the
same
Discus
(
or
Surface
)
according
as
the
Moons
position
is
in
its
greatest
North
or
South
Latitude
;
For
,
if
it
be
North
,
some
of
its
parts
towards
the
North
are
hid
,
and
some
of
those
parts
towards
the
South
are
discovered
,
and
so
on
the
contrary
.
Now
that
these
consequences
are
really
true
,
Two
spots
in
the
Moon
,
by
which
it
is
perceived
that
she
hath
respect
to
the
centre
of
the
Earth
in
her
motion
.
is
verified
by
the
Telescope
,
for
there
be
in
the
Moon
two
remarkable
spots
,
one
of
which
,
when
the
Moon
is
in
the
meridian
,
is
situate
to
the
Northwest
,
and
the
other
is
almost
diametrically
opposite
unto
it
;
and
the
first
of
these
is
visible
even
without
the
Telescope
;
but
the
other
is
not
.
That
towards
the
Northwest
is
a
reasonable
great
spot
of
oval
figure
,
separated
from
the
other
great
ones
;
the
opposite
one
is
lesse
,
and
also
severed
from
the
biggest
,
and
situate
in
a
very
cleer
field
;
in
both
these
we
may
manifestly
discern
the
foresaid
variations
,
and
see
them
one
after
another
;
now
neer
the
edge
or
limb
of
the
Lunar
Discus
,
and
anon
remote
,
with
so
great
difference
that
the
distance
betwixt
the
Northwest
and
the
circumference
of
the
Discus
is
more
than
twice
as
great
at
one
time
,
as
at
the
other
;
and
as
to
the
second
spot
(
because
it
is
neerer
to
the
circumference
)
such
mutation
importeth
more
,
than
twice
so
much
in
the
former
.
Hence
its
manifest
,
that
the
Moon
,
as
if
it
were
drawn
by
a
magnetick
vertue
,
constantly
beholds
the
Terrestrial
Globe
with
one
and
the
same
aspect
,
never
deviating
from
the
same
.
SAGR.
Oh!
when
will
there
be
an
end
put
to
the
new
observations
and
discoveries
of
this
admirable
Instrument
?
SALV
.
If
this
succeed
according
to
the
progresse
of
other
great
inventions
,
it
is
to
be
hoped
,
that
in
processe
of
time
,
one
may
arrive
to
the
sight
of
things
,
to
us
at
present
not
to
be
imagined
.
But
returning
to
our
first
discourse
,
Sixthly
,
The
Earth
and
Moon
interchangeably
do
illuminate
.
I
say
for
the
sixth
resemblance
betwixt
the
Moon
and
Earth
,
that
as
the
Moon
for
a
great
part
of
time
,
supplies
the
want
of
the
Suns
light
,
and
makes
the
nights
,
by
the
reflection
of
its
own
,
reasonable
clear
;
so
the
Earth
,
in
recompence
,
affordeth
it
when
it
stands
in
most
need
,
by
reflecting
the
Solar
rayes
,
a
very
cleer
illumination
,
and
so
much
,
in
my
opinion
,
greater
than
that
which
cometh
from
her
to
us
,
by
how
much
the
superficies
of
the
Earth
is
greater
than
that
of
the
Moon
.
SAGR.
Hold
there
,
Salviatus
hold
there
,
and
permit
me
the
pleasure
of
relating
to
you
,
how
at
this
first
hint
I
have
penetrated
the
cause
of
an
accident
,
which
I
have
a
thousand
times
thought
upon
,
Light
reflected
from
the
Earth
into
the
Moon
.
but
could
never
find
out
.
You
would
say
,
that
the
imperfect
light
which
is
seen
in
the
Moon
,
especially
when
it
is
horned
,
comes
from
the
reflection
of
the
light
of
the
Sun
on
the
Supersicies
of
the
Earth
and
Sea
;
and
that
light
is
more
clear
,
by
how
much
the
horns
are
lesse
,
for
then
the
luminous
part
of
the
Earth
,
beheld
by
the
Moon
,
is
greater
,
according
to
that
which
was
a
little
before
proved
;
to
wit
,
that
the
luminous
part
of
the
Earth
,
exposed
to
the
Moon
,
is
alway
as
great
as
the
obscure
part
of
the
Moon
,
that
is
visible
to
the
Earth
;
whereupon
,
at
such
time
as
the
Moon
is
sharp-forked
,
and
consequently
its
tenebrous
part
great
,
great
also
is
the
illuminated
part
of
the
Earth
beheld
from
the
Moon
,
and
its
reflection
of
light
so
much
the
more
potent
.
SALV
.
This
is
exactly
the
same
with
what
I
was
about
to
say
.
In
a
word
,
it
is
a
great
pleasure
to
speak
with
persons
judicious
and
apprehensive
,
and
the
rather
to
me
,
for
that
whilest
others
converse
and
discourse
touching
Axiomatical
truths
,
I
have
many
times
creeping
into
my
brain
such
arduous
Paradoxes
,
that
though
I
have
a
thousand
times
rehearsed
this
which
you
at
the
very
first
,
have
of
your self
apprehended
,
yet
could
I
never
beat
it
into
mens
brains
.
SIMPL.
If
you
mean
by
your
not
being
able
to
perswade
them
to
it
,
that
you
could
not
make
them
understand
the
same
,
I
much
wonder
thereat
,
and
am
very
confident
that
if
they
did
not
understand
it
by
your
demonstration
(
your
way
of
expression
,
being
,
in
my
judgment
,
very
plain
)
they
would
very
hardly
have
apprehended
it
upon
the
explication
of
any
other
man
;
but
if
you
mean
you
have
not
perswaded
them
,
so
as
to
make
them
believe
it
,
I
wonder
not
,
in
the
least
,
at
this
;
for
I
confesse
my self
to
be
one
of
those
who
understand
your
discourses
,
but
am
not
satisfied
therewith
;
for
there
are
in
this
,
and
some
of
the
other
six
congruities
,
or
resemblances
,
many
difficulties
,
which
I
shall
instance
in
,
when
you
have
gone
through
them
all
.
SALV
.
The
desire
I
have
to
find
out
any
truth
,
in
the
acquist
whereof
the
objections
of
intelligent
persons
(
such
as
your self
)
may
much
assist
me
,
will
cause
me
to
be
very
brief
in
dispatching
that
which
remains
.
Seventhly
,
The
Earth
and
Moon
do
mutually
eclipse
.
For
a
seventh
conformity
,
take
their
reciprocal
responsion
as
well
to
injuries
,
as
favours
;
whereby
the
Moon
,
which
very
often
in
the
height
of
its
illumination
,
by
the
interposure
of
the
Earth
betwixt
it
and
the
Sun
,
is
deprived
of
light
,
and
eclipsed
,
doth
by
way
of
revenge
,
in
like
manner
,
interpose
it self
between
the
Earth
and
the
Sun
,
and
with
its
shadow
obscureth
the
Earth
;
and
although
the
revenge
be
not
answerable
to
the
injury
,
for
that
the
Moon
often
continueth
,
and
that
for
a
reasonable
long
time
,
wholly
immersed
in
the
Earths
shadow
,
but
never
was
the
Earth
wholly
,
nor
for
any
long
time
,
eclipsed
by
the
Moon
;
yet
,
neverthelesse
,
having
respect
to
the
smalnesse
of
the
body
of
this
,
in
comparision
to
the
magnitude
of
the
other
,
it
cannot
be
denied
but
that
the
will
and
as
it
were
valour
of
this
,
is
very
great
.
Thus
much
for
their
congruities
or
resemblances
.
It
should
next
follow
that
we
discourse
touching
their
disparity
;
but
because
Simplicius
will
favour
us
with
his
objections
against
the
former
,
its
necessary
that
we
hear
and
examine
them
,
before
we
proceed
any
farther
.
SAGR.
And
the
rather
,
because
it
is
to
be
supposed
that
Simplicius
will
not
any
wayes
oppose
the
disparities
,
and
incongruities
betwixt
the
Earth
and
Moon
,
since
that
he
accounts
their
substances
extremely
different
.
SIMPL.
Amongst
the
resemblances
by
you
recited
,
in
the
parallel
you
make
betwixt
the
Earth
and
Moon
,
I
find
that
I
can
admit
none
confidently
save
onely
the
first
,
and
two
others
;
I
grant
the
first
,
namely
,
the
spherical
figure
;
howbeit
,
even
in
this
there
is
some
kind
of
difference
,
for
that
I
hold
that
of
the
Moon
to
be
very
smooth
and
even
,
as
a
looking-glasse
,
whereas
,
we
find
and
feel
this
of
the
Earth
to
be
extraordinary
montuous
and
rugged
;
but
this
belonging
to
the
inequality
of
superficies
,
it
shall
be
anon
considered
,
in
another
of
those
Resemblances
by
you
alledged
;
I
shall
therefore
reserve
what
I
have
to
say
thereof
,
till
I
come
to
the
consideration
of
that
.
Of
what
you
affirm
next
,
that
the
Moon
seemeth
,
as
you
say
in
your
second
Resemblance
,
opacous
and
obscure
in
its
self
,
like
the
Earth
;
I
admit
not
any
more
than
the
first
attribute
of
opacity
,
of
which
the
Eclipses
of
the
Sun
assure
me
.
For
were
the
Moon
transparent
,
the
air
in
the
total
obscuration
of
the
Sun
,
would
not
become
so
duskish
,
as
at
such
a
time
it
is
,
but
by
means
of
the
transparency
of
the
body
of
the
Moon
,
a
refracted
light
would
passe
through
it
,
as
we
see
it
doth
through
the
thickest
clouds
.
But
as
to
the
obscurity
,
I
believe
not
that
the
Moon
is
wholly
deprived
of
light
,
as
the
Earth
;
nay
,
that
clarity
which
is
seen
in
the
remainder
ot
its
Discus
,
over
and
the
above
the
small
crescent
enlightened
by
the
Sun
,
I
repute
to
be
its
proper
and
natural
light
,
and
not
a
reflection
of
the
Earth
,
The
second
clarity
of
the
Moon
esteemed
to
be
its
native
light
.
which
I
esteem
unable
,
by
reason
of
its
asperity
(
cragginesse
)
and
obscurity
,
to
reflect
the
raies
of
the
Sun
.
In
the
third
Parallel
I
assent
unto
you
in
one
part
,
The
Earth
unable
to
reflect
the
Suns
raies
.
and
dissent
in
another
:
I
agree
in
judging
the
body
of
the
Moon
to
be
most
solid
and
hard
,
like
the
Earth
,
yea
much
more
;
for
if
from
Aristotle
we
receive
that
the
Heavens
are
impenetrable
,
The
substance
of
the
Heavens
impenetrable
,
according
to
Aristotle
.
and
the
Stars
the
most
dense
parts
of
Heaven
,
it
must
necessarily
follow
,
that
they
are
most
solid
and
most
impenetrable
.
SAGR.
What
excellent
matter
would
the
Heavens
afford
us
for
to
make
Pallaces
of
,
if
we
could
procure
a
substance
so
hard
and
so
transparent
?
SALV
.
Rather
how
improper
,
for
being
by
its
transparence
,
wholly
invisible
,
a
man
would
not
be
able
without
stumbling
at
the
thresholds
,
and
breaking
his
head
against
the
Walls
,
to
pass
from
room
to
room
.
SAGR.
This
danger
would
not
befall
him
,
The
substance
of
Heaven
intangible
.
if
it
be
true
,
as
some
Peripateticks
say
,
that
it
is
intangible
:
and
if
one
cannot
touch
it
,
much
less
can
it
hurt
him
.
SALV
.
This
would
not
serve
the
turn
,
for
though
the
matter
of
the
Heavens
cannot
be
touch
,
as
wanting
tangible
qualities
:
yet
may
it
easily
touch
the
elementary
bodies
;
and
to
offend
us
it
is
as
sufficient
that
it
strike
us
,
nay
worse
,
than
if
we
should
strike
it
.
But
let
us
leave
these
Pallaces
,
or
,
to
say
better
,
these
Castles
in
the
air
,
and
not
interrupt
Simplicius
.
SIMPL.
The
question
which
you
have
so
casually
started
,
is
one
of
the
most
difficulty
that
is
disputed
in
Philosophy
;
and
I
have
on
that
subject
most
excellent
conceits
of
a
very
learned
Doctor
of
Padoua
,
but
it
is
not
now
time
to
enter
upon
them
.
Therefore
returning
to
our
purpose
,
I
say
that
the
Moon
,
in
my
opinion
,
is
much
more
solid
than
the
Earth
,
but
do
not
infer
the
same
,
as
you
do
,
The
superficies
of
the
Moon
more
sleek
than
any
Looking-glass
.
from
the
cragginess
and
montuousity
of
its
superficies
;
but
rather
from
the
contrary
,
namely
,
from
its
aptitude
to
receive
(
as
we
see
it
experimented
in
the
hardest
stones
)
a
polish
and
lustre
exceeding
that
of
the
smoothest
glass
,
for
such
necessarily
must
its
superficies
be
,
to
render
it
apt
to
make
so
lively
reflection
of
the
Suns
rays
.
And
for
those
appearances
which
you
mention
,
of
Mountains
,
Cliffs
,
Hills
,
Valleys
,
&c.
they
are
all
illusions
:
and
I
have
been
present
at
certain
publick
disputes
,
where
I
have
heard
it
strongly
maintained
against
these
introducers
of
novelties
,
The
eminencies
and
cavities
in
the
Moon
are
illusions
of
its
opacous
and
perspicuous
parts
.
that
such
appearances
proceed
from
nothing
else
,
but
from
the
unequal
distribution
of
the
opacous
and
perspicuous
parts
,
of
which
the
Moon
is
inwardly
and
outwardly
composed
:
as
we
see
it
often
fall
out
in
chrystal
,
amber
,
and
many
other
precious
stones
of
perfect
lustre
;
in
which
by
reason
of
the
opacity
of
some
parts
,
and
the
transparency
of
others
,
there
doth
appear
several
concavities
and
prominencies
.
In
the
fourth
resemblance
,
I
grant
,
that
the
superficies
of
Terrestrial
Globe
beheld
from
afar
,
would
make
two
different
appearances
,
namely
,
one
more
clear
,
the
other
more
dark
;
but
I
believe
that
such
diversity
would
succeed
quite
contrary
to
what
you
say
;
that
is
,
I
hold
that
the
surface
of
the
water
would
appear
lucid
,
because
that
it
is
smooth
and
transparent
;
and
that
of
the
Earth
would
appear
obscure
,
by
reason
of
its
opacity
and
scabrosity
,
ill
accommodated
for
reflecting
the
light
of
the
Sun
.
Concerning
the
fifth
comparison
,
I
grant
it
wholly
,
and
am
able
,
in
case
the
Earth
did
shine
as
the
Moon
,
to
show
the
same
to
any
one
that
should
from
thence
above
behold
it
,
represented
by
figures
answerable
to
those
which
we
see
in
the
Moon
:
I
comprehend
also
,
how
the
period
of
its
illumination
and
variation
of
figure
,
would
be
monthly
,
albeit
the
Sun
revolves
round
about
it
in
twenty
four
hours
:
and
lastly
,
I
do
not
scruple
to
admit
,
that
the
half
onely
of
the
Moon
seeth
all
the
Earth
,
and
that
all
the
Earth
seeth
but
onely
half
of
the
Moon
.
For
what
remains
,
I
repute
it
most
false
,
that
the
Moon
can
receive
light
from
the
Earth
,
which
is
most
obscure
,
opacous
,
and
utterly
unapt
to
reflect
the
Suns
light
,
as
the
Moon
doth
reflect
it
to
us
:
and
as
I
have
said
,
I
hold
that
that
light
which
we
see
in
the
remainder
of
the
Moons
face
(
the
splendid
crescents
subducted
)
by
the
illumination
,
is
the
proper
and
natural
light
of
the
Moon
,
and
no
easie
matter
would
induce
me
to
believe
otherwise
.
The
seventh
,
touching
the
mutual
Eclipses
,
may
be
also
admitted
;
howbeit
that
is
wont
to
be
called
the
eclipse
of
the
Sun
,
which
you
are
pleased
to
phrase
the
eclipse
of
the
Earth
.
And
this
is
what
I
have
at
this
time
to
say
in
opposition
to
your
seven
congruities
or
resemblances
,
to
which
objections
,
if
you
are
minded
to
make
any
reply
,
I
shall
willingly
hear
you
.
SALV
.
If
I
have
well
apprehended
what
you
have
answered
,
it
seems
to
me
,
that
there
still
remains
in
controversie
between
us
,
certain
conditions
,
which
I
made
common
betwixt
the
Moon
&
Earth
,
and
they
are
these
;
You
esteem
the
Moon
to
be
smooth
and
polisht
,
as
a
Looking-glass
,
and
as
such
,
able
to
reflect
the
Suns
light
;
and
contrarily
,
the
Earth
,
by
reason
of
its
montuosity
,
unable
to
make
such
reflection
:
You
yield
the
Moon
to
be
solid
and
hard
,
and
that
you
argue
from
its
being
smooth
and
polite
,
and
not
from
its
being
montuous
;
and
for
its
appearing
montuous
,
you
assign
as
the
cause
,
that
it
consists
of
parts
more
and
less
opacous
and
perspicuous
.
And
lastly
,
you
esteem
that
secondary
light
,
to
be
proper
to
the
Moon
,
and
not
reflected
from
the
Earth
;
howbeit
you
seem
not
to
deny
the
sea
,
as
being
of
a
smooth
surface
,
some
kind
of
reflection
.
As
to
the
convincing
you
of
that
error
,
that
the
reflection
of
the
Moon
is
made
,
as
it
were
,
like
that
of
a
Looking-glass
,
I
have
small
hope
,
whilst
I
see
,
that
what
hath
been
read
in
the
[
](A61244-e14890-b)*
*
Il
Saggiatore
,
&
Lettere
Solari
,
two
Treatises
of
Galilaeus
.
Saggiator
and
in
the
Solar
Letters
of
our
Common
Friend
,
hath
profited
nothing
in
your
judgment
,
if
haply
you
have
attentively
read
what
he
hath
there
written
on
this
subject
.
SIMPL.
I
have
perused
the
same
so
superficially
,
according
to
the
small
time
of
leasure
allowed
me
from
more
solid
studies
;
therefore
,
if
you
think
you
can
,
either
by
repeating
some
of
those
reasons
,
or
by
alledging
others
,
resolve
me
these
doubts
,
I
will
hearken
to
them
attentively
.
SALV
.
I
will
tell
you
what
comes
into
my
mind
upon
the
instant
,
and
its
possible
it
may
be
a
commixtion
of
my
own
conceipts
,
and
those
which
I
have
sometime
read
in
the
fore-said
Books
,
by
which
I
well
remember
,
that
I
was
then
perfectly
satisfied
,
although
the
conclusions
,
at
first
sight
seem'd
unto
me
strange
Paradoxes
.
We
enquire
Simplicius
,
whether
to
the
making
a
reflection
of
light
,
like
that
which
we
receive
from
the
Moon
,
it
be
necessary
that
the
superficies
from
whence
the
reflection
commeth
,
be
so
smooth
and
polite
,
as
the
face
of
a
Looking-Glasse
,
or
whether
a
superficies
not
smooth
or
polisht
,
but
rough
and
uneven
,
be
more
apt
for
such
a
purpose
.
Now
supposing
two
reflections
should
come
unto
us
,
one
more
bright
,
the
other
lesse
,
from
two
superficies
opposite
unto
us
,
I
demand
of
you
,
which
of
the
two
superficies
you
think
would
represent
it self
to
our
sight
,
to
be
the
clearest
,
and
which
the
obscurest
.
SIMPL.
I
am
very
confident
,
that
that
same
,
which
most
forcibly
reflected
the
light
upon
me
,
would
shew
its
self
in
its
aspect
the
clearer
,
and
the
other
darker
.
SALV
.
Be
pleased
to
take
that
Glasse
which
hangs
on
yonder
Wall
,
It
is
proved
at
large
that
the
Moons
surface
is
sharp
.
and
let
us
go
out
into
the
Court-yard
.
Come
Sagredus
.
Now
hang
the
glasse
yonder
,
against
that
same
Wall
,
on
which
the
Sun
shines
,
and
now
let
us
with-draw
our selves
into
the
shade
.
See
yonder
two
superficies
beaten
by
the
Sun
,
namely
,
the
Wall
and
the
Glasse
.
Tell
me
now
which
appears
clearest
unto
you
,
that
of
the
Wall
or
that
of
the
Glasse
?
Why
do
you
not
answer
me
?
SAGR.
I
leave
the
reply
to
Simplicius
,
who
made
the
question
;
but
I
,
for
my
own
part
,
am
perswaded
upon
this
small
beginning
of
the
experiment
,
that
the
Moon
must
be
of
a
very
unpolisht
surface
.
SALV
.
What
say
you
Simplicius
,
if
you
were
to
depaint
that
Wall
,
and
that
Glasse
fastened
unto
it
,
where
would
you
use
your
darkest
colours
,
in
designing
the
Wall
,
or
else
in
painting
the
Looking-Glasse
.
SIMPL.
Much
the
darker
in
depainting
the
Glasse
.
SALV
.
Now
if
from
the
superficies
,
which
represents
it self
more
clear
,
there
proceedeth
a
more
powerful
reflection
of
light
,
the
Wall
will
more
forcibly
reflect
the
raies
of
the
Sun
,
than
the
Glasse
.
SIMPL.
Very
well
,
Sir
,
have
you
ever
a
better
experiment
than
this
?
you
have
placed
us
where
the
Glasses
doth
not
reverberate
upon
us
;
but
come
along
with
me
a
little
this
way
;
how
,
will
you
not
stir
?
SAGR.
You
perhaps
seek
the
place
of
the
reflection
,
which
the
Glasse
maketh
.
SIMPL.
I
do
so
.
SAGR.
Why
look
you
,
there
it
is
upon
the
opposite
Wall
,
just
as
big
as
the
Glasse
,
and
little
lesse
bright
than
if
the
Sun
had
directly
shined
upon
it
.
SIMPL.
Come
hither
therefore
,
and
see
from
hence
the
surface
of
the
Glasse
,
and
tell
me
whether
you
think
it
more
obscure
than
that
of
the
Wall
.
SAGR.
Look
on
it
your self
,
for
I
have
no
mind
at
this
time
,
to
dazle
my
eyes
;
and
I
know
very
well
,
without
seeing
it
,
that
it
there
appears
as
splendid
and
bright
as
the
Sun
it self
,
or
little
lesse
.
SIMPL.
What
say
you
therefore
,
is
the
reflection
of
a
Glasse
lesse
powerful
than
that
of
a
Wall
?
I
see
,
that
in
this
opposite
Wall
,
where
the
reflection
of
the
other
illuminated
Wall
comes
,
together
with
that
of
the
Glasse
,
this
of
the
Glasse
is
much
clearer
;
and
I
see
likewise
,
that
,
from
this
place
where
I
stand
,
the
glasse
it self
appears
with
much
more
lustre
than
the
Wall
.
SALV
.
You
have
prevented
me
with
your
subtlety
;
for
I
stood
in
need
of
this
very
observation
to
demonstrate
what
remains
.
You
see
then
the
difference
which
happens
betwixt
the
two
reflections
made
by
the
two
superficies
of
the
Wall
and
Glasse
,
percu●t
in
the
self-same
manner
,
by
the
rayes
of
the
Sun
;
and
you
see
,
how
the
reflection
which
comes
from
the
Wall
,
diffuseth
it self
towards
all
the
parts
opposite
to
it
,
but
that
of
the
Glasse
goeth
towards
one
part
onely
,
not
at
all
bigger
than
the
Glasse
it self
:
you
see
likewise
,
how
the
superficies
of
the
Wall
,
beheld
from
what
part
soever
,
alwayes
shews
it self
of
one
and
the
same
cleernesse
,
and
every
way
,
much
clearer
than
that
of
the
Glasse
,
excepting
only
in
that
little
place
,
on
which
the
Glasses
reflection
reverberates
,
for
from
thence
indeed
the
Glasse
appears
much
more
lucid
than
the
Wall
.
By
these
so
sensible
,
and
palpable
experiments
,
my
thinks
one
may
soon
come
to
know
,
whether
the
reflection
which
the
Moon
sends
upon
us
,
proceed
as
from
a
Glasse
,
or
else
,
as
from
a
Wall
,
that
is
,
from
a
smooth
superficies
,
or
a
rugged
.
SAGR.
If
I
were
in
the
Moon
it self
,
I
think
I
could
not
with
my
hands
more
plainly
feel
the
unevennesse
of
its
superficies
,
than
I
do
now
perceive
it
,
by
apprehending
your
discourse
.
The
Moon
beheld
in
any
posture
,
in
respect
of
the
Sun
and
us
,
sheweth
us
its
superficies
,
touch't
by
the
Suns
rayes
,
alwayes
equally
clear
;
an
effect
,
which
answers
to
an
hair
that
of
the
Wall
,
which
beheld
from
what
place
soever
,
appeareth
equally
bright
,
and
differeth
from
the
Glasse
,
which
from
one
place
onely
appeareth
lucid
,
and
from
all
others
obscure
.
Moreover
,
the
light
which
cometh
to
me
from
the
reflection
of
the
Wall
,
is
tollerable
,
and
weak
,
in
comparison
of
that
of
the
Glasse
,
which
is
little
lesse
forcible
and
offensive
to
the
sight
,
than
that
primary
and
direct
light
of
the
Sun
.
And
thus
without
trouble
do
we
behold
the
face
of
the
Moon
;
which
were
it
as
a
Glasse
,
it
appearing
to
us
by
reason
of
its
vicinity
,
as
big
as
the
Sun
it self
,
its
splendor
would
be
absolutely
intollerable
,
and
would
seem
as
if
we
beheld
another
Sun
.
SALV
.
Ascribe
not
,
I
beseech
you
Sagredus
,
more
to
my
demonstration
,
than
it
produceth
.
I
will
oppose
you
with
an
instance
,
which
I
see
not
well
how
you
can
easily
resolve
.
You
insist
upon
it
as
a
grand
difference
between
the
Moon
and
Glasse
,
that
it
emits
its
reflection
towards
all
parts
equally
,
as
doth
the
Wall
;
whereas
the
Glasse
casts
it
upon
one
onely
determinate
place
;
and
from
hence
you
conclude
the
Moon
to
be
like
to
the
Wall
,
and
not
to
the
Glasse
:
Flat
Looking-glasses
cast
forth
the
reflection
towards
but
one
place
,
but
the
spherical
every
way
.
But
I
must
tell
you
,
that
that
same
Glasse
casts
its
reflection
on
one
place
onely
,
because
its
surface
is
flat
,
and
the
reflex
rayes
being
to
depart
at
angles
equal
to
those
of
the
rayes
of
incidence
,
it
must
follow
that
from
a
plane
or
flat
superficies
,
they
do
depart
unitedly
towards
the
same
place
;
but
in
regard
that
the
superficies
of
the
Moon
is
not
plain
,
but
spherical
,
and
the
incident
rayes
upon
such
a
superficies
,
being
to
reflect
themselves
at
angles
equal
to
those
of
the
incidence
towards
all
parts
,
by
means
of
the
infinity
of
the
inclinations
which
compose
the
spherical
superficies
,
therefore
the
Moon
may
send
forth
its
reflection
every
way
;
and
there
is
no
necessity
for
its
repercussion
upon
one
place
onely
,
as
that
Glasse
which
is
flat
.
SIMPL.
This
is
one
of
the
very
same
objections
,
which
I
intended
to
have
made
against
him
.
SAGR.
If
this
be
one
,
you
had
need
have
more
of
them
;
yet
I
tell
you
,
that
as
to
this
first
,
it
seems
to
me
to
make
more
against
you
,
than
for
you
.
SIMPL.
You
have
pronounced
as
a
thing
manifest
,
that
the
reflection
made
by
that
Wall
,
is
as
cleer
and
lucid
as
that
which
the
Moon
sends
forth
,
and
I
esteem
it
nothing
in
comparison
thereto
.
For
,
in
this
businesse
of
the
illumination
,
its
requisite
to
respect
,
and
to
distinguish
the
Sphere
of
Activity
The
sphere
of
Activity
greater
in
the
Coelestial
bodies
than
in
Elementary
.
and
who
questions
but
the
Coelestial
bodies
have
greater
Spheres
of
activity
,
than
these
our
elementary
,
frail
,
and
mortal
ones
?
and
that
Wall
,
finally
,
what
else
is
it
but
a
little
obscure
Earth
,
unapt
to
shine
?
;
SAGR.
And
here
also
I
believe
,
that
you
very
much
deceive
your
felf
.
But
I
come
to
the
first
objection
moved
by
Salviatus
;
and
I
consider
,
that
to
make
a
body
appear
unto
us
luminous
,
it
sufficeth
not
that
the
rayes
of
the
illuminating
body
fall
upon
it
,
but
it
is
moreover
requisite
that
the
reflex
rayes
arrive
to
our
eye
;
as
is
manifestly
seen
in
the
example
of
that
Glasse
,
upon
which
,
without
question
,
the
illuminating
rayes
of
the
Sun
do
come
;
yet
neverthelesse
,
it
appears
not
to
us
bright
and
shining
,
unlesse
we
set
our
eye
in
that
particular
place
,
where
the
reflection
arriveth
.
Now
let
us
consider
what
would
succeed
,
were
the
glasse
of
a
spherical
figure
;
for
without
doubt
,
we
should
find
,
that
of
the
reflection
made
by
the
whole
surface
illuminated
,
that
to
be
but
a
very
small
part
,
which
arriveth
to
the
eye
of
a
particular
beholder
;
by
reason
that
that
is
but
an
incosiderable
particle
of
the
whole
spherical
superficies
,
the
inclination
of
which
casts
the
ray
to
the
particular
place
of
the
eye
;
whence
the
part
of
the
spherical
superficies
,
which
shews
it self
shining
to
the
eye
,
must
needs
be
very
small
;
all
the
rest
being
represented
obscure
.
So
that
were
the
Moon
smooth
,
as
a
Looking-glasse
,
The
Moon
if
it
were
smooth
,
like
a
spherical
glasse
,
would
be
invisible
.
a
very
small
part
would
be
seen
by
any
particular
eye
to
be
illustrated
by
the
Sun
,
although
its
whole
Hemisphere
were
exposed
to
the
Suns
rayes
;
and
the
rest
would
appear
to
the
eye
of
the
beholder
as
not
illuminated
,
and
therefore
invisible
;
and
finally
,
the
whole
Moon
would
be
likewise
invisible
,
for
so
much
as
that
particle
,
whence
the
reflection
should
come
,
by
reason
of
its
smalnesse
and
remotenesse
,
would
be
lost
.
And
as
it
would
be
invisible
to
the
eye
,
so
would
it
not
afford
any
light
;
for
it
is
altogether
impossible
,
that
a
bright
body
should
take
away
our
darknesse
by
its
splendor
,
and
we
not
to
see
it
.
SALV
.
Stay
good
Sagredus
,
for
I
see
some
emotions
in
the
face
and
eyes
of
Simplicius
,
which
are
to
me
as
indices
that
he
is
not
either
very
apprehensive
of
,
or
satisfied
with
this
which
you
,
with
admirable
proof
,
and
absolute
truth
have
spoken
.
And
yet
I
now
call
to
mind
,
that
I
can
by
another
experiment
remove
all
scruple
.
I
have
seen
above
in
a
Chamber
,
a
great
spherical
Looking-glasse
;
let
us
send
for
it
hither
,
and
whilest
it
is
in
bringing
,
let
Simplicius
return
to
consider
,
how
great
the
clarity
is
which
cometh
to
the
Wall
here
,
under
the
penthouse
,
from
the
reflection
of
the
flat
glasse
.
SIMPL.
I
see
it
is
little
lesse
shining
,
than
if
the
Sun
had
directly
beat
upon
it
.
SALV
.
So
indeed
it
is
.
Now
tell
me
,
if
taking
away
that
small
flat
glasse
,
we
should
put
that
great
spherical
one
in
the
same
place
,
what
effect
(
think
you
)
would
its
reflection
have
upon
the
same
Wall
?
SIMPL.
I
believe
that
it
would
eject
upon
it
a
far
greater
and
more
diffused
light
.
SALV
.
But
if
the
illumination
should
be
nothing
,
or
so
small
,
that
you
would
scarse
discern
it
,
what
would
you
say
then
?
SIMPL.
When
I
have
seen
the
effect
,
I
will
bethink
my self
of
an
answer
.
SALV
.
See
here
is
the
glasse
,
which
I
would
have
to
be
placed
close
to
the
other
.
But
first
let
us
go
yonder
towards
the
reflection
of
that
flat
one
,
and
attentively
observe
its
clarity
;
see
how
bright
it
is
here
where
it
shines
,
and
how
distinctly
one
may
discern
these
small
unevennesses
in
the
Wall
.
SIMPL.
I
have
seen
and
very
well
observed
the
same
,
now
place
the
other
glasse
by
the
side
of
the
first
.
SALV
.
See
where
it
is
.
It
was
placed
there
assoon
as
you
began
to
look
upon
the
Walls
small
unevennesses
,
and
you
perceived
it
not
,
so
great
was
the
encrease
of
the
light
all
over
the
rest
of
the
Wall
.
Now
take
away
the
flat
glasse
.
Behold
now
all
reflection
removed
,
though
the
great
convex
glasse
still
remaineth
.
Remove
this
also
,
and
place
it
there
again
if
you
please
,
and
you
shall
see
no
alteration
of
light
in
all
the
Wall
.
See
here
then
demonstrated
to
sense
,
that
the
reflection
of
the
Sun
,
made
upon
a
spherical
convex
glasse
,
doth
not
sensibly
illuminate
the
places
neer
unto
it
.
Now
what
say
you
to
this
experiment
?
SIMPL.
I
am
afraid
that
there
may
be
some
Leigerdemain
,
used
in
this
affair
;
yet
in
beholding
that
glasse
I
see
it
dart
forth
a
great
splendor
,
which
dazleth
my
eyes
;
and
that
which
imports
most
of
all
,
I
see
it
from
what
place
soever
I
look
upon
it
;
and
I
see
it
go
changing
situation
upon
the
superficies
of
the
glasse
,
which
way
soever
I
place
my self
to
look
upon
it
;
a
necessary
argument
,
that
the
light
is
livelily
reflected
towards
every
side
,
and
consequently
,
as
strongly
upon
all
that
Wall
,
as
upon
my
eye
.
SALV
.
Now
you
see
how
cautiously
and
reservedly
you
ought
to
proceed
in
lending
your
assent
to
that
,
which
discourse
alone
representeth
to
you
.
There
is
no
doubt
but
that
this
which
you
say
,
carrieth
with
it
probability
enough
,
yet
you
may
see
,
how
sensible
experience
proves
the
contrary
.
SIMPL.
How
then
doth
this
come
to
pass
?
SALV
.
I
will
deliver
you
my
thoughts
thereof
,
but
I
cannot
tell
how
you
may
be
pleas'd
therewith
.
And
first
,
that
lively
splendor
which
you
see
upon
the
glass
,
and
which
you
think
occupieth
a
good
part
thereof
,
is
nothing
near
so
great
,
nay
is
very
exceeding
small
;
but
its
liveliness
occasioneth
in
your
eye
,
(
by
means
of
the
reflection
made
on
the
humidity
of
the
extream
parts
of
the
eye-brows
,
which
distendeth
upon
the
pupil
)
an
adventitious
irradiation
,
like
to
that
blaze
which
we
think
we
see
about
the
flame
of
a
candle
placed
at
some
distance
;
or
if
you
will
,
you
may
resemble
it
to
the
adventitious
splendor
of
a
star
;
The
small
body
of
the
stars
fringed
round
about
with
rays
,
appeareth
very
much
bigger
than
plain
and
naked
,
and
in
its
native
clarity
for
if
you
should
compare
the
small
body
v.
g.
of
the
Canicula
,
seen
in
the
day
time
with
the
Telescope
,
when
it
is
seen
without
such
irradiation
,
with
the
same
seen
by
night
by
the
eye
it self
,
you
will
doubtless
comprehend
that
being
irradiated
,
it
appeareth
above
a
thousand
times
bigger
than
the
naked
and
real
body
:
and
a
like
or
greater
augmentation
doth
the
image
of
the
Sun
make
,
which
you
see
in
that
glass
.
I
say
greater
,
for
that
it
is
more
lively
than
the
star
,
as
is
manifest
from
our
being
able
to
behold
the
star
with
much
less
offence
,
than
this
reflection
of
the
glass
.
The
reverberation
therefore
which
is
to
dispere
it self
all
over
this
wall
,
cometh
from
a
small
part
of
that
glass
,
and
that
which
even
now
came
from
the
whole
flat
glass
dispersed
and
restrain'd
it self
to
a
very
small
part
of
the
said
wall
.
What
wonder
is
it
then
,
that
the
first
reflection
very
lively
illuminates
,
and
that
this
other
is
almost
imperceptible
?
SIMPL.
I
find
my self
more
perplexed
than
ever
,
and
there
presents
it self
unto
me
the
other
difficulty
,
how
it
can
be
that
that
wall
,
being
of
a
matter
so
obscure
,
and
of
a
superficies
so
unpolish'd
,
should
be
able
to
dart
from
it
greater
light
,
than
a
glass
very
smooth
and
polite
.
SALV
.
Greater
light
it
is
not
,
but
more
universal
;
for
as
to
the
degree
of
brightness
,
you
see
that
the
reflection
of
that
small
flat
glass
,
where
it
beamed
forth
yonder
under
the
shadow
of
the
penthouse
,
illuminateth
very
much
;
and
the
rest
of
the
wall
which
receiveth
the
reflection
of
the
wall
on
which
the
glass
is
placed
,
is
not
in
any
great
measure
illuminated
,
as
was
the
small
part
on
which
the
reflection
of
the
glass
fell
.
And
if
you
would
understand
the
whole
of
this
business
,
you
must
consider
that
the
superficies
of
that
wall
's
being
rough
,
The
reflex
light
of
uneven
bodies
,
is
more
universal
than
that
of
the
smooth
,
&
why
.
is
the
same
as
if
it
were
composed
of
innumerable
small
superficies
,
disposed
according
to
innumerable
diversities
of
inclinations
:
amongst
which
it
necessarily
happens
,
that
there
are
many
disposed
to
send
forth
their
reflex
rays
from
them
into
such
a
place
,
many
others
into
another
:
and
in
sum
,
there
is
not
any
place
to
which
there
comes
not
very
many
rays
,
reflected
from
very
many
small
superficies
,
dispersed
throughout
the
whole
superficies
of
the
rugged
body
,
upon
which
the
rays
of
the
Sun
fall
.
From
which
it
necessarily
followeth
,
That
upon
any
,
whatsoever
,
part
of
any
superficies
,
opposed
to
that
which
receiveth
the
primary
incident
rays
,
there
is
produced
reflex
rays
,
and
consequently
illumination
.
There
doth
also
follow
thereupon
,
That
the
same
body
upon
which
the
illuminating
rays
fall
,
beheld
from
whatsoever
place
,
appeareth
all
illuminated
and
shining
:
and
therefore
the
Moon
,
as
being
of
a
superficies
rugged
and
not
smooth
,
The
Moon
,
if
it
were
smooth
and
sle●k
,
would
be
invisible
.
beameth
forth
the
light
of
the
Sun
on
every
side
,
and
to
all
beholders
appeareth
equally
lucid
.
But
if
the
surface
of
it
,
being
spherical
,
were
also
smooth
as
a
glass
,
it
would
become
wholly
invisible
;
forasmuch
as
that
small
part
,
from
which
the
image
of
the
Sun
should
be
reflected
unto
the
eye
of
a
particular
person
,
by
reason
of
its
great
distance
would
be
invisible
,
as
I
have
said
before
.
SIMPL.
I
am
very
apprehensive
of
your
discourse
;
yet
methinks
I
am
able
to
resolve
the
same
with
very
little
trouble
;
and
easily
to
maintain
,
that
the
Moon
is
rotund
and
polite
,
and
that
it
reflects
the
Suns
light
unto
us
in
manner
of
a
glass
;
nor
therefore
ought
the
image
of
the
Sun
to
be
seen
in
the
middle
of
it
,
forasmuch
as
the
species
of
the
Sun
it self
admits
not
its
small
figure
to
be
seen
at
so
great
a
distance
,
but
the
light
produced
by
the
Sun
may
help
us
to
conceive
that
it
illuminateth
the
whole
Lunar
Body
:
a
like
effect
we
may
see
in
a
plate
gilded
and
well
pollish'd
,
which
touch't
by
a
luminous
body
,
appeareth
to
him
that
beholds
it
at
some
distance
to
be
all
shining
;
and
onely
near
at
hand
one
may
discover
in
the
middle
of
it
the
small
image
of
the
luminous
body
.
SALV
.
Ingenuously
confessing
my
dullness
of
apprehension
,
I
must
tell
you
,
that
I
understand
not
any
thing
of
this
your
discourse
,
save
onely
what
concerns
the
gilt
plate
:
and
if
you
permit
me
to
speak
freely
,
I
have
a
great
conceit
that
you
also
understand
not
the
same
,
but
have
learnt
by
heart
those
words
written
by
some
one
out
of
a
desire
of
contradiction
,
and
to
shew
himself
more
intelligent
than
his
adversary
;
but
it
must
be
to
those
,
which
to
appear
also
more
wise
,
applaud
that
which
they
do
not
understand
,
and
entertain
a
greater
conceit
of
persons
,
the
less
they
are
by
them
understood
:
and
the
writer
himself
may
be
one
of
those
(
of
which
there
are
many
)
who
write
what
they
do
not
understand
,
Some
write
what
they
understand
not
,
and
therefore
understand
not
what
they
write
.
and
consequently
understand
not
what
they
write
.
Therefore
,
omitting
the
rest
,
I
reply
,
as
to
the
gilt
plate
,
that
if
it
be
flat
and
not
very
big
,
it
may
appear
at
a
distance
very
bright
,
whilst
a
great
light
beameth
upon
it
,
but
yet
it
must
be
when
the
eye
is
in
a
determinate
line
,
namely
in
that
of
the
reflex
rays
:
and
it
will
appear
the
more
shining
,
if
it
were
v.
g.
of
silver
,
by
means
of
its
being
burnished
,
and
apt
through
the
great
density
of
the
metal
,
to
receive
a
perfect
polish
.
And
though
its
superficies
,
being
very
well
brightned
,
were
not
exactly
plain
,
but
should
have
various
inclinations
,
yet
then
also
would
its
splendor
be
seen
many
ways
;
namely
,
from
as
many
places
as
the
various
reflections
,
made
by
the
several
superficies
,
Diamonds
ground
to
divers
sides
,
&
why
.
do
reach
:
for
therefore
are
Diamonds
ground
to
many
sides
,
that
so
their
pleasing
lustre
might
be
beheld
from
many
places
.
But
if
the
Plate
were
very
big
,
though
it
should
be
all
plain
,
yet
would
it
not
at
a
distance
appear
all
over
shining
:
and
the
better
to
express
my self
,
Let
us
suppose
a
very
large
gilt
plate
exposed
to
the
Sun
,
it
will
shew
to
an
eye
far
distant
,
the
image
of
the
Sun
,
to
occupy
no
more
but
a
certain
part
of
the
said
plate
;
to
wit
,
that
from
whence
the
reflection
of
the
incident
solar
rays
come
:
but
it
is
true
that
by
the
vivacity
of
the
light
,
the
said
image
will
appear
fringed
about
with
many
rays
,
and
so
will
seem
to
occupie
a
far
greater
part
of
the
plate
,
than
really
it
doth
.
And
to
shew
that
this
is
true
,
when
you
have
noted
the
particular
place
of
the
plate
from
whence
the
reflection
cometh
,
and
conceived
likewise
how
great
the
shining
place
appeared
to
you
,
cover
the
greater
part
of
that
same
space
,
leaving
it
only
visible
about
the
midst
;
and
all
this
shall
not
any
whit
diminish
the
apparent
splendor
to
one
that
beholds
it
from
afar
;
but
you
shall
see
it
largely
dispers'd
upon
the
cloth
or
other
matter
,
wherewith
you
covered
it
.
If
therefore
any
one
,
by
seeing
from
a
good
distance
a
small
gilt
plate
to
be
all
over
shining
,
should
imagine
that
the
same
would
also
even
in
a
plate
as
broad
as
the
Moon
,
he
is
no
less
deceived
,
than
if
he
should
believe
the
Moon
to
be
no
bigger
than
the
bottom
of
a
tub
.
If
again
the
plate
were
turn'd
into
a
spherical
superficies
,
the
reflection
would
be
seen
strong
in
but
one
sole
particle
of
it
;
but
yet
by
reason
of
its
liveliness
,
it
will
appear
fringed
about
with
many
glittering
rays
:
the
rest
of
the
Ball
would
appear
according
as
it
was
burnished
;
Silver
〈◊〉
wished
appears
ma●e
obscu●e
,
〈◊〉
the
not
burnished
,
&
why
.
and
this
also
onely
then
when
it
was
not
very
much
polished
,
for
should
it
be
perfectly
brightned
,
it
would
appear
obscure
.
An
example
of
this
we
have
dayly
before
our
eyes
in
silver
vessels
,
which
whilst
they
are
only
boyl'd
in
the
Argol
and
Salt
,
they
are
all
as
white
as
snow
,
and
do
not
reflect
any
image
;
but
if
they
be
in
any
part
burnish'd
,
they
become
in
that
place
presently
obscure
:
and
in
them
one
may
see
the
representation
of
any
thing
as
in
Looking-glasses
.
And
that
chanto
obscurity
,
proceeds
from
nothing
else
but
the
smoothing
and
plaining
of
a
fine
grain
,
which
made
the
superficies
of
the
silver
rough
,
and
yet
such
,
as
that
it
reflected
the
light
into
all
parts
,
whereby
it
seemed
from
all
parts
equally
illuminated
:
which
small
unevennesses
,
when
they
come
to
be
exquisitely
plained
by
the
burnish
,
so
that
the
reflection
of
the
rays
of
incidence
are
all
directed
unto
one
determinate
place
;
then
,
from
that
same
place
,
the
burnish'd
part
shall
shew
much
more
bright
and
shining
than
the
rest
which
is
onely
whitened
by
boyling
;
but
from
all
other
places
it
looks
very
obscure
.
And
note
,
that
the
diversity
of
sights
of
looking
upon
burnish'd
superficies
,
Burnish'd
Steel
〈◊〉
from
one
〈…〉
very
〈…〉
from
〈◊〉
,
very
obscure
.
occasioneth
such
difference
in
appearances
,
that
to
imitate
and
represent
in
picture
,
v.
g.
a
polish'd
Cuirace
,
one
must
couple
black
plains
with
white
,
one
sideways
to
the
other
,
in
those
parts
of
the
arms
where
the
light
falleth
equally
.
SAGR.
If
therefore
these
great
Philosophers
would
acquiese
in
granting
,
that
the
Moon
,
Venus
and
the
other
Planets
,
were
not
of
so
bright
and
smooth
a
surface
as
a
Looking-glass
,
but
wanted
some
small
matter
of
it
,
namely
,
were
as
a
silver
plate
,
onely
boyled
white
,
but
not
burnished
;
would
this
yet
suffice
to
the
making
of
it
visible
,
and
apt
for
darting
forth
the
light
of
the
Sun
?
SALV
.
It
would
suffice
in
part
;
but
would
not
give
a
light
so
strong
,
as
it
doth
being
mountainous
,
and
in
sum
,
full
of
eminencies
and
great
cavities
.
But
these
Philosophers
will
never
yield
it
to
be
lesse
polite
than
a
glasse
;
but
far
more
,
if
more
it
can
be
imagined
;
for
they
esteeming
that
to
perfect
bodies
perfect
figures
are
most
sutable
;
it
is
necessary
,
that
the
sphericity
of
those
Coelestial
Globes
be
most
exact
;
besides
,
that
if
they
should
grant
me
some
inequality
,
though
never
so
small
,
I
would
not
scruple
to
take
any
other
greater
;
for
that
such
perfection
consisting
in
indivisibles
,
an
hair
doth
as
much
detract
from
its
perfection
as
a
mountain
.
SAGR.
Here
I
meet
with
two
difficulties
,
one
is
to
know
the
reason
why
the
greater
inequality
of
superficies
maketh
the
stronger
reflection
of
light
;
the
other
is
,
why
these
Peripatetick
Gentlemen
are
for
this
exact
figure
.
SALV
.
I
will
answer
to
the
first
;
The
more
rough
superficies
make
greater
reflection
of
light
,
than
the
less
rough
.
and
leave
to
Simplicius
the
care
of
making
reply
to
the
second
.
You
must
know
therefore
,
that
the
same
superficies
happen
to
be
by
the
same
light
more
or
less
illuminated
,
according
as
the
rayes
of
illumination
fall
upon
them
more
or
lesse
obliquely
;
Perpendicular
rays
illuminate
more
than
the
oblique
,
and
why
.
so
that
the
greatest
illumination
is
where
the
rayes
are
perpendicular
.
And
see
,
how
I
will
prove
it
to
your
sense
.
I
bend
this
paper
,
so
,
that
one
part
of
it
makes
an
angle
upon
the
other
:
and
exposing
both
these
parts
to
the
reflection
of
the
light
of
that
opposite
Wall
,
you
see
how
this
side
which
receiveth
the
rayes
obliquely
,
is
lesse
shining
than
this
other
,
where
the
reflection
fals
at
right
angles
;
and
observe
,
that
as
I
by
degrees
receive
the
illumination
more
obliquely
,
it
groweth
weaker
.
SAGR.
I
see
the
effect
,
but
comprehend
not
the
cause
.
SALV
.
If
you
thought
upon
it
but
a
minute
of
an
hour
,
you
would
find
it
;
but
that
I
may
not
waste
the
time
,
see
a
kind
of
demonstration
thereof
in
Fig.
7.
SAGR.
The
bare
sight
of
this
Figure
hath
fully
satisfied
me
,
therefore
proceed
.
SIMPL.
Pray
you
let
me
hear
you
out
,
for
I
am
not
of
so
quick
an
apprehension
.
SALV
.
Fancie
to
your self
,
that
all
the
paralel
lines
,
which
you
see
to
depart
from
the
terms
A.
B.
are
the
rays
which
fall
upon
the
line
C.
D.
at
right
angles
:
The
more
oblique
Rayes
illuminate
less
,
and
why
.
then
incline
the
said
C.
D.
till
it
hang
as
D.
O.
now
do
not
you
see
that
a
great
part
of
those
rays
which
peirce
C.
D.
pass
by
without
touching
D.
O?
If
therefore
D.
O.
be
illuminated
by
fewer
rays
,
it
is
very
reasonable
,
that
the
light
received
by
it
be
more
weak
.
Let
us
return
now
to
the
Moon
,
which
being
of
a
spherical
figure
,
if
its
superficies
were
smooth
,
as
this
paper
,
the
parts
of
its
hemisphere
illuminated
by
the
Sun
,
which
are
towards
its
extremity
,
would
receive
much
less
light
,
than
the
middle
parts
;
the
rays
falling
upon
them
most
obliquely
,
and
upon
these
at
right
angles
;
whereupon
at
the
time
of
full
Moon
,
when
we
see
almost
its
whole
Hemisphere
illuminated
,
the
parts
towards
the
midst
,
would
shew
themselves
to
us
with
more
splendor
,
than
those
others
towards
the
circumference
:
which
is
not
so
in
effect
.
Now
the
face
of
the
Moon
being
represented
to
me
full
of
indifferent
high
mountains
,
do
not
you
see
how
their
tops
and
continuate
ridges
,
being
elevated
above
the
convexity
of
the
perfect
spherical
superficies
,
come
to
be
exposed
to
the
view
of
the
Sun
,
and
accommodated
to
receive
its
rays
much
less
obliquely
,
and
consequently
to
appear
as
luminous
as
the
rest
?
SAGR.
All
this
I
well
perceive
:
and
if
there
are
such
mountains
,
its
true
,
the
Sun
will
dart
upon
them
much
more
directly
than
it
would
do
upon
the
inclination
of
a
polite
superficies
:
but
it
is
also
true
,
that
betwixt
those
mountains
all
the
valleys
would
become
obscure
,
by
reason
of
the
vast
shadows
,
which
in
that
time
would
be
cast
from
the
mountains
,
whereas
the
parts
towards
the
middle
,
though
full
of
valleys
and
hills
,
by
reason
they
have
the
Sun
elevated
,
would
appear
without
shadow
,
and
therefore
more
lucid
by
far
than
the
extreme
parts
,
which
are
no
less
diffused
with
shadow
than
light
,
and
yet
we
can
perceive
no
such
difference
.
SIMPL.
I
was
ruminating
upon
the
like
difficulty
.
SALV
.
How
much
readier
is
Simplicius
to
apprehend
the
objections
which
favour
the
opinions
of
Aristotle
,
than
their
solutions
?
I
have
a
kind
of
suspition
,
that
he
strives
also
sometimes
to
dissemble
them
;
and
in
the
present
case
,
he
being
of
himself
able
to
hit
upon
the
doubt
,
which
yet
is
very
ingenious
,
I
cannot
believe
but
that
he
also
was
advis'd
of
the
answer
;
wherefore
I
will
attempt
to
wrest
the
same
(
as
they
say
)
out
of
his
mouth
.
Therefore
tell
me
,
Simplicius
,
do
you
think
there
can
be
any
shadow
,
where
the
rays
of
the
Sun
do
shine
?
SIMPL.
I
believe
,
nay
I
am
certain
that
there
cannot
;
for
that
it
being
the
grand
luminary
,
which
with
its
rays
driveth
away
darkness
,
it
is
impossible
any
tenebrosity
should
remain
where
it
cometh
;
moreover
,
we
have
the
definition
,
that
Tenebrae
sunt
privatio
luminis
.
SALV
.
Therefore
the
Sun
,
beholding
the
Earth
,
Moon
or
other
opacous
body
,
never
seeth
any
of
its
shady
parts
,
it
not
having
any
other
eyes
to
see
with
,
save
its
rays
,
the
conveyers
of
light
:
and
consequently
,
one
standing
in
the
Sun
would
never
see
any
thing
of
umbrage
,
forasmuch
as
his
visive
rays
would
ever
go
accompanied
with
those
illuminating
beams
of
the
Sun
.
SIMPL.
This
is
true
,
without
any
contradiction
.
SALV
.
But
when
the
Moon
is
opposite
to
the
Sun
,
what
difference
is
there
between
the
tract
of
the
rayes
of
your
sight
,
and
that
motion
which
the
Suns
rayes
make
?
SIMPL.
Now
I
understand
you
;
for
you
would
say
,
that
the
rayes
of
the
sight
and
those
of
the
Sun
,
moving
by
the
same
lines
,
we
cannot
perceive
any
of
the
obscure
valleys
of
the
Moon
.
Be
pleased
to
change
this
your
opinion
,
that
I
have
either
simulation
or
dissimulation
in
me
;
for
I
protest
unto
you
,
as
I
am
a
Gentleman
,
that
I
did
not
guesse
at
this
solution
,
nor
should
I
have
thought
upon
it
,
without
your
help
,
or
without
long
study
.
SAGR.
The
resolutions
,
which
between
you
two
have
been
alledged
touching
this
last
doubt
,
hath
,
to
speak
the
truth
,
satisfied
me
also
.
But
at
the
same
time
this
consideration
of
the
visible
rayes
accompanying
the
rayes
of
the
Sun
,
hath
begotten
in
me
another
scruple
,
about
the
other
part
,
but
I
know
not
whether
I
can
expresse
it
right
,
or
no
:
for
it
but
just
now
comming
into
my
mind
,
I
have
not
yet
methodized
it
to
my
mind
:
but
let
us
see
if
we
can
,
all
together
,
make
it
intelligible
.
There
is
no
question
,
but
that
the
parts
towards
the
circumference
of
that
polish't
,
but
not
burnish't
Hemisphere
,
which
is
illuminated
by
the
Sun
,
receiving
the
rayes
obliquely
,
receive
much
fewer
thereof
,
than
the
middlemost
parts
,
which
receive
them
directly
.
And
its
possible
,
that
a
tract
or
space
of
v.
g.
twenty
degrees
in
breadth
,
and
which
is
towards
the
extremity
of
the
Hemisphere
,
may
not
receive
more
rays
than
another
towards
the
middle
parts
,
of
but
four
degree
broad
:
so
that
that
doubtless
will
be
much
more
obscure
than
this
;
and
such
it
will
appear
to
whoever
shall
behold
them
both
in
the
face
,
or
(
as
I
may
say
)
in
their
full
magnitude
.
But
if
the
eye
of
the
beholder
were
constituted
in
such
a
place
,
that
the
breadth
of
the
twenty
degrees
of
the
obscure
space
,
appeared
not
to
it
longer
than
one
of
four
degrees
,
placed
in
the
midst
of
the
Hemisphere
,
I
hold
it
not
impossible
for
it
to
appear
to
the
said
beholder
equally
clear
and
lucid
with
the
other
;
because
,
finally
,
between
two
equal
angles
,
to
wit
,
of
four
degrees
apiece
,
there
come
to
the
eye
the
reflections
of
two
equal
numbers
of
rayes
:
namely
,
those
which
are
reflected
from
the
middlemost
space
,
four
degrees
in
breadth
,
and
those
reflected
from
the
other
of
twenty
degrees
,
but
seen
by
compression
,
under
the
quantity
of
four
degrees
:
and
such
a
situation
shall
the
eye
obtain
,
when
it
is
placed
between
the
said
Hemisphere
,
and
the
body
which
illuminates
it
;
for
then
the
sight
and
rayes
move
in
the
same
lines
.
It
seemeth
not
impossible
therefore
,
but
that
the
Moon
may
be
of
a
very
equal
superficies
;
and
that
neverthelesse
,
it
may
appear
when
it
is
at
the
full
,
no
less
light
in
the
extremities
,
than
in
the
middle
parts
.
SALV
.
The
doubt
is
ingenious
and
worthy
of
consideration
;
and
as
it
but
just
now
came
into
your
mind
unawares
,
so
I
will
like
wise
answer
with
what
first
comes
into
my
thoughts
,
and
it
may
happily
fall
out
,
that
by
thinking
more
upon
it
,
I
may
stumble
upon
a
better
reply
.
But
before
,
that
I
labyrinth
my self
any
farther
,
it
would
be
necessary
,
that
we
assure
our selves
by
some
experiment
,
whether
your
objection
prove
in
effect
,
what
it
seemeth
to
conclude
in
appearance
;
and
therefore
taking
once
more
the
same
paper
,
and
making
it
to
incline
,
by
bending
a
little
part
thereof
upon
the
remainder
,
let
us
try
whether
exposing
it
to
the
Sun
,
so
that
the
rayes
of
light
fall
upon
the
lesser
part
directly
,
and
upon
the
other
obliquely
;
this
which
receiveth
the
rayes
directly
appeareth
more
lucid
;
and
see
here
by
manifest
experience
,
that
it
is
notably
more
clear
.
Now
if
your
objection
be
conclusive
,
it
will
follow
,
that
stooping
with
our
eye
so
,
that
in
beholding
the
other
greater
part
,
less
illuminated
,
in
compression
or
fore-shortning
,
it
appear
unto
us
no
bigger
than
the
other
,
more
shining
;
and
that
consequently
,
it
be
not
beheld
at
a
greater
angle
than
that
;
it
will
necessarily
ensue
,
I
say
,
that
its
light
be
encreased
,
so
that
it
do
seem
to
us
as
bright
as
the
other
.
See
how
I
behold
,
and
look
upon
it
so
obliquely
,
that
it
appeareth
to
me
narrower
than
the
other
;
but
yet
,
notwithstanding
its
obscurity
,
doth
not
to
my
perceiving
,
at
all
grow
clearer
.
Try
now
if
the
same
succeed
to
you
.
SAGR.
I
have
look't
upon
it
,
and
though
I
have
stooped
with
my
eye
,
yet
cannot
I
see
the
said
superficies
encrease
in
light
or
clarity
;
nay
me
thinks
it
rather
grows
more
dusky
.
SALV
.
We
are
hitherto
confident
of
the
invalidity
of
the
objection
;
In
the
next
place
,
as
to
the
solution
,
I
believe
,
that
,
by
reason
the
Superficies
of
this
paper
is
little
lesse
than
smooth
,
the
rayes
are
very
few
,
which
be
reflected
towards
the
point
of
incidence
,
in
comparison
of
the
multitude
,
which
are
reflected
towards
the
opposite
parts
;
and
that
of
those
few
more
and
more
are
lost
,
the
nearer
the
visive
rayes
approach
to
those
lucid
rayes
of
incidence
;
and
because
it
is
not
the
incident
rayes
,
but
those
which
are
reflected
to
the
eye
,
that
make
the
object
appear
luminous
;
therefore
,
in
stooping
the
eye
,
there
is
more
lost
than
got
,
as
you
your self
confesse
to
have
seen
in
looking
upon
the
obscurer
part
of
the
paper
.
SAGR.
I
rest
satisfied
with
this
experiment
and
reason
:
It
remains
now
,
that
Simplicius
answer
to
my
other
question
,
and
tell
me
what
moves
the
Peripateticks
to
require
this
so
exact
rotundity
in
the
Coelestial
bodies
.
SIMPL.
The
Coelestial
bodies
being
ingenerable
,
inalterable
,
impassible
,
immortal
,
Perfect
〈◊〉
why
ascribed
is
Coelestial
bodies
,
by
the
Peripateticks
.
&c.
they
must
needs
be
absolutely
perfect
;
and
their
being
absolute
perfect
,
necessarily
implies
that
there
is
in
them
all
kinds
of
perfection
;
and
consequently
,
that
their
figure
be
also
perfect
,
that
is
to
say
,
spherical
;
and
absolutely
and
perfectly
spherical
,
and
not
rough
and
irregular
.
SALV
.
And
this
incorruptibility
,
from
whence
do
you
prove
it
?
SIMPL.
Immediately
by
its
freedom
from
contraries
,
and
mediately
,
by
its
simple
circular
motion
.
SALV
.
So
that
;
The
Figure
is
not
the
cause
of
incorruptibili●r
,
but
of
longer
duration
.
by
what
I
gather
from
your
discourse
,
in
making
the
essence
of
the
Coelestial
bodies
to
be
incorruptible
,
inalterable
,
&c
,
there
is
no
need
of
rotundity
as
a
cause
,
or
requisite
;
for
if
this
should
cause
inalterability
,
we
might
at
our
pleasure
make
wood
,
wax
,
and
other
Elementary
matters
,
incorruptible
,
by
reducing
them
to
a
spherical
figure
.
SIMPL.
And
is
it
not
manifest
that
a
ball
of
Wood
will
better
and
longer
be
preserved
,
than
an
oblong
,
or
other
angular
figure
,
made
of
a
like
quantity
of
the
same
wood
.
SALV
.
This
is
most
certain
,
but
yet
it
doth
not
of
corruptible
become
incorruptible
,
but
still
remains
corruptible
,
though
of
a
much
longer
duration
.
Corruptibility
admits
of
more
or
lesse
;
so
doth
not
incorruptibili●y
.
Therefore
you
must
note
,
that
a
thing
corruptible
,
is
capable
of
being
more
or
lesse
such
,
and
we
may
properly
say
this
is
lesse
corruptible
than
that
;
as
for
example
,
the
Jasper
,
than
the
Pietra
Sirena
;
but
incorruptibility
admits
not
of
more
,
or
lesse
,
so
as
that
it
may
be
said
this
is
more
incorruptible
than
that
,
The
perfection
of
figure
,
operateth
in
corruptible
bodies
,
but
not
in
the
eternal
.
if
both
be
incorruptible
and
eternal
.
The
diversity
of
figure
therefore
cannot
operate
:
save
onely
in
matters
capable
of
more
or
lesse
duration
;
but
in
the
eternal
,
which
cannot
be
other
than
equally
eternal
,
the
operation
of
figure
ceaseth
.
And
therefore
,
since
the
Coelestial
matter
is
not
incorruptible
by
figure
,
but
otherwayes
no
man
needs
to
be
so
solicitous
for
this
perfect
sphericity
;
for
if
the
matter
be
incorruptible
,
let
it
have
what
figure
it
will
,
it
shall
be
alwayes
such
.
SAGR.
But
I
am
considering
another
thing
,
If
the
spherical
figure
conferreth
eternity
,
all
bodies
would
be
eternal
.
and
say
,
that
if
we
should
grant
the
spherical
figure
a
faculty
of
conferring
incorruptibility
,
all
bodies
of
whatsoever
figure
,
would
be
incorruptible
;
forasmuch
as
if
the
rotund
body
be
incorruptible
,
corruptibility
would
then
subsist
in
those
parts
which
alter
the
perfect
rotundity
;
as
for
instance
,
there
is
in
a
Die
a
body
perfectly
round
,
and
,
as
such
,
incorruptible
;
therefore
it
remaineth
that
those
angles
be
corruptible
which
cover
and
hide
the
rotundity
;
so
that
the
most
that
could
happen
,
would
be
,
that
those
angles
,
and
(
to
so
speak
)
excrescencies
,
would
corrupt
.
But
if
we
proceed
to
a
more
inward
consideration
,
that
in
those
parts
also
towards
the
angles
,
there
are
comprised
other
lesser
bals
of
the
same
matter
;
and
therefore
they
also
,
as
being
round
,
must
be
also
incorruptible
;
and
likewise
in
the
remainders
,
which
environ
these
eight
lesser
Spheres
,
a
man
may
understand
that
there
are
others
:
so
that
in
the
end
,
resolving
the
whole
Die
into
innumerable
balls
,
it
must
necessarily
be
granted
incorruptible
.
And
the
same
discourse
and
resolution
may
be
made
in
all
other
figures
.
SALV
.
Your
method
in
making
the
conclusion
,
for
if
v.
g.
a
round
Chrystal
were
,
by
reason
of
its
figure
,
incorruptible
;
namely
,
received
from
thence
a
faculy
of
resisting
all
internal
and
external
alterations
,
we
should
not
find
,
that
the
joyning
to
it
other
Chrystal
,
and
reducing
it
v.
g.
into
a
Cube
,
would
any
whit
alter
it
within
,
or
without
;
so
as
that
it
would
thereupon
become
lesse
apt
to
resist
the
new
ambient
,
made
of
the
same
matter
,
than
it
was
to
resist
the
other
,
of
a
matter
different
;
and
especially
,
if
it
be
true
,
that
corruption
is
generated
by
contraries
,
as
Aristotle
saith
;
and
with
what
can
you
enclose
that
ball
of
Crystal
,
that
is
lesse
contrary
to
it
,
than
Crystal
it self
?
But
we
are
not
aware
how
time
flies
away
;
and
it
will
be
too
late
before
we
come
to
an
end
of
our
dispute
,
if
we
should
make
so
long
discourses
,
upon
every
particular
;
besides
our
memories
are
so
confounded
in
the
multiplicity
of
notions
,
that
I
can
very
hardly
recal
to
mind
the
Propotsiions
,
which
I
proposed
in
order
to
Simplicius
,
for
our
consideration
.
SIMPL.
I
very
well
remember
them
:
And
as
to
this
particular
question
of
the
montuosity
of
the
Moon
,
there
yet
remains
unanswered
that
which
I
have
alledged
,
as
the
cause
,
(
and
which
may
very
well
serve
for
a
solution
)
of
that
Phaenomenon
,
saying
,
that
it
is
an
illusion
proceeding
from
the
parts
of
the
Moon
,
being
unequally
opacous
,
and
perspicuous
.
SAGR.
Even
now
,
when
Simplicius
ascribed
the
apparent
Protnberancies
or
unevennesses
of
the
Moon
(
according
to
the
opinion
of
a
certain
Peripatetick
his
friend
)
to
the
diversly
opacous
,
and
perspicuous
parts
of
the
said
Moon
,
Mother
of
Pearl
accommodated
to
imitate
the
apparent
unevennesses
of
the
Moons
surface
.
conformable
to
which
the
like
illusions
are
seen
in
Crystal
,
and
Jems
of
divers
kinds
,
I
bethought
my self
of
a
matter
much
more
commodious
for
the
representing
such
effects
;
which
is
such
,
that
I
verily
believe
,
that
that
Philosopher
would
give
any
price
for
it
;
and
it
is
the
mother
of
Pearl
,
which
is
wrought
into
divers
figures
,
and
though
it
be
brought
to
an
extreme
evennesse
,
yet
it
seemeth
to
the
eye
in
several
parts
,
so
variously
hollow
and
knotty
,
that
we
can
scarce
credit
our
feeling
of
their
evennesse
.
SALV
.
This
invention
is
truly
ingenious
;
and
that
which
hath
not
been
done
already
,
may
be
done
in
time
to
come
;
and
if
there
have
been
produced
other
Jems
,
and
Crystals
,
which
have
nothing
to
do
with
the
illusions
of
the
mother
of
Pearl
,
these
may
be
produced
also
;
in
the
mean
time
,
that
I
may
not
prevent
any
one
,
I
will
suppresse
the
answer
which
might
be
given
,
and
onely
for
this
time
betake
my self
to
satisfie
the
objections
brought
by
Simplicius
.
I
say
therefore
,
that
this
reason
of
yours
is
too
general
,
and
as
you
apply
it
not
to
all
the
appearances
one
by
one
;
which
are
seen
in
the
Moon
,
and
for
which
my self
and
others
are
induced
to
hold
it
mountainous
,
I
believe
you
will
not
find
any
one
that
will
be
satisfied
with
such
a
doctrine
;
nor
can
I
think
,
that
either
you
,
or
the
Author
himself
,
find
in
it
any
greater
quietude
,
The
apparent
unevennesses
of
the
Moon
cannot
be
imitated
by
way
of
more
and
less
opacity
&
perspicuity
.
than
in
any
other
thing
wide
from
the
purpose
.
Of
the
very
many
several
appearances
which
are
seen
night
by
night
in
the
course
of
Moon
,
you
cannot
imitate
so
much
as
one
,
by
making
a
Ball
at
your
choice
,
more
or
less
opacous
and
perspicuous
,
and
that
is
of
a
polite
superficies
;
The
various
aspects
of
the
Moon
,
imitable
with
any
opacous
matter
.
whereas
on
the
contrary
,
one
may
make
Balls
of
any
solid
matter
whatsoever
,
that
is
not
transparent
,
which
onely
with
eminencies
and
cavities
,
and
by
receiving
the
illumination
several
ways
,
shall
represent
the
same
appearances
and
mutations
to
an
hair
,
Various
appearances
from
which
the
Moons
montuosity
is
argued
.
which
from
hour
to
hour
are
discovered
in
the
Moon
.
In
them
you
shall
see
the
ledges
of
Hills
exposed
to
the
Suns
light
,
to
be
very
shining
,
and
after
them
the
projections
of
their
shadows
very
obscure
;
you
shall
see
them
greater
and
less
,
according
as
the
said
eminencies
shall
be
more
or
less
distant
from
the
confines
which
distinguish
the
parts
of
the
Moon
illuminated
,
from
the
obscure
:
you
shall
see
the
same
term
and
confine
,
not
equally
distended
,
as
it
would
be
if
the
Ball
were
polish'd
,
but
craggie
and
rugged
.
You
shall
see
beyond
the
same
term
,
in
the
dark
parts
of
the
Moon
many
bright
prominencies
,
and
distinct
from
the
rest
of
the
illuminations
:
you
shall
see
the
shadows
aforesaid
,
according
as
the
illumination
gradually
riseth
,
to
deminish
by
degrees
,
till
they
wholly
disappear
;
nor
are
there
any
of
them
to
be
seen
when
the
whole
Hemisphere
is
enlightned
.
Again
on
the
contrary
,
in
the
lights
passage
towards
the
other
Hemisphere
of
the
Moon
,
you
shall
again
observe
the
same
eminencies
that
were
marked
,
and
you
shall
see
the
projections
of
their
shadows
to
be
made
a
contrary
way
,
and
to
decrease
by
degrees
:
of
which
things
,
once
more
I
say
,
you
cannot
shew
me
so
much
as
one
in
yours
that
are
opacous
and
perspicuous
.
SAGR.
One
of
them
certainly
he
may
imitate
,
namely
,
that
of
the
Full-Moon
,
when
by
reason
of
its
being
all
illuminated
,
there
is
not
to
be
seen
either
shadow
,
or
other
thing
,
which
receiveth
any
alteration
from
its
eminencies
and
cavities
.
But
I
beseech
you
,
Salviatus
,
let
us
spend
no
more
time
on
this
Argument
,
for
a
person
that
hath
had
but
the
patience
to
make
observation
of
but
one
or
two
Lunations
,
and
is
not
satisfied
with
this
most
sensible
truth
,
may
well
be
adjudged
void
of
all
judgment
;
and
upon
such
why
should
we
throw
away
our
time
and
breath
in
vain
?
SIMPL.
I
must
confess
I
have
not
made
the
observations
,
for
that
I
never
had
so
much
curiosity
,
or
the
Instruments
proper
for
the
business
;
but
I
will
not
fail
to
do
it
.
In
the
mean
time
,
we
may
leave
this
question
in
suspense
,
and
pass
to
that
point
which
follows
,
producing
the
motives
inducing
you
to
think
that
the
Earth
may
reflect
the
light
of
the
Sun
no
less
forceably
than
the
Moon
,
for
it
seems
to
me
so
obscure
and
opacous
,
that
I
judg
such
an
effect
altogether
impossible
.
SALV
.
The
cause
for
which
you
repute
the
Earth
unapt
for
illumination
,
may
rather
evince
the
contrary
:
And
would
it
not
be
strange
,
Simplicius
,
if
I
should
apprehend
your
discourses
better
than
you
your self
?
SIMPL.
Whether
I
argue
well
or
ill
,
it
may
be
,
that
you
may
better
understand
the
same
than
I
;
but
be
it
ill
or
well
that
I
discourse
,
I
shall
never
believe
that
you
can
penetrate
what
I
mean
better
than
I
my self
.
SALV
.
Well
,
I
will
make
you
believe
the
same
presently
.
Tell
me
a
little
,
when
the
Moon
is
near
the
Full
,
so
that
it
may
be
seen
by
day
,
and
also
at
midnight
,
at
what
do
you
think
it
more
splendid
,
by
day
or
by
night
?
SIMPL.
By
night
,
The
Moon
appears
brighter
by
night
than
by
day
.
without
all
comparison
.
And
methinks
the
Moon
resembleth
that
pillar
of
Clouds
and
pillar
of
Fire
,
which
guided
the
Israelites
;
which
at
the
presence
of
the
Sun
,
appeared
like
a
Cloud
,
but
in
the
night
was
very
glorious
.
Thus
I
have
by
day
observed
the
Moon
amidst
certain
small
Clouds
,
The
Moon
beheld
in
the
day
time
,
is
like
to
a
little
cloud
.
just
as
if
one
of
them
had
been
coloured
white
,
but
by
night
it
shines
with
much
splendor
.
SALV
.
So
that
if
you
had
never
happened
to
see
the
Moon
,
save
onely
in
the
day
time
,
you
would
not
have
thought
it
more
shining
than
one
of
those
Clouds
.
SIMPL.
I
verily
believe
I
should
not
.
SALV
.
Tell
me
now
;
do
you
believe
that
the
Moon
is
really
more
shining
in
the
night
than
day
,
or
that
by
some
accident
it
seemeth
so
?
SIMPL.
I
am
of
opinion
,
that
it
resplends
in
it self
as
much
in
the
day
as
night
,
but
that
its
light
appears
greater
by
night
,
because
we
behold
it
in
the
dark
mantle
of
Heaven
;
and
in
the
day
time
,
the
whole
Atmosphere
being
very
clear
,
so
that
she
little
exceedeth
it
in
lustre
,
she
seems
to
us
much
less
bright
.
SALV
.
Now
tell
me
;
have
you
ever
at
midnight
seen
the
Terrestrial
Globe
illuminated
by
the
Sun
?
SIMPL.
This
seemeth
to
me
a
question
not
to
be
ask'd
,
unless
in
jest
,
or
of
some
person
known
to
be
altogether
void
of
sense
.
SALV
.
No
,
no
;
I
esteem
you
to
be
a
very
rational
man
,
and
do
ask
the
question
seriously
;
and
therefore
answer
me
:
and
if
afterwards
you
shall
think
that
I
speak
impertinently
,
I
will
be
content
to
be
the
senseless
man
:
for
he
is
much
more
a
fool
who
interrogates
simply
,
than
he
to
whom
the
question
is
put
.
SIMPL.
If
then
you
do
not
think
me
altogether
simple
,
take
it
for
granted
that
I
have
answered
you
already
,
and
said
,
that
it
is
impossible
,
that
one
that
is
upon
the
Earth
,
as
we
are
,
should
see
by
night
that
part
of
the
Earth
where
it
is
day
,
namely
,
that
is
illuminated
by
the
Sun
.
SALV
.
Therefore
you
have
never
seen
the
Earth
enlightned
,
save
onely
by
day
;
but
you
see
the
Moon
to
shine
also
in
the
dead
of
night
.
And
this
is
the
cause
,
Simplicius
,
which
makes
you
believe
that
the
Earth
doth
not
shine
like
the
Moon
;
but
if
you
could
see
the
Earth
illuminated
,
whilst
you
were
in
some
dark
place
,
like
our
night
,
you
would
see
it
shine
brighter
than
the
Moon
.
Now
if
you
desire
that
the
comparison
may
proceed
well
,
you
must
compare
the
light
of
the
Earth
,
with
that
of
the
Moon
seen
in
the
day
time
,
and
not
with
the
same
by
night
:
for
it
is
not
in
our
power
to
see
the
Earth
illuminated
,
save
onely
in
the
day
.
Is
it
not
so
?
SIMPL.
So
it
ought
to
be
.
SALV
.
And
forasmuch
as
you
your self
have
already
confessed
to
have
seen
the
Moon
by
day
among
some
little
white
Clouds
,
and
very
nearly
,
as
to
its
aspect
,
resembling
one
of
them
;
you
did
thereby
grant
,
Clouds
are
no
less
apt
than
the
Moon
to
be
illuminated
by
the
Sun
.
that
those
Clouds
,
which
yet
are
Elementary
matters
,
are
as
apt
to
receive
illumination
,
as
the
Moon
,
yea
more
,
if
you
will
but
call
to
mind
that
you
have
sometimes
seen
some
Clouds
of
vast
greatness
,
and
as
perfect
white
as
the
Snow
;
and
there
is
no
question
,
but
that
if
such
a
Cloud
could
be
continued
so
luminous
in
the
deep
of
night
,
it
would
illuminate
the
places
near
about
it
,
more
than
an
hundred
Moons
.
If
therefore
we
were
assured
that
the
Earth
is
illuminated
by
the
Sun
,
like
one
of
those
Clouds
,
it
would
be
undubitable
,
but
that
it
would
be
no
less
shining
than
the
Moon
.
But
of
this
there
is
no
question
to
be
made
,
in
regard
we
see
those
very
Clouds
in
the
absence
of
the
Sun
,
to
remain
by
night
,
as
obscure
as
the
Earth
:
and
that
which
is
more
,
there
is
not
any
one
of
us
,
but
hath
seen
many
times
some
such
Clouds
low
,
and
far
off
,
and
questioned
whether
they
were
Clouds
or
Mountains
:
an
evident
sign
that
the
Mountains
are
no
less
luminous
than
those
Clouds
.
A
wall
illuminated
by
the
Sun
,
compared
to
the
Moon
shineth
no
less
than
it
.
SAGR.
But
what
needs
more
discourse
?
See
yonder
the
Moon
is
risen
,
and
more
than
half
of
it
illuminated
;
see
there
that
wall
,
on
which
the
Sun
shineth
;
retire
a
little
this
way
,
so
that
you
see
the
Moon
sideways
with
the
wall
:
look
now
;
which
of
them
shews
more
lucid
?
Do
not
you
see
,
that
if
there
is
any
advantage
,
the
wall
hath
it
?
The
Sun
shineth
on
that
wall
;
from
thence
it
is
reverberated
upon
the
wall
of
the
Hall
,
The
third
reflection
of
a
Wall
illuminates
more
than
the
first
of
the
Moon
.
from
thence
it
's
reflected
upon
that
chamber
,
so
that
it
falls
on
it
at
the
third
reflection
:
and
I
am
very
certain
,
that
there
is
in
that
place
more
light
,
than
if
the
Moons
light
had
directly
faln
upon
it
.
SIMPL.
But
this
I
cannot
believe
;
for
the
illumination
of
the
Moon
,
especially
when
it
is
at
the
full
,
is
very
great
.
SAGR.
It
seemeth
great
by
reason
of
the
circumjacent
dark
places
;
The
light
of
the
Moon
weaker
than
that
of
the
twilight
.
but
absolutely
it
is
not
much
,
and
is
less
than
that
of
the
twilight
half
an
hour
after
the
Sun
is
set
;
which
is
manifest
,
because
you
see
not
the
shadows
of
the
bodies
illuminated
by
the
Moon
till
then
,
to
begin
to
be
distinguished
on
the
Earth
.
Whether
,
again
,
that
third
reflection
upon
that
chamber
,
illuminates
more
than
the
first
of
the
Moon
,
may
be
known
by
going
thether
,
and
reading
a
Book
,
and
afterwards
standing
there
in
the
night
by
the
Moons
light
,
which
will
shew
by
which
of
them
lights
one
may
read
more
or
less
plainly
,
but
I
believe
without
further
tryal
,
that
one
should
see
less
distinctly
by
this
later
.
SALV
.
Now
,
Simplicius
,
(
if
haply
you
be
satisfied
)
you
may
conceive
,
as
you
your self
know
very
well
,
that
the
Earth
doth
shine
no
less
than
the
Moon
;
and
the
only
remembring
you
of
some
things
,
which
you
knew
of
your self
,
and
learn'd
not
of
me
,
hath
assured
you
thereof
:
for
I
taught
you
not
that
the
Moon
shews
lighter
by
night
than
by
day
,
but
you
understood
it
of
your self
;
as
also
you
could
tell
me
that
a
little
Cloud
appeareth
as
lucid
as
the
Moon
:
you
knew
also
,
that
the
illumination
of
the
Earth
cannot
be
seen
by
night
;
and
in
a
word
,
you
knew
all
this
,
without
knowing
that
you
knew
it
.
So
that
you
have
no
reason
to
be
scrupulous
of
granting
,
that
the
dark
part
of
the
Earth
may
illuminate
the
dark
part
of
the
Moon
,
with
no
less
a
light
than
that
wherewith
the
Moon
illuminates
the
obscurities
of
the
night
,
yea
rather
so
much
the
greater
,
inasmuch
as
the
Earth
is
forty
times
bigger
than
the
Moon
.
SIMPL.
I
must
confess
that
I
did
believe
,
that
that
secondary
light
had
been
the
natural
light
of
the
Moon
.
SALV
.
And
this
also
you
know
of
your self
,
and
perceive
not
that
you
know
it
.
Tell
me
,
do
not
you
know
without
teaching
,
that
the
Moon
shews
it self
more
bright
by
night
than
by
day
,
Lum
nous
bodies
appear
the
brighter
in
an
obscurer
ambient
.
in
respect
of
the
obscurity
of
the
space
of
the
ambient
?
and
confequently
,
do
you
not
know
in
genere
,
that
every
bright
body
shews
the
clearer
,
by
how
much
the
ambient
is
obscurer
?
SIMPL.
This
I
know
very
well
.
SALV
.
When
the
Moon
is
horned
,
and
that
secondary
light
seemeth
to
you
very
bright
,
is
it
not
ever
nigh
the
Sun
,
and
consequently
,
in
the
light
of
the
crepusculum
,
(
twilight
?
)
SIMPL.
It
is
so
;
and
I
have
oftentimes
wish'd
that
the
Air
would
grow
thicker
,
that
I
might
be
able
to
see
that
same
light
more
plainly
;
but
it
ever
disappeared
before
dark
night
.
SALV
.
You
know
then
very
certainly
,
that
in
the
depth
of
night
,
that
light
would
be
more
conspicuous
.
SIMPL.
I
do
so
;
and
also
more
than
that
,
if
one
could
but
take
away
the
great
light
of
the
crescent
illuminated
by
the
Sun
,
the
presence
of
which
much
obscureth
the
other
lesser
.
SALV
.
Why
,
doth
it
not
sometimes
come
to
pass
,
that
one
may
in
a
very
dark
night
see
the
whole
face
of
the
Moon
,
without
being
at
all
illuminated
by
the
Sun
?
SIMPL.
I
know
not
whether
this
ever
happeneth
,
save
onely
in
the
total
Ecclipses
of
the
Moon
.
SALV
.
Why
,
at
that
time
this
its
light
would
appear
very
clear
,
being
in
a
most
obscure
medium
,
and
not
darkned
by
the
clarity
of
the
luminous
crescents
:
but
in
that
position
,
how
light
did
it
appear
to
you
?
SIMPL.
I
have
sometimes
seen
it
of
the
colour
of
brass
,
and
a
little
whitish
;
but
at
other
times
it
hath
been
so
obscure
,
that
I
have
wholly
lost
the
sight
of
it
.
SALV
.
How
then
can
that
light
be
so
natural
,
which
you
see
so
cleer
in
the
close
of
the
twilight
,
notwithstanding
the
impediment
of
the
great
and
contiguous
splendor
of
the
crescents
;
and
which
again
,
in
the
more
obscure
time
of
night
,
all
other
light
removed
,
appears
not
at
all
?
SIMPL.
I
have
heard
of
some
that
believed
that
same
light
to
be
participated
to
these
crescents
from
the
other
Stars
,
and
in
particular
from
Venus
,
the
Moons
neighbour
.
SALV
.
And
this
likewise
is
a
vanity
;
because
in
the
time
of
its
total
obscuration
,
it
ought
to
appear
more
shining
than
ever
;
for
you
cannot
say
,
that
the
shadow
of
the
Earth
intercepts
the
sight
of
Venus
,
or
the
other
Stars
.
But
to
say
true
,
it
is
not
at
that
instant
wholly
deprived
thereof
,
for
that
the
Terrestrial
Hemisphere
,
which
in
that
time
looketh
towards
the
Moon
,
is
that
where
it
is
night
,
that
is
,
an
intire
privation
of
the
light
of
the
Sun
.
And
if
you
but
diligently
observe
,
you
will
very
sensibly
perceive
,
that
like
as
the
Moon
,
when
it
is
sharp-horned
,
doth
give
very
little
light
to
the
Earth
;
and
according
as
in
her
the
parts
illuminated
by
the
Suns
light
do
encrease
:
so
likewise
the
splendor
to
our
seeming
encreaseth
,
which
from
her
is
reflected
towards
us
;
thus
the
Moon
,
whilst
it
is
sharp-forked
,
and
that
by
being
between
the
Sun
and
the
Earth
,
it
discovereth
a
very
great
part
of
the
Terrestrial
Hemisphere
illuminated
,
appeareth
very
clear
:
and
departing
from
the
Sun
,
and
passing
towards
the
[
](A61244-e19070-b)*
*
By
the
Moons
two
Quadratures
you
are
to
understand
its
first
and
last
quarters
,
as
Astrologers
call
them
▪
Quadrature
,
you
may
see
the
said
light
by
degrees
to
grow
dim
;
and
after
the
Quadrature
,
the
same
appears
very
weak
,
because
it
continually
loseth
more
and
more
of
the
view
of
the
luminous
part
of
the
Earth
:
and
yet
it
should
succeed
quite
contrary
,
if
that
light
were
its
own
,
or
communicated
to
it
from
the
Stars
;
for
then
we
should
see
it
in
the
depth
of
night
,
and
in
so
very
dark
an
ambient
.
SIMPL.
Stay
a
little
;
for
I
just
now
remember
,
that
I
have
read
in
a
little
modern
tract
,
full
of
many
novelties
;
That
this
secondary
light
is
not
derived
from
the
Stars
,
nor
innate
in
the
Moon
,
and
least
of
all
communicated
by
the
Earth
,
but
that
it
is
received
from
the
same
illumination
of
the
Sun
,
The
secondary
light
of
the
Moon
caused
by
the
Sun
,
according
to
some
.
which
,
the
substance
of
the
Lunar
Globe
being
somewhat
transparent
,
penetrateth
thorow
all
its
body
;
but
more
livelily
illuminateth
the
superficies
of
the
Hemisphere
exposed
to
the
rays
of
the
Sun
▪
and
its
profundity
imbuing
,
and
(
as
I
may
say
)
swallowing
that
light
,
after
the
manner
of
a
cloud
or
chrystal
,
transmits
it
,
and
renders
it
visibly
lucid
.
And
this
(
if
I
remember
aright
)
he
proveth
by
Authority
,
Experience
and
Reason
;
citing
Cleomedes
,
Vitellion
,
Macrobius
,
and
a
certain
other
modern
Author
:
and
adding
,
That
it
is
seen
by
experience
to
shine
most
in
the
days
nearest
the
Conjunction
,
that
is
,
when
it
is
horned
,
and
is
chiefly
bright
about
its
limb
.
And
he
farther
writes
,
That
in
the
Solar
Ecclipses
,
when
it
is
under
the
Discus
of
the
Sun
,
it
may
be
seen
translucid
,
and
more
especially
towards
its
utmost
Circle
.
And
in
the
next
place
,
for
Arguments
,
as
I
think
,
he
saith
,
That
it
not
being
able
to
derive
that
light
either
from
the
Earth
,
or
from
the
Stars
,
or
from
it self
,
it
necessarily
follows
,
that
it
cometh
from
the
Sun
.
Besides
that
,
if
you
do
but
grant
this
supposition
,
one
may
easily
give
convenient
reasons
for
all
the
particulars
that
occur
.
For
the
reason
why
that
secundary
light
shews
more
lively
towards
the
outmost
limb
,
is
,
the
shortness
of
the
space
that
the
Suns
rays
hath
to
penetrate
,
in
regard
that
of
the
lines
which
pass
through
a
circle
,
the
greatest
is
that
which
passeth
through
the
centre
,
and
of
the
rest
,
those
which
are
farthest
from
it
,
are
always
less
than
those
that
are
nearer
.
From
the
same
principle
,
he
saith
,
may
be
shewn
why
the
said
light
doth
not
much
diminish
.
And
lastly
,
by
this
way
the
cause
is
assigned
whence
it
comes
,
that
that
same
more
shining
circle
about
the
utmost
edge
of
the
Moon
,
is
seen
at
the
time
of
the
Solar
Ecclipse
,
in
that
part
which
lyeth
just
under
the
Discus
of
the
Sun
,
but
not
in
that
which
is
beside
the
Discus
:
which
happeneth
because
the
rays
of
the
Sun
pass
directly
to
our
eye
,
through
the
parts
of
the
Moon
underneath
:
but
as
for
the
parts
which
are
besides
it
,
they
fall
besides
the
eye
.
SALV
.
If
this
Philosopher
had
been
the
first
Author
of
this
opinion
,
I
would
not
wonder
that
he
should
be
so
affectionate
to
it
,
as
to
have
received
it
for
truth
;
but
borrowing
it
from
others
,
I
cannot
find
any
reason
sufficient
to
excuse
him
for
not
perceiving
it●
fallacies
;
and
especially
after
he
had
heard
the
true
cause
of
that
effect
,
and
had
it
in
his
power
to
satisfie
himself
by
a
thousand
experiments
,
and
manifest
circumstances
,
that
the
same
proceeded
from
the
reflection
of
the
Earth
,
and
from
nothing
else
:
and
the
more
this
speculation
makes
something
to
be
desired
,
in
the
judgment
of
this
Author
,
and
of
all
those
who
give
no
credit
to
it
:
so
much
the
more
doth
their
not
having
understood
and
remembred
it
,
excuse
those
more
recess
Antients
,
who
,
I
am
very
certain
,
did
they
now
understand
it
,
would
without
the
least
repugnance
admit
thereof
.
And
if
I
may
freely
tell
you
what
I
think
,
I
cannot
believe
but
that
this
Modern
doth
in
his
heart
believe
it
;
but
I
rather
think
,
that
the
conceit
he
should
not
be
the
first
Author
thereof
,
did
a
little
move
him
to
endeavour
to
suppresse
it
,
or
to
disparage
it
at
least
amongst
the
simple
,
whose
number
we
know
to
be
very
great
;
and
many
there
are
,
who
much
more
affect
the
numerous
applauds
of
the
people
,
than
the
approbation
of
a
few
not
vulgar
judgments
.
SAGR.
Hold
good
Salviatus
,
for
me
thinks
,
I
see
that
you
go
not
the
way
to
hit
the
true
mark
in
this
your
discourse
,
for
these
that
[
](A61244-e19260-b)*
*
Tendono
le
parete
al
commune
.
confound
all
propriety
,
know
also
how
to
make
themselves
Authors
of
others
Inventions
,
provided
they
be
not
so
stale
,
and
publick
in
the
Schools
and
Market-places
,
as
that
they
are
more
then
notorious
to
every
one
.
SALV
.
Ha!
well
aimed
,
you
blame
me
for
roving
from
the
point
in
hand
;
but
what
have
you
to
do
with
Schools
and
Markets
?
It
s
all
one
whether
opinions
be
new
to
men
,
or
men
new
to
opinions
.
Is
it
not
all
one
whether
opinions
and
inventions
be
new
to
men
,
or
the
men
new
to
them
?
If
you
[
](A61244-e19310-b)*
*
Contestare
falsly
rendered
in
the
Latine
Translation
contentare
.
contend
about
the
esteem
of
the
Founders
of
Sciences
,
which
in
all
times
do
start
up
,
you
may
make
your self
their
inventor
,
even
to
the
Alphabet
it self
,
and
so
gain
admiration
amongst
that
illiterate
rabble
;
and
though
in
processe
of
time
your
craft
should
be
perceived
,
that
would
but
little
prejudice
your
designe
;
for
that
others
would
succeed
them
in
maintaining
the
number
of
your
fautors
;
but
let
us
return
to
prove
to
Simplicius
the
invalidity
of
the
reasons
of
his
modern
Author
,
in
which
there
are
several
falsities
,
inconsequencies
,
The
secondary
light
of
the
Mo●n
appears
in
form
of
a
Ring
,
that
is
to
say
,
bright
in
the
extreme
circumference
,
and
not
●n
the
midst
,
and
why
▪
and
incredible
Paradoxes
.
And
first
,
it
is
false
that
this
secondary
light
is
clearer
about
the
utmost
limb
than
in
the
middle
parts
,
so
as
to
form
,
as
it
were
,
a
ring
or
circle
more
bright
than
the
rest
of
its
space
or
contence
.
True
it
is
,
indeed
,
that
looking
on
the
Moon
at
the
time
of
twilight
,
at
first
sight
there
is
the
resemblance
of
such
a
circle
,
but
by
an
illusion
arising
from
the
diversity
of
confines
that
bound
the
Moons
Discus
,
which
are
confused
by
means
of
this
secondary
light
;
forasmuch
as
on
the
part
towards
the
Sun
it
is
bounded
by
the
lucid
horns
of
the
Moon
,
and
on
the
other
part
,
its
confining
term
is
the
obscure
tract
of
the
twilight
;
whose
relation
makes
us
think
the
candor
of
the
Moons
Discus
to
be
so
much
the
clearer
;
the
which
happens
to
be
obfuscated
in
the
opposite
part
,
by
the
greater
clarity
of
the
crescents
;
but
if
this
modern
Author
had
essaied
to
make
an
interposition
between
the
eye
and
the
primary
splendor
,
The
way
to
observe
the
secondary
light
of
the
Moon
.
by
the
ridg
of
some
house
,
or
some
other
screen
,
so
as
to
have
left
visible
only
the
grose
of
the
Moon
,
the
horns
excluded
,
he
might
have
seen
it
all
alike
luminous
.
SIMPL
,
I
think
,
now
I
remember
,
that
he
writes
of
his
making
use
of
such
another
Artifice
,
to
hide
from
us
the
false
lucidum
.
SALV
.
Oh!
how
is
this
(
as
I
believed
)
inadvertency
of
his
,
changed
into
a
lie
,
bordering
on
rashnesse
;
for
that
every
one
may
frequently
make
proof
of
the
contrary
.
That
in
the
next
place
,
The
Moons
Discus
in
a
solar
Eclipse
can
be
seen
onely
by
privation
.
at
the
Suns
Eclipse
,
the
Moons
Discus
is
seen
otherwayes
than
by
privation
,
I
much
doubt
,
and
specially
when
the
Eclipse
is
not
total
,
as
those
must
necessarily
have
been
,
which
were
observed
by
the
Author
;
but
if
also
he
should
have
discovered
somewhat
of
light
,
this
contradicts
not
,
rather
favoureth
our
opinion
;
for
that
at
such
a
time
,
the
whole
Terrestrial
Hemisphere
illuminated
by
the
Sun
,
is
opposite
to
the
Moon
,
so
that
although
the
Moons
shadow
doth
obscure
a
part
thereof
,
yet
this
is
very
small
in
comparison
of
that
which
remains
illuminated
.
That
which
he
farther
adds
,
that
in
this
case
,
the
part
of
the
limb
,
lying
under
the
Sun
,
doth
appear
very
lucid
,
but
that
which
lyeth
besides
it
,
not
so
;
and
that
to
proceed
from
the
coming
of
the
solar
rayes
directly
through
that
part
to
the
eye
,
but
not
through
this
,
is
really
one
of
those
fopperies
,
which
discover
the
other
fictions
,
of
him
which
relates
them
:
For
if
it
be
requisite
to
the
making
a
secondary
light
visible
in
the
lunar
Discus
,
that
the
rayes
of
the
Sun
came
directly
through
it
to
our
eyes
,
doth
not
this
pitiful
Philosopher
perceive
,
that
we
should
never
see
this
same
secondary
light
,
save
onely
at
the
Eclipse
of
the
Sun
?
And
if
a
part
onely
of
the
Moon
,
far
lesse
than
half
a
degree
,
by
being
remote
from
the
Suns
Discus
,
can
deflect
or
deviate
the
rayes
of
the
Sun
,
so
that
they
arrive
not
at
our
eye
;
what
shall
it
do
when
it
is
distant
twenty
or
thirty
degrees
,
as
it
is
at
its
first
apparition
?
and
what
course
shall
the
rayes
of
the
Sun
keep
,
which
are
to
passe
thorow
the
body
of
the
Moon
,
that
they
may
find
out
our
eye
?
The
Author
of
the
Book
of
conclusions
,
accommodates
the
things
to
his
purposes
,
and
not
his
purposes
to
the
things
.
This
man
doth
go
successively
considering
what
things
ought
to
be
,
that
they
may
serve
his
purpose
,
but
doth
not
gradually
proceed
,
accommodating
his
conceits
to
the
things
,
as
really
they
are
.
As
for
instance
,
to
make
the
light
of
the
Sun
capable
to
penetrate
the
substance
of
the
Moon
,
he
makes
her
in
part
diaphanous
,
as
is
v.
g.
the
transparence
of
a
cloud
,
or
crystal
:
but
I
know
not
what
he
would
think
of
such
a
transparency
,
in
case
the
solar
rayes
were
to
passe
a
depth
of
clouds
of
above
two
thousand
miles
;
but
let
it
be
supposed
that
he
should
boldly
answer
,
that
might
well
be
in
the
Coelestial
,
which
are
quite
other
things
from
these
our
Elementary
,
impure
,
and
feculent
bodies
;
and
let
us
convict
his
error
by
such
wayes
,
as
admit
him
no
reply
,
or
(
to
say
better
)
subter-fuge
.
If
he
will
maintain
,
that
the
substance
of
the
Moon
is
diaphanous
,
he
must
say
that
it
is
so
,
whilest
that
the
rayes
of
the
Sun
are
to
penetrate
its
whole
profundity
,
that
is
,
more
than
two
thousand
miles
;
but
that
if
you
oppose
unto
them
onely
one
mile
,
or
lesse
,
they
should
no
more
penetrate
that
,
than
they
penetrate
one
of
our
mountains
.
SAGR.
You
put
me
in
mind
of
a
man
,
A
jest
put
upon
one
that
would
sell
a
certain
secret
for
holding
correspondency
with
a
person
a
thousand
miles
off
.
who
would
have
sold
me
a
secret
how
to
correspond
,
by
means
of
a
certain
sympathy
of
magnetick
needles
,
with
one
,
that
should
be
two
or
three
thousand
miles
distant
;
and
I
telling
him
,
that
I
would
willingly
buy
the
same
,
but
that
I
desired
first
to
see
the
experiment
thereof
,
and
that
it
did
suffice
me
to
make
it
,
I
being
in
one
Chamber
,
and
he
in
the
next
,
he
answered
me
,
that
in
so
small
a
distance
one
could
not
so
well
perceive
the
operation
;
whereupon
I
turn'd
him
going
,
telling
him
,
that
I
had
no
mind
,
at
that
time
,
to
take
a
journey
unto
Grand
Cairo
,
or
to
Muscovy
,
to
make
the
experiment
;
but
that
,
if
he
would
go
himself
,
I
would
perform
the
other
part
,
staying
in
Venice
.
But
let
us
hear
whither
the
deduction
of
our
Author
tendeth
,
and
what
necessity
there
is
,
that
he
must
grant
the
matter
of
the
Moon
to
be
most
perforable
by
the
rayes
of
the
Sun
,
in
a
depth
of
two
thousand
miles
,
but
more
opacous
than
one
of
our
mountains
,
in
a
thicknesse
of
one
mile
onely
.
SALV
.
The
very
mountains
of
the
Moon
themselves
are
a
proof
thereof
,
which
percussed
on
one
side
of
the
Sun
,
do
cast
on
the
contrary
side
very
dark
shadows
,
terminate
,
and
more
distinct
by
much
,
than
the
shadows
of
ours
;
but
had
these
mountains
been
diaphanous
,
we
could
never
have
come
to
the
knowledg
of
any
unevennesse
in
the
superficies
of
the
Moon
,
not
have
seen
those
luminous
montuosities
distinguished
by
the
terms
which
separate
the
lucid
parts
from
the
dark
:
much
lesse
,
should
we
see
this
same
term
so
distinct
,
if
it
were
true
,
that
the
Suns
light
did
penetrate
the
whole
thicknesse
of
the
Moon
;
yea
rather
,
according
to
the
Authors
own
words
,
we
should
of
necessity
discern
the
passage
,
and
confine
,
between
the
part
of
the
Sun
seen
,
and
the
part
not
seen
,
to
be
very
confused
,
and
mixt
with
light
and
darknesse
;
for
that
that
matter
which
admits
the
passage
of
the
Suns
rayes
thorow
a
space
of
two
thousand
miles
,
must
needs
be
so
transparent
,
that
it
would
very
weakly
resist
them
in
a
hundredth
,
or
lesser
part
of
that
thicknesse
;
neverthelesse
,
the
term
which
separateth
the
part
illuminated
from
the
obscure
,
is
incident
,
and
as
distinct
,
as
white
is
distinct
from
black
;
and
especially
where
the
Section
passeth
through
the
part
of
the
Moon
,
that
is
naturally
more
clear
and
montanous
;
but
where
the
old
spots
do
part
,
which
are
certain
plains
,
that
by
means
of
their
spherical
inclination
,
receive
the
rayes
of
the
Sun
obliquely
,
there
the
term
is
not
so
distinct
,
by
reason
of
the
more
dimme
illumination
.
That
,
lastly
,
which
he
saith
,
how
that
the
secondary
light
doth
not
diminish
and
languish
,
according
as
the
Moon
encreaseth
,
but
conserveth
it self
continually
in
the
same
efficacy
;
is
most
false
;
nay
it
is
hardly
seen
in
the
quadrature
,
when
,
on
the
contrary
,
it
should
appear
more
splendid
,
and
be
visible
after
the
crepusculum
in
the
dark
of
night
.
Let
us
conclude
therefore
,
that
the
Earths
reflection
is
very
strong
upon
the
Moon
;
and
that
,
which
you
ought
more
to
esteem
,
we
may
deduce
from
thence
another
admirable
congruity
between
the
Moon
and
Earth
;
namely
,
The
Earth
may
reciprocally
operate
upon
Coelestial
bodies
,
with
its
light
.
that
if
it
be
true
,
the
Planets
operate
upon
the
Earth
by
their
motion
and
light
,
the
Earth
may
probably
be
no
lesse
potent
in
operating
reciprocally
upon
them
with
the
same
light
,
and
peradventure
,
motion
also
.
And
though
it
should
not
move
,
yet
may
it
retain
the
same
operation
;
because
,
as
it
hath
been
proved
already
,
the
action
of
the
light
is
the
self
same
,
I
mean
of
the
light
of
the
Sun
reflected
;
and
motion
doth
nothing
,
save
only
vary
the
aspects
,
which
fall
out
in
the
same
manner
,
whether
we
make
the
Earth
move
,
and
the
Sun
stand
still
,
or
the
contrary
.
SIMPL.
None
of
the
Philosophers
are
found
to
have
said
,
that
these
inferiour
bodies
operate
on
the
Coelestial
,
nay
,
Aristotle
affirmes
the
direct
contrary
.
SALV
.
Aristotle
and
the
rest
,
who
knew
not
that
the
Earth
and
Moon
mutually
illuminated
each
other
,
are
to
be
excused
;
but
they
would
justly
deserve
our
censure
,
if
whilest
they
desire
that
we
should
grant
and
believe
with
them
,
that
the
Moon
operateth
upon
the
Earth
with
light
,
they
should
deny
to
us
,
who
have
taught
them
that
the
Earth
illuminates
the
Moon
,
the
operation
the
Earth
hath
on
the
Moon
.
SIMPL.
In
short
,
I
find
in
my self
a
great
unwillingnesse
to
admit
this
commerce
,
which
you
would
perswade
me
to
be
betwixt
the
Earth
and
Moon
,
placing
it
,
as
we
say
,
amongst
the
number
of
the
Stars
;
for
if
there
were
nothing
else
,
the
great
separation
and
distance
between
it
and
the
Coelestial
bodies
,
doth
in
my
opinion
necessarily
conclude
a
vast
disparity
between
them
.
SALV
.
See
Simplicius
what
an
inveterate
affection
and
radicated
opinion
can
do
,
since
it
is
so
powerful
,
that
it
makes
you
think
that
those
very
things
favour
you
,
which
you
produce
against
your self
.
For
if
separation
and
distance
are
accidents
sufficient
to
perswade
with
you
a
great
diversity
of
natures
,
it
must
follow
that
proximity
and
contiguity
import
similitude
.
Affinity
between
the
Earth
&
Moon
in
respect
of
their
vicinity
.
Now
how
much
more
neerer
is
the
Moon
to
the
Earth
,
than
to
any
other
of
the
Coelestial
Orbs
?
You
must
acknowledg
therefore
,
according
to
your
own
concession
(
and
you
shall
have
other
Philosophers
bear
you
company
)
that
there
is
a
very
great
affinity
betwixt
the
Earth
and
Moon
.
Now
let
us
proceed
,
and
see
whether
any
thing
remains
to
be
considered
,
touching
those
objections
which
you
made
against
the
resemblances
that
are
between
these
two
bodies
.
SIMPL.
It
rests
,
that
we
say
something
touching
the
solidity
of
the
Moon
,
which
I
argued
from
its
being
exquisite
smooth
and
polite
,
and
you
from
its
montuosity
.
There
is
another
scruple
also
comes
into
my
mind
,
from
an
opinion
which
I
have
,
that
the
Seas
reflection
ought
by
the
equality
of
its
surface
,
to
be
rendered
stronger
than
that
of
the
Earth
,
whose
superficies
is
so
rough
and
opacous
.
SALV
.
As
to
the
first
objection
;
I
say
,
that
like
as
among
the
parts
of
the
Earth
,
Solidity
of
the
Lunar
Globe
argued
from
its
being
montainous
.
which
all
by
their
gravity
strive
to
approach
the
nearest
they
can
possible
to
the
center
,
some
of
them
alwayes
are
more
remote
from
it
than
the
rest
,
as
the
mountains
more
than
the
valleys
,
and
that
by
reason
of
their
solidity
and
firmnesse
(
for
if
they
were
of
fluid
,
they
would
be
even
)
so
the
seeing
some
parts
of
the
Moon
to
be
elevated
above
the
sphericity
of
the
lower
parts
,
argueth
their
hardnesse
;
for
it
is
probable
that
the
matter
of
the
Moon
is
reduced
into
a
spherical
form
by
the
harmonious
conspiration
of
all
its
parts
to
the
same
sentense
.
Touching
the
second
doubt
,
my
thinks
that
the
particulars
already
observed
to
happen
in
the
Looking-glasses
,
may
very
well
assure
us
,
that
the
reflection
of
light
comming
from
the
Sea
,
The
Seas
reflection
of
light
much
weaker
than
that
of
the
Earth
.
is
far
weaker
than
that
which
cometh
from
Land
;
understanding
it
alwayes
of
the
universal
reflection
;
for
as
to
that
particular
,
on
which
the
water
being
calm
,
casteth
upon
a
determinate
place
,
there
is
no
doubt
,
but
that
he
who
shall
stand
in
that
place
,
shall
see
a
very
great
reflection
in
the
water
,
but
every
way
else
he
shall
see
the
surface
of
the
Water
more
obscure
than
that
of
the
Land
;
An
experimen●
to
prove
the
reflection
of
the
Water
lesse
clear
than
that
of
the
Land
.
and
to
prove
it
to
your
senses
,
let
us
go
into
yonder
Hall
,
and
power
forth
a
little
water
upon
the
Pavement
.
Tell
me
now
,
doth
not
this
wet
brick
shew
more
dull
than
the
other
dry
ones
?
Doubtlesse
it
doth
,
and
will
so
appear
,
from
what
place
soever
you
behold
it
,
except
one
onely
,
and
this
is
that
way
which
the
light
cometh
,
that
entereth
in
at
yonder
window
;
go
backwards
therefore
by
a
little
and
a
little
.
SIMPL.
Here
I
see
the
west
part
shine
more
than
all
the
rest
of
the
pavement
,
and
I
see
that
it
so
hapneth
,
because
the
reflection
of
the
light
which
entereth
in
at
the
window
,
cometh
towards
me
.
SALV
.
That
moisture
hath
done
no
more
but
filled
those
little
cavities
which
are
in
the
brick
with
water
,
and
reduced
its
superficies
to
an
exact
evenesse
;
whereupon
the
reflex
rayes
issue
unitedly
towards
one
and
the
same
place
;
but
the
rest
of
the
pavement
which
is
dry
,
hath
its
protuberances
,
that
is
,
an
innumerable
variety
of
inclinations
in
its
smallest
particles
;
whereupon
the
reflections
of
the
light
scatter
towards
all
parts
,
but
more
weakly
than
if
they
had
gone
all
united
together
;
and
therefore
,
the
same
sheweth
almost
all
alike
,
beheld
several
wayes
,
but
far
lesse
clear
than
the
moistned
brick
.
I
conclude
therefore
,
that
the
surface
of
the
Sea
,
beheld
from
the
Moon
,
in
like
manner
,
as
it
would
appear
most
equal
,
(
the
Islands
and
Rocks
deducted
)
so
it
would
shew
lesse
clear
than
that
of
the
Earth
,
which
is
montanous
and
uneven
.
And
but
that
I
would
not
seem
,
as
the
saying
is
,
to
harp
too
much
on
one
string
,
I
could
tell
you
that
I
have
observed
in
the
Moon
that
secondary
light
which
I
told
you
came
to
her
from
the
reflection
of
the
Terrestrial
Globe
,
to
be
notably
more
clear
two
or
three
dayes
before
the
conjunction
,
The
secondary
light
of
the
Moon
clearer
before
the
conjunction
,
than
after
.
than
after
,
that
is
,
when
we
see
it
before
break
of
day
in
the
East
,
than
when
it
is
seen
at
night
after
Sun-set
in
the
West
;
of
which
difference
the
cause
is
,
that
the
Terrestrial
Hemisphere
,
which
looks
towards
the
Eastern
Moon
,
hath
little
Sea
,
and
much
Land
,
to
wit
,
all
Asia
,
whereas
,
when
it
is
in
the
West
,
it
beholds
very
great
Seas
,
that
is
,
the
whole
Atlantick
Ocean
as
far
as
America
:
An
Argument
sufficiently
probable
that
the
surface
of
the
water
appears
lesse
splendid
than
that
of
the
Earth
.
SIMPL.
So
that
perhaps
you
believe
,
those
great
spots
discovered
in
the
face
of
the
Moon
,
to
be
Seas
,
and
the
other
clearer
parts
to
be
Land
,
or
some
such
thing
?
SALV
.
This
which
you
ask
me
,
is
the
beginning
of
those
incongruities
which
I
esteem
to
be
between
the
Moon
and
the
Earth
,
out
of
which
it
is
time
to
dis-ingage
our selves
,
for
we
have
stayed
too
long
in
the
Moon
.
I
say
therefore
,
that
if
there
were
in
nature
but
one
way
onely
,
to
make
two
superficies
illustrated
by
the
Sun
,
to
appear
one
more
clear
than
the
other
,
and
that
this
were
by
the
being
of
the
one
Earth
,
and
the
other
Water
;
it
would
be
necessary
to
say
that
the
surface
of
the
Moon
were
part
earthy
and
part
aquatick
;
but
because
we
know
many
wayes
to
produce
the
same
effect
(
and
others
there
may
be
which
we
know
not
of
;
)
therefore
I
dare
not
affirm
the
Moon
to
consist
of
one
thing
more
than
another
:
It
hath
been
seen
already
that
a
silver
plate
boiled
,
being
toucht
with
the
Burnisher
,
becometh
of
white
obscure
;
that
the
moist
part
of
the
Earth
shews
more
obscure
than
the
dry
;
that
in
the
tops
of
Hills
,
the
woody
parts
appear
more
gloomy
than
the
naked
and
barren
;
which
hapneth
because
there
falleth
very
much
shadow
among
the
Trees
,
but
the
open
places
are
illuminated
all
over
by
the
Sun
.
And
this
mixtion
of
shadow
hath
such
operation
,
that
in
tufted
velvet
,
the
silk
which
is
cut
,
is
of
a
far
darker
colour
than
that
which
is
not
cut
,
by
means
of
the
shadows
diffused
betwixt
thred
and
thred
,
and
a
plain
velvet
shews
much
blacker
than
a
Taffata
,
made
of
the
same
silk
.
So
that
if
there
were
in
the
Moon
things
which
should
look
like
great
Woods
,
their
aspect
might
represent
unto
us
the
spots
which
we
discover
;
alike
difference
would
be
occasioned
,
if
there
were
Seas
in
her
:
and
lastly
,
nothing
hindreth
,
but
that
those
spots
may
really
be
of
an
obscurer
colour
than
the
rest
;
for
thus
the
snow
makes
the
mountains
shew
brighter
.
The
obscurer
parts
of
the
Moon
are
plains
,
and
the
more
bright
mountainous
.
That
which
is
plainly
observed
in
the
Moon
is
,
that
its
most
obscure
parts
are
all
plains
,
with
few
rises
and
bancks
in
them
;
though
some
there
be
;
the
rest
which
is
of
a
brighter
colour
,
is
all
full
of
rocks
,
mountains
,
hillocks
of
spherical
and
other
figures
;
and
in
particular
,
round
about
the
spots
are
very
great
ledges
of
mountains
.
Long
ledges
of
mountains
about
the
spots
of
the
Moon
.
That
the
spots
be
plain
superficies
,
we
have
assured
proof
,
in
that
we
see
,
how
that
the
term
which
distinguisheth
the
part
illuminated
from
the
obscure
,
in
crossing
the
spots
makes
the
intersection
even
,
but
in
the
clear
parts
it
shews
all
craggy
and
shagged
.
But
I
know
not
as
yet
whether
this
evennesse
of
superficies
may
be
sufficient
of
it self
alone
,
to
make
the
obscurity
appear
,
and
I
rather
think
not
.
Besides
,
I
account
the
Moon
exceeding
different
from
the
Earth
;
for
although
I
imagine
to
my self
that
those
are
not
idle
and
dead
Regions
,
There
are
not
generated
in
the
Moon
things
like
to
ours
,
but
if
there
be
any
productions
,
they
are
very
different
.
yet
I
affirm
not
,
that
there
are
in
them
motion
and
life
,
much
less
that
there
are
bred
plants
,
animals
or
other
things
like
to
ours
;
but
,
if
such
there
be
,
they
should
nevertheless
be
very
different
,
and
remote
from
our
imagination
.
And
I
am
induced
so
to
think
,
because
in
the
first
place
,
I
esteem
that
the
matter
of
the
Lunar
Globe
consists
not
of
Earth
and
Water
;
and
this
alone
sufficeth
to
take
away
the
generations
and
alterations
resembling
ours
:
The
Moon
not
composed
of
Water
and
Earth
.
but
now
supposing
that
there
were
in
the
Moon
,
Water
and
Earth
,
yet
would
they
not
produce
plants
and
animals
like
to
ours
;
Those
aspects
of
the
Sun
necessary
for
our
generations
,
are
not
so
in
the
Moon
.
and
this
for
two
principal
reasons
:
The
first
is
,
that
unto
our
productions
there
are
required
so
many
variable
aspects
of
the
Sun
,
that
without
them
they
would
all
miscarry
:
now
the
habitudes
of
the
Sun
towards
the
Earth
are
far
different
from
those
towards
the
Moon
.
We
as
to
the
diurnal
illumination
,
have
,
in
the
greater
part
of
the
Earth
,
every
twenty
four
hours
part
day
,
and
part
night
,
which
effect
in
the
Moon
is
monethly
:
and
that
annual
declination
and
elevation
of
the
Sun
in
the
Zodiack
,
Natural
dayes
in
the
Moon
are
of
a
Moneth
long
.
by
which
it
produceth
diversity
of
Seasons
,
and
inequality
of
dayes
and
nights
,
are
finished
in
the
Moon
in
a
moneth
;
and
whereas
the
Sun
to
us
riseth
and
declineth
so
much
,
To
the
Moon
the
Sun
ascendeth
and
declineth
with
a
difference
of
ten
degrees
,
and
to
the
Earth
of
forty
seven
degrees
.
that
from
the
greatest
to
the
least
altitude
,
there
is
a
difference
of
almost
47
degrees
,
for
so
much
is
the
distance
from
one
to
the
other
Tropick
;
this
is
in
the
Moon
but
ten
degrees
only
,
or
little
more
;
namely
,
as
much
as
the
greatest
Latitudes
of
the
Dragon
on
each
side
the
Ecliptick
.
Now
consider
what
effect
the
Sun
would
have
in
the
torrid
Zone
,
should
it
continually
for
fifteen
dayes
together
beam
forth
its
Rayes
upon
it
;
which
without
all
question
would
destroy
plants
,
herbs
,
and
living
creatures
:
and
if
it
should
chance
that
there
were
any
production
,
it
would
be
of
herbs
,
plants
,
and
creatures
very
different
from
those
which
are
now
there
.
There
are
no
rains
in
the
Moon
.
Secondly
,
I
verily
believe
that
in
the
Moon
there
are
no
rains
,
for
if
Clouds
should
gather
in
any
part
thereof
,
as
they
do
about
the
Earth
,
they
would
thereupon
hide
from
our
sight
some
of
those
things
,
which
we
with
the
Telescope
behold
in
the
Moon
,
and
in
a
word
,
would
some
way
or
other
change
its
Phaenomenon
,
an
effect
which
I
could
never
by
long
and
diligent
observations
discover
;
but
alwayes
beheld
it
in
a
even
and
pure
serenity
.
SAGR.
To
this
may
be
answered
,
either
that
there
might
be
great
mists
,
or
that
it
might
rain
in
the
time
of
their
night
,
that
is
,
when
the
Sun
doth
not
illuminate
it
.
SALV
.
If
other
passages
did
but
assure
us
,
that
there
were
generations
in
it
like
to
ours
,
and
that
there
was
onely
wanting
the
concourse
of
rains
,
we
might
find
out
this
,
or
some
other
temperament
to
serve
instead
thereof
,
as
it
happens
in
Egypt
by
the
inundation
of
Nile
:
but
not
meeting
with
any
accident
,
which
corresponds
with
ours
,
of
many
that
have
been
sought
out
for
the
production
of
the
like
effects
,
we
need
not
trouble
our selves
to
introduce
one
alone
;
and
that
also
,
not
because
we
have
certain
observation
of
it
,
but
for
a
bare
non-repugnance
that
we
find
therein
.
Moreover
,
if
I
was
demanded
what
my
first
apprehension
,
and
pure
natural
reason
dictated
to
me
concerning
the
production
of
things
like
or
unlike
there
above
,
I
would
alwayes
reply
,
that
they
are
most
different
,
and
to
us
altogether
unimaginable
,
for
so
me
thinks
the
riches
of
Nature
,
and
the
omnipotence
of
our
Creator
and
Governour
,
do
require
.
SAGR.
I
ever
accounted
extraordinary
madnesse
that
of
those
,
who
would
make
humane
comprehension
the
measure
of
what
nature
hath
a
power
or
knowledge
to
effect
;
whereas
on
the
contrary
there
is
not
any
the
least
effect
in
Nature
,
The
having
a
perfect
knowledg
of
nothing
,
maketh
some
believe
they
understand
all
things
.
which
can
be
fully
understood
by
the
most
speculative
wits
in
the
world
.
This
their
so
vain
presumption
of
knowing
all
,
can
take
beginning
from
nothing
,
unlesse
from
their
never
having
known
any
thing
;
for
if
one
hath
but
once
onely
experienced
the
perfect
knowledg
of
one
onely
thing
,
and
but
truly
tasted
what
it
is
to
know
,
he
shall
perceive
that
of
infinite
other
conclusions
,
he
understands
not
so
much
as
one
.
SALV
.
Your
discourse
is
very
concluding
;
in
confirmation
of
which
we
have
the
example
of
those
who
understand
,
or
have
known
some
thing
,
which
the
more
knowing
they
are
,
the
more
they
know
,
and
freely
confesse
that
they
know
little
;
nay
,
the
wisest
man
in
all
Greece
,
and
for
such
pronounced
by
the
Oracle
,
openly
professed
to
know
that
he
knew
nothing
.
SIMPL.
It
must
be
granted
therefore
,
either
that
Socrates
or
that
the
Oracle
it self
was
a
lyar
,
that
declaring
him
to
be
most
wise
,
and
he
confessing
that
he
knew
himself
to
be
most
ignorant
.
SALV
.
Neither
one
nor
the
other
doth
follow
,
The
answer
of
the
Oracle
true
in
judging
Socrates
the
wisest
of
his
time
.
for
that
both
the
assertions
may
be
true
.
The
Oracle
adjudged
Socrates
the
wisest
of
all
men
,
whose
knowledg
is
limited
;
Socrates
acknowledgeth
that
he
knew
nothing
in
relation
to
absolute
wisdome
,
which
is
infinite
;
and
because
of
infinite
,
much
is
the
same
part
,
as
is
little
,
and
as
is
nothing
(
for
to
arrive
v.
g.
to
the
infinite
number
,
it
is
all
one
to
accumulate
thousands
,
tens
,
or
ciphers
,
)
therefore
Socrates
well
perceived
his
wisdom
to
be
nothing
,
in
comparison
of
the
infinite
knowledg
which
he
wanted
.
But
yet
,
because
there
is
some
knowledg
found
amongst
men
,
and
this
not
equally
shared
to
all
,
Socrates
might
have
a
greater
share
thereof
than
others
,
and
therefore
verified
the
answer
of
the
Oracle
.
SAGR.
I
think
I
very
well
understand
this
particular
amongst
men
,
Simplicius
there
is
a
power
of
operating
,
but
not
equally
dispensed
to
all
;
and
it
is
without
question
,
that
the
power
of
an
Emperor
is
far
greater
than
that
of
a
private
person
;
but
,
both
this
and
that
are
nothing
in
comparison
of
the
Divine
Omnipotence
.
Amongst
men
,
there
are
some
that
better
understand
Agriculture
than
many
others
;
but
the
knowledg
of
planting
a
Vine
in
a
trench
,
what
hath
it
to
do
with
the
knowledg
of
making
it
to
sprout
forth
,
to
attract
nourishment
,
to
select
this
good
part
from
that
other
,
for
to
make
thereof
leaves
,
another
to
make
sprouts
,
another
to
make
grapes
,
another
to
make
raisins
,
another
to
make
the
huskes
of
them
,
which
are
the
works
of
most
wise
Nature
?
This
is
one
only
particular
act
of
the
innumerable
,
which
Nature
doth
,
Divine
Wisdom
infinitely
infinite
.
and
in
it
alone
is
discovered
an
infinite
wisdom
,
so
that
Divine
Wisdom
may
be
concluded
to
be
infinitely
infinite
.
SALV
.
Take
hereof
another
example
.
Do
we
not
say
that
the
judicious
discovering
of
a
most
lovely
Statua
in
a
piece
of
Marble
,
hath
sublimated
the
wit
of
Buonarruotti
far
above
the
vulgar
wits
of
other
men
?
Buonarruotti
,
a
statuary
of
admirable
ingenitity
.
And
yet
this
work
is
onely
the
imitation
of
a
meer
aptitude
and
disposition
of
exteriour
and
superficial
members
of
an
immoveable
man
;
but
what
is
it
in
comparison
of
a
man
made
by
nature
,
composed
of
as
many
exteriour
and
interiour
members
,
of
so
many
muscles
,
tendons
,
nerves
,
bones
,
which
serve
to
so
many
and
sundry
motions
?
but
what
shall
we
say
of
the
senses
,
and
of
the
powers
of
the
soul
,
and
lastly
,
of
the
understanding
?
May
we
not
say
,
and
that
with
reason
,
that
the
structure
of
a
Statue
fals
far
short
of
the
formation
of
a
living
man
,
yea
more
of
a
contemptible
worm
?
SAGR.
And
what
difference
think
you
,
was
there
betwixt
the
Dove
of
Architas
,
and
one
made
by
Nature
?
SIMPL.
Either
I
am
none
of
these
knowing
men
,
or
else
there
is
a
manifest
contradiction
in
this
your
discourse
.
You
account
understanding
amongst
the
greatest
(
if
you
make
it
not
the
chief
of
the
)
Encomiums
ascribed
to
man
made
by
Nature
,
and
a
little
before
you
said
with
Socrates
,
that
he
had
no
knowledg
at
all
;
therefore
you
must
say
,
that
neither
did
Nature
understand
how
to
make
an
understanding
that
understandeth
.
SALV
.
You
argue
very
cunningly
,
but
to
reply
to
your
objection
I
must
have
recourse
to
a
Philosophical
distinction
,
and
say
that
the
understanding
is
to
be
taken
too
ways
,
Man
understandeth
very
well
intensivè
,
but
little
extensivè
.
that
is
intensivè
,
or
extensivè
;
and
that
extensivè
,
that
is
,
as
to
the
multitude
of
intelligibles
,
which
are
infinite
,
the
understanding
of
man
is
as
nothing
,
though
he
should
understand
a
thousand
propositions
;
for
that
a
thousand
,
in
respect
of
infinity
is
but
as
a
cypher
:
but
taking
the
understanding
intensive
,
(
in
as
much
as
that
term
imports
)
intensively
,
that
is
,
perfectly
some
propositions
,
I
say
,
that
humane
wisdom
understandeth
some
propositions
so
perfectly
,
and
is
as
absolutely
certain
thereof
,
as
Nature
her self
;
and
such
are
the
pure
Mathematical
sciences
,
to
wit
,
Geometry
and
Arithmetick
:
in
which
Divine
Wisdom
knows
infinite
more
propositions
,
because
it
knows
them
all
;
but
I
believe
that
the
knowledge
of
those
few
comprehended
by
humane
understanding
,
equalleth
the
divine
,
as
to
the
certainty
objectivè
,
for
that
it
arriveth
to
comprehend
the
necessity
thereof
,
than
which
there
can
be
no
greater
certainty
.
SIMPL.
This
seemeth
to
me
a
very
bold
and
rash
expression
.
SALV
.
These
are
common
notions
,
and
far
from
all
umbrage
of
temerity
,
or
boldness
,
and
detract
not
in
the
least
from
the
Majesty
of
divine
wisdom
;
as
it
nothing
diminisheth
the
omnipotence
thereof
to
say
,
that
God
cannot
make
what
is
once
done
,
to
be
undone
:
but
I
doubt
,
Simplicius
,
that
your
scruple
ariseth
from
an
opinion
you
have
,
that
my
words
are
somewhat
equivocal
;
therefore
the
better
to
express
my self
I
say
,
that
as
to
the
truth
,
of
which
Mathematical
demonstrations
give
us
the
knowledge
,
it
is
the
same
,
which
the
divine
wisdom
knoweth
;
but
this
I
must
grant
you
,
G●ds
manner
of
knowing
different
from
that
of
men
.
that
the
manner
whereby
God
knoweth
the
infinite
propositions
,
of
which
we
understand
some
few
,
is
highly
more
excellent
than
ours
,
Humane
understanding
done
by
raciocination
.
which
proceedeth
by
ratiocination
,
and
passeth
from
conclusion
to
conclusion
,
whereas
his
is
done
at
one
single
thought
or
intuition
;
and
whereas
we
,
for
example
,
to
attain
the
knowledg
of
some
passion
of
the
Circle
,
which
hath
infinite
,
beginning
from
one
of
the
most
simple
,
and
taking
that
for
its
definition
,
do
proceed
with
argumentation
to
another
,
and
from
that
to
a
third
,
and
then
to
a
fourth
,
&c.
the
Divine
Wisdom
,
by
the
apprehension
of
its
essence
comprehends
,
without
temporary
raciocination
,
all
these
infinite
passions
;
which
notwithstanding
,
are
in
effect
virtually
comprised
in
the
definitions
of
all
things
;
Definitions
contein
virtually
all
the
passions
of
the
things
defined
.
and
,
to
conclude
,
as
being
infinite
,
perhaps
are
but
one
alone
in
their
nature
,
and
in
the
Divine
Mind
;
the
which
neither
is
wholly
unknown
to
humane
understanding
,
Infinite
Passions
are
perhaps
but
one
onely
.
but
onely
be-clouded
with
thick
and
grosse
mists
;
which
come
in
part
to
be
dissipated
and
clarified
,
when
we
are
made
Masters
of
any
conclusions
,
firmly
demonstrated
,
and
so
perfectly
made
ours
,
as
that
we
can
speedily
run
through
them
;
for
in
sum
,
what
other
,
is
that
proposition
,
that
the
square
of
the
side
subtending
the
right
angle
in
any
triangle
,
is
equal
to
the
squares
of
the
other
two
,
which
include
it
,
but
onely
the
Paralellograms
being
upon
common
bases
,
and
between
parallels
equal
amongst
themselves
?
and
this
,
lastly
,
is
it
not
the
same
,
as
to
say
that
those
two
superficies
are
equal
,
of
which
equal
parts
applyed
to
equal
parts
,
The
discourses
which
humane
reason
makes
in
a
certain
time
,
the
Divine
Wisdom
resolveth
in
a
moment
;
that
is
,
hath
them
alwayes
present
.
possesse
equal
place
?
Now
these
inferences
,
which
our
intellect
apprehendeth
with
time
and
a
gradual
motion
,
the
Divine
Wisdom
,
like
light
,
penetrateth
in
an
instant
,
which
is
the
same
as
to
say
,
hath
them
alwayes
present
:
I
conclude
therefore
,
that
our
understanding
,
both
as
to
the
manner
and
the
multitude
of
the
things
comprehended
by
us
,
is
infinitely
surpast
by
the
Divine
Wisdom
;
but
yet
I
do
not
so
vilifie
it
,
as
to
repute
it
absolutely
nothing
;
yea
rather
,
when
I
consider
how
many
and
how
great
misteries
men
have
understood
,
discovered
,
and
contrived
,
I
very
plainly
know
and
understand
the
mind
of
man
to
be
one
of
the
works
,
yea
one
of
the
most
excellent
works
of
God
.
SAGR.
I
have
oft
times
considered
with
my self
,
The
wit
of
man
admirably
acute
.
in
pursuance
of
that
which
you
speak
of
,
how
great
the
wit
of
man
is
;
and
whil'st
I
run
thorow
such
and
so
many
admirable
inventions
found
out
by
him
,
as
well
in
the
Arts
,
as
Sciences
;
and
again
reflecting
upon
my
own
wit
,
so
far
from
promising
me
the
discovery
of
any
thing
new
,
that
I
despair
of
comprehending
what
is
already
discovered
,
confounded
with
wonder
,
and
surprised
with
desperation
,
I
account
my self
little
lesse
than
miserable
.
If
I
behold
a
Statue
of
some
excellent
Master
,
I
say
with
my self
;
When
wilt
thou
know
how
to
chizzle
away
the
refuse
of
a
piece
of
Marble
,
and
discover
so
lovely
a
figure
,
as
lyeth
hid
therein
?
When
wilt
thou
mix
and
spread
so
many
different
colours
upon
a
Cloth
,
or
Wall
,
and
represent
therewith
all
visible
objects
,
like
a
Michael
Angelo
,
a
Raphaello
,
or
a
Tizvano
?
If
I
behold
what
inventions
men
have
in
comparting
Musical
intervals
,
in
establishing
Precepts
and
Rules
for
the
management
thereof
with
admirable
delight
to
the
ear
:
When
shall
I
cease
my
astonishment
?
What
shall
I
say
of
such
and
so
various
Instruments
of
that
Art
?
The
reading
of
excellent
Poets
,
with
what
admiration
doth
it
swell
any
one
that
attentively
considereth
the
invention
of
conceits
,
and
their
explanation
?
What
shall
we
say
of
Architecture
?
What
of
Navigation
?
The
invention
of
writing
stupendious
above
all
others
.
But
,
above
all
other
stupendious
inventions
,
what
sublimity
of
mind
was
that
in
him
,
that
imagined
to
himself
to
find
out
a
way
to
communicate
his
most
secret
thoughts
to
any
other
person
,
though
very
far
distant
from
him
either
in
time
,
or
place
,
speaking
with
those
that
are
in
the
India's
;
speaking
to
those
that
are
not
yet
born
,
nor
shall
be
this
thousand
,
or
ten
thousand
years
?
and
with
how
much
facility
?
but
by
the
various
collocation
of
[
](A61244-e21040-b)*
*
For
of
so
many
only
the
Italian
Alphabet
consists
.
twenty
little
letters
upon
a
paper
?
Let
this
be
the
Seal
of
all
the
admirable
inventions
of
man
,
and
the
close
of
our
Discourse
for
this
day
:
For
the
warmer
hours
being
past
,
I
suppose
that
Salviatus
hath
a
desire
to
go
and
take
the
air
in
his
Gondelo
;
but
too
morrow
we
will
both
wait
upon
you
,
to
continue
the
Discourses
we
have
begun
,
&c.
GALILAEUS
Galilaeus
Lyncaeus
,
HIS
SYSTEME
OF
THE
WORLD
.
The
Second
Dialogue
.
INTERLOCVTORS
.
SALVIATUS
,
SAGREDUS
,
and
SIMPLICIUS
.
SALV
.
THe
yester-dayes
diversions
which
led
us
out
of
the
path
of
our
principal
discourse
,
were
such
and
so
many
,
that
I
know
not
how
I
can
without
your
assistance
recover
the
track
in
which
I
am
to
proceed
.
SAGR.
I
wonder
not
,
that
you
,
who
have
your
fancy
charged
and
laden
with
both
what
hath
been
,
and
is
to
be
spoken
,
do
find
your self
in
some
confusion
;
but
I
,
who
as
being
onely
an
Auditor
,
have
nothing
to
burthen
my
memory
withal
,
but
such
things
as
I
have
heard
,
may
haply
by
a
succinct
rehearsal
of
them
,
recover
the
first
thred
of
our
Discourse
.
As
far
therefore
as
my
memory
serves
me
,
the
sum
of
yester-dayes
conferences
were
an
examination
of
the
Principles
of
Ptolomy
and
Copernicus
,
and
which
of
their
opinions
is
the
more
probable
and
rational
;
that
,
which
affirmeth
the
substance
of
the
Coelestial
bodies
to
be
ingenerable
,
incorruptible
,
unalterable
,
impassible
,
and
in
a
word
,
exempt
from
all
kind
of
change
,
save
that
of
local
,
and
therefore
to
be
a
fifth
essence
,
quite
different
from
this
of
our
Elementary
bodies
,
which
are
generable
,
corruptible
,
alterable
,
&c.
or
else
the
other
,
which
taking
away
such
deformity
from
the
parts
of
the
World
,
holdeth
the
Earth
to
enjoy
the
same
perfections
as
the
other
integral
bodies
of
the
universe
;
and
esteemeth
it
a
moveable
and
erratick
Globe
,
no
lesse
than
the
Moon
,
Jupiter
,
Venus
,
or
any
other
Planet
:
And
lastly
,
maketh
many
particular
parallels
betwixt
the
Earth
and
Moon
;
and
more
with
the
Moon
,
than
with
any
other
Planet
;
haply
by
reason
we
have
greater
and
more
certain
notice
of
it
,
as
being
lesse
distant
from
us
.
And
having
,
lastly
,
concluded
this
second
opinion
to
have
more
of
probability
with
it
than
the
first
,
I
should
think
it
best
in
the
subsequent
discourses
to
begin
to
examine
whether
the
Earth
be
esteemed
immoveable
,
as
it
hath
been
till
now
believed
by
most
men
,
or
else
moveable
,
as
some
ancient
Philosophers
held
,
and
others
of
not
very
recesse
times
,
were
of
opinion
;
and
if
it
be
moveable
,
to
enquire
of
what
kind
its
motion
may
be
?
SALV
.
I
see
already
what
way
I
am
to
take
;
but
before
we
offer
to
proceed
any
farther
,
I
am
to
say
something
to
you
touching
those
last
words
which
you
spake
,
how
that
the
opinion
which
holds
the
Earth
to
be
endued
with
the
same
conditions
that
the
Coelestial
bodies
enjoy
,
seems
to
be
more
true
than
the
contrary
;
for
that
I
affirmed
no
such
thing
,
nor
would
I
have
any
of
the
Propositions
in
controversie
,
be
made
to
speak
to
any
definitive
sense
:
but
I
onely
intended
to
produce
on
either
part
,
those
reasons
and
answers
,
arguments
and
solutions
,
which
have
been
hitherto
thought
upon
by
others
,
together
with
certain
others
,
which
I
have
stumbled
upon
in
my
long
searching
thereinto
,
alwayes
remitting
the
decision
thereof
to
the
judgment
of
others
.
SAGR.
I
was
unawares
transported
by
my
own
sense
of
the
thing
;
and
believing
that
others
ought
to
judg
as
I
did
,
I
made
that
conclusion
universal
,
which
should
have
been
particular
;
and
therefore
confesse
I
have
erred
,
and
the
rather
,
in
that
I
know
not
what
Simplicius
his
judgment
is
in
this
particular
.
SIMPL.
I
must
confesse
,
that
I
have
been
ruminating
all
this
night
of
what
past
yesterday
,
and
to
say
the
truth
,
I
meet
therein
with
many
acute
,
new
,
aud
plausible
notions
;
yet
nevertheless
,
I
find
my self
over-perswaded
by
the
authority
of
so
many
great
Writers
,
and
in
particular
—
&c.
I
see
you
shake
your
head
Sagredus
,
and
smile
to
your self
,
as
if
I
had
uttered
some
great
absurdity
.
SAGR.
I
not
onely
smile
,
but
to
tell
you
true
,
am
ready
to
burst
with
holding
in
my self
from
laughing
outright
,
for
you
have
put
me
in
mind
of
a
very
pretty
passage
,
that
I
was
a
witnesse
of
,
not
many
years
since
,
together
with
some
others
of
my
worthy
friends
,
which
I
could
yet
name
unto
you
.
SALV
.
It
would
be
well
that
you
told
us
what
it
was
,
that
so
Simplicius
may
not
still
think
that
he
gave
you
the
occasion
of
laughter
.
SAGR.
I
am
content
.
I
found
one
day
,
at
home
in
his
house
,
at
Venice
,
a
famous
Phisician
,
to
whom
some
flockt
for
their
studies
,
and
others
out
of
curiosity
,
sometimes
came
thither
to
see
certain
Anatomies
diffected
by
the
hand
of
a
no
lesse
learned
,
than
careful
and
experienced
Anatomist
.
The
original
of
the
Nerves
according
to
Aristotle
,
and
according
to
Phisicians
.
It
chanced
upon
that
day
,
when
I
was
there
,
that
he
was
in
search
of
the
original
and
rise
of
the
Nerves
,
about
which
there
is
a
famous
controversie
between
the
Galenists
and
Peripateticks
;
and
the
Anatomist
shewing
,
how
that
the
great
number
of
Nerves
departing
from
the
Brain
,
as
their
root
,
and
passing
by
the
nape
of
the
Neck
,
distend
themselves
afterwards
along
by
the
Back-bone
,
and
branch
themselves
thorow
all
the
Body
;
and
that
a
very
small
filament
,
as
fine
as
a
thred
went
to
the
Heart
;
he
turned
to
a
Gentleman
whom
he
knew
to
be
a
Peripatetick
Philosopher
,
and
for
whose
sake
he
had
with
extraordinary
exactnesse
,
discovered
and
proved
every
thing
,
and
demanded
of
him
,
if
he
was
at
length
satisfied
and
perswaded
that
the
original
of
the
Nerves
proceeded
from
the
Brain
,
and
not
from
the
Heart
?
The
ridiculous
answer
of
a
Philosopher
,
determining
the
original
of
the
Nerves
.
To
which
the
Philosopher
,
after
he
had
stood
musing
a
while
,
answered
;
you
have
made
me
to
see
this
businesse
so
plainly
and
sensibly
,
that
did
not
the
Text
of
Aristotle
assert
the
contrary
,
which
positively
affirmeth
the
Nerves
to
proceed
from
the
Heart
,
I
should
be
constrained
to
confesse
your
opinion
to
be
true
.
SIMPL.
I
would
have
you
know
my
Masters
,
that
this
controversie
about
the
original
of
the
Nerves
is
not
yet
so
proved
and
decided
,
as
some
may
perhaps
perswade
themselves
.
SAGR.
Nor
questionlesse
ever
shall
it
be
,
if
it
find
such
like
contradictors
;
but
that
which
you
say
,
doth
not
at
all
lessen
the
extravagance
of
the
answer
of
that
Peripatetick
,
who
against
such
sensible
experience
produced
not
other
experiments
,
or
reasons
of
Aristotle
,
but
his
bare
authority
and
pure
ipse
dixit
.
SIMPL.
Aristotle
had
not
gained
so
great
authority
,
but
for
the
force
of
his
Demonstrations
,
and
the
profoundnesse
of
his
arguments
;
but
it
is
requisite
that
we
understand
him
,
and
not
onely
understand
him
,
but
have
so
great
familiarity
with
his
Books
,
that
we
form
a
perfect
Idea
thereof
in
our
minds
,
so
as
that
every
saying
of
his
may
be
alwayes
as
it
were
,
present
in
our
memory
for
he
did
not
write
to
the
vulgar
,
nor
is
he
obliged
to
spin
out
his
Sillogismes
with
the
trivial
method
of
disputes
;
nay
rather
,
using
a
freedome
,
he
hath
sometimes
placed
the
proof
of
one
Proposition
amongst
Texts
,
which
seem
to
treat
of
quite
another
point
;
Requisites
to
fit
a
man
to
philosophate
well
after
the
manner
of
Aristotle
.
and
therefore
it
is
requisite
to
be
master
of
all
that
vast
Idea
,
and
to
learn
how
to
connect
this
passage
with
that
,
and
to
combine
this
Text
with
another
far
remote
from
it
;
for
it
is
not
to
be
questioned
but
that
he
who
hath
thus
studied
him
,
knows
how
to
gather
from
his
Books
the
demonstrations
of
every
knowable
deduction
,
for
that
they
contein
all
things
.
SAGR.
But
good
Simplicius
,
like
as
the
things
scattered
here
and
there
in
Aristotle
,
give
you
no
trouble
in
collecting
them
,
but
that
you
perswade
your self
to
be
able
by
comparing
and
connecting
several
small
sentences
to
extract
thence
the
juice
of
some
desired
conclusion
,
A
cunning
way
to
gather
Philosophy
out
of
any
book
whatsoever
.
so
this
,
which
you
and
other
egregious
Philosophers
do
with
the
Text
of
Aristotle
,
I
could
do
by
the
verses
of
Virgil
,
or
of
Ovid
,
composing
thereof
[
](A61244-e21850-b)*
*
A
word
signifying
works
composed
of
many
fragments
of
verses
collected
out
of
the
Poets
.
Centones
,
and
therewith
explaining
all
the
affairs
of
men
,
and
secrets
of
Nature
.
But
what
talk
I
of
Virgil
,
or
any
other
Poet
?
I
have
a
little
Book
much
shorter
than
Aristotle
and
Ovid
,
in
which
are
conteined
all
the
Sciences
,
and
with
very
little
study
,
one
may
gather
out
of
it
a
most
perfect
Idea
,
and
this
is
the
Alphabet
;
and
there
is
no
doubt
but
that
he
who
knows
how
to
couple
and
dispose
aright
this
and
that
vowel
,
with
those
,
or
those
other
consonants
,
may
gather
thence
the
infallible
answers
to
all
doubts
,
and
deduce
from
them
the
principles
of
all
Sciences
and
Arts
,
just
in
the
same
manner
as
the
Painter
from
divers
simple
colours
,
laid
severally
upon
his
Pallate
,
proceedeth
by
mixing
a
little
of
this
and
a
little
of
that
,
with
a
little
of
a
third
,
to
represent
to
the
life
men
,
plants
,
buildings
,
birds
,
fishes
,
and
in
a
word
,
counterfeiting
what
ever
object
is
visible
,
though
there
be
not
on
the
Pallate
all
the
while
,
either
eyes
,
or
feathers
,
or
fins
,
or
leaves
,
or
stones
.
Nay
,
farther
,
it
is
necessary
,
that
none
of
the
things
to
be
imitated
,
or
any
part
of
them
,
be
actually
among
colours
,
if
you
would
be
able
therewith
to
represent
all
things
;
for
should
there
be
amongst
them
v.
gr
.
feathers
,
these
would
serve
to
represent
nothing
save
birds
,
and
plumed
creatures
.
SALV
.
And
there
are
certain
Gentlemen
yet
living
,
and
in
health
,
who
were
present
,
when
a
Doctor
,
that
was
Professor
in
a
famous
Academy
,
Invention
of
the
Telescope
taken
from
Aristotle
.
hearing
the
description
of
the
Telescope
,
by
him
not
seen
as
then
,
said
,
that
the
invention
was
taken
from
Aristotle
,
and
causing
his
works
to
be
fetch
't
,
he
turned
to
a
place
where
the
Philosopher
gives
the
reason
,
whence
it
commeth
,
that
from
the
bottom
of
a
very
deep
Well
,
one
may
see
the
stars
in
Heaven
,
at
noon
day
;
and
,
addressing
himself
to
the
company
,
see
here
,
saith
he
,
the
Well
,
which
representeth
the
Tube
,
see
here
the
gross
vapours
,
from
whence
is
taken
the
invention
of
the
Crystals
,
and
see
here
lastly
the
sight
fortified
by
the
passage
of
the
rays
through
a
diaphanous
,
but
more
dense
and
obscure
medium
.
SAGR.
This
is
a
way
to
comprehend
all
things
knowable
,
much
like
to
that
wherewith
a
piece
of
marble
conteineth
in
it
one
,
yea
,
a
thousand
very
beautiful
Statua's
,
but
the
difficulty
lieth
in
being
able
to
discover
them
;
or
we
may
say
,
that
it
is
like
to
the
prophesies
of
Abbot
Joachim
,
or
the
answers
of
the
Heathen
Oracles
,
which
are
not
to
be
understood
,
till
after
the
things
fore-told
are
come
to
passe
.
SALV
.
And
why
do
you
not
adde
the
predictions
of
the
Genethliacks
,
which
are
with
like
cleernesse
seen
after
the
event
,
in
their
Horoscopes
,
or
,
if
you
will
,
Configurations
of
the
Heavens
.
SAGR.
In
this
manner
the
Chymists
find
,
Chymists
interpret
the
Fables
of
the
Poets
to
be
secrets
for
making
of
Gold
.
being
led
by
their
melancholly
humour
,
that
all
the
sublimest
wits
of
the
World
have
writ
of
nothing
else
in
reality
,
than
of
the
way
to
make
Gold
;
but
,
that
they
might
transmit
the
secret
to
posterity
without
discovering
it
to
the
vulgar
,
they
contrived
some
one
way
,
and
some
another
how
to
conceal
the
same
under
several
maskes
;
and
it
would
make
one
merry
to
hear
their
comments
upon
the
ancient
Poets
,
finding
out
the
important
misteries
,
which
lie
hid
under
their
Fables
;
and
the
signification
of
the
Loves
of
the
Moon
,
and
her
descending
to
the
Earth
for
Endimion
;
her
displeasure
against
Acteon
,
and
what
was
meant
by
Jupiters
turning
himself
into
a
showre
of
Gold
;
and
into
flames
of
fire
;
and
what
great
secrets
of
Art
are
conteined
in
that
Mercury
the
Interpreter
;
in
those
thefts
of
Pluto
;
and
in
those
Branches
of
Gold
.
SIMPL.
I
believe
,
and
in
part
know
,
that
there
want
not
in
the
World
very
extravagant
heads
,
the
vanities
of
whom
ought
not
to
redound
to
the
prejudice
of
Aristotle
,
of
whom
my
thinks
you
speak
sometimes
with
too
little
respect
,
and
the
onely
antiquity
and
bare
name
that
he
hath
acquired
in
the
opinions
of
so
many
famous
men
,
should
suffice
to
render
him
honourable
with
all
that
professe
themselves
learned
.
SALV
.
You
state
not
the
matter
rightly
,
Simplicius
;
There
are
some
of
his
followers
that
fear
before
they
are
in
danger
,
who
give
us
occasion
,
or
,
to
say
better
,
would
give
us
cause
to
esteem
him
lesse
,
Some
of
Aristotles
Sectators
impare
the
reputation
of
their
Master
,
in
going
about
to
enhanse
it
.
should
we
consent
to
applaud
their
Capricio's
.
And
you
,
pray
you
tell
me
,
are
you
for
your
part
so
simple
,
as
not
to
know
that
had
Aristotle
been
present
,
to
have
heard
the
Doctor
that
would
have
made
him
Author
of
the
Telescope
,
he
would
have
been
much
more
displeased
with
him
,
than
with
those
,
who
laught
at
the
Doctor
and
his
Comments
?
Do
you
question
whether
Aristotle
,
had
he
but
seen
the
novelties
discovered
in
Heaven
,
would
not
have
changed
his
opinion
,
amended
his
Books
,
and
embraced
the
more
sensible
Doctrine
;
rejecting
those
silly
Gulls
,
which
too
scrupulously
go
about
to
defend
what
ever
he
hath
said
;
not
considering
,
that
if
Aristotle
were
such
a
one
as
they
fancy
him
to
themselves
,
he
would
be
a
man
of
an
untractable
wit
,
an
obstinate
mind
,
a
barbarous
soul
,
a
stubborn
will
,
that
accounting
all
men
else
but
as
silly
sheep
,
would
have
his
Oracles
preferred
before
the
Senses
,
Experience
,
and
Nature
her self
?
They
are
the
Sectators
of
Aristotle
that
have
given
him
this
Authority
,
and
not
he
that
hath
usurped
or
taken
it
upon
him
;
and
because
it
is
more
easie
for
a
man
to
sculk
under
anothers
shield
than
to
shew
himself
openly
,
they
tremble
,
and
are
affraid
to
stir
one
step
from
him
;
and
rather
than
they
will
admit
some
alterations
in
the
Heaven
of
Aristotle
,
they
will
impertinently
deny
those
they
behold
in
the
Heaven
of
Nature
.
SAGR.
These
kind
of
Drolleries
put
me
in
mind
of
that
Statuary
which
having
reduced
a
great
piece
of
Marble
to
the
Image
of
an
Hercules
,
A
ridiculous
passage
of
a
certain
Statuary
.
or
a
thundring
Jupiter
,
I
know
not
whether
,
and
given
it
with
admirable
Art
such
a
vivacity
and
threatning
fury
,
that
it
moved
terror
in
as
many
as
beheld
it
;
he
himself
began
also
to
be
affraid
thereof
,
though
all
its
sprightfulnesse
,
and
life
was
his
own
workmanship
;
and
his
affrightment
was
such
,
that
he
had
no
longer
the
courage
to
affront
it
with
his
Chizzels
and
Mallet
.
SALV
.
I
have
many
times
wondered
how
these
nice
maintainers
of
what
ever
fell
from
Aristotle
,
are
not
aware
how
great
a
prejudice
they
are
to
his
reputation
and
credit
;
and
how
that
the
more
they
go
about
to
encrease
his
Authority
,
the
more
they
diminish
it
;
for
whilest
I
see
them
obstinate
in
their
attempts
to
maintain
those
Propositions
which
I
palpably
discover
to
be
manifestly
false
;
and
in
their
desires
to
perswade
me
that
so
to
do
,
is
the
part
of
a
Philosopher
;
and
that
Aristotle
himself
would
do
the
same
,
it
much
abates
in
me
of
the
opinion
that
he
hath
rightly
philosophated
about
other
conclusions
,
to
me
more
abstruse
:
for
if
I
could
see
them
concede
and
change
opinion
in
a
manifest
truth
,
I
would
believe
,
that
in
those
in
which
they
should
persist
,
they
may
have
some
solid
demonstrations
to
me
unknown
,
and
unheard
of
.
SAGR.
Or
when
they
should
be
made
to
see
that
they
have
hazarded
too
much
of
their
own
and
Aristotle's
repuatation
in
confessing
,
that
they
had
not
understood
this
or
that
conclusion
found
out
by
some
other
man
;
would
it
not
be
a
less
evil
for
them
to
seek
for
it
amongst
his
Texts
,
by
laying
many
of
them
together
,
according
to
the
art
intimated
to
us
by
Simplicius
?
for
if
his
works
contain
all
things
knowable
,
it
must
follow
also
that
they
may
be
therein
discovered
.
SALV
.
Good
Sagredus
,
make
no
jest
of
this
advice
,
which
me
thinks
you
rehearse
in
too
Ironical
a
way
;
for
it
is
not
long
since
that
a
very
eminent
Philosopher
having
composed
a
Book
de
animà
,
wherein
,
citing
the
opinion
of
Aristotle
,
about
its
being
or
not
being
immortal
,
he
alledged
many
Texts
,
(
not
any
of
those
heretofore
quoted
by
Alexander
ab
Alexandro
:
for
in
those
he
said
,
that
Aristotle
had
not
so
much
as
treated
of
that
matter
,
much
less
determined
any
thing
pertaining
to
the
same
,
but
others
)
by
himself
found
out
in
other
more
abstruse
places
,
which
tended
to
an
erroneous
sense
:
and
being
advised
,
that
he
would
find
it
an
hard
matter
to
get
a
Licence
from
the
Inquisitors
,
A
brave
resolution
of
a
certain
Peripatetick
Philosopher
.
he
writ
back
unto
his
friend
,
that
he
would
notwithstanding
,
with
all
expedition
procure
the
same
,
for
that
if
no
other
obstacle
should
interpose
,
he
would
not
much
scruple
to
change
the
Doctrine
of
Aristotle
,
and
with
other
expositions
,
and
other
Texts
to
maintain
the
contrary
opinion
,
which
yet
should
be
also
agreeable
to
the
sense
of
Aristotle
.
SAGR.
Oh
most
profound
Doctor
,
this
!
that
can
command
me
that
I
stir
not
a
step
from
Aristotle
,
but
will
himself
lead
him
by
the
nose
,
and
make
him
speak
as
he
pleaseth
.
See
how
much
it
importeth
to
learn
to
take
Time
by
the
Fore-top
.
Nor
is
it
seasonable
to
have
to
do
with
Hercules
,
whil'st
he
is
enraged
,
and
amongst
the
Furies
,
but
when
he
is
telling
merry
tales
amongst
the
Meonion
Damosels
.
The
servile
spirit
of
some
of
Aristotles
followers
.
Ah
,
unheard
of
sordidnesse
of
servile
souls
!
to
make
themselves
willing
slaves
to
other
mens
opinions
;
to
receive
them
for
inviolable
Decrees
,
to
engage
themselves
to
seem
satisfied
and
convinced
by
arguments
,
of
such
efficacy
,
and
so
manifestly
concludent
,
that
they
themselves
cannot
certainly
resolve
whether
they
were
really
writ
to
that
purpose
,
or
serve
to
prove
that
assumption
in
hand
,
or
the
contrary
.
But
,
which
is
a
greater
madnesse
,
they
are
at
variance
amongst
themselves
,
whether
the
Author
himself
hath
held
the
affirmative
part
,
or
the
negative
.
What
is
this
,
but
to
make
an
Oracle
of
a
Log
,
and
to
run
to
that
for
answers
,
to
fear
that
,
to
reverence
and
adore
that
?
SIMPL.
But
in
case
we
should
recede
from
Aristotle
,
who
have
we
to
be
our
Guid
in
Philosophy
?
Name
you
some
Author
.
SALV
.
We
need
a
Guid
in
unknown
and
uncouth
wayes
,
but
in
champion
places
,
and
open
plains
,
the
blind
only
stand
in
need
of
a
Leader
;
and
for
such
,
it
is
better
that
they
stay
at
home
.
But
he
that
hath
eyes
in
his
head
,
and
in
his
mind
,
him
should
a
man
choose
for
his
Guid.
Too
close
adhering
to
Aristotle
is
blameable
.
Yet
mistake
me
not
,
thinking
that
I
speak
this
,
for
that
I
am
against
hearing
of
Aristotle
;
for
on
the
contrary
,
I
commend
the
reading
,
and
diligently
studying
of
him
;
and
onely
blame
the
servile
giving
ones
self
up
a
slave
unto
him
,
so
,
as
blindly
to
subscribe
to
what
ever
he
delivers
,
and
without
search
of
any
farther
reason
thereof
,
to
receive
the
same
for
an
inviolable
decree
.
Which
is
an
abuse
,
that
carrieth
with
it
another
great
inconvenience
,
to
wit
,
that
others
will
no
longer
take
pains
to
understand
the
validity
of
his
Demonstrations
.
And
what
is
more
shameful
,
than
in
the
middest
of
publique
disputes
,
whilest
one
person
is
treating
of
demonstrable
conclusions
,
to
hear
another
interpose
with
a
passage
of
Aristotle
,
and
not
seldome
writ
to
quite
another
purpose
,
and
with
that
to
stop
the
mouth
of
his
opponent
?
But
if
you
will
continue
to
study
in
this
manner
,
I
would
have
you
lay
aside
the
name
of
Philosophers
;
and
call
your selves
either
Historians
or
Doctors
of
Memory
,
It
is
not
just
,
that
those
who
never
philosophate
,
should
●surp
the
title
of
Philosophers
.
for
it
is
not
fit
,
that
those
who
never
philosophate
,
should
usurp
the
honourable
title
of
Philosophers
.
But
it
is
best
for
us
to
return
to
shore
,
and
not
lanch
farther
into
a
boundlesse
Gulph
,
out
of
which
we
shall
not
be
able
to
get
before
night
.
Therefore
Simplicius
,
come
either
with
arguments
and
demonstrations
of
your
own
,
or
of
Aristotle
,
and
bring
us
no
more
Texts
and
naked
authorities
,
The
Sensible
World
.
for
our
disputes
are
about
the
Sensible
World
,
and
not
one
of
Paper
.
And
forasmuch
as
in
our
discourses
yesterday
,
we
retriev'd
the
Earth
from
darknesse
,
and
exposed
it
to
the
open
skie
,
shewing
,
that
the
attempt
to
enumerate
it
amongst
those
which
we
call
Coelestial
bodies
,
was
not
a
position
so
foil'd
,
and
vanquish't
,
as
that
it
had
no
life
left
in
it
;
it
followeth
next
,
that
we
proceed
to
examine
what
probability
there
is
for
holding
of
it
fixt
,
and
wholly
immoveable
,
scilicet
as
to
its
entire
Globe
,
what
likelihood
there
is
for
making
it
moveable
with
some
motion
,
and
of
what
kind
that
may
be
.
And
forasmuch
as
in
this
same
question
I
am
ambiguous
,
and
Simplicius
is
resolute
,
as
likewise
Aristotle
for
the
opinion
of
its
immobility
,
he
shall
one
by
one
produce
the
arguments
in
favour
of
their
opinion
,
and
I
will
alledge
the
answers
and
reasons
on
the
contrary
part
;
and
next
Sagredus
shall
tell
us
his
thoughts
,
and
to
which
side
he
finds
himself
inclined
.
SAGR.
Content
;
provided
alwayes
that
I
may
reserve
the
liberty
to
my self
of
alledging
what
pure
natural
reason
shall
sometimes
dictate
to
me
.
SALV
.
Nay
more
,
it
is
rhat
which
I
particularly
beg
of
you
;
for
,
amongst
the
more
easie
,
and
,
to
so
speak
,
material
considerations
,
I
believe
there
are
but
few
of
them
that
have
been
omitted
by
Writers
,
so
that
onely
some
of
the
more
subtle
,
and
remote
can
be
desired
,
or
wanting
;
and
to
investigate
these
,
what
other
ingenuity
can
be
more
fit
than
that
of
the
most
acute
and
piercing
wit
of
Sagredus
?
SAGR.
I
am
what
ever
pleaseth
Salviatus
,
but
I
pray
you
,
let
us
not
sally
out
into
another
kind
of
digression
complemental
;
for
at
this
time
I
am
a
Philosopher
,
and
in
the
Schools
,
not
in
the
Court.
SALV
.
Let
our
contemplation
begin
therefore
with
this
consideration
,
that
whatsoever
motion
may
be
ascribed
to
the
Earth
,
it
is
necessary
that
it
be
to
us
,
(
as
inhabitants
upon
it
,
and
consequently
partakers
of
the
same
)
altogether
imperceptible
,
and
as
if
it
were
not
at
all
,
so
long
as
we
have
regard
onely
to
terrestrial
things
;
The
motions
of
the
Earth
are
imperceptible
to
its
inhabitants
.
but
yet
it
is
on
the
contrary
,
as
necessary
that
the
same
motion
do
seem
common
to
all
other
bodies
,
and
visible
objects
,
that
being
separated
from
the
Earth
,
participate
not
of
the
same
.
So
that
the
true
method
to
find
whether
any
kind
of
motion
may
be
ascribed
to
the
Earth
,
and
that
found
,
to
know
what
it
is
,
is
to
consider
and
observe
if
in
bodies
separated
from
the
Earth
,
The
Earth
can
have
no
other
motions
,
than
those
which
to
us
appear
commune
to
all
the
rest
of
the
Vniverse
,
the
Earth
excepted
.
one
may
discover
any
appearance
of
motion
,
which
equally
suiteth
to
all
the
rest
;
for
a
motion
that
is
onely
seen
,
v.
gr
.
in
the
Moon
,
and
that
hath
nothing
to
do
with
Venus
or
Jupiter
,
or
any
other
Stars
,
cannot
any
way
belong
to
the
Earth
,
or
to
any
other
save
the
Moon
alone
.
Now
there
is
a
most
general
and
grand
motion
above
all
others
,
and
it
is
that
by
which
the
Sun
,
the
Moon
,
The
Diurnal
Motion
,
seemeth
commune
to
all
the
Vniverse
,
save
onely
the
Earth
excepted
.
the
other
Planets
,
and
the
Fixed
Stars
,
and
in
a
word
,
the
whole
Universe
,
the
Earth
onely
excepted
,
appeareth
in
our
thinking
to
move
from
the
East
towards
the
West
,
in
the
space
of
twenty
four
hours
;
and
this
,
as
to
this
first
appearance
,
hath
no
obstacle
to
hinder
it
,
that
it
may
not
belong
to
the
Earth
alone
,
as
well
as
to
all
the
World
besides
,
the
Earth
excepted
;
for
the
same
aspects
will
appear
in
the
one
position
,
as
in
the
other
.
Hence
it
is
that
Aristotle
and
Ptolomy
,
Aristotle
and
Ptolomy
argue
against
the
Diurnal
Motion
attributed
to
the
Earth
.
as
having
hit
upon
this
consideration
,
in
going
about
to
prove
the
Earth
to
be
immoveable
,
argue
not
against
any
other
than
this
Diurnal
Motion
;
save
onely
that
Aristotle
hinteth
something
in
obscure
terms
against
another
Motion
ascribed
to
it
by
an
Ancient
,
of
which
we
shall
speak
in
its
place
.
SAGR.
I
very
well
perceive
the
necessity
of
your
illation
:
but
I
meet
with
a
doubt
which
I
know
not
how
to
free
my self
from
,
and
this
it
is
,
That
Copernicus
assigning
to
the
Earth
another
motion
beside
the
Diurnal
,
which
,
according
to
the
rule
even
now
laid
down
,
ought
to
be
to
us
,
as
to
appearance
,
imperceptible
in
the
Earth
,
but
visible
in
all
the
rest
of
the
World
;
me
thinks
I
may
necessarily
infer
,
either
that
he
hath
manifestly
erred
in
assigning
the
Earth
a
motion
,
to
which
there
appears
not
a
general
correspondence
in
Heaven
;
or
else
that
if
there
be
such
a
congruity
therein
,
Ptolomy
on
the
other
hand
hath
been
deficient
in
not
confuting
this
,
as
he
hath
done
the
other
.
SALV
.
You
have
good
cause
for
your
doubt
:
and
when
we
come
to
treat
of
the
other
Motion
,
you
shall
see
how
far
Copernicus
excelled
Ptolomey
in
clearness
and
sublimity
of
wit
,
in
that
he
saw
what
the
other
did
not
,
I
mean
the
admirable
harmony
wherein
that
Motion
agreed
with
all
the
other
Coelestial
Bodies
.
But
for
the
present
we
will
suspend
this
particular
,
and
return
to
our
first
consideration
;
touching
which
I
will
proceed
to
propose
(
begining
with
things
more
general
)
those
reasons
which
seem
to
favour
the
mobility
of
the
Earth
,
Why
the
diurnal
motion
more
probably
should
belong
to
the
Earth
,
than
to
the
rest
of
the
Vniverse
.
and
then
wait
the
answers
which
Simplicius
shall
make
thereto
.
And
first
,
if
we
consider
onely
the
immense
magnitude
of
the
Starry
Sphere
,
compared
to
the
smalness
of
the
Terrestrial
Globe
,
contained
therein
so
many
millions
of
times
;
and
moreover
weigh
the
velocity
of
the
motion
which
must
in
a
day
and
night
make
an
entire
revolution
thereof
,
I
cannot
perswade
my self
,
that
there
is
any
man
who
believes
it
more
reasonable
and
credible
,
that
the
Coelestial
Sphere
turneth
round
,
and
the
Terrestrial
Globe
stands
still
.
SAGR.
If
from
the
universality
of
effects
,
which
may
in
nature
have
dependence
upon
such
like
motions
,
there
should
indifferently
follow
all
the
same
consequences
to
an
hair
,
aswell
in
one
Hypothesis
as
in
the
other
;
yet
I
for
my
part
,
as
to
my
first
and
general
apprehension
,
would
esteem
,
that
he
which
should
hold
it
more
rational
to
make
the
whole
Universe
move
,
and
thereby
to
salve
the
Earths
mobility
,
is
more
unreasonable
than
he
that
being
got
to
the
top
of
your
Turret
,
should
desire
,
to
the
end
onely
that
he
might
behold
the
City
,
and
the
Fields
about
it
,
that
the
whole
Country
might
turn
round
,
that
so
he
might
not
be
put
to
the
trouble
to
stir
his
head
.
And
yet
doubtless
the
advantages
would
be
many
and
great
which
the
Copernican
Hypothesis
is
attended
with
,
above
those
of
the
Ptolomaique
,
which
in
my
opinion
resembleth
,
nay
surpasseth
that
other
folly
;
so
that
all
this
makes
me
think
that
far
more
probable
than
this
.
But
haply
Aristotle
Ptolomey
,
and
Simplicius
may
find
the
advantages
of
their
Systeme
,
which
they
would
do
well
to
communicate
to
us
also
,
if
any
such
there
be
;
or
else
declare
to
me
,
that
there
neither
are
or
can
be
any
such
things
.
SALV
.
For
my
part
,
as
I
have
not
been
able
,
as
much
as
I
have
thought
upon
it
,
to
find
any
diversity
therein
;
so
I
think
I
have
found
,
that
no
such
diversity
can
be
in
them
:
in
so
much
that
I
esteem
it
to
no
purpose
to
seek
farther
after
it
.
Motion
,
as
to
the
things
that
equally
move
thereby
,
is
as
if
it
never
were
,
&
so
far
operates
as
it
hath
relation
to
things
deprived
of
motion
.
Therefore
observe
:
Motion
is
so
far
Motion
,
and
as
Motion
operateth
,
by
how
far
it
hath
relation
to
things
which
want
Motion
:
but
in
those
things
which
all
equally
partake
thereof
it
hath
nothing
to
do
,
and
is
as
if
it
never
were
.
And
thus
the
Merchandises
with
which
a
ship
is
laden
,
so
far
move
,
by
how
far
leaving
London
,
they
pass
by
France
,
Spain
,
Italy
,
and
sail
to
Aleppo
,
which
London
,
France
,
Spain
&c.
stand
still
,
not
moving
with
the
ship
:
but
as
to
the
Chests
,
Bales
and
other
Parcels
,
wherewith
the
ship
is
stow'd
and
and
laden
,
and
in
respect
of
the
ship
it self
,
the
Motion
from
London
to
Syria
is
as
much
as
nothing
;
and
nothing-altereth
the
relation
which
is
between
them
:
and
this
,
because
it
is
common
to
all
,
and
is
participated
by
all
alike
:
and
of
the
Cargo
which
is
in
the
ship
,
if
a
Bale
were
romag'd
from
a
Chest
but
one
inch
onely
,
this
alone
would
be
in
that
Cargo
,
a
greater
Motion
in
respect
of
the
Chest
,
than
the
whole
Voyage
of
above
three
thousand
miles
,
made
by
them
as
they
were
stived
together
.
SIMPL.
This
Doctrine
is
good
,
sound
,
and
altogether
Peripatetick
.
SALV
.
I
hold
it
to
be
much
more
antient
:
A
proposition
taken
by
Aristotle
from
the
Antients
,
but
somewhat
altered
by
him
.
and
suspect
that
Aristotle
in
receiving
it
from
some
good
School
,
did
not
fully
understand
it
,
and
that
therefore
,
having
delivered
it
with
some
alteration
,
it
hath
been
an
occasion
of
confusion
amongst
those
,
who
would
defend
whatever
he
saith
.
And
when
he
writ
,
that
whatsoever
moveth
,
doth
move
upon
something
immoveable
,
I
suppose
that
he
equivocated
,
and
meant
,
that
whatever
moveth
,
moveth
in
respect
to
something
immoveable
;
which
proposition
admitteth
no
doubt
,
and
the
other
many
.
SAGR.
Pray
you
make
no
digression
,
but
proceed
in
the
dissertation
you
began
.
SALV
.
It
being
therefore
manifest
,
The
first
discourse
to
prove
that
the
diurnal
motion
belongs
to
the
Earth
.
that
the
motion
which
is
common
to
many
moveables
,
is
idle
,
and
as
it
were
,
null
as
to
the
relation
of
those
moveables
between
themselves
,
because
that
among
themselves
they
have
made
no
change
:
and
that
it
is
operative
onely
in
the
relation
that
those
moveables
have
to
other
things
,
which
want
that
motion
,
among
which
the
habitude
is
changed
:
and
we
having
divided
the
Universe
into
two
parts
,
one
of
which
is
necessarily
moveable
,
and
the
other
immoveable
;
for
the
obtaining
of
whatsoever
may
depend
upon
,
or
be
required
from
such
a
motion
,
it
may
as
well
be
done
by
making
the
Earth
alone
,
as
by
making
all
the
rest
of
the
World
to
move
:
for
that
the
operation
of
such
a
motion
consists
in
nothing
else
,
save
in
the
relation
or
habitude
which
is
between
the
Coelestial
Bodies
,
and
the
Earth
,
the
which
relation
is
all
that
is
changed
.
Now
if
for
the
obtaining
of
the
same
effect
ad
unguem
,
it
be
all
one
whether
the
Earth
alone
moveth
,
the
rest
of
the
Universe
standing
still
;
Nature
never
doth
that
by
many
things
,
which
may
be
done
by
a
few
.
or
that
,
the
Earth
onely
standing
still
,
the
whole
Universe
moveth
with
one
and
the
same
motion
;
who
would
believe
,
that
Nature
(
which
by
common
consent
,
doth
not
that
by
many
things
,
which
may
be
done
by
few
)
hath
chosen
to
make
an
innumerable
number
of
most
vast
bodies
move
,
and
that
with
an
unconceivable
velocity
,
to
perform
that
,
which
might
be
done
by
the
moderate
motion
of
one
alone
about
its
own
Centre
?
SIMPL.
I
do
not
well
understand
,
how
this
grand
motion
signifieth
nothing
as
to
the
Sun
,
as
to
the
Moon
,
as
to
the
other
Planets
,
and
as
to
the
innumerable
multitude
of
fixed
stars
:
or
why
you
should
say
that
it
is
to
no
purpose
for
the
Sun
to
pass
from
one
Meridian
to
another
;
to
rise
above
this
Horizon
,
to
set
beneath
that
other
;
to
make
it
one
while
day
,
another
while
night
:
the
like
variations
are
made
by
the
Moon
,
the
other
Planets
,
and
the
fixed
stars
themselves
.
SALV
.
All
these
alterations
instanced
by
you
,
are
nothing
,
save
onely
in
relation
to
the
Earth
:
and
that
this
is
true
,
do
but
imagine
the
Earth
to
move
,
The
diurnal
motion
causeth
no
mutation
amongst
the
Coelestial
Bodies
,
but
all
changes
have
relation
to
the
Earth
.
and
there
will
be
no
such
thing
in
the
World
as
the
rising
or
setting
of
the
Sun
or
Moon
,
nor
Horizons
,
nor
Meridians
,
nor
days
,
nor
nights
;
nor
,
in
a
word
,
will
such
a
motion
cause
any
mutation
between
the
Moon
and
Sun
,
or
any
other
star
whatsoever
,
whether
fixed
or
erratick
;
but
all
these
changes
have
relation
to
the
Earth
:
which
all
do
yet
in
sum
import
no
other
than
as
if
the
Sun
should
shew
it self
now
to
China
,
anon
to
Persia
,
then
to
Egypt
,
Greece
,
France
,
Spain
,
America
,
&c.
and
the
like
holdeth
in
the
Moon
,
and
the
rest
of
the
Coelestial
Bodies
:
which
self
same
effect
falls
out
exactly
in
the
same
manner
,
if
,
without
troubling
so
great
a
part
of
the
Universe
,
the
Terrestrial
Globe
be
made
to
revolve
in
it self
.
A
second
confirmation
that
the
diurnal
motion
belongs
to
the
Earth
.
But
we
will
augment
the
difficulty
by
the
addition
of
this
other
,
which
is
a
very
great
one
,
namely
,
that
if
you
will
ascribe
this
Great
Motion
to
Heaven
,
you
must
of
necessity
make
it
contrary
to
the
particular
motion
of
all
the
Orbs
of
the
Planets
,
each
of
which
without
controversie
hath
its
peculiar
motion
from
the
West
towards
the
East
,
and
this
but
very
easie
and
moderate
:
and
then
you
make
them
to
be
hurried
to
the
contrary
part
,
i.
e.
from
East
to
West
,
by
this
most
furious
diurnal
motion
:
whereas
,
on
the
contrary
,
making
the
Earth
to
move
in
it self
,
the
contrariety
of
motions
is
taken
away
,
and
the
onely
motion
from
West
to
East
is
accommodated
to
all
appearances
,
and
exactly
satisfieth
every
Phoenomenon
.
SIMPL.
As
to
the
contrariety
of
Motions
it
would
import
little
,
Circular
motions
are
not
contrary
,
according
to
Aristotle
.
for
Aristotle
demonstrateth
,
that
circular
motions
,
are
not
contrary
to
one
another
;
and
that
theirs
cannot
be
truly
called
contrariety
.
SALV
.
Doth
Aristotle
demonstrate
this
,
or
doth
he
not
rather
barely
affirm
it
,
as
serving
to
some
certain
design
of
his
?
If
contraries
be
those
things
,
that
destroy
one
another
,
as
he
himself
affirmeth
,
I
do
not
see
how
two
moveables
that
encounter
each
other
in
a
circular
line
,
should
lesse
prejudice
one
another
,
than
if
they
interfered
in
a
right
line
.
SAGR.
Hold
a
little
,
I
pray
you
.
Tell
me
Simplicius
,
when
two
Knights
encounter
each
other
,
tilting
in
open
field
,
or
when
two
whole
Squadrons
,
or
two
Fleets
at
Sea
,
make
up
to
grapple
,
and
are
broken
and
sunk
,
do
you
call
these
encounters
contrary
to
one
another
?
SIMPL.
Yes
,
we
say
they
are
contrary
.
SAGR.
How
then
,
is
there
no
contrariety
in
circular
motions
.
These
motions
,
being
made
upon
the
superficies
of
the
Earth
or
Water
,
which
are
,
as
you
know
,
spherical
,
come
to
be
circular
.
Can
you
tell
,
Simplicius
,
which
those
circular
motions
be
,
that
are
not
contrary
to
each
other
?
They
are
(
if
I
mistake
not
)
those
of
two
circles
,
which
touching
one
another
without
,
one
thereof
being
turn'd
round
,
naturally
maketh
the
other
move
the
contrary
[
](A61244-e24160-b)*
*
As
you
see
in
a
Mill
,
wherein
the
implicated
cogs
set
the
wheels
on
moving
.
way
;
but
if
one
of
them
shall
be
within
the
other
,
it
is
impossible
that
their
motion
being
made
towards
different
points
,
they
should
not
justle
one
another
.
SALV
.
But
be
they
contrary
,
or
not
contrary
,
these
are
but
alterations
of
words
;
and
I
know
,
that
upon
the
matter
,
it
would
be
far
more
proper
and
agreeable
with
Nature
,
if
we
could
salve
all
with
one
motion
onely
,
than
to
introduce
two
that
are
(
if
you
will
not
call
them
contrary
)
opposite
;
yet
do
I
not
censure
this
introduction
(
of
contrary
motions
)
as
impossible
;
nor
pretend
I
from
the
denial
thereof
,
to
inferre
a
necessary
Demonstration
,
but
onely
a
greater
probability
,
A
third
confirmation
of
the
same
Doctrine
.
of
the
other
.
A
third
reason
which
maketh
the
Ptolomaique
Hypothesis
lesse
probable
is
,
that
it
most
unreasonably
confoundeth
the
order
,
which
we
assuredly
see
to
be
amongst
those
Coelestial
Bodies
,
the
circumgyration
of
which
is
not
questionable
,
The
greater
Orbs
make
their
conversions
in
greater
times
.
but
most
certain
.
And
that
Order
is
,
that
according
as
an
Orb
is
greater
,
it
finisheth
its
revolution
in
a
longer
time
,
and
the
lesser
,
in
shorter
.
And
thus
Saturn
describing
a
greater
Circle
than
all
the
other
Planets
,
compleateth
the
same
in
thirty
yeares
:
Jupiter
finisheth
his
;
that
is
lesse
,
in
twelve
years
:
Mars
in
two
:
The
Moon
runneth
thorow
hers
,
so
much
lesse
than
the
rest
,
in
a
Moneth
onely
.
Nor
do
we
lesse
sensibly
see
that
of
the
Medicean
Stars
,
The
times
of
the
Medicean
Planets
conversions
.
which
is
nearest
to
Jupiter
,
to
make
its
revolution
in
a
very
short
time
,
that
is
,
in
four
and
forty
hours
,
or
thereabouts
,
the
next
to
that
in
three
dayes
and
an
half
,
the
third
in
seven
dayes
,
and
the
most
remote
in
sixteen
.
And
this
rate
holdeth
well
enough
,
nor
will
it
at
all
alter
,
whilest
we
assign
the
motion
of
24
hours
to
the
Terrestrial
Globe
,
for
it
to
move
round
its
own
center
in
that
time
;
but
if
you
would
have
the
Earth
immoveable
,
it
is
necessary
,
that
when
you
have
past
from
the
short
period
of
the
Moon
,
to
the
others
successively
bigger
,
until
you
come
to
that
of
Mars
in
two
years
,
and
from
thence
to
that
of
the
bigger
Sphere
of
Jupiter
in
twelve
years
,
and
from
this
to
the
other
yet
bigger
of
Saturn
,
whose
period
is
of
thirty
years
,
it
is
necessary
,
I
say
,
that
you
passe
to
another
Sphere
incomparably
greater
still
than
that
,
and
make
this
to
accomplish
an
entire
revolution
in
twenty
four
hours
.
The
motion
of
24
hours
ascribed
to
the
highest
Sphere
disorders
the
period
of
the
inferiour
.
And
this
yet
is
the
least
disorder
that
can
follow
.
For
if
any
one
should
passe
from
the
Sphere
of
Saturn
to
the
Starry
Orb
,
and
make
it
so
much
bigger
than
that
of
Saturn
,
as
proportion
would
require
,
in
respect
of
its
very
slow
motion
,
of
many
thousands
of
years
,
then
it
must
needs
be
a
Salt
much
more
absurd
,
to
skip
from
this
to
another
bigger
,
and
to
make
it
convertible
in
twenty
four
hours
.
But
the
motion
of
the
Earth
being
granted
,
the
order
of
the
periods
will
be
exactly
observed
,
and
from
the
very
slow
Sphere
of
Saturn
,
we
come
to
the
fixed
Stars
,
which
are
wholly
immoveable
,
The
fourth
Confirmation
.
and
so
avoid
a
fourth
difficulty
,
which
we
must
of
necessity
admit
,
if
the
Starry
Sphere
be
supposed
moveable
,
and
that
is
the
immense
disparity
between
the
motions
of
those
stars
themselves
;
Great
disparity
amongst
the
motions
of
the
particular
fixed
stars
,
if
their
Sphere
be
moveable
.
of
which
some
would
come
to
move
most
swiftly
in
most
vast
circles
,
others
most
slowly
in
circles
very
small
,
according
as
those
or
these
should
be
found
nearer
,
or
more
remote
from
the
Poles
;
which
still
is
accompanied
with
an
inconvenience
,
as
well
because
we
see
those
,
of
whose
motion
there
is
no
question
to
be
made
,
to
move
all
in
very
immense
circles
;
as
also
,
because
it
seems
to
be
an
act
done
with
no
good
consideration
,
to
constitute
bodies
,
that
are
designed
to
move
circularly
,
at
immense
distances
from
the
centre
,
and
afterwards
to
make
them
move
in
very
small
circles
.
And
not
onely
the
magnitudes
of
the
circles
,
and
consequently
the
velocity
of
the
motions
of
these
Stars
,
shall
be
most
different
from
the
circles
and
motions
of
those
others
,
The
fifth
Confirmation
.
but
(
which
shall
be
the
fifth
inconvenience
)
the
self-same
Stars
shall
successively
vary
its
circles
and
velocities
:
The
motions
of
the
fixed
stars
would
accelerate
and
grow
slow
in
divers
times
,
if
the
starry
Sphere
were
moueable
.
For
that
those
,
which
two
thousand
years
since
were
in
the
Equinoctial
,
and
consequently
did
with
their
motion
describe
very
vast
circles
,
being
in
our
dayes
many
degrees
distant
from
thence
,
must
of
necessity
become
more
slow
of
motion
,
and
be
reduced
to
move
in
lesser
circles
,
and
it
is
not
altogether
impossible
but
that
a
time
may
come
,
in
which
some
of
them
which
in
aforetime
had
continually
moved
,
shall
be
reduced
by
uniting
with
the
Pole
,
to
a
state
of
rest
,
and
then
after
some
time
of
cessation
,
shall
return
to
their
motion
again
;
whereas
the
other
Stars
,
touching
whose
motion
none
stand
in
doubt
,
do
all
describe
,
as
hath
been
said
,
the
great
circle
of
their
Orb
,
and
in
that
maintain
themselves
without
any
variation
.
The
sixth
Confirmation
.
The
absurdity
is
farther
enlarged
(
which
let
be
the
sixth
inconvenience
)
to
him
that
more
seriously
examineth
the
thing
,
in
that
no
thought
can
comprehend
what
ought
to
be
the
solidity
of
that
immense
Sphere
,
whose
depth
so
stedfastly
holdeth
fast
such
a
multitude
of
Stars
,
which
without
ever
changing
site
among
themselves
,
are
with
so
much
concord
carried
about
,
with
so
great
disparity
of
motions
.
Or
else
,
supposing
the
Heavens
to
be
fluid
,
as
we
are
with
more
reason
to
believe
,
so
as
that
every
Star
wandereth
to
and
fro
in
it
,
by
wayes
of
its
own
,
what
rules
shall
regulate
their
motions
,
and
to
what
purpose
,
so
,
as
that
being
beheld
from
the
Earth
,
they
appear
as
if
they
were
made
by
one
onely
Sphere
?
It
is
my
opinion
,
that
they
might
so
much
more
easily
do
that
,
and
in
a
more
commodious
manner
,
by
being
constituted
immoveable
,
than
by
being
made
errant
,
by
how
much
more
facile
it
is
to
number
the
quarries
in
the
Pavement
of
a
Piazza
,
than
the
rout
of
boyes
which
run
up
and
down
upon
them
.
The
Seventh
Confirmation
.
And
lastly
,
which
is
the
seventh
instance
,
if
we
attribute
the
Diurnal
Motion
to
the
highest
Heaven
,
it
must
be
constituted
of
such
a
force
and
efficacy
,
as
to
carry
along
with
it
the
innumerable
multitude
of
fixed
Stars
,
Bodies
all
of
vast
magnitude
,
and
far
bigger
than
the
Earth
;
and
moreover
all
the
Spheres
of
the
Planets
;
notwithstanding
that
both
these
and
those
of
their
own
nature
move
the
contrary
way
.
And
besides
all
this
,
it
must
be
granted
,
that
also
the
Element
of
Fire
,
and
the
greater
part
of
the
Air
,
are
likewise
forcibly
hurried
along
with
the
rest
,
and
that
the
sole
little
Globe
of
the
Earth
pertinaciously
stands
still
,
and
unmoved
against
such
an
impulse
;
a
thing
,
which
in
my
thinking
,
is
very
difficult
;
nor
can
I
see
how
the
Earth
,
a
pendent
body
,
The
Earth
a
pendent
Body
,
and
equilibrated
in
a
fluid
Medium
seems
unable
to
resist
the
rapture
of
the
Diurnal
Motion
.
and
equilibrated
upon
its
centre
,
exposed
indifferently
to
either
motion
or
rest
,
and
environed
with
a
liquid
ambient
,
should
not
yield
also
as
the
rest
,
and
be
carried
about
.
But
we
find
none
of
these
obstacles
in
making
the
Earth
to
move
;
a
small
body
,
and
insensible
,
compared
to
the
Universe
,
and
therefore
unable
to
offer
it
any
violence
.
SAGR.
I
find
my
fancy
disturbed
with
certain
conjectures
so
confusedly
sprung
from
your
later
discourses
;
that
,
if
I
would
be
enabled
to
apply
my self
with
atention
to
what
followeth
,
I
must
of
necessity
attempt
whether
I
can
better
methodize
them
,
and
gather
thence
their
true
construction
,
if
haply
any
can
be
made
of
them
;
and
peradventure
,
the
proceeding
by
interrogations
may
help
me
the
more
easily
to
expresse
my self
.
Therefore
I
demand
first
of
Simplicius
,
whether
he
believeth
,
that
divers
motions
may
naturally
agree
to
one
and
the
same
moveable
body
,
or
else
that
it
be
requisite
its
natural
and
proper
motion
be
onely
one
.
SIMPL.
To
one
single
moveable
,
A
single
moveable
hath
but
onely
one
natural
motion
,
and
all
the
rest
are
by
participation
.
there
can
naturally
agree
but
one
sole
motion
,
and
no
more
;
the
rest
all
happen
accidentally
and
by
participation
;
like
as
to
him
that
walketh
upon
the
Deck
of
a
Ship
,
his
proper
motion
is
that
of
his
walk
,
his
motion
by
participation
that
which
carrieth
him
to
his
Port
,
whither
he
would
never
with
his
walking
have
arrived
,
if
the
Ship
with
its
motion
had
not
wafted
him
thither
.
SAGR.
Tell
me
secondly
.
That
motion
,
which
is
communicated
to
any
moveable
by
participation
,
whilest
it
moveth
by
it self
,
with
another
motion
different
from
the
participated
,
is
it
necessary
,
that
it
do
reside
in
some
certain
subject
by
it self
,
or
else
can
it
subsist
in
nature
alone
,
without
other
support
.
SIMPL.
Aristotle
giveth
you
an
answer
to
all
these
questions
,
Motion
cannot
be
made
without
its
moveable
subject
.
and
tels
you
,
that
as
of
one
sole
moveable
the
motion
is
but
one
;
so
of
one
sole
motion
the
moveable
is
but
one
;
and
consequently
,
that
without
the
inherence
in
its
subject
,
no
motion
can
either
subsist
,
or
be
imagined
.
SAGR.
I
would
have
you
tell
me
in
the
third
place
,
whether
you
beblieve
that
the
Moon
and
the
other
Planets
and
Coelestial
bodies
,
have
their
proper
motions
,
and
what
they
are
.
SIMPL.
They
have
so
,
and
they
be
those
according
to
which
they
run
through
the
Zodiack
,
the
Moon
in
a
Moneth
,
the
Sun
in
a
Year
,
Mars
in
two
,
the
Starry
Sphere
in
those
so
many
thousand
.
And
these
are
their
proper
,
or
natural
motions
.
SAGR.
But
that
motion
wherewith
I
see
the
fixed
Stars
,
and
with
them
all
the
Planets
go
unitedly
from
East
to
West
,
and
return
round
to
the
East
again
in
twenty
four
hours
,
how
doth
it
agree
with
them
?
SIMPL.
It
suiteth
with
them
by
participation
.
SAGR.
This
then
resides
not
in
them
,
and
not
residing
in
them
,
nor
being
able
to
subsist
without
some
subject
in
which
it
is
resident
,
it
must
of
force
be
the
proper
and
natural
motion
of
some
other
Sphere
.
SIMPL.
For
this
purpose
Astronomers
,
and
Philosophers
have
found
another
high
Sphere
,
above
all
the
rest
,
without
Stars
,
to
which
Natural
agreeth
the
Diurnal
Motion
;
and
this
they
call
the
Primum
mobile
;
the
which
carrieth
along
with
it
all
the
inferiour
Spheres
,
contributing
and
imparting
its
motion
to
them
.
SAGR.
But
when
,
without
introducing
other
Spheres
unknown
and
hugely
vast
,
without
other
motions
or
communicated
raptures
,
with
leaving
to
each
Sphere
its
sole
and
simple
motion
,
without
intermixing
contrary
motions
,
but
making
all
turn
one
way
,
as
it
is
necessary
that
they
do
,
depending
all
upon
one
sole
principle
,
all
things
proceed
orderly
,
and
correspond
with
most
perfect
harmony
,
why
do
we
reject
this
Phoenomenon
,
and
give
our
assent
to
those
prodigious
and
laborious
conditions
?
SIMPL.
The
difficulty
lyeth
in
finding
out
this
so
natural
and
expeditous
way
.
SAGR.
In
my
judgment
this
is
found
.
Make
the
Earth
the
Primum
mobile
,
that
is
,
make
it
turn
round
its
own
axis
in
twenty
four
hours
,
and
towards
the
same
point
with
all
the
other
Spheres
;
and
without
participating
this
same
motion
to
any
other
Planet
or
Star
,
all
shall
have
their
risings
,
settings
,
and
in
a
word
,
all
their
other
appearances
.
SIMPL.
The
business
is
,
to
be
able
to
make
the
Earth
move
without
a
thousand
inconveniences
.
SALV
.
All
the
inconveniences
shall
be
removed
as
fast
as
you
propound
them
:
and
the
things
spoken
hitherto
are
onely
the
primary
and
more
general
inducements
which
give
us
to
believe
that
the
diurnal
conversion
may
not
altogether
without
probability
be
applyed
to
the
Earth
,
rather
than
to
all
the
rest
of
the
Universe
:
the
which
inducements
I
impose
not
upon
you
as
inviolable
Axioms
,
but
as
hints
,
which
carry
with
them
somewhat
of
likelihood
.
One
single
experiment
,
or
sound
demonstration
batereth
down
all
arguments
meerly
probable
.
And
in
regard
I
know
very
well
,
that
one
sole
experiment
,
or
concludent
demonstration
,
produced
on
the
contrary
part
,
sufficeth
to
batter
to
the
ground
these
and
a
thousand
other
probable
Arguments
;
therefore
it
is
not
fit
to
stay
here
,
but
proceed
forwards
and
hear
what
Simplicius
answereth
,
and
what
greater
probabilities
,
or
stronger
arguments
he
alledgeth
on
the
contrary
.
SIMPL.
I
will
first
say
something
in
general
upon
all
these
considerations
together
,
and
then
I
will
descend
to
some
particulars
.
It
seems
that
you
universally
bottom
all
you
say
upon
the
greater
simplicity
and
facility
of
producing
the
same
effects
,
whilst
you
hold
,
that
as
to
the
causing
of
them
,
the
motion
of
the
Earth
alone
,
serveth
as
well
as
that
of
all
the
rest
of
the
World
,
the
Earth
deducted
:
but
as
to
the
operations
,
you
esteem
that
much
easier
than
this
.
To
which
I
reply
,
that
I
am
also
of
the
same
opinion
,
so
long
as
I
regard
my
own
not
onely
finite
,
but
feeble
power
;
but
having
a
respect
to
the
strength
of
the
Mover
,
which
is
infinite
,
it
s
no
lesse
easie
to
move
the
Universe
,
than
the
Earth
,
yea
than
a
straw
.
And
if
his
power
be
infinite
,
Of
an
infinite
power
one
would
think
a
greater
part
should
rather
be
imploy'd
than
a
lesse
.
why
should
he
not
rather
exercise
a
greater
part
thereof
than
a
lesse
?
Therefore
,
I
hold
that
your
discourse
in
general
is
not
convincing
.
SALV
.
If
I
had
at
any
time
said
,
that
the
Universe
moved
not
for
want
of
power
in
the
Mover
,
I
should
have
erred
,
and
your
reproof
would
have
been
seasonable
;
and
I
grant
you
,
that
to
an
infinite
power
,
it
is
as
easie
to
move
an
hundred
thousand
,
as
one
.
But
that
which
I
did
say
,
concerns
not
the
Mover
,
but
onely
hath
respect
to
the
Moveables
;
and
in
them
,
not
onely
to
their
resistance
,
which
doubtlesse
is
lesser
in
the
Earth
,
than
in
the
Universe
;
but
to
the
many
other
particulars
,
but
even
now
considered
.
As
to
what
you
say
in
the
next
place
,
that
of
an
infinite
power
it
is
better
to
exercise
a
great
part
than
a
small
:
I
answer
,
that
of
infinite
one
part
is
not
greater
than
another
,
since
both
are
infinite
;
Of
infinity
,
one
part
is
no
bigger
than
another
,
although
they
are
comparatively
unequal
.
nor
can
it
be
said
,
that
of
the
infinite
number
,
an
hundred
thousand
is
a
greater
part
than
two
,
though
that
be
fifty
thousand
times
greater
than
this
;
and
if
to
the
moving
of
the
Universe
there
be
required
a
finite
power
,
though
very
great
in
comparison
of
that
which
sufficeth
to
move
the
Earth
onely
;
yet
is
there
not
implied
therein
a
greater
part
of
the
infinite
power
,
nor
is
that
part
lesse
infinite
which
remaineth
unimploy'd
.
So
that
to
apply
unto
a
particular
effect
,
a
little
more
,
or
a
little
lesse
power
,
importeth
nothing
;
besides
that
the
operation
of
such
vertue
,
hath
not
for
its
bound
or
end
the
Diurnal
Motion
onely
;
but
there
are
several
other
motions
in
the
World
,
which
we
know
of
,
and
many
others
there
may
be
,
that
are
to
us
unknown
.
Therefore
if
we
respect
the
Moveables
,
and
granting
it
as
out
of
question
,
that
it
is
a
shorter
and
easier
way
to
move
the
Earth
,
than
the
Universe
;
and
moreover
,
having
an
eye
to
the
so
many
other
abreviations
,
and
facilities
that
onely
this
way
are
to
be
obtained
,
an
infallible
Maxime
of
Aristotle
,
which
he
teacheth
us
,
that
,
frustra
fit
per
plura
,
quod
potest
fieri
per
pauciora
,
rendereth
it
more
probable
that
the
Diurnal
Motion
belongs
to
the
Earth
alone
,
than
to
the
Universe
,
the
Earth
subducted
.
SIMPL.
In
reciting
that
Axiom
,
you
have
omitted
a
small
clause
,
which
importeth
as
much
as
all
the
rest
,
especially
in
our
case
,
that
is
to
say
,
the
words
aequè
bene
.
It
is
requisite
therefore
to
examine
whether
this
Hypothesis
doth
equally
well
satisfie
in
all
particulars
,
as
the
other
.
SALV
.
The
knowledg
whether
both
these
positions
do
aequè
bene
,
satisfie
,
may
be
comprehended
from
the
particular
examination
of
the
appearances
which
they
are
to
satisfie
;
for
hitherto
we
have
discoursed
,
and
will
continue
to
argue
ex
hypothesi
,
namely
,
supposing
,
that
as
to
the
satisfaction
of
the
appearances
,
both
the
assumptions
are
equally
accomodated
.
In
the
Axiome
Frustra
fit
per
plura
,
&c.
the
addition
of
aeque
benè
,
is
superfluous
.
As
to
the
clause
which
you
say
was
omitted
by
me
,
I
have
more
reason
to
suspect
that
it
was
superfluously
inserted
by
you
.
For
the
expression
aequè
bene
,
is
a
relative
that
necessarily
requireth
two
terms
at
least
,
for
a
thing
cannot
have
relation
to
its
self
,
nor
do
we
say
,
v.
gr
.
rest
to
be
equally
good
,
as
rest
.
And
because
,
when
we
say
,
that
is
done
in
vain
by
many
means
,
which
may
be
done
with
fewer
,
we
mean
,
that
that
which
is
to
be
done
,
ought
to
be
the
same
thing
,
not
two
different
ones
;
and
because
the
same
thing
cannot
be
said
to
be
done
as
well
as
its
self
;
therefore
,
the
addition
of
the
Phrase
aequè
bene
is
superfluous
,
and
a
relation
,
that
hath
but
one
term
onely
.
SAGR.
Unlesse
you
will
have
the
same
befal
us
,
as
did
yesterday
,
let
us
return
to
our
matter
in
hand
;
and
let
Simplicius
begin
to
produce
those
difficulties
that
seem
in
his
opinion
,
to
thwart
this
new
disposition
of
the
World
.
SIMPL.
That
disposition
is
not
new
,
but
very
old
;
and
that
you
may
see
it
is
so
,
Aristotle
confuteth
it
;
and
his
confutations
are
these
:
Aristotles
Arguments
for
the
Earths
quiessence
.
First
if
the
Earth
moveth
either
in
it self
about
its
own
Centre
,
or
in
an
Excentrick
Circle
,
it
is
necessary
that
that
same
motion
be
violent
;
for
it
is
not
its
natural
motion
,
for
if
it
were
,
each
of
its
parts
would
partake
thereof
;
but
each
of
them
moveth
in
a
right
line
towards
its
Centre
.
It
being
therefore
violent
and
pteternatural
,
it
could
never
be
perpetual
:
But
the
order
of
the
World
is
perpetual
.
Therefore
,
&c.
Secondly
,
all
the
other
moveables
that
move
circularly
,
seem
to
[
](A61244-e25480-b)*
*
Resti●
indietz●
,
which
is
meant
here
of
that
motion
which
a
bowl
makes
when
is
born
by
its
by
as
to
one
side
or
other
,
and
so
hindered
in
its
direct
motion
.
●
stay
behind
,
and
to
move
with
more
than
one
motion
,
the
Prmum
Mobile
excepted
:
Whence
it
would
be
necessary
that
the
Earth
also
do
move
with
two
motions
;
and
if
that
should
be
so
,
it
would
inevitably
follow
,
that
mutations
should
be
made
in
the
Fixed
Stars
,
the
which
none
do
perceive
;
nay
without
any
variation
,
the
same
Stars
alwayes
rise
from
towards
the
same
places
,
and
in
the
same
places
do
set
.
Thirdly
,
the
motion
of
the
parts
is
the
same
with
that
of
the
whole
,
and
naturally
tendeth
towards
the
Centre
of
the
Universe
;
and
for
the
same
cause
rest
,
being
arrived
thither
.
He
thereupon
moves
the
question
whether
the
motion
of
the
parts
hath
a
tendency
to
centre
of
the
Universe
,
or
to
the
centre
of
the
Earth
;
and
concludeth
that
it
goeth
by
proper
instinct
to
the
centre
of
the
Universe
,
and
per
accidence
to
that
of
the
Earth
;
of
which
point
we
largely
discoursed
yesterday
.
He
lastly
confirmeth
the
same
with
a
fourth
argument
taken
from
the
experiment
of
grave
bodies
,
which
faling
from
on
high
,
descend
perpendicularly
unto
the
Earths
surface
;
and
in
the
same
manner
Projections
shot
perpendicularly
upwards
,
do
by
the
same
lines
return
perpendicularly
down
again
,
though
they
were
shot
to
a
very
great
height
.
All
which
arguments
necessarily
prove
their
motion
to
be
towards
the
Centre
of
the
Earth
,
which
without
moving
at
all
waits
for
,
and
receiveth
them
.
He
intimateth
in
the
last
place
that
the
Astronomers
alledg
other
reasons
in
confirmation
of
the
same
conclusions
,
I
mean
of
the
Earths
being
in
the
Centre
of
the
Universe
,
and
immoveable
;
and
instanceth
onely
in
one
of
them
,
to
wit
,
that
all
the
Phaenomena
or
appearances
that
are
seen
in
the
motions
of
the
Stars
,
perfectly
agree
with
the
position
of
the
Earth
in
the
Centre
;
which
would
not
be
so
,
were
the
Earth
seated
otherwise
.
The
rest
produced
by
Ptolomy
and
the
other
Astronomers
,
I
can
give
you
now
if
you
please
,
or
after
you
have
spoken
what
you
have
to
say
in
answer
to
these
of
Aristotle
.
SALV
.
The
arguments
which
are
brought
upon
this
occasion
are
of
two
kinds
:
Two
kindes
of
Arguments
touching
the
Earths
motion
or
rest
.
some
have
respect
to
the
accidents
Terrestrial
,
without
any
relation
to
the
Stars
,
and
others
are
taken
from
the
Phaenomena
and
observations
of
things
Coelestial
.
The
arguments
of
Aristotle
are
for
the
most
part
taken
from
things
neer
at
hand
,
and
he
leaveth
the
others
to
Astronomers
;
and
therefore
it
is
the
best
way
,
if
you
like
of
it
,
to
examine
these
taken
from
experiments
touching
the
Earth
,
and
then
proceed
to
those
of
the
other
kind
.
Arguments
of
Ptolomy
and
Tycho
,
and
other
persons
,
over
and
above
those
of
Aristotle
.
And
because
Ptolomy
,
Tycho
,
and
the
other
Astronomers
and
Philosophers
,
besides
the
arguments
of
Aristotle
by
them
assumed
,
confirmed
,
and
made
good
,
do
produce
certain
others
;
we
will
put
them
all
together
,
that
so
we
may
not
answer
twice
to
the
same
,
or
the
like
objections
.
Therefore
Simplicius
,
choose
whether
you
will
recite
them
your self
,
or
cause
me
to
ease
you
of
this
task
,
for
I
am
ready
to
serve
you
.
SIMPL.
It
is
better
that
you
quote
them
,
because
,
as
having
taken
more
pains
in
the
study
of
them
,
you
can
produce
them
with
more
readinesse
,
and
in
greater
number
.
SALV
.
All
,
The
first
argument
taken
from
grave
bodies
falling
from
on
high
to
the
ground
.
for
the
strongest
reason
,
alledge
that
of
grave
bodies
,
which
falling
downwards
from
on
high
,
move
by
a
right
line
,
that
is
perpendicular
to
the
surface
of
the
Earth
,
an
argument
which
is
held
undeniably
to
prove
that
the
Earth
is
immoveable
:
for
in
case
it
should
have
the
diurnal
motion
,
a
Tower
,
from
the
top
of
which
a
stone
is
let
fall
,
being
carried
along
by
the
conversion
of
the
Earth
,
in
the
time
that
the
stone
spends
in
falling
,
would
be
transported
many
hundred
yards
Eastward
,
and
so
far
distant
from
the
Towers
foot
would
the
stone
come
to
ground
.
The
which
effect
they
back
with
another
experiment
;
Which
is
confirmed
by
the
experiment
of
a
body
let
fall
from
the
round
top
of
a
Ship
.
to
wit
,
by
letting
a
bullet
of
lead
fall
from
the
round
top
of
a
Ship
,
that
lieth
at
anchor
,
and
observing
the
mark
it
makes
where
it
lights
,
which
they
find
to
be
neer
the
[
](A61244-e25800-b)*
*
That
is
,
at
the
foot
of
the
Mast
,
upon
the
upper
deck
.
partners
of
the
Mast
;
but
if
the
same
bullet
be
let
fall
from
the
same
place
when
the
ship
is
under
sail
,
it
shall
light
as
far
from
the
former
place
,
as
the
ship
hath
run
in
the
time
of
the
leads
descent
;
and
this
for
no
other
reason
,
than
because
the
natural
motion
of
the
ball
being
at
liberty
is
by
a
right
line
towards
the
centre
of
the
Earth
.
The
second
argument
taken
from
a
Projection
shot
very
high
.
They
fortifie
this
argument
with
the
experiment
of
a
projection
shot
on
high
at
a
very
great
distance
;
as
for
example
,
a
ball
sent
out
of
a
Cannon
,
erected
perpendicular
to
the
horizon
,
the
which
spendeth
so
much
time
in
ascending
and
falling
,
that
in
our
parallel
the
Cannon
and
we
both
should
be
carried
by
the
Earth
many
miles
towards
the
East
,
so
that
the
ball
in
its
return
could
never
come
neer
the
Peece
,
but
would
fall
as
far
West
,
The
third
argument
taken
from
the
shots
of
a
Cannon
,
towards
the
East
,
and
towards
the
West
▪
as
the
Earth
had
run
East
.
They
againe
adde
a
third
,
and
very
evident
experiment
,
scilicet
,
that
shooting
a
bullet
point
blank
(
or
as
Gunners
say
,
neither
above
nor
under
metal
)
out
of
a
Culverin
towards
the
East
,
and
afterwards
another
,
with
the
same
charge
,
and
at
the
same
elevation
or
disport
towards
the
West
,
the
range
towards
the
West
should
be
very
much
greater
then
the
other
towards
the
East
:
for
that
whil'st
the
ball
goeth
Westward
,
and
the
Peece
is
carried
along
by
the
Earth
Eastward
,
the
ball
will
fall
from
the
Peece
as
far
distant
as
is
the
aggregate
of
the
two
motions
,
one
made
by
it self
towards
the
West
,
and
the
other
by
the
Peece
carried
about
by
the
Earth
towards
the
East
;
and
on
the
contrary
,
from
the
range
of
the
ball
shot
Eastward
you
are
to
substract
the
space
the
Peece
moved
,
being
carried
after
it
.
Now
suppose
,
for
example
,
that
the
range
of
the
ball
shot
West
were
five
miles
,
and
that
the
Earth
in
the
same
parallel
and
in
the
time
of
the
Bals
ranging
should
remove
three
miles
,
the
Ball
in
this
case
would
fall
eight
miles
distant
from
the
Culverin
,
namely
,
it
s
own
five
Westward
,
and
the
Culverins
three
miles
Eastward
:
but
the
range
of
the
shot
towards
the
East
would
be
but
two
miles
long
,
for
so
much
is
the
remainder
,
after
you
have
substracted
from
the
five
miles
of
the
range
,
the
three
miles
which
the
Peece
had
moved
towards
the
same
part
.
But
experience
sheweth
the
Ranges
to
be
equal
,
therefore
the
Culverin
,
and
consequently
the
Earth
are
immoveable
.
This
argument
is
confirmed
by
two
shots
towards
the
South
and
towards
the
North.
And
the
stability
of
the
Earth
is
no
lesse
confirmed
by
two
other
shots
made
North
and
South
;
for
they
would
never
hit
the
mark
,
but
the
Ranges
would
be
alwayes
wide
,
or
towards
the
West
,
by
meanes
of
the
remove
the
mark
would
make
,
being
carried
along
with
the
Earth
towards
the
East
,
whil'st
the
ball
is
flying
.
And
it
is
likewise
confirmed
by
two
shots
towards
the
East
,
and
towards
the
West
.
And
not
onely
shots
made
by
the
Meridians
,
but
also
those
aimed
East
or
West
would
prove
uncertain
;
for
those
aim'd
East
would
be
too
high
,
and
those
directed
West
too
low
,
although
they
were
shot
point
blank
,
as
I
said
.
For
the
Range
of
the
Ball
in
both
the
shots
being
made
by
the
Tangent
,
that
is
,
by
a
line
parallel
to
the
Horizon
,
and
being
that
in
the
diurnal
motion
,
if
it
be
of
the
Earth
,
the
Horizon
goeth
continually
descending
towards
the
East
,
and
rising
from
the
West
(
therefore
the
Oriental
Stars
seem
to
rise
,
and
the
Occidental
to
decline
)
so
that
the
Oriental
mark
would
descend
below
the
aime
,
and
thereupon
the
shot
would
fly
too
high
,
and
the
ascending
of
the
Western
mark
would
make
the
shot
aimed
that
way
range
too
low
;
so
that
the
Peece
would
never
carry
true
towards
any
point
;
and
for
that
experience
telleth
us
the
contrary
,
it
is
requisite
to
say
,
that
the
Earth
is
immoveable
.
SIMPL.
These
are
solid
reasons
,
and
such
as
I
believe
no
man
can
answer
.
SALV
.
Perhaps
they
are
new
to
you
?
SIMPL.
Really
they
are
;
and
now
I
see
with
how
many
admirable
experiments
Nature
is
pleased
to
favour
us
,
wherewith
to
assist
us
in
the
knowledge
of
the
Truth
.
Oh!
how
exactly
one
truth
agreeth
with
another
,
and
all
conspire
to
render
each
other
inexpugnable
!
SAGR.
What
pity
it
is
that
Guns
were
not
used
in
Aristotles
age
,
he
would
with
help
of
them
have
easily
battered
down
ignorance
,
and
spoke
without
haesitation
of
these
mundane
points
.
SALV
.
I
am
very
glad
that
these
reasons
are
new
unto
you
,
that
so
you
may
not
rest
in
the
opinion
of
the
major
part
of
Peripateticks
,
who
believe
,
that
if
any
one
forsakes
the
Doctrine
of
Aristotle
,
it
is
because
they
did
not
understand
or
rightly
apprehend
his
demonstrations
.
Copernicus
his
followers
are
not
moved
through
ignorance
of
the
arguments
on
the
other
part
.
But
you
may
expect
to
hear
of
other
Novelties
,
and
you
shall
see
the
followers
of
this
new
Systeme
produce
against
themselves
observations
,
experiences
,
and
reasons
of
farre
greater
force
than
those
alledged
by
Aristotle
,
Ptolomy
,
and
other
opposers
of
the
same
conclusions
,
and
by
this
means
you
shall
come
to
ascertain
your self
that
they
were
not
induced
through
want
of
knowledge
or
expetience
to
follow
that
opinion
.
SAGR.
It
is
requisite
that
upon
this
occasion
I
relate
unto
you
some
accidents
that
befell
me
,
so
soon
as
I
first
began
to
hear
speak
of
this
new
doctrine
.
Being
very
young
,
and
having
scarcely
finished
my
course
of
Philosophy
,
which
I
left
off
,
as
being
set
upon
other
employments
,
there
chanced
to
come
into
these
parts
a
certain
Foreigner
of
Rostock
,
whose
name
,
as
I
remember
,
was
Christianus
Vurstitius
,
Christianus
Vurstitius
read
certain
Lectures
touching
the
opinion
of
Copernicus
,
&
what
ensued
thereupon
.
a
follower
of
Copernicus
,
who
in
an
Academy
made
two
or
three
Lectures
upon
this
point
,
to
whom
many
flock't
as
Auditors
;
but
I
thinking
they
went
more
for
the
novelty
of
the
subject
than
otherwise
,
did
not
go
to
hear
him
:
for
I
had
concluded
with
my self
that
that
opinion
could
be
no
other
than
a
solemn
madnesse
.
And
questioning
some
of
those
who
had
been
there
,
I
perceived
they
all
made
a
jest
thereof
,
execpt
one
,
who
told
me
that
the
businesse
was
not
altogether
to
be
laugh't
at
,
and
because
this
man
was
reputed
by
me
to
be
very
intelligent
and
wary
,
I
repented
that
I
was
not
there
,
and
began
from
that
time
forward
as
oft
as
I
met
with
any
one
of
the
Copernican
perswasion
,
to
demand
of
them
,
if
they
had
been
alwayes
of
the
same
judgment
;
and
of
as
many
as
I
examined
,
I
found
not
so
much
as
one
,
who
told
me
not
that
he
had
been
a
long
time
of
the
contrary
opinion
,
but
to
have
changed
it
for
this
,
as
convinced
by
the
strength
of
the
reasons
proving
the
same
:
and
afterwards
questioning
them
,
one
by
one
,
to
see
whether
they
were
well
possest
of
the
reasons
of
the
other
side
,
I
found
them
all
to
be
very
ready
and
perfect
in
them
;
The
followers
of
Copernicus
were
all
first
against
that
opinion
,
but
the
Sectators
of
Aristotle
&
Ptolomy
,
were
never
of
the
other
side
.
so
that
I
could
not
truly
say
,
that
they
had
took
up
this
opinion
out
of
ignorance
,
vanity
,
or
to
shew
the
acutenesse
of
their
wits
.
On
the
contrary
,
of
as
many
of
the
Peripateticks
and
Ptolomeans
as
I
have
asked
(
and
out
of
curiosity
I
have
talked
with
many
)
what
pains
they
had
taken
in
the
Book
of
Copernicus
,
I
found
very
few
that
had
so
much
as
superficially
perused
it
;
but
of
those
whom
,
I
thought
,
had
understood
the
same
,
not
one
;
and
moreover
,
I
have
enquired
amongst
the
followers
of
the
Peripatetick
Doctrine
,
if
ever
any
of
them
had
held
the
contrary
opinion
,
and
likewise
found
none
that
had
.
Whereupon
considering
that
there
was
no
man
who
followed
the
opinion
of
Copernicus
,
that
had
not
been
first
on
the
contrary
side
,
and
that
was
not
very
well
acquainted
with
the
reasons
of
Aristotle
and
Ptolomy
;
and
,
on
the
contrary
,
that
there
is
not
one
of
the
followers
of
Ptolomy
that
had
ever
been
of
the
judgment
of
Copernicus
,
and
had
left
that
,
to
imbrace
this
of
Aristotle
,
considering
,
I
say
,
these
things
,
I
began
to
think
,
that
one
,
who
leaveth
an
opinion
imbued
with
his
milk
,
and
followed
by
very
many
,
to
take
up
another
owned
by
very
few
,
and
denied
by
all
the
Schools
,
and
that
really
seems
a
very
great
Paradox
,
must
needs
have
been
moved
,
not
to
say
forced
,
by
more
powerful
reasons
.
For
this
cause
,
I
am
become
very
curious
to
dive
,
as
they
say
,
into
the
bottom
of
this
businesse
,
and
account
it
my
great
good
fortune
that
I
have
met
you
two
,
from
whom
I
may
without
any
trouble
,
hear
all
that
hath
been
,
and
,
haply
,
can
be
said
on
this
argument
,
assuring
my self
that
the
strength
of
your
reasons
will
resolve
all
scruples
,
and
bring
me
to
a
certainty
in
this
subject
.
SIMPL.
But
it
s
possible
your
opinion
and
hopes
may
be
disappointed
,
and
that
you
may
find
your selves
more
at
a
losse
in
the
end
than
you
was
at
first
.
SAGR.
I
am
very
confident
that
this
can
in
no
wise
befal
me
.
SIMPL.
And
why
not
?
I
have
a
manifest
example
in
my self
,
that
the
farther
I
go
,
the
more
I
am
confounded
.
SAGR.
This
is
a
sign
that
those
reasons
that
hitherto
seemed
concluding
unto
you
,
and
assured
you
in
the
truth
of
your
opinion
,
begin
to
change
countenance
in
your
mind
,
and
to
let
you
by
degrees
,
if
not
imbrace
,
at
least
look
towards
the
contrary
tenent
;
but
I
,
that
have
been
hitherto
indifferent
,
do
greatly
hope
to
acquire
rest
and
satisfaction
by
our
future
discourses
,
and
you
will
not
deny
but
I
may
,
if
you
please
but
to
hear
what
perswadeth
me
to
this
expectation
.
SIMPL.
I
will
gladly
hearken
to
the
same
,
and
should
be
no
lesse
glad
that
the
like
effect
might
be
wrought
in
me
.
SAGR.
Favour
me
therefore
with
answering
to
what
I
shall
ask
you
.
And
first
,
tell
me
,
Simplicius
,
is
not
the
conclusion
,
which
we
seek
the
truth
of
,
Whether
we
ought
to
hold
with
Aristotle
and
Ptolomy
,
that
the
Earth
onely
abiding
without
motion
in
the
Centre
of
the
Universe
,
the
Coelestial
bodies
all
move
,
or
else
,
Whether
the
Starry
Sphere
and
the
Sun
standing
still
in
the
Centre
,
the
Earth
is
without
the
same
,
and
owner
of
all
those
motions
that
in
our
seeming
belong
to
the
Sun
and
fixed
Stars
?
SIMPL.
These
are
the
conclusions
which
are
in
dispute
.
SAGR.
And
these
two
conclusions
,
are
they
not
of
such
a
nature
,
that
one
of
them
must
necessarily
be
true
,
and
the
other
false
?
SIMPL.
They
are
so
.
We
are
in
a
Dilemma
,
one
part
of
which
must
of
necessity
be
true
,
and
the
other
untrue
;
for
between
Motion
and
Rest
,
which
are
contradictories
,
there
cannot
be
instanced
a
third
,
so
as
that
one
cannot
say
the
Earth
moves
not
,
nor
stands
still
;
the
Sun
and
Stars
do
not
move
,
and
yet
stand
not
still
.
SAGR.
The
Earth
,
the
Sun
,
and
Stars
,
what
things
are
they
in
nature
?
are
they
petite
things
not
worth
our
notice
,
or
grand
and
worthy
of
consideration
?
SIMPL.
They
are
principal
,
noble
,
integral
bodies
of
the
Universe
,
most
vast
and
considerable
.
SAGR.
And
Motion
,
and
Rest
,
what
accidents
are
they
in
Nature
?
SIMPL.
So
great
and
principal
,
Motion
and
rest
principal
accidents
in
nature
.
that
Nature
her self
is
defined
by
them
.
SAGR.
So
that
moving
eternally
,
and
the
being
wholly
immoveable
are
two
conditions
very
considerable
in
Nature
,
and
indicate
very
great
diversity
;
and
especially
when
ascribed
to
the
principal
bodies
of
the
Universe
,
from
which
can
ensue
none
but
very
different
events
.
SIMPL.
Yea
doubtlesse
.
SAGR.
Now
answer
me
to
another
point
.
Do
you
believe
that
in
Logick
,
Rhethorick
,
the
Physicks
,
Metaphysicks
,
Mathematicks
,
and
finally
,
in
the
universa●ity
of
Disputations
there
are
arguments
sufficient
to
perswade
and
demonstrate
to
a
person
the
fallacious
,
no
lesse
then
the
true
conclusions
?
SIMPL.
No
Sir
;
Vntruths
cannot
be
demonstrated
,
as
Truths
are
.
rather
I
am
very
confident
and
certain
,
that
for
the
proving
of
a
true
and
necessary
conclusion
,
there
are
in
nature
not
onely
one
,
For
proof
of
true
conclusions
,
many
solid
arguments
may
be
produced
,
but
to
prove
a
falsity
,
none
.
but
many
very
powerfull
demonstrations
:
and
that
one
may
discusse
and
handle
the
same
divers
and
sundry
wayes
,
without
ever
falling
into
any
absurdity
;
and
that
the
more
any
Sophist
would
disturb
and
muddy
it
,
the
more
clear
would
its
certainty
appear
:
And
that
on
the
contrary
to
make
a
false
position
passe
for
true
,
and
to
perswade
the
belief
thereof
,
there
cannot
be
any
thing
produced
but
fallacies
,
Sophisms
,
Paralogismes
,
Equivocations
,
and
Discourses
vain
,
inconsistant
,
and
full
of
repugnances
and
contradictions
.
SAGR.
Now
if
eternal
motion
,
and
eternal
rest
be
so
principal
accidents
of
Nature
,
and
so
different
,
that
there
can
depend
on
them
only
most
different
consequences
,
and
especially
when
applyed
to
the
Sun
,
and
to
the
Earth
,
so
vast
and
famous
bodies
of
the
Universe
;
and
it
being
,
moreover
,
impossible
,
that
one
of
two
contradictory
Propositions
,
should
not
be
true
,
and
the
other
false
;
and
that
for
proof
of
the
false
one
,
any
thing
can
be
produced
but
fallacies
;
but
the
true
one
being
perswadeable
by
all
kind
of
concluding
and
demonstrative
arguments
,
why
should
you
think
that
he
,
of
you
two
,
who
shall
be
so
fortunate
as
to
maintain
the
true
Proposition
ought
not
to
perswade
me
?
You
must
suppose
me
to
be
of
a
stupid
wit
,
perverse
judgment
,
dull
mind
and
intellect
,
and
of
a
blind
reason
,
that
I
should
not
be
able
to
distinguish
light
from
darknesse
,
jewels
from
coals
,
or
truth
from
falshood
.
SIMPL.
I
tell
you
now
,
and
have
told
you
upon
other
occasions
,
that
the
best
Master
to
teach
us
how
to
discern
Sophismes
,
Paralogismes
,
and
other
fallacies
,
was
Aristotle
,
who
in
this
particular
can
never
be
deceived
.
SAGR.
You
insist
upon
Aristotle
,
who
cannot
speak
.
Yet
I
tell
you
,
Aristotle
would
either
refute
his
adversaries
arguments
,
or
would
alter
his
opinion
.
that
if
Aristotle
were
here
,
he
would
either
yield
himself
to
be
perswaded
by
us
,
or
refuting
our
arguments
,
convince
us
by
better
of
his
own
.
And
you
your self
,
when
you
heard
the
experiments
of
the
Suns
related
,
did
you
not
acknowledg
and
admire
them
,
and
confesse
them
more
concludent
than
those
of
Aristotle
?
Yet
neverthelesse
I
cannot
perceive
that
Salviatus
,
who
hath
produced
them
,
examined
them
,
and
with
exquisite
care
scan'd
them
,
doth
confesse
himself
perswaded
by
them
;
no
nor
by
others
of
greater
force
,
which
he
intimated
that
he
was
about
to
give
us
an
account
of
.
And
I
know
not
on
what
grounds
you
should
censure
Nature
,
as
one
that
for
many
Ages
hath
been
lazie
,
and
forgetful
to
produce
speculative
wits
;
and
that
knoweth
not
how
to
make
more
such
,
unlesse
they
be
such
kind
of
men
as
slavishly
giving
up
their
judgments
to
Aristotle
,
do
understand
with
his
brain
,
and
resent
with
his
senses
.
But
let
us
hear
the
residue
of
those
reasons
which
favour
his
opinion
,
that
we
may
thereupon
proceed
to
speak
to
them
;
comparing
and
weighing
them
in
the
ballance
of
impartiality
.
SALV
.
Before
I
proceed
any
farther
,
I
must
tell
Sagredus
,
that
in
these
our
Disputations
,
I
personate
the
Copernican
,
and
imitate
him
,
as
if
I
were
his
Zany
;
but
what
hath
been
effected
in
my
private
thoughts
by
these
arguments
which
I
seem
to
alledg
in
his
favour
,
I
would
not
have
you
to
judg
by
what
I
say
,
whil'st
I
am
in
the
heat
of
acting
my
part
in
the
Fable
;
but
after
I
have
laid
by
my
disguise
,
for
you
may
chance
to
find
me
different
from
what
you
see
me
upon
the
Stage
.
Now
let
us
go
on
.
Ptolomy
and
his
followers
produce
another
experiment
like
to
that
of
the
Projections
,
An
argument
taken
from
the
Clouds
,
and
from
Birds
.
and
it
is
of
things
that
being
separated
from
the
Earth
,
continue
a
good
space
of
time
in
the
Air
,
such
as
are
the
Clouds
,
Birds
of
flight
;
and
as
of
them
it
cannot
be
said
that
they
are
rapt
or
transparted
by
the
Earth
,
having
no
adhesion
thereto
,
it
seems
not
possible
,
that
they
should
be
able
to
keep
pace
with
the
velocity
thereof
;
nay
it
should
rather
seem
to
us
,
that
they
all
swiftly
move
towards
the
West
:
And
if
being
carried
about
by
the
Earth
,
passe
our
parallel
in
twenty
four
hours
,
which
yet
is
at
least
sixteen
thousand
miles
,
how
can
Birds
follow
such
a
course
or
revolution
?
Whereas
on
the
contrary
,
we
see
them
fly
as
well
towards
the
East
,
as
towards
the
West
,
An
argument
taken
from
the
air
which
we
feel
to
beat
upon
us
when
we
run
a
Horse
at
full
speed
.
or
any
other
part
,
without
any
sensible
difference
.
Moreover
,
if
when
we
run
a
Horse
at
his
speed
,
we
feel
the
air
beat
vehemently
against
our
face
,
what
an
impetuous
blast
ought
we
perpetually
to
feel
from
the
East
,
being
carried
with
so
rapid
a
course
against
the
wind
?
and
yet
no
such
effect
is
perceived
.
Take
another
very
ingenious
argument
inferred
from
the
following
experiment
.
An
argument
taken
from
the
whirling
of
circular
motion
,
which
hath
a
faculty
to
extrude
and
dissipate
.
The
circular
motion
hath
a
faculty
to
extrude
and
dissipate
from
its
Centre
the
parts
of
the
moving
body
,
whensoever
either
the
motion
is
not
very
slow
,
or
those
parts
are
not
very
well
fastened
together
;
and
therefore
,
if
v.
g.
we
should
turn
one
of
those
great
wheels
very
fast
about
,
wherein
one
or
more
men
walking
,
crane
up
very
great
weights
,
as
the
huge
massie
stone
,
used
by
the
Callander
for
pressing
of
Cloaths
;
or
the
fraighted
Barks
which
being
haled
on
shore
,
are
hoisted
out
of
one
river
into
another
;
in
case
the
parts
of
that
same
Wheel
so
swiftly
turn'd
round
,
be
not
very
well
joyn'd
and
pin'd
together
,
they
would
all
be
shattered
to
pieces
;
and
though
many
stones
or
other
ponderous
substances
,
should
be
very
fast
bound
to
its
outward
Rimme
,
yet
could
they
not
resist
the
impetuosity
,
which
with
great
violence
would
hurl
them
every
way
far
from
the
Wheel
,
and
consequently
from
its
Centre
.
So
that
if
the
Earth
did
move
with
such
and
so
much
greater
velocity
,
what
gravity
,
what
tenacity
of
lime
or
plaister
would
keep
together
Stones
,
Buildings
,
and
whole
Cities
,
that
they
should
not
be
tost
into
the
Air
by
so
precipitous
a
motion
?
And
both
men
and
beasts
,
which
are
not
fastened
to
the
Earth
,
how
could
they
resist
so
great
an
impetus
?
Whereas
,
on
the
other
side
,
we
see
both
these
,
and
far
lesse
resistances
of
pebles
,
sands
,
leaves
rest
quietly
on
the
Earth
,
and
to
return
to
it
in
falling
,
though
with
a
very
slow
motion
.
See
here
,
Simplicius
,
the
most
potent
arguments
,
taken
,
to
so
speak
,
from
things
Terrestrial
;
there
remain
those
of
the
other
kind
,
namely
,
such
as
have
relation
to
the
appearances
of
Heaven
,
which
reasons
,
to
confesse
the
truth
,
tend
more
to
prove
the
Earth
to
be
in
the
centre
of
the
Universe
,
and
consequently
,
to
deprive
it
of
the
annual
motion
about
the
same
,
ascribed
unto
it
by
Copernicus
.
Which
arguments
,
as
being
of
somewhat
a
different
nature
,
may
be
produced
,
after
we
have
examined
the
strength
of
these
already
propounded
.
SAGR.
What
say
you
Simplicius
?
do
you
think
that
Salviatus
is
Master
of
,
and
knoweth
how
to
unfold
the
Ptolomean
and
Aristotelian
arguments
?
Or
do
you
think
that
any
Peripatetick
is
equally
verst
in
the
Copernican
demonstrations
?
SIMPL.
Were
it
not
for
the
high
esteem
,
that
the
past
discourses
have
begot
in
me
of
the
learning
of
Salviatus
,
and
of
the
acutenesse
of
Sagredus
,
I
would
by
their
good
leave
have
gone
my
way
without
staying
for
their
answers
;
it
seeming
to
me
a
thing
impossible
,
that
so
palpable
experiments
should
be
contradicted
;
and
would
,
without
hearing
them
farther
,
confirm
my self
in
my
old
perswasion
;
for
though
I
should
be
made
to
see
that
it
was
erroneous
,
its
being
upheld
by
so
many
probable
reasons
,
would
render
it
excuseable
.
And
if
these
are
fallacies
,
what
true
demonstrations
were
ever
so
fair
?
SAGR.
Yet
its
good
that
we
hear
the
responsions
of
Salviatus
;
which
if
they
be
true
,
must
of
necessity
be
more
fair
,
and
that
by
infinite
degrees
;
and
those
must
be
deformed
,
yea
most
deformed
,
if
the
Metaphysical
Axiome
hold
,
True
and
fair
are
one
and
the
same
,
as
also
false
and
deformed
.
That
true
and
fair
are
one
and
the
same
thing
;
as
also
false
and
deformed
.
Therefore
Salviatus
let
's
no
longer
lose
time
.
SALV
.
The
first
Argument
alledged
by
Simplicius
,
if
I
well
remember
it
,
was
this
.
The
Earth
cannot
move
circularly
,
because
such
motion
would
be
violent
to
the
same
,
and
therefore
not
perpetual
:
that
it
is
violent
,
the
reason
was
:
Because
,
that
had
it
been
natural
,
its
parts
would
likewise
naturally
move
round
,
which
is
impossible
,
for
that
it
is
natural
for
the
parts
thereof
to
move
with
a
right
motion
downwards
.
To
this
my
reply
is
,
that
I
could
gladly
wish
,
The
answer
t●
Aristotles
first
argument
.
that
Aristotle
had
more
cleerly
exprest
himself
,
where
he
said
;
That
its
parts
would
likewise
move
circularly
;
for
this
moving
circularly
is
to
be
understood
two
wayes
,
one
is
,
that
every
particle
or
atome
separated
from
its
Whole
would
move
circularly
about
its
particular
centre
,
describing
its
small
Circulets
;
the
other
is
,
that
the
whole
Globe
moving
about
its
centre
in
twenty
four
hours
,
the
parts
also
would
turn
about
the
same
centre
in
four
and
twenty
hours
.
The
first
would
be
no
lesse
an
impertinency
,
than
if
one
should
say
,
that
every
part
of
the
circumference
of
a
Circle
ought
to
be
a
Circle
;
or
because
that
the
Earth
is
Spherical
,
that
therefore
every
part
thereof
be
a
Globe
,
for
so
doth
the
Axiome
require
:
Eadem
est
ratio
totius
,
&
partium
.
But
if
he
took
it
in
the
other
sense
,
to
wit
,
that
the
parts
in
imitation
of
the
Whole
should
move
naturally
round
the
Centre
of
the
whole
Globe
in
twenty
four
hours
,
I
say
,
that
they
do
so
;
and
it
concerns
you
,
instead
of
Aristotle
,
to
prove
that
they
do
not
.
SIMPL.
This
is
proved
by
Aristotle
in
the
same
place
,
when
he
saith
,
that
the
natural
motion
of
the
parts
is
the
right
motion
downwards
to
the
centre
of
the
Universe
;
so
that
the
circular
motion
cannot
naturally
agree
therewith
.
SALV
.
But
do
not
you
see
,
that
those
very
words
carry
in
them
a
confutation
of
this
solution
?
SIMPL.
How
?
and
where
?
SALV
.
Doth
not
he
say
that
the
circular
motion
of
the
Earth
would
be
violent
?
and
therefore
not
eternal
?
and
that
this
is
absurd
,
for
that
the
order
of
the
World
is
eternal
?
SIMPL.
He
saith
so
.
SALV
.
But
if
that
which
is
violent
cannot
be
eternal
,
That
which
is
violent
,
cannot
be
eternal
,
and
that
which
cannot
be
eternal
,
cannot
be
natural
.
then
by
conversion
,
that
which
cannot
be
eternal
,
cannot
be
natural
:
but
the
motion
of
the
Earth
downwards
cannot
be
otherwise
eternal
;
therefore
much
lesse
can
it
be
natural
:
nor
can
any
other
motion
be
natural
to
it
,
save
onely
that
which
is
eternal
.
But
if
we
make
the
Earth
move
with
a
circular
motion
,
this
may
be
eternal
to
it
,
and
to
its
parts
,
and
therefore
natural
.
SIMPL.
The
right
motion
is
most
natural
to
the
parts
of
the
Earth
,
and
is
to
them
eternal
;
nor
shall
it
ever
happen
that
they
move
not
with
a
right
motion
;
alwayes
provided
that
the
impediments
be
removed
.
SALV
.
You
equivocate
Simplicius
;
and
I
will
try
to
free
you
from
the
equivoke
.
Tell
me
,
therefore
,
do
you
think
that
a
Ship
which
should
sail
from
the
Strait
of
Gibralter
towards
Palestina
can
eternally
move
towards
that
Coast
?
keeping
alwayes
an
equal
course
?
SIMPL.
No
doubtlesse
.
SALV
.
And
why
not
?
SIMPL.
Because
that
Voyage
is
bounded
and
terminated
between
the
Herculean
Pillars
,
and
the
shore
of
the
Holy-land
;
and
the
distance
being
limited
,
it
is
past
in
a
finite
time
,
unlesse
one
by
returning
back
should
with
a
contrary
motion
begin
the
same
Voyage
anew
;
but
this
would
be
an
interrupted
and
no
continued
motion
.
SALV
.
Very
true
.
But
the
Navigation
from
the
Strait
of
Magalanes
by
the
Pacifick
Ocean
,
the
Moluccha's
,
the
Cape
di
buona
Speranza
,
and
from
thence
by
the
same
Strait
,
and
then
again
by
the
Pacifick
Ocean
,
&c.
do
you
believe
that
it
may
be
perpetuated
?
SIMPL.
It
may
;
for
this
being
a
circumgyration
,
which
returneth
about
its
self
,
with
infinite
replications
,
it
may
be
perpetuated
without
any
interruption
.
SALV
.
A
Ship
then
may
in
this
Voyage
continue
sailing
eternally
.
SIMPL.
It
may
,
in
case
the
Ship
were
incorruptible
,
but
the
Ship
decaying
,
the
Navigation
must
of
necessity
come
to
an
end
.
SALV
.
But
in
the
Mediterrane
,
though
the
Vessel
were
incorruptible
,
yet
could
she
not
sail
perpetually
towards
Palestina
,
that
Voyage
being
determined
.
Two
things
requisite
to
the
end
a
motion
may
perpetuate
it self
;
an
unlimited
space
,
and
an
incorruptible
moveable
.
Two
things
then
are
required
,
to
the
end
a
moveable
may
without
intermission
move
perpetually
;
the
one
is
,
that
the
motion
may
of
its
own
nature
be
indeterminate
and
infinite
;
the
other
,
that
the
moveable
be
likewise
incorruptible
and
eternal
.
SIMPL.
All
this
is
necessary
.
SALV
.
Therefore
you
may
see
how
of
your
own
accord
you
have
confessed
it
impossible
that
any
moveable
should
move
eternally
in
a
right
line
,
Right
motion
cannot
be
eternal
,
and
consequently
cannot
be
natural
to
the
Earth
.
in
regard
that
right
motion
,
whether
it
be
upwards
,
or
downwards
,
is
by
you
your self
bounded
by
the
circumference
and
centre
;
so
that
if
a
Moveable
,
as
suppose
the
Earth
be
eternal
,
yet
forasmuch
as
the
right
motion
is
not
of
its
own
nature
eternall
,
but
most
[
](A61244-e28270-b)*
*
Terminatissimo
.
terminate
,
it
cannot
naturally
suit
with
the
Earth
.
Nay
,
as
was
said
[
](A61244-e28280-b)*
*
By
this
expression
he
every
where
means
the
preceding
Dialogue
,
or
Giornata
.
yesterday
,
Aristotle
himself
is
constrained
to
make
the
Terrestrial
Globe
eternally
immoveable
.
When
again
you
say
,
that
the
parts
of
the
Earth
evermore
move
downwards
,
all
impediments
being
removed
,
you
egregiously
equivocate
;
for
then
,
on
the
other
side
they
must
be
impeded
,
contraried
,
and
forced
,
if
you
would
have
them
move
;
for
,
when
they
are
once
fallen
to
the
ground
,
they
must
be
violently
thrown
upwards
,
that
they
may
a
second
time
fall
;
and
as
to
the
impediments
,
these
only
hinder
its
arrival
at
the
centre
;
but
if
there
were
a
Well
,
that
did
passe
thorow
and
beyond
the
centre
,
yet
would
not
a
cold
of
Earth
passe
beyond
it
,
unlesse
inasmuch
as
being
transported
by
its
impetus
,
it
should
passe
the
same
to
return
thither
again
,
and
in
the
end
there
to
rest
.
As
therefore
to
the
defending
,
that
the
motion
by
a
right
line
doth
or
can
agree
naturally
neither
to
the
Earth
,
nor
to
any
other
moveable
,
whil'st
the
Universe
retaineth
its
perfect
order
,
I
would
have
you
take
no
further
paines
about
it
,
but
(
unlesse
you
will
grant
them
the
circular
motion
)
your
best
way
will
be
to
defend
and
maintain
their
immobility
.
SIMPL.
As
to
their
immoveablenesse
,
the
arguments
of
Aristotle
,
and
moreover
those
alledged
by
your self
seem
in
my
opinion
necessarily
to
conclude
the
same
,
as
yet
;
and
I
conceive
it
will
be
a
hard
matter
to
refute
them
.
SALV
.
Come
we
therefore
to
the
second
Argument
,
which
was
,
That
those
bodies
,
The
answer
to
the
second
argument
.
which
we
are
assured
do
move
circularly
,
have
more
than
one
motion
,
unlesse
it
be
the
Primum
Mobile
;
and
therefore
,
if
the
Earth
did
move
circularly
,
it
ought
to
have
two
motions
;
from
which
alterations
would
follow
in
the
rising
and
setting
of
the
Fixed
Stars
:
Which
effect
is
not
perceived
to
ensue
.
Therefore
,
&c.
The
most
proper
and
genuine
answer
to
this
Allegation
is
contained
in
the
Argument
it self
;
and
even
Aristotle
puts
it
in
our
mouths
,
which
it
is
impossible
,
Simplicius
,
that
you
should
not
have
seen
.
SIMPL.
I
neither
have
seen
it
,
nor
do
I
yet
apprehend
it
.
SALV
.
This
cannot
be
,
sure
,
the
thing
is
so
very
plain
.
SIMPL.
I
will
with
your
leave
,
cast
an
eye
upon
the
Text.
SAGR.
We
will
command
the
Text
to
be
brought
forthwith
.
SIMPL.
I
alwayes
carry
it
about
with
me
:
See
here
it
is
,
and
I
know
the
place
perfectly
well
,
which
is
in
lib.
2.
De
Coelo
,
cap.
16.
Here
it
is
,
Text
97.
Preterea
omnia
,
quae
feruntur
latione
circulari
subdeficere
videntur
,
ac
moveri
pluribus
una
latione
,
praeter
primam
Sphaeram
;
quare
&
Terram
necessariam
est
,
sive
circa
medium
,
sive
in
medio
posita
feratur
,
duabus
moveri
lationibus
.
Si
autem
hoc
acciderit
,
necessariam
est
fieri
mutationes
,
ac
conversiones
fixorum
astrorum
.
Hoc
autem
non
videtur
fieri
,
sed
semper
eadem
,
apud
eadem
loca
ipsius
,
&
oriuntur
,
&
occidunt
.
[
In
English
thus
:
]
Furthermore
all
that
are
carried
with
circular
motion
,
seem
to
[
](A61244-e28630-b)*
*
Subdeficere
.
foreslow
,
and
to
move
with
more
than
one
motion
,
except
the
first
Sphere
;
wherefore
it
is
necessary
that
the
Earth
move
with
two
motions
,
whether
it
be
carried
about
the
[
](A61244-e28640-b)*
*
Or
Centre
.
middle
,
or
placed
in
the
middle
.
But
if
it
be
so
,
there
would
of
necessity
be
alterations
and
conversions
made
amongst
the
fixed
Stars
.
But
no
such
thing
is
seen
to
be
done
,
but
the
same
Star
doth
alwayes
rise
and
set
in
the
same
place
.
In
all
this
I
find
not
any
falacy
,
and
my
thinks
the
argument
is
very
forcible
.
SALV
.
And
this
new
reading
of
the
place
hath
confirmed
me
in
the
fallacy
of
the
Sillogisme
,
and
moreover
,
discovered
another
falsity
.
Therefore
observe
.
The
Positions
,
or
if
you
will
,
Conclusions
,
which
Aristotle
endeavours
to
oppose
,
are
two
;
one
is
that
of
those
,
who
placing
the
Earth
in
the
midst
of
the
World
,
do
make
it
move
in
it self
about
its
own
centre
.
The
other
is
of
those
,
who
constituting
it
far
from
the
middle
,
do
make
it
revolve
with
a
circular
motion
about
the
middle
of
the
Universe
.
And
both
these
Positions
he
conjointly
impugneth
with
one
and
the
same
argument
.
Now
I
affirm
that
he
is
out
in
both
the
one
and
the
other
impugnation
;
and
that
his
error
against
the
first
Position
is
an
Equivoke
or
Paralogisme
;
Aristotles
argument
against
the
Earth●
motion
,
is
defective
in
two
things
and
his
mistake
touching
the
second
is
a
false
consequence
.
Let
us
begin
with
the
first
Assertion
,
which
constituteth
the
Earth
in
the
midst
of
the
World
,
and
maketh
it
move
in
it self
about
its
own
centre
;
and
let
us
confront
it
with
the
objection
of
Aristotle
;
saying
,
All
moveables
,
that
move
circularly
,
seem
to
[
](A61244-e28720-b)*
*
The
same
word
which
a
little
a●●ve
I
tendred
stay
behind
,
as
a
bowle
when
it
meets
with
●ul●s
.
foreslow
,
and
more
with
more
than
one
Byas
,
except
the
first
Sphere
(
that
is
the
primum
mobile
)
therefore
the
Earth
moving
about
its
own
centre
,
being
placed
in
the
middle
,
must
of
necessity
have
two
byasse
,
and
foreslow
.
But
if
this
were
so
,
it
would
follow
,
that
there
should
be
a
variation
in
the
rising
and
setting
of
the
fixed
Stars
,
which
we
do
not
perceive
to
be
done
:
Therefore
the
Earth
doth
not
move
,
&c.
Here
is
the
Paralogisme
,
and
to
discover
it
,
I
will
argue
with
Aristotle
in
this
manner
.
Thou
saist
,
oh
Aristotle
,
that
the
Earth
placed
in
the
middle
of
the
World
,
cannot
move
in
it self
(
i.
e.
upon
its
own
axis
)
for
then
it
would
be
requisite
to
allow
it
two
byasses
;
so
that
,
if
it
should
not
be
necessary
to
allow
it
more
than
one
Byas
onely
,
thou
wouldest
not
then
hold
it
impossible
for
it
to
move
onely
with
that
one
;
for
thou
would'st
unnecessarily
have
confined
the
impossibility
to
the
plurality
of
byasses
,
if
in
case
it
had
no
more
but
one
,
yet
it
could
not
move
with
that
.
And
because
that
of
all
the
moveables
in
the
World
,
thou
makest
but
one
alone
to
move
with
one
sole
byas
;
and
all
the
rest
with
more
than
one
;
and
this
same
moveable
thou
affirmest
to
be
the
first
Sphere
,
namely
,
that
by
which
all
the
fixed
and
erratick
Stars
seem
harmoniously
to
move
from
East
to
West
,
if
in
case
the
Earth
may
be
that
first
Sphere
,
that
by
moving
with
one
byas
onely
,
may
make
the
Stars
appear
to
move
from
East
to
West
,
thou
wilt
not
deny
them
it
:
But
he
that
affirmeth
,
that
the
Earth
being
placed
in
the
midst
of
the
World
,
moveth
about
its
own
Axis
,
ascribes
unto
it
no
other
motion
,
save
that
by
which
all
the
Stars
appear
to
move
from
East
to
West
;
and
so
it
cometh
to
be
that
first
Sphere
,
which
thou
thy self
acknowledgest
to
move
with
but
one
byas
onely
.
It
is
therefore
necessary
,
oh
Aristotle
,
if
thou
wilt
conclude
any
thing
,
that
thou
demonstrate
,
that
the
Earth
being
placed
in
the
midst
of
the
World
,
cannot
move
with
so
much
as
one
byas
onely
;
or
else
,
that
much
lesse
can
the
first
Sphere
have
one
sole
motion
;
for
otherwise
thou
doest
in
thy
very
Sillogisme
both
commit
the
falacy
,
and
detect
it
,
denying
,
and
at
that
very
time
proving
the
same
thing
.
I
come
now
to
the
second
Position
,
namely
,
of
those
who
placing
the
Earth
far
from
the
midst
of
the
Universe
,
make
it
moveable
about
the
same
;
that
is
,
make
it
a
Planet
and
erratick
Star
;
against
which
the
argument
is
directed
,
and
as
to
form
is
concludent
,
but
faileth
in
matter
.
For
it
being
granted
,
that
the
Earth
doth
in
that
manner
move
,
and
that
with
two
byasses
,
yet
doth
it
not
necessarily
follow
that
though
it
were
so
,
it
should
make
alterations
in
the
risings
and
settings
of
the
fixed
Stars
,
as
I
shall
in
its
proper
place
declare
.
And
here
I
could
gladly
excuse
Aristotle
;
rather
I
could
highly
applaud
him
for
having
light
upon
the
most
subtil
argument
that
could
be
produced
against
the
Copernican
Hypothesis
;
and
if
the
objection
be
ingenious
,
and
to
outward
appearance
most
powerful
,
you
may
see
how
much
more
acute
and
ingenious
the
solution
must
be
,
and
not
to
be
found
by
a
wit
lesse
piercing
than
that
of
Copernicus
;
and
again
from
the
difficulty
in
understanding
it
,
you
may
argue
the
so
much
greater
difficulty
in
finding
it
.
But
let
us
for
the
present
suspend
our
answer
,
which
you
shall
understand
in
due
time
and
place
,
after
we
have
repeated
the
objection
of
Aristotle
,
and
that
in
his
favour
,
much
strengthened
.
Now
passe
we
to
Aristotles
third
Argument
,
The
answer
to
the
third
argument
.
touching
which
we
need
give
no
farther
reply
,
it
having
been
sufficiently
answered
betwixt
the
discourses
of
yesterday
and
to
day
:
In
as
much
as
he
urgeth
,
that
the
motion
of
grave
bodies
is
naturally
by
a
right
line
to
the
centre
;
and
then
enquireth
,
whether
to
the
centre
of
the
Earth
,
or
to
that
of
the
Universe
,
and
concludeth
that
they
tend
naturally
to
the
centre
of
the
Universe
,
but
accidentally
to
that
of
the
Earth
.
Therefore
we
may
proceed
to
the
fourth
,
The
answer
to
the
fourth
argument
.
upon
which
its
requisite
that
we
stay
some
time
,
by
reason
it
is
founded
upon
that
experiment
,
from
whence
the
greater
part
of
the
remaining
arguments
derive
all
their
strength
.
Aristotle
saith
therefore
,
that
it
is
a
most
convincing
argument
of
the
Earths
immobility
,
to
see
that
projections
thrown
or
shot
upright
,
return
perpendicularly
by
the
same
line
unto
the
same
place
from
whence
they
were
shot
or
thrown
.
And
this
holdeth
true
,
although
the
motion
be
of
a
very
great
height
;
which
could
never
come
to
passe
,
did
the
Earth
move
:
for
in
the
time
that
the
projected
body
is
moving
upwards
and
downwards
in
a
state
of
separation
from
the
Earth
,
the
place
from
whence
the
motion
of
the
projection
began
,
would
be
past
,
by
means
of
the
Earths
revolution
,
a
great
way
towards
the
East
,
and
look
how
great
that
space
was
,
so
far
from
that
place
would
the
projected
body
in
its
descent
come
to
the
ground
.
So
that
hither
may
be
referred
the
argument
taken
from
a
bullet
shot
from
a
Canon
directly
upwards
;
as
also
that
other
used
by
Aristotle
and
Ptolomy
,
of
the
grave
bodies
that
falling
from
on
high
,
are
observed
to
descend
by
a
direct
and
perpendicular
line
to
the
surface
of
the
Earth
.
Now
that
I
may
begin
to
unite
these
knots
,
I
demand
of
Simplicius
that
in
case
one
should
deny
to
Ptolomy
and
Aristotle
that
weights
in
falling
freely
from
on
high
,
descend
by
a
right
and
perpendicular
line
,
that
is
,
directly
to
the
centre
,
what
means
he
would
use
to
prove
it
?
SIMPL.
The
means
of
the
senses
;
the
which
assureth
us
,
that
that
Tower
or
other
altitude
,
is
upright
and
perpendicular
,
and
sheweth
us
that
that
stone
,
or
other
grave
body
,
doth
slide
along
the
Wall
,
without
inclining
a
hairs
breadth
to
one
side
or
another
,
and
light
at
the
foot
thereof
just
under
the
place
from
whence
it
was
let
fall
.
SALV
.
But
if
it
should
happen
that
the
Terrestrial
Globe
did
move
round
,
and
consequently
carry
the
Tower
also
along
with
it
,
and
that
the
stone
did
then
also
grate
and
slide
along
the
side
of
the
Tower
,
what
must
its
motion
be
then
?
SIMPL.
In
this
case
we
may
rather
say
its
motions
:
for
it
would
have
one
wherewith
to
descend
from
the
top
of
the
Tower
to
the
bottom
,
and
should
necessarily
have
another
to
follow
the
course
of
the
said
Tower
.
SALV
.
So
that
its
motion
should
be
compounded
of
two
,
to
wit
,
of
that
wherewith
it
measureth
the
Tower
,
and
of
that
other
wherewith
it
followeth
the
same
:
From
which
composition
would
follow
,
that
the
stone
would
no
longer
describe
that
simple
right
and
perpendicular
line
,
but
one
transverse
,
and
perhaps
not
streight
.
SIMPL.
I
can
say
nothing
of
its
non-rectitude
,
but
this
I
know
very
well
,
that
it
would
of
necessity
be
transverse
,
and
different
from
the
other
directly
perpendicular
,
which
it
doth
describe
,
the
Earth
standing
still
.
SALV
.
You
see
then
,
that
upon
the
meer
observing
the
falling
stone
to
glide
along
the
Tower
,
you
cannot
certainly
affirm
that
it
describeth
a
line
which
is
streight
and
perpendicular
,
unless
you
first
suppose
that
the
Earth
standeth
still
.
SIMPL.
True
;
for
if
the
Earth
should
move
,
the
stones
motion
would
be
transverse
,
and
not
perpendicular
.
SALV
.
Behold
then
the
Paralogism
of
Aristotle
and
Ptolomey
to
be
evident
and
manifest
,
Th●
Paralogism
of
Aristotle
and
Ptolomey
in
supposing
that
for
known
,
which
is
in
question
.
and
discovered
by
you
your self
,
wherein
that
is
supposed
for
known
,
which
is
intended
to
be
demonstrated
.
SIMPL.
How
can
that
be
?
To
me
it
appeareth
that
the
Syllogism
is
rightly
demonstrated
without
petitionem
principii
.
SALV
.
You
shall
see
how
it
is
;
answer
me
a
little
.
Doth
he
not
lay
down
the
conclusion
as
unknown
?
SIMPL.
Unknown
;
why
otherwise
the
demonstrating
it
would
be
superfluous
.
SALV
.
But
the
middle
term
,
ought
not
that
to
be
known
?
SIMPL.
It
s
necessary
that
it
should
;
for
otherwise
it
would
be
a
proving
ignotum
per
aequè
ignotum
.
SALV
.
Our
conclusion
which
is
to
be
proved
,
and
which
is
unknown
,
is
it
not
the
stability
of
the
Earth
?
SIMPL.
It
is
the
same
.
SALV
.
The
middle
term
,
which
ought
to
be
known
,
is
it
not
the
streight
and
perpendicular
descent
of
the
stone
?
SIMPL.
It
is
so
.
SALV
.
But
was
it
not
just
now
concluded
,
that
we
can
have
no
certain
knowledg
whether
that
same
shall
be
direct
and
perpendicular
,
unless
we
first
know
that
the
Earth
stands
still
?
Therefore
in
your
Syllogism
the
certainty
of
the
middle
term
is
assumed
from
the
uncertainty
of
the
conclusion
.
You
may
see
then
,
what
and
how
great
the
Paralogism
is
.
SAGR.
I
would
,
in
favour
of
Simplicius
,
defend
Aristotle
if
it
were
possible
,
or
at
least
better
satisfie
my self
concerning
the
strength
of
your
illation
.
You
say
,
that
the
seeing
the
stone
rake
along
the
Tower
,
is
not
sufficient
to
assure
us
,
that
its
motion
is
perpendicular
(
which
is
the
middle
term
of
the
Syllogism
)
unless
it
be
presupposed
,
that
the
Earth
standeth
still
,
which
is
the
conclusion
to
be
proved
:
For
that
if
the
Tower
did
move
together
with
the
Earth
,
and
the
stone
did
slide
along
the
same
,
the
motion
of
the
stone
would
be
transverse
,
and
not
perpendicular
.
But
I
shall
answer
,
that
should
the
Tower
move
,
it
would
be
impossible
that
the
stone
should
fail
gliding
along
the
side
of
it
;
and
therefore
from
its
falling
in
that
manner
the
stability
of
the
Earth
is
inferred
.
SIMPL.
It
is
so
;
for
if
you
would
have
the
stone
in
descending
to
grate
upon
the
Tower
,
though
it
were
carried
round
by
the
Earth
,
you
must
allow
the
stone
two
natural
motions
,
to
wit
,
the
straight
motion
towards
the
Centre
,
and
the
circular
about
the
Centre
,
the
which
is
impossible
.
SALV
.
Aristotles
defense
then
consisteth
in
the
impossibilitie
,
or
at
least
in
his
esteeming
it
an
impossibility
,
that
the
stone
should
move
with
a
motion
mixt
of
right
and
circular
:
for
if
he
did
not
hold
it
impossible
that
the
stone
could
move
to
the
Centre
,
and
about
the
Centre
at
once
,
he
must
have
understood
,
that
it
might
come
to
pass
that
the
cadent
stone
might
in
its
descent
,
race
the
Tower
as
well
when
it
moved
as
when
it
stood
still
;
and
consequently
he
must
have
perceived
,
that
from
this
grating
nothing
could
be
inferred
touching
the
mobility
or
immobility
of
the
Earth
.
But
this
doth
not
any
way
excuse
Aristotle
;
aswell
because
he
ought
to
have
exprest
it
,
if
he
had
had
such
a
conceit
,
it
being
so
material
a
part
of
his
Argument
;
as
also
because
it
can
neither
be
said
that
such
an
effect
is
impossible
,
nor
that
Aristotle
did
esteem
it
so
.
The
first
cannot
be
affirmed
,
for
that
by
and
by
I
shall
shew
that
it
is
not
onely
possible
,
but
necessary
:
nor
much
less
can
the
second
be
averred
,
Aristotle
admitteth
that
the
Fire
moveth
directly
upwards
by
nature
,
and
round
abent
by
participation
.
for
that
Aristotle
himself
granteth
fire
to
move
naturally
upwards
in
a
right
line
,
and
to
move
about
with
the
diurnal
motion
,
imparted
by
Heaven
to
the
whole
Element
of
Fire
,
and
the
greater
part
of
the
Air
:
If
therefore
he
held
it
not
impossible
to
mix
the
right
motion
upwards
,
with
the
circular
communicated
to
the
Fire
and
Air
from
the
concave
of
the
Moon
,
much
less
ought
he
to
account
impossible
the
mixture
of
the
right
motion
downwards
of
the
stone
,
with
the
circular
which
we
presuppose
natural
to
the
whole
Terrestrial
Globe
,
of
which
the
stone
is
a
part
.
SIMPL.
I
see
no
such
thing
:
for
if
the
element
of
Fire
revolve
round
together
with
the
Air
,
it
is
a
very
easie
,
yea
a
necessary
thing
,
that
a
spark
of
fire
which
from
the
Earth
mounts
upwards
,
in
passing
thorow
the
moving
air
,
should
receive
the
same
motion
,
being
a
body
so
thin
,
light
,
and
easie
to
be
moved
:
but
that
a
very
heavy
stone
,
or
a
Canon
bullet
,
that
descendeth
from
on
high
,
and
that
is
at
liberty
to
move
whither
it
will
,
should
suffer
it self
to
be
transported
either
by
the
air
or
any
other
thing
,
is
altogether
incredible
.
Besides
that
,
we
have
the
Experiment
,
which
is
so
proper
to
our
purpose
,
of
the
stone
let
fall
from
the
round
top
of
the
Mast
of
a
ship
,
which
when
the
ship
lyeth
still
,
falleth
at
the
Partners
of
the
Mast
;
but
when
the
ship
saileth
,
falls
so
far
distant
from
that
place
,
by
how
far
the
ship
in
the
time
of
the
stones
falling
had
run
forward
;
which
will
not
be
a
few
fathoms
,
when
the
ships
course
is
swift
.
SALV
.
There
is
a
great
disparity
between
the
case
of
the
Ship
and
that
of
the
Earth
,
The
disparity
between
the
fall
of
a
stone
from
the
round
top
of
a
ship
,
and
from
the
top
of
a
tower
.
if
the
Terrestrial
Globe
be
supposed
to
have
a
diurnal
motion
.
For
it
is
a
thing
very
manifest
,
that
the
motion
of
the
Ship
,
as
it
is
not
natural
to
it
,
so
the
motion
of
all
those
things
that
are
in
it
is
accidental
,
whence
it
is
no
wonder
that
the
stone
which
was
retained
in
the
round
top
,
being
left
at
liberty
,
descendeth
downwards
without
any
obligation
to
follow
the
motion
of
the
Ship
.
But
the
diurnal
conversion
is
ascribed
to
the
Terrestrial
Globe
for
its
proper
and
natural
motion
,
and
consequently
,
it
is
so
to
all
the
parts
of
the
said
Globe
;
and
,
as
being
impress'd
by
nature
,
is
indelible
in
them
;
and
therefore
that
stone
that
is
on
the
top
of
the
Tower
hath
an
intrinsick
inclination
of
revolving
about
the
Centre
of
its
Whole
in
twenty
four
hours
,
and
this
same
natrual
instinct
it
exerciseth
eternally
,
be
it
placed
in
any
state
whatsoever
.
And
to
be
assured
of
the
truth
of
this
,
you
have
no
more
to
do
but
to
alter
an
antiquated
impression
made
in
your
mind
;
and
to
say
,
Like
as
in
that
I
hitherto
holding
it
to
be
the
property
of
the
Terrestrial
Globe
to
rest
immoveable
about
its
Centre
,
did
never
doubt
or
question
but
that
all
whatsoever
particles
thereof
do
also
naturally
remain
in
the
same
state
of
rest
:
So
it
is
reason
,
in
case
the
Terrestrial
Globe
did
move
round
by
natural
instinct
in
twenty
four
hours
,
that
the
intrinsick
and
natural
inclination
of
all
its
parts
should
also
be
,
not
to
stand
still
,
but
to
follow
the
same
revolution
.
And
thus
without
running
into
any
inconvenience
,
one
may
conclude
,
that
in
regard
the
motion
conferred
by
the
force
of
[
](A61244-e29790-b)*
*
That
you
may
not
suspect
my
translation
,
or
wonder
what
Oars
have
to
do
with
a
ship
,
you
are
to
know
that
the
Author
intends
the
Gallies
used
in
the
Mediterrane
.
Oars
on
the
Ship
,
and
by
it
on
all
the
things
that
are
contained
within
her
,
is
not
natural
but
forreign
,
it
is
very
reasonable
that
that
stone
,
it
being
separated
from
the
ship
,
do
reduce
its
self
to
its
natural
disposure
,
and
return
to
exercise
its
pure
simple
instinct
given
it
by
nature
.
The
part
of
the
Air
inferiour
to
the
higher
mountains
doth
follow
the
motion
of
the
Earth
.
To
this
I
add
,
that
it
's
necessary
,
that
at
least
that
part
of
the
Air
which
is
beneath
the
greater
heights
of
mountains
,
should
be
transported
and
carried
round
by
the
roughness
of
the
Earths
surface
;
or
that
,
as
being
mixt
with
many
Vapours
,
and
terrene
Exhalations
,
it
do
naturally
follow
the
diurnal
motion
,
which
occurreth
not
in
the
Air
about
the
ship
rowed
by
Oars
:
So
that
your
arguing
from
the
ship
to
the
Tower
hath
not
the
force
of
an
illation
;
because
that
stone
which
falls
from
the
round
top
of
the
Mast
,
entereth
into
a
medium
,
which
is
unconcern'd
in
the
motion
of
the
ship
:
but
that
which
departeth
from
the
top
of
the
Tower
,
finds
a
medium
that
hath
a
motion
in
common
with
the
whole
Terrestrial
Globe
;
so
that
without
being
hindred
,
rather
being
assisted
by
the
motion
of
the
air
,
it
may
follow
the
universal
course
of
the
Earth
.
SIMPL.
I
cannot
conceive
that
the
air
can
imprint
in
a
very
great
stone
,
The
motion
of
the
Air
apt
to
carry
with
it
light
things
but
not
heavy
.
or
in
a
gross
Globe
of
Wood
or
Ball
of
Lead
,
as
suppose
of
two
hundred
weight
,
the
motion
wherewith
its
self
is
moved
,
and
which
it
doth
perhaps
communicate
to
feathers
,
snow
,
and
other
very
light
things
:
nay
,
I
see
that
a
weight
of
that
nature
,
being
exposed
to
any
the
most
impetuous
wind
,
is
not
thereby
removed
an
inch
from
its
place
;
now
consider
with
your self
whether
the
air
will
carry
it
along
therewith
.
SALV
.
There
is
great
difference
between
your
experiment
and
our
case
.
You
introduce
the
wind
blowing
against
that
stone
,
supposed
in
a
state
of
rest
,
and
we
expose
to
the
air
,
which
already
moveth
,
the
stone
which
doth
also
move
with
the
same
velocity
;
so
that
the
air
is
not
to
conferr
a
new
motion
upon
it
,
but
onely
to
maintain
,
or
to
speak
better
,
not
to
hinder
the
motion
already
acquired
:
you
would
drive
the
stone
with
a
strange
and
preternatural
motion
,
and
we
desire
to
conserve
it
in
its
natural
.
If
you
would
produce
a
more
pertinent
experiment
,
you
should
say
,
that
it
is
observed
,
if
not
with
the
eye
of
the
forehead
,
yet
with
that
of
the
mind
,
what
would
evene
,
if
an
eagle
that
is
carried
by
the
course
of
the
wind
,
should
let
a
stone
fall
from
its
talons
;
which
,
in
regard
that
at
its
being
let
go
,
it
went
along
with
the
wind
,
and
after
it
was
let
fall
it
entered
into
a
medium
that
moved
with
equal
velocity
,
I
am
very
confident
that
it
would
not
be
seen
to
descend
in
its
fall
perpendicularly
,
but
that
following
the
course
of
the
wind
,
and
adding
thereto
that
of
its
particular
gravity
,
it
would
move
with
a
transverse
motion
.
SIMPL.
But
it
would
first
be
known
how
such
an
experiment
may
be
made
;
and
then
one
might
judg
according
to
the
event
.
In
the
mean
time
the
effect
of
the
ship
doth
hitherto
incline
to
favour
our
opinion
.
SALV
.
Well
said
you
hitherto
,
for
perhaps
it
may
anon
change
countenance
.
And
that
I
may
no
longer
hold
you
in
suspense
,
tell
me
,
Simplicius
,
do
you
really
believe
,
that
the
Experiment
of
the
ship
squares
so
very
well
with
our
purpose
,
as
that
it
ought
to
be
believed
,
that
that
which
we
see
happen
in
it
,
ought
also
to
evene
in
the
Terrestrial
Globe
?
SIMPL.
As
yet
I
am
of
that
opinion
;
and
though
you
have
alledged
some
small
disparities
,
I
do
not
think
them
of
so
great
moment
,
as
that
they
should
make
me
change
my
judgment
.
SALV
.
I
rather
desire
that
you
would
continue
therein
,
and
hold
for
certain
,
that
the
effect
of
the
Earth
would
exactly
answer
that
of
the
ship
:
provided
,
that
when
it
shall
appear
prejudicial
to
your
cause
,
you
would
not
be
humorous
and
alter
your
thoughts
.
You
may
haply
say
,
Forasmuch
as
when
the
ship
stands
still
,
the
stone
falls
at
the
foot
of
the
Mast
,
and
when
she
is
under
sail
,
it
lights
far
from
thence
,
that
therefore
by
conversion
,
from
the
stones
falling
at
the
foot
is
argued
the
ships
standing
still
,
and
from
its
falling
far
from
thence
is
argued
her
moving
;
and
because
that
which
occurreth
to
the
ship
,
ought
likewise
to
befall
the
Earth
:
that
therefore
from
the
falling
of
the
stone
at
the
foot
of
the
Tower
is
necessarily
inferred
the
immobility
of
the
Terrestrial
Globe
.
Is
not
this
your
argumentation
?
SIMPL.
It
is
,
and
reduced
into
that
conciseness
,
as
that
it
is
become
most
easie
to
be
apprehended
.
SALV
.
Now
tell
me
;
if
the
stone
let
fall
from
the
Round-top
,
when
the
ship
is
in
a
swift
course
,
should
fall
exactly
in
the
same
place
of
the
ship
,
in
which
it
falleth
when
the
ship
is
at
anchor
,
what
service
would
these
experiments
do
you
,
in
order
to
the
ascertaining
whether
the
vessel
doth
stand
still
or
move
?
SIMPL.
Just
none
:
Like
as
,
for
exemple
,
from
the
beating
of
the
pulse
one
cannot
know
whether
a
person
be
asleep
or
awake
,
seeing
that
the
pulse
beateth
after
the
same
manner
in
sleeping
as
in
waking
.
SALV
.
Very
well
.
Have
you
ever
tryed
the
experiment
of
the
Ship
?
SIMPL.
I
have
not
;
but
yet
I
believe
that
those
Authors
which
alledg
the
same
,
have
accurately
observed
it
;
besides
that
the
cause
of
the
disparity
is
so
manifestly
known
,
that
it
admits
of
no
question
.
SALV
.
That
it
is
possible
that
those
Authors
instance
in
it
,
without
having
made
tryal
of
it
,
you
your self
are
a
good
testimony
,
that
without
having
examined
it
,
alledg
it
as
certain
,
and
in
a
credulous
way
remit
it
to
their
authority
;
as
it
is
now
not
onely
possible
,
but
very
probable
that
they
likewise
did
;
I
mean
,
did
remit
the
same
to
their
Predecessors
,
without
ever
arriving
at
one
that
had
made
the
experiment
:
for
whoever
shall
examine
the
same
,
shall
find
the
event
succeed
quite
contrary
to
what
hath
been
written
of
it
:
that
is
,
he
shall
see
the
stone
fall
at
all
times
in
the
same
place
of
the
Ship
,
whether
it
stand
still
,
or
move
with
any
whatsoever
velocity
.
The
stone
falling
from
the
Mast
of
a
ship
lights
in
the
same
place
,
whether
the
ship
doth
move
or
ly
still
.
So
that
the
same
holding
true
in
the
Earth
,
as
in
the
Ship
,
one
cannot
from
the
stones
falling
perpendicularly
at
the
foot
of
the
Tower
,
conclude
any
thing
touching
the
motion
or
rest
of
the
Earth
.
SIMPL.
If
you
should
refer
me
to
any
other
means
than
to
experience
,
I
verily
believe
our
Disputations
would
not
come
to
an
end
in
haste
;
for
this
seemeth
to
me
a
thing
so
remote
from
all
humane
reason
,
as
that
it
leaveth
not
the
least
place
for
credulity
or
probability
.
SALV
.
And
yet
it
hath
left
place
in
me
for
both
.
SIMPL.
How
is
this
?
You
have
not
made
an
hundred
,
no
nor
one
proof
thereof
,
and
do
you
so
confidently
affirm
it
for
true
?
I
for
my
part
will
return
to
my
incredulity
,
and
to
the
confidence
I
had
that
the
Experiment
hath
been
tried
by
the
principal
Authors
who
made
use
thereof
,
and
that
the
event
succeeded
as
they
affirm
.
SALV
.
I
am
assured
that
the
effect
will
ensue
as
I
tell
you
;
for
so
it
is
necessary
that
it
should
:
and
I
farther
add
,
that
you
know
your self
that
it
cannot
fall
out
otherwise
,
however
you
feign
or
seem
to
feign
that
you
know
it
not
.
Yet
I
am
so
good
at
taming
of
wits
,
that
I
will
make
you
confess
the
same
whether
you
will
or
no.
But
Sagredus
stands
very
mute
,
and
yet
,
if
I
mistake
not
,
I
saw
him
make
an
offer
to
speak
somewhat
.
SAGR.
I
had
an
intent
to
say
something
,
but
to
tell
you
true
,
I
know
not
what
it
was
;
for
the
curiosity
that
you
have
moved
in
me
,
by
promising
that
you
would
force
Simplicius
to
discover
the
knowledg
which
he
would
conceal
from
us
,
hath
made
me
to
depose
all
other
thoughts
:
therefore
I
pray
you
to
make
good
your
vaunt
.
SALV
.
Provided
that
Simplicius
do
consent
to
reply
to
what
I
shall
ask
him
,
I
will
not
fail
to
do
it
.
SIMPL.
I
will
answer
what
I
know
,
assured
that
I
shall
not
be
much
put
to
it
,
for
that
of
those
things
which
I
hold
to
be
false
,
I
think
nothing
can
be
known
,
in
regard
that
Science
respecteth
truths
and
not
falshoods
.
SALV
.
I
desire
not
that
you
should
say
or
reply
,
that
you
know
any
thing
,
save
that
which
you
most
assuredly
know
.
Therefore
tell
me
;
If
you
had
here
a
flat
superficies
as
polite
as
a
Looking-glass
,
and
of
a
substance
as
hard
as
steel
,
and
that
it
were
not
paralel
to
the
Horizon
,
but
somewhat
inclining
,
and
that
upon
it
you
did
put
a
Ball
perfectly
spherical
,
and
of
a
substance
grave
and
hard
,
as
suppose
of
brass
;
what
think
you
it
would
do
being
let
go
?
do
not
you
believe
(
as
for
my
part
I
do
)
that
it
would
lie
still
?
SIMPL.
If
that
superficies
were
inclining
?
SALV
.
Yes
;
for
so
I
have
already
supposed
.
SIMPL.
I
cannot
conceive
how
it
should
lie
still
:
nay
,
I
am
confident
that
it
would
move
towards
the
declivity
with
much
propensness
.
SALV
.
Take
good
heed
what
you
say
,
Simplicius
,
for
I
am
confident
that
it
would
lie
still
in
what
ever
place
you
should
lay
it
.
SIMPL.
So
long
as
you
make
use
of
such
suppositions
,
Salvictus
,
I
shall
cease
to
wonder
if
you
inferr
most
absurd
conclusions
.
SALV
.
Are
you
assured
,
then
,
that
it
would
freely
move
towards
the
declivity
?
SIMPL.
Who
doubts
it
?
SALV
.
And
this
you
verily
believe
,
not
because
I
told
you
so
,
(
for
I
endeavoured
to
perswade
you
to
think
the
contrary
)
but
of
your self
,
and
upon
your
natural
judgment
.
SIMPL.
Now
I
see
what
you
would
be
at
;
you
spoke
not
this
as
really
believing
the
same
;
but
to
try
me
,
and
to
wrest
matter
out
of
my
own
mouth
wherewith
to
condemn
me
.
SALV
.
You
are
in
the
right
.
And
how
long
would
that
Ball
move
,
and
with
what
velocity
?
But
take
notice
that
I
instanced
in
a
Ball
exactly
round
,
and
a
plain
exquisitely
polished
,
that
all
external
and
accidental
impediments
might
be
taken
away
.
And
so
would
I
have
you
remove
all
obstructions
caused
by
the
Airs
resistance
to
division
,
and
all
other
casual
obstacles
,
if
any
other
there
can
be
.
SIMPL.
I
very
well
understand
your
meaning
,
and
as
to
your
demand
,
I
answer
,
that
the
Ball
would
continue
to
move
in
infinitum
,
if
the
inclination
of
the
plain
should
so
long
last
,
and
continually
with
an
accelerating
motion
;
for
such
is
the
nature
of
ponderous
moveables
,
that
vires
acquirant
eundo
:
and
the
greater
the
declivity
was
,
the
greater
the
velocity
would
be
.
SALV
.
But
if
one
should
require
that
that
Ball
should
move
upwards
on
that
same
superficies
,
do
you
believe
that
it
would
so
do
?
SIMPL.
Not
spontaneously
;
but
being
drawn
,
or
violently
thrown
,
it
may
.
SALV
.
And
in
case
it
were
thrust
forward
by
the
impression
of
some
violent
impetus
from
without
,
what
and
how
great
would
its
motion
be
?
SIMPL.
The
motion
would
go
continually
decreasing
and
retarding
,
as
being
contrary
to
nature
;
and
would
be
longer
or
shorter
,
according
to
the
greater
or
less
impulse
,
and
according
to
the
greater
or
less
acclivity
.
SALV
.
It
seems
,
then
,
that
hitherto
you
have
explained
to
me
the
accidents
of
a
moveable
upon
two
different
Planes
;
and
that
in
the
inclining
plane
,
the
grave
moveable
doth
spontaneously
descend
,
and
goeth
continually
accelerating
,
and
that
to
retain
it
in
rest
,
force
must
be
used
therein
:
but
that
on
the
ascending
plane
,
there
is
required
a
force
to
thrust
it
forward
,
and
also
to
stay
it
in
rest
,
and
that
the
motion
impressed
goeth
continually
diminishing
,
till
that
in
the
end
it
cometh
to
nothing
.
You
say
yet
farther
,
that
in
both
the
one
and
the
other
case
,
there
do
arise
differences
from
the
planes
having
a
greater
or
less
declivity
or
acclivity
;
so
that
the
greater
inclination
is
attended
with
the
greater
velocity
;
and
contrariwise
,
upon
the
ascending
plane
,
the
same
moveable
thrown
with
the
same
force
,
moveth
a
greater
distance
,
by
how
much
the
elevation
is
less
.
Now
tell
me
,
what
would
befall
the
same
moveable
upon
a
superficies
that
had
neither
acclivity
nor
declivity
?
SIMPL.
Here
you
must
give
me
a
little
time
to
consider
of
an
answer
.
There
being
no
declivity
,
there
can
be
no
natural
inclination
to
motion
:
and
there
being
no
acclivity
,
there
can
be
no
resistance
to
being
moved
;
so
that
there
would
arise
an
indifference
between
propension
and
resistance
of
motion
;
therefore
,
methinks
it
ought
naturally
to
stand
still
.
But
I
had
forgot
my self
:
it
was
but
even
now
that
Sagredus
gave
me
to
understand
that
it
would
so
do
.
SALV
.
So
I
think
,
provided
one
did
lay
it
down
gently
:
but
if
it
had
an
impetus
given
it
towards
any
part
,
what
would
follow
?
SIMP.
There
would
follow
,
that
it
should
move
towards
that
part
.
SALV
.
But
with
what
kind
of
motion
?
with
the
continually
accelerated
,
as
in
declining
planes
;
or
with
the
successively
retarded
,
as
in
those
ascending
.
SIMP.
I
cannot
tell
how
to
discover
any
cause
of
acceleration
,
or
retardation
,
there
being
no
declivity
or
acclivity
.
SALV
.
Well
:
but
if
there
be
no
cause
of
retardation
,
much
less
ought
there
to
be
any
cause
of
rest
.
How
long
therefore
would
you
have
the
moveable
to
move
?
SIMP.
As
long
as
that
superficies
,
neither
inclined
nor
declined
shall
last
.
SALV
.
Therefore
if
such
a
space
were
interminate
,
the
motion
upon
the
same
would
likewise
have
no
termination
,
that
is
,
would
be
perpetual
.
SIMP.
I
think
so
,
if
so
be
the
moveable
be
of
a
matter
durable
.
SALV
.
That
hath
been
already
supposed
,
when
it
was
said
,
that
all
external
and
accidental
impediments
were
removed
,
and
the
brittlenesse
of
the
moveable
in
this
our
case
,
is
one
of
those
impediments
accidental
.
Tell
me
now
,
what
do
you
think
is
the
cause
that
that
same
Ball
moveth
spontaneously
upon
the
inclining
plane
,
and
not
without
violence
upon
the
erected
?
SIMP.
Because
the
inclination
of
grave
bodies
is
to
move
towards
the
centre
of
the
Earth
,
and
onely
by
violence
upwards
towards
the
circumference
;
and
the
inclining
superficies
is
that
which
acquireth
vicinity
to
the
centre
,
and
the
ascending
one
,
remotenesse
.
SALV
.
Therefore
a
superficies
,
which
should
be
neither
declining
nor
ascending
,
ought
in
all
its
parts
to
be
equally
distant
from
the
centre
.
But
is
there
any
such
superficies
in
the
World
?
SIMP.
There
is
no
want
thereof
:
Such
is
our
Terrestrial
Globe
,
if
it
were
more
even
,
and
not
as
it
is
rough
and
montainous
;
but
you
have
that
of
the
Water
,
at
such
time
as
it
is
calm
and
still
.
SALV
.
Then
a
ship
which
moveth
in
a
calm
at
Sea
,
is
one
of
those
moveables
,
which
run
along
one
of
those
superficies
that
are
neither
declining
nor
ascending
,
and
therefore
disposed
,
in
case
all
obstacles
external
and
accidental
were
removed
,
to
move
with
the
impulse
once
imparted
incessantly
and
uniformly
.
SIMPL.
It
should
seem
to
be
so
.
SALV
.
And
that
stone
which
is
on
the
round
top
,
doth
not
it
move
,
as
being
together
with
the
ship
carried
about
by
the
circumference
of
a
Circle
about
the
Centre
;
and
therefore
consequently
by
a
motion
in
it
indelible
,
if
all
extern
obstacles
be
removed
?
And
is
not
this
motion
as
swift
as
that
of
the
ship
.
SIMPL.
Hitherto
all
is
well
.
But
what
followeth
?
SALV
.
Then
in
good
time
recant
,
I
pray
you
,
that
your
last
conclusion
,
if
you
are
satisfied
with
the
truth
of
all
the
premises
.
SIMPL.
By
my
last
conclusion
,
you
mean
,
That
that
same
stone
moving
with
a
motion
indelibly
impressed
upon
it
,
is
not
to
leave
,
nay
rather
is
to
follow
the
ship
,
and
in
the
end
to
light
in
the
self
same
place
,
where
it
falleth
when
the
ship
lyeth
still
;
and
so
I
also
grant
it
would
do
,
in
case
there
were
no
outward
impediments
that
might
disturb
the
stones
motion
,
after
its
being
let
go
,
the
which
impediments
are
two
,
the
one
is
the
moveables
inability
to
break
through
the
air
with
its
meer
impetus
onely
,
it
being
deprived
of
that
of
the
strength
of
Oars
,
of
which
it
had
been
partaker
,
as
part
of
the
ship
,
at
the
time
that
it
was
upon
the
Mast
;
the
other
is
the
new
motion
of
descent
,
which
also
must
needs
be
an
hinderance
of
that
other
progressive
motion
.
SALV
.
As
to
the
impediment
of
the
Air
,
I
do
not
deny
it
you
;
and
if
the
thing
falling
were
a
light
matter
,
as
a
feather
,
or
a
lock
of
wool
,
the
retardation
would
be
very
great
,
but
in
an
heavy
stone
is
very
exceeding
small
.
And
you
your self
but
even
now
did
say
,
that
the
force
of
the
most
impetuous
wind
sufficeth
not
to
stir
a
great
stone
from
its
place
;
now
do
but
consider
what
the
calmer
air
is
able
to
do
,
being
encountred
by
a
stone
no
more
swift
than
the
whole
ship
.
Neverthelesse
,
as
I
said
before
,
I
do
allow
you
this
small
effect
,
that
may
depend
upon
such
an
impediment
;
like
as
I
know
,
that
you
will
grant
to
me
,
that
if
the
air
should
move
with
the
same
velocity
that
the
ship
and
stone
hath
,
then
the
impediment
would
be
nothing
at
all
.
As
to
the
other
of
the
additional
motion
downwards
;
in
the
first
place
it
is
manifest
,
that
these
two
,
I
mean
the
circular
,
about
the
centre
,
and
the
streight
,
towards
the
centre
,
are
not
contraries
,
or
destructive
to
one
another
,
or
incompatible
.
Because
that
as
to
the
moveable
,
it
hath
no
repugnance
at
all
to
such
motions
,
for
you
your self
have
already
confest
the
repugnance
to
be
against
the
motion
which
removeth
from
the
centre
,
and
the
inclination
to
be
towards
the
motion
which
approacheth
to
the
centre
.
Whence
it
doth
of
necessity
follow
,
that
the
moveable
hath
neither
repugnance
,
nor
propension
to
the
motion
which
neither
approacheth
,
nor
goeth
from
the
centre
,
nor
consequently
is
there
any
cause
for
the
diminishing
in
it
the
faculty
impressed
.
And
forasmuch
as
the
moving
cause
is
not
one
alone
,
which
it
hath
attained
by
the
new
operation
of
retardation
;
but
that
they
are
two
,
distinct
from
each
other
,
of
which
,
the
gravity
attends
only
to
the
drawing
of
the
moveable
towards
the
centre
,
and
the
vertue
impress't
to
the
conducting
it
about
the
centre
,
there
remaineth
no
occasion
of
impediment
.
SIMPL.
Your
argumentation
,
to
give
you
your
due
,
is
very
probable
;
but
in
reality
it
is
invelloped
with
certain
intricacies
,
that
are
not
easie
to
be
extricated
.
You
have
all
along
built
upon
a
supposition
,
The
project
according
to
Aristotle
,
is
not
moved
by
vertue
impressed
,
but
by
the
medium
.
which
the
Peripatetick
Schools
will
not
easily
grant
you
,
as
being
directly
contrary
to
Aristotle
,
and
it
is
to
take
for
known
and
manifest
,
That
the
project
separated
from
the
projicient
,
continueth
the
motion
by
vertue
impressed
on
it
by
the
said
projicient
,
which
vertue
impressed
is
a
thing
as
much
detested
in
Peripatetick
Philosophy
,
as
the
passage
of
any
accident
from
one
subject
into
another
.
Which
doctrine
doth
hold
,
as
I
believe
it
is
well
known
unto
you
,
that
the
project
is
carried
by
the
medium
,
which
in
our
case
happeneth
to
be
the
Air.
And
therefore
if
that
stone
let
fall
from
the
round
top
,
ought
to
follow
the
motion
of
the
ship
,
that
effect
should
be
ascribed
to
the
Air
,
and
not
to
the
vertue
impressed
.
But
you
presuppose
that
the
Air
doth
not
follow
the
motion
of
the
ship
,
but
is
tranquil
.
Moreover
,
he
that
letteth
it
fall
,
is
not
to
throw
it
,
or
to
give
it
impetus
with
his
arm
,
but
ought
barely
to
open
his
hand
and
let
it
go
;
and
by
this
means
,
the
stone
,
neither
through
the
vertue
impressed
by
the
projicient
,
nor
through
the
help
of
the
Air
,
shall
be
able
to
follow
the
ships
motion
,
and
therefore
shall
be
left
behind
.
SALV
.
I
think
then
that
you
would
say
,
that
if
the
stone
be
not
thrown
by
the
arm
of
that
person
,
it
is
no
longer
a
projection
.
SIMPL.
It
cannot
be
properly
called
a
motion
of
projection
.
SALV
.
So
then
that
which
Aristotle
speaks
of
the
motion
,
the
moveable
,
and
the
mover
of
the
projects
,
hath
nothing
to
do
with
the
businesse
in
hand
;
and
if
it
concern
not
our
purpose
,
why
do
you
alledg
the
same
?
SIMP.
I
produce
it
on
the
oceasion
of
that
impressed
vertue
,
named
and
introduced
by
you
,
which
having
no
being
in
the
World
,
can
be
of
no
force
;
for
non-entium
nullae
sunt
operationes
;
and
therefore
not
onely
of
projected
,
but
of
all
other
preternatural
motions
,
the
moving
cause
ought
to
be
ascribed
to
the
medium
,
of
which
there
hath
been
no
due
consideration
had
;
and
therefore
all
that
hath
been
said
hitherto
is
to
no
purpose
.
SALV
.
Go
to
now
,
in
good
time
.
But
tell
me
,
seeing
that
your
instance
is
wholly
grounded
upon
the
nullity
of
the
vertue
impressed
,
if
I
shall
demonstrate
to
you
,
that
the
medium
hath
nothing
to
do
in
the
continuation
of
projects
,
after
they
are
separated
from
the
projicient
,
will
you
admit
of
the
impressed
vertue
,
or
will
you
make
another
attempt
to
overthrow
it
?
SIMP.
The
operation
of
the
medium
being
removed
,
I
see
not
how
one
can
have
recourse
to
any
thing
else
save
the
faculty
impressed
by
the
mover
.
SALV
.
It
would
be
well
,
for
the
removing
,
as
much
as
is
possible
,
the
occasions
of
multiplying
contentions
,
that
you
would
explain
with
as
much
distinctnesse
as
may
be
,
what
is
that
operation
of
the
medium
in
continuing
the
motion
of
the
project
.
Operation
of
the
medium
in
continuing
the
motion
of
the
project
.
SIMP.
The
projicient
hath
the
stone
in
his
hand
,
and
with
force
and
violence
throws
his
arm
,
with
which
jactation
the
stone
doth
not
move
so
much
as
the
circumambient
Air
;
so
that
when
the
stone
at
its
being
forsaken
by
the
hand
,
findeth
it self
in
the
Air
,
which
at
the
same
time
moveth
with
impetousity
,
it
is
thereby
born
away
;
for
,
if
the
air
did
not
operate
,
the
stone
would
fall
at
the
foot
of
the
projicient
or
thrower
.
SALV
.
And
was
you
so
credulous
,
Many
experiments
,
and
reasons
against
the
cause
of
the
motion
of
projects
,
assigned
by
Aristotle
.
as
to
suffer
your self
to
be
perswaded
to
believe
these
fopperies
,
so
long
as
you
had
your
senses
about
you
to
confute
them
,
and
to
understand
the
truth
thereof
?
Therefore
tell
me
,
that
great
stone
,
and
that
Canon
bullet
,
which
but
onely
laid
upon
a
table
,
did
continue
immoveable
against
the
most
impetuous
winds
,
according
as
you
a
little
before
did
affirm
,
if
it
had
been
a
ball
of
cork
or
other
light
stuffe
,
think
you
that
the
wind
would
have
removed
it
from
its
place
?
SIMP.
Yes
,
and
I
am
assured
that
it
would
have
blown
it
quite
away
,
and
with
so
much
more
velocity
,
by
how
much
the
matter
was
lighter
,
for
upon
this
reason
we
see
the
clouds
to
be
transported
with
a
velocity
equal
to
that
of
the
wind
that
drives
them
.
SALV
.
And
what
is
the
Wind
?
SIMP.
The
Wind
is
defined
to
be
nothing
else
but
air
moved
.
SALV
.
Then
the
moved
air
doth
carry
light
things
more
swiftly
,
and
to
a
greater
distance
,
then
it
doth
heavy
.
SIMP.
Yes
certainly
.
SALV
.
But
if
you
were
to
throw
with
your
arm
a
stone
,
and
a
lock
of
cotton
wool
,
which
would
move
swiftest
and
farthest
?
SIMP.
The
stone
by
much
;
nay
the
wool
would
fall
at
my
feet
.
SALV
.
But
,
if
that
which
moveth
the
projected
substance
,
after
it
is
delivered
from
the
hand
,
be
no
other
than
the
air
moved
by
the
arm
,
and
the
moved
air
do
more
easily
bear
away
light
than
grave
matters
,
how
cometh
it
that
the
project
of
wool
flieth
not
farther
,
and
swifter
than
that
of
stone
?
Certainly
it
argueth
that
the
stone
hath
some
other
impulse
besides
the
motion
of
the
air
.
Furthermore
,
if
two
strings
of
equal
length
did
hang
at
yonder
beam
,
and
at
the
end
of
one
there
was
fastened
a
bullet
of
lead
,
and
a
ball
of
cotton
wool
at
the
other
,
and
both
were
carried
to
an
equal
distance
from
the
perpendicular
,
and
then
let
go
;
it
is
not
to
be
doubted
,
but
that
both
the
one
and
the
other
would
move
towards
the
perpendicular
,
and
that
being
carried
by
their
own
impetus
,
they
would
go
a
certain
space
beyond
it
,
and
afterwards
return
thither
again
.
But
which
of
these
two
pendent
Globes
do
you
think
,
would
continue
longest
in
motion
,
before
that
it
would
come
to
rest
in
its
perpendicularity
?
SIMP.
The
ball
of
lead
would
swing
to
and
again
many
times
,
and
that
of
wool
but
two
or
three
at
the
most
.
SALV
.
So
that
the
impetus
and
that
mobility
whatsoever
is
the
cause
thereof
,
would
conserve
its
self
longer
in
grave
substances
,
than
light
;
I
proceed
now
to
another
particular
,
and
demand
of
you
,
why
the
air
doth
not
carry
away
that
Lemon
which
is
upon
that
same
Table
?
SIMP.
Because
that
the
air
it self
is
not
moved
SALV
.
It
is
requisite
then
,
that
the
projicient
do
confer
motion
on
the
Air
,
with
which
it
afterward
moveth
the
project
.
But
if
such
a
motion
cannot
be
impressed
[
i.
e.
imparted
]
it
being
impossible
to
make
an
accident
passe
out
of
one
subject
into
another
,
how
can
it
passe
from
the
arm
into
the
Air
?
Will
you
say
that
the
Air
is
not
a
subject
different
from
the
arm
?
SIMP.
To
this
it
is
answered
that
the
Air
,
in
regard
it
is
neither
heavy
nor
light
in
its
own
Region
,
is
disposed
with
facility
to
receive
every
impulse
,
and
also
to
retain
the
same
.
SALV
.
But
if
those
penduli
even
now
named
,
did
prove
unto
us
,
that
the
moveable
,
the
lesse
it
had
of
gravity
,
the
lesse
apt
it
was
to
conserve
its
motion
,
how
can
it
be
that
the
Air
which
in
the
Air
hath
no
gravity
at
all
,
doth
of
it self
alone
retain
the
motion
acquired
?
I
believe
,
and
know
that
you
by
this
time
are
of
the
same
opinion
,
that
the
arm
doth
not
sooner
return
to
rest
,
than
doth
the
circumambient
Air.
Let
's
go
into
the
Chamber
,
and
with
a
towel
let
us
agitate
the
Air
as
much
as
we
can
,
and
then
holding
the
cloth
still
,
let
a
little
candle
be
brought
,
that
was
lighted
in
the
next
room
,
or
in
the
same
place
let
a
leaf
of
beaten
Gold
be
left
at
liberty
to
flie
any
way
,
and
you
shall
by
the
calm
vagation
of
them
be
assured
that
the
Air
is
immediately
reduced
to
tranquilty
.
I
could
alledg
many
other
experiments
to
the
same
purpose
,
but
if
one
of
these
should
not
suffice
,
I
should
think
your
folly
altogether
incurable
.
SAGR.
When
an
arrow
is
shot
against
the
Wind
,
how
incredible
a
thing
is
it
,
that
that
same
small
filament
of
air
,
impelled
by
the
bow-string
,
should
in
despite
of
fate
go
along
with
the
arrow
?
But
I
would
willingly
know
another
particular
of
Aristotle
,
to
which
I
intreat
Simplicius
would
vouchsafe
me
an
answer
.
Supposing
that
with
the
same
Bow
there
were
shot
two
arrows
,
one
just
after
the
usual
manner
,
and
the
other
side-wayes
,
placing
it
long-wayes
upon
the
Bow-string
,
and
then
letting
it
flie
,
I
would
know
which
of
them
would
go
farthest
.
Favour
me
,
I
pray
you
with
an
answer
,
though
the
question
may
seem
to
you
rather
ridiculous
than
otherwise
;
and
excuse
me
,
for
that
I
,
who
am
,
as
you
see
,
rather
blockish
,
than
not
,
can
reach
no
higher
with
my
speculative
faculty
.
SIMPL.
I
have
never
seen
an
arrow
shot
in
that
manner
,
yet
neverthelesse
I
believe
,
that
it
would
not
flie
side-long
,
the
twentieth
part
of
the
space
that
it
goeth
end-wayes
.
SAGR.
And
for
that
I
am
of
the
same
opinion
,
hence
it
is
,
that
I
have
a
doubt
risen
in
me
,
whether
Aristotle
doth
not
contradict
experience
.
For
as
to
experience
,
if
I
lay
two
arrows
upon
this
Table
,
in
a
time
vvhen
a
strong
Wind
blovveth
,
one
tovvards
the
course
of
the
wind
,
and
the
other
sidelong
,
the
wind
will
quickly
carry
away
this
later
,
and
leave
the
other
where
it
was
;
and
the
same
to
my
seeming
,
ought
to
happen
,
if
the
Doctrine
of
Aristotle
were
true
,
of
those
two
shot
out
of
a
Bow
:
forasmuch
as
the
arrow
shot
sideways
is
driven
by
a
great
quantity
of
Air
,
moved
by
the
bowstring
,
to
wit
by
as
much
as
the
said
string
is
long
,
whereas
the
other
arrow
receiveth
no
greater
a
quantity
of
air
,
than
the
small
circle
of
the
strings
thickness
.
And
I
cannot
imagine
what
may
be
the
reason
of
such
a
difference
,
but
would
fain
know
the
same
.
SIMP.
The
cause
seemeth
to
me
sufficiently
manifest
;
and
it
is
,
because
the
arrow
shot
endways
,
hath
but
a
little
quantity
of
air
to
penetrate
,
and
the
other
is
to
make
its
way
through
a
quantity
as
great
as
its
whole
length
.
SALV
.
Then
it
seems
the
arrows
shot
,
are
to
penetrate
the
air
?
but
if
the
air
goeth
along
with
them
,
yea
,
is
that
which
carrieth
them
,
what
penetration
can
they
make
therein
?
Do
you
not
see
that
,
in
this
case
,
the
arrow
would
of
necessity
move
with
greater
velocity
than
the
air
?
and
this
greater
velocity
,
what
doth
confer
it
on
the
arrow
?
Will
you
say
the
air
giveth
them
a
velocity
greater
than
its
own
?
Know
then
,
Simplicius
,
that
the
business
proceeds
quite
contrary
to
that
which
Aristotle
saith
,
The
medium
doth
impede
and
not
confer
the
motion
of
projects
.
and
that
the
medium
conferreth
the
motion
on
the
project
,
is
as
false
,
as
it
is
true
,
that
it
is
the
onely
thing
which
procureth
its
obstruction
;
and
having
known
this
,
you
shall
understand
without
finding
any
thing
whereof
to
make
question
,
that
if
the
air
be
really
moved
,
it
doth
much
better
carry
the
dart
along
with
it
longways
,
than
endways
,
for
that
the
air
which
impelleth
it
in
that
posture
,
is
much
,
and
in
this
very
little
.
But
shooting
with
the
Bow
,
forasmuch
as
the
air
stands
still
,
the
transverse
arrow
,
being
to
force
its
passage
through
much
air
,
comes
to
be
much
impeded
,
and
the
other
that
was
nock't
easily
overcometh
the
obstruction
of
the
small
quantity
of
air
,
which
opposeth
it self
thereto
.
SALV
.
How
many
Propositions
have
I
observed
in
Aristotle
,
(
meaning
still
in
Natural
Philosophy
)
that
are
not
onely
false
,
but
false
in
such
sort
,
that
its
diametrical
contrary
is
true
,
as
it
happens
in
this
case
.
But
pursuing
the
point
in
hand
,
I
think
that
Simplicius
is
perswaded
,
that
,
from
seeing
the
stone
always
to
fall
in
the
same
place
,
he
cannot
conjecture
either
the
motion
or
stability
of
the
Ship
:
and
if
what
hath
been
hitherto
spoken
,
should
not
suffice
,
there
is
the
Experiment
of
the
medium
which
may
thorowly
assure
us
thereof
;
in
which
experiment
,
the
most
that
could
be
seen
would
be
,
that
the
cadent
moveable
might
be
left
behind
,
if
it
were
light
,
and
that
the
air
did
not
follow
the
motion
of
the
ship
:
but
in
case
the
air
should
move
with
equal
velocity
,
no
imaginable
diversity
could
be
found
either
in
this
,
or
any
other
experiment
whatsoever
,
as
I
am
anon
to
tell
you
.
Now
if
in
this
case
there
appeareth
no
difference
at
all
,
what
can
be
pretended
to
be
seen
in
the
stone
falling
from
the
top
of
the
Tower
,
where
the
motion
in
gyration
is
not
adventitious
,
and
accidental
,
but
natural
and
eternal
;
and
where
the
air
exactly
followeth
the
motion
of
the
Tower
,
and
the
Tower
that
of
the
Terrestrial
Globe
?
have
you
any
thing
else
to
say
,
Simplicius
,
upon
this
particular
?
SIMP.
No
more
but
this
,
that
I
see
not
the
mobility
of
the
Earth
as
yet
proved
.
SALV
.
Nor
have
I
any
intention
at
this
time
,
but
onely
to
shew
,
that
nothing
can
be
concluded
from
the
experiments
alledged
by
our
adversaries
for
convincing
Arguments
:
as
I
think
I
shall
prove
the
others
to
be
.
SAGR.
I
beseech
you
,
Salviatus
,
before
you
proceed
any
farther
,
to
permit
me
to
start
certain
questions
,
which
have
been
rouling
in
my
fancy
all
the
while
that
you
with
so
much
patience
and
equanimity
,
was
minutely
explaining
to
Simplicius
the
experiment
of
the
Ship
.
SALV
.
We
are
here
met
with
a
purpose
to
dispute
,
and
it
's
fit
that
every
one
should
move
the
difficulties
that
he
mets
withall
;
for
this
is
the
way
to
come
to
the
knowledg
of
the
truth
.
Therefore
speak
freely
.
SAGR.
If
it
be
true
,
that
the
impetus
wherewith
the
ship
moves
,
doth
remain
indelibly
impress'd
in
the
stone
,
after
it
is
let
fall
from
the
Mast
;
and
if
it
be
farther
true
,
that
this
motion
brings
no
impediment
or
retardment
to
the
motion
directly
downwards
,
natural
to
the
stone
:
An
admirable
accident
in
the
motion
of
projects
.
it
's
necessary
,
that
there
do
an
effect
ensue
of
a
very
wonderful
nature
.
Let
a
Ship
be
supposed
to
stand
still
,
and
let
the
time
of
the
falling
of
a
stone
from
the
Masts
Round-top
to
the
ground
,
be
two
beats
of
the
pulse
;
let
the
Ship
afterwards
be
under
sail
,
and
let
the
same
stone
depart
from
the
same
place
,
and
it
,
according
to
what
hath
been
premised
,
shall
still
take
up
the
time
of
two
pulses
in
its
fall
,
in
which
time
the
ship
will
have
run
,
suppose
,
twenty
yards
;
so
that
the
true
motion
of
the
stone
will
be
a
transverse
line
,
considerably
longer
than
the
first
straight
and
perpendicular
line
,
which
is
the
length
of
the
[
](A61244-e33140-b)*
*
By
the
length
of
the
mast
he
means
the
distance
between
the
upperdeck
and
Round-top
.
Mast
,
and
yet
nevertheless
the
[
](A61244-e33150-b)*
*
La
palla
.
stone
will
have
past
it
in
the
same
time
.
Let
it
be
farther
supposed
,
that
the
Ships
motion
is
much
more
accelerated
,
so
that
the
stone
in
falling
shall
be
to
pass
a
transverse
line
much
longer
than
the
other
;
and
in
sum
,
increasing
the
Ships
velocity
as
much
as
you
will
,
the
falling
stone
shall
describe
its
transverse
lines
still
longer
and
longer
,
and
yet
shall
pass
them
all
in
those
self
same
two
pulses
.
And
in
this
fashion
,
if
a
Canon
were
level'd
on
the
top
of
a
Tower
,
and
shots
were
made
therewith
point
blank
,
that
is
,
paralel
to
the
Horizon
,
let
the
Piece
have
a
greater
or
less
charge
,
so
as
that
the
ball
may
fall
sometimes
a
thousand
yards
distant
,
sometimes
four
thousand
,
sometimes
six
,
sometimes
ten
,
&c.
and
all
these
shots
shall
curry
or
finish
their
ranges
in
times
equal
to
each
other
,
and
every
one
equal
to
the
time
which
the
ball
would
take
to
pass
from
the
mouth
of
the
Piece
to
the
ground
,
being
left
,
without
other
impulse
,
to
fall
simply
downwards
in
a
perpendicular
line
.
Now
it
seems
a
very
admirable
thing
,
that
in
the
same
short
time
of
its
falling
perpendicularly
down
to
the
ground
,
from
the
height
of
,
suppose
,
an
hundred
yards
,
the
same
ball
,
being
thrust
violently
out
of
the
Piece
by
the
Fire
,
should
be
able
to
pass
one
while
four
hundred
,
another
while
a
thousand
,
another
while
four
,
another
while
ten
thousand
yards
,
so
as
that
the
said
ball
in
all
shots
made
point
blank
,
always
continueth
an
equal
time
in
the
air
.
SALV
.
The
consideration
for
its
novelty
is
very
pretty
,
and
if
the
effect
be
true
,
very
admirable
:
and
of
the
truth
thereof
,
I
make
no
question
:
and
were
it
not
for
the
accidental
impediment
of
the
air
,
I
verily
believe
,
that
,
if
at
the
time
of
the
balls
going
out
of
the
Piece
,
another
were
let
fall
from
the
same
height
directly
downwards
,
they
would
both
come
to
the
ground
at
the
same
instant
,
though
that
should
have
curried
ten
thousand
miles
in
its
range
,
and
this
but
an
hundred
onely
:
presupposing
the
surface
of
the
Earth
to
be
equal
,
which
to
be
assured
of
,
the
experiment
may
be
made
upon
some
lake
.
As
for
the
impediment
which
might
come
from
the
air
,
it
would
consist
in
retarding
the
extreme
swift
motion
of
the
shot
.
Now
,
if
you
think
fit
,
we
will
proceed
to
the
solution
of
the
other
Objections
,
seeing
that
Simplicius
(
as
far
as
I
can
see
)
is
convinc'd
of
the
nullity
of
this
first
,
taken
from
things
falling
from
on
high
downwards
.
SIMP.
I
find
not
all
my
scruples
removed
,
but
it
may
be
the
fault
is
my
own
,
as
not
being
of
so
easie
and
quick
an
apprehension
as
Sagredus
.
And
it
seems
to
me
,
that
if
this
motion
,
of
which
the
stone
did
partake
whilst
it
was
on
the
Round-top
of
the
Ships
Mast
,
be
,
as
you
say
,
to
conserve
it self
indelibly
in
the
said
stone
,
even
after
it
is
separated
from
the
Ship
,
it
would
follow
,
that
likewise
in
case
any
one
,
riding
a
horse
that
was
upon
his
speed
,
should
let
a
bowl
drop
out
of
his
hand
,
that
bowl
being
fallen
to
the
ground
would
continue
its
motion
and
follow
the
horses
steps
,
without
tarrying
behind
him
:
the
which
effect
,
I
believe
,
is
not
to
be
seen
,
unless
when
he
that
is
upon
the
horse
should
throw
it
with
violence
that
way
towards
which
he
runneth
;
but
otherwise
,
I
believe
it
will
stay
on
the
ground
in
the
same
place
where
it
fell
.
SALV
.
I
believe
that
you
very
much
deceive
your self
,
and
am
certain
,
that
experience
will
shew
you
the
contrary
,
and
that
the
ball
being
once
arrived
at
the
ground
,
will
run
together
with
the
horse
,
not
staying
behind
him
,
unless
so
far
as
the
asperity
and
unevenness
of
the
Earth
shall
hinder
it
.
And
the
reason
seems
to
me
very
manifest
:
for
if
you
,
standing
still
,
throw
the
said
ball
along
the
ground
,
do
you
think
it
would
not
continue
its
motion
even
after
you
had
delivered
it
out
of
your
hand
?
and
that
for
so
much
a
greater
space
,
by
how
much
the
superficies
were
more
smooth
,
so
that
v.
g.
upon
ice
it
would
run
a
great
way
?
SIMP.
There
is
no
doubt
of
it
,
if
I
give
it
impetus
with
my
arm
;
but
in
the
other
case
it
is
supposed
,
that
he
who
is
upon
the
horse
,
onely
drops
it
out
of
his
hand
.
SALV
.
So
I
desire
that
it
should
be
:
but
when
you
throw
it
with
your
arm
,
what
other
remaineth
to
the
ball
being
once
gone
out
of
your
hand
,
than
the
motion
received
from
your
arm
,
which
motion
being
conserved
in
the
boul
,
it
doth
continue
to
carry
it
forward
?
Now
,
what
doth
it
import
,
that
that
impetus
be
conferred
on
the
ball
rather
from
the
arm
than
from
the
horse
?
Whilst
you
were
on
horseback
,
did
not
your
hand
,
and
consequently
the
ball
run
as
fast
as
the
horse
it self
?
Doubtless
it
did
:
therefore
in
onely
opening
of
the
hand
,
the
ball
departs
with
the
motion
already
coceived
,
not
from
your
arm
,
by
your
particular
motion
,
but
from
the
motion
dependant
on
the
said
horse
,
which
cometh
to
be
communicated
to
you
,
to
your
arm
,
to
your
hand
,
and
lastly
to
the
ball
.
Nay
,
I
will
tell
you
farther
,
that
if
the
rider
upon
his
speed
fling
the
ball
with
his
arm
to
the
part
contrary
to
the
course
,
it
shall
,
after
it
is
fallen
to
the
ground
,
sometimes
(
albeit
thrown
to
the
contrary
part
)
follow
the
course
of
the
horse
,
and
sometimes
lie
still
on
the
ground
;
and
shall
onely
move
contrary
to
the
said
course
,
when
the
motion
received
from
the
arm
,
shall
exceed
that
of
the
carrier
in
velocity
.
And
it
is
a
vanity
,
that
of
some
,
who
say
that
a
horseman
is
able
to
cast
a
javelin
thorow
the
air
,
that
way
which
the
horse
runs
,
and
with
the
horse
to
follow
and
overtake
the
same
;
and
lastly
,
to
catch
it
again
.
It
is
,
I
say
,
a
vanity
,
for
that
to
make
the
project
return
into
the
hand
,
it
is
requisite
to
cast
it
upwards
,
in
the
same
manner
as
if
you
stood
still
.
For
,
let
the
carrier
be
never
so
swift
,
provided
it
be
uniform
,
and
the
project
not
over-light
,
it
shall
always
fall
back
again
into
the
hand
of
the
projicient
,
though
never
so
high
thrown
.
SAGR.
By
this
Doctrine
I
come
to
know
some
Problems
very
curious
upon
this
subject
of
projections
;
Sundry
curious
Problems
,
touching
the
motions
of
projects
.
the
first
of
which
must
seem
very
strange
to
Simplicius
.
And
the
Problem
is
this
;
I
affirm
it
to
be
possible
,
that
the
ball
being
barely
dropt
or
let
fall
,
by
one
that
any
way
runneth
very
swiftly
,
being
arrived
at
the
Earth
,
doth
not
onely
follow
the
course
of
that
person
,
but
doth
much
out
go
him
.
Which
Problem
is
connexed
with
this
,
that
the
moveable
being
thrown
by
the
projicient
above
the
plane
of
the
Horizon
,
may
acquire
new
velocity
,
greater
by
far
than
that
confer'd
upon
it
by
the
projicient
.
The
which
effect
I
have
with
admiration
observed
,
in
looking
upon
those
who
use
the
sport
of
tops
,
which
,
so
soon
as
they
are
set
out
of
the
hand
,
are
seen
to
move
in
the
air
with
a
certain
velocity
,
the
which
they
afterwards
much
encrease
at
their
coming
to
the
ground
;
and
if
whipping
them
,
they
rub
at
any
uneven
place
that
makes
them
skip
on
high
,
they
are
seen
to
move
very
slowly
through
the
air
,
and
falling
again
to
the
Earth
,
they
still
come
to
move
with
a
greater
velocity
:
But
that
which
is
yet
more
strange
,
I
have
farther
observed
,
that
they
not
onely
turn
always
more
swiftly
on
the
ground
,
than
in
the
air
,
but
of
two
spaces
both
upon
the
Earth
,
sometimes
a
motion
in
the
second
space
is
more
swift
than
in
the
first
.
Now
what
would
Simplicius
say
to
this
?
SIMP.
He
would
say
in
the
first
place
,
that
he
had
never
made
such
an
observation
.
Secondly
,
he
would
say
,
that
he
did
not
believe
the
same
.
He
would
say
again
,
in
the
third
place
,
that
if
you
could
assure
him
thereof
,
and
demonstratively
convince
him
of
the
same
,
he
would
account
you
a
great
Daemon
.
SAGR.
I
hope
then
that
it
is
one
of
the
Socratick
,
not
infernal
ones
.
But
that
I
may
make
you
understand
this
particular
,
you
must
know
,
that
if
a
person
apprehend
not
a
truth
of
himself
,
it
is
impossible
that
others
should
make
him
understand
it
:
I
may
indeed
instruct
you
in
those
things
which
are
neither
true
nor
false
;
but
the
true
,
that
is
,
the
necessary
,
namely
,
such
as
it
is
impossible
should
be
otherwise
,
every
common
capacity
either
comprehendeth
them
of
himself
,
or
else
it
is
impossible
he
should
ever
know
them
.
And
of
this
opinion
I
am
confident
is
Salviatus
also
:
and
therefore
I
tell
you
,
that
the
reasons
of
the
present
Problems
are
known
by
you
,
but
it
may
be
,
not
apprehended
.
SIMP.
Let
us
,
for
the
present
,
pass
by
that
controversie
,
and
permit
me
to
plead
ignorance
of
these
things
you
speak
of
,
and
try
whether
you
can
make
me
capable
of
understanding
these
Problems
.
SAGR.
This
first
dependeth
upon
another
,
which
is
,
Whence
cometh
it
,
that
setting
a
top
with
the
lash
,
it
runneth
farther
,
and
consequently
with
greater
force
,
than
when
it
s
set
with
the
fingers
?
SIMP.
Aristotle
also
makes
certain
Problems
about
these
kinds
of
projects
.
SALV
.
He
doth
so
;
and
very
ingenious
they
are
:
particularly
,
That
,
Whence
it
cometh
to
pass
that
round
tops
run
better
than
the
square
?
SAGR.
And
cannot
you
,
Simplicius
,
give
a
reason
for
this
,
without
others
prompting
you
?
SIMP.
Very
good
,
I
can
so
;
but
leave
your
jeering
.
SAGR.
In
like
manner
you
do
know
the
reason
of
this
other
〈◊〉
.
Tell
me
therefore
;
know
you
that
a
thing
which
moveth
,
being
impeded
stands
still
?
SIMP.
I
know
it
doth
,
if
the
impediment
be
so
great
as
to
suffice
.
SAGR.
Do
you
know
,
that
moving
upon
the
Earth
is
a
greater
impediment
to
the
moveable
,
than
moving
in
the
air
,
the
Earth
being
rough
and
hard
,
and
the
air
soft
and
yielding
?
SIMP.
And
knowing
this
,
I
know
that
the
top
will
turn
faster
in
the
air
,
than
on
the
ground
,
so
that
my
knowledg
is
quite
contrary
to
what
you
think
it
.
SAGR.
Fair
and
softly
,
Simplicius
.
You
know
that
in
the
parts
of
a
moveable
,
that
turneth
about
its
centre
,
there
are
found
motions
towards
all
sides
;
so
that
some
ascend
,
others
descend
;
some
go
forwards
,
others
backwards
?
SIMP.
I
know
it
,
and
Aristotle
taught
me
the
same
.
SAGR.
And
with
what
demonstration
,
I
pray
you
?
SIMP.
With
that
of
sense
.
SAGR.
Aristotle
,
then
,
hath
made
you
see
that
which
without
him
you
would
not
have
seen
?
Did
he
ever
lend
you
his
eyes
?
You
would
say
,
that
Aristotle
hath
told
,
advertised
,
remembered
you
of
the
same
;
and
not
taught
you
it
.
When
then
a
top
,
without
changing
place
,
turns
round
,
(
or
in
the
childrens
phrase
,
sleepeth
)
not
paralel
,
but
erect
to
the
Horizon
,
some
of
its
parts
ascend
,
and
the
opposite
descend
;
the
superiour
go
one
way
,
the
inferiour
another
.
Fancie
now
to
your self
,
a
top
,
that
without
changing
place
,
swiftly
turns
round
in
that
manner
,
and
stands
suspended
in
the
air
,
and
that
in
that
manner
turning
,
it
be
let
fall
to
the
Earth
perpendicularly
,
do
you
believe
,
that
when
it
is
arrived
at
the
ground
,
it
will
continue
to
turn
round
in
the
same
manner
,
without
changing
place
,
as
before
?
SIMP.
No
,
Sir
.
SAGR.
What
will
it
do
then
?
SIMP.
It
will
run
along
the
ground
very
fast
.
SAGR.
And
towards
what
part
?
SIMP.
Towards
that
,
whither
its
[
](A61244-e34160-b)*
*
Vert●gine
.
reeling
carrieth
it
.
SAGR.
In
its
reeling
there
are
parts
,
that
is
the
uppermost
,
which
do
move
contrary
to
the
inferiour
;
therefore
you
must
instance
which
it
shall
obey
:
for
as
to
the
parts
ascending
and
descending
,
the
one
kind
will
not
yield
to
the
other
;
nor
will
they
all
go
downwards
,
being
hindered
by
the
Earth
,
nor
upwards
as
being
heavy
.
SIMP.
The
top
will
run
reeling
along
the
floor
towards
that
part
whither
its
upper
parts
encline
it
.
SAGR.
And
why
not
whither
the
contrary
parts
tend
,
namely
,
those
which
touch
the
ground
?
SIMP.
Because
those
upon
the
ground
happen
to
be
impeded
by
the
roughness
of
the
touch
,
that
is
,
by
the
floors
unevenness
;
but
the
superiour
,
which
are
in
the
tenuous
and
flexible
air
,
are
hindred
very
little
,
if
at
all
;
and
therefore
the
top
will
obey
their
inclination
.
SAGR.
So
that
that
taction
,
if
I
may
so
say
,
of
the
neither
parts
on
the
floor
,
is
the
cause
that
they
stay
,
and
onely
the
upper
parts
spring
the
top
forward
.
SALV
.
And
therefore
,
if
the
top
should
fall
upon
the
ice
,
or
other
very
smooth
superficies
,
it
would
not
so
well
run
forward
,
but
might
peradventure
continue
to
revolve
in
it self
,
(
or
sleep
)
without
acquiring
any
progressive
motion
.
SAGR.
It
is
an
easie
thing
for
it
so
to
do
;
but
yet
nevertheless
,
it
would
not
so
speedily
come
to
sleep
,
as
when
it
falleth
on
a
superficies
somewhat
rugged
.
But
tell
me
,
Simplicius
,
when
the
top-turning
round
about
it self
,
in
that
manner
,
is
let
fall
,
why
doth
it
not
move
forwards
in
the
air
,
as
it
doth
afterwards
when
it
is
upon
the
ground
?
SIMP.
Because
having
air
above
it
,
and
beneath
,
neither
those
parts
,
nor
these
have
any
where
to
touch
,
and
not
having
more
occasion
to
go
forward
than
backward
,
it
falls
perpendicularly
.
SAGR.
So
then
the
onely
reeling
about
its
self
,
without
other
impetus
,
can
drive
the
top
forward
,
being
arrived
at
the
ground
,
very
nimbly
.
Now
proceed
we
to
what
remains
.
That
lash
,
which
the
driver
tyeth
to
his
Top-stick
,
and
with
which
,
winding
it
about
the
top
,
he
sets
it
(
i.
e.
makes
it
go
)
what
effect
hath
it
on
the
said
top
?
SIMP.
It
constrains
it
to
turn
round
upon
its
toe
,
that
so
it
may
free
it self
from
the
Top-lash
.
SAGR.
So
then
,
when
the
top
arriveth
at
the
ground
,
it
cometh
all
the
way
turning
about
its
self
,
by
means
of
the
lash
.
Hath
it
not
reason
then
to
move
in
it self
more
swiftly
upon
the
ground
,
than
it
did
whilst
it
was
in
the
air
?
SIMP.
Yes
doubtless
;
for
in
the
air
it
had
no
other
impulse
than
that
of
the
arm
of
the
projicient
;
and
if
it
had
also
the
reeling
,
this
(
as
hath
been
said
)
in
the
air
drives
it
not
forward
at
all
▪
but
arriving
at
the
floor
,
to
the
motion
of
the
arm
is
added
the
progression
of
the
reeling
,
whereby
the
velocity
is
redoubled
.
And
I
know
already
very
well
,
that
the
top
skipping
from
the
ground
,
its
velocity
will
deminish
,
because
the
help
of
its
circulation
is
wanting
;
and
returning
to
the
Earth
will
get
it
again
,
and
by
that
means
move
again
faster
,
than
in
the
air
.
It
onely
rests
for
me
to
understand
,
whether
in
this
second
motion
on
the
Earth
it
move
more
swiftly
,
than
in
the
first
;
for
then
it
would
move
in
infinitum
,
alwayes
accelerating
.
SAGR.
I
did
not
absolutely
affirm
,
that
this
second
motion
is
more
swift
than
the
first
;
but
that
it
may
happen
so
to
be
sometimes
.
SIMP.
This
is
that
,
which
I
apprehend
not
,
and
which
I
desire
to
know
.
SAGR.
And
this
also
you
know
of
your self
.
Therefore
tell
me
:
When
you
let
the
top
fall
out
of
your
hand
,
without
making
it
turn
round
(
i.
e.
setting
it
)
what
will
it
do
at
its
coming
to
the
ground
?
SIMP.
Nothing
,
but
there
lie
still
.
SAGR.
May
it
not
chance
,
that
in
its
fall
to
the
ground
it
may
acquire
a
motion
?
Think
better
on
it
.
SIMP.
Unlesse
we
let
it
fall
upon
some
inclining
stone
,
as
children
do
playing
at
[
](A61244-e34760-b)*
*
A
Game
in
Italy
,
which
is
,
to
glide
bullets
down
an
inclining
stone
,
&c.
Chiosa
,
and
that
falling
side-wayes
upon
the
same
,
it
do
acquire
the
motion
of
turning
round
upon
its
toe
,
wherewith
it
afterwards
continueth
to
move
progressively
on
the
floor
,
I
know
not
in
what
other
manner
it
can
do
any
thing
but
lie
still
where
it
falleth
.
SAGR.
You
see
then
that
in
some
case
it
may
acquire
a
new
revolution
.
When
then
the
top
jerked
up
from
the
ground
,
falleth
down
again
,
why
may
it
not
casually
hit
upon
the
declivity
of
some
stone
fixed
in
the
floor
,
and
that
hath
an
inclination
that
way
towards
which
it
moveth
,
and
acquiring
by
that
slip
a
new
whirle
over
and
above
that
conferred
by
the
lash
,
why
may
it
not
redouble
its
motion
,
and
make
it
swifter
than
it
was
at
its
first
lighting
upon
the
ground
?
SIMP.
Now
I
see
that
the
same
may
easily
happen
.
And
I
am
thinking
that
if
the
top
should
turn
the
contrary
way
,
in
arriving
at
the
ground
,
it
would
work
a
contrary
effect
,
that
is
,
the
motion
of
the
accidental
whirl
would
retard
that
of
the
projicient
.
SAGR.
And
it
would
sometimes
wholly
retard
and
stop
it
,
in
case
the
revolution
of
the
top
were
very
swift
.
And
from
hence
ariseth
the
resolution
of
that
slight
,
which
the
more
skilful
Tennis
Players
use
to
their
advantage
;
that
is
,
to
gull
their
adversary
by
cutting
(
for
so
is
their
Phrase
)
the
Ball
;
which
is
,
to
return
it
with
a
side
Rachet
,
in
such
a
manner
,
that
it
doth
thereby
acquire
a
motion
by
it self
contrary
to
the
projected
motion
,
and
so
by
that
means
,
at
its
coming
to
the
ground
,
the
rebound
,
which
if
the
ball
did
not
turn
in
that
manner
,
would
be
towards
the
adversary
,
giving
him
the
usual
time
to
tosse
it
back
again
,
doth
fail
,
and
the
ball
runs
tripping
along
the
ground
,
or
rebounds
lesse
than
usual
,
and
breaketh
the
time
of
the
return
.
Hence
it
is
that
you
see
,
those
who
play
at
[
](A61244-e34890-b)*
*
A
Game
in
Italy
,
wherein
they
strive
who
shall
trundle
or
throw
a
wooden
bowle
neerest
to
an
assigned
mark
.
Stool-ball
,
when
they
play
in
a
stony
way
,
or
a
place
full
of
holes
and
rubs
that
make
the
ball
trip
an
hundred
several
wayes
,
never
suffering
it
to
come
neer
the
mark
,
to
avoid
them
all
,
they
do
not
trundle
the
ball
upon
the
ground
,
but
throw
it
,
as
if
they
were
to
pitch
a
quait
.
But
because
in
throwing
the
ball
,
it
issueth
out
of
the
hand
with
some
roling
conferred
by
the
fingers
,
when
ever
the
hand
is
under
the
ball
,
as
it
is
most
commonly
held
;
whereupon
the
ball
in
its
lighting
on
the
ground
neer
to
the
mark
,
between
the
motion
of
the
projicient
and
that
of
the
roling
,
would
run
a
great
way
from
the
same
:
To
make
the
ball
stay
,
they
hold
it
artificially
,
with
their
hand
uppermost
,
and
it
undermost
,
which
in
its
delivery
hath
a
contrary
twirl
or
roling
conferred
upon
it
by
the
fingers
,
by
means
whereof
in
its
coming
to
the
ground
neer
the
mark
it
stays
there
,
or
runs
very
very
little
forwards
.
But
to
return
to
our
principal
problem
which
gave
occasion
for
starting
these
others
;
I
say
it
is
possible
that
a
person
carried
very
swiftly
,
may
let
a
ball
drop
out
of
his
hand
,
that
being
come
to
the
Earth
,
shall
not
onely
follow
his
motion
,
but
also
out-go
it
,
moving
with
a
greater
velocity
.
And
to
see
such
an
effect
,
I
desire
that
the
course
may
be
that
of
a
Chariot
,
to
which
on
the
out-side
let
a
declining
board
be
fastened
;
so
as
that
the
neither
part
may
be
towards
the
horses
,
and
the
upper
towards
the
hind
Wheel
.
Now
,
if
in
the
Chariots
full
career
,
a
man
within
it
,
let
a
ball
fall
gliding
along
the
declivity
of
that
board
,
it
shall
in
roling
downward
acquire
a
particular
vertigo
or
turning
,
the
which
added
to
the
motion
impressed
by
the
Chariot
,
will
carrie
the
ball
along
the
ground
much
faster
than
the
Chariot
.
And
if
one
accommodate
another
declining
board
over
against
it
,
the
motion
of
the
Chariot
may
be
qualified
so
,
that
the
ball
,
gliding
downwards
along
the
board
,
in
its
coming
to
the
ground
shall
rest
immoveable
,
and
also
shall
sometimes
run
the
contrary
way
to
the
Chariot
.
But
we
are
strayed
too
far
from
the
purpose
,
therefore
if
Simplicius
be
satisfied
with
the
resolution
of
the
first
arg●ment
against
the
Earths
mobility
,
taken
from
things
falling
perpendicularly
,
we
may
passe
to
the
rest
.
SALV
.
The
digressions
made
hitherto
,
are
not
so
alienated
from
the
matter
in
hand
,
as
that
one
can
say
they
are
wholly
strangers
to
it
.
Besides
these
argumentations
depend
on
those
things
that
start
up
in
the
fancy
not
of
one
person
,
but
of
three
,
that
we
are
:
And
moreover
we
discourse
for
our
pleasure
,
nor
are
we
obliged
to
that
strictnesse
of
one
who
ex
professo
treateth
methodically
of
an
argument
,
with
an
intent
to
publish
the
same
.
I
will
not
consent
that
our
Poem
should
be
so
confined
to
that
unity
,
as
not
to
leave
us
fields
open
for
Epsody's
,
which
every
smalll
connection
should
suffice
to
introduce
;
but
with
almost
as
much
liberry
as
if
we
were
met
to
tell
stories
,
it
shall
be
lawful
for
me
to
speak
,
what
ever
your
discourse
brings
into
mymind
.
SAGR.
I
like
this
motion
very
well
;
and
since
we
are
at
this
liberty
,
let
me
take
leave
,
before
we
passe
any
farther
to
ask
of
you
Salviatus
,
whether
you
did
ever
consider
what
that
line
may
be
that
is
described
by
the
grave
moveable
naturally
falling
down
from
the
top
of
a
Tower
;
and
if
you
have
reflected
on
it
,
be
pleased
to
tell
me
what
you
think
thereof
.
SALV
.
I
have
sometimes
considered
of
it
,
and
make
no
question
,
that
if
one
could
be
certain
of
the
nature
of
that
motion
wherewith
the
grave
body
descendeth
to
approach
the
centre
of
the
Terrestrial
Globe
,
mixing
it self
afterwards
with
the
common
circular
motion
of
the
diurnal
conversion
;
it
might
be
exactly
found
what
kind
of
line
that
is
,
that
the
centre
of
gravity
of
the
moveable
describeth
in
those
two
motions
.
SAGR.
Touching
the
simple
motion
towards
the
centre
dependent
on
the
gravity
,
I
think
that
one
may
confidently
,
without
error
,
believe
that
it
is
by
a
right
line
,
as
it
would
be
,
were
the
Earth
immoveable
.
SALV
.
As
to
this
particular
,
we
may
not
onely
believe
it
,
but
experience
rendereth
us
certain
of
the
same
.
SAGR.
But
how
doth
experience
assure
us
thereof
,
if
we
never
see
any
motions
but
such
as
are
composed
of
the
two
,
circular
and
descending
.
SALV
.
Nay
rather
Sagredus
we
onely
see
the
simple
motion
of
descent
;
since
that
other
circular
one
common
to
the
Earth
,
the
Tower
and
our selves
remains
imperceptible
,
and
as
if
it
never
were
,
and
there
remaineth
perceptible
to
us
that
of
the
stone
,
onely
not
participated
by
us
,
and
for
this
,
sense
demonstrateth
that
it
is
by
a
right
line
,
ever
parallel
to
the
said
Tower
,
which
is
built
upright
and
perpendicular
upon
the
Terrestrial
surface
.
SAGR.
You
are
in
the
right
;
and
this
was
but
too
plainly
demonstrated
to
me
even
now
,
seeing
that
I
could
not
remember
so
easie
a
thing
;
but
this
being
so
manifest
,
what
more
is
it
that
you
say
you
desire
,
for
understanding
the
nature
of
this
motion
downwards
?
SALV
.
It
sufficeth
not
to
know
that
it
is
streight
,
but
its
requisite
to
know
whether
it
be
uniform
,
or
irregular
;
that
is
,
whether
it
maintain
alwayes
one
and
the
same
velocity
,
or
else
goeth
retarding
or
accelerating
.
SAGR.
It
is
already
clear
,
that
it
goeth
continually
accellerating
.
SALV
.
Neither
doth
this
suffice
,
but
its
requisite
to
know
according
to
what
proportion
such
accelleration
is
made
;
a
Problem
,
that
I
believe
was
never
hitherto
understood
by
any
Philosopher
or
Mathematician
;
although
Philosophers
,
and
particularly
the
Peripateticks
,
have
writ
great
and
entire
Volumes
,
touching
motion
.
SIMP.
Philosophers
principally
busie
themselves
about
universals
;
they
find
the
definitions
and
more
common
symptomes
,
omitting
certain
subtilties
and
niceties
,
which
are
rather
curiosities
to
the
Mathematicians
.
And
Aristotle
did
content
himself
to
define
excellently
what
motion
was
in
general
;
and
of
the
local
,
to
shew
the
principal
qualities
,
to
wit
,
that
one
is
natural
,
another
violent
;
one
is
simple
,
another
compound
;
one
is
equal
,
another
accellerate
;
and
concerning
the
accelerate
,
contents
himself
to
give
the
reason
of
acceleration
,
remitting
the
finding
out
of
the
proportion
of
such
acceleration
,
and
other
particular
accidents
to
the
Mechanitian
,
or
other
inferiour
Artist
.
SAGR.
Very
well
Simplicius
.
But
you
Salviatus
,
when
you
descend
sometimes
from
the
Throne
of
Peripatetick
Majesty
,
have
you
ever
thrown
away
any
of
your
hours
in
studying
to
find
this
proportion
of
the
acceleration
of
the
motion
of
descending
grave
bodies
?
SALV
.
There
was
no
need
that
I
should
study
for
it
,
in
regard
that
the
Academick
our
common
friend
,
heretofore
shewed
me
a
Treatise
of
his
[
](A61244-e35430-b)*
*
This
is
that
excellent
tract
which
we
give
the
first
place
in
our
second
Volume
.
De
Motu
,
where
this
,
and
many
other
accidents
were
demonstrated
.
But
it
would
be
too
great
a
digression
,
if
for
this
particular
,
we
should
interrupt
our
present
discourse
,
(
which
yet
it self
is
also
no
better
than
a
digression
)
and
make
as
the
Saying
is
,
a
Comedy
within
a
Comedy
.
SAGR.
I
am
content
to
excuse
you
from
this
narration
for
the
present
,
provided
that
this
may
be
one
of
the
Propositions
reserved
to
be
examined
amongst
the
rest
in
another
particular
meeting
,
for
that
the
knowledg
thereof
is
by
me
very
much
desired
;
and
in
the
mean
time
let
us
return
to
the
line
described
by
the
grave
body
in
its
fall
from
the
top
of
the
Tower
to
its
base
.
SALV
.
If
the
right
motion
towards
the
centre
of
the
Earth
was
uniforme
,
the
circular
towards
the
East
being
also
uniforme
,
you
would
see
composed
of
them
both
a
motion
by
a
spiral
line
,
of
that
kind
with
those
defined
by
Archimedes
in
his
Book
De
Spiralibus
;
which
are
,
when
a
point
moveth
uniformly
upon
a
right
line
,
whilest
that
line
in
the
mean
time
turneth
uniformly
about
one
of
its
extreme
points
fixed
,
as
the
centre
of
his
gyration
.
But
because
the
right
motion
of
grave
bodies
falling
,
is
continually
accelerated
,
it
is
necessary
,
that
the
line
resulting
of
the
composition
of
the
two
motions
do
go
alwayes
receding
with
greater
and
greater
proportion
from
the
circumference
of
that
circle
,
which
the
centre
of
the
stones
gravity
would
have
designed
,
if
it
had
alwayes
staid
upon
the
Tower
;
it
followeth
of
necessity
that
this
recession
at
the
first
be
but
little
,
yea
very
small
,
yea
,
more
,
as
small
as
can
be
imagined
,
seeing
that
the
descending
grave
body
departing
from
rest
,
that
is
,
from
the
privation
of
motion
,
towards
the
bottom
and
entring
into
the
right
motion
downwards
,
it
must
needs
passe
through
all
the
degrees
of
tardity
,
that
are
betwixt
rest
,
and
any
assigned
velocity
;
the
which
degrees
are
infinite
;
as
already
hath
been
at
large
discoursed
and
proved
.
It
being
supposed
therefore
,
that
the
progresse
of
the
acceleration
being
after
this
manner
,
and
it
being
moreover
true
,
that
the
descending
grave
body
goeth
to
terminate
in
the
centre
of
the
Earth
,
The
line
described
by
a
moveable
in
its
natural
descent
,
the
motion
of
the
Earth
about
its
own
centre
being
presupposed
,
would
probably
be
the
circumference
of
a
circle
.
it
is
necessary
that
the
line
of
its
mixt
motion
be
such
,
that
it
go
continually
receding
with
greater
and
greater
proportion
from
the
top
of
the
Tower
,
or
to
speak
more
properly
,
from
the
circumference
of
the
circle
described
by
the
top
of
the
Tower
,
by
means
of
the
Earths
conversion
;
but
that
such
recessions
be
lesser
and
lesser
in
infinitum
;
by
how
much
the
moveable
finds
it self
to
be
lesse
and
lesse
removed
from
the
first
term
where
it
rested
.
Moreover
it
is
necessary
,
that
this
line
of
the
compounded
motion
do
go
to
terminate
in
the
centre
of
the
Earth
.
Now
having
presupposed
these
two
things
,
I
come
to
describe
about
the
centre
A
[
in
Fig.
1.
of
this
second
Dialogue
;
]
with
the
semidiameter
AB
,
the
circle
BI
,
representing
to
me
the
Terrestrial
Globe
,
and
prolonging
the
semidiameter
AB
to
C
,
I
have
described
the
height
of
the
Tower
BC
;
the
which
being
carried
about
by
the
Earth
along
the
circumference
BI
,
describeth
with
its
top
the
arch
CD
:
Dividing
,
in
the
next
place
,
the
line
CA
in
the
middle
at
E
;
upon
the
centre
E
,
at
the
distance
EC
,
I
describe
the
semicircle
CIA
:
In
which
,
I
now
affirm
,
that
it
is
very
probable
that
a
stone
falling
from
the
top
of
the
Tower
C
,
doth
move
,
with
a
motion
mixt
of
the
circular
,
which
is
in
common
,
and
of
its
peculiar
right
motion
.
If
therefore
in
the
circumference
CD
,
certain
equal
parts
CF
,
FG
,
GH
,
HL
,
be
marked
,
and
from
the
points
F
,
G
,
H
,
L
,
right
lines
be
drawn
towards
the
centre
A
,
the
parts
of
them
intercepted
between
the
two
circumferences
CD
and
BI
,
shall
represent
unto
us
the
same
Tower
CB
,
transported
by
the
Terrestrial
Globe
towards
DI
;
in
which
lines
the
points
where
they
come
to
be
intersected
by
the
arch
of
the
semicircle
CI
,
are
the
places
by
which
from
time
to
time
the
falling
stone
doth
passe
;
which
points
go
continually
with
greater
and
greater
proportion
receding
from
the
top
of
the
Tower
.
And
this
is
the
cause
vvhy
the
right
motion
made
along
the
side
of
the
Tower
apeareth
to
us
more
and
more
accelerate
.
It
appeareth
also
,
how
by
reason
of
the
infinite
acutenesse
of
the
contact
of
those
two
circles
DC
,
CI
,
the
recession
of
the
cadent
moveable
from
the
circumference
CFD
;
namely
,
from
the
top
of
the
Tower
,
is
towards
the
beginning
extream
small
,
which
is
as
much
as
if
one
said
its
motion
downwards
is
very
slow
,
and
more
and
more
slow
in
infinitum
,
according
to
its
vicinity
to
the
term
C
,
that
is
to
the
state
of
rest
.
And
lastly
it
is
seen
how
in
the
end
this
same
motion
goeth
to
terminate
in
the
centre
of
the
Earth
A.
SAGR.
I
understand
all
this
very
well
,
nor
can
I
perswade
my self
that
the
falling
moveable
doth
describe
with
the
centre
of
its
gravity
any
other
line
,
but
such
an
one
as
this
.
SALV
.
But
stay
a
little
Sagredus
,
for
I
am
to
acquaint
you
also
with
three
Observations
of
mine
,
that
its
possible
will
not
displease
you
.
A
moveable
falling
from
the
top
of
the
Tower
,
moveth
in
the
circumference
of
a
circle
.
The
first
of
which
is
,
that
if
we
do
well
consider
,
the
moveable
moveth
not
really
with
any
more
than
onely
one
motion
simply
circular
,
as
when
being
placed
upon
the
Tower
,
it
moved
with
one
single
and
circular
motion
.
The
second
is
yet
more
pleasant
;
for
,
It
moveth
neither
more
nor
lesse
,
than
if
it
had
staid
alwayes
there
.
it
moveth
neither
more
nor
lesse
then
if
it
had
staid
continually
upon
the
Tower
,
being
that
to
the
arches
CF
,
FG
,
GH
,
&c.
that
it
would
have
passed
continuing
alwayes
upon
the
Tower
,
the
arches
of
the
circumference
CI
are
exactly
equal
,
answering
under
the
same
CF
,
FG
,
GH
,
&c.
Whence
followeth
the
third
wonder
,
It
moveth
with
an
uniform
,
not
an
accelerate
motion
.
That
the
true
and
real
motion
of
the
stone
is
never
accelerated
,
but
alwayes
even
and
uniforme
,
since
that
all
the
equal
arches
noted
in
the
circumference
CD
,
and
their
respondent
ones
marked
in
the
circumference
CI
,
are
past
in
equal
times
;
so
that
we
are
left
at
liberty
to
seek
new
causes
of
acceleration
,
or
of
other
motions
,
seeing
that
the
moveable
,
as
well
standing
upon
the
Tower
,
as
descending
thence
,
alwayes
moveth
in
the
same
fashion
,
that
is
,
circularly
,
with
the
same
velocity
,
and
with
the
same
uniformity
.
Now
tell
me
what
you
think
of
this
my
fantastical
conjecture
.
SAGR.
I
must
tell
you
,
that
I
cannot
with
words
sufficiently
expresse
how
admirable
it
seemeth
to
me
;
and
for
vvhat
at
present
offereth
it self
to
my
understanding
,
I
cannot
think
that
the
business
happeneth
otherwise
;
and
vvould
to
God
that
all
the
demonstrations
of
Philosophers
were
but
half
so
probable
as
this
.
However
for
my
perfect
satisfaction
I
would
gladly
hear
how
you
prove
those
arches
to
be
equal
.
SALV
.
The
demonstration
is
most
easie
.
Suppose
to
your self
a
line
drawn
from
I
to
E.
And
the
Semidiameter
of
the
circle
CD
,
that
is
,
the
line
CA
,
being
double
the
Semidiameter
CE
of
the
circle
CI
,
the
circumference
shall
be
double
to
the
circumference
,
and
every
arch
of
the
greater
circle
double
to
every
like
arch
of
the
lesser
;
and
consequently
,
the
half
of
the
arch
of
the
greater
circle
,
equal
to
the
whole
arch
of
the
lesse
.
And
because
the
angle
CEI
made
in
the
centre
E
of
the
lesser
circle
,
and
which
insisteth
upon
the
arch
CI
,
is
double
the
angle
CAD
,
made
in
the
centre
A
of
the
greater
circle
,
to
which
the
arch
CD
subtendeth
;
therefore
the
arch
CD
is
half
of
the
arch
of
the
greater
circle
like
to
the
arch
CI
,
and
therefore
the
two
arches
CD
and
CI
are
equal
;
and
in
the
same
manner
we
may
demonstrate
of
all
their
parts
.
But
that
the
business
,
as
to
the
motion
of
descending
grave
bodies
,
proceedeth
exactly
thus
,
I
will
not
at
this
time
affirm
;
but
this
I
will
say
,
that
if
the
line
described
by
the
cadent
moveable
be
not
exactly
the
same
with
this
,
it
doth
extream
neerly
resemble
the
same
.
SAGR.
But
I
,
Right
motion
seemeth
wholly
excluded
in
nature
.
Salviatus
,
am
just
now
considering
another
particular
very
admirable
;
and
this
it
is
;
That
admitting
these
considerations
,
the
right
motion
doth
go
wholly
[
](A61244-e35790-b)*
*
Vadia
del
tutto
a
monte
,
rendered
in
the
Latine
omnino
pessum
eat
.
mounting
,
and
that
Nature
never
makes
use
thereof
,
since
that
,
even
that
that
use
,
which
was
from
the
beginning
granted
to
it
,
which
was
of
reducing
the
parts
of
integral
bodies
to
their
place
,
when
they
were
separated
from
their
whole
,
and
therefore
constituted
in
a
depraved
disposition
,
is
taken
from
it
,
and
assigned
to
the
circular
motion
.
SALV
.
This
would
necessarily
follow
,
if
it
were
concluded
that
the
Terrestrial
Globe
moveth
circularly
;
a
thing
,
which
I
pretend
not
to
be
done
,
but
have
onely
hitherto
attempted
,
as
I
shall
still
,
to
examine
the
strength
of
those
reasons
,
which
have
been
alledged
by
Philosophers
to
prove
the
immobility
of
the
Earth
,
of
which
this
first
taken
from
things
falling
perpendicularly
,
hath
begat
the
doubts
,
that
have
been
mentioned
;
which
I
know
not
of
what
force
they
may
have
seemed
to
Simplicius
;
and
therefore
before
I
passe
to
the
examination
of
the
remaining
arguments
,
it
would
be
convenient
that
he
produce
what
he
hath
to
reply
to
the
contrary
.
SIMP.
As
to
this
first
,
I
confesse
indeed
that
I
have
heard
sundry
pretty
notions
,
which
I
never
thought
upon
before
,
and
in
regard
they
are
new
unto
me
,
I
cannot
have
answers
so
ready
for
them
,
but
this
argument
taken
●rom
things
falling
perpendicularly
,
I
esteem
it
not
one
of
the
strongest
proofs
of
the
mobility
of
the
Earth
;
and
I
know
not
what
may
happen
touching
the
shots
of
great
Guns
,
especially
those
aimed
contrary
to
the
diurnal
motion
.
SAGR.
The
flying
of
the
birds
as
much
puzzleth
me
as
the
objection
of
the
Gun-shot
,
and
all
the
other
experiments
above
alledged
.
For
these
birds
which
at
their
pleasure
flie
forwards
and
backwards
,
and
wind
to
and
again
in
a
thousand
fashions
,
and
,
which
more
importeth
,
lie
whole
hours
upon
the
wing
,
these
I
say
do
not
a
little
pose
me
,
nor
do
I
see
,
how
amongst
so
many
circumgyrations
,
they
should
not
lose
the
motion
of
the
Earth
,
and
how
they
should
be
able
to
keep
pace
with
so
great
a
velocity
as
that
which
they
so
far
exceed
with
their
flight
.
SALV
.
To
speak
the
truth
,
your
scruple
is
not
without
reason
,
and
its
possible
Copernicus
himself
could
not
find
an
answer
for
it
,
that
was
to
himself
entirely
satisfactory
;
and
therefore
haply
past
it
over
in
silence
;
albeit
he
was
,
indeed
,
very
brief
in
examining
the
other
allegations
of
his
adversaries
,
I
believe
through
his
height
of
wit
,
placed
on
greater
aud
sublimer
contemplations
,
like
as
Lions
are
not
much
moved
at
the
barking
of
little
Dogs
.
We
will
therefore
reserve
the
instance
of
birds
to
the
last
place
,
and
for
the
present
,
see
if
we
can
give
Simplicius
satisfaction
in
the
others
,
by
shewing
him
in
our
wonted
manner
,
that
he
himself
hath
their
answers
at
hand
,
though
upon
first
thoughts
he
doth
not
discover
them
.
And
to
begin
with
the
shots
made
at
randome
,
with
the
self
same
piece
,
powder
,
and
ball
,
the
one
towards
the
East
,
the
other
towards
the
West
(
if
the
diurnal
conversion
belonged
to
the
Earth
)
ought
to
be
much
longer
than
that
towards
the
East
.
SIMP.
I
am
moved
so
to
think
;
because
in
the
shot
made
towards
the
East
,
The
reason
why
a
Gun
should
seem
to
carry
farther
towards
the
West
than
towards
the
East
.
the
ball
whil'st
it
is
out
of
the
piece
,
is
followed
by
the
said
piece
,
the
which
being
carried
round
by
the
Earth
,
runneth
also
with
much
velocity
towards
the
same
part
,
whereupon
the
fall
of
the
ball
to
the
ground
,
cometh
to
be
but
little
distant
from
the
piece
.
On
the
contrary
in
the
shot
towards
the
West
,
before
that
the
ball
falleth
to
the
ground
,
the
piece
is
retired
very
far
towards
the
East
,
by
which
means
the
space
between
the
ball
and
the
piece
,
that
is
Range
,
will
appear
longer
than
the
other
,
by
how
much
the
piece
,
that
is
the
Earth
,
had
run
in
the
time
that
both
the
bals
were
in
the
air
.
SALV
.
I
could
wish
,
that
we
did
know
some
way
to
make
an
experiment
corresponding
to
the
motion
of
these
projects
,
as
that
of
the
ship
doth
to
the
motion
of
things
perpendicularly
falling
from
on
high
;
and
I
am
thinking
how
it
may
be
done
.
SAGR.
I
believe
,
that
it
would
be
a
very
opposite
proof
,
to
take
an
open
Chariot
,
The
experiment
of
a
running
chariot
to
find
out
the
difference
of
Ranges
.
and
to
accomodate
therein
a
[
](A61244-e36080-b)*
*
Balestrone
da
bolzoni
.
Stock-bow
at
half
elevation
,
to
the
end
the
flight
may
prove
the
greatest
that
my
be
,
and
whil'st
the
horses
shall
run
,
to
shoot
first
towards
the
part
whither
you
drive
,
and
then
another
backwards
towards
the
contrary
part
,
causing
some
one
to
mark
diligently
where
the
Chariot
was
in
that
moment
●f
time
when
the
shaft
came
to
the
ground
,
as
well
in
the
one
shot
as
in
the
other
:
for
thus
you
may
see
exactly
how
much
one
shaft
flew
farther
than
the
other
.
SIMP.
In
my
thoughts
this
experiment
is
very
proper
:
and
I
do
not
doubt
but
that
the
flight
,
that
is
,
the
space
between
the
shaft
and
the
place
where
the
chariot
was
at
the
shafts
fall
,
will
be
less
by
much
when
one
shooteth
towards
the
chariots
course
,
than
when
one
shooteth
the
contrary
way
.
For
an
example
,
let
the
flight
of
it self
be
three
hundred
yards
,
and
the
course
of
the
chariot
in
the
time
whilst
the
shaft
stayeth
in
the
air
,
an
hundred
yards
,
therefore
shooting
towards
the
course
,
of
the
three
hundred
yards
of
the
flight
,
the
chariot
will
have
gone
one
hundred
;
so
then
at
the
shafts
coming
to
the
ground
,
the
space
between
it
and
the
chariot
,
shall
be
but
two
hundred
yards
onely
;
but
on
the
contrary
,
in
the
other
shoot
,
the
chariot
running
contrary
to
the
shaft
,
when
the
shaft
shall
have
passed
its
three
hundred
yards
,
and
the
chariot
it
s
other
hundred
the
contrary
way
,
the
distance
interposing
shall
be
found
to
be
four
hundred
yards
.
SALV
.
Is
there
any
way
to
shoot
so
that
these
flights
may
be
equal
?
SIMP.
I
know
no
other
way
,
unless
by
making
the
chariot
to
stand
still
.
SALV
.
This
we
know
;
but
I
mean
when
the
chariot
runneth
in
full
carreer
.
SIMP.
In
that
case
you
are
to
draw
the
Bow
higher
in
shooting
forwards
,
and
to
slack
it
in
shooting
the
contrary
way
.
SALV
.
Then
you
see
that
there
is
one
way
more
.
But
how
much
is
the
bow
to
be
drawn
,
and
how
much
slackened
?
SIMP.
In
our
case
,
where
we
have
supposed
that
the
bow
carried
three
hundred
yards
,
it
would
be
requisite
to
draw
it
so
,
as
that
it
might
carry
four
hundred
,
and
in
the
other
to
slacken
it
so
,
as
that
it
might
carry
no
more
than
two
hundred
.
For
so
each
of
the
flights
would
be
but
three
hundred
in
relation
to
the
chariot
,
the
which
,
with
its
course
of
an
hundred
yards
which
it
substracts
from
the
shoot
of
four
hundred
,
and
addeth
to
that
of
two
hundred
,
would
reduce
them
both
to
three
hundred
.
SALV
.
But
what
effect
hath
the
greater
or
less
intensness
of
the
bow
upon
the
shaft
?
SIMP.
The
stiffer
bow
carrieth
it
with
greater
velocity
,
and
the
weaker
with
less
;
and
the
same
shaft
flieth
so
much
farther
at
one
time
than
another
,
with
how
much
greater
velocity
it
goeth
out
of
the
tiller
at
one
time
,
than
another
.
SALV
.
So
that
to
make
the
shaft
shot
either
way
,
to
flie
at
equal
distance
from
the
running
chariot
,
it
is
requisite
,
that
if
in
the
first
shoot
of
the
precedent
example
,
it
goeth
out
of
the
tiller
with
v.
g.
four
degrees
of
velocity
,
that
then
in
the
other
shoot
it
depart
but
with
two
onely
:
but
if
the
same
bow
be
used
,
it
always
receiveth
thence
three
degrees
.
SIMP.
It
doth
so
;
and
for
this
reason
,
shooting
with
the
same
bow
in
the
chariots
course
,
the
shoots
cannot
be
equal
.
SALV
.
I
had
forgot
to
ask
,
with
what
velocity
it
is
supposed
in
this
particular
experiment
,
that
the
chariot
runneth
.
SIMP.
The
velocity
of
the
chariot
must
be
supposed
to
be
one
degree
in
comparison
to
that
of
the
bow
,
which
is
three
,
SALV
.
Very
right
,
for
so
computation
gives
it
.
But
tell
me
,
when
the
chariot
moveth
,
doth
not
all
things
in
the
same
move
with
the
same
velocity
?
SIMP.
Yes
doubtless
.
SALV
.
Then
so
doth
the
shaft
also
,
and
the
bow
,
and
the
string
,
upon
which
the
shaft
is
nock't
.
SIMP.
They
do
so
.
SALV
.
Why
then
,
in
discharging
the
shaft
towards
the
course
of
the
chariot
,
the
bow
impresseth
its
three
degrees
of
velocity
on
a
shaft
that
had
one
degree
of
velocity
before
,
by
means
of
the
chariot
which
transported
it
so
fast
towards
that
part
;
so
that
in
its
going
off
it
hath
four
degrees
of
velocity
.
On
the
contrary
,
in
the
other
shoot
,
the
same
bow
conferreth
its
same
three
degrees
of
velocity
on
a
shaft
that
moveth
the
contrary
way
,
with
one
degree
;
so
that
in
its
departing
from
the
bow-string
,
it
hath
no
more
left
but
onely
two
degrees
of
velocity
.
But
you
your self
have
already
said
,
that
the
way
to
make
the
shoots
equal
,
is
to
cause
that
the
shaft
be
let
flie
the
first
time
with
four
degrees
of
velocity
,
and
the
second
time
with
two
.
Therefore
without
changing
the
bow
,
the
very
course
of
the
chariot
is
that
which
adjusteth
the
flights
,
The
solution
of
the
argument
taken
from
great-Guns
shot
towards
the
East
&
West
.
and
the
experiment
doth
so
represent
them
to
any
one
who
is
not
either
wilfully
or
naturally
incapable
of
reason
.
Now
apply
this
discourse
to
Gunnery
,
and
you
shall
find
,
that
whether
the
Earth
move
or
stand
still
,
the
shots
made
with
the
same
force
,
will
always
curry
equal
ranges
,
to
what
part
soever
aimed
.
The
error
of
Aristotle
,
Ptolomey
,
Tycho
,
your self
,
and
all
the
rest
,
is
grounded
upon
that
fixed
and
strong
persuasion
,
that
the
Earth
standeth
still
,
which
you
have
not
judgment
nor
power
to
depose
,
no
not
when
you
have
a
desire
to
argue
of
that
which
would
ensue
,
presupposing
the
Earth
to
move
.
And
thus
,
in
the
other
argument
,
not
considering
that
whil'st
the
stone
is
upon
the
Tower
,
it
doth
,
as
to
moving
or
not
moving
,
the
same
that
the
Terrestrial
Globe
doth
,
because
you
have
concluded
with
your self
,
that
the
Earth
stands
still
,
you
always
discourse
touching
the
fall
of
the
stone
,
as
if
it
were
to
depart
from
rest
:
whereas
it
behooveth
to
say
,
that
if
the
Earth
standeth
still
,
the
stone
departeth
from
rest
,
and
descendeth
perpendicularly
;
but
if
the
Earth
do
move
,
the
stone
likewise
moveth
with
like
velocity
,
nor
doth
it
depart
from
rest
,
but
from
a
motion
equal
to
that
of
the
Earth
,
wherewith
it
intermixeth
the
supervenient
motion
of
descent
,
and
of
those
two
composeth
a
third
which
is
transversal
or
side-ways
.
SIMP.
But
for
Gods
sake
,
if
it
move
transversly
,
how
is
it
that
I
behold
it
to
move
directly
and
perpendicularly
?
This
is
no
better
than
the
denial
of
manifest
sense
;
and
if
we
may
not
believe
sense
,
at
what
other
door
shall
we
enter
into
disquisitions
of
Philosophy
?
SALV
.
In
respect
to
the
Earth
,
to
the
Tower
,
and
to
our selves
,
which
all
as
one
piece
move
with
the
diurnal
motion
together
with
the
stone
,
the
diurnal
motion
is
as
if
it
never
had
been
,
and
becometh
insensible
,
imperceptible
,
and
without
any
action
at
all
;
and
the
onely
motion
which
we
can
perceive
,
is
that
of
which
we
partake
not
,
that
is
the
descent
gliding
along
the
side
of
the
Tower
:
You
are
not
the
first
that
hath
felt
great
repugnance
in
apprehending
this
non-operating
of
motion
upon
things
to
which
it
is
common
.
SAGR.
Now
I
do
remember
a
certain
conceipt
,
A
notable
case
of
Sagredus
,
to
shew
the
non-operating
of
common
motion
.
that
came
one
day
into
my
fancy
,
whilst
I
sailed
in
my
voyage
to
Aleppo
,
whither
I
went
Consul
for
our
Countrey
,
and
possibly
it
may
be
of
some
use
,
for
explaining
this
nullity
of
operation
of
common
motion
,
and
being
as
if
it
never
were
to
all
the
partakers
thereof
.
And
if
it
stand
with
the
good
liking
of
Simplicius
,
I
will
reason
with
him
upon
that
which
then
I
thought
of
by
my self
alone
.
SIMP.
The
novelty
of
the
things
which
I
hear
,
makes
me
not
so
much
a
patient
,
as
a
greedy
and
curious
auditor
:
therefore
go
on
.
SAGR.
If
the
neb
of
a
writing
pen
,
that
I
carried
along
with
me
in
the
ship
,
through
all
my
navigation
from
Venice
to
[
](A61244-e36860-b)*
*
Alessandretta
.
Scanderon
,
had
had
a
facultie
of
leaving
visible
marks
of
its
whole
voyage
,
what
signs
,
what
marks
,
what
lines
would
it
have
left
?
SIMP.
It
would
have
left
a
line
distended
from
Venice
thither
,
not
perfectly
streight
,
or
to
say
better
,
distended
in
a
perfect
arch
of
a
circle
,
but
in
some
places
more
,
in
some
less
curved
,
according
as
the
vessel
had
gone
more
or
less
fluctuating
;
but
this
its
inflecting
in
some
places
a
fathom
or
two
to
the
right
hand
or
to
the
left
,
upwards
or
downwards
,
in
a
length
of
many
hundred
miles
,
would
have
brought
but
little
alteration
to
the
intire
tract
of
the
line
,
so
that
it
would
have
been
hardly
sensible
;
and
without
any
considerable
error
,
might
have
been
called
the
part
of
a
perfect
arch
.
SAGR.
So
that
the
true
and
most
exact
motion
of
the
neb
of
my
pen
would
have
also
been
an
arch
of
a
perfect
circle
,
if
the
vessels
motion
,
the
fluctuation
of
the
billows
ceasing
,
had
been
calm
and
tranquill
.
And
if
I
had
continually
held
that
per
in
my
hand
,
and
had
onely
moved
it
sometimes
an
inch
or
two
this
way
or
that
way
,
what
alteration
should
I
have
made
in
that
its
principal
,
and
very
long
tract
or
stroke
?
SIMP.
Less
than
that
which
the
declining
in
several
places
from
absolute
rectitude
,
but
the
quantity
of
a
flea's
eye
makes
in
a
right
line
of
a
thousand
yards
long
.
SAGR.
If
a
Painter
,
then
,
at
our
launching
from
the
Port
,
had
began
to
design
upon
a
paper
with
that
pen
,
and
continued
his
work
till
he
came
to
Scanderon
,
he
would
have
been
able
to
have
taken
by
its
motion
a
perfect
draught
of
all
those
figures
perfectly
interwoven
and
shadowed
on
several
sides
with
countreys
,
buildings
,
living
creatures
,
and
other
things
;
albeit
all
the
true
,
real
,
and
essential
motion
traced
out
by
the
neb
of
that
pen
,
would
have
been
no
other
than
a
very
long
,
but
simple
line
:
and
as
to
the
proper
operation
of
the
Painter
,
he
would
have
delineated
the
same
to
an
hair
,
if
the
ship
had
stood
still
.
That
therefore
of
the
huge
long
motion
of
the
pen
there
doth
remain
no
other
marks
,
than
those
tracks
drawn
upon
the
paper
,
the
reason
thereof
is
because
the
grand
motion
from
Venice
to
Scanderon
,
was
common
to
the
paper
,
the
pen
,
and
all
that
which
was
in
the
ship
:
but
the
petty
motions
forwards
and
backwards
,
to
the
right
,
to
the
left
,
communicated
by
the
fingers
of
the
Painter
unto
the
pen
,
and
not
to
the
paper
,
as
being
peculiar
thereunto
,
might
leave
marks
of
it self
upon
the
paper
,
which
did
not
move
with
that
motion
.
Thus
it
is
likewise
true
,
that
the
Earth
moving
,
the
motion
of
the
stone
in
descending
downwards
,
was
really
a
long
tract
of
many
hundreds
and
thousands
of
yards
,
and
if
it
could
have
been
able
to
have
delineated
in
a
calm
air
,
or
other
superficies
,
the
track
of
its
course
,
it
would
have
left
behind
an
huge
long
transverse
line
.
But
that
part
of
all
this
motion
which
is
common
to
the
stone
,
the
Tower
,
and
our selves
,
is
imperceptible
to
us
,
and
as
if
it
had
never
been
,
and
that
part
onely
remaineth
observable
,
of
which
neither
the
Tower
nor
we
are
partakers
,
which
is
in
fine
,
that
wherewith
the
stone
falling
measureth
the
Tower
.
SALV
.
A
most
witty
conceipt
to
clear
up
this
point
,
which
was
not
a
little
difficult
to
many
capacities
.
Now
if
Simplicius
will
make
no
farther
reply
,
we
may
pass
to
the
other
experiments
,
the
unfolding
of
which
will
receive
no
small
facility
from
the
things
already
declared
.
SIMP.
I
have
nothing
more
to
say
:
and
I
was
well-nigh
transported
with
that
delineation
,
and
with
thinking
how
those
strokes
drawn
so
many
ways
,
hither
,
thither
,
upwards
,
downwards
,
forwards
,
backwards
,
and
interwoven
with
thousands
of
turnings
,
are
not
essentially
or
really
other
,
than
small
pieces
of
one
sole
line
drawn
all
one
way
,
and
the
same
without
any
other
alteration
save
the
declining
the
direct
rectitude
,
sometimes
a
very
insensible
matter
towards
one
side
or
another
,
and
the
pens
moving
its
neb
one
while
softer
,
another
while
slower
,
but
with
very
small
inequality
.
And
I
think
that
it
would
in
the
same
manner
write
a
letter
,
and
that
those
frollike
penmen
,
who
to
shew
their
command
of
hand
,
without
taking
their
pen
from
the
paper
in
one
sole
stroke
,
with
infinite
turnings
draw
a
pleasant
knot
,
if
they
were
in
a
boat
that
did
tide
it
along
swiftly
they
would
convert
the
whole
motion
of
the
pen
,
which
in
reality
is
but
one
sole
line
,
drawn
all
towards
one
and
the
same
part
,
and
very
little
curved
,
or
declining
from
perfect
rectitude
,
into
a
knot
or
flourish
.
And
I
am
much
pleased
that
Sagredus
hath
helped
me
to
this
conceit
:
therefore
let
us
go
on
,
for
the
hope
of
meeting
with
more
of
them
,
will
make
me
the
stricter
in
my
attention
.
SAGR.
If
you
have
a
curiosity
to
hear
such
like
subtilties
,
Subtilties
sufficiently
insipid
,
ironically
,
spoken
and
taken
from
a
certain
Encyclopaedia
.
which
occurr
not
thus
to
every
one
,
you
will
find
no
want
of
them
,
especially
in
this
particular
of
Navigation
;
and
do
you
not
think
that
a
witty
conceit
which
I
met
with
likewise
in
the
same
voyage
,
when
I
observed
that
the
mast
of
the
ship
,
without
either
breaking
or
bending
,
had
made
a
greater
voyage
with
its
round-top
,
that
is
with
its
top-gallant
,
than
with
its
foot
;
for
the
round
top
being
more
distant
from
the
centre
of
the
Earth
than
the
foot
is
,
it
had
described
the
arch
of
a
circle
bigger
than
the
circle
by
which
the
foot
had
passed
.
SIMP.
And
thus
when
a
man
walketh
he
goeth
farther
with
his
head
than
with
his
feet
.
SAGR.
You
have
found
out
the
matter
your self
by
help
of
your
own
mother-vvit
:
But
let
us
not
interrupt
Salviatus
.
SALV
.
It
pleaseth
me
to
see
Simplicius
hovv
he
sootheth
up
himself
in
this
conceit
,
if
happly
it
be
his
ovvn
,
and
that
he
hath
not
borrovved
it
from
a
certain
little
pamphlet
of
conclusions
,
vvhere
there
are
a
great
many
more
such
fancies
no
less
pleasant
&
vvitty
.
It
follovveth
that
vve
speak
of
the
peice
of
Ordinance
mounted
perpendicular
to
the
Horizon
,
An
instance
against
the
deurnal
motion
of
the
earth
,
taken
from
the
shot
of
a
Peece
of
Ordinance
perpendicularly
.
that
is
,
of
a
shot
tovvards
our
vertical
point
,
and
to
conclude
,
of
the
return
of
the
ball
by
the
same
line
unto
the
same
peice
,
though
that
in
the
long
time
vvhich
it
is
separated
from
the
peice
,
the
earth
hath
transported
it
many
miles
tovvards
the
East
;
novv
it
seemeth
,
that
the
ball
ought
to
fall
a
like
distance
from
the
peice
tovvards
the
West
;
the
vvhich
doth
not
happen
:
therefore
the
peice
vvithout
having
been
moved
did
stay
expecting
the
same
.
The
ansvver
is
the
same
vvith
that
of
the
stone
falling
from
the
Tovver
;
The
answer
to
the
objection
,
shewing
the
equivoke
.
and
all
the
fallacy
,
and
equivocation
consisteth
in
supposing
still
for
true
,
that
vvhich
is
in
question
;
for
the
Opponent
hath
it
still
fixed
in
his
conceit
that
the
ball
departs
from
its
rest
,
being
discharged
by
the
fire
from
the
piece
;
and
the
departing
from
the
state
of
rest
,
cannot
be
,
unlesse
the
immobility
of
the
Terrestrial
Globe
be
presupposed
,
which
is
the
conclusion
of
that
was
in
dispute
;
Therefore
,
I
reply
,
that
those
who
make
the
Earth
moveable
,
answer
,
that
the
piece
,
and
the
ball
that
is
in
it
,
partake
of
the
same
motion
with
the
Earth
;
nay
that
they
have
this
together
with
her
from
nature
;
and
that
therefore
the
ball
departs
in
no
other
manner
from
its
quiescence
,
but
conjoyned
with
its
motion
about
the
centre
,
the
which
by
its
projection
upwards
,
is
neither
taken
away
,
nor
hindered
;
and
in
this
manner
following
,
the
universal
motion
of
the
Earth
towards
the
East
,
it
alwayes
keepeth
perpendicular
over
the
said
piece
,
as
well
in
its
rise
as
in
its
return
.
And
the
same
you
see
to
ensue
,
in
making
the
experiment
in
a
ship
with
a
bullet
shot
upwards
perpendicularly
with
a
Crosse-bow
,
which
returneth
to
the
same
place
whether
the
ship
doth
move
,
or
stand
still
.
SAGR.
This
satisfieth
very
well
to
all
;
Another
answer
to
the
same
objection
.
but
because
that
I
have
seen
that
Simplicius
taketh
pleasure
with
certain
subtilties
to
puzzle
his
companions
,
I
will
demand
of
him
whether
,
supposing
for
this
time
that
the
Earth
standeth
still
,
and
the
piece
erected
upon
it
perpendicularly
,
directed
to
our
Zenith
,
he
do
at
all
question
that
to
be
the
true
perpendicular
shot
,
and
that
the
ball
in
departing
,
and
in
its
return
is
to
go
by
the
same
right
line
,
still
supposing
all
external
and
accidental
impediments
to
be
removed
?
SIMP.
I
understand
that
the
matter
ought
to
succeed
exactly
in
that
manner
.
SAGR.
But
if
the
piece
were
placed
,
not
prependicularly
,
but
inclining
towards
some
place
,
what
would
the
motion
of
the
ball
be
?
Would
it
go
haply
,
as
in
the
other
shot
,
by
the
perpendicular
line
,
and
return
again
by
the
same
?
SIMP.
It
would
not
so
do
;
but
issuing
out
of
the
piece
,
it
would
pursue
its
motion
by
a
right
line
which
prolongeth
the
erect
perpendicularity
of
the
concave
cylinder
of
the
piece
,
unlesse
so
far
as
its
own
vveight
vvould
make
it
decline
from
that
erection
towards
the
Earth
.
SAGR.
So
that
the
mounture
of
the
cylinder
is
the
regulator
of
the
motion
of
the
ball
,
nor
doth
it
,
or
would
it
move
out
of
that
line
,
if
its
own
gravity
did
not
make
it
decline
downwards
.
And
therefore
placing
the
cylinder
perpendicularly
,
Projects
continue
their
motion
by
the
right
line
that
followeth
the
direction
of
the
motion
,
made
together
with
the
proficient
,
whil'st
they
were
conjoin'd
therewith
.
and
shooting
the
ball
upwards
,
it
returneth
by
the
same
right
line
downvvards
;
because
the
motion
of
the
ball
dependent
on
its
gravity
is
downward
,
by
the
same
perpendicular
.
The
journey
therefore
of
the
ball
out
of
the
piece
,
continueth
or
prolongeth
the
rectitude
or
perpendicularity
of
that
small
part
of
the
said
journey
,
vvhich
it
made
vvithin
the
said
piece
;
is
it
not
so
?
SIMP.
So
it
is
,
in
my
opinion
.
SAGR.
Now
imagine
the
cylinder
to
be
erected
,
and
that
the
Earth
doth
revolve
about
vvith
a
diurnal
motion
,
carrying
the
piece
along
vvith
it
,
tell
me
vvhat
shall
be
the
motion
of
the
ball
vvithin
the
cylinder
,
having
given
fire
?
SIMP.
It
shall
be
a
streight
and
perpendicular
motion
,
the
cylinder
being
erected
perpendicularly
.
SAGR.
Consider
vvell
vvhat
you
say
:
for
I
believe
that
it
vvill
not
be
perpendicular
.
It
vvould
indeed
be
perpendicular
,
if
the
Earth
stood
still
,
for
so
the
ball
vvould
have
no
other
motion
but
that
proceeding
from
the
fire
.
The
revolution
of
the
Earth
supposed
,
the
ball
in
the
piece
erected
perpendicularly
,
doth
not
move
by
a
perpendicular
,
but
an
inclined
line
.
But
in
case
the
Earth
turns
round
,
the
ball
that
is
in
the
piece
,
hath
likewise
a
diurnal
motion
,
so
that
there
being
added
to
the
same
the
impulse
of
the
fire
,
it
moveth
from
the
breech
of
the
piece
to
the
muzzle
with
two
motions
,
from
the
composition
whereof
it
cometh
to
passe
that
the
motion
made
by
the
centre
of
the
balls
gravity
is
an
inclining
line
.
And
for
your
clearer
understanding
the
same
,
let
the
piece
AC
[
in
Fig.
2.
]
be
erected
,
and
in
it
the
ball
B
;
it
is
manifest
,
that
the
piece
standing
immoveable
,
and
fire
being
given
to
it
,
the
ball
will
make
its
way
out
by
the
mouth
A
,
and
with
its
centre
,
passing
thorow
the
the
piece
,
shall
have
described
the
perpendicular
line
BA
,
and
it
shall
pursue
that
rectitude
when
it
is
out
of
the
piece
,
moving
toward
the
Zenith
.
But
in
case
the
Earth
should
move
round
,
and
consequently
carry
the
piece
along
with
it
,
in
the
time
that
the
ball
driven
out
of
the
piece
shall
move
along
the
cylinder
,
the
piece
being
carried
by
the
Earth
,
shall
passe
into
the
situation
DE
,
and
the
ball
B
,
in
going
off
,
would
be
at
the
cornish
D
,
and
the
motion
of
the
bals
centre
,
would
have
been
according
to
the
line
BD
,
no
longer
perpendicular
,
but
inclining
towards
the
East
;
and
the
ball
(
as
hath
been
concluded
)
being
to
continue
its
motion
through
the
air
,
according
to
the
direction
of
the
motion
made
in
the
piece
,
the
said
motion
shall
continue
on
according
to
the
inclination
of
the
line
BD
,
and
so
shall
no
longer
be
perpendicular
,
but
inclined
towards
the
East
,
to
which
part
the
piece
doth
also
move
;
whereupon
the
ball
may
follow
the
motion
of
the
Earth
,
and
of
the
piece
.
Now
Simplicius
,
you
see
it
demonstrated
,
that
the
Range
which
you
took
to
be
perpendicular
,
is
not
so
.
SIMP.
I
do
not
very
well
understand
this
business
;
do
you
,
Salviatus
?
SALV
.
I
apprehend
it
in
part
;
but
I
have
a
certain
kind
of
scruple
,
which
I
wish
I
knew
how
to
express
.
It
seems
to
me
,
that
according
to
what
hath
been
said
,
if
the
Piece
be
erected
perpendicular
,
and
the
Earth
do
move
,
the
ball
would
not
be
to
fall
,
as
Aristotle
and
Tycho
will
have
it
,
far
from
the
Piece
towards
the
West
,
nor
as
you
would
have
it
,
upon
the
Piece
,
but
rather
far
distant
towards
the
East
.
For
according
to
your
explanation
,
it
would
have
two
motions
,
the
which
would
with
one
consent
carry
it
thitherward
,
to
wit
,
the
common
motion
of
the
Earth
,
which
carrieth
the
Piece
and
the
ball
from
CA
towards
ED
;
and
the
fire
which
carrieth
it
by
the
inclined
line
BD
,
both
motions
towards
the
East
,
and
therefore
they
are
superiour
to
the
motion
of
the
Earth
.
SAGR.
Not
so
,
Sir
.
The
motion
which
carrieth
the
ball
towards
the
East
,
cometh
all
from
the
Earth
,
and
the
fire
hath
no
part
at
all
therein
:
the
motion
which
mounteth
the
ball
upwards
,
is
wholly
of
fire
,
wherewith
the
Earth
hath
nothing
to
do
.
And
that
it
is
so
,
if
you
give
not
fire
,
the
ball
will
never
go
out
of
the
Piece
,
nor
yet
rise
upwards
a
hairs
breadth
;
as
also
if
you
make
the
Earth
immoveable
,
and
give
fire
,
the
ball
without
any
inclination
shall
go
perpendicularly
upwards
.
The
ball
therefore
having
two
motions
,
one
upwards
,
and
the
other
in
gyration
,
of
both
which
the
transverse
line
BD
is
compounded
,
the
impulse
upward
is
wholly
of
fire
,
the
circular
cometh
wholly
from
the
Earth
,
and
is
equal
to
the
Earths
motion
:
and
being
equal
to
it
,
the
ball
maintaineth
it self
all
the
way
directly
over
the
mouth
of
the
Piece
,
and
at
last
falleth
back
into
the
same
:
and
because
it
always
observeth
the
erection
of
the
Piece
,
it
appeareth
also
continually
over
the
head
of
him
that
is
near
the
Piece
,
and
therefore
it
appeareth
to
mount
exactly
perpendicular
towards
our
Zenith
,
or
vertical
point
.
SIMP.
I
have
yet
one
doubt
more
remaining
,
and
it
is
,
that
in
regard
the
motion
of
the
ball
is
very
swift
in
the
Piece
,
it
seems
not
possible
,
that
in
that
moment
of
time
the
transposition
of
the
Piece
from
CA
to
AD
should
confer
such
an
inclination
upon
the
transverse
line
CD
,
that
by
means
thereof
,
the
ball
when
it
cometh
afterwards
into
the
air
should
be
able
to
follow
the
course
of
the
Earth
.
SAGR.
You
err
upon
many
accounts
;
and
first
,
the
inclination
of
the
transverse
line
CD
,
I
believe
it
is
much
greater
than
you
take
it
to
be
,
for
I
verily
think
that
the
velocity
of
the
Earths
motion
,
not
onely
under
the
Equinoctial
,
but
in
our
paralel
also
,
is
greater
than
that
of
the
ball
whilst
it
moveth
in
the
Piece
;
so
that
the
interval
CE
would
be
absolutely
much
bigger
than
the
whole
length
of
the
Piece
,
and
the
inclination
of
the
transverse
line
consequently
bigger
than
half
a
right
angle
:
but
be
the
velocity
of
the
Earth
more
,
or
be
it
less
,
in
comparison
of
the
velocity
of
the
fire
,
this
imports
nothing
;
for
if
the
velocity
of
the
Earth
be
small
,
and
consequently
the
inclination
of
the
transverse
line
be
little
also
;
there
is
then
also
need
but
of
little
inclination
to
make
the
ball
suspend
it self
in
its
range
directly
over
the
Piece
.
And
in
a
word
,
if
you
do
but
attentively
consider
,
you
will
comprehend
,
that
the
motion
of
the
Earth
in
transferring
the
Piece
along
with
it
from
CA
to
ED
,
conferreth
upon
the
transverse
line
CD
,
so
much
of
little
or
great
inclination
,
as
is
required
to
adjust
the
range
to
its
perpendicularity
.
But
you
err
,
secondly
,
in
that
you
referr
the
faculty
of
carrying
the
ball
along
with
the
Earth
to
the
impulse
of
the
fire
,
and
you
run
into
the
same
error
,
into
which
Salviatus
,
but
even
now
seemed
to
have
fallen
;
for
the
faculty
of
following
the
motion
of
the
Earth
,
is
the
primary
and
perpetual
motion
,
indelibly
and
inseparably
imparted
to
the
said
ball
,
as
to
a
thing
terrestrial
,
and
that
of
its
own
nature
doth
and
ever
shall
possess
the
same
.
SALV
.
Let
us
yield
,
The
manner
how
Fowlers
shoot
birds
flying
.
Simplicius
,
for
the
business
is
just
as
he
saith
.
And
now
from
this
discourse
let
us
come
to
understand
the
reason
of
a
Venatorian
Problem
,
of
those
Fowlers
who
with
their
guns
shoot
a
bird
flying
;
and
because
I
did
imagine
,
that
in
regard
the
bird
flieth
a
great
pace
,
therefore
they
should
aim
their
shot
far
from
the
bird
,
anticipating
its
flight
for
a
certain
space
,
and
more
or
less
according
to
its
velocity
and
the
distance
of
the
bird
,
that
so
the
bullet
hasting
directly
to
the
mark
aimed
at
,
it
might
come
to
arrive
at
the
self
same
time
in
the
same
point
with
its
motion
,
and
the
bird
with
its
flight
,
and
by
that
means
one
to
encounter
the
other
:
and
asking
one
of
them
,
if
their
practise
was
not
so
to
do
;
He
told
me
,
no
;
but
that
the
slight
was
very
easie
and
certain
,
and
that
they
took
aim
just
in
the
same
manner
as
if
they
had
shot
at
a
bird
that
did
sit
still
;
that
is
,
they
made
the
flying
bird
their
mark
,
and
by
moving
their
fowling-piece
they
followed
her
,
keeping
their
aim
still
full
upon
her
,
till
such
time
as
they
let
fly
,
and
in
this
manner
shot
her
as
they
did
others
sitting
still
.
It
is
necessary
therefore
that
that
motion
,
though
slow
,
which
the
fowling-piece
maketh
in
turning
and
following
after
the
flight
of
the
bird
do
communicate
it self
to
the
bullet
also
,
and
that
it
be
joyned
with
that
of
the
fire
;
so
that
the
ball
hath
from
the
fire
the
motion
directly
upwards
,
and
from
the
concave
Cylinder
of
the
barrel
the
declination
according
to
the
flight
of
the
Bird
,
just
as
was
said
before
of
the
shot
of
a
Canon
;
where
the
ball
receiveth
from
the
fire
a
virtue
of
mounting
upwards
towards
the
Zenith
,
and
from
the
motion
of
the
Earth
its
winding
towards
the
East
,
and
of
both
maketh
a
compound
motion
that
followeth
the
course
of
the
Earth
,
and
that
to
the
beholder
seemeth
onely
to
go
directly
upwards
,
and
return
again
downwards
by
the
same
line
.
The
holding
therefore
of
the
gun
continually
directed
towards
the
mark
,
maketh
the
shoot
hit
right
,
and
that
you
may
keep
your
gun
directed
to
the
mark
,
in
case
the
mark
stands
still
,
you
must
also
hold
your
gun
still
;
and
if
the
mark
shall
move
,
the
gun
must
be
kept
upon
the
mark
by
moving
.
The
answer
to
the
objection
tak●n
from
the
shots
of
great
Guns
ma●e
towards
the
North
and
South
.
And
upon
this
dependeth
the
proper
answer
to
the
other
argument
taken
from
the
shot
of
a
Canon
,
at
the
mark
placed
towards
the
South
or
North
:
wherein
is
alledged
,
that
if
the
Earth
should
move
,
the
shots
would
all
range
Westward
of
the
mark
,
because
that
in
the
time
whilst
the
ball
,
being
forc'd
out
of
the
Piece
,
goeth
through
the
air
to
the
mark
,
the
said
mark
being
carried
toward
the
East
,
would
leave
the
ball
to
the
Westward
.
I
answer
therefore
,
demanding
whether
if
the
Canon
be
aimed
true
at
the
mark
,
and
permitted
so
to
continue
,
it
will
constantly
hit
the
said
mark
,
whether
the
Earth
move
or
stand
still
?
It
must
be
replied
,
that
the
aim
altereth
not
at
all
,
for
if
the
mark
doth
stand
still
,
the
Piece
also
doth
stand
still
,
and
if
it
,
being
transported
by
the
Earths
motion
,
doth
move
,
the
Piece
doth
also
move
at
the
same
rate
,
and
,
the
aim
maintained
,
the
shot
proveth
always
true
,
as
by
what
hath
been
said
above
,
is
manifest
.
SAGR.
Stay
a
little
,
I
entreat
you
,
Salviatus
,
till
I
have
propounded
a
certain
conceit
touching
these
shooters
of
birds
flying
,
whose
proceeding
I
believe
to
be
the
same
which
you
relate
,
and
believe
the
effect
of
hitting
the
bird
doth
likewise
follow
:
but
yet
I
cannot
think
that
act
altogether
conformable
to
this
of
shooting
in
great
Guns
,
which
ought
to
hit
as
well
when
the
piece
and
mark
moveth
,
as
when
they
both
stand
still
;
and
these
,
in
my
opinion
,
are
the
particulars
in
which
they
disagree
.
In
shooting
with
a
great
Gun
both
it
and
the
mark
move
with
equal
velocity
,
being
both
transported
by
the
motion
of
the
Terrestrial
Globe
:
and
albeit
sometimes
the
piece
being
planted
more
towards
the
Pole
,
than
the
mark
,
and
consequently
its
motion
being
somewhat
flower
than
the
motion
of
the
mark
,
as
being
made
in
a
lesser
circle
,
such
a
difference
is
insensible
,
at
that
little
distance
of
the
piece
from
the
mark
:
but
in
the
shot
of
the
Fowler
the
motion
of
the
Fowling-piece
wherewith
it
goeth
following
the
bird
,
is
very
slow
in
comparison
of
the
flight
of
the
said
bird
;
whence
me
thinks
it
should
follow
,
that
that
small
motion
which
the
turning
of
the
Birding-piece
conferreth
on
the
bullet
that
is
within
it
,
cannot
,
when
it
is
once
gone
forth
of
it
,
multiply
it self
in
the
air
,
untill
it
come
to
equal
the
velocity
of
the
birds
flight
,
so
as
that
the
said
bullet
should
always
keep
direct
upon
it
:
nay
,
me
thinketh
the
bird
would
anticipate
it
and
leave
it
behind
.
Let
me
add
,
that
in
this
act
,
the
air
through
which
the
bullet
is
to
pass
,
partaketh
not
of
the
motion
of
the
bird
:
whereas
in
the
case
of
the
Canon
,
both
it
,
the
mark
,
and
the
intermediate
air
,
do
equally
partake
of
the
common
diurnal
motion
.
So
that
the
true
cause
of
the
Marks-man
his
hitting
the
mark
,
as
it
should
seem
,
moreover
and
besides
the
following
the
birds
flight
with
the
piece
,
is
his
somewhat
anticipating
it
,
taking
his
aim
before
it
;
as
also
his
shooting
(
as
I
believe
)
not
with
one
bullet
,
but
with
many
small
balls
(
called
shot
)
the
which
scattering
in
the
air
possess
a
great
space
;
and
also
the
extreme
velocity
wherewith
these
shot
,
being
discharged
from
the
Gun
,
go
towards
the
bird
.
SALV
.
See
how
far
the
winged
wit
of
Sagredus
anticipateth
,
and
out-goeth
the
dulness
of
mine
;
which
perhaps
would
have
light
upon
these
disparities
,
The
answer
to
the
Argument
taken
from
the
shots
at
point
blanck
towards
the
East
&
West
.
but
not
without
long
studie
.
Now
turning
to
the
matter
in
hand
,
there
do
remain
to
be
considered
by
us
the
shots
at
point
blank
,
towards
the
East
and
towards
the
West
;
the
first
of
which
,
if
the
Earth
did
move
,
would
always
happen
to
be
too
high
above
the
mark
,
and
the
second
too
low
;
forasmuch
as
the
parts
of
the
Earth
Eastward
,
by
reason
of
the
diurnal
motion
,
do
continually
descend
beneath
the
tangent
paralel
to
the
Horizon
,
whereupon
the
Eastern
stars
to
us
appear
to
ascend
;
and
on
the
contrary
,
the
parts
Westward
do
more
and
more
ascend
,
whereupon
the
Western
stars
do
in
our
seeming
descend
:
and
therefore
the
ranges
which
are
leveled
according
to
the
said
tangent
at
the
Oriental
mark
,
(
which
whilst
the
ball
passeth
along
by
the
tangent
descendeth
)
should
prove
too
high
,
and
the
Occidental
too
low
by
means
of
the
elevation
of
the
mark
,
whilst
the
ball
passeth
along
the
tangent
.
The
answer
is
like
to
the
rest
:
for
as
the
Eastern
mark
goeth
continually
descending
,
by
reason
of
the
Earths
motion
,
under
a
tangent
that
continueth
immoveable
;
so
likewise
the
piece
for
the
same
reason
goeth
continually
inclining
,
and
with
its
mounture
pursuing
the
said
mark
:
by
which
means
the
shot
proveth
true
.
But
here
I
think
it
a
convenient
opportunity
to
give
notice
of
certain
concessions
,
The
followers
of
Copernicus
too
freely
admit
certain
propositions
for
true
,
which
are
very
doubtfull
.
which
are
granted
perhaps
over
liberally
by
the
followers
of
Copernicus
unto
their
Adversaries
:
I
mean
of
yielding
to
them
certain
experiments
for
sure
and
certain
,
which
yet
the
Adversaries
themselves
had
never
made
tryal
of
:
as
for
example
,
that
of
things
falling
from
the
round-top
of
a
ship
whilst
it
is
in
motion
,
and
many
others
;
amongst
which
I
verily
believe
,
that
this
of
experimenting
whether
the
shot
made
by
a
Canon
towards
the
East
proveth
too
high
,
and
the
Western
shot
too
low
,
is
one
:
and
because
I
believe
that
they
have
never
made
tryal
thereof
,
I
desire
that
they
would
tell
me
what
difference
they
think
ought
to
happen
between
the
said
shots
,
supposing
the
Earth
moveable
,
or
supposing
it
moveable
;
and
let
Simplicius
for
this
time
answer
for
them
.
SIMP.
I
will
not
undertake
to
answer
so
confidently
as
another
more
intelligent
perhaps
might
do
;
but
shall
speak
what
thus
upon
the
sudden
I
think
they
would
reply
;
which
is
in
effect
the
same
with
that
which
hath
been
said
already
,
namely
,
that
in
case
the
Earth
should
move
,
the
shots
made
Eastward
would
prove
too
high
,
&c.
the
ball
,
as
it
is
probable
,
being
to
move
along
the
tangent
.
SALV
.
But
if
I
should
say
,
that
so
it
falleth
out
upon
triall
,
how
would
you
censure
me
?
SIMP.
It
is
necessary
to
proceed
to
experiments
for
the
proving
of
it
.
SALV
.
But
do
you
think
,
that
there
is
to
be
found
a
Gunner
so
skilful
,
as
to
hit
the
mark
at
every
shoot
,
in
a
distance
of
v.g.
five
hundred
paces
?
SIMP.
No
Sir
;
nay
I
believe
that
there
is
no
one
,
how
good
a
marks-man
soever
that
would
promise
to
come
within
a
pace
of
the
mark
,
SALV
.
How
can
we
then
,
with
shots
so
uncertain
,
assure
our selves
of
that
which
is
in
dispute
?
SIMP.
We
may
be
assured
thereof
two
wayes
;
one
,
by
making
many
shots
;
the
other
,
because
in
respect
of
the
great
velocity
of
the
Earths
motion
,
the
deviation
from
the
mark
would
in
my
opinion
be
very
great
.
SALV
.
Very
great
,
that
is
more
than
one
pace
;
in
regard
that
the
varying
so
much
,
yea
and
more
,
is
granted
to
happen
ordinarily
even
in
the
Earths
mobility
.
SIMP.
I
verily
believe
the
variation
from
the
mark
would
be
more
than
so
.
SALV
.
Now
I
desire
that
for
our
satisfaction
we
do
make
thus
in
grosse
a
slight
calculation
,
A
Computation
how
much
the
ranges
of
great
shot
ought
to
vary
from
the
marke
,
the
Earths
motion
being
granted
.
if
you
consent
thereto
,
which
will
stand
us
in
stead
likewise
(
if
the
computation
succeed
as
I
expect
)
for
a
warning
how
we
do
in
other
occurrences
suffer
our selves
,
as
the
saying
is
,
to
be
taken
with
the
enemies
shouts
,
and
surrender
up
our
belief
to
what
ever
first
presents
it self
to
our
fancy
.
And
now
to
give
all
advantages
to
the
Peripateticks
and
Tychonicks
,
let
us
suppose
our selves
to
be
under
the
Equinoctial
,
there
to
shoot
a
piece
of
Ordinance
point
blank
Eastwards
at
a
mark
five
hundred
paces
off
.
First
,
let
us
see
thus
(
as
I
said
)
in
a
level
,
what
time
the
shot
after
it
is
gone
out
of
the
Piece
taketh
to
arrive
at
the
mark
;
which
we
know
to
be
very
little
,
and
is
certainly
no
more
than
that
wherein
a
travailer
walketh
two
steps
,
which
also
is
less
than
the
second
of
a
minute
of
an
hour
;
for
supposing
that
the
travailer
walketh
three
miles
in
an
hour
,
which
are
nine
thousand
paces
,
being
that
an
hour
containes
three
thousand
,
six
hundred
second
minutes
,
the
travailer
walketh
two
steps
and
an
half
in
a
second
,
a
second
therefore
is
more
than
the
time
of
the
balls
motion
.
And
for
that
the
diurnal
revolution
is
twenty
four
hours
,
the
Western
horizon
riseth
fifteen
degrees
in
an
hour
,
that
is
,
fifteen
first
minutes
of
a
degree
,
in
one
first
minute
of
an
hour
;
that
is
,
fifteen
seconds
of
a
degree
,
in
one
second
of
an
hour
;
and
because
one
second
is
the
time
of
the
shot
,
therefore
in
this
time
the
Western
horizon
riseth
fifteen
seconds
of
a
degree
,
and
so
much
likewise
the
mark
;
and
therefore
fifteen
seconds
of
that
circle
,
whose
semidiameter
is
five
hundred
paces
(
for
so
much
the
distance
of
the
mark
from
the
Piece
was
supposed
.
)
Now
let
us
look
in
the
table
of
Arches
and
Chords
(
see
here
is
Copernicus
his
book
)
what
part
is
the
chord
of
fifteen
seconds
of
the
semidiameter
,
that
is
,
five
hundred
paces
.
Here
you
see
the
chord
(
or
subtense
)
of
a
first
minute
to
be
less
than
thirty
of
those
parts
,
of
which
the
semidiameter
is
an
hundred
thousand
.
Therefore
the
chord
of
a
second
minute
shall
be
less
then
half
of
one
of
those
parts
,
that
is
less
than
one
of
those
parts
,
of
which
the
semidiameter
is
two
hundred
thousand
;
and
therefore
the
chord
of
fifteen
conds
shall
be
less
than
fifteen
of
those
same
two
hundred
thousand
parts
;
but
that
which
is
less
than
[
](A61244-e38370-b)a
a
That
is
,
in
plainer
termes
the
fraction
15/200000
,
is
more
than
the
fraction
4/50000
,
for
dividing
the
denominators
by
their
●ominators
,
and
the
first
produceth
13333
1/3
,
the
other
but
12500.
fifteen
parts
of
two
hundred
thousand
,
is
also
more
than
that
which
is
four
centesmes
of
five
hundred
;
therefore
the
ascent
of
the
mark
in
the
time
of
the
balls
motion
is
lesse
than
four
centesmes
,
that
is
,
than
one
twenty
fifth
part
of
a
pace
;
it
shall
be
therefore
[
](A61244-e38380-b)b
b
It
shall
be
neer
2
2/5
inches
,
accounting
the
pace
to
be
Geometrical
,
containing
5
foot
.
about
two
inches
:
And
so
much
consequently
shall
be
the
variation
of
each
Western
shot
,
the
Earth
being
supposed
to
have
a
diurnal
motion
.
Now
if
I
shall
tell
you
,
that
this
variation
(
I
mean
of
falling
two
inches
short
of
what
they
would
do
in
case
the
Earth
did
not
move
)
upon
triall
doth
happen
in
all
shots
,
how
will
you
convince
me
Simplicius
,
shewing
me
by
an
experiment
that
it
is
not
so
?
Do
you
not
see
that
it
is
impossible
to
confute
me
,
unless
you
first
find
out
a
way
to
shoot
at
a
mark
with
so
much
exactnesse
,
as
never
to
misse
an
hairs
bredth
?
For
whilst
the
ranges
of
great
shot
consist
of
different
numbers
of
paces
,
as
de
facto
they
do
,
I
will
affirm
that
in
each
of
those
variations
there
is
contained
that
of
two
inches
caused
by
the
motion
of
the
Earth
.
SAGR.
Pardon
me
,
It
is
demonstrated
with
great
subtilty
,
that
the
Earths
motion
supposed
,
Canon
shot
ought
not
to
vary
more
than
in
rest
.
Salviatus
,
you
are
too
liberal
.
For
I
would
tell
the
Peripateticks
,
that
though
every
shot
should
hit
the
very
centre
of
the
mark
,
that
should
not
in
the
least
disprove
the
motion
of
the
Earth
.
For
the
Gunners
are
so
constantly
imployed
in
levelling
the
sight
and
gun
to
the
mark
,
as
that
they
can
hit
the
same
,
notwithstanding
the
motion
of
the
Earth
.
And
I
say
,
that
if
the
Earth
should
stand
still
,
the
shots
would
not
prove
true
;
but
the
Occidental
would
be
too
low
,
and
the
Oriental
too
high
:
now
let
Simplicius
disprove
me
if
he
can
.
SALV
.
This
is
a
subtilty
worthy
of
Sagredus
:
But
whether
this
variation
be
to
be
observed
in
the
motion
,
or
in
the
rest
of
the
Earth
,
it
must
needs
be
very
small
,
it
must
needs
be
swallowed
up
in
those
very
great
ones
which
sundry
accidents
continually
produce
.
It
is
requisite
to
be
very
cautious
in
admitting
experim●nts
for
true
,
to
those
who
never
tried
them
.
And
all
this
hath
been
spoken
and
granted
on
good
grounds
to
Simplicius
,
and
only
with●n
intent
to
advertise
him
how
much
it
importeth
to
be
cautious
in
granting
many
experiments
for
true
to
those
who
never
had
tried
them
,
but
only
eagerly
alledged
them
just
as
they
ought
to
be
for
the
serving
their
purpose
:
This
is
spoken
,
I
say
,
by
way
of
surplussage
and
Corollary
to
Simplicius
,
for
the
real
truth
is
,
Experiments
and
arguments
against
the
Earths
motion
seem
so
far
concluding
,
as
they
lie
hid
under
equivokes
.
that
as
concerning
these
shots
,
the
same
ought
exactly
to
befall
aswell
in
the
motion
as
in
the
rest
of
the
Terrestrial
Globe
;
as
likewise
it
will
happen
in
all
the
other
experiments
that
either
have
been
or
can
be
produced
,
which
have
at
first
blush
so
much
semblance
of
truth
,
as
the
antiquated
opinion
of
the
Earths
motion
hath
of
equivocation
.
SAGR.
As
for
my
part
I
am
fully
satisfied
,
and
very
well
understand
that
who
so
shall
imprint
in
his
fancy
this
general
community
of
the
diurnal
conversion
amongst
all
things
Terrestrial
,
to
all
which
it
naturally
agreeth
,
aswell
as
in
the
old
conceit
of
its
rest
about
the
centre
,
shall
doubtlesse
discern
the
fallacy
and
equivoke
which
made
the
arguments
produced
seem
eoncluding
.
There
yet
remains
in
me
some
haesitancy
(
as
I
have
hinted
before
)
touching
the
flight
of
birds
;
the
which
having
as
it
were
an
animate
faculty
of
moving
at
their
pleasure
with
a
thousand
motions
,
and
to
stay
long
in
the
Air
separated
from
the
Earth
,
and
therein
with
most
irregular
windings
to
go
fluttering
to
and
again
,
I
cannot
conceive
how
amongst
so
great
a
confusion
of
motions
,
they
should
be
able
to
retain
the
first
commune
motion
;
and
in
what
manner
,
having
once
made
any
stay
behind
,
they
can
get
it
up
again
,
and
overtake
the
same
with
flying
,
and
keep
pace
with
the
Towers
and
trees
which
hurry
with
so
precipitant
a
course
towards
the
East
;
I
say
so
precipitant
,
for
in
the
great
circle
of
the
Globe
it
is
little
lesse
than
a
thousand
miles
an
hour
,
whereof
the
flight
of
the
swallow
I
believe
makes
not
fifty
.
SALV
.
If
the
birds
were
to
keep
pace
with
the
course
of
the
trees
by
help
of
their
wings
,
they
would
of
necessity
flie
very
fast
;
and
if
they
were
deprived
of
the
universal
conversion
,
they
would
lag
as
far
behind
;
and
their
flight
would
seem
as
furious
towards
the
West
,
and
to
him
that
could
discern
the
same
,
it
would
much
exceed
the
flight
of
an
arrow
;
but
I
think
we
could
not
be
able
to
perceive
it
,
no
more
than
we
see
a
Canon
bullet
,
whil'st
driven
by
the
fury
of
the
fire
,
it
flieth
through
the
Air
:
But
the
truth
is
that
the
proper
motion
of
birds
,
I
mean
of
their
flight
,
hath
nothing
to
do
with
the
universal
motion
,
to
which
it
is
neither
an
help
,
nor
an
hinderance
;
and
that
which
maintaineth
the
said
motion
unaltered
in
the
birds
,
is
the
Air
it self
,
thorough
which
they
flie
,
which
naturally
follovving
the
Vertigo
of
the
Earth
,
like
as
it
carrieth
the
clouds
along
with
it
,
so
it
transporteth
birds
and
every
thing
else
which
is
pendent
in
the
same
;
in
so
much
that
as
to
the
businesse
of
keeping
pace
vvith
the
Earth
,
the
birds
need
take
no
care
thereof
,
but
for
that
work
might
sleep
perpetually
.
SAGR.
That
the
Air
can
carry
the
clouds
along
with
it
,
as
being
matters
easie
for
their
lightnesse
to
be
moved
and
deprived
of
all
other
contrary
inclination
,
yea
more
,
as
being
matters
that
partake
also
of
the
conditions
and
properties
of
the
Earth
;
I
comprehend
without
any
difficulty
;
but
that
birds
,
which
as
having
life
,
may
move
with
a
motion
quite
contrary
to
the
diurnal
,
once
having
surceased
the
said
motion
,
the
Air
should
restore
them
to
it
,
seems
to
me
a
little
strange
,
and
the
rather
for
that
they
are
solid
and
weighty
bodies
;
and
withal
,
we
see
;
as
hath
been
said
,
stones
and
other
grave
bodies
to
lie
unmoved
against
the
impetus
of
the
air
;
and
when
they
suffer
themselves
to
be
overcome
thereby
,
they
never
acquire
so
much
velocity
as
the
wind
which
carrieth
them
.
SALV
.
We
ascribe
not
so
little
force
,
Sagredus
,
to
the
moved
Air
,
which
is
able
to
move
and
bear
before
it
ships
full
fraught
,
to
tear
up
trees
by
the
roots
,
and
overthrow
Towers
when
it
moveth
swiftly
;
and
yet
we
cannot
say
that
the
motion
of
the
Air
in
these
violent
operations
is
neer
so
violent
,
as
that
of
the
diurnal
revolution
.
SIMP.
You
see
then
that
the
moved
Air
may
also
cotinue
the
motion
of
projects
,
according
to
the
Doctrine
of
Aristotle
;
and
it
seemed
to
me
very
strange
that
he
should
have
erred
in
this
particular
.
SALV
.
It
may
without
doubt
,
in
case
it
could
continue
it self
,
but
lik
as
when
the
wind
ceasing
neither
ships
go
on
,
nor
trees
are
blown
down
,
so
the
motion
in
the
Air
not
continuing
after
the
stone
is
gone
out
of
the
hand
,
and
the
Air
ceasing
to
move
,
it
followeth
that
it
must
be
something
else
besides
the
Air
that
maketh
the
projects
to
move
.
SIMP.
But
how
upon
the
winds
being
laid
,
doth
the
ship
cease
to
move
?
Nay
you
may
see
that
when
the
wind
is
down
,
and
the
sails
furl'd
,
the
vessel
continueth
to
run
whole
miles
.
SALV
.
But
this
maketh
against
your self
Simplicius
,
for
that
the
wind
being
laid
that
filling
the
sails
drove
on
the
ship
,
yet
neverthelesse
doth
it
without
help
of
the
medium
continue
its
course
.
SIMP.
It
might
be
said
that
the
water
was
the
medium
which
carried
forward
the
ship
,
and
maintain'd
it
in
motion
.
SALV
.
It
might
indeed
be
so
affirmed
,
if
you
would
speak
quite
contrary
to
truth
;
for
the
truth
is
,
that
the
water
,
by
reason
of
its
great
resistance
to
the
division
made
by
the
hull
of
the
ship
,
doth
with
great
noise
resist
the
same
;
nor
doth
it
permit
it
of
a
great
while
to
acquire
that
velocity
which
the
wind
would
confer
upon
it
,
were
the
obstacle
of
the
water
removed
.
Perhaps
Simplicius
you
have
never
considered
with
what
fury
the
water
besets
a
bark
,
whil'st
it
forceth
its
way
through
a
standing
water
by
help
of
Oars
or
Sails
:
for
if
you
had
ever
minded
that
effect
,
you
would
not
now
have
produced
such
an
absurdity
.
And
I
am
thinking
that
you
have
hitherto
been
one
of
those
who
to
find
out
how
such
things
succeed
,
and
to
come
to
the
knowledg
of
natural
effects
,
do
not
betake
themselves
to
a
Ship
,
a
Crosse-bow
,
or
a
piece
of
Ordinance
,
but
retire
into
their
studies
,
and
turn
over
Indexes
and
Tables
to
see
whether
Aristotle
hath
spoken
any
thing
thereof
,
and
being
assured
of
the
true
sense
of
the
Text
,
neither
desire
nor
care
for
knowing
any
more
.
SAGR.
This
is
a
great
felicity
,
The
great
felicity
for
which
they
are
much
to
be
envied
who
perswade
themselves
that
they
know
every
thing
.
and
they
are
to
be
much
envied
for
it
.
For
if
knowledg
be
desired
by
all
,
and
if
to
be
wise
,
be
to
think
ones
self
so
,
they
enjoy
a
very
great
happinesse
,
for
that
they
may
perswade
themselves
that
they
know
and
understand
all
things
,
in
soorn
of
those
who
knowing
,
that
they
understand
not
what
these
think
they
understand
,
and
consequently
seeking
that
they
know
not
the
very
least
particle
of
what
is
knowable
,
kill
themselves
with
waking
and
studying
,
and
consume
their
days
in
experiments
and
observations
.
But
pray
you
let
us
return
to
our
birds
;
touching
which
you
have
said
,
that
the
Air
being
moved
with
great
velocity
,
might
restore
unto
them
that
part
of
the
diurnal
motion
which
amongst
the
windings
of
their
flight
they
might
have
lost
;
to
which
I
reply
,
that
the
agitated
Air
seemeth
unable
to
confer
on
a
solid
and
grave
body
,
so
great
a
velocity
as
its
own
:
And
because
that
of
the
Air
is
as
great
as
that
of
the
Earth
,
I
cannot
think
that
the
Air
is
able
to
make
good
the
losse
of
the
birds
retardation
in
flight
.
SALV
.
Your
discourse
hath
in
it
much
of
probability
,
and
to
stick
at
trivial
doubts
is
not
for
an
acute
wit
;
yet
neverthelesse
the
probability
being
removed
,
I
believed
that
it
hath
not
a
jot
more
force
than
the
others
already
considered
and
resolved
.
SAGR.
It
is
most
certain
that
if
it
be
not
necessarily
concludent
,
its
efficacy
must
needs
be
just
nothing
at
all
,
for
it
is
onely
when
the
conclusion
is
necessary
that
the
opponent
hath
nothing
to
alledg
on
the
contrary
.
SALV
.
Your
making
a
greater
scruple
of
this
than
of
the
other
instances
dependeth
,
if
I
mistake
not
,
upon
the
birds
being
animated
,
and
thereby
enabled
to
use
their
strength
at
pleasure
against
the
primary
motion
in-bred
in
terrene
bodies
:
like
as
for
example
,
we
see
them
whil'st
they
are
alive
to
fly
upwards
,
a
thing
altogether
impossible
for
them
to
do
as
they
are
grave
bodies
;
whereas
being
dead
they
can
onely
fall
downwards
;
and
therefore
you
hold
that
the
reasons
that
are
of
force
in
all
the
kinds
of
projects
above
named
,
cannot
take
place
in
birds
:
Now
this
is
very
true
;
and
because
it
is
so
,
Sagredus
,
that
doth
not
appear
to
be
done
in
those
projects
,
The
answer
to
the
argument
taken
from
the
flight
of
birds
contrary
to
the
motion
of
the
Earth
.
which
we
see
the
birds
to
do
.
For
if
from
the
top
of
a
Tower
you
let
fall
a
dead
bird
and
a
live
one
,
the
dead
bird
shall
do
the
same
that
a
stone
doth
,
that
is
,
it
shall
first
follow
the
general
motion
diurnal
,
and
then
the
motion
of
descent
,
as
grave
;
but
if
the
bird
let
fall
,
be
a
live
,
what
shall
hinder
it
,
(
there
ever
remaining
in
it
the
diurnal
motion
)
from
soaring
by
help
of
its
wings
to
what
place
of
the
Horizon
it
shall
please
?
and
this
new
motion
,
as
being
peculiar
to
the
bird
,
and
not
participated
by
us
,
must
of
necessity
be
visible
to
us
;
and
if
it
be
moved
by
help
of
its
wings
towards
the
West
,
what
shall
hinder
it
from
returning
with
a
like
help
of
its
wings
unto
the
Tower
.
And
,
because
,
in
the
last
place
,
the
bird
swending
its
flight
towards
the
West
was
no
other
than
a
withdrawing
from
the
diurnal
motion
,
(
which
hath
,
suppose
ten
degrees
of
velocity
)
one
degree
onely
,
there
did
thereupon
remain
to
the
bird
whil'st
it
was
in
its
flight
nine
degrees
of
velocity
,
and
so
soon
as
it
did
alight
upon
the
the
Earth
,
the
ten
common
degrees
returned
to
it
,
to
which
,
by
flying
towards
the
East
it
might
adde
one
,
and
with
those
eleven
overtake
the
Tower
.
And
in
short
,
if
we
well
consider
,
and
more
narrowly
examine
the
effects
of
the
flight
of
birds
,
they
differ
from
the
projects
shot
or
thrown
to
any
part
of
the
World
in
nothing
,
save
onely
that
the
projects
are
moved
by
an
external
projicient
,
An
experiment
with
which
alone
is
shewn
the
nullity
of
all
the
objections
produced
against
the
motion
of
the
Earth
.
and
the
birds
by
an
internal
principle
.
And
here
for
a
final
proof
of
the
nullity
of
all
the
experiments
before
illedged
,
I
conceive
it
now
a
time
and
place
convenient
to
demonstrate
a
way
how
to
make
an
exact
trial
of
them
all
.
Shut
your self
up
with
some
friend
in
the
grand
Cabbin
between
the
decks
of
some
large
Ship
,
and
there
procure
gnats
,
flies
,
and
such
other
small
winged
creatures
:
get
also
a
great
tub
(
or
other
vessel
)
full
of
water
,
and
within
it
put
certain
fishes
;
let
also
a
certain
bottle
be
hung
up
,
which
drop
by
drop
letteth
forth
its
water
into
another
bottle
placed
underneath
,
having
a
narrow
neck
:
and
,
the
Ship
lying
still
,
observe
diligently
how
those
small
winged
animals
fly
with
like
velocity
towards
all
parts
of
the
Cabin
;
how
the
fishes
swim
indifferently
towards
all
sides
;
and
how
the
distilling
drops
all
fall
into
the
bottle
placed
underneath
.
And
casting
any
thing
towards
your
friend
,
you
need
not
throw
it
with
more
force
one
way
then
another
,
provided
the
distances
be
equal
:
and
leaping
,
as
the
saying
is
,
with
your
feet
closed
,
you
will
reach
as
far
one
way
as
another
.
Having
observed
all
these
particulars
,
though
no
man
doubteth
that
so
long
as
the
vessel
stands
still
,
they
ought
to
succeed
in
this
manner
;
make
the
Ship
to
move
with
what
velocity
you
please
;
for
(
so
long
as
the
motion
is
uniforme
,
and
not
fluctuating
this
way
and
that
way
)
you
shall
not
discern
any
the
least
alteration
in
all
the
forenamed
effects
;
nor
can
you
gather
by
any
of
them
whether
the
Ship
doth
move
or
stand
still
.
In
leaping
you
shall
reach
as
far
upon
the
floor
,
as
before
;
nor
for
that
the
Ship
moveth
shall
you
make
a
greater
leap
towards
the
poop
than
towards
the
prow
;
howbeit
in
the
time
that
you
staid
in
the
Air
,
the
floor
under
your
feet
shall
have
run
the
contrary
way
to
that
of
your
jump
;
and
throwing
any
thing
to
your
companion
you
shall
not
need
to
cast
it
with
more
strength
that
it
may
reach
him
,
if
he
shall
be
towards
the
prow
,
and
you
towards
the
poop
,
then
if
you
stood
in
a
contrary
situation
;
the
drops
shall
all
distill
as
before
into
the
inferiour
bottle
,
and
not
so
much
as
one
shall
fall
towards
the
poop
,
albeit
whil'st
the
drop
is
in
the
Air
,
the
Ship
shall
have
run
many
feet
;
the
Fishes
in
their
water
shall
not
swim
with
more
trouble
towards
the
fore-part
,
than
towards
the
hinder
part
of
the
tub
;
but
shall
with
equal
velocity
make
to
the
bait
placed
on
any
side
of
the
tub
;
and
lastly
,
the
flies
and
gnats
shall
continue
their
flight
indifferently
towards
all
parts
;
nor
shall
they
ever
happen
to
be
driven
together
towards
the
side
of
the
Cabbin
next
the
prow
,
as
if
they
were
wearied
with
following
the
swift
course
of
the
Ship
,
from
which
through
their
suspension
in
the
Air
,
they
had
been
long
separated
;
and
if
burning
a
few
graines
of
incense
you
make
a
little
smoke
,
you
shall
see
it
ascend
on
high
,
and
there
in
manner
of
a
cloud
suspend
it self
,
and
move
indifferently
,
not
inclining
more
to
one
side
than
another
:
and
of
this
correspondence
of
effects
the
cause
is
for
that
the
Ships
motion
is
common
to
all
the
things
contained
in
it
,
and
to
the
Air
also
;
I
mean
if
those
things
be
shut
up
in
the
Cabbin
:
but
in
case
those
things
were
above
deck
in
the
open
Air
,
and
not
obliged
to
follow
the
course
of
the
Ship
,
differences
more
or
lesse
notable
would
be
observed
in
some
of
the
fore-named
effects
,
and
there
is
no
doubt
but
that
the
smoke
would
stay
behind
as
much
as
the
Air
it self
;
the
flies
also
,
and
the
gnats
being
hindered
by
the
Air
would
not
be
able
to
follow
the
motion
of
the
Ship
,
if
they
were
separated
at
any
distance
from
it
.
But
keeping
neer
thereto
,
because
the
Ship
it self
as
being
an
unfractuous
Fabrick
,
carrieth
along
with
it
part
of
its
neerest
Air
,
they
would
follow
the
said
Ship
without
any
pains
or
difficulty
.
And
for
the
like
reason
we
see
sometimes
in
riding
post
,
that
the
troublesome
flies
and
[
](A61244-e39110-b)*
*
Tafaris
,
horse-flyes
.
hornets
do
follow
the
horses
flying
sometimes
to
one
,
sometimes
to
another
part
of
the
body
,
but
in
the
falling
drops
the
difference
would
be
very
small
;
and
in
the
salts
,
and
projections
of
grave
bodies
altogether
imperceptible
.
SAGR.
Though
it
came
not
into
my
thoughts
to
make
triall
of
these
observations
,
when
I
was
at
Sea
,
yet
am
I
confident
that
they
will
succeed
in
the
same
manner
,
as
you
have
related
;
in
confirmation
of
which
I
remember
that
being
in
my
Cabbin
I
have
asked
an
hundred
times
whether
the
Ship
moved
or
stood
still
;
and
sometimes
I
have
imagined
that
it
moved
one
way
,
when
it
steered
quite
another
way
.
I
am
therefore
as
hitherto
satisfied
and
convinced
of
the
nullity
of
all
those
experiments
that
have
been
produced
in
proof
of
the
negative
part
.
There
now
remains
the
objection
founded
upon
that
which
experience
shews
us
,
namely
,
that
a
swift
Vertigo
or
whirling
about
hath
a
faculty
to
extrude
and
disperse
the
matters
adherent
to
the
machine
that
turns
round
;
whereupon
many
were
of
opinion
,
and
Ptolomy
amongst
the
rest
,
that
if
the
Earth
should
turn
round
with
so
great
velocity
,
the
stones
and
creatures
upon
it
should
be
tost
into
the
Skie
,
and
that
there
could
not
be
a
morter
strong
enough
to
fasten
buildings
so
to
their
foundations
,
but
that
they
would
likewise
suffer
a
like
extrusion
.
SALV
.
Before
I
come
to
answer
this
objection
,
I
cannot
but
take
notice
of
that
which
I
have
an
hundred
times
observed
,
and
not
without
laughter
,
to
come
into
the
minds
of
most
men
so
soon
as
ever
they
hear
mention
made
of
this
motion
of
the
Earth
,
which
is
believed
by
them
so
fixt
and
immoveable
,
that
they
not
only
never
doubted
of
that
rest
,
but
have
ever
strongly
believed
that
all
other
men
aswell
as
they
,
have
held
it
to
be
created
immoveable
,
and
so
to
have
continued
through
all
succeeding
ages
:
The
stupidity
of
some
that
think
the
Earth
to
have
begun
to
move
,
when
Pythagoras
began
to
affirme
that
it
did
so
.
and
being
setled
in
this
perswasion
,
they
stand
amazed
to
hear
that
any
one
should
grant
it
motion
,
as
if
,
after
that
he
had
held
it
to
be
immoveable
,
he
had
fondly
thought
it
to
commence
its
motion
then
(
and
not
till
then
)
when
Pythagoras
(
or
whoever
else
was
the
first
hinter
of
its
mobility
)
said
that
it
did
move
.
Now
that
such
a
foolish
conceit
(
I
mean
of
thinking
that
those
who
admit
the
motion
of
the
Earth
,
have
first
thought
it
to
stand
still
from
its
creation
,
untill
the
time
of
Pythagoras
,
and
have
onely
made
it
moveable
after
that
Pythagoras
esteemed
it
so
)
findeth
a
place
in
the
mindes
of
the
vulgar
,
and
men
of
shallow
capacities
,
I
do
not
much
wonder
;
but
that
such
persons
as
Aristotle
and
Ptolomy
should
also
run
into
this
childish
mistake
,
is
to
my
thinking
a
more
admirable
and
unpardonable
folly
.
SAGR.
You
believe
then
,
Salviatus
,
that
Ptolomy
thought
,
that
in
his
Disputation
he
was
to
maintain
the
stability
of
the
Earth
against
such
persons
,
as
granting
it
to
have
been
immoveable
,
untill
the
time
of
Pythagoras
,
did
affirm
it
to
have
been
but
then
made
moveable
,
when
the
said
Pythagoras
ascribed
unto
it
motion
.
SALV
.
We
can
think
no
other
,
if
we
do
but
consider
the
way
he
taketh
to
confute
their
assertion
;
Aristotle
and
Ptolomy
seem
to
confute
the
mobility
of
the
Earth
against
those
who
thought
that
it
having
a
long
time
stood
still
,
did
begin
to
move
in
the
time
of
Pythagoras
the
confutation
of
which
consists
in
the
demolition
of
buildings
,
and
the
tossing
of
stones
,
living
creatures
and
men
themselves
up
into
the
Air.
And
because
such
overthrows
and
extrusions
cannot
be
made
upon
buildings
and
men
,
which
were
not
before
on
the
Earth
,
nor
can
men
be
placed
,
nor
buildings
erected
upon
the
Earth
,
unlesse
when
it
standeth
still
;
hence
therefore
it
is
cleer
,
that
Ptolomy
argueth
against
those
,
who
having
granted
the
stability
of
the
Earth
for
some
time
,
that
is
,
so
long
as
living
creatures
,
stones
,
and
Masons
were
able
to
abide
there
,
and
to
build
Palaces
and
Cities
,
make
it
afterwards
precipitately
moveable
to
the
overthrow
and
destructiof
Edifices
,
and
living
creatures
,
&c.
For
if
he
had
undertook
to
dispute
against
such
as
had
ascribed
that
revolution
to
the
Earth
from
its
first
creation
,
he
would
have
confuted
them
by
saying
,
that
if
the
Earth
had
alwayes
moved
,
there
could
never
have
been
placed
upon
it
either
men
or
stones
;
much
less
could
buildings
have
been
erected
,
or
Cities
founded
,
&c.
SIMP.
I
do
not
well
conceive
these
Aristotelick
and
Ptolomaick
inconveniences
.
SALV
.
Ptolomey
either
argueth
against
those
who
have
esteemed
the
Earth
always
moveable
;
or
against
such
as
have
held
that
it
stood
for
some
time
still
,
and
hath
since
been
set
on
moving
.
If
against
the
first
,
he
ought
to
say
,
that
the
Earth
did
not
always
move
,
for
that
then
there
would
never
have
been
men
,
animals
,
or
edifices
on
the
Earth
,
its
vertigo
not
permitting
them
to
stay
thereon
.
But
in
that
he
arguing
,
saith
that
the
Earth
doth
not
move
,
because
that
beasts
,
men
,
and
houses
before
plac'd
on
the
Earth
would
precipitate
,
he
supposeth
the
Earth
to
have
been
once
in
such
a
state
,
as
that
it
did
admit
men
and
beasts
to
stay
,
and
build
thereon
;
the
which
draweth
on
the
consequence
,
that
it
did
for
some
time
stand
still
,
to
wit
,
was
apt
for
the
abode
of
animals
and
erection
of
buildings
.
Do
you
now
conceive
what
I
would
say
?
SIMP.
I
do
,
and
I
do
not
:
but
this
little
importeth
to
the
merit
of
the
cause
;
nor
can
a
small
mistake
of
Ptolomey
,
committed
through
inadvertencie
be
sufficient
to
move
the
Earth
,
when
it
is
immoveable
.
But
omitting
cavils
,
let
us
come
to
the
substance
of
the
argument
,
which
to
me
seems
unanswerable
.
SALV
.
And
I
,
Simplicius
,
will
drive
it
home
,
and
re-inforce
it
,
by
shewing
yet
more
sensibly
,
that
it
is
true
that
grave
bodies
turn'd
with
velocity
about
a
settled
centre
,
do
acquire
an
impetus
of
moving
,
and
receding
to
a
distance
from
that
centre
,
even
then
when
they
are
in
a
state
of
having
a
propension
of
moving
naturally
to
the
same
.
Tie
a
bottle
that
hath
water
in
it
,
to
the
end
of
a
cord
,
and
holding
the
other
end
fast
in
your
hand
,
and
making
the
cord
and
your
arm
the
semi-diameter
,
and
the
knitting
of
the
shoulder
the
centre
,
swing
the
bottle
very
fast
about
,
so
as
that
it
may
describe
the
circumference
of
a
circle
,
which
,
whether
it
be
parallel
to
the
Horizon
,
or
perpendicular
to
it
,
or
any
way
inclined
,
it
shall
in
all
cases
follow
,
that
the
water
will
not
fall
out
of
the
bottle
:
nay
,
he
that
shall
swing
it
,
shall
find
the
cord
always
draw
,
and
strive
to
go
farther
from
the
shoulder
.
And
if
you
bore
a
hole
in
the
bottom
of
the
bottle
,
you
shall
see
the
water
spout
forth
no
less
upwards
into
the
skie
,
than
laterally
,
and
downwards
to
the
Earth
;
and
if
instead
of
water
,
you
shall
put
little
pebble
stones
into
the
bottle
,
and
swing
it
in
the
same
manner
,
you
shall
find
that
they
will
strive
in
the
like
manner
against
the
cord
.
And
lastly
,
we
see
boys
throw
stones
a
great
way
,
by
swinging
round
a
piece
of
a
stick
,
at
the
end
of
which
the
stone
is
let
into
a
slit
(
which
stick
is
called
by
them
a
sling
;
)
all
which
are
arguments
of
the
truth
of
the
conclusion
,
to
wit
,
that
the
vertigo
or
swing
conferreth
upon
the
moveable
,
a
motion
towards
the
circumference
,
in
case
the
motion
be
swift
:
and
therefore
if
the
Earth
revolve
about
its
own
centre
,
the
motion
of
the
superficies
,
and
especially
towards
the
great
circle
,
as
being
incomparably
more
swift
than
those
before
named
,
ought
to
extrude
all
things
up
into
the
air
.
SIMP.
The
Argument
seemeth
to
me
very
well
proved
and
inforced
;
and
I
believe
it
would
be
an
hard
matter
to
answer
and
overthrow
it
.
SALV
.
It
s
solution
dependeth
upon
certain
notions
no
less
known
and
believed
by
you
,
than
by
my self
:
but
because
they
come
not
into
your
mind
,
therefore
it
is
that
you
perceive
not
the
answer
;
wherefore
,
without
telling
you
it
(
for
that
you
know
the
same
already
)
I
shall
with
onely
assisting
your
memory
,
make
you
to
refute
this
argument
.
SIMP.
I
have
often
thought
of
your
way
of
arguing
,
which
hath
made
me
almost
think
that
you
lean
to
that
opinion
of
Plato
,
Our
knowledg
is
a
kind
of
reminiscence
according
to
Plato
.
Quòd
nostrum
scire
sit
quoddam
reminisci
;
therefore
I
intreat
you
to
free
me
from
this
doubt
,
by
letting
me
know
your
judgment
.
SALV
.
What
I
think
of
the
opinion
of
Plato
,
you
may
gather
from
my
words
and
actions
.
I
have
already
in
the
precedent
conferences
expresly
declared
my self
more
than
once
;
I
will
pursue
the
same
style
in
the
present
case
,
which
may
hereafter
serve
you
for
an
example
,
thereby
the
more
easily
to
gather
what
my
opinion
is
touching
the
attainment
of
knowledg
,
when
a
time
shall
offer
upon
some
other
day
:
but
I
would
not
have
Sagred●s
offended
at
this
digression
.
SAGR.
I
am
rather
very
much
pleased
with
it
,
for
that
I
remember
that
when
I
studied
Logick
,
I
could
never
comprehend
that
so
much
cry'd
up
and
most
potent
demonstration
of
Aristotle
.
SALV
.
Let
us
go
on
therefore
;
and
let
Simplicius
,
tell
me
what
that
motion
is
which
the
stone
maketh
that
is
held
fast
in
the
slit
of
the
sling
,
when
the
boy
swings
it
about
to
throw
it
a
great
way
?
SIMP.
The
motion
of
the
stone
,
so
long
as
it
is
in
the
slit
,
is
circular
,
that
is
,
moveth
by
the
arch
of
a
circle
,
whose
stedfast
centre
is
the
knitting
of
the
shoulder
,
and
its
semi-diameter
the
arm
and
stick
.
SALV
.
And
when
the
stone
leaveth
the
sling
,
what
is
its
motion
?
Doth
it
continue
to
follow
its
former
circle
,
or
doth
it
go
by
another
line
?
SIMP.
It
will
continue
no
longer
to
swing
round
,
for
then
it
would
not
go
farther
from
the
arm
of
the
projicient
,
whereas
we
see
it
go
a
great
way
off
.
SALV
.
With
what
motion
doth
it
move
then
?
SIMP.
Give
me
a
little
time
to
think
thereof
;
For
I
have
never
considered
it
before
.
SALV
.
Hark
hither
,
Sagredus
;
this
is
the
Quoddam
reminisci
in
a
subject
well
understood
.
You
have
paused
a
great
while
,
Simplicius
.
SIMP.
As
far
as
I
can
see
,
the
motion
received
in
going
out
of
the
sling
,
can
be
no
other
than
by
a
right
line
;
nay
,
it
must
necessarily
be
so
,
if
we
speak
of
the
pure
adventitious
impetus
.
I
was
a
little
puzled
to
see
it
make
an
arch
,
but
because
that
arch
bended
all
the
way
upwards
,
and
no
other
way
,
I
conceive
that
that
incurvation
cometh
from
the
gravity
of
the
stone
,
Th●
motion
impressed
by
the
projicient
is
onely
by
a
right
line
.
vvhich
naturally
dravveth
it
dovvnvvards
.
The
impressed
impetus
,
I
say
,
vvithout
respecting
the
natural
,
is
by
a
right
line
.
SALV
.
But
by
what
right
line
?
Because
infinite
,
and
towards
every
side
may
be
produced
from
the
slit
of
the
sling
,
and
from
the
point
of
the
stones
separation
from
the
sling
.
SIMP.
It
moveth
by
that
line
which
goeth
directly
from
the
motion
which
the
stone
made
in
the
sling
.
SALV
.
The
motion
of
the
stone
whilst
it
was
in
the
slit
,
you
have
affirmed
already
to
be
circular
;
now
circularity
opposeth
directness
,
there
not
being
in
the
circular
line
any
part
that
is
direct
or
streight
.
SIMP.
I
mean
not
that
the
projected
motion
is
direct
in
respect
of
the
whole
circle
,
but
in
reference
to
that
ultimate
point
,
where
the
circular
motion
determineth
.
I
know
what
I
would
say
,
but
do
not
well
know
how
to
express
my self
.
SALV
.
And
I
also
perceive
that
you
understand
the
business
,
but
that
you
have
not
the
proper
terms
,
wherewith
to
express
the
same
.
Now
these
I
can
easily
teach
you
;
teach
you
,
that
is
,
as
to
the
words
,
but
not
as
to
the
truths
,
which
are
things
.
And
that
you
may
plainly
see
that
you
know
the
thing
I
ask
you
,
and
onely
want
language
to
express
it
,
tell
me
,
when
you
shoot
a
bullet
out
of
a
gun
,
towards
what
part
is
it
,
that
it
s
acquired
impetus
carrieth
it
?
SIMP.
It
s
acquired
impetus
carrieth
it
in
a
right
line
,
which
continueth
the
rectitude
of
the
barrel
,
that
is
,
which
inclineth
neither
to
the
right
hand
nor
to
the
left
,
nor
upwards
nor
downwards
.
SALV
.
Which
in
short
is
asmuch
as
to
say
,
it
maketh
no
angle
with
the
line
of
streight
motion
made
by
the
sling
.
SIMP.
So
I
would
have
said
.
SALV
.
If
then
the
line
of
the
projects
motion
be
to
continue
without
making
an
angle
upon
the
circular
line
described
by
it
,
whilst
it
was
with
the
projicient
;
and
if
from
this
circular
motion
it
ought
to
pass
to
the
right
motion
,
what
ought
this
right
line
to
be
?
SIMP.
It
must
needs
be
that
which
toucheth
the
circle
in
the
point
of
separation
,
for
that
all
others
,
in
my
opinion
,
being
prolonged
would
intersect
the
circumference
,
and
by
that
means
make
some
angle
therewith
.
SALV
.
You
have
argued
very
well
,
and
shewn
your self
half
a
Geometrician
.
Keep
in
mind
therefore
,
that
your
true
opinion
is
exprest
in
these
words
,
namely
,
That
the
project
acquireth
an
impetus
of
moving
by
the
Tangent
,
the
arch
described
by
the
motion
of
the
projicient
,
in
the
point
of
the
said
projects
separation
from
the
projicient
.
SIMP.
I
understand
you
very
well
,
and
this
is
that
which
I
would
say
.
SALV
.
Of
a
right
line
which
toucheth
a
circle
,
which
of
its
points
is
the
nearest
to
the
centre
of
that
circle
?
SIMP.
That
of
the
contact
without
doubt
:
for
that
is
in
the
circumference
of
a
circle
,
and
the
rest
without
:
and
the
points
of
the
circumference
are
all
equidistant
from
the
centre
.
SALV
.
Therefore
a
moveable
departing
from
the
contact
,
and
moving
by
the
streight
Tangent
,
goeth
continually
farther
and
farther
from
the
contact
,
and
also
from
the
centre
of
the
circle
.
SIMP.
It
doth
so
doubtless
.
SALV
.
Now
if
you
have
kept
in
mind
the
propositions
,
which
you
have
told
me
,
lay
them
together
,
and
tell
me
what
you
gather
from
them
.
SIMP.
I
think
I
am
not
so
forgetful
,
but
that
I
do
remember
them
.
The
project
moveth
by
the
Tangent
of
the
circle
of
the
motion
precedent
in
the
point
of
separation
.
From
the
things
premised
I
gather
that
the
project
swiftly
swinged
round
by
the
projicient
,
in
its
separating
from
it
,
doth
retain
an
impetus
of
continuing
its
motion
by
the
right
line
,
which
toucheth
the
circle
described
by
the
motion
of
the
projicient
in
the
point
of
separation
,
by
which
motion
the
project
goeth
continually
receding
from
the
centre
of
the
circle
described
by
the
motion
of
the
projicient
.
SALV
.
You
know
then
by
this
time
the
reason
why
grave
bodies
sticking
to
the
rim
of
a
wheele
,
swiftly
moved
,
are
extruded
and
thrown
beyond
the
circumference
to
yet
a
farther
distance
from
the
centre
.
SIMP.
I
think
I
understand
this
very
well
;
but
this
new
knowledg
rather
increaseth
than
lesseneth
my
incredulity
that
the
Earth
can
turn
round
with
so
great
velocity
,
without
extruding
up
into
the
sky
,
stones
,
animals
,
&c.
SALV
.
In
the
same
manner
that
you
have
understood
all
this
,
you
shall
,
nay
you
do
understand
the
rest
:
and
with
recollecting
your self
,
you
may
remember
the
same
without
the
help
of
others
:
but
that
we
may
lose
no
time
,
I
will
help
your
memory
therein
.
You
do
already
know
of
your self
,
that
the
circular
motion
of
the
projicient
impresseth
on
the
project
an
impetus
of
moving
(
when
they
come
to
separate
)
by
the
right
Tangent
,
the
circle
of
the
motion
in
the
point
of
separation
,
and
continuing
along
by
the
same
the
motion
ever
goeth
receding
farther
and
farther
from
the
projicient
:
and
you
have
said
,
that
the
project
would
continue
to
move
along
by
that
right
line
,
if
there
were
not
by
its
proper
weight
an
inclination
of
descent
added
unto
it
;
from
which
the
incurvation
of
the
line
of
motion
is
derived
.
It
seems
moreover
that
you
knew
of
your self
,
that
this
incurvation
always
bended
towards
the
centre
of
the
Earth
,
for
thither
do
all
grave
bodies
tend
.
Now
I
proceed
a
little
farther
,
and
ask
you
,
whether
the
moveable
after
its
separation
,
in
continuing
the
right
motion
goeth
always
equally
receding
from
the
centre
,
or
if
you
will
,
from
the
circumference
of
that
circle
,
of
which
the
precedent
motion
was
a
part
;
which
is
as
much
as
to
say
,
Whether
a
moveable
,
that
forsaking
the
point
of
a
Tangent
,
and
moving
along
by
the
said
Tangent
,
doth
equally
recede
from
the
point
of
contact
,
and
from
the
circumference
of
the
circle
?
SIMP.
No
,
Sir
:
for
the
Tangent
near
to
the
point
of
contact
,
recedeth
very
little
from
the
circumference
,
wherewith
it
keepeth
a
very
narrow
angle
,
but
in
its
going
farther
and
farther
off
,
the
distance
always
encreaseth
with
a
greater
proportion
;
so
that
in
a
circle
that
should
have
v.
g.
ten
yards
of
diameter
,
a
point
of
the
Tangent
that
was
distant
from
the
contact
but
two
palms
,
would
be
three
or
four
times
as
far
distant
from
the
circumference
of
the
circle
,
as
a
point
that
was
distant
from
the
contaction
one
palm
,
and
the
point
that
was
distant
half
a
palm
,
I
likewise
believe
would
fearse
recede
the
fourth
part
of
the
distance
of
the
second
:
so
that
within
an
inch
or
two
of
the
contact
,
the
separation
of
the
Tangent
from
the
circumference
is
scarse
discernable
.
SALV
.
So
that
the
recession
of
the
project
from
the
circumference
of
the
precedent
circular
motion
is
very
small
in
the
begining
?
SIMP.
Almost
insensible
.
SALV
.
Now
tell
me
a
little
;
the
project
,
which
from
the
motion
of
the
projicient
receiveth
an
impetus
of
moving
along
the
Tangent
in
a
right
line
,
and
that
would
keep
unto
the
same
,
did
not
its
own
weight
depress
it
downwards
,
how
long
is
it
after
the
separation
,
ere
it
begin
to
decline
downwards
.
SIMP.
I
believe
that
it
beginneth
presently
;
for
it
not
having
any
thing
to
uphold
it
,
its
proper
gravity
cannot
but
operate
.
A
grave
project
,
as
s●on
as
it
is
separated
from
the
projicient
begineth
to
decline
.
SALV
.
So
that
,
if
that
same
stone
,
which
being
extruded
from
that
wheel
turn'd
about
very
fast
,
had
as
great
a
natural
propension
of
moving
towards
the
centre
of
the
said
wheel
,
as
it
hath
to
move
towards
the
centre
of
the
Earth
,
it
would
be
an
easie
matter
for
it
to
return
unto
the
wheel
,
or
rather
not
to
depart
from
it
;
in
regard
that
upon
the
begining
of
the
separation
,
the
recession
being
so
small
,
by
reason
of
the
infinite
acuteness
of
the
angle
of
contact
,
every
very
little
of
inclination
that
draweth
it
back
towards
the
centre
of
the
wheel
,
would
be
sufficient
to
retain
it
upon
the
rim
or
circumference
.
SIMP.
I
question
not
,
but
that
if
one
suppose
that
which
neither
is
,
nor
can
be
,
to
wit
,
that
the
inclination
of
those
grave
bodies
was
to
go
towards
the
centre
of
the
wheel
,
they
would
never
come
to
be
extruded
or
shaken
off
.
SALV
.
But
I
neither
do
,
nor
need
to
suppose
that
which
is
not
;
for
I
will
not
deny
but
that
the
stones
are
extruded
.
Yet
I
speak
this
by
way
of
supposition
,
to
the
end
that
you
might
grant
me
the
rest
.
Now
fancy
to
your self
,
that
the
Earth
is
that
great
wheel
,
which
moved
with
so
great
velocity
is
to
extrude
the
stones
.
You
could
tell
me
very
well
even
now
,
that
the
motion
of
projection
ought
to
be
by
that
right
line
which
toucheth
the
Earth
in
the
point
of
separation
:
and
this
Tangent
,
how
doth
it
notably
recede
from
the
superficies
of
the
Terrestrial
Globe
?
SIMP.
I
believe
,
that
in
a
thousand
yards
,
it
will
not
recede
from
the
Earth
an
inch
.
SALV
.
And
did
you
not
say
,
that
the
project
being
drawn
by
its
own
weight
,
declineth
from
the
Tangent
towards
the
centre
of
the
Earth
?
SIMP.
I
said
so
,
and
also
confesse
the
rest
:
and
do
now
plainly
understand
that
the
stone
will
not
separate
from
the
Earth
,
for
that
its
recession
in
the
beginning
would
be
such
,
and
so
small
,
that
it
is
a
thousand
times
exceeded
by
the
inclination
which
the
stone
hath
to
move
towards
the
centre
of
the
Earth
,
which
centre
in
this
case
is
also
the
centre
of
the
wheel
.
And
indeed
it
must
be
confessed
that
the
stones
,
the
living
creatures
,
and
the
other
grave
bodies
cannot
be
extruded
;
but
here
again
the
lighter
things
beget
in
me
a
new
doubt
,
they
having
but
a
very
weak
propension
of
descent
towards
the
centre
;
so
that
there
being
wanting
in
them
that
faculty
of
withdrawing
from
the
superficies
,
I
see
not
,
but
that
they
may
be
extruded
;
and
you
know
the
rule
,
that
ad
destruendum
sufficit
unum
.
SAVL
.
We
will
also
give
you
satisfaction
in
this
.
Tell
me
therefore
in
the
first
place
,
what
you
understand
by
light
matters
,
that
is
,
whether
you
thereby
mean
things
really
so
light
,
as
that
they
go
upvvards
,
or
else
not
absolutely
light
,
but
of
so
small
gravity
,
that
though
they
descend
downwards
,
it
is
but
very
slowly
;
for
if
you
mean
the
absolutely
light
,
I
will
be
readier
than
your self
to
admit
their
extrusion
.
SIMP.
I
speak
of
the
other
sort
,
such
as
are
feathers
,
wool
,
cotton
,
and
the
like
;
to
lift
up
which
every
small
force
sufficeth
:
yet
neverthelesse
we
see
they
rest
on
the
Earth
very
quietly
.
SALV
.
This
pen
,
as
it
hath
a
natural
propension
to
descend
towards
the
superficies
of
the
Earth
,
though
it
be
very
small
,
yet
I
must
tell
you
that
it
sufficeth
to
keep
it
from
mounting
upwards
:
and
this
again
is
not
unknown
to
you
your self
;
therefore
tell
me
if
the
pen
were
extruded
by
the
Vertigo
of
the
Earth
,
by
what
line
would
it
move
?
SIMP.
By
the
tangent
in
the
point
of
separation
.
SALV
.
And
when
it
should
be
to
return
,
and
re-unite
it self
to
the
Earth
,
by
what
line
would
it
then
move
?
SIMP.
By
that
which
goeth
from
it
to
the
centre
of
the
Earth
.
SALV
.
So
then
here
falls
under
our
consideration
two
motions
;
one
the
motion
of
projection
,
which
beginneth
from
the
point
of
contact
,
and
proceedeth
along
the
tangent
;
and
the
other
the
motion
of
inclination
downwards
,
which
beginneth
from
the
project
it self
,
and
goeth
by
the
secant
towards
the
centre
;
and
if
you
desire
that
the
projection
follow
,
it
is
necessary
that
the
impetus
by
the
tangent
overcome
the
inclination
by
the
secant
:
is
it
not
so
?
SIMP.
So
it
seemeth
to
me
.
SALV
.
But
what
is
it
that
you
think
necessary
in
the
motion
of
the
projicient
,
to
make
that
it
may
prevail
over
that
inclination
,
from
which
ensueth
the
separation
and
elongation
of
the
pen
from
the
Earth
?
SIMP.
I
cannot
tell
.
SALV
.
How
,
do
you
not
know
that
?
The
moveable
is
here
the
same
,
that
is
,
the
same
pen
;
now
how
can
the
same
moveable
superate
and
exceed
it self
in
motion
?
SIMP.
I
do
not
see
how
it
can
overcome
or
yield
to
it self
in
motion
,
unlesse
by
moving
one
while
faster
,
and
another
while
slower
.
SALV
.
You
see
then
,
that
you
do
know
it
.
If
therefore
the
projection
of
the
pen
ought
to
follow
,
and
its
motion
by
the
tangent
be
to
overcome
its
motion
by
the
secant
,
what
is
it
requisite
that
their
velocities
should
be
?
SIMP.
It
is
requisite
that
the
motion
by
the
tangent
be
greater
than
that
other
by
the
secant
.
But
wretch
that
I
am
!
Is
it
not
only
many
thousand
times
greater
than
the
descending
motion
of
the
pen
,
but
than
that
of
the
stone
?
And
yet
like
a
simple
fellow
I
had
suffered
my self
to
be
perswaded
,
that
stones
could
not
be
extruded
by
the
revolution
of
the
Earth
.
I
do
therefore
revoke
my
former
sentence
,
and
say
,
that
if
the
Earth
should
move
,
stones
,
Elephants
,
Towers
,
and
whole
Cities
would
of
necessity
be
tost
up
into
the
Air
;
and
because
that
that
doth
not
evene
,
I
conclude
that
the
Earth
doth
not
move
.
SALV
.
Softly
Simplicius
,
you
go
on
so
fast
,
that
I
begin
to
be
more
afraid
for
you
,
than
for
the
pen.
Rest
a
little
,
and
observe
what
I
am
going
to
speap
.
If
for
the
reteining
of
the
stone
or
pen
annexed
to
the
Earths
surface
it
were
necessary
that
its
motion
of
descent
were
greater
,
or
as
much
as
the
motion
made
by
the
tangent
;
you
would
have
had
reason
to
say
,
that
it
ought
of
necessity
to
move
as
fast
,
or
faster
by
the
secant
downwards
,
than
by
the
tangent
Eastwards
:
But
did
not
you
tell
me
even
now
,
that
a
thousand
yards
of
distance
by
the
tangent
from
the
contact
,
do
remove
hardly
an
inch
from
the
circumference
?
It
is
not
sufficient
therefore
that
the
motion
by
the
tangent
,
which
is
the
same
with
that
of
the
diurnall
Vertigo
,
(
or
hasty
revolution
)
be
simply
more
swift
than
the
motion
by
the
secant
,
which
is
the
same
with
that
of
the
pen
in
descending
;
but
it
is
requisite
that
the
same
be
so
much
more
swift
as
that
the
time
which
sufficeth
for
the
pen
to
move
v.
g.
a
thousand
yards
by
the
tangent
,
be
insufficient
for
it
to
move
one
sole
inch
by
the
secant
.
The
which
I
tell
you
shall
never
be
,
though
you
should
make
that
motion
never
so
swift
,
and
this
never
so
slow
.
SIMP.
And
why
might
not
that
by
the
tangent
be
so
swift
,
as
not
to
give
the
pen
time
to
return
to
the
surface
of
the
Earth
?
SALV
.
Try
whether
you
can
state
the
case
in
proper
termes
,
and
I
will
give
you
an
answer
.
Tell
me
therefore
,
how
much
do
you
think
sufficeth
to
make
that
motion
swifter
than
this
?
SIMP.
I
will
say
for
example
,
that
if
that
motion
by
the
tangent
were
a
million
of
times
swifter
than
this
by
the
secant
,
the
pen
,
yea
,
and
the
stone
also
would
come
to
be
extruded
.
SALV
.
You
say
so
,
and
say
that
which
is
false
,
onely
for
want
,
not
of
Logick
,
Physicks
,
or
Metaphysicks
,
but
of
Geometry
;
for
if
you
did
but
understand
its
first
elements
,
you
would
know
,
that
from
the
centre
of
a
circle
a
right
line
may
be
drawn
to
meet
the
tangent
,
which
intersecteth
it
in
such
a
manner
,
that
the
part
of
the
tangent
between
the
contact
and
the
secant
,
may
be
one
,
two
,
or
three
millions
of
times
greater
than
that
part
of
the
secant
which
lieth
between
the
tangent
and
the
circumference
,
and
that
the
neerer
and
neerer
the
secant
shall
be
to
the
contact
,
this
proportion
shall
grow
greater
and
greater
in
infinitum
;
so
that
it
need
not
be
feared
,
though
the
vertigo
be
swift
,
and
the
motion
downwards
slow
,
that
the
pen
or
other
lighter
matter
can
begin
to
rise
upwards
,
for
that
the
inclination
downwards
always
exceedeth
the
velocity
of
the
projection
.
SAGR.
I
do
not
perfectly
apprehend
this
businesse
.
SALV
.
I
will
give
you
a
most
universal
yet
very
easie
demonstration
thereof
.
A
geometrical
demonstration
to
prove
the
impossibility
of
extrusion
by
means
of
the
terrestrial
vertigo
.
Let
a
proportion
be
given
between
BA
[
in
Fig.
3.
]
and
C
:
And
let
BA
be
greater
than
C
at
pleasure
.
And
let
there
be
described
a
circle
,
whose
centre
is
D.
From
which
it
is
required
to
draw
a
secant
,
in
such
manner
,
that
the
tangent
may
be
in
proportion
to
the
said
secant
,
as
BA
to
C.
Let
AI
be
supposed
a
third
proportional
to
BA
and
C.
And
as
BI
is
to
IA
,
so
let
the
diameter
FE
be
to
EG
;
and
from
the
point
G
,
let
there
be
drawn
the
tangent
GH
.
I
say
that
all
this
is
done
as
was
required
;
and
as
BA
is
to
C
,
so
is
HG
to
GE.
And
in
regard
that
as
BI
is
to
IA
,
so
is
FE
to
EG
;
therefore
by
composition
,
as
BA
is
to
AI
;
so
shall
FG
be
to
GE.
And
because
C
is
the
middle
proportion
between
BA
and
AI
;
and
GH
is
a
middle
term
between
FG
and
GE
;
therefore
,
as
BA
is
to
C
,
so
shall
FG
be
to
GH
;
that
is
HG
to
GE
,
which
was
to
be
demonstrated
.
SAGR.
I
apprehend
this
demonstration
;
yet
neverthelesse
,
I
am
not
left
wholly
without
haesitation
;
for
I
find
certain
confused
scruples
role
to
and
again
in
my
mind
,
which
like
thick
and
dark
clouds
,
permit
me
not
to
discern
the
cleernesse
and
necessity
of
the
conclusion
with
that
perspicuity
,
which
is
usual
in
Mathematical
Demonstrations
.
And
that
which
I
stick
at
is
this
.
It
is
true
that
the
spaces
between
the
tangent
and
the
circumference
do
gradually
diminish
in
infinitum
towards
the
contact
;
but
it
is
also
true
on
the
contrary
,
that
the
propension
of
the
moveable
to
descending
groweth
less
&
less
in
it
,
the
nearer
it
is
to
the
first
term
of
its
descent
;
that
is
,
to
the
state
of
rest
;
as
is
manifest
from
that
which
you
declare
unto
us
,
demonstrating
that
the
descending
grave
body
departing
from
rest
,
ought
to
passe
thorow
all
the
degrees
of
tardity
comprehended
between
the
said
rest
,
&
any
assigned
degree
of
velocity
,
the
which
grow
less
and
in
infinitum
.
To
which
may
be
added
,
that
the
said
velocity
and
propension
to
motion
,
doth
for
another
reason
diminish
to
infinity
;
and
it
is
because
the
gravity
of
the
said
moveable
may
infinitely
diminish
.
So
that
the
causes
which
diminish
the
propension
of
ascending
,
and
consequently
favour
the
projection
,
are
two
;
that
is
,
the
levity
of
the
moveable
,
and
its
vicinity
to
the
state
of
rest
;
both
which
are
augmentable
in
infinit
.
and
these
two
on
the
contrary
being
to
contract
but
with
one
sole
cause
of
making
the
projection
,
I
cannot
conceive
how
it
alone
,
although
it
also
do
admit
of
infinite
augmentation
,
should
be
able
to
remain
invincible
against
the
union
&
confederacy
of
the
others
,
which
are
two
,
and
are
in
like
manner
capable
of
infinite
augmentation
.
SALV
.
This
is
a
doubt
worthy
of
Sagredus
;
and
to
explain
it
so
as
that
we
may
more
cleerly
apprehend
it
,
for
that
you
say
that
you
your self
have
but
a
confused
Idea
of
it
,
we
will
distinguish
of
the
same
by
reducing
it
into
figure
;
which
may
also
perhaps
afford
us
some
ease
in
resolving
the
same
.
Let
us
therefore
[
in
Fig.
4.
]
draw
a
perpendicular
line
towards
the
centre
,
and
let
it
be
AC
,
and
to
it
at
right
angles
let
there
be
drawn
the
Horizontal
line
AB
,
upon
which
the
motion
of
the
projection
ought
to
be
made
;
now
the
project
would
continue
to
move
along
the
same
with
an
even
motion
,
if
so
be
its
gravity
did
not
incline
it
downwards
.
Let
us
suppose
from
the
point
A
a
right
line
to
be
drawn
,
that
may
make
any
angle
at
pleasure
with
the
line
AB
;
which
let
be
AE
,
and
upon
AB
let
us
mark
some
equal
spaces
AF
,
FH
,
HK
,
and
from
them
let
us
let
fall
the
perpendiculars
FG
,
HI
,
KL
,
as
far
as
AE.
And
because
,
as
already
hath
been
said
,
the
descending
grave
body
departing
from
rest
,
goeth
from
time
to
time
acquiring
a
greater
degrees
of
velocity
,
according
as
the
said
time
doth
successively
encrease
;
we
may
conceive
the
spaces
AF
,
FH
,
HK
,
to
represent
unto
us
equal
times
;
and
the
perpendiculars
FG
,
HI
,
KL
,
degrees
of
velocity
acquired
in
the
said
times
;
so
that
the
degree
of
velocity
acquired
in
the
whole
time
AK
,
is
as
the
line
KL
,
in
respect
to
the
degree
HI
,
acquired
in
the
time
AH
,
and
the
degree
FG
in
the
time
AF
;
the
which
degrees
KL
,
HI
,
FG
,
are
(
as
is
manifest
)
the
same
in
proportion
,
as
the
times
KA
,
HA
,
FA
,
and
if
other
perpendiculars
were
drawn
from
the
points
marked
at
pleasure
in
the
line
FA
,
one
might
successively
find
degrees
lesse
and
lesse
in
infinitum
,
proceeding
towards
the
point
A
,
representing
the
first
instant
of
time
,
and
the
first
state
of
rest
.
And
this
retreat
towards
A
,
representeth
the
first
propension
to
the
motion
of
descent
,
diminished
in
infinitum
by
the
approach
of
the
moveable
to
the
first
state
of
rest
,
which
approximation
is
augmentable
in
infinitum
.
Now
let
us
find
the
other
diminution
of
velocity
,
which
likewise
may
proceed
to
infinity
,
by
the
diminution
of
the
gravity
of
the
moveable
,
and
this
shall
be
represented
by
drawing
other
lines
from
the
point
A
,
which
contein
angles
lesse
than
the
angle
BAE
,
which
would
be
this
line
AD
,
the
which
intersecting
the
parallels
KL
,
HI
,
FG
,
in
the
points
M
,
N
,
and
O
,
represent
unto
us
the
degrees
FO
,
HN
,
KM
,
acquired
in
the
times
AF
,
AH
,
AK
,
lesse
than
the
other
degrees
FG
,
HI
,
KL
,
acquired
in
the
same
times
;
but
these
latter
by
a
moveable
more
ponderous
,
and
those
other
by
a
moveable
more
light
.
And
it
is
manifest
,
that
by
the
retreat
of
the
line
EA
towards
AB
,
contracting
the
angle
EAB
(
the
which
may
be
done
in
infinitum
,
like
as
the
gravity
may
in
infinitum
be
diminished
)
the
velocity
of
the
cadent
moveable
may
in
like
manner
be
diminished
in
infinitum
,
and
so
consequently
the
cause
that
impeded
the
projection
;
and
therefore
my
thinks
that
the
union
of
these
two
reasons
against
the
projection
,
diminished
to
infinity
,
cannot
be
any
impediment
to
the
said
projection
.
And
couching
the
whole
argument
in
its
shortest
terms
,
we
will
say
,
that
by
contracting
the
angle
EAB
,
the
degrees
of
velocity
LK
,
IH
,
GF
,
are
diminished
;
and
moreover
by
the
retreat
of
the
parallels
KL
,
HI
,
FG
,
towards
the
angle
A
,
the
same
degrees
are
again
diminished
;
and
both
these
diminutions
extend
to
infinity
:
Therefore
the
velocity
of
the
motion
of
descent
may
very
well
diminish
so
much
,
(
it
admitting
of
a
twofold
diminution
in
infinitum
)
as
that
it
may
not
suffice
to
restore
the
moveable
to
the
circumference
of
the
wheel
,
and
thereupon
may
occasion
the
projection
to
be
hindered
and
wholly
obviated
.
Again
on
the
contrary
,
to
impede
the
projection
,
it
is
necessary
that
the
spaces
by
which
the
project
is
to
descend
for
the
reuniting
it self
to
the
Wheel
,
be
made
so
short
and
close
together
,
that
though
the
descent
of
the
moveable
be
retarded
,
yea
more
,
diminished
in
infinitum
,
yet
it
sufficeth
to
reconduct
it
thither
:
and
therefore
it
would
be
requisite
,
that
you
find
out
a
diminution
of
the
said
spaces
,
not
only
produced
to
infinity
,
but
to
such
an
infinity
,
as
that
it
may
superate
the
double
infinity
that
is
made
in
the
diminution
of
the
velocity
of
the
descending
moveable
.
But
how
can
a
magnitude
be
diminished
more
than
another
,
which
hath
a
twofold
diminution
in
infinitum
?
Now
let
Simplicius
observe
how
hard
it
is
to
philosophate
well
in
nature
,
without
Geometry
.
The
degrees
of
velocity
diminished
in
infinitum
,
as
well
by
the
diminution
of
the
gravity
of
the
moveable
,
as
by
the
approxination
to
the
first
term
of
the
motion
,
that
is
,
to
the
state
of
rest
,
are
alwayes
determinate
,
and
answer
in
proportion
to
the
parallels
comprehended
between
two
right
lines
that
concur
in
an
angle
,
like
to
the
angle
BAE
,
or
BAD
,
or
any
other
infinitely
more
acute
,
alwayes
provided
it
be
rectilineall
.
But
the
diminution
of
the
spaces
thorow
which
the
moveable
is
to
be
conducted
along
the
circumference
of
the
wheel
,
is
proportionate
to
another
kind
of
diminution
,
comprehended
between
lines
that
contain
an
angle
infinitely
more
narrow
and
acute
,
than
any
rectilineal
angle
,
how
acute
soever
,
which
is
that
in
our
present
case
.
Let
any
point
be
taken
in
the
perpendicular
AC
,
and
making
it
the
centre
,
describe
at
the
distance
CA
,
an
arch
AMP
,
the
which
shall
intersect
the
parallels
that
determine
the
degrees
of
velocity
,
though
they
be
very
minute
,
and
comprehended
within
a
most
acute
rectilineal
angle
;
of
which
parallels
the
parts
that
lie
between
the
arch
and
the
tangent
AB
,
are
the
quantities
of
the
spaces
,
and
of
the
returns
upon
the
wheel
,
alwayes
lesser
(
and
with
greater
proportion
lesser
,
by
how
much
neerer
they
approach
to
the
contact
)
than
the
said
parallels
of
which
they
are
parts
.
The
parallels
comprehended
between
the
right
lines
in
retiring
towards
the
angle
diminish
alwayes
at
the
same
rate
,
as
v.
g.
AH
being
divided
in
two
equal
parts
in
F
,
the
parallel
HI
shall
be
double
to
FG
,
and
sub-dividing
FA
,
in
two
equal
parts
,
the
parallel
produced
from
the
point
of
the
division
shall
be
the
half
of
FG
;
and
continuing
the
sub-division
in
infinitum
,
the
subsequent
parallels
shall
be
alwayes
half
of
the
next
preceding
;
but
it
doth
not
so
fall
out
in
the
lines
intercepted
between
the
tangent
and
the
circumference
of
the
circle
:
For
if
the
same
sub-division
be
made
in
FA
;
and
supposing
for
example
,
that
the
parallel
which
cometh
from
the
point
H
,
were
double
unto
that
which
commeth
from
F
,
this
shall
be
more
then
double
to
the
next
following
,
and
c●●●inually
the
neerer
we
come
towards
the
contact
A
,
we
shall
fi●●
the
precedent
lines
contein
the
next
following
three
,
four
,
ten
,
an
hundred
,
a
thousand
,
an
hundred
thousand
,
an
hundred
millions
of
times
,
and
more
in
infinitum
.
The
brevity
therefore
of
such
lines
is
so
reduced
,
that
it
far
exceeds
what
is
requisite
to
make
the
project
,
though
never
so
light
,
return
,
nay
more
,
continue
unremoveable
upon
the
circumference
.
SAGR.
I
very
well
comprehend
the
whole
discourse
,
and
upon
what
it
layeth
all
its
stresse
,
yet
neverthelesse
methinks
that
he
that
would
take
pains
to
pursue
it
,
might
yet
start
some
further
questions
,
by
saying
,
that
of
those
two
causes
which
render
the
descent
of
the
moveable
slower
and
slower
in
infinitum
,
it
is
manifest
,
that
that
which
dependeth
on
the
vicinity
to
the
first
term
of
the
descent
,
increaseth
alwayes
in
the
same
proportion
,
like
as
the
parallels
alwayes
retain
the
same
proportion
to
each
other
,
&c.
but
that
the
diminution
of
the
same
velocity
,
dependent
on
the
diminution
of
the
gravity
of
the
moveable
(
which
vvas
the
second
cause
)
doth
also
observe
the
same
proportion
,
doth
not
so
plainly
appear
,
And
vvho
shall
assure
us
that
it
doth
not
proceed
according
to
the
proportion
of
the
lines
intercepted
between
the
secant
,
and
the
circumference
;
or
vvhether
vvith
a
greater
proportion
?
SALV
.
I
have
assumed
for
a
truth
,
that
the
velocities
of
moveables
descending
naturally
,
vvill
follovv
the
proportion
of
their
gravities
,
with
the
favour
of
Simplicius
,
and
of
Aristotle
,
who
doth
in
many
places
affirm
the
same
,
as
a
proposition
manifest
:
You
,
in
favour
of
my
adversary
,
bring
the
same
into
question
,
and
say
that
its
possible
that
the
velocity
increaseth
with
greater
proportion
,
yea
and
greater
in
infinitum
than
that
of
the
gravity
;
so
that
all
that
hath
been
said
falleth
to
the
ground
:
For
maintaining
whereof
,
I
say
,
that
the
proportion
of
the
velocities
is
much
lesse
than
that
of
the
gravities
;
and
thereby
I
do
not
onely
support
but
confirme
the
premises
.
And
for
proof
of
this
I
appeal
unto
experience
,
which
will
shew
us
,
that
a
grave
body
,
howbeit
thirty
or
fourty
times
bigger
then
another
;
as
for
example
,
a
ball
of
lead
,
and
another
of
sugar
,
will
not
move
much
more
than
twice
as
fast
.
Now
if
the
projection
would
not
be
made
,
albeit
the
velocity
of
the
cadent
body
should
diminish
according
to
the
proportion
of
the
gravity
,
much
lesse
would
it
be
made
so
long
as
the
velocity
is
but
little
diminished
,
by
abating
much
from
the
gravity
.
But
yet
supposing
that
the
velocity
diminisheth
with
a
proportion
much
greater
than
that
wherewith
the
gravity
decreaseth
,
nay
though
it
were
the
self-same
wherewith
those
parallels
conteined
between
the
tangent
and
circumference
do
decrease
,
yet
cannot
I
see
any
necessity
why
I
should
grant
the
projection
of
matters
of
never
so
great
levity
;
yea
I
farther
averre
,
that
there
could
no
such
projection
follow
,
meaning
alwayes
of
matters
not
properly
and
absolutely
light
,
that
is
,
void
of
all
gravity
,
and
that
of
their
own
natures
move
upwards
,
but
that
descend
very
slowly
,
and
have
very
small
gravity
.
And
that
which
moveth
me
so
to
think
is
,
that
the
diminution
of
gravity
,
made
according
to
the
proportion
of
the
parallels
between
the
tangent
and
the
circumference
,
hath
for
its
ultimate
and
highest
term
the
nullity
of
weight
,
as
those
parallels
have
for
their
last
term
of
their
diminution
the
contact
it self
,
which
is
an
indivisible
point
:
Now
gravity
never
diminisheth
so
far
as
to
its
last
term
,
for
then
the
moveable
would
cease
to
be
grave
;
but
yet
the
space
of
the
reversion
of
the
project
to
the
circumference
is
reduced
to
the
ultimate
minuity
,
which
is
when
the
moveable
resteth
upon
the
circumference
in
the
very
point
of
contact
;
so
as
that
to
return
thither
it
hath
no
need
of
space
:
and
therefore
let
the
propension
to
the
motion
of
descent
be
never
so
small
,
yet
is
it
alwayes
more
than
sufficient
to
reconduct
the
moveable
to
the
circumference
,
from
which
it
is
distant
but
its
least
space
,
that
is
,
nothing
at
all
.
SAGR.
Your
discourse
,
I
must
confess
,
is
very
accurate
;
and
yet
no
less
concluding
than
it
is
ingenuous
;
and
it
must
be
granted
that
to
go
about
to
handle
natural
questions
,
without
Geometry
,
is
to
attempt
an
impossibility
.
SALV
.
But
Simplicius
will
not
say
so
;
and
yet
I
do
not
think
that
he
is
one
of
those
Peripateticks
that
disswade
their
Disciples
from
studying
the
Mathematicks
,
as
Sciences
that
vitiate
the
reason
,
and
render
it
lesse
apt
for
contemplation
.
SIMP.
I
would
not
do
so
much
wrong
to
Plato
,
but
yet
I
may
truly
say
with
Aristotle
,
that
he
too
much
lost
himself
in
,
and
too
much
doted
upon
that
his
Geometry
:
for
that
in
conclusion
these
Mathematical
subtilties
Salviatus
are
true
in
abstract
,
but
applied
to
sensible
and
Physical
matter
,
they
hold
not
good
.
For
the
Mathematicians
will
very
well
demonstrate
for
example
,
that
Sphaera
tangit
planum
in
puncto
;
a
position
like
to
that
in
dispute
,
but
when
one
cometh
to
the
matter
,
things
succeed
quite
another
way
.
And
so
I
may
say
of
these
angles
of
contact
,
and
these
proportions
;
which
all
evaporate
into
Air
,
when
they
are
applied
to
things
material
and
sensible
.
SALV
.
You
do
not
think
then
,
that
the
tangent
toucheth
the
superficies
of
the
terrestrial
Globe
in
one
point
only
?
SIMP.
No
,
not
in
one
sole
point
;
but
I
believe
that
a
right
line
goeth
many
tens
and
hundreds
of
yards
touching
the
surface
not
onely
of
the
Earth
,
but
of
the
water
,
before
it
separate
from
the
same
.
SALV
.
But
if
I
grant
you
this
,
do
not
you
perceive
that
it
maketh
so
much
the
more
against
your
cause
?
For
if
it
be
supposed
that
the
tangent
was
separated
from
the
terrestrial
superficies
,
yet
it
hath
been
however
demonstrated
that
by
reason
of
the
great
acuity
of
the
angle
of
contingence
(
if
happily
it
may
be
call'd
an
angle
)
the
project
would
not
separate
from
the
same
;
how
much
lesse
cause
of
separation
would
it
have
,
if
that
angle
should
be
wholly
closed
,
The
truth
sometimes
gaines
strength
by
contradiction
.
and
the
superficies
and
the
tangent
become
all
one
?
Perceive
you
not
that
the
Projection
would
do
the
same
thing
upon
the
surface
of
the
Earth
,
which
is
asmuch
as
to
say
,
it
would
do
just
nothing
at
all
?
You
see
then
the
power
of
truth
,
which
while
you
strive
to
oppose
it
,
your
own
assaults
themselves
uphold
and
defend
it
.
But
in
regard
that
you
have
retracted
this
errour
,
I
would
be
loth
to
leave
you
in
that
other
which
you
hold
,
namely
,
that
a
material
Sphere
doth
not
touch
a
plain
in
one
sole
point
:
and
I
could
wish
some
few
hours
conversation
with
some
persons
conversant
in
Geometry
,
might
make
you
a
little
more
intelligent
amongst
those
who
know
nothing
thereof
.
Now
to
shew
you
how
great
their
errour
is
who
say
,
that
a
Sphere
v.
g.
of
brasse
,
doth
not
touch
a
plain
v.
g.
of
steel
in
one
sole
point
,
Tell
me
what
conceipt
you
would
entertain
of
one
that
should
constantly
aver
,
that
the
Sphere
is
not
truly
a
Sphere
.
SIMP.
I
would
esteem
him
wholly
devoid
of
reason
.
SALV
.
He
is
in
the
same
case
who
saith
that
the
material
Sphere
doth
not
touch
a
plain
,
The
sphere
although
material
,
toucheth
the
material
plane
but
in
one
point
onely
.
also
material
,
in
one
onely
point
;
for
to
say
this
is
the
same
,
as
to
affirm
that
the
Sphere
is
not
a
Sphere
.
And
that
this
is
true
,
tell
me
in
what
it
is
that
you
constitute
the
Sphere
to
consist
,
that
is
,
what
it
is
that
maketh
the
Sphere
differ
from
all
other
solid
bodies
.
SIMP.
I
believe
that
the
essence
of
a
Sphere
consisteth
in
having
all
the
right
lines
produced
from
its
centre
to
the
circumference
,
The
definition
of
the
sphere
.
equal
.
SALV
.
So
that
,
if
those
lines
should
not
be
equal
,
that
same
solidity
would
be
no
longer
a
sphere
?
SIMP.
True
.
SALV
.
Go
to
;
tell
me
whether
you
believe
that
amongst
the
many
lines
that
may
be
drawn
between
two
points
,
there
may
be
more
than
one
right
line
onely
.
SIMP.
There
can
be
but
one
.
SALV
.
But
yet
you
understand
that
this
onely
right
line
shall
again
of
necessity
be
the
shortest
of
them
all
?
SIMP.
I
know
it
,
and
also
have
a
demonstration
thereof
,
produced
by
a
great
Peripatetick
Philosopher
,
and
as
I
take
it
,
if
my
memory
do
not
deceive
me
,
he
alledgeth
it
by
way
of
reprehending
Archimedes
,
that
supposeth
it
as
known
,
when
it
may
be
demonstrated
.
SALV
.
This
must
needs
be
a
great
Mathematician
,
that
knew
how
to
demonstrate
that
which
Archimedes
neither
did
,
nor
could
demonstrate
.
And
if
you
remember
his
demonstration
,
I
would
gladly
hear
it
:
for
I
remember
very
well
,
that
Archimedes
in
his
Books
,
de
Sphaer●
&
Cylindro
,
placeth
this
Proposition
amongst
the
Postulata
;
and
I
verily
believe
that
he
thought
it
demonstrated
.
SIMP.
I
think
I
shall
remember
it
,
for
it
is
very
easie
and
short
.
SALV
.
The
disgrace
of
Archimedes
,
and
the
honour
of
this
Philosopher
shall
be
so
much
the
greater
.
SIMP.
I
will
describe
the
Figure
of
it
.
Between
the
points
A
and
B
,
The
demonstration
of
a
Peripatetick
▪
to
prove
the
right
line
to
be
t●e
shortest
of
all
lines
.
[
in
Fig.
5.
]
draw
the
right
line
AB
,
and
the
curve
line
ACB
,
of
which
we
will
prove
the
right
to
be
the
shorter
:
and
the
proof
is
this
;
take
a
point
in
the
curve-line
,
which
let
be
C
,
and
draw
two
other
lines
,
AC
and
CB
,
which
two
lines
together
,
are
longer
than
the
sole
line
AB
,
for
so
demonstrateth
Euclid
.
But
the
curve-line
ACB
,
is
greater
than
the
two
right-lines
AC
,
and
CB
;
therefore
,
à
fortiori
,
the
curve-line
ACB
,
is
much
greater
than
the
right
line
AB
,
which
was
to
be
demonstrated
.
SALV
.
I
do
not
think
that
if
one
should
ransack
all
the
Paralogisms
of
the
world
,
The
Paralogism
of
the
same
Peripatetick
▪
which
proveth
ignotum
per
ignotius
.
there
could
be
found
one
more
commodious
than
this
,
to
give
an
example
of
the
most
solemn
fallacy
of
all
fallacies
,
namely
,
than
that
which
proveth
ignotum
per
ignotius
.
SIMP.
How
so
?
SALV
.
Do
you
ask
me
how
so
?
The
unknown
conclusion
which
you
desire
to
prove
,
is
it
not
,
that
the
curved
line
ACB
,
is
longer
than
the
right
line
AB
;
the
middle
term
which
is
taken
for
known
,
is
that
the
curve-line
ACB
,
is
greater
than
the
two
lines
AC
and
CB
,
the
which
are
known
to
be
greater
than
AB
;
And
if
it
be
unknown
whether
the
curve-line
be
greater
than
the
single
right-line
AB
,
shall
it
not
be
much
more
unknown
whether
it
be
greater
than
the
two
right
lines
AC
&
CB
,
which
are
known
to
be
greater
than
the
sole
line
AB
,
&
yet
you
assume
it
as
known
?
SIMP.
I
do
not
yet
very
well
perceive
wherein
lyeth
the
fallacy
.
SALV
.
As
the
two
right
lines
are
greater
than
AB
,
(
as
may
be
known
by
Euclid
)
and
in
as
much
as
the
curve
line
is
longer
than
the
two
right
lines
AC
and
BC
,
shall
it
not
not
be
much
greater
than
the
sole
right
line
AB
?
SIMP.
It
shall
so
.
SALV
.
That
the
curve-line
ACB
,
is
greater
than
the
right
line
AB
,
is
the
conclusion
more
known
than
the
middle
term
,
which
is
,
that
the
same
curve-line
is
greater
than
the
two
right-lines
AC
and
CB.
Now
when
the
middle
term
is
less
known
than
the
conclusion
,
it
is
called
a
proving
ignotum
per
ignotius
.
But
to
return
to
our
purpose
,
it
is
sufficient
that
you
know
the
right
line
to
be
the
shortest
of
all
the
lines
that
can
be
drawn
between
two
points
.
And
as
to
the
principal
conclusion
,
you
say
,
that
the
material
sphere
doth
not
touch
the
sphere
in
one
sole
point
.
What
then
is
its
contact
?
SIMP.
It
shall
be
a
part
of
its
superficies
.
SALV
.
And
the
contact
likewise
of
another
sphere
equal
to
the
first
,
shall
be
also
a
like
particle
of
its
superficies
?
SIMP.
There
is
no
reason
vvhy
it
should
be
othervvise
.
SALV
.
Then
the
tvvo
spheres
vvhich
touch
each
other
,
shall
touch
vvith
the
tvvo
same
particles
of
a
superficies
,
for
each
of
them
agreeing
to
one
and
the
same
plane
,
they
must
of
necessity
agree
in
like
manner
to
each
other
.
A
demonstration
that
the
sphere
toucheth
the
plane
but
in
one
point
.
Imagine
now
that
the
two
spheres
[
in
Fig.
6.
]
whose
centres
are
A
and
B
,
do
touch
one
another
:
and
let
their
centres
be
conjoyned
by
the
right
line
AB
,
which
passeth
through
the
contact
.
It
passeth
thorow
the
point
C
,
and
another
point
in
the
contact
being
taken
as
D
,
conjoyn
the
two
right
lines
AD
and
BD
,
so
as
that
they
make
the
triangle
ADB
;
of
which
the
two
sides
AD
and
DB
shall
be
equal
to
the
other
one
ACB
,
both
those
and
this
containing
two
semidiameters
,
which
by
the
definition
of
the
sphere
are
all
equal
:
and
thus
the
right
line
AB
,
drawn
between
the
two
centres
A
and
B
,
shall
not
be
the
shortest
of
all
,
the
two
lines
AD
and
DB
being
equal
to
it
:
which
by
your
own
concession
is
absurd
.
SIMP.
This
demonstration
holdeth
in
the
abstracted
,
but
not
in
the
material
spheres
.
SALV
.
Instance
then
wherein
the
fallacy
of
my
argument
consisteth
,
if
as
you
say
it
is
not
concluding
in
the
material
spheres
,
but
holdeth
good
in
the
immaterial
and
abstracted
.
SIMP.
The
material
spheres
are
subject
to
many
accidents
,
Why
the
sphere
in
abstract
,
toucheth
the
plane
onely
in
one
point
,
and
not
the
material
in
concrete
.
which
the
immaterial
are
free
from
.
And
because
it
cannot
be
,
that
a
sphere
of
metal
passing
along
a
plane
,
it
s
own
weight
should
not
so
depress
it
,
as
that
the
plain
should
yield
somewhat
,
or
that
the
sphere
it self
should
not
in
the
contact
admit
of
some
impression
.
Moreover
,
it
is
very
hard
for
that
plane
to
be
perfect
,
if
for
nothing
else
,
yet
at
least
for
that
its
matter
is
porous
:
and
perhaps
it
will
be
no
less
difficult
to
find
a
sphere
so
perfect
,
as
that
it
hath
all
the
lines
from
the
centre
to
the
superficies
,
exactly
equal
.
SALV
.
I
very
readily
grant
you
all
this
that
you
have
said
;
but
it
is
very
much
beside
our
purpose
:
for
whilst
you
go
about
to
shew
me
that
a
material
sphere
toucheth
not
a
material
plane
in
one
point
alone
,
you
make
use
of
a
sphere
that
is
not
a
sphere
,
and
of
a
plane
that
is
not
a
plane
;
for
that
,
according
to
what
you
say
,
either
these
things
cannot
be
found
in
the
world
,
or
if
they
may
be
found
,
they
are
spoiled
in
applying
them
to
work
the
effect
.
It
had
been
therefore
a
less
evil
,
for
you
to
have
granted
the
conclusion
,
but
conditionally
,
to
wit
,
that
if
there
could
be
made
of
matter
a
sphere
and
a
plane
that
were
and
could
continue
perfect
,
they
would
touch
in
one
sole
point
,
and
then
to
have
denied
that
any
such
could
be
made
.
SIMP.
I
believe
that
the
proposition
of
Philosophers
is
to
be
understood
in
this
sense
;
for
it
is
not
to
be
doubted
,
but
that
the
imperfection
of
the
matter
,
maketh
the
matters
taken
in
concrete
,
to
disagree
with
those
taken
in
abstract
.
SALV
.
What
,
do
they
not
agree
?
Why
,
that
which
you
your self
say
at
this
instant
,
proveth
that
they
punctually
agree
.
SIMP.
How
can
that
be
?
SALV
.
Do
you
not
say
,
that
through
the
imperfection
of
the
matter
,
that
body
which
ought
to
be
perfectly
spherical
,
and
that
plane
which
ought
to
be
perfectly
level
,
do
not
prove
to
be
the
same
in
concrete
,
as
they
are
imagined
to
be
in
abstract
?
SIMP.
This
I
do
affirm
.
SALV
.
Then
when
ever
in
concrete
you
do
apply
a
material
Sphere
to
a
material
plane
,
Things
are
exactly
the
same
in
abstract
as
in
concrete
.
you
apply
an
imperfect
Sphere
to
an
imperfect
plane
,
&
these
you
say
do
not
touch
only
in
one
point
.
But
I
must
tell
you
,
that
even
in
abstract
an
immaterial
Sphere
,
that
is
,
not
a
perfect
Sphere
,
may
touch
an
immaterial
plane
,
that
is
,
not
a
perfect
plane
,
not
in
one
point
,
but
with
part
of
its
superficies
,
so
that
hitherto
that
which
falleth
out
in
concrete
,
doth
in
like
manner
hold
true
in
abstract
.
And
it
would
be
a
new
thing
that
the
computations
and
rates
made
in
abstract
numbers
,
should
not
afterwards
answer
to
the
Coines
of
Gold
and
Silver
,
and
to
the
merchandizes
in
concrete
.
But
do
you
know
Simplicius
,
how
this
commeth
to
passe
?
Like
as
to
make
that
the
computations
agree
with
the
Sugars
,
the
Silks
,
the
Wools
,
it
is
necessary
that
the
accomptant
reckon
his
tares
of
chests
,
bags
,
and
such
other
things
▪
So
when
the
Geometricall
Philosopher
would
observe
in
concrete
the
effects
demonstrated
in
abstract
,
he
must
defalke
the
impediments
of
the
matter
,
and
if
he
know
how
to
do
that
,
I
do
assure
you
,
the
things
shall
jump
no
lesse
exactly
,
than
Arithmetical
computations
.
The
errours
therefore
lyeth
neither
in
abstract
,
nor
in
concrete
,
nor
in
Geometry
,
nor
in
Physicks
,
but
in
the
Calculator
,
that
knoweth
not
how
to
adjust
his
accompts
.
Therefore
if
you
had
a
perfect
Sphere
and
plane
,
though
they
were
material
,
you
need
not
doubt
but
that
they
would
touch
onely
in
one
point
.
And
if
such
a
Sphere
was
and
is
impossible
to
be
procured
,
it
was
much
besides
the
purpose
to
say
,
Quod
Sphaera
aenea
non
tangit
in
puncto
.
Furthermore
,
if
I
grant
you
Simplicius
,
that
in
matter
a
figure
cannot
be
procured
that
is
perfectly
spherical
,
or
perfectly
level
:
Do
you
think
there
may
be
had
two
materiall
bodies
,
whose
superficies
in
some
part
,
and
in
some
sort
are
incurvated
as
irregularly
as
can
be
desired
?
SIMP.
Of
these
I
believe
that
there
is
no
want
.
SALV
.
If
such
there
be
,
Contact
in
a
single
point
is
not
peculiar
to
the
perfect
Spheres
onely
,
but
belongeth
to
all
curved
figures
.
then
they
also
will
touch
in
one
sole
point
;
for
this
contact
in
but
one
point
alone
is
not
the
sole
and
peculiar
priviledge
of
the
perfect
Sphere
and
perfect
plane
.
Nay
,
he
that
should
prosecute
this
point
with
more
subtil
contemplations
would
finde
that
it
is
much
harder
to
procure
two
bodies
that
touch
with
part
of
their
s●perficies
,
It
is
more
difficult
to
find
Figures
that
touch
with
a
part
of
their
surface
,
than
in
one
sole
point
.
than
with
one
point
onely
.
For
if
two
superficies
be
required
to
combine
well
together
,
it
is
necessary
either
,
that
they
be
both
exactly
plane
,
or
that
if
one
be
convex
,
the
other
be
concave
;
but
in
such
a
manner
concave
,
that
the
concavity
do
exactly
answer
to
the
convexity
of
the
other
:
the
which
conditions
are
much
harder
to
be
found
,
in
regard
of
their
too
narrow
determination
,
than
those
others
,
which
in
their
casuall
latitude
are
infinite
.
SIMP.
You
believe
then
,
that
two
stones
,
or
two
pieces
of
Iron
taken
at
chance
,
and
put
together
,
do
for
the
most
part
touch
in
one
sole
point
?
SALV
.
In
casual
encounters
,
I
do
not
think
they
do
;
as
well
because
for
the
most
part
there
will
be
some
small
yielding
filth
upon
them
,
as
because
that
no
diligence
is
used
in
applying
them
without
striking
one
another
;
and
every
small
matter
sufficeth
to
make
the
one
superficies
yield
somewhat
to
the
other
;
so
that
they
interchangeably
,
at
least
in
some
small
particle
,
receive
figure
from
the
impression
of
each
other
.
But
in
case
their
superficies
were
very
terse
and
polite
,
and
that
they
were
both
laid
upon
a
table
,
that
so
one
might
not
presse
upon
the
other
,
and
gently
put
towards
one
another
,
I
question
not
,
but
that
they
might
be
brought
to
the
simple
contact
in
one
onely
point
.
SAGR.
It
is
requisite
,
with
your
permission
,
that
I
propound
a
certain
scruple
of
mine
,
which
came
into
my
minde
,
whil'st
I
heard
proposed
by
Simplicius
,
the
impossibility
of
finding
a
materiall
and
solid
body
,
that
is
,
perfectly
of
a
Spherical
figure
,
and
whil'st
I
saw
Salviatus
in
a
certain
manner
,
not
gainsaying
,
to
give
his
consent
thereto
;
therefore
I
would
know
,
whether
there
would
be
the
same
difficulty
in
forming
a
solid
of
some
other
figure
,
that
is
,
to
expresse
my self
better
,
whether
there
is
more
difficulty
in
reducing
a
piece
of
Marble
into
the
figure
of
a
perfect
Sphere
,
than
into
a
perfect
Pyramid
,
or
into
a
perfect
Horse
,
or
into
a
perfect
Grasse-hopper
?
SALV
.
To
this
I
will
make
you
the
first
answer
:
and
in
the
first
place
,
I
will
acquit
my self
of
the
assent
which
you
think
I
gave
to
Simplicius
,
which
was
only
for
a
time
;
for
I
had
it
also
in
my
thoughts
,
before
I
intended
to
enter
upon
any
other
matter
,
to
speak
that
,
which
,
it
may
be
,
is
the
same
,
or
very
like
to
that
which
you
are
about
to
say
;
The
Sphericall
Figure
is
easier
to
be
made
than
any
other
.
And
answering
to
your
first
question
,
I
say
,
that
if
any
figure
can
be
given
to
a
Solid
,
the
Spherical
is
the
easiest
of
all
others
,
as
it
is
likewise
the
most
simple
,
and
holdeth
the
same
place
amongst
solid
figures
,
The
circular
Figure
only
is
placed
amongst
the
postulat●
of
Mathematicians
.
as
the
Circle
holdeth
amongst
the
superficial
.
The
description
of
which
Circle
,
as
being
more
easie
than
all
the
rest
,
hath
alone
been
judged
by
Mathematicians
worthy
to
be
put
amongst
the
[
](A61244-e44260-b)*
*
Demands
or
Petitions
.
postulata
belonging
to
the
description
of
all
other
figures
.
And
the
formation
of
the
Sphere
is
so
very
easie
,
that
if
in
a
plain
plate
of
hard
metal
you
take
an
empty
or
hollow
circle
,
within
which
any
Solid
goeth
casually
revolving
that
was
before
but
grosly
rounded
,
it
shall
,
without
any
other
artifice
be
reduced
to
a
Spherical
figure
,
as
perfect
as
is
possible
for
it
to
be
;
provided
,
that
that
same
Solid
be
not
lesse
than
the
Sphere
that
would
passe
thorow
that
Circle
.
And
that
which
is
yet
more
worthy
of
our
consideration
is
,
that
within
the
self-same
incavity
one
may
form
Spheres
of
several
magnitudes
.
Sphericall
Figures
of
sundry
magnitudes
may
be
made
with
one
onely
instrument
.
But
what
is
required
to
the
making
of
an
Horse
,
or
(
as
you
say
)
of
a
Grass-hopper
,
I
leave
to
you
to
judge
,
who
know
that
there
are
but
few
statuaries
in
the
world
able
to
undertake
such
a
piece
of
work
.
And
I
think
that
herein
Simplicius
will
not
dissent
from
me
.
SIMP.
I
know
not
whether
I
do
at
all
dissent
from
you
;
my
opinion
is
this
,
that
none
of
the
afore-named
figures
can
be
perfectly
obteined
;
but
for
the
approaching
as
neer
as
is
possible
to
the
most
perfect
degree
,
I
believe
that
it
is
incomparably
more
easie
to
reduce
the
Solid
into
a
Spherical
figure
,
than
into
the
shape
of
an
Horse
,
or
Grasse-hopper
?
SAGR.
And
this
greater
difficulty
,
wherein
think
you
doth
it
depend
?
SIMP.
Like
as
the
great
facility
in
forming
the
Sphere
ariseth
from
its
absolute
simplicity
and
uniformity
so
the
great
irregularity
rendereth
the
construction
of
all
other
figures
difficult
.
Irregular
forms
difficult
to
be
introduced
.
SAGR.
Therefore
the
irregularity
being
the
cause
of
the
difficulty
,
than
the
figure
of
a
stone
broken
with
an
hammer
by
chance
,
shall
be
one
of
the
figures
that
are
difficult
to
be
introduced
,
it
being
perhaps
more
irregular
than
that
of
the
horse
?
SIMP.
So
it
should
be
.
SAGR.
But
tell
me
;
that
figure
what
ever
it
is
which
the
stone
hath
,
hath
it
the
same
in
perfection
,
or
no
?
SIMP.
What
it
hath
,
it
hath
so
perfectly
,
that
nothing
can
be
more
exact
.
SAGR.
Then
,
if
of
figures
that
are
irregular
,
and
consequently
hard
to
be
procured
,
there
are
yet
infinite
which
are
most
perfectly
obteined
,
with
what
reason
can
it
be
said
,
that
the
most
simple
,
and
consequently
the
most
easie
of
all
,
is
impossible
to
be
procured
?
SALV
.
Gentlemen
,
with
your
favour
,
I
may
say
that
we
have
sallied
out
into
a
dispute
not
much
more
worth
than
the
wool
of
a
goat
;
and
whereas
our
argumentations
should
continually
be
conversant
about
serious
and
weighty
points
,
we
consume
our
time
in
frivolous
and
impertinent
wranglings
.
The
constitution
of
the
Vniverse
is
one
of
the
most
noble
Problems
.
Let
us
call
to
minde
,
I
pray
you
,
that
the
search
of
the
worlds
constitution
,
is
one
of
the
greatest
and
noblest
Problems
that
are
in
nature
;
and
so
much
the
greater
,
inasmuch
as
it
is
directed
to
the
resolving
of
that
other
;
to
wit
,
of
the
cause
of
the
Seas
ebbing
and
flowing
,
enquired
into
by
all
the
famous
men
,
that
have
hitherto
been
in
the
world
,
and
possibly
found
out
by
none
of
them
.
Therefore
if
we
have
nothing
more
remaining
for
the
full
confutation
of
the
argument
taken
from
the
Earths
vertigo
,
which
was
the
last
,
alledged
to
prove
its
immobility
upon
its
own
centre
,
let
us
passe
to
the
examination
of
those
things
that
are
alledged
for
,
and
against
the
Annual
Motion
.
SAGR.
I
would
not
have
you
,
Salviatus
,
measure
our
wits
by
the
scale
of
yours
:
you
,
who
use
to
be
continually
busied
about
the
sublimest
contemplations
,
esteem
those
notions
frivolous
and
below
you
,
which
we
think
matters
worthy
of
our
profoundest
thoughts
:
yet
sometimes
for
our
satisfaction
do
not
disdain
to
stoop
so
low
as
to
give
way
a
little
to
our
curiosity
.
As
to
the
refutation
of
the
last
argument
,
taken
from
the
extrusions
of
the
diurnal
vertigo
,
far
less
than
what
hath
been
said
,
would
have
given
me
satisfaction
:
and
yet
the
things
superfluously
spoken
,
seemed
to
me
so
ingenious
,
that
they
have
been
so
far
from
wearying
my
fancy
,
as
that
they
have
,
by
reason
of
their
novelty
,
entertained
me
all
along
with
so
great
delight
,
that
I
know
not
how
to
desire
greater
:
Therefore
,
if
you
have
any
other
speculation
to
add
,
produce
it
,
for
I
,
as
to
my
own
particular
,
shall
gladly
hearken
to
it
.
SALV
.
I
have
always
taken
great
delight
in
those
things
which
I
have
had
the
fortune
to
discover
,
and
next
to
that
,
which
is
my
chief
content
,
I
find
great
pleasure
in
imparting
them
to
some
friends
,
that
apprehendeth
and
seemeth
to
like
them
:
Now
,
in
regard
you
are
one
of
these
,
slacking
a
little
the
reins
of
my
ambition
,
which
is
much
pleased
when
I
shew
my self
more
perspicacious
,
than
some
other
that
hath
the
reputation
of
a
sharp
sight
,
I
will
for
a
full
and
true
measure
of
the
past
dispute
,
produce
another
fallacy
of
the
Sectators
of
Ptolomey
and
Aristotle
,
which
I
take
from
the
argument
alledged
.
SAGR.
See
how
greedily
I
wait
to
hear
it
.
SALV
.
We
have
hitherto
over-passed
,
and
granted
to
Ptolomey
,
as
an
effect
indubitable
,
that
the
extrusion
of
the
stone
proceeding
from
the
velocity
of
the
wheel
turn'd
round
upon
its
centre
,
the
cause
of
the
said
extrusion
encreaseth
in
proportion
,
as
the
velocity
of
the
vertigo
(
or
whirling
)
is
augmented
:
from
whence
it
was
inferred
,
that
the
velocity
of
the
Earth's
vertigo
being
very
much
greater
than
that
of
any
machin
whatsoever
,
that
we
can
make
to
turn
round
artificially
;
the
extrusion
of
stones
,
of
animals
,
&c.
would
consequently
be
far
more
violent
.
Now
,
I
observe
that
there
is
a
great
fallacy
in
this
discourse
,
in
that
we
do
compare
these
velocities
indifferently
and
absolutely
to
one
another
.
It
's
true
,
that
if
I
compare
the
velocities
of
the
same
wheel
,
or
of
two
wheels
equal
to
each
other
,
that
which
shall
be
more
swiftly
turn'd
round
,
shall
extrude
the
stone
with
greater
violence
;
and
the
velocity
encreasing
,
the
cause
of
the
projection
shall
likewise
encrease
:
but
when
the
velocity
is
augmented
,
not
by
encreasing
the
velocity
in
the
same
wheel
,
which
would
be
by
causing
it
to
make
a
greater
number
of
revolutions
in
equal
times
;
but
by
encreasing
the
diameter
,
and
making
the
wheel
greater
,
so
as
that
the
conversion
taking
up
the
same
time
in
the
lesser
wheel
,
as
in
the
greater
,
The
cause
of
the
projection
increaseth
not
according
to
the
proportion
of
the
velocity
,
increased
by
making
the
wheel
bigger
.
the
velocity
is
greater
onely
in
the
bigger
wheel
,
for
that
its
circumference
is
bigger
;
there
is
no
man
that
thinketh
that
the
cause
of
the
extrusion
in
the
great
wheel
will
encrease
according
to
the
proportion
of
the
velocity
of
its
circumference
,
to
the
velocity
of
the
circumference
of
the
other
lesser
wheel
;
for
that
this
is
most
false
,
as
by
a
most
expeditious
experiment
I
shall
thus
grosly
declare
:
We
may
sling
a
stone
with
a
stick
of
a
yard
long
,
farther
than
we
can
do
with
a
stick
six
yards
long
,
though
the
motion
of
the
end
of
the
long
stick
,
that
is
of
the
stone
placed
in
the
slit
thereof
,
were
more
than
double
as
swift
as
the
motion
of
the
end
of
the
other
shorter
stick
,
as
it
would
be
if
the
velocities
were
such
that
the
lesser
stick
should
turn
thrice
round
in
the
time
whilst
the
greater
is
making
one
onely
conversion
.
SAGR.
This
which
you
tell
me
,
Salviatus
,
must
,
I
see
,
needs
succeed
in
this
very
manner
;
but
I
do
not
so
readily
apprehend
the
cause
why
equal
velocities
should
not
operate
equally
in
extruding
projects
,
but
that
of
the
lesser
wheel
much
more
than
the
other
of
the
greater
wheel
;
therefore
I
intreat
you
to
tell
me
how
this
cometh
to
pass
?
SIMP.
Herein
,
Sagredus
,
you
seem
to
differ
much
from
your self
,
for
that
you
were
wont
to
penetrate
all
things
in
an
instant
,
and
now
you
have
overlook'd
a
fallacy
couched
in
the
experiment
of
the
stick
,
which
I
my self
have
been
able
to
discover
:
and
this
is
the
different
manner
of
operating
,
in
making
the
projection
one
while
with
the
short
sling
and
another
while
with
the
long
one
,
for
if
you
will
have
the
stone
fly
out
of
the
slit
,
you
need
not
continue
its
motion
uniformly
,
but
at
such
time
as
it
is
at
the
swiftest
,
you
are
to
stay
your
arm
,
and
stop
the
velocity
of
the
stick
;
whereupon
the
stone
which
was
in
its
swiftest
motion
,
flyeth
out
,
and
moveth
with
impetuosity
:
but
now
that
stop
cannot
be
made
in
the
great
stick
,
which
by
reason
of
its
length
and
flexibility
,
doth
not
entirely
obey
the
check
of
the
arm
,
but
continueth
to
accompany
the
stone
for
some
space
,
and
holdeth
it
in
with
so
much
less
force
,
and
not
as
if
you
had
with
a
stiff
sling
sent
it
going
with
a
jerk
:
for
if
both
the
sticks
or
slings
should
be
check'd
by
one
and
the
same
obstacle
,
I
do
believe
they
would
fly
aswell
out
of
the
one
,
as
out
of
the
other
,
howbeit
their
motions
were
equally
swift
.
SAGR.
With
the
permission
of
Salviatus
,
I
will
answer
something
to
Simplicius
,
in
regard
he
hath
addressed
himself
to
me
;
and
I
say
,
that
in
his
discourse
there
is
somewhat
good
and
somewhat
bad
:
good
,
because
it
is
almost
all
true
;
bad
,
because
it
doth
not
agree
with
our
case
:
Truth
is
,
that
when
that
which
carrieth
the
stones
with
velocity
,
shall
meet
with
a
check
that
is
immoveable
,
they
shall
fly
out
with
great
impetuosity
:
the
same
effect
following
in
that
case
,
which
we
see
dayly
to
fall
out
in
a
boat
that
running
a
swift
course
,
runs
a-ground
,
or
meets
with
some
sudden
stop
,
for
all
those
in
the
boat
,
being
surprized
,
Gran●i●g
the
diurnal
vertigo
of
the
Earth
,
&
that
by
some
sudden
stop
or
obstacle
it
were
arrested
,
houses
,
mountains
themselves
,
and
perhaps
the
whole
Globe
would
be
shake
●n
pieces
.
stumble
forwards
,
and
fall
towards
the
part
whither
the
boat
steered
.
And
in
case
the
Earth
should
meet
with
such
a
check
,
as
should
be
able
to
resist
and
arrest
its
vertigo
,
then
indeed
I
do
believe
that
not
onely
beasts
,
buildings
and
cities
,
but
mountains
,
lakes
and
seas
would
overturn
,
and
the
globe
it self
would
go
near
to
shake
in
pieces
;
but
nothing
of
all
this
concerns
our
present
purpose
,
for
we
speak
of
what
may
follow
to
the
motion
of
the
Earth
,
it
being
turn'd
round
uniformly
,
and
quietly
about
its
own
centre
,
howbeit
with
a
great
velocity
.
That
likewise
which
you
say
of
the
slings
,
is
true
in
part
;
but
was
not
alledged
by
Salviatus
,
as
a
thing
that
punctually
agreed
with
the
matter
whereof
we
treat
,
but
onely
,
as
an
example
,
for
so
in
gross
it
may
prompt
us
in
the
more
accurate
consideration
of
that
point
,
whether
,
the
velocity
increasing
at
any
rate
,
the
cause
of
the
projection
doth
increase
at
the
same
rate
:
so
that
v.
g.
if
a
wheel
of
ten
yards
diameter
,
moving
in
such
a
manner
that
a
point
of
its
circumference
will
pass
an
hundred
yards
in
a
minute
of
an
hour
,
and
so
hath
an
impetus
able
to
extrude
a
stone
,
that
same
impetus
shall
be
increased
an
hundred
thousand
times
in
a
wheel
of
a
million
of
yards
diameter
;
the
which
Salviatus
denieth
,
and
I
incline
to
his
opinion
;
but
not
knowing
the
reason
thereof
,
I
have
requested
it
of
him
,
and
stand
impatiently
expecting
it
.
SALV
.
I
am
ready
to
give
you
the
best
satisfaction
,
that
my
abilities
will
give
leave
:
And
though
in
my
first
discourse
you
thought
that
I
had
enquired
into
things
estranged
from
our
purpose
,
yet
neverthelesse
I
believe
that
in
the
sequel
of
the
dispute
,
you
will
find
that
they
do
not
prove
so
.
Therefore
let
Sagredus
tell
me
wherein
he
hath
observed
that
the
resistance
of
any
moveable
to
motion
doth
consist
.
SAGR.
I
see
not
for
the
present
that
the
moveable
hath
any
internal
resistance
to
motion
,
unlesse
it
be
its
natural
inclination
and
propension
to
the
contrary
motion
,
as
in
grave
bodies
,
that
have
a
propension
to
the
motion
downwards
,
the
resistance
is
to
the
motion
upwards
;
and
I
said
an
internal
resistance
,
because
of
this
,
I
think
,
it
is
you
intend
to
speak
,
and
not
of
the
external
resistances
,
which
are
many
and
accidental
.
SALV
.
It
is
that
indeed
I
mean
,
and
your
nimblenesse
of
wit
hath
been
too
hard
for
my
craftinesse
,
but
if
I
have
been
too
short
in
asking
the
question
,
I
doubt
whether
Sagredus
hath
been
full
enough
in
his
answer
to
satisfie
the
demand
;
and
whether
there
be
not
in
the
moveable
,
besides
the
natural
inclination
to
the
contrary
term
,
another
intrinsick
and
natural
quality
,
The
inclination
of
grave
bodies
to
the
motion
downwards
,
is
equal
to
their
resistance
to
the
motion
upwards
.
which
maketh
it
averse
to
motion
.
Therefore
tell
me
again
;
do
you
not
think
that
the
inclination
v.
g.
of
grave
bodies
to
move
downwards
,
is
equal
to
the
resistance
of
the
same
to
the
motion
of
projection
upwards
?
SAGR.
I
believe
that
it
is
exactly
the
same
.
And
for
this
reason
I
see
that
two
equal
weights
being
put
into
a
ballance
,
they
do
stand
still
in
equilibrium
,
the
gravity
of
the
one
resisting
its
being
raised
by
the
gravity
wherewith
the
other
pressing
downwards
would
raise
it
.
SALV
.
Very
well
;
so
that
if
you
would
have
one
raise
up
the
other
,
you
must
encrease
the
weight
of
that
which
depresseth
,
or
lessen
the
weight
of
the
other
.
But
if
the
resistance
to
ascending
motion
cunsist
onely
in
gravity
,
how
cometh
it
to
passe
,
that
in
ballances
of
unequal
arms
,
to
wit
in
the
[
](A61244-e45220-b)*
*
A
portable
ballance
wherewith
market-people
weigh
their
commodities
,
giving
it
gravity
by
removing
the
weight
farther
from
the
cock
:
call'd
by
the
Latines
,
Campana
trutina
.
Stiliard
,
a
weight
sometimes
of
an
hundred
pounds
,
with
its
pression
downwards
,
doth
not
suffice
to
raise
up
on
of
four
pounds
;
that
shall
counterpoise
with
it
,
nay
this
of
four
,
descending
shall
raise
up
that
of
an
hundred
;
for
such
is
the
effect
of
the
pendant
weight
upon
the
weight
which
vve
vvould
vveigh
?
If
the
resistance
to
motion
resideth
onely
in
the
gravity
,
hovv
can
the
arm
with
its
vveight
of
four
pounds
onely
,
resist
the
vveight
of
a
sack
of
wool
,
or
bale
of
silk
,
vvhich
shall
be
eight
hundred
,
or
a
thousand
vveight
;
yea
more
,
hovv
can
it
overcome
the
sack
vvith
its
moment
,
and
raise
it
up
?
It
must
therefore
be
confest
Sagredus
,
that
here
it
maketh
use
of
some
other
resistance
,
and
other
force
,
besides
that
of
simple
gravity
.
SAGR.
It
must
needs
be
so
;
therefore
tell
me
vvhat
this
second
virtue
should
be
.
SALV
.
It
is
that
vvhich
vvas
not
in
the
ballance
of
equal
arms
;
you
see
then
vvhat
variety
there
is
in
the
Stiliard
;
and
upon
this
doubtlesse
dependeth
the
cause
of
the
nevv
effect
.
SAGR.
I
think
that
your
putting
me
to
it
a
second
time
,
hath
made
me
remember
something
that
may
be
to
the
purpose
.
In
both
these
beams
the
business
is
done
by
the
weight
,
and
by
the
motion
;
in
the
ballance
,
the
motions
are
equal
,
and
therefore
the
one
weight
must
exceed
it
in
gravity
before
it
can
move
it
;
in
the
stiliard
,
the
lesser
weight
will
not
move
the
greater
,
unless
when
this
latter
moveth
little
,
as
being
hung
at
a
lesser
distance
,
and
the
other
much
,
as
hanging
at
a
greater
distance
from
the
lacquet
or
cock
.
It
is
necessary
therefore
to
conclude
,
that
the
lesser
weight
overcometh
the
resistance
of
the
greater
,
by
moving
much
,
whilst
the
other
is
moved
but
little
.
SALV
.
Which
is
as
much
as
to
say
,
that
the
velocity
of
the
moveable
less
grave
,
compensateth
the
gravity
of
the
moveable
more
grave
and
less
swift
.
SAGR.
But
do
you
think
that
the
velocity
doth
fully
make
good
the
gravity
?
The
greater
velocity
exactly
compensates
the
greater
gravity
.
that
is
,
that
the
moment
and
force
of
a
moveable
of
v.
g.
four
pounds
weight
,
is
as
great
as
that
of
one
of
an
hundred
weight
,
whensoever
that
the
first
hath
an
hundred
degrees
of
velocity
,
and
the
later
but
four
onely
?
SALV
.
Yes
doubtless
,
as
I
am
able
by
many
experiments
to
demonstrate
:
but
for
the
present
,
let
this
onely
of
the
stiliard
suffice
:
in
which
you
see
that
the
light
end
of
the
beam
is
then
able
to
sustain
and
equilibrate
the
great
Wool-sack
,
when
its
distance
from
the
centre
,
upon
which
the
stiliard
resteth
and
turneth
,
shall
so
much
exceed
the
lesser
distance
,
by
how
much
the
absolute
gravity
of
the
Wool-sack
exceedeth
that
of
the
pendent
weight
.
And
we
see
nothing
that
can
cause
this
insufficiencie
in
the
great
sack
of
Wool
,
to
raise
with
its
weight
the
pendent
weight
so
much
less
grave
,
save
the
disparity
of
the
motions
which
the
one
and
the
other
should
make
,
whilst
that
the
Wool-sack
by
descending
but
one
inch
onely
,
will
raise
the
pendent
weight
an
hundred
inches
:
(
supposing
that
the
sack
did
weigh
an
hundred
times
as
much
,
and
that
the
distance
of
the
small
weight
from
the
centre
of
the
beam
were
an
hundred
times
greater
,
than
the
distance
between
the
said
centre
and
the
point
of
the
sacks
suspension
.
)
And
again
,
the
pendent
weight
its
moving
the
space
of
an
hundred
inches
,
in
the
time
that
the
sack
moveth
but
one
inch
onely
,
is
the
same
as
to
say
,
that
the
velocity
of
the
motion
of
the
little
pendent
weight
,
is
an
hundred
times
greater
than
the
velocity
of
the
motion
of
the
sack
.
Now
fix
it
in
your
belief
,
as
a
true
and
manifest
axiom
,
that
the
resistance
which
proceedeth
from
the
velocity
of
motion
,
compensateth
that
which
dependeth
on
the
gravity
of
another
moveable
:
So
that
consequently
,
a
moveable
of
one
pound
,
that
moveth
with
an
hundred
degrees
of
velocity
,
doth
as
much
resist
all
obstruction
,
as
another
moveable
of
an
hundred
weight
,
whose
velocity
is
but
one
degree
onely
.
And
two
equal
moveables
will
equally
resist
their
being
moved
,
if
that
they
shall
be
moved
with
equal
velocity
:
but
if
one
be
to
be
moved
more
swiftly
than
the
other
,
it
shall
make
greater
resistance
,
according
to
the
greater
velocity
that
shall
be
conferred
on
it
.
These
things
being
premised
,
let
us
proceed
to
the
explanation
of
our
Problem
;
and
for
the
better
understanding
of
things
,
let
us
make
a
short
Scheme
thereof
.
Let
two
unequal
wheels
be
described
about
this
centre
A
,
[
in
Fig.
7.
]
and
let
the
circumference
of
the
lesser
be
BG
,
and
of
the
greater
CEH
,
and
let
the
semidiameter
ABC
,
be
perpendicular
to
the
Horizon
;
and
by
the
points
B
and
C
,
let
us
draw
the
right
lined
Tangents
BF
and
CD
;
and
in
the
arches
BG
and
CE
,
take
two
equal
parts
BG
and
CE
:
and
let
the
two
wheels
be
supposed
to
be
turn'd
round
upon
their
centres
with
equal
velocities
,
so
as
that
two
moveables
,
which
suppose
for
example
to
be
two
stones
placed
in
the
points
B
and
C
,
come
to
be
carried
along
the
circumferences
BG
and
CE
,
with
equal
velocities
;
so
that
in
the
same
time
that
the
stone
B
shall
have
run
the
arch
BG
,
the
stone
C
will
have
past
the
arch
CE.
I
say
now
,
that
the
whirl
or
vertigo
of
the
lesser
wheel
is
much
more
potent
to
make
the
projection
of
the
stone
B
,
than
the
vertigo
of
the
bigger
wheel
to
make
that
of
the
stone
C.
Therefore
the
projection
,
as
we
have
already
declared
,
being
to
be
made
along
the
tangent
,
when
the
stones
B
and
C
are
to
separate
from
their
wheel
,
and
to
begin
the
motion
of
projection
from
the
points
B
and
C
,
then
shall
they
be
extruded
by
the
impetus
conceived
from
the
vertigo
by
(
or
along
)
the
tangents
BF
and
CD
.
The
two
stones
therefore
have
equal
impetuosities
of
running
along
the
tangents
BF
and
CD
,
and
would
run
along
the
same
,
if
they
were
not
turn'd
aside
by
some
other
force
:
is
it
not
so
Sagredus
?
SAGR.
In
my
opinion
the
businesse
is
as
you
say
.
SALV
.
But
what
force
,
think
you
,
should
that
be
which
averts
the
stones
from
moving
by
the
tangents
,
along
which
they
are
certainly
driven
by
the
impetus
of
the
vertigo
.
SAGR.
It
is
either
their
own
gravity
,
or
else
some
glutinous
matter
that
holdeth
them
fast
and
close
to
the
wheels
.
SALV
.
But
for
the
diverting
of
a
moveable
from
the
motion
to
which
nature
inciteth
it
,
is
there
not
required
greater
or
lesser
force
,
according
as
the
deviation
is
intended
to
be
greater
or
lesser
?
that
is
,
according
as
the
said
moveable
in
its
deviation
hath
a
greater
or
lesser
space
to
move
in
the
same
time
?
SAGR.
Yes
certainly
:
for
it
was
concluded
even
now
,
that
to
make
a
moveable
to
move
;
the
movent
vertue
must
be
increased
in
proportion
to
the
velocity
wherewith
it
is
to
move
.
SALV
.
Now
consider
,
that
for
the
deviating
the
stone
upon
the
lesse
wheel
from
the
motion
of
projection
,
which
it
would
make
by
the
tangent
BF
,
and
for
the
holding
of
it
fast
to
the
wheel
,
it
is
required
,
that
its
own
gravity
draw
it
back
the
whole
length
of
the
secant
FG
,
or
of
the
perpendicular
raised
from
the
point
G
,
to
the
line
BF
,
whereas
in
the
greater
wheel
the
retraction
needs
to
be
no
more
than
the
secant
DE
,
or
the
perpendicular
let
fall
from
the
tangent
DC
to
the
point
E
,
lesse
by
much
than
FG
,
and
alwayes
lesser
and
lesser
according
as
the
wheel
is
made
bigger
.
And
forasmuch
as
these
retractions
(
as
I
may
call
them
)
are
required
to
be
made
in
equal
times
,
that
is
,
whil'st
the
wheels
passe
the
two
equal
arches
BG
and
CE
,
that
of
the
stone
B
,
that
is
,
the
retraction
FG
ought
to
be
more
swift
than
the
other
DE
;
and
therefore
much
greater
force
will
be
required
for
holding
fast
the
stone
B
to
its
little
wheel
,
than
for
the
holding
the
stone
C
to
its
great
one
,
which
is
as
much
as
to
say
,
that
such
a
small
thing
will
impede
the
extrusion
in
the
great
wheel
,
as
will
not
at
all
hinder
it
in
the
little
one
.
It
is
manifest
therefore
that
the
more
the
wheel
augmenteth
,
the
more
the
cause
of
the
projection
diminisheth
.
SAGR.
From
this
which
I
now
understand
,
by
help
of
your
minute
dissertation
,
I
am
induced
to
think
,
that
I
am
able
to
satisfie
my
judgment
in
a
very
few
words
.
For
equal
impetus
being
impressed
on
both
the
stones
that
move
along
the
tangents
,
by
the
equal
velocity
of
the
two
wheels
,
we
see
the
great
circumference
,
by
means
of
its
small
deviation
from
the
tangent
,
to
go
seconding
,
as
it
were
,
and
in
a
fair
way
refraining
in
the
stone
the
appetite
,
if
I
may
so
say
,
of
separating
from
the
circumference
;
so
that
any
small
retention
,
either
of
its
own
inclination
,
or
of
some
glutination
sufficeth
to
hold
it
fast
to
the
wheel
.
Which
,
again
,
is
not
able
to
work
the
like
effect
in
the
little
wheel
,
which
but
little
prosecuting
the
direction
of
the
tangent
,
seeketh
with
too
much
eagernesse
to
hold
fast
the
stone
;
and
the
restriction
and
glutination
not
being
stronger
than
that
which
holdeth
the
other
stone
fast
to
the
greater
wheel
,
it
[
](A61244-e45760-b)*
*
Strappar
la
cavezza
,
is
to
break
the
bridle
.
breaks
loose
,
and
runneth
along
the
tangent
.
Therefore
I
do
not
only
finde
that
all
those
have
erred
,
who
have
believed
the
cause
of
the
projection
to
increase
according
to
the
augmentation
of
the
vertigo's
velocity
;
but
I
am
further
thinking
,
that
the
projection
diminishing
in
the
inlarging
of
the
wheel
,
so
long
as
the
same
velocity
is
reteined
in
those
wheels
;
it
may
possibly
be
true
,
that
he
that
would
make
the
great
wheel
extrude
things
like
the
little
one
,
would
be
forced
to
increase
them
as
much
in
velocity
;
as
they
increase
in
diameter
,
which
he
might
do
,
by
making
them
to
finish
their
conversions
in
equal
times
;
and
thus
we
may
conclude
,
that
the
Earths
revolution
or
vertigo
would
be
no
more
able
to
extrude
stones
,
than
any
little
wheel
that
goeth
so
slowly
,
as
that
it
maketh
but
one
turn
in
twenty
four
hours
.
SALV
.
We
will
enquire
no
further
into
this
point
for
the
present
:
let
it
suffice
that
we
have
abundantly
(
if
I
deceive
not
my self
)
demonstrated
the
invalidity
of
the
argument
,
which
at
first
sight
seemed
very
concluding
,
and
was
so
held
by
very
famous
men
:
and
I
shall
think
my
time
and
words
well
bestowed
,
if
I
have
but
gained
some
belief
in
the
opinion
of
Simplicius
,
I
will
not
say
of
the
Earths
mobility
,
but
only
that
the
opinion
of
those
that
believe
it
,
is
not
so
ridiculous
and
fond
,
as
the
rout
of
vulgar
Philosophers
esteem
it
.
SIMP.
The
answers
hitherto
produced
against
the
arguments
brought
against
this
Diurnal
Revolution
of
the
Earth
taken
from
grave
bodies
falling
from
the
top
of
a
Tower
,
and
from
projections
made
perpendicularly
upwards
,
or
according
to
any
inclination
sidewayes
towards
the
East
,
West
,
North
,
South
,
&c.
have
somewhat
abated
in
me
the
antiquated
incredulity
I
had
conceived
against
that
opinion
:
but
other
greater
doubts
run
in
my
mind
at
this
very
instant
,
which
I
know
not
in
the
least
how
to
free
my self
of
,
and
haply
you
your self
will
not
be
able
to
resolve
them
;
nay
,
it
s
possible
you
may
not
have
heard
them
,
for
they
are
very
modern
.
And
these
are
the
objections
of
two
Authours
,
that
ex
professo
write
against
Copernicus
.
Other
objections
of
two
modern
Authors
against
Copernicus
.
Some
of
which
are
read
in
a
little
Tract
of
natural
conclusions
;
The
rest
are
by
a
great
both
Philosopher
and
Mathematician
,
inserted
in
a
Treatise
which
he
hath
written
in
favour
of
Aristotle
,
and
his
opinion
touching
the
inalterability
of
the
Heavens
,
where
he
proveth
,
that
not
onely
the
Comets
,
but
also
the
new
stars
,
namely
,
that
anno
1572.
in
Cassiopeia
,
and
that
anno
1604.
in
Sagittarius
were
not
above
the
Spheres
of
the
Planets
,
but
absolutely
beneath
the
concave
of
the
Moon
in
the
Elementary
Sphere
,
and
this
he
demonstrateth
against
Tycho
,
Kepler
,
and
many
other
Astronomical
Observators
,
and
beateth
them
at
their
own
weapon
;
to
wit
,
the
Doctrine
of
Parallaxes
.
If
you
like
thereof
,
I
will
give
you
the
reasons
of
both
these
Authours
,
for
I
have
read
them
more
than
once
,
with
attention
;
and
you
may
examine
their
strength
,
and
give
your
opinion
thereon
.
SALV
.
In
regard
that
our
principal
end
is
to
bring
upon
the
stage
,
and
to
consider
what
ever
hath
been
said
for
,
or
against
the
two
Systemes
,
Ptolomaick
,
and
Copernican
,
it
is
not
good
to
omit
any
thing
that
hath
been
written
on
this
subject
.
SIMP.
I
will
begin
therefore
with
the
objections
which
I
finde
in
the
Treatise
of
Conclusions
,
and
afterwards
proceed
to
the
rest
.
The
first
objection
of
the
modern
Author
of
the
little
tract
of
Conclusions
.
In
the
first
place
then
,
he
bestoweth
much
paines
in
calculating
exactly
how
many
miles
an
hour
a
point
of
the
terrestrial
Globe
situate
under
the
Equinoctial
,
goeth
,
and
how
many
miles
are
past
by
other
points
situate
in
other
parallels
:
and
not
being
content
with
finding
out
such
motions
in
horary
times
,
he
findeth
them
also
in
a
minute
of
an
hour
;
and
not
contenting
himself
with
a
minute
,
he
findes
them
also
in
a
second
minute
;
yea
more
,
he
goeth
on
to
shew
plainly
,
how
many
miles
a
Cannon
bullet
would
go
in
the
same
time
,
A
Cannon
bullet
would
spend
more
than
six
days
in
falling
from
the
Concave
of
the
Moon
to
the
centre
of
the
Earth
,
according
to
the
opinion
of
that
modern
Author
of
the
Conclusions
.
being
placed
in
the
concave
of
the
Lunar
Orb
,
supposing
it
also
as
big
as
Copernicus
himself
representeth
it
,
to
take
away
all
subterfuges
from
his
adversary
.
And
having
made
this
most
ingenious
and
exquisite
supputation
,
he
sheweth
,
that
a
grave
body
falling
from
thence
above
would
consume
more
than
six
dayes
in
attaining
to
the
centre
of
the
Earth
,
to
which
all
grave
bodies
naturally
move
.
Now
if
by
the
absolute
Divine
Power
,
or
by
some
Angel
,
a
very
great
Cannon
bullet
were
carried
up
thither
,
and
placed
in
our
Zenith
or
vertical
point
,
and
from
thence
let
go
at
liberty
,
it
is
in
his
,
and
also
in
my
opinion
,
a
most
incredible
thing
that
it
,
in
descending
downwards
,
should
all
the
way
maintain
it self
in
our
vertical
line
,
continuing
to
turn
round
with
the
Earth
,
about
its
centre
,
for
so
many
dayes
,
describing
under
the
Equinoctial
a
Spiral
line
in
the
plain
of
the
great
circle
it self
;
and
under
other
Parallels
,
Spiral
lines
about
Cones
,
and
under
the
Poles
falling
by
a
simple
right
line
.
He
,
in
the
next
place
,
stablisheth
and
confirmeth
this
great
improbability
by
proving
,
in
the
way
of
interrogations
,
many
difficulties
impossible
to
be
removed
by
the
followers
of
Copernicus
;
and
they
are
,
if
I
do
well
remember
—
.
SALV
.
Take
up
a
little
,
good
Simplicius
,
and
do
not
load
me
with
so
many
novelties
at
once
:
I
have
but
a
bad
memory
,
and
therefore
I
must
not
go
too
fast
.
And
in
regard
it
cometh
into
my
minde
,
that
I
once
undertook
to
calculate
how
long
time
such
a
grave
body
falling
from
the
concave
of
the
Moon
,
would
be
in
passing
to
the
centre
of
the
Earth
,
and
that
I
think
I
remember
that
the
time
would
not
be
so
long
;
it
would
be
fit
that
you
shew
us
by
what
rule
this
Author
made
his
calculation
.
SIMP.
He
hath
done
it
by
proving
his
intent
à
fortiori
,
a
sufficient
advantage
for
his
adversaries
,
supposing
that
the
velocity
of
the
body
falling
along
the
vertical
line
,
towards
the
centre
of
the
Earth
,
were
equal
to
the
velocity
of
its
circular
motion
,
which
it
made
in
the
grand
circle
of
the
concave
of
the
Lunar
Orb.
Which
by
equation
would
come
to
passe
in
an
hour
,
twelve
thousand
six
hundred
German
miles
,
a
thing
which
indeed
savours
of
impossibility
:
Yet
neverthelesse
,
to
shew
his
abundant
caution
,
and
to
give
all
advantages
to
his
adversaries
,
he
supposeth
it
for
true
,
and
concludeth
,
that
the
time
of
the
fall
ought
however
to
be
more
than
six
dayes
.
SALV
.
And
is
this
the
sum
of
his
method
?
And
doth
he
by
this
demonstration
prove
the
time
of
the
fall
to
be
above
six
dayes
?
SAGR.
Me
thinks
that
he
hath
behaved
himself
too
modestly
,
for
that
having
it
in
the
power
of
his
will
to
give
what
velocity
he
pleased
to
such
a
descending
body
,
and
might
aswell
have
made
it
six
moneths
,
nay
,
six
years
in
falling
to
the
Earth
,
he
is
content
with
six
dayes
.
But
,
good
Salviatus
,
sharpen
my
appetite
a
little
,
by
telling
me
in
what
manner
you
made
your
computation
,
in
regard
you
say
,
that
you
have
heretofore
cast
it
up
:
for
I
am
confident
that
if
the
question
had
not
required
some
ingenuity
in
working
it
,
you
would
never
have
applied
your
minde
unto
it
.
SALV
.
It
is
not
enough
,
Sagredus
,
that
the
subjects
be
noble
and
great
,
but
the
businesse
consists
in
handling
it
nobly
.
And
who
knoweth
not
,
that
in
the
dissection
of
the
members
of
a
beast
,
there
may
be
discovered
infinite
wonders
of
provident
and
prudent
Nature
;
and
yet
for
one
,
that
the
Anatomist
dissects
,
the
butcher
cuts
up
a
thousand
.
Thus
I
,
who
am
now
seeking
how
to
satisfie
your
demand
,
cannot
tell
with
which
of
the
two
shapes
I
had
best
to
appear
on
the
Stage
;
but
yet
,
taking
heart
from
the
example
of
Simplicius
,
his
Authour
,
I
will
,
without
more
delays
,
give
you
an
account
(
if
I
have
not
forgot
)
how
I
proceeded
.
But
before
I
go
any
further
,
I
must
not
omit
to
tell
you
,
that
I
much
fear
that
Simplicius
hath
not
faithfully
related
the
manner
how
this
his
Authour
found
,
that
the
Cannon
bullet
in
coming
from
the
concave
of
the
Moon
to
the
centre
of
the
Earth
,
would
spend
more
than
six
dayes
:
for
if
he
had
supposed
that
its
velocity
in
descending
was
equal
to
that
of
the
concave
(
as
Simplicius
saith
he
doth
suppose
)
he
would
have
shewn
himself
ignorant
of
the
first
,
and
more
simple
principles
of
Geometry
;
yea
,
I
admire
that
Simplicius
,
in
admitting
the
supposition
which
he
speaketh
of
,
doth
not
see
the
monstrous
absurdity
that
is
couched
in
it
.
SIMP.
It
s
possible
that
I
may
have
erred
in
relating
it
;
but
that
I
see
any
fallacy
in
it
,
I
am
sure
is
not
true
.
SALV
.
Perhaps
I
did
not
rightly
apprehend
that
which
you
said
,
Do
you
not
say
,
that
this
Authour
maketh
the
velocity
of
the
bullet
in
descending
equall
to
that
which
it
had
in
turning
round
,
being
in
the
concave
of
the
Moon
,
and
that
comming
down
with
the
same
velocity
,
it
would
reach
to
the
centre
in
six
dayes
?
SIMP.
So
,
as
I
think
,
he
writeth
.
SALV
.
And
do
not
you
pe●ceive
a
shamefull
errour
therein
?
But
questionlesse
you
dissemble
it
:
For
it
cannot
be
,
but
that
you
should
know
that
the
semidiameter
of
the
Circle
is
lesse
than
the
sixth
part
of
the
circumference
;
A
shamefull
errour
in
the
Argument
taken
from
the
bullets
falling
out
of
the
Moons
concave
.
and
that
consequently
,
the
time
in
which
the
moveable
shall
passe
the
semidiameter
,
shall
be
lesse
than
the
sixth
part
of
the
time
;
in
which
,
being
moved
with
the
same
velocity
,
it
would
passe
the
circumference
;
and
that
therefore
the
bullet
descending
with
the
velocity
,
wherewith
it
moved
in
the
concave
,
will
arrive
in
lesse
than
four
hours
at
the
centre
,
supposing
that
in
the
concave
one
revolution
should
be
consummate
in
twenty
four
hours
,
as
he
must
of
necessity
have
supposed
it
,
for
to
keep
it
all
the
way
in
the
same
vertical
line
.
SIMP.
Now
I
thorowly
perceive
the
mistake
:
but
yet
I
would
not
lay
it
upon
him
undeservedly
,
for
it
's
possible
that
I
may
have
erred
in
rehearsing
his
Argument
,
and
to
avoid
running
into
the
same
mistakes
for
the
future
,
I
could
wish
I
had
his
Book
;
and
if
you
had
any
body
to
send
for
it
,
I
would
take
it
for
a
great
favour
.
SAGR.
You
shall
not
want
a
Lacquey
that
will
runne
for
it
with
all
speed
:
and
he
shall
do
it
presently
,
without
losing
any
time
;
in
the
mean
time
Salviatus
may
please
to
oblige
us
with
his
computation
.
SIMP.
If
he
go
,
he
shall
finde
it
lie
open
upon
my
Desk
,
together
with
that
of
the
other
Author
,
who
also
argueth
against
Copernicus
.
SAGR.
We
will
make
him
bring
that
also
for
the
more
certainty
:
and
in
the
interim
Salviatus
shall
make
his
calculation
:
I
have
dispatch't
away
a
messenger
.
SALV
.
Above
all
things
it
must
be
considered
,
that
the
motion
of
descending
grave
bodies
is
not
uniform
,
but
departing
from
rest
they
go
continually
accelerating
:
An
exact
compute
of
the
time
of
the
fall
of
the
Canon
bullet
from
the
Moons
concave
to
the
Earths
centre
.
An
effect
known
and
observed
by
all
men
,
unlesse
it
be
by
the
forementioned
modern
Authour
,
who
not
speaking
of
acceleration
,
maketh
it
even
and
uniforme
.
But
this
general
notion
is
of
no
avail
,
if
it
be
not
known
according
to
what
proportion
this
increase
of
velocity
is
made
;
a
conclusion
that
hath
been
until
our
times
unknown
to
all
Philosophers
;
and
was
first
found
out
&
demonstrated
by
the
[
](A61244-e46690-b)*
*
The
Author
.
Academick
,
our
common
friend
,
who
in
some
of
his
[
](A61244-e46710-b)*
*
By
these
Writings
,
he
every
where
meanes
his
Dialogues
,
De
motu
,
which
I
promise
to
give
you
in
my
second
Volume
.
writings
not
yet
published
,
but
in
familiarity
shewn
to
me
,
and
some
others
of
his
acquaintance
he
proveth
,
how
that
the
acceleration
of
the
right
motion
of
grave
bodies
,
is
made
according
to
the
numbers
uneven
beginning
ab
unitate
,
that
is
,
any
number
of
equal
times
being
assigned
,
if
in
the
first
time
the
moveable
departing
from
rest
shall
have
passed
such
a
certain
space
,
Acceleration
of
the
natural
motion
of
grave
bodies
is
made
according
to
the
odde
numbers
beginning
at
unity
.
as
for
example
,
an
ell
,
in
the
second
time
it
shall
have
passed
three
ells
,
in
the
third
five
,
in
the
fourth
seven
,
and
so
progressively
,
according
to
the
following
odd
numbers
;
which
in
short
is
the
same
,
as
if
I
should
say
,
that
the
spaces
passed
by
the
moveable
departing
from
its
rest
,
The
spaces
past
by
the
falling
grave
body
are
as
the
squares
of
their
times
.
are
unto
each
other
in
proportion
double
to
the
proportion
of
the
times
,
in
which
those
spaces
are
measured
;
or
we
will
say
,
that
the
spaces
passed
are
to
each
other
,
as
the
squares
of
their
times
.
SAGR.
This
is
truly
admirable
:
and
do
you
say
that
there
is
a
Mathematical
demonstration
for
it
?
SALV
.
Yes
,
purely
Mathematical
;
and
not
onely
for
this
,
but
for
many
other
very
admirable
passions
,
pertaining
to
natural
motions
,
An
intire
and
new
Science
of
the
Academick
concerning
local
motion
.
and
to
projects
also
,
all
invented
,
and
demonstrated
by
Our
Friend
,
and
I
have
seen
and
considered
them
all
to
my
very
great
content
and
admiration
,
seeing
a
new
compleat
Doctrine
to
spring
up
touching
a
subject
,
upon
which
have
been
written
hundreds
of
Volumes
;
and
yet
not
so
much
as
one
of
the
infinite
admirable
conclusions
that
those
his
writings
contain
,
hath
ever
been
observed
,
or
understood
by
any
one
,
before
Our
Friend
made
them
out
.
SAGR.
You
make
me
lose
the
desire
I
had
to
understand
more
in
our
disputes
in
hand
,
onely
that
I
may
hear
some
of
those
demonstrations
which
you
speak
of
;
therefore
either
give
them
me
presently
,
or
at
least
promise
me
upon
your
word
,
to
appoint
a
particular
conference
concerning
them
,
at
which
Simplicius
also
may
be
present
,
if
he
shall
have
a
mind
to
hear
the
passions
and
accidents
of
the
primary
effect
in
Nature
.
SIMP.
I
shall
undoubtedly
be
much
pleased
therewith
,
though
indeed
,
as
to
what
concerneth
Natural
Philosophy
,
I
do
not
think
that
it
is
necessary
to
descend
unto
minute
particularities
,
a
general
knowledg
of
the
definition
of
motion
,
and
of
the
distinction
of
natural
and
violent
,
even
and
accelerate
,
and
the
like
,
sufficing
:
For
if
this
were
not
sufficient
,
I
do
not
think
that
Aristotle
would
have
omitted
to
have
taught
us
what
ever
more
was
necessary
.
SALV
.
It
may
be
so
.
But
let
us
not
lose
more
time
about
this
,
which
I
promise
to
spend
half
a
day
apart
in
,
for
your
satisfaction
;
nay
,
now
I
remember
,
I
did
promise
you
once
before
to
satisfie
you
herein
.
Returning
therefore
to
our
begun
calculation
of
the
time
,
wherein
the
grave
cadent
body
would
pass
from
the
concave
of
the
Moon
to
the
centre
of
the
earth
,
that
we
may
not
proceed
arbitrarily
and
at
randon
,
but
with
a
Logical
method
,
we
will
first
attempt
to
ascertain
our selves
by
experiments
often
repeated
,
in
how
long
time
a
ball
v.
g.
of
Iron
descendeth
to
the
Earth
from
an
altitude
of
an
hundred
yards
.
SAGR.
Let
us
therefore
take
a
ball
of
such
a
determinate
weight
,
and
let
it
be
the
same
wherewith
we
intend
to
make
the
computation
of
the
time
of
descent
from
the
Moon
.
SALV
.
This
is
not
material
,
for
that
a
ball
of
one
,
of
ten
,
of
an
hundred
,
of
a
thousand
pounds
,
will
all
measure
the
same
hundred
yards
in
the
same
time
.
SIMP.
But
this
I
cannot
believe
,
nor
much
less
doth
Aristotle
think
so
,
who
writeth
,
that
the
velocities
of
descending
grave
bodies
,
are
in
the
same
proportion
to
one
another
,
as
their
gravities
.
SALV
.
If
you
will
admit
this
for
true
,
The
error
of
Aristotle
in
affirming
,
falling
grave
bodies
to
move
according
to
the
proportion
of
their
gravities
.
you
must
believe
also
,
that
two
balls
of
the
same
matter
,
being
let
fall
in
the
same
moment
,
one
of
an
hundred
pounds
,
and
another
of
one
,
from
an
altitude
of
an
hundred
yards
,
the
great
one
arriveth
at
the
ground
,
before
the
other
is
descended
but
one
yard
onely
:
Now
bring
your
fancy
,
if
you
can
,
to
imagine
,
that
you
see
the
great
ball
got
to
the
ground
,
when
the
little
one
is
still
within
less
than
a
yard
of
the
top
of
the
Tower
.
SAGR.
That
this
proposition
is
most
false
,
I
make
no
doubt
in
the
world
;
but
yet
that
yours
is
absolutely
true
,
I
cannot
well
assure
my self
:
nevertheless
,
I
believe
it
,
seeing
that
you
so
resolutely
affirm
it
;
which
I
am
sure
you
would
not
do
,
if
you
had
not
certain
experience
,
or
some
clear
demonstration
thereof
.
SALV
.
I
have
both
:
and
when
we
shall
handle
the
business
of
motions
apart
,
I
will
communicate
them
:
in
the
interim
,
that
we
may
have
no
more
occasions
of
interrupting
our
discourse
,
we
will
suppose
,
that
we
are
to
make
our
computation
upon
a
ball
of
Iron
of
an
hundred
[
](A61244-e47200-b)a
a
Note
that
these
Calculations
are
made
in
Italian
weights
and
measu●es
.
And
100
pounds
Haverdupoise
make
1●1
l.
Florentine
.
And
100
Engl●●
〈◊〉
makes
150●
〈◊〉
Florent
.
so
that
the
brace
or
yard
of
our
Author
is
1/4
of
our
yard
.
pounds
,
the
which
by
reiterated
experiments
descendeth
from
the
altitude
of
an
hundred
[
](A61244-e47260-b)b
b
Note
that
these
Calculations
are
made
in
Italian
weights
and
measures
.
And
100
pounds
Haverdupoise
make
1●1
l.
Florentine
.
And
100
Engl●●
〈◊〉
makes
150●
〈◊〉
Florent
.
so
that
the
brace
or
yard
of
our
Author
is
1/4
of
our
yard
.
yards
,
in
five
second-minutes
of
an
hour
.
And
because
,
as
we
have
said
,
the
spaces
that
are
measured
by
the
cadent
moveable
,
increase
in
double
proportion
;
that
is
,
according
to
the
squares
of
the
times
,
being
that
the
time
of
one
first-minute
is
duodecuple
to
the
time
of
five
seconds
,
if
we
multiply
the
hundred
yards
by
the
square
of
12
,
that
is
by
144
,
we
shall
have
14400
,
which
shall
be
the
number
of
yards
that
the
same
moveable
shall
pass
in
one
first-minute
of
an
hour
:
and
following
the
same
rule
because
one
hour
is
60
minutes
,
multiplying
14400
,
the
number
of
yards
past
in
one
minute
,
by
the
square
of
60
,
that
is
,
by
3600
,
there
shall
come
forth
51840000
,
the
number
of
yards
to
be
passed
in
an
hour
,
which
make
17280
miles
.
And
desiring
to
know
the
space
that
the
said
ball
would
pass
in
4
hours
,
let
us
multiply
17280
by
16
,
(
which
is
the
square
of
4
)
and
the
product
will
be
276480
miles
:
which
number
is
much
greater
than
the
distance
from
the
Lunar
concave
to
the
centre
of
the
Earth
,
which
is
but
196000
miles
,
making
the
distance
of
the
concave
56
semidiameters
of
the
Earth
,
as
that
modern
Author
doth
;
and
the
semidiameter
of
the
Earth
3500
miles
,
of
3000
[
](A61244-e47320-b)*
*
The
Italian
measure
which
I
commonly
transl●te
yards
.
Braces
to
a
[
](A61244-e47350-b)†
†
The
Italian
m●le
is
〈◊〉
of
our
mile
.
mile
,
which
are
our
Italian
miles
.
Therefore
,
Simplicius
,
that
space
from
the
concave
of
the
Moon
to
the
centre
of
the
Earth
,
which
your
Accomptant
said
could
not
be
passed
under
more
than
six
days
,
you
see
that
(
computing
by
experience
,
and
not
upon
the
fingers
ends
)
that
it
shall
be
passed
in
much
less
than
four
hours
;
and
making
the
computation
exact
,
it
shall
be
passed
by
the
moveable
in
3
hours
,
22
min.
prim
.
and
4
seconds
.
SAGR.
I
beseech
you
,
dear
Sir
,
do
not
defraud
me
of
this
exact
calculation
,
for
it
must
needs
be
very
excellent
.
SALV
.
So
indeed
it
is
:
therefore
having
(
as
I
have
said
)
by
diligent
tryal
observed
,
that
such
a
moveable
passeth
in
its
descent
,
the
height
of
100
yards
in
5
seconds
of
an
hour
,
we
will
say
,
if
100
yards
are
passed
in
5
seconds
;
in
how
many
seconds
shall
588000000
yards
(
for
so
many
are
in
56
diameters
of
the
Earth
)
be
passed
?
The
rule
for
this
work
is
,
that
the
third
number
must
be
multiplied
by
the
square
of
the
second
,
of
which
doth
come
14700000000
,
which
ought
to
be
divided
by
the
first
,
that
is
,
by
100
,
and
the
root
square
of
the
quotient
,
that
is
,
12124
is
the
number
sought
,
namely
12124
min.
secun
.
of
an
hour
,
which
are
3
hours
,
22
min.
prim
.
and
4
seconds
.
SAGR.
I
have
seen
the
working
,
but
I
know
nothing
of
the
reason
for
so
working
,
nor
do
I
now
think
it
a
time
to
ask
it
.
SALV
.
Yet
I
will
give
it
,
though
you
do
not
ask
it
,
because
it
is
very
easie
.
Let
us
mark
these
three
numbers
with
the
Letters
A
first
,
B
second
,
C
third
.
A
and
C
are
the
numbers
of
the
spaces
,
B
is
the
number
of
the
time
;
the
fourth
number
is
sought
,
of
the
time
also
.
And
because
we
know
,
that
look
what
proportion
the
space
A
,
hath
to
the
spuace
C
,
the
same
proportion
shall
the
square
of
the
time
B
have
to
the
sqare
of
the
time
,
which
is
sought
.
100.
|
5.
|
588000000.
|
A
|
B
|
C
|
25
|
1
|
-
14700000000
-
35956
-
10
|
22
|
241
|
60
|
-
12124
-
202
-
3
|
2422
|
24240
|
Therefore
by
the
Golden
Rule
,
let
the
number
C
be
multiplied
by
the
square
of
the
number
B
,
and
let
the
product
be
divided
by
the
number
A
,
and
the
quotient
shall
be
the
square
of
the
number
sought
,
and
its
square
root
shall
be
the
number
it self
that
is
sought
.
Now
you
see
how
easie
it
is
to
be
understood
.
SAGR.
So
are
all
truths
,
when
once
they
are
found
out
,
but
the
difficulty
lyeth
in
finding
them
I
very
well
apprehend
it
,
and
kindly
thank
you
.
And
if
there
remain
any
other
curiosity
touching
this
point
,
I
pray
you
let
us
hear
it
;
for
if
I
may
speak
my
mind
,
I
will
with
the
favour
of
Simplicius
,
that
from
your
discourses
I
alwayes
learn
some
new
motion
,
but
from
those
of
his
Philosophers
,
I
do
not
remember
that
I
have
learn't
any
thing
of
moment
.
SALV
.
There
might
be
much
more
said
touching
these
local
motions
;
but
according
to
agreement
,
we
will
reserve
it
to
a
particular
conference
;
and
for
the
present
I
will
speak
something
touching
the
Author
named
by
Simplicius
,
who
thinketh
he
hath
given
a
great
advantage
to
the
adverse
party
in
granting
that
,
that
Canon
bullet
in
falling
from
the
concave
of
the
Moon
may
descend
with
a
velocity
equal
to
the
velocity
wherewith
it
would
turn
round
,
staying
there
above
,
and
moving
along
with
the
diurnal
conversion
.
Now
I
tell
him
,
that
that
same
ball
falling
from
the
concave
unto
the
centre
,
will
acquire
a
degree
of
velocity
much
more
than
double
the
velocity
of
the
diurnal
motion
of
the
Lunar
concave
;
The
falling
moveable
if
it
move
with
a
degree
of
velocity
acquired
in
a
like
time
with
an
uniform
motion
,
it
shall
pass
a
space
double
to
that
passed
with
the
accelerated
motion
.
and
this
I
will
make
out
by
solid
and
not
impertinent
suppositions
.
You
must
know
therefore
that
the
grave
body
falling
and
acquiring
all
the
way
new
velocity
according
to
the
proportion
already
mentioned
,
hath
in
any
whatsoever
place
of
the
line
of
its
motion
such
a
degree
of
velocity
,
that
if
it
should
continue
to
move
therewith
,
uniformly
without
farther
encreasing
it
;
in
another
time
like
to
that
of
its
descent
,
it
would
passe
a
space
double
to
that
passed
in
the
line
of
the
precedent
motion
of
descent
.
And
thus
for
example
,
if
that
ball
in
coming
from
the
concave
of
the
Moon
to
its
centre
hath
spent
three
hours
,
22
min.
prim
.
and
4
seconds
,
I
say
,
that
being
arrived
at
the
centre
,
it
shall
find
it self
constituted
in
such
a
degree
of
velocity
,
that
if
with
that
,
without
farther
encreasing
it
,
it
should
continue
to
move
uniformly
,
it
would
in
other
3
hours
,
22
min.
prim
.
and
4
seconds
,
passe
double
that
space
,
namely
as
much
as
the
whole
diameter
of
the
Lunar
Orb
;
and
because
from
the
Moons
concave
to
the
centre
are
196000
miles
,
which
the
ball
passeth
in
3
hours
22
prim
.
min.
and
4
seconds
,
therefore
(
according
to
what
hath
been
said
)
the
ball
continuing
to
move
with
the
velocity
which
it
is
found
to
have
in
its
arrival
at
the
centre
,
it
would
passe
in
other
3
hours
22
min.
prim
.
and
4
seconds
,
a
space
double
to
that
,
namely
392000
miles
;
but
the
same
continuing
in
the
concave
of
the
Moon
,
which
is
in
circuit
1232000
miles
,
and
moving
therewith
in
a
diurnal
motion
,
it
would
make
in
the
same
time
,
that
is
in
3
hours
22
min.
prim
.
and
4
seconds
,
172880
miles
,
which
are
fewer
by
many
than
the
half
of
the
392000
miles
.
You
see
then
that
the
motion
in
the
concave
is
not
as
the
modern
Author
saith
,
that
is
,
of
a
velocity
impossible
for
the
falling
ball
to
partake
of
,
&c.
SAGR.
The
discourse
would
pass
for
current
,
and
would
give
me
full
satisfaction
,
if
that
particular
was
but
salved
,
of
the
moving
of
the
moveable
by
a
double
space
to
that
passed
in
falling
in
another
time
equal
to
that
of
the
descent
,
in
case
it
doth
continue
to
move
uniformly
with
the
greatest
degree
of
velocity
acquired
in
descending
.
A
proposition
which
you
also
once
before
supposed
as
true
,
but
never
demonstrated
.
SALV
.
This
is
one
of
the
demonstrations
of
Our
Friend
,
and
you
shall
see
it
in
due
time
;
but
for
the
present
,
I
will
with
some
conjectures
(
not
teach
you
any
thing
that
is
new
,
but
)
remember
you
of
a
certain
contrary
opinion
,
and
shew
you
,
that
it
may
haply
so
be
.
A
bullet
of
lead
hanging
in
a
long
and
fine
thread
fastened
to
the
roof
,
if
we
remove
it
far
from
perpendicularity
,
and
then
let
it
go
,
have
you
not
observed
that
,
it
declining
,
will
pass
freely
,
and
well
near
as
far
to
the
other
side
of
the
perpendicular
?
SAGR.
I
have
observed
it
very
well
,
and
find
(
especially
if
the
plummet
be
of
any
considerable
weight
)
that
it
riseth
so
little
less
than
it
descended
,
so
that
I
have
sometimes
thought
,
that
the
ascending
arch
is
equal
to
that
descending
,
and
thereupon
made
it
a
question
whether
the
vibrations
might
not
perpetuate
themselves
;
and
I
believe
that
they
might
,
The
motion
of
grave
penduli
might
be
perpetuated
,
impediments
being
removed
.
if
that
it
were
possible
to
remove
the
impediment
of
the
Air
,
which
resisting
penetration
,
doth
some
small
matter
retard
and
impede
the
motion
of
the
pendulum
,
though
indeed
that
impediment
is
but
small
:
in
favour
of
which
opinion
the
great
number
of
vibrations
that
are
made
before
the
moveable
wholly
ceaseth
to
move
,
seems
to
plead
.
SALV
.
The
motion
would
not
be
perpetual
,
Sagredus
,
although
the
impediment
of
the
Air
were
totally
removed
,
because
there
is
another
much
more
abstruse
.
SAGR.
And
what
is
that
?
as
for
my
part
I
can
think
of
no
other
?
SALV
.
You
will
be
pleased
when
you
hear
it
,
but
I
shall
not
tell
it
you
till
anon
:
in
the
mean
time
,
let
us
proceed
.
I
have
proposed
the
observation
of
this
Pendulum
,
to
the
intent
,
that
you
should
understand
,
that
the
impetus
acquired
in
the
descending
arch
,
where
the
motion
is
natural
,
is
of
it self
able
to
drive
the
said
ball
with
a
violent
motion
,
as
far
on
the
other
side
in
the
like
ascending
arch
;
if
so
,
I
say
,
of
it self
,
all
external
impediments
being
removed
:
I
believe
also
that
every
one
takes
it
for
granted
,
that
as
in
the
descending
arch
the
velocity
all
the
way
increaseth
,
till
it
come
to
the
lowest
point
,
or
its
perpendicularity
;
so
from
this
point
,
by
the
other
ascending
arch
,
it
all
the
way
diminisheth
,
untill
it
come
to
its
extreme
and
highest
point
:
and
diminishing
with
the
same
proportions
,
wherewith
it
did
before
increase
,
so
that
the
dgrees
of
the
velocities
in
the
points
equidistant
from
the
point
of
perpendicularity
,
are
equal
to
each
other
.
Hence
it
seemeth
to
me
(
arguing
with
all
due
modesty
)
that
I
might
easily
be
induced
to
believe
,
If
the
Terrestrial
Globe
were
perforated
,
a
grave
body
descending
by
that
bore
,
would
pass
and
ascend
as
far
beyond
the
centre
,
as
it
did
descend
.
that
if
the
Terrestrial
Globe
were
bored
thorow
the
centre
,
a
Canon
bullet
descending
through
that
Well
,
would
acquire
by
that
time
it
came
to
the
centre
,
such
an
impulse
of
velocity
,
that
,
it
having
passed
beyond
the
centre
,
would
spring
it
upwards
the
other
way
,
as
great
a
space
,
as
that
was
wherewith
it
had
descended
,
all
the
way
beyond
the
centre
diminishing
the
velocity
with
decreasements
like
to
the
increasements
acquired
in
the
descent
:
and
the
time
spent
in
this
second
motion
of
ascent
,
I
believe
,
would
be
equal
to
the
time
of
descent
.
Now
if
the
moveable
by
diminishing
that
its
greatest
degree
of
velocity
which
it
had
in
the
centre
,
successively
until
it
come
to
total
extinction
,
do
carry
the
moveable
in
such
a
time
such
a
certain
space
,
as
it
had
gone
in
such
a
like
quantity
of
time
,
by
the
acquist
of
velocity
from
the
total
privation
of
it
until
it
came
to
that
its
greatest
degree
;
it
seemeth
very
reasonable
,
that
if
it
should
move
always
with
the
said
greatest
degree
of
velocity
it
would
pass
,
in
such
another
quantity
of
time
,
both
those
spaces
:
For
if
we
do
but
in
our
mind
successively
divide
those
velocities
into
rising
and
falling
degrees
,
as
v.
g.
these
numbers
in
the
margine
;
so
that
the
first
sort
unto
10
be
supposed
the
increasing
velocities
,
and
the
others
unto
one
1
,
be
the
increasing
;
and
let
those
of
the
time
of
the
descent
,
and
the
others
of
the
time
of
the
ascent
being
added
all
together
,
make
as
many
,
as
if
one
of
the
two
sums
of
them
had
been
all
of
the
greatest
degrees
,
and
therefore
the
whole
space
passed
by
all
the
degrees
of
the
increasing
velocities
,
and
decreasing
,
(
which
put
together
is
the
whole
diameter
)
ought
to
be
equal
to
the
space
passed
by
the
greatest
velocities
,
that
are
in
number
half
the
aggregate
of
the
increasing
and
decreasing
velocities
.
I
know
that
I
have
but
obscurely
expressed
my self
,
and
I
wish
I
may
be
understood
.
SAGR.
I
think
I
understand
you
very
well
;
and
also
that
I
can
in
a
few
words
shew
,
that
I
do
understand
you
.
You
had
a
mind
to
say
,
that
the
motion
begining
from
rest
,
and
all
the
way
increasing
the
velocity
with
equal
augmentations
,
such
as
are
those
of
continuate
numbers
beginning
at
1
,
rather
at
0
,
which
representeth
the
state
of
rest
,
disposed
as
in
the
margine
:
and
continued
at
pleasure
,
so
as
that
the
least
degree
may
be
0
,
and
the
greatest
v.
g.
5
,
all
these
degrees
of
velocity
wherewith
the
moveable
is
moved
,
make
the
sum
of
15
;
but
if
the
moveable
should
move
with
as
many
degrees
in
number
as
these
are
,
and
each
of
them
equal
to
the
biggest
,
which
is
5
,
the
aggregate
of
all
these
last
velocities
would
be
double
to
the
others
,
namely
30.
And
therefore
the
moveable
moving
with
a
like
time
,
but
with
uniform
velocity
,
which
is
that
of
the
highest
degree
5
,
ought
to
pass
a
space
double
to
that
which
it
passeth
in
the
accelerate
time
,
which
beginneth
at
the
state
of
rest
.
SALV
.
According
to
your
quick
and
piercing
way
of
apprehending
things
,
you
have
explained
the
whole
business
with
more
plainness
than
I
my self
;
and
put
me
also
in
mind
of
adding
something
more
:
for
in
the
accelerate
motion
,
the
augmentation
being
continual
,
you
cannot
divide
the
degrees
of
velocity
,
which
continually
increase
,
into
any
determinate
number
,
because
changing
every
moment
,
they
are
evermore
infinite
.
Therefore
we
shall
be
the
better
able
to
exemplifie
our
intentions
by
describing
a
Triangle
,
which
let
be
this
ABC
,
[
in
Fig.
8.
]
taking
in
the
side
AC
,
as
many
equal
parts
as
we
please
,
AD
,
DE
,
EF
,
FG
,
and
drawing
by
the
points
D
,
E
,
F
,
G
,
right
lines
parallel
to
the
〈◊〉
BC.
Now
let
us
imagine
the
parts
marked
in
the
line
AC
,
to
be
equal
times
,
and
let
the
parallels
drawn
by
the
points
D
,
E
,
F
,
G
,
represent
unto
us
the
degrees
of
velocity
accelerated
,
and
increasing
equally
in
equal
times
;
and
let
the
Point
A
be
the
state
of
rest
,
from
which
the
moveable
departing
,
hath
v.
g.
in
the
time
AD
,
acquired
the
degree
of
velocity
DH
,
in
the
second
time
we
will
suppose
,
that
it
hath
increased
the
velocity
from
DH
,
as
far
as
to
EI
,
and
so
supposing
it
to
have
grown
greater
in
the
succeeding
times
,
The
acceleration
of
grave
bodies
naturally
descendent
,
increaseth
from
moment
to
moment
.
according
to
the
increase
of
the
lines
FK
,
GL
,
&c.
but
because
the
acceleration
is
made
continually
from
moment
to
moment
,
and
not
disjunctly
from
one
certain
part
of
time
to
another
;
the
point
A
being
put
for
the
lowest
moment
of
velocity
,
that
is
,
for
the
state
of
rest
,
and
AD
for
the
first
instant
of
time
following
;
it
is
manifest
,
that
before
the
acquist
of
the
degree
of
velocity
DH
,
made
in
the
time
AD
,
the
moveable
must
have
past
by
infinite
other
lesser
and
lesser
degrees
gained
in
the
infinite
instants
that
are
in
the
time
DA
,
answering
the
infinite
points
that
are
in
the
line
DA
;
therefore
to
represent
unto
us
the
infinite
degrees
of
velocity
that
precede
the
degree
DH
,
it
is
necessary
to
imagine
infinite
lines
successively
lesser
and
lesser
,
which
are
supposed
to
be
drawn
by
the
infinite
points
of
the
line
DA
,
and
parallels
to
DH
,
the
which
infinite
lines
represent
unto
us
the
superficies
of
the
Triangle
AHD
,
and
thus
we
may
imagine
any
space
passed
by
the
moveable
,
with
a
motion
which
begining
at
rest
,
goeth
uniformly
accelerating
,
to
have
spent
and
made
use
of
infinite
degrees
of
velocity
,
increasing
according
to
the
infinite
lines
that
begining
from
the
point
A
,
are
supposed
to
be
drawn
parallel
to
the
line
HD
,
and
to
the
rest
IE
,
KF
,
LG
,
the
motion
continuing
as
far
as
one
will
.
Now
let
us
compleat
the
whole
Parallelogram
AMBC
,
and
let
us
prolong
as
far
as
to
the
side
thereof
BM
,
not
onely
the
Parallels
marked
in
the
Triangle
,
but
those
infinite
others
imagined
to
be
drawn
from
all
the
points
of
the
side
AC
;
and
like
as
BC
,
was
the
greatest
of
those
infinite
parallels
of
the
Triangle
,
representing
unto
us
the
greatest
degree
of
velocity
acquired
by
the
moveable
in
the
accelerate
motion
,
and
the
whole
superficies
of
the
said
Triangle
,
was
the
mass
and
sum
of
the
whole
velocity
,
wherewith
in
the
time
AC
it
passed
such
a
certain
space
,
so
the
parallelogram
is
now
a
mass
and
aggregate
of
a
like
number
of
degrees
of
velocity
,
but
each
equal
to
the
greatest
BC
,
the
which
mass
of
velocities
will
be
double
to
the
mass
of
the
increasing
velocities
in
the
Triangle
,
like
as
the
said
Parallelogram
is
double
to
the
Triangle
:
and
therefore
if
the
moveable
,
that
falling
did
make
use
of
the
accelerated
degrees
of
velocity
,
answering
to
the
triangle
ABC
,
hath
passed
in
such
a
time
such
a
space
,
it
is
very
reasonable
and
probable
,
that
making
use
of
the
uniform
velocities
answering
to
the
parallelogram
,
it
shall
passe
with
an
even
motion
in
the
same
time
a
space
double
to
that
passed
by
the
accelerate
motion
.
SAGR.
I
am
entirely
satisfied
.
And
if
you
call
this
a
probable
Discourse
,
what
shall
the
necessary
demonstrations
be
?
I
wish
that
in
the
whole
body
of
common
Philosophy
,
I
could
find
one
that
was
but
thus
concludent
.
SIMP.
It
is
not
necessary
in
natural
Philosophy
to
seek
exquisite
Mathematical
evidence
.
In
natural
Sciences
it
is
not
necessary
to
seek
Mathematicall
evidence
.
SAGR.
But
this
point
of
motion
,
is
it
not
a
natural
question
?
and
yet
I
cannot
find
that
Aristotle
hath
demonstrated
any
the
least
accident
of
it
.
But
let
us
no
longer
divert
our
intended
Theme
,
nor
do
you
fail
,
I
pray
you
Salviatus
,
to
tell
me
that
which
you
hinted
to
me
to
be
the
cause
of
the
Pendulum's
quiescence
,
besides
the
resistance
of
the
Medium
ro
penetration
.
SALV
.
Tell
me
;
of
two
penduli
hanging
at
unequal
distances
,
doth
not
that
which
is
fastned
to
the
longer
threed
make
its
vibrations
more
seldome
?
SAGR.
Yes
,
The
pendulum
hanging
at
a
longer
th●eed
,
maketh
its
vibrations
more
seldome
than
the
pendulum
hanging
at
a
shorter
threed
.
if
they
be
moved
to
equall
distances
from
their
perpendicularity
.
SALV
.
This
greater
or
lesse
elongation
importeth
nothing
at
all
,
for
the
same
pendulum
alwayes
maketh
its
reciprocations
in
equall
times
,
be
they
longer
or
shorter
,
that
is
,
though
the
pendulum
be
little
or
much
removed
from
its
perpendicularity
,
The
vibrations
of
the
same
pendulum
are
made
with
the
same
frequency
,
whether
they
be
small
or
great
.
and
if
they
are
not
absolutely
equal
,
they
are
insensibly
different
,
as
experience
may
shew
you
:
and
though
they
were
very
unequal
,
yet
would
they
not
discountenance
,
but
favour
our
cause
.
Therefore
let
us
draw
the
perpendicular
AB
[
in
Fig.
9.
]
and
hang
from
the
point
A
,
upon
the
threed
AC
,
a
plummet
C
,
and
another
upon
the
same
threed
also
,
which
let
be
E
,
and
the
threed
AC
,
being
removed
from
its
perpendicularity
,
and
then
letting
go
the
plummets
C
and
E
,
they
shall
move
by
the
arches
CBD
,
EGF
,
and
the
plummet
E
,
as
hanging
at
a
lesser
distance
,
and
withall
,
as
(
by
what
you
said
)
lesse
removed
,
will
return
back
again
faster
,
and
make
its
vibrations
more
frequent
than
the
plummet
C
,
and
therefore
shall
hinder
the
said
plummet
C
,
from
running
so
much
farther
towards
the
term
D
,
as
it
would
do
,
if
it
were
free
:
and
thus
the
plummet
E
bringing
unto
it
in
every
vibration
continuall
impediment
,
The
cause
which
impedeth
the
pendulum
and
reduceth
it
to
rest
.
it
shall
finally
reduce
it
to
quiescence
.
Now
the
same
threed
,
(
raking
away
the
middle
plummet
)
is
a
composition
of
many
grave
penduli
,
that
is
,
each
of
its
parts
is
such
a
pendulum
fastned
neerer
and
neerer
to
the
point
A
,
and
therefore
disposed
to
make
it
,
vibrations
successively
more
and
more
frequent
;
and
consequently
is
able
to
bring
a
continual
impediment
to
the
plummet
C
;
and
for
a
proof
that
this
is
so
,
if
we
do
but
observe
the
thread
AC
,
we
shall
see
it
distended
not
directly
,
but
in
an
arch
;
and
if
instead
of
the
thread
we
take
a
chain
,
we
shall
discern
the
effect
more
perfectly
;
The
thread
or
chain
to
which
a
pendulum
is
fastned
,
maketh
an
arch
,
and
doth
not
stretch
it selfe
streight
out
in
its
vibrations
.
and
especially
removing
the
gravity
C
,
to
a
considerable
distance
from
the
perpendicular
AB
,
for
that
the
chain
being
composed
of
many
loose
particles
,
and
each
of
them
of
some
weight
,
the
arches
AEC
,
and
AFD
,
will
appear
notably
incurvated
.
By
reason
therefore
,
that
the
parts
of
the
chain
,
according
as
they
are
neerer
to
the
point
A
,
desire
to
make
their
vibrations
more
frequent
,
they
permit
not
the
lower
parts
of
the
said
chain
to
swing
so
far
as
naturally
they
would
:
and
by
continual
detracting
from
the
vibrations
of
the
plummet
C
,
they
finally
make
it
cease
to
move
,
although
the
impediment
of
the
air
might
be
removed
.
SAGR.
The
books
are
now
come
;
here
take
them
Simplicius
,
and
find
the
place
you
are
in
doubt
of
.
SIMP.
See
,
here
it
is
where
he
beginneth
to
argue
against
the
diurnal
motion
of
the
Earth
,
he
having
first
confuted
the
annual
.
Motus
terrae
annuus
asserere
Copernicanos
cogit
conversionem
ejusdem
quotidianam
;
alias
idem
terrae
Hemisphaerium
continenter
ad
Solem
esset
conversum
obumbrato
semper
averso
.
[
In
English
thus
:
]
The
annual
motion
of
the
Earth
doth
compell
the
Copernicans
to
assert
the
daily
conversion
thereof
;
otherwise
the
same
Hemisphere
of
the
Earth
would
be
continually
turned
towards
the
Sun
,
the
shady
side
being
always
averse
.
And
so
one
half
of
the
Earth
would
never
come
to
see
the
Sun
.
SALV
.
I
find
at
the
very
first
sight
,
that
this
man
hath
not
rightly
apprehended
the
Copernican
Hypothesis
,
for
if
he
had
but
taken
notice
how
he
alwayes
makes
the
Axis
of
the
terrestrial
Globe
perpetually
parallel
to
it self
,
he
would
not
have
said
,
that
one
half
of
the
Earth
would
never
see
the
Sun
,
but
that
the
year
would
be
one
entire
natural
day
,
that
is
,
that
thorow
all
parts
of
the
Earth
there
would
be
six
moneths
day
,
and
six
moneths
night
,
as
it
now
befalleth
to
the
inhabitants
under
the
Pole
,
but
let
this
mistake
be
forgiven
him
,
and
let
us
come
to
what
remaineth
.
SIMP.
It
followeth
,
Hanc
autem
gyrationem
Terrae
impossibilem
esse
sic
demonstramus
.
Which
speaks
in
English
thus
:
That
this
gyration
of
the
Earth
is
impossible
we
thus
demonstrate
.
That
which
ensueth
is
the
declaration
of
the
following
figure
,
wherein
is
delineated
many
descending
grave
bodies
,
and
ascending
light
bodies
,
and
birds
that
fly
to
and
again
in
the
air
,
&c.
SAGR.
Let
us
see
them
,
I
pray
you
.
Oh!
what
fine
figures
,
what
birds
,
what
balls
,
and
what
other
pretty
things
are
here
?
SIMP.
These
are
balls
which
come
from
the
concave
of
the
Moon
.
SAGR.
and
what
is
this
?
SIMP.
This
is
a
kind
of
Shell-fish
,
which
here
at
Venice
they
call
buovoli
;
and
this
also
came
from
the
Moons
concave
.
SAGR.
Indeed
,
it
seems
then
,
that
the
Moon
hath
a
great
power
over
these
Oyster-fishes
,
which
we
call
[
](A61244-e49370-b)*
*
Pesci
armai
,
or
armati
.
armed
sishes
.
SIMP.
And
this
is
that
calculation
,
which
I
mentioned
▪
of
this
Journey
in
a
natural
day
,
in
an
hour
,
in
a
first
minute
,
and
in
a
second
,
which
a
point
of
the
Earth
would
make
placed
under
the
Equinoctial
,
and
also
in
the
parallel
of
48
gr.
And
then
followeth
this
,
which
I
doubted
I
had
committed
some
mistake
in
reciting
,
therefore
let
us
read
it
.
His
positis
,
necesse
est
,
terra
circulariter
mota
,
omnia
ex
aëre
eidem
,
&c.
Quod
si
hasce
pilas
aequales
ponemus
pondere
,
magnitudine
,
gravitate
,
&
in
concavo
Sphaerae
Lunaris
positas
libero
descensui
permittamus
,
si
motum
deorsum
aequemus
celeritate
motui
circum
,
(
quod
tamen
secus
est
,
cum
pila
A
,
&c.
)
elabentur
minimum
(
ut
multum
cedamus
adversariis
)
dies
sex
:
quo
tempore
sexies
circa
terram
,
&c.
[
In
English
thus
.
]
These
things
being
supposed
,
it
is
necessary
,
the
Earth
being
circularly
moved
,
that
all
things
from
the
air
to
the
same
,
&c.
So
that
if
we
suppose
these
balls
to
be
equal
in
magnitude
and
gravity
,
and
being
placed
in
the
concave
of
the
Lunar
Sphere
,
we
permit
them
a
free
descent
,
and
if
we
make
the
motion
downwards
equal
in
velocity
to
the
motion
about
,
(
which
nevertheless
is
otherwise
,
if
the
ball
A
,
&c.
)
they
shall
be
falling
at
least
(
that
we
may
grant
much
to
our
adversaries
)
six
dayes
;
in
which
time
they
shall
be
turned
six
times
about
the
Earth
,
&c.
SALV
.
You
have
but
too
faithfully
cited
the
argument
of
this
person
.
From
hence
you
may
collect
Simplicius
,
with
what
caution
they
ought
to
proceed
,
who
would
give
themselves
up
to
believe
others
in
those
things
,
which
perhaps
they
do
not
believe
themselves
.
For
me
thinks
it
a
thing
impossible
,
but
that
this
Author
was
advised
,
that
he
did
design
to
himself
a
circle
,
whose
diameter
(
which
amongst
Mathematicians
,
is
lesse
than
one
third
part
of
the
circumference
)
is
above
72
times
bigger
than
it self
:
an
errour
that
affirmeth
that
to
be
considerably
more
than
200
which
is
lesse
than
one
.
SAGR.
It
may
be
,
that
these
Mathematical
proportions
,
which
are
true
in
abstract
,
being
once
applied
in
concrete
to
Physical
and
Elementary
circles
,
do
not
so
exactly
agree
:
And
yet
,
I
think
,
that
the
Cooper
,
to
find
the
semidiameter
of
the
bottom
,
which
he
is
to
fit
to
the
Cask
,
doth
make
use
of
the
rule
of
Mathematicians
in
abstract
,
although
such
bottomes
be
things
meerly
material
,
and
concrete
:
therefore
let
Simplicius
plead
in
excuse
of
this
Author
;
and
whether
he
thinks
that
the
Physicks
can
differ
so
very
much
from
the
Mathematicks
.
SIMP.
The
substractions
are
in
my
opinion
insufficient
to
salve
this
difference
,
which
is
so
extreamly
too
great
to
be
reconciled
:
and
in
this
case
I
have
no
more
to
say
but
that
,
Quandoque
bonus
dormilet
Homerus
.
But
supposing
the
calculation
of
[
](A61244-e49570-b)*
*
Not
Sagredus
,
as
the
Latine
hath
it
.
Salviatus
to
be
more
exact
,
and
that
the
time
of
the
descent
of
the
ball
were
no
more
than
three
hours
;
yet
me
thinks
,
that
coming
from
the
concave
of
the
Moon
,
which
is
so
great
a
distance
off
,
it
would
be
an
admirable
thing
,
that
it
should
have
an
instinct
of
maintaining
it self
all
the
way
over
the
self-same
point
of
the
Earth
,
over
which
it
did
hang
in
its
departure
thence
,
and
not
rather
be
left
a
very
great
way
behind
.
SALV
.
The
effect
may
be
admirable
,
and
not
admirable
,
but
natural
and
ordinary
,
according
as
the
things
precedent
may
fall
out
.
For
if
the
ball
(
according
to
the
Authors
suppositions
)
whilst
it
staid
in
the
concave
of
the
Moon
,
had
the
circular
motion
of
twenty
four
hours
together
with
the
Earth
,
and
with
the
rest
of
the
things
contained
within
the
said
Concave
;
that
very
vertue
which
made
it
turn
round
before
its
descent
,
will
continue
it
in
the
same
motion
in
its
descending
.
And
so
far
it
is
from
not
keeping
pace
with
the
motion
of
the
Earth
,
and
from
staying
behind
,
that
it
is
more
likely
to
out-go
it
;
being
that
in
its
approaches
to
the
Earth
,
the
motion
of
gyration
is
to
be
made
with
circles
continually
lesser
and
lesser
;
so
that
the
ball
retaining
in
it self
that
self-same
velocity
which
it
had
in
the
concave
,
it
ought
to
anticipate
,
as
I
have
said
,
the
vertigo
or
conversion
of
the
Earth
.
But
if
the
ball
in
the
concave
did
want
that
circulation
,
it
is
not
obliged
in
descending
to
maintain
it self
perpendicularly
over
that
point
of
the
Earth
,
which
was
just
under
it
when
the
descent
began
.
Nor
will
.
Copernicus
,
or
any
of
his
followers
affirm
the
same
.
SIMP.
But
the
Author
maketh
an
objection
,
as
you
see
,
demanding
on
what
principle
this
circular
motion
of
grave
and
light
bodies
,
doth
depend
:
that
is
,
whether
upon
an
internal
or
an
external
principle
.
SALV
.
Keeping
to
the
Probleme
of
which
we
speak
,
I
say
,
that
that
very
principle
which
made
the
ball
turn
round
,
whil'st
it
was
in
the
Lunar
concave
,
is
the
same
that
maintaineth
also
the
circulation
in
the
descent
:
yet
I
leave
the
Author
at
liberty
to
make
it
internal
or
external
at
his
pleasure
.
SIMP.
The
Author
proveth
,
that
it
can
neither
be
inward
nor
outward
.
SALV
.
And
I
will
say
then
,
that
the
ball
in
the
concave
did
not
move
,
and
so
he
shall
not
be
bound
to
shew
how
that
in
descending
it
continueth
all
the
way
vertically
over
one
point
,
for
that
it
will
not
do
any
such
thing
.
SIMP.
Very
well
;
But
if
grave
bodies
,
and
light
can
have
no
principle
,
either
internal
or
external
of
moving
circularly
,
than
neither
can
the
terrestrial
Globe
move
with
a
circular
motion
:
and
thus
you
have
the
intent
of
the
Author
.
SALV
.
I
did
not
say
,
that
the
Earth
had
no
principle
,
either
interne
,
or
externe
to
the
motion
of
gyration
,
but
I
say
,
that
I
do
not
know
which
of
the
two
it
hath
;
and
yet
my
not
knowing
it
hath
not
a
power
to
deprive
it
of
the
same
;
but
if
this
Author
can
tell
by
what
principle
other
mundane
bodies
are
moved
round
,
of
whose
motion
there
is
no
doubt
;
I
say
,
that
that
which
maketh
the
Earth
to
move
,
is
a
vertue
,
like
to
that
,
by
which
Mars
and
Jupiter
are
moved
,
and
wherewith
he
believes
that
the
starry
Sphere
it self
also
doth
move
;
and
if
he
will
but
assure
me
,
who
is
the
mover
of
one
of
these
moveables
,
I
will
undertake
to
be
able
to
tell
him
who
maketh
the
Earth
to
move
.
Nay
more
;
I
will
undertake
to
do
the
same
,
if
he
can
but
tell
me
,
who
moveth
the
parts
of
the
Earth
downwards
.
SIMP.
The
cause
of
this
is
most
manifest
,
and
every
one
knows
that
it
is
gravity
.
SALV
.
You
are
out
,
Simplicius
,
you
should
say
,
that
every
one
knowes
,
that
it
is
called
Gravity
:
but
I
do
not
question
you
about
the
name
,
but
the
essence
of
the
thing
,
of
which
essence
you
know
not
a
tittle
more
than
you
know
the
essence
of
the
mover
of
the
stars
in
gyration
;
unlesse
it
be
the
name
that
hath
been
put
to
this
,
and
made
familiar
,
and
domestical
,
by
the
many
experiences
which
we
see
thereof
every
hour
in
the
day
,
:
We
know
〈◊〉
more
who
moveth
grave
b●dus
downwards
;
than
who
moveth
the
Stars
round
,
nor
kn●w
we
any
thing
of
these
cause●
,
more
than
the
names
imposed
on
them
by
us
.
but
not
as
if
we
really
understand
any
more
,
what
principle
or
vertue
that
is
which
moveth
a
stone
downwards
,
than
we
know
who
moveth
it
upwards
,
when
it
is
separated
from
the
projicient
,
or
who
moveth
the
Moon
round
,
except
(
as
I
have
said
)
onely
the
name
,
which
more
particularly
and
properly
we
have
assigned
to
the
motion
of
descent
,
namely
,
Gravity
;
whereas
for
the
cause
of
circular
motion
,
in
more
general
termes
,
we
assign
the
Vertue
impressed
,
and
call
the
same
an
Intelligence
,
either
assisting
,
or
informing
;
and
to
infinite
other
motions
we
ascribe
Nature
for
their
cause
.
SIMP.
It
is
my
opinion
,
that
this
Author
asketh
far
lesse
than
that
,
to
which
you
deny
to
make
answer
;
for
he
doth
not
ask
what
is
nominally
and
particularly
the
principle
that
moveth
grave
and
light
bodies
circularly
,
but
whatsoever
it
be
,
he
desireth
to
know
,
whether
you
think
it
intrinsecal
,
or
extrinsecal
:
For
howbeit
,
v.
gr
.
I
do
not
know
,
what
kind
of
thing
that
gravity
is
,
by
which
the
Earth
descendeth
;
yet
I
know
that
it
is
an
intern
principle
,
seeing
that
if
it
be
not
hindered
,
it
moveth
spontaneously
:
and
on
the
contrary
,
I
know
that
the
principle
which
moveth
it
upwards
,
is
external
;
although
that
I
do
not
know
,
what
thing
that
vertue
is
,
impressed
on
it
by
the
projicient
.
SALV
.
Into
how
many
questions
must
we
excurre
,
if
we
would
decide
all
the
difficulties
,
which
successively
have
dependance
one
upon
another
!
You
call
that
an
external
(
and
you
also
call
it
a
preternatural
and
violent
)
principle
,
which
moveth
the
grave
project
upwards
;
but
its
possible
that
it
may
be
no
lesse
interne
and
natural
,
than
that
which
moveth
it
downwards
;
it
may
peradventure
be
called
external
and
violent
,
The
vertue
which
carrieth
grave
projects
upwards
,
is
no
lesse
natural
to
them
,
than
the
gravity
which
moveth
them
downwards
.
so
long
as
the
moveable
is
joyned
to
the
projicient
;
but
being
separated
,
what
external
thing
remaineth
for
a
mover
of
the
arrow
,
or
ball
?
In
summe
,
it
must
necessarliy
be
granted
,
that
that
vertue
which
carrieth
such
a
moveable
upwards
,
is
no
lesse
interne
,
than
that
which
moveth
it
downwards
;
and
I
think
the
motion
of
grave
bodies
ascending
by
the
impetus
conceived
,
to
be
altogether
as
natural
,
as
the
motion
of
descent
depending
on
gravity
.
SIMP.
I
will
never
grant
this
;
for
the
motion
of
descent
hath
its
principle
internal
,
natural
,
and
perpetual
,
and
the
motion
of
ascent
hath
its
principle
externe
,
violent
,
and
finite
.
SALV
.
If
you
refuse
to
grant
me
,
that
the
principles
of
the
motions
of
grave
bodies
downwards
and
upwards
,
Contrary
principles
cannot
naturally
reside
in
the
same
subject
.
are
equally
internal
and
natural
;
what
would
you
do
,
if
I
should
say
,
that
they
may
also
be
the
same
in
number
?
SIMP.
I
leave
it
to
you
to
judge
.
SALV
.
But
I
desire
you
your self
to
be
the
Judge
:
Therefore
tell
me
,
Do
you
believe
that
in
the
same
natural
body
,
there
may
reside
interne
principles
,
that
are
contrary
to
one
another
?
SIMP.
I
do
verily
believe
there
cannot
.
SALV
.
What
do
you
think
to
be
the
natural
inclination
of
Earth
,
of
Lead
,
of
Gold
,
and
in
sum
,
of
the
most
ponderous
matters
;
that
is
,
to
what
motion
do
you
believe
that
their
interne
principle
draweth
them
?
SIMP.
To
that
towards
the
centre
of
things
grave
,
that
is
,
to
the
centre
of
the
Universe
,
and
of
the
Earth
,
whither
,
if
they
be
not
hindered
,
it
will
carry
them
.
SALV
.
So
that
,
if
the
Terrestrial
Globe
were
bored
thorow
,
and
a
Well
made
that
should
passe
through
the
centre
of
it
,
a
Cannon
bullet
being
let
fall
into
the
same
,
as
being
moved
by
a
natural
and
intrinsick
principle
,
would
passe
to
the
centre
;
and
it
would
make
all
this
motion
spontaneously
,
and
by
intrinsick
principle
,
is
it
not
so
?
SIMP.
So
I
verily
believe
.
SALV
.
But
when
it
is
arrived
at
the
centre
,
do
you
think
that
it
will
passe
any
further
,
or
else
that
there
it
would
immediately
stand
still
,
and
move
no
further
?
SIMP.
I
believe
that
it
would
continue
to
move
a
great
way
further
.
SALV
.
But
this
motion
beyond
the
centre
,
would
it
not
be
upwards
,
and
according
to
your
assertion
preternatural
,
and
violent
?
And
yet
on
what
other
principle
do
you
make
it
to
depend
,
but
only
upon
the
self
same
,
which
did
carry
the
ball
to
the
centre
,
and
which
you
called
intrinsecal
,
and
natural
?
Finde
,
if
you
can
,
another
external
projicient
,
that
overtaketh
it
again
to
drive
it
upwards
.
And
this
that
hath
been
said
of
the
motion
thorow
the
centre
,
The
natural
motion
changeth
it selfe
into
that
which
is
called
preternatural
and
violent
.
is
also
seen
by
us
here
above
;
for
the
interne
impetus
of
a
grave
body
falling
along
a
declining
superficies
,
if
the
said
superficies
be
reflected
the
other
way
,
it
shall
carry
it
,
without
a
jot
interrupting
the
motion
,
also
upwards
.
A
ball
of
lead
that
hangeth
by
a
thread
,
being
removed
from
its
perpendicularity
,
descendeth
spontaneously
,
as
being
drawn
by
its
internal
inclination
,
and
without
any
interposure
of
rest
,
passeth
beyond
the
lowest
point
of
perpendicularity
:
and
without
any
additional
mover
,
moveth
upwards
.
I
know
that
you
will
not
deny
,
but
that
the
principle
of
grave
bodies
that
moveth
them
downwards
,
is
no
less
natural
,
and
intrinsecal
,
than
that
principle
of
light
bodies
,
vvhich
moveth
them
upwards
:
so
that
I
propose
to
your
consideration
a
ball
of
lead
,
vvhich
descending
through
the
Air
from
a
great
altitude
,
and
so
moving
by
an
intern
principle
,
and
comming
to
a
depth
of
vvater
,
continueth
its
descent
,
and
without
any
other
externe
mover
,
submergeth
a
great
vvay
;
and
yet
the
motion
of
descent
in
the
vvater
is
preternatural
unto
it
;
but
yet
nevertheless
dependeth
on
a
principle
that
is
internal
,
and
not
external
to
the
ball
.
You
see
it
demonstrated
then
,
that
a
moveable
may
be
moved
by
one
and
the
same
internal
principle
,
with
contrary
motions
.
SIMP.
I
believe
there
are
solutions
to
all
these
objections
,
though
for
the
present
I
do
not
remember
them
;
but
however
it
be
,
the
Author
continueth
to
demand
,
on
what
principle
this
circular
motion
of
grave
and
light
bodies
dependeth
;
that
is
,
whether
on
a
principle
internal
,
or
external
;
and
proceeding
forvvards
,
sheweth
,
that
it
can
be
neither
on
the
one
,
nor
on
the
other
,
saying
;
Si
ab
externo
;
Deusne
illum
excitat
per
continuum
miraculum
?
an
verò
Angelus
,
an
aër
?
Et
hunc
quidem
multi
assignant
.
Sed
contra
—
[
In
English
thus
]
If
from
an
externe
principle
;
Whether
God
doth
not
excite
it
by
a
continued
Miracle
?
or
an
Angel
,
or
the
Air
?
And
indeed
many
do
assign
this
.
But
on
the
contrary
—
.
SALV
.
Trouble
not
your self
to
read
his
argument
;
for
I
am
none
of
those
who
ascribe
that
principle
to
the
ambient
air
.
As
to
the
Miracle
,
or
an
Angel
,
I
should
rather
incline
to
this
side
;
for
that
which
taketh
beginning
from
a
Divine
Miracle
,
or
from
an
Angelical
operation
;
as
for
instance
,
the
transportation
of
a
Cannon
ball
or
bullet
into
the
concave
of
the
Moon
,
doth
in
all
probability
depend
on
the
vertue
of
the
same
principle
for
performing
the
rest
.
But
,
as
to
the
Air
,
it
serveth
my
turn
,
that
it
doth
not
hinder
the
circular
motion
of
the
moveables
,
which
we
did
suppose
to
move
thorow
it
.
And
to
prove
that
,
it
sufficeth
(
nor
is
more
required
)
that
it
moveth
with
the
same
motion
,
and
finisheth
its
circulations
with
the
same
velocity
,
that
the
Terrestrial
Globe
doth
.
SIMP.
And
he
likewise
makes
his
opposition
to
this
also
;
demanding
who
carrieth
the
air
about
,
Nature
,
or
Violence
?
And
proveth
,
that
it
cannot
be
Nature
,
alledging
that
that
is
contrary
to
truth
,
experience
,
and
to
Copernicus
himself
.
SALV
.
It
is
not
contrary
to
Copernicus
in
the
least
,
who
writeth
no
such
thing
;
and
this
Author
ascribes
these
things
to
him
with
two
excessive
courtesie
.
It
's
true
,
he
saith
,
and
for
my
part
I
think
he
saith
well
,
that
the
part
of
the
air
neer
to
the
Earth
,
being
rather
a
terrestrial
evaporation
,
may
have
the
same
nature
,
and
naturally
follow
its
motion
;
or
,
as
being
contiguous
to
it
,
may
follow
it
in
the
same
manner
,
as
the
Peripateticks
say
,
that
the
superiour
part
of
it
,
and
the
Element
of
fire
,
follow
the
motion
of
the
Lunar
Concave
,
so
that
it
lyeth
upon
them
to
declare
,
whether
that
motion
be
natural
,
or
violent
.
SIMP.
The
Author
will
reply
,
that
if
Copernicus
maketh
only
the
inferiour
part
of
the
Air
to
move
,
and
supposeth
the
upper
part
thereof
to
want
the
said
motion
,
he
cannot
give
a
reason
,
how
that
quiet
air
can
be
able
to
carry
those
grave
bodies
along
with
it
,
and
make
them
keep
pace
with
the
motion
of
the
Earth
.
SALV
.
Copernicus
will
say
,
The
propension
of
elementary
bodies
to
follow
the
Earth
,
hath
a
limited
Sphere
of
activity
.
that
this
natural
propension
of
the
elementary
bodies
to
follow
the
motion
of
the
Earth
,
hath
a
limited
Sphere
,
out
of
which
such
a
natural
inclination
would
cease
;
besides
that
,
as
I
have
said
,
the
Air
is
not
that
which
carrieth
the
moveables
along
with
it
;
which
being
separated
from
the
Earth
,
do
follow
its
motion
;
so
that
all
the
objections
come
to
nothing
,
which
this
Author
produceth
to
prove
,
that
the
Air
cannot
cause
such
effects
.
SIMP.
To
shew
therefore
,
that
that
cannot
be
,
it
will
be
necessary
to
say
,
that
such
like
effects
depend
on
an
interne
principle
,
against
which
position
,
oboriuntur
difficillimae
,
immò
inextricabiles
quaestiones
secundae
,
of
which
sort
are
these
that
follow
.
Principium
illud
internum
vel
est
accidens
,
vel
substantia
.
Si
primum
;
quale
nam
illud
?
nam
qualitas
locomotiva
circum
,
hactenus
nulla
videtur
agnita
.
(
In
English
thus
:
)
Contrary
to
which
position
there
do
arise
most
difficult
,
yea
inextricable
second
questions
,
such
as
these
;
That
intern
principle
is
either
an
accident
,
or
a
substance
.
If
the
first
;
what
manner
of
accident
is
it
?
For
a
locomotive
quality
about
the
centre
,
seemeth
to
be
hitherto
acknowledged
by
none
.
SALV
.
How
,
is
there
no
such
thing
acknowledged
?
Is
it
not
known
to
us
,
that
all
these
elementary
matters
move
round
,
together
with
the
Earth
?
You
see
how
this
Author
supposeth
for
true
,
that
which
is
in
question
.
SIMP.
He
saith
,
that
we
do
not
see
the
same
;
and
me
thinks
,
he
hath
therein
reason
on
his
side
.
SALV
.
We
see
it
not
,
because
we
turn
round
together
with
them
.
SIMP.
Hear
his
other
Argument
.
Quae
etiam
si
esset
,
quomodò
tamen
inveniretur
in
rebus
tam
contrariis
?
in
igne
,
ut
in
aquâ
;
in
aëre
,
ut
in
terra
;
in
viventibus
,
ut
in
animà
carentibus
?
[
in
English
thus
:
]
Which
although
it
were
,
yet
how
could
it
be
found
in
things
so
contrary
?
in
the
fire
,
as
in
the
water
?
in
the
air
,
as
in
the
earth
?
in
living
creatures
,
as
in
things
wanting
life
?
SALV
.
Supposing
for
this
time
,
that
water
and
fire
are
contraries
;
as
also
the
air
and
earth
;
(
of
which
yet
much
may
be
said
)
the
most
that
could
follow
from
thence
would
be
,
that
those
motions
cannot
be
common
to
them
,
that
are
contrary
to
one
another
:
so
that
v.
g.
the
motion
upwards
,
which
naturally
agreeth
to
fire
,
cannot
agree
to
water
;
but
that
,
like
as
it
is
by
nature
contrary
to
fire
:
so
to
it
that
motion
suiteth
,
which
is
contrary
to
the
motion
of
fire
,
which
shall
be
the
motion
deorsum
;
but
the
circular
motion
,
which
is
not
contrary
either
to
the
motion
sursum
,
or
to
the
motion
deorsum
,
but
may
mix
with
both
,
as
Aristotle
himself
affirmeth
,
why
may
it
not
equally
suit
with
grave
bodies
and
with
light
?
The
motions
in
the
next
place
,
which
cannot
be
common
to
things
alive
,
and
dead
,
are
those
which
depend
on
the
soul
:
but
those
which
belong
to
the
body
,
in
as
much
as
it
is
elementary
,
and
consequently
participateth
of
the
qualities
of
the
elements
,
why
may
not
they
be
common
as
well
to
the
dead
corps
,
as
to
the
living
body
?
And
therefore
,
if
the
circular
motion
be
proper
to
the
elements
,
it
ought
to
be
common
to
the
mixt
bodies
also
.
SAGR.
It
must
needs
be
,
that
this
Author
holdeth
,
that
a
dead
cat
,
falling
from
a
window
,
it
is
not
possible
that
a
live
cat
also
could
fall
;
it
not
being
a
thing
convenient
,
that
a
carcase
should
partake
of
the
qualities
which
suit
with
things
alive
.
SALV
.
Therefore
the
discourse
of
this
Author
concludeth
nothing
against
one
that
should
affirm
,
that
the
principle
of
the
circular
motions
of
grave
and
light
bodies
is
an
intern
accident
:
I
know
not
how
he
may
prove
,
that
it
cannot
be
a
substance
.
SIMP.
He
brings
many
Arguments
against
this
.
The
first
of
which
is
in
these
words
:
Si
secundum
(
nempè
,
si
dicas
tale
principium
esse
substantiam
)
illud
est
aut
materia
,
aut
forma
,
aut
compositum
.
Sed
repugnant
iterum
tot
diversae
rerum
naturae
,
quales
sunt
aves
,
limaces
,
saxa
,
sagittae
,
nives
,
fumi
,
grandines
,
pisces
,
&c.
quae
tamen
omnia
specie
&
genere
differentia
,
moverentur
à
naturà
suâ
circulariter
,
ipsa
naturis
diversissima
,
&c.
[
In
English
thus
]
If
the
second
,
(
that
is
,
if
you
shall
say
that
this
principle
is
a
substance
)
it
is
either
matter
,
or
form
,
or
a
compound
of
both
.
But
such
diverse
natures
of
things
are
again
repugnant
,
such
as
are
birds
,
snails
,
stones
,
darts
,
snows
,
smoaks
,
hails
,
fishes
,
&c.
all
which
notwithstanding
their
differences
in
species
and
kind
,
are
moved
of
their
own
nature
circularly
,
they
being
of
their
natures
most
different
,
&c.
SALV
.
If
these
things
before
named
are
of
diverse
natures
,
and
things
of
diverse
natures
cannot
have
a
motion
in
common
,
it
must
follow
,
if
you
would
give
satisfaction
to
all
,
that
you
are
to
think
of
,
more
than
two
motions
onely
of
upwards
and
downwards
:
and
if
there
must
be
one
for
the
arrows
,
another
for
the
snails
,
another
for
the
stones
,
and
another
for
fishes
;
then
are
you
to
bethink
your self
of
worms
,
topazes
and
mushrums
,
which
are
not
less
different
in
nature
from
one
another
,
than
snow
and
hail
.
SIMP.
It
seems
that
you
make
a
jest
of
these
Arguments
.
SALV
.
No
indeed
,
Simplicius
,
but
it
hath
been
already
answered
above
,
to
wit
,
that
if
one
motion
,
whether
downwards
or
upwards
,
can
agree
with
all
those
things
afore
named
,
a
circular
motion
may
no
less
agree
with
them
:
and
as
you
are
a
Peripatetick
,
do
not
you
put
a
greater
difference
between
an
elementary
comet
and
a
celestial
star
,
than
between
a
fish
and
a
bird
?
and
yet
both
those
move
circularly
.
Now
propose
your
second
Argument
.
SIMP.
Si
terra
staret
per
voluntatem
Dei
,
rotaréntne
caetera
,
an
non
?
si
hoc
,
falsum
est
à
naturâ
gyrare
;
si
illud
,
redeunt
priores
quaestiones
.
Et
sanè
mirum
esset
,
quòd
Gavia
pisciculo
,
Alauda
nidulo
suo
,
&
corvus
limaci
,
petraque
,
etiam
volans
,
imminere
non
posset
.
[
Which
I
thus
render
:
]
If
the
Earth
be
supposed
to
stand
still
by
the
will
of
God
,
should
the
rest
of
bodies
turn
round
or
no
?
If
not
,
then
it
's
false
that
they
are
revolved
by
nature
;
if
the
other
,
the
former
questions
will
return
upon
us
.
And
truly
it
would
be
strange
that
the
Sea-pie
should
not
be
able
to
hover
over
the
small
fish
,
the
Lark
over
her
nest
,
and
the
Crow
over
the
snail
and
rock
,
though
flying
.
SALV
.
I
would
answer
for
my self
in
general
terms
,
that
if
it
were
appointed
by
the
will
of
God
,
that
the
Earth
should
cease
from
its
diurnal
revolution
,
those
birds
would
do
what
ever
should
please
the
same
Divine
will
.
But
if
this
Author
desire
a
more
particular
answer
,
I
should
tell
him
,
that
they
would
do
quite
contrary
to
what
they
do
now
,
if
whilst
they
,
being
separated
from
the
Earth
,
do
bear
themselves
up
in
the
air
,
the
Terrestrial
Globe
by
the
will
of
God
,
should
all
on
a
sudden
be
put
upon
a
precipitate
motion
;
it
concerneth
this
Author
now
to
ascertain
us
what
would
in
this
case
succeed
.
SAGR.
I
pray
you
,
Salviatus
,
at
my
request
to
grant
to
this
Author
,
that
the
Earth
standing
still
by
the
will
of
God
,
the
other
things
,
separated
from
it
,
would
continue
to
turn
round
of
their
own
natural
motion
,
and
let
us
hear
what
impossibilities
or
inconveniences
would
follow
:
for
I
,
as
to
my
own
particular
,
do
not
see
how
there
can
be
greater
disorders
,
than
these
produced
by
the
Author
himself
,
that
is
,
that
Larks
,
though
they
should
flie
,
could
not
be
able
to
hover
over
their
nests
,
nor
Crows
over
snails
,
or
rocks
:
from
whence
would
follow
,
that
Crows
must
suffer
for
want
of
snails
,
and
young
Larks
must
die
of
hunger
,
and
cold
,
not
being
able
to
be
fed
or
sheltered
by
the
wings
of
the
old
ones
.
This
is
all
the
ruine
that
I
can
conceive
would
follow
,
supposing
the
Authors
speech
to
be
true
.
Do
you
see
,
Simplicius
,
if
greater
inconveniences
would
happen
?
SIMP.
I
know
not
how
to
discover
greater
;
but
it
is
very
credible
,
that
the
Author
besides
these
,
discovered
other
disorders
in
Nature
,
which
perhaps
in
reverend
respect
of
her
,
he
was
not
willing
to
instance
in
.
Therefore
let
us
proceed
to
the
third
Objection
.
Insuper
quî
fit
,
ut
istae
res
tam
variae
tantùm
moveantur
ab
Occasu
in
Ortum
,
parallelae
ad
Aequatorem
?
ut
semper
moveantur
,
nunquam
quiescant
?
[
which
speaks
to
this
sense
:
]
Moreover
,
how
comes
it
to
pass
that
these
things
,
so
diverse
,
are
onely
moved
from
the
West
towards
the
East
,
parallel
to
the
Aequinoctial
?
that
they
always
move
,
and
never
rest
?
SALV
.
They
move
from
West
to
East
parallel
to
the
Aequinoctial
without
ceasing
,
in
the
same
manner
as
you
believe
the
fixed
stars
to
move
from
East
to
West
,
parallel
to
the
Aequinoctial
,
without
ever
resting
.
SIMP.
Quarè
,
quò
sunt
altiores
,
celeriùs
;
quò
humiliores
,
tardiùs
?
(
i.
e.
)
Why
are
the
higher
the
swifter
,
and
the
lower
the
●lower
?
SALV
.
Because
that
in
a
Sphere
or
circle
,
that
turns
about
upon
its
own
centre
,
the
remoter
parts
describe
greater
circuits
,
and
the
parts
nearer
at
hand
describe
lesser
in
the
same
time
.
SIMP.
Quare
,
quae
Aequinoctiali
propriores
,
in
majori
;
quae
remotiores
,
in
minori
circulo
feruntur
?
[
scilicet
:
]
Why
are
those
near
the
Aequinoctial
carried
about
in
a
greater
circle
,
and
those
which
are
remote
in
a
lesser
?
SALV
.
To
imitate
the
starry
Sphere
,
in
which
those
nearest
to
the
Aequinoctial
,
move
in
greater
circles
,
than
the
more
remote
.
SIMP.
Quarè
Pila
eadem
sub
Aequinoctiali
tota
circa
centrum
terrae
,
ambitu
maximo
,
celeritate
incredibili
;
sub
Polo
verò
circa
centrum
proprium
,
gyro
nullo
,
tarditate
supremà
volveretur
?
[
That
is
:
]
Why
is
the
same
ball
under
the
Aequinoctial
wholly
turned
round
the
centre
of
the
Earth
in
the
greatest
circumference
,
with
an
incredible
celerity
;
but
under
the
Pole
about
its
own
centre
,
in
no
circuite
,
but
with
the
ultimate
degree
of
tardity
?
SALV
.
To
imitate
the
stars
of
the
Firmament
,
that
would
do
the
like
if
they
had
the
diurnal
motion
.
SIMP.
Quare
eadem
res
,
pila
v.
g.
plumbea
,
si
semel
terram
circuivit
,
descripto
circulo
maximo
,
eandem
ubique
non
circummigret
secundùm
circulum
maximum
,
sed
translata
extra
Aequinoctialem
in
circulis
minoribus
agetur
?
[
Which
speaketh
thus
:
]
Why
doth
not
the
same
thing
,
as
for
example
,
a
ball
of
lead
turn
round
every
where
according
to
the
same
great
circle
,
if
once
describing
a
great
circle
,
it
hath
incompassed
the
Earth
,
but
being
removed
from
the
Aequinoctial
,
doth
move
in
lesser
circles
?
SALV
.
Because
so
would
,
nay
,
according
to
the
doctrine
of
Ptolomey
,
so
have
some
fixed
stars
done
,
which
once
were
very
near
the
Aequinoctial
,
and
described
very
vast
circles
,
and
now
that
they
are
farther
off
,
describe
lesser
.
SAGR.
If
I
could
now
but
keep
in
mind
all
these
fine
notions
,
I
should
think
that
I
had
made
a
great
purchase
;
I
must
needs
intreat
you
,
Simplicius
,
to
lend
me
this
Book
,
for
there
cannot
chuse
but
be
a
sea
of
rare
and
ingenious
matters
contained
in
it
.
SIMP.
I
will
present
you
with
it
.
SAGR.
Not
so
,
Sir
;
I
would
not
deprive
you
of
it
:
but
are
the
Queries
yet
at
an
end
?
SIMP.
No
Sir
;
hearken
therefore
.
Si
latio
circularis
gravibus
&
levibus
est
naturalis
,
qualis
est
ea
quae
fit
secundùm
lineam
rectam
?
Nam
si
naturalis
,
quomodo
&
is
motus
qui
circum
est
,
naturalis
est
,
cùm
specie
differat
à
recto
?
Si
violentus
,
quî
fit
,
ut
missile
ignitum
sursum
evolans
scintillosum
caput
sursùm
à
terrâ
,
non
autem
circum
volvatur
,
&c.
[
Which
take
in
our
idiom
:
]
If
a
circular
lation
is
natural
to
heavy
and
light
things
,
what
is
that
which
is
made
according
to
a
right
line
?
For
if
it
be
natural
,
how
then
is
that
motion
which
is
about
the
centre
natural
,
seeing
it
differs
in
species
from
a
right
motion
?
If
it
be
violent
,
how
is
it
that
a
fiery
dart
flying
upwards
,
sparkling
over
our
heads
at
a
distance
from
the
Earth
,
but
not
turning
about
,
&c.
SALV
.
It
hath
been
said
already
very
often
,
Of
the
mixt
motion
we
see
not
the
part
that
is
circular
,
because
we
partake
thereof
.
that
the
circular
motion
is
natural
to
the
whole
,
and
to
its
parts
,
whilst
they
are
in
perfect
disposure
,
and
the
right
is
to
reduce
to
order
the
parts
disordered
;
though
indeed
it
is
better
to
say
,
that
neither
the
parts
ordered
or
disordered
ever
move
with
a
right
motion
,
but
with
one
mixed
,
which
might
as
well
be
averred
meerly
circular
:
but
to
us
but
one
part
onely
of
this
motion
is
visible
and
observable
,
that
is
,
the
part
of
the
right
,
the
other
part
of
the
circular
being
imperceptible
to
us
,
because
we
partake
thereof
.
And
this
answers
to
the
rays
which
move
upwards
,
and
round
about
,
but
we
cannot
distinguish
their
circular
motion
,
for
that
,
with
that
we
our selves
move
also
.
But
I
believe
that
this
Author
never
thought
of
this
mixture
;
for
you
may
see
that
he
resolutely
saith
,
that
the
rays
go
directly
upwards
,
and
not
at
all
in
gyration
.
SIMP.
Quare
centrum
sphaere
delapsae
sub
Aequatore
spiram
describit
in
ejus
plano
:
sub
aliis
parallelis
spiram
describit
in
cono
?
sub
Polo
descendit
in
axe
lineam
gyralem
,
decurrens
in
superficie
cylindricâ
consignatam
?
(
In
English
to
this
purpose
:
)
Why
doth
the
centre
of
a
falling
Globe
under
the
Aequinoctial
describe
a
spiral
line
in
the
plane
of
the
Aequator
;
and
in
other
parallels
a
spiral
about
a
Cone
;
and
under
the
Pole
descend
in
the
axis
describing
a
gyral
line
,
running
in
a
Cylindrical
Superficie
?
SALV
.
Because
of
the
lines
drawn
from
the
Centre
to
the
circumference
of
the
sphere
,
which
are
those
by
which
graves
descend
,
that
which
terminates
in
the
Aequinoctial
designeth
a
circle
,
and
those
that
terminate
in
other
parallels
describe
conical
superficies
;
now
the
axis
describeth
nothing
at
all
,
but
continueth
in
its
own
being
.
And
if
I
may
give
you
my
judgment
freely
,
I
will
say
,
that
I
cannot
draw
from
all
these
Queries
,
any
sense
that
interfereth
with
the
motion
of
the
Earth
;
for
if
I
demand
of
this
Author
,
(
granting
him
that
the
Earth
doth
not
move
)
what
would
follow
in
all
these
particulars
,
supposing
that
it
do
move
,
as
Copernicus
will
have
it
;
I
am
very
confident
,
that
he
would
say
that
all
these
effects
would
happen
,
that
he
hath
objected
,
as
inconveniences
to
disprove
its
mobility
:
so
that
in
this
mans
opinion
necessary
consequences
are
accounted
absurdities
:
but
I
beseech
you
,
if
there
be
any
more
,
dispatch
them
,
and
free
us
speedily
from
this
wearisom
task
.
SIMP.
In
this
which
follows
he
opposes
Copernicus
&
his
Sectators
,
who
affirm
,
that
the
motion
of
the
parts
separated
from
their
whole
,
is
onely
to
unite
themselves
to
their
whole
;
but
that
the
moving
circularly
along
with
the
vertigenous
diurnal
revolution
is
absolutely
natural
:
against
which
he
objecteth
,
saying
,
that
according
to
these
mens
opinion
;
Si
tota
terra
,
unà
cum
aquà
in
nihilum
redigeretur
,
nulla
grando
aut
pluvia
è
nube
decideret
,
sed
naturalater
tantùm
circumferetur
,
neque
ignis
ullus
,
aut
igneum
ascenderet
,
cùm
illorum
non
improbabili
sententià
ignis
nullus
sit
suprà
.
[
Which
I
translate
to
this
sense
:
]
If
the
whole
Earth
,
together
with
the
Water
were
reduced
into
nothing
,
no
hail
or
rain
would
fall
from
the
clouds
,
but
would
be
onely
naturally
carried
round
;
neither
any
fire
or
fiery
thing
would
ascend
,
seeing
to
these
that
men
it
is
no
improbable
opinion
that
there
is
no
fire
above
.
SALV
.
The
providence
of
this
Philosopher
is
admirable
,
and
worthy
of
great
applause
;
for
he
is
not
content
to
provide
for
things
that
might
happen
,
the
course
of
Nature
continuing
,
but
will
shew
hic
care
in
what
may
follow
from
those
things
that
he
very
well
knows
shall
never
come
to
pass
.
I
will
grant
him
therefore
,
(
that
I
may
get
som
pretty
passages
out
of
him
)
that
if
the
Earth
and
Water
should
be
reduced
to
nothing
,
there
would
be
no
more
hails
or
rains
,
nor
would
igneal
matters
ascend
any
longer
upwards
,
but
would
continually
turn
round
:
what
will
follow
?
what
will
the
Philosopher
say
then
?
SIMP.
The
objection
is
in
the
words
which
immediately
follow
;
here
they
are
:
Quibus
tamen
experientia
&
ratio
adversatur
.
Which
nevertheless
(
saith
he
)
is
contrary
to
experience
and
reason
.
SALV
.
Now
I
must
yield
,
seeing
he
hath
so
great
an
advantage
of
me
as
experience
,
of
which
I
am
unprovided
.
For
as
yet
I
never
had
the
fortune
to
see
the
Terrestrial
Globe
and
the
element
of
Water
turn'd
to
nothing
,
so
as
to
have
been
able
to
observe
what
the
hail
and
water
did
in
that
little
Chaos
.
But
he
perhaps
tells
us
for
our
instruction
what
they
did
.
SIMP.
No
,
he
doth
not
.
SALV
.
I
would
give
any
thing
to
change
a
word
or
two
with
this
person
,
to
ask
him
,
whether
when
this
Globe
vanished
,
it
carried
away
with
it
the
common
centre
of
gravity
,
as
I
believe
it
did
;
in
which
case
,
I
think
that
the
hail
and
water
would
remain
insensate
and
stupid
amongst
the
clouds
,
without
knowing
what
to
do
with
themselves
.
It
might
be
also
,
that
attracted
by
that
great
void
Vacuum
,
left
by
the
Earths
absenting
,
all
the
ambients
would
be
rarified
,
and
particularly
,
the
air
,
which
is
extreme
easily
drawn
,
and
would
run
thither
with
very
great
haste
to
fill
it
up
.
And
perhaps
the
more
solid
and
material
bodies
,
as
birds
,
(
for
there
would
in
all
probability
be
many
of
them
scattered
up
and
down
in
the
air
)
would
retire
more
towards
the
centre
of
the
great
vacant
sphere
;
(
for
it
seemeth
very
reasonable
,
that
substances
that
under
small
bulk
contain
much
matter
,
should
have
narrower
places
assigned
them
,
leaving
the
more
spacious
to
the
more
ra●ified
)
and
there
being
dead
of
hunger
,
and
resolved
into
Earth
,
would
form
a
new
little
Globe
,
with
that
little
water
,
which
at
that
time
was
among
the
clouds
.
It
might
be
also
,
that
those
matters
as
not
beholding
the
light
,
would
not
perceive
the
Earths
departure
,
but
like
blind
things
,
would
descend
according
to
their
usual
custom
to
the
centre
,
whither
they
would
now
go
,
if
that
globe
did
not
hinder
them
.
And
lastly
,
that
I
may
give
this
Philosopher
a
less
irresolute
answer
,
I
do
tell
him
,
that
I
know
as
much
of
what
would
follow
upon
the
annihilation
of
the
Terrestrial
Globe
,
as
he
would
have
done
that
was
to
have
followed
in
and
about
the
same
,
before
it
was
created
.
And
because
I
am
certain
he
will
say
,
that
he
would
never
have
been
able
to
have
known
any
of
all
those
things
which
experience
alone
hath
made
him
knowing
in
,
he
ought
not
to
deny
me
pardon
,
and
to
excuse
me
if
I
know
not
that
which
he
knows
,
touching
what
would
ensue
upon
the
annihilation
of
the
said
Globe
:
for
that
I
want
that
experience
which
he
hath
.
Let
us
hear
if
he
have
any
thing
else
to
say
.
SIMP.
There
remains
this
figure
,
which
represents
the
Terrestrial
Globe
with
a
great
cavity
about
its
centre
,
full
of
air
;
and
to
shew
that
Graves
move
not
downwards
to
unite
with
the
Terrestrial
Globe
,
as
Copernicus
saith
,
he
constituteth
this
stone
in
the
centre
;
and
demandeth
,
it
being
left
at
liberty
,
what
it
would
do
;
and
he
placeth
another
in
the
space
of
this
great
vacuum
,
and
asketh
the
same
question
.
Saying
,
as
to
the
first
:
Lapis
in
centro
constitutus
,
aut
ascendet
ad
terram
in
punctum
aliquod
,
aut
non
.
Si
secundum
;
falsum
est
,
partes
ob
solam
sejunctionem
à
toto
,
ad
illud
moveri
.
Si
primum
;
omnis
ratio
&
experientia
renititur
,
neque
gravia
in
suae
gravitatis
centro
conquiescent
.
Item
si
suspensus
lapis
,
liberatus
decidat
in
centrum
,
separabit
se
à
toto
,
contra
Copernicum
:
si
pendeat
,
refragatur
omnis
experientia
,
cùm
videamus
integros
fornices
corruere
.
(
Wherein
he
saith
:
)
The
stone
placed
in
the
centre
,
either
ascendeth
to
the
Earth
in
some
point
,
or
no.
If
the
second
,
it
is
false
that
the
parts
separated
from
the
whole
,
move
unto
it
.
If
the
first
;
it
contradicteth
all
reason
and
experience
,
nor
doth
the
grave
body
rest
in
the
centre
of
its
gravity
.
And
if
the
stone
being
suspended
in
the
air
,
be
let
go
,
do
descend
to
the
centre
,
it
will
separate
from
its
vvhole
,
contrary
to
Copernicus
:
if
it
do
hang
in
the
air
,
it
contradicteth
all
experience
:
since
we
see
whole
Vaults
to
fall
dovvn
.
SALV
.
I
vvill
ansvver
,
though
vvith
great
disadvantage
to
my self
,
seeing
I
have
to
do
vvith
one
vvho
hath
seen
by
experience
,
vvhat
these
stones
do
in
this
great
Cave
:
a
thing
,
vvhich
for
my
part
I
have
not
seen
;
and
vvill
say
,
that
things
grave
have
an
existence
before
the
common
centre
of
gravity
:
Things
grave
are
before
the
centre
of
gravity
.
so
that
it
is
not
one
centre
alone
,
vvhich
is
no
other
than
indivisible
point
,
and
therefore
of
no
efficacie
,
that
can
attract
unto
it
grave
matters
;
but
that
those
matters
conspiring
naturally
to
unite
,
form
to
themselves
a
common
centre
,
which
is
that
about
which
parts
of
equal
moment
consist
:
The
great
ma●
of
grave
bodies
being
transfe●red
cut
of
their
place
,
the
separated
parts
would
follow
that
〈◊〉
.
so
that
I
hold
,
that
if
the
great
aggregate
of
grave
bodies
vvere
gathered
all
into
any
one
place
,
the
small
parts
that
vvere
separated
from
their
vvhole
,
vvould
follovv
the
same
,
and
if
they
vvere
not
hindered
,
vvould
penetrate
vvherever
they
should
find
parts
less
grave
than
themselves
:
but
coming
vvhere
they
should
meet
vvith
matters
more
grave
,
they
vvould
descend
no
farther
.
And
therefore
I
hold
,
that
in
the
Cave
full
of
air
,
the
vvhole
Vault
vvould
press
,
and
violently
rest
it self
onely
upon
that
air
,
in
case
its
hardness
could
not
be
overcome
and
broken
by
its
gravity
;
but
loose
stones
,
I
believe
,
would
descend
to
the
centre
,
and
not
swim
above
in
the
air
:
nor
may
it
be
said
,
that
they
move
not
to
their
whole
,
though
they
move
whither
all
the
parts
of
the
whole
would
transfer
themselves
,
if
all
impediments
were
removed
.
SIMP.
That
which
remaineth
,
is
a
certain
Errour
which
he
observeth
in
a
Disciple
of
Copernicus
,
who
making
the
Earth
to
move
with
an
annual
motion
,
and
a
diurnal
,
in
the
same
manner
as
the
Cart-wheel
moveth
upon
the
circle
of
the
Earth
,
and
in
it self
,
did
constitute
the
Terrestrial
Globe
too
great
,
or
the
great
Orb
too
little
;
for
that
365
revolutions
of
the
Aequinoctial
,
are
less
by
far
than
the
circumference
of
the
great
Orb.
SALV
.
Take
notice
that
you
mistake
,
and
tell
us
the
direct
contrary
to
what
must
needs
be
written
in
that
Book
;
for
you
should
say
,
that
that
same
Copernican
Author
did
constitute
the
Terrestrial
Globe
too
little
,
and
the
great
Orb
too
big
;
and
not
the
Terrestrial
Globe
too
big
,
and
the
annual
too
little
.
SIMP.
The
mistake
is
not
mine
;
see
here
the
words
of
the
Book
.
Non
videt
,
quòd
vel
circulum
annuum
aequo
minorem
,
vel
orbem
terreum
justo
multò
fabricet
majorem
.
(
In
English
thus
:
)
He
seeth
not
,
that
he
either
maketh
the
annual
circle
equal
to
the
less
,
or
the
Terrestrial
Orb
much
too
big
.
SALV
.
I
cannot
tell
whether
the
first
Author
erred
or
no
,
since
the
Author
of
this
Tractate
doth
not
name
him
;
but
the
error
of
this
Book
is
certain
and
unpardonable
,
whether
that
follower
of
Copernicus
erred
or
not
erred
;
for
that
your
Author
passeth
by
so
material
an
error
,
without
either
detecting
or
correcting
it
.
But
let
him
be
forgiven
this
fault
,
as
an
error
rather
of
inadvertencie
,
than
of
any
thing
else
:
Farthermore
,
were
it
not
,
that
I
am
already
wearied
and
tired
with
talking
and
spending
so
much
time
with
very
little
profit
,
in
these
frivolous
janglings
and
altercations
,
I
could
shew
,
that
it
is
not
impossible
for
a
circle
,
though
no
bigger
than
a
Cart-wheel
,
It
is
not
impo●sible
with
the
circumference
of
a
small
〈◊〉
for
times
●●volved
to
measure
and
describ●●
〈…〉
great
circle
whatsoever
.
with
making
not
365
,
but
lesse
than
20
revolutions
,
to
describe
and
measure
the
circumference
,
not
onely
of
the
grand
Orb
,
but
of
one
a
thousand
times
greater
;
and
this
I
s●y
to
shew
,
that
there
do
not
want
far
greater
subtilties
,
than
this
wherewith
your
Author
goeth
about
to
detect
the
errour
of
Copernicus
:
but
I
pray
you
,
let
us
breath
a
little
,
that
so
we
may
proceed
to
the
other
Philosopher
,
that
opposeth
of
the
same
Copernicus
.
SAGR.
To
confesse
the
truth
,
I
stand
as
much
in
need
of
respite
as
either
of
you
;
though
I
have
onely
wearied
my
eares
:
and
were
it
not
that
I
hope
to
hear
more
ingenious
things
from
this
other
Author
,
I
question
whether
I
should
not
go
my
ways
,
to
take
the
air
in
my
[
](A61244-e52470-b)*
*
Go●d●
la.
Pleasure-boat
.
SIMP.
I
believe
that
you
will
hear
things
of
greater
moment
;
for
this
is
a
most
accomplished
Philosopher
,
and
a
great
Mathematician
,
and
hath
confuted
Tycho
in
the
businesse
of
the
Comets
,
and
new
Stars
.
[
](A61244-e52520-b)*
*
The
●ame
of
the
Author
is
Scipio
Claramontius
.
SALV
.
Perhaps
he
is
the
same
with
the
Author
of
the
Book
,
called
Anti-Tycho
?
SIMP.
He
is
the
very
same
:
but
the
confutation
of
the
new
Stars
is
not
in
his
Anti-Tycho
,
onely
so
far
as
he
proveth
,
that
they
were
not
prejudicial
to
the
inalterability
and
ingenerability
of
the
Heavens
,
as
I
told
you
before
;
but
after
he
had
published
his
Anti-Tycho
,
having
found
out
,
by
help
of
the
Parallaxes
,
a
way
to
demonstrate
,
that
they
also
are
things
elementary
,
and
contained
within
the
concave
of
the
Moon
,
he
hath
writ
this
other
Book
,
de
tribus
novis
Stellis
,
&c.
and
therein
also
inserted
the
Arguments
against
Copernicus
:
I
have
already
shewn
you
what
he
hath
written
touching
these
new
Stars
in
his
Anti-Tycho
,
where
he
denied
not
,
but
that
they
were
in
the
Heavens
;
but
he
proved
,
that
their
production
altered
not
the
inalterability
of
the
Heavens
,
and
that
he
did
,
with
a
Discourse
purely
philosophical
,
in
the
same
manner
as
you
have
already
heard
.
And
I
then
forgot
to
tell
you
,
how
that
he
afterwards
did
finde
out
a
way
to
remove
them
out
of
the
Heavens
;
for
he
proceeding
in
this
confutation
,
by
way
of
computations
and
parallaxes
,
matters
little
or
nothing
at
all
understood
by
me
,
I
did
not
mention
them
to
you
,
but
have
bent
all
my
studies
upon
these
arguments
against
the
motion
of
the
Earth
,
which
are
purely
natural
.
SALV
.
I
understand
you
very
well
:
and
it
will
be
convenient
after
we
have
heard
what
he
hath
to
say
against
Copernicus
,
that
we
hear
,
or
see
at
least
the
manner
wherewith
he
,
by
way
of
Parallaxes
,
proveth
those
new
stars
to
be
elementary
,
which
so
many
famous
Astronomers
constitute
to
be
all
very
high
,
and
amongst
the
stars
of
the
Firmament
;
and
as
this
Author
accomplisheth
such
an
enterprize
of
pulling
the
new
stars
out
of
heaven
,
and
placing
them
in
the
elementary
Sphere
,
he
shall
be
worthy
to
be
highly
exalted
,
and
transferred
himself
amongst
the
stars
,
or
at
least
,
that
his
name
be
by
fame
etern●●ed
amongst
them
.
Yet
before
we
enter
upon
this
,
let
us
hear
what
he
alledgeth
against
the
opinion
of
Copernicus
,
and
do
you
begin
to
recite
his
Arguments
.
SIMP.
It
will
not
be
necessary
that
we
read
them
ad
verbum
,
because
they
are
very
prolix
;
but
I
,
as
you
may
see
,
in
reading
them
several
times
attentively
,
have
marked
in
the
margine
those
words
,
wherein
the
strength
of
his
arguments
lie
,
and
it
will
suffice
to
read
them
.
The
opinion
of
Copernicus
overthrows
the
Criterium
of
Philosophy
The
first
Argument
beginneth
here
.
Et
primo
,
si
opinio
Copernici
recipiatur
,
Criterium
naturalis
Philosophiae
,
ni
prorsus
tollatur
,
vehementer
sal●em
labefactari
videtur
.
[
In
our
Idiom
thus
]
And
first
,
if
Copernicus
his
opinion
be
imbraced
,
the
Criterium
of
natural
Philosophy
will
be
,
if
not
wholly
subverted
,
yet
at
least
extreamly
shaken
.
Which
,
according
to
the
opinion
of
all
the
sects
of
Philosophers
requireth
,
that
Sense
and
Experience
be
our
guides
in
philosophating
:
But
in
the
Copernican
position
the
Senses
are
greatly
deluded
,
whil'st
that
they
visibly
discover
neer
at
hand
in
a
pure
Medium
,
the
gravest
bodies
to
descend
perpendicularly
downwards
,
never
deviating
a
single
hairs
breadth
from
rectitude
;
and
yet
according
to
the
opinion
of
Copernicus
,
the
sight
in
so
manifest
a
thing
is
deceived
,
and
that
motion
is
not
reall
straight
,
but
mixt
of
right
and
circular
.
SALV
.
This
is
the
first
argument
,
that
Aristotle
,
Ptolomy
,
and
all
their
followers
do
produce
;
to
vvhich
we
have
abundantly
answered
,
and
shewn
the
Paralogisme
,
and
with
sufficient
plainnesse
proved
,
that
the
motion
in
common
to
us
and
other
moveables
,
is
,
as
if
there
were
no
such
thing
;
but
because
true
conclusions
meet
with
a
thousand
accidents
,
Common
motion
is
,
as
if
it
never
were
.
that
confirme
them
,
I
vvill
,
with
the
favour
of
this
Philosopher
,
adde
something
more
;
and
you
Simplicius
personating
him
,
answer
me
to
vvhat
I
shall
ask
you
:
The
argument
taken
from
things
falling
perpendicularly
,
another
way
confuted
.
And
first
tell
me
,
vvhat
effect
hath
that
stone
upon
you
,
which
falling
from
the
top
of
the
Tower
,
is
the
cause
that
you
perceive
that
motion
;
for
if
its
fall
doth
operate
upon
you
neither
more
nor
lesse
,
than
its
standing
still
on
the
Towers
top
,
you
doubtlesse
could
not
discern
its
descent
,
or
distinguish
its
moving
from
its
lying
still
.
SIMP.
I
comprehend
its
moving
,
in
relation
to
the
Tower
,
for
that
I
see
it
one
while
just
against
such
a
mark
in
the
said
Tower
,
and
another
while
against
another
lower
,
and
so
successively
,
till
that
at
last
I
perceive
it
arrived
at
the
ground
.
SALV
.
Then
if
that
stone
were
let
fall
from
the
tallons
of
an
Eagle
flying
,
and
should
descend
thorow
the
simple
invisible
Air
,
and
you
had
no
other
object
visible
and
stable
,
wherewith
to
make
comparisons
to
that
,
you
could
not
perceive
its
motion
?
SIMP.
No
,
nor
the
stone
it self
;
for
if
I
would
see
it
,
when
it
is
at
the
highest
,
Where
●e
motion
of
〈◊〉
body
is
collected
.
I
must
raise
up
my
head
,
and
as
it
descendeth
,
I
must
hold
it
lower
and
lower
,
and
in
a
word
,
must
continually
move
either
that
,
or
my
eyes
,
following
the
motion
of
the
said
stone
.
SALV
.
You
have
novv
rightly
answered
:
you
knovv
then
that
the
stone
lyeth
still
,
The
motion
of
the
eye
argueth
the
motion
of
the
ob●ect
looked
on
.
vvhen
without
moving
your
eye
,
you
alwayes
see
it
before
you
;
and
you
know
that
it
moveth
,
when
for
the
keeping
it
in
sight
,
you
must
move
the
organ
of
sight
,
the
eye
.
So
then
vvhen
ever
without
moving
your
eye
,
you
continually
behold
an
object
in
the
self
same
aspect
,
you
do
alvvays
judge
it
immoveable
.
SIMP.
I
think
it
must
needs
be
so
.
SALV
.
Novv
fancy
your self
to
be
in
a
ship
,
and
to
have
fixed
your
eye
on
the
point
of
the
Sail-yard
:
Do
you
think
,
that
because
the
ship
moveth
very
fast
,
you
must
move
your
eye
,
to
keep
your
sight
alvvayes
upon
the
point
of
the
Sail-yard
,
and
to
follow
its
motion
?
SIMP.
I
am
certain
,
that
I
should
need
to
make
no
change
at
all
;
and
that
not
only
in
the
sight
;
but
if
I
had
aimed
a
Musket
at
it
,
I
should
never
have
need
,
let
the
ship
move
how
it
vvill
,
to
stir
it
an
hairs
breadth
to
keep
it
full
upon
the
same
.
SALV
.
And
this
happens
because
the
motion
,
which
the
Ship
conferreth
on
the
Sail-yard
,
it
conferreth
also
upon
you
,
and
upon
your
eye
;
so
that
you
need
not
stir
it
a
jot
to
behold
the
top
of
the
Sail-yard
:
and
consequently
,
it
vvill
seem
to
you
immoveaable
.
Now
this
Discourse
being
applied
to
the
revolution
of
the
Earth
,
and
to
the
stone
placed
in
the
top
of
the
Tower
,
in
which
you
cannot
discern
any
motion
,
because
that
you
have
that
motion
vvhich
is
necessary
for
the
following
of
it
,
in
common
with
it
from
the
Earth
;
so
that
you
need
not
move
your
eye
.
When
again
there
is
conferred
upon
it
the
motion
of
descent
,
which
is
its
particular
motion
,
and
not
yours
,
and
that
it
is
intermixed
with
the
circular
,
that
part
of
the
circular
which
is
common
to
the
stone
,
and
to
the
eye
,
continueth
to
be
imperceptible
,
and
the
right
onely
is
perceived
,
for
that
to
the
perception
of
it
,
you
must
follow
it
with
your
eye
,
looking
lower
and
lower
.
I
wish
for
the
undeceiving
of
this
Philosopher
,
that
I
could
advise
him
,
that
some
time
or
other
going
by
water
,
An
experiment
that
〈◊〉
how
the
common
motion
is
imperc●ptible
.
he
would
carry
along
with
him
a
Vessel
of
reasonable
depth
full
of
water
,
and
prepare
a
ball
of
wax
,
or
other
matter
that
would
descend
very
slowly
to
the
bottome
,
so
that
in
a
minute
of
an
hour
,
it
would
scarce
sink
a
yard
;
and
that
rowing
the
boat
as
fast
as
could
be
,
so
that
in
a
minute
of
an
hour
it
should
run
above
an
hundred
yards
,
he
would
let
the
ball
submerge
into
the
water
,
&
freely
descend
,
&
diligently
observe
its
motion
.
If
he
would
but
do
thus
,
he
should
see
,
first
,
that
it
would
go
in
a
direct
line
towards
that
point
of
the
bottom
of
the
vessel
,
whither
it
would
tend
,
if
the
boat
should
stand
still
;
&
to
his
eye
,
and
in
relation
to
the
vessel
,
that
motion
would
appear
most
straight
and
perpendicular
,
and
yet
he
could
not
say
,
but
that
it
would
be
composed
of
the
right
motion
downwards
,
and
of
the
circular
about
the
element
of
water
.
And
if
these
things
befall
in
matters
not
natural
,
and
in
things
that
we
may
experiment
in
their
state
of
rest
;
&
then
again
in
the
contrary
state
of
motion
,
and
yet
as
to
appearance
no
diversity
at
all
is
discovered
,
&
that
they
seem
to
deceive
our
sense
what
can
we
distinguish
touching
the
Earth
,
which
hath
been
perpetually
in
the
same
constitution
,
as
to
motion
and
rest
?
And
in
what
time
can
we
experiment
whether
any
difference
is
discernable
amongst
these
accidents
of
local
motion
,
in
its
diverse
states
of
motion
and
rest
,
if
it
eternally
indureth
in
but
one
onely
of
them
?
SAGR.
These
Discourses
have
somewhat
whetted
my
stomack
,
which
those
fishes
,
and
snails
had
in
part
nauseated
;
and
the
former
made
me
call
to
minde
the
correction
of
an
errour
,
that
hath
so
much
appearance
of
truth
,
that
I
know
not
whether
one
of
a
thousand
would
refuse
to
admit
it
as
unquestionable
.
And
it
was
this
,
that
sailing
into
Syria
,
and
carrying
with
me
a
very
good
Telescope
,
that
had
been
bestowed
on
me
by
our
Common
Friend
,
who
not
many
dayes
before
had
invented
,
I
proposed
to
the
Mariners
,
that
it
would
be
of
great
benefit
in
Navigation
to
make
use
of
it
upon
the
round
top
of
a
ship
,
to
discover
and
kenne
Vessels
afar
off
.
The
benefit
was
approved
,
but
there
was
objected
the
difficulty
of
using
it
,
An
ingenuous
consideration
about
the
possibility
of
using
the
Telescope
with
as
much
facility
on
the
round
top
of
the
Mast
of
a
ship
,
as
on
the
Deck
.
by
reason
of
the
Ships
continual
fluctuation
;
and
especially
on
the
round
top
,
where
the
agitation
is
so
much
greater
,
and
that
it
would
be
better
for
any
one
that
would
make
use
thereof
to
stand
at
the
Partners
upon
the
upper
Deck
,
where
the
tossing
is
lesse
than
in
any
other
place
of
the
Ship
.
I
(
for
I
will
not
conceal
my
errour
)
concurred
in
the
same
opinion
,
and
for
that
time
said
no
more
:
nor
can
I
tell
you
by
what
hints
I
was
moved
to
return
to
ruminate
with
my self
upon
this
businesse
,
and
in
the
end
came
to
discover
my
simplicity
(
although
excusable
)
in
admitting
that
for
true
,
which
is
most
false
;
false
I
say
,
that
the
great
agitation
of
the
basket
or
round
top
,
in
comparison
of
the
small
one
below
,
at
the
partners
of
the
Mast
,
should
render
the
use
of
the
Telescope
more
difficult
in
finding
out
the
object
.
SALV
.
I
should
have
accompanied
the
Mariners
,
and
your self
at
the
beginning
.
SIMP.
And
so
should
I
have
done
,
and
still
do
:
nor
can
I
believe
,
if
I
should
think
of
it
an
hundred
years
,
that
I
could
understand
it
otherwise
.
SAGR.
I
may
then
,
it
seems
,
for
once
prove
a
Master
to
you
both
.
And
because
the
proceeding
by
interrogatories
doth
in
my
opinion
much
dilucidate
things
,
besides
the
pleasure
which
it
affords
of
confounding
our
companion
,
forcing
from
him
that
which
he
thought
he
knew
not
,
I
will
make
use
of
that
artifice
.
And
first
,
I
suppose
that
the
Ship
,
Gally
,
or
other
Vessel
,
which
we
would
discover
,
is
a
great
way
off
,
that
is
,
four
,
six
,
ten
,
or
twenty
[
](A61244-e53380-b)*
*
I
deviate
here
from
the
strict
Sea
Diallect
,
which
denominates
all
distances
by
Leagues
.
miles
,
for
that
to
kenne
those
neer
at
hand
there
is
no
need
of
these
Glasses
:
&
consequently
,
the
Telescope
may
at
such
a
distance
of
four
or
six
miles
conveniently
discover
the
whole
Vessel
,
&
a
muchgreater
bulk
.
Now
I
demand
what
for
species
,
&
how
many
for
number
are
the
motions
that
are
made
upon
the
round
top
,
depending
on
the
fluctuation
of
the
Ship
.
SALV
.
We
will
suppose
that
the
Ship
goeth
towards
the
East
.
First
,
Different
motions
depending
on
the
fluctuation
of
the
Ship
.
in
a
calme
Sea
,
it
would
have
no
other
motion
than
this
of
progression
,
but
adding
the
undulation
of
the
Waves
,
there
shall
result
thence
one
,
which
alternately
hoysting
and
lowering
the
poop
and
prow
,
maketh
the
round
top
,
to
lean
forwards
and
backwards
;
other
waves
driving
the
vessel
sidewayes
,
bow
the
Mast
to
the
Starboard
and
Larboard
;
others
,
may
bring
the
ship
somewhat
abovt
,
and
bear
her
away
by
the
Misne
from
East
,
one
while
towards
the
[
](A61244-e53440-b)*
*
Greco
,
which
the
Latine
Translator
according
to
his
usual
carelessenesse
(
to
call
it
no
worse
)
translates
Corum
Ventum
,
the
Northwest
Wind
;
for
Ventum
Libanotum
.
Northeast
,
another
while
toward
the
Southeast
;
others
bearing
her
up
by
the
Carine
may
make
her
onely
to
rise
,
and
fall
;
and
in
sum
,
these
motions
are
for
species
two
,
one
that
changeth
the
direction
of
the
Telescope
angularly
,
the
other
lineally
,
without
changing
angle
,
that
is
,
alwayes
keeping
the
tube
of
the
Instrument
parallel
to
its
self
.
SAGR.
Tell
me
,
Two
mutations
made
in
the
Telescope
,
depending
on
the
agitation
of
the
Ship
.
in
the
next
place
,
if
we
,
having
first
directed
the
Telescope
yonder
away
towards
the
Tower
of
[
](A61244-e53540-b)*
*
This
is
a
Castle
six
Italian
miles
from
Venice
Northwards
.
Burano
,
six
miles
from
hence
,
do
turn
it
angularly
to
the
right
hand
,
or
to
the
left
,
or
else
upwards
or
downwards
,
but
a
[
](A61244-e53570-b)*
*
Vn
nero
d'
ugna
,
the
black
or
paring
of
a
nail
.
straws
breadth
,
what
effect
shall
it
have
upon
us
touching
the
finding
out
of
the
said
tower
?
SALV
.
It
would
make
us
immediately
lose
sight
of
it
,
for
such
a
declination
,
though
small
here
,
may
import
there
hundreds
and
thousands
of
yards
.
SAGR.
But
if
without
changing
the
angle
,
keeping
the
tube
alwayes
parallel
to
it self
,
we
should
transfer
it
ten
or
twelve
yards
farther
off
to
the
right
or
left
hand
,
upwards
or
downwards
,
what
alteration
would
it
make
as
to
the
Tower
?
SALV
.
The
change
would
be
absolutely
undiscernable
;
for
that
the
spaces
here
and
there
being
contained
between
parallel
rayes
,
the
mutations
made
here
and
there
,
ought
to
be
equal
,
and
because
the
space
which
the
Instrument
discovers
yonder
,
is
capable
of
many
of
those
Towers
;
therefore
we
shall
not
lose
sight
of
it
.
SAGR.
Returning
now
to
the
Ship
,
we
may
undoubtedly
affirm
,
that
the
Telescope
moving
to
the
right
or
left
,
upwards
,
or
downwards
,
and
also
forwards
or
backwards
ten
or
fifteen
fathom
;
keeping
it
all
the
while
parallel
to
its
self
,
the
visive
ray
cannot
stray
from
the
point
observed
in
the
object
,
more
than
those
fifteen
fathom
;
and
because
in
a
distance
of
eight
or
ten
miles
,
the
Instrument
takes
in
a
much
greater
space
than
the
Gally
or
other
Vessel
kenn'd
;
therefore
that
small
mutation
shall
not
make
me
lose
sight
of
her
.
The
impediment
therefore
,
and
the
cause
of
losing
the
object
cannot
befall
us
,
unlesse
upon
the
mutation
made
angularly
;
since
that
Telescopes
transportation
higher
or
lower
,
to
the
right
,
or
to
the
left
,
by
the
agitation
of
the
ship
,
cannot
import
any
great
number
of
fathomes
.
Now
suppose
that
you
had
two
Telescopes
fixed
,
one
at
the
Partners
close
by
the
Deck
,
and
the
other
at
the
round
top
,
nay
at
the
main
top
,
or
main
top-gallant
top
,
where
you
hang
forth
the
Pennon
or
streamer
,
and
that
they
be
both
directed
to
the
Vessel
that
is
ten
miles
off
,
tell
me
,
whether
you
believe
that
any
agitation
of
the
ship
,
&
inclination
of
the
Mast
,
can
make
greater
changes
,
as
to
the
angle
,
in
the
higher
tube
,
than
in
the
lower
?
One
wave
arising
,
the
prow
will
make
the
main
top
give
back
fifteen
or
twenty
fathom
more
than
the
foot
of
the
Mast
,
and
it
shall
carry
the
upper
tube
along
with
it
so
greata
space
,
&
the
lower
it
may
be
not
a
palm
;
but
the
angle
shall
change
in
one
Instrument
aswell
as
in
the
other
;
and
likewise
a
side-billow
shall
bear
the
higher
tube
an
hundred
times
as
far
to
the
Larboard
or
Starboard
,
as
it
will
the
other
below
;
but
the
angles
change
not
at
all
,
or
else
alter
both
alike
.
But
the
mutation
to
the
right
hand
or
left
,
forwards
or
backwards
,
upwards
or
downwards
,
bringeth
no
sensible
impediment
in
the
kenning
of
objects
remote
,
though
the
alteration
of
the
angle
maketh
great
change
therein
;
Therefore
it
must
of
necessity
be
confessed
,
that
the
use
of
the
Telescope
on
the
round
top
is
no
more
difficult
than
upon
the
Deck
at
the
Partners
;
seeing
that
the
angular
mutations
are
alike
in
both
places
.
SALV
.
How
much
circumspection
is
there
to
be
used
in
affirming
or
denying
a
proposition
?
I
say
again
,
that
hearing
it
resolutely
affirmed
,
that
there
is
a
greater
motion
made
on
the
Masts
top
,
than
at
its
partners
,
every
one
will
perswade
himself
,
that
the
use
of
the
Telescope
is
much
more
difficult
above
than
below
.
And
thus
also
I
will
excuse
those
Philosophers
,
who
grow
impatient
and
fly
out
into
passion
against
such
as
will
not
grant
them
,
that
that
Cannon
bullet
which
they
cleerly
see
to
fall
in
a
right
line
perpendicularly
,
doth
absolutely
move
in
that
manner
;
but
will
have
its
motion
to
be
by
an
arch
,
and
also
very
much
inclined
and
transversal
:
but
let
us
leave
them
in
these
labyrinths
,
and
let
us
hear
the
other
objections
,
that
our
Author
in
hand
brings
against
Copernicus
.
SIMP.
The
Author
goeth
on
to
demonstrate
that
in
the
Doctrine
of
Copernicus
,
it
is
requisite
to
deny
the
Senses
,
and
the
greatest
Sensations
,
The
annual
motion
of
the
〈…〉
a
perpetual
and
strong
winde
.
as
for
instance
it
would
be
,
if
we
that
feel
the
respirations
of
a
gentle
gale
,
should
not
feel
the
impulse
of
a
perpetual
winde
that
beateth
upon
us
with
a
velocity
that
runs
more
than
2529
miles
an
hour
,
for
so
much
is
the
space
that
the
centre
of
the
Earth
in
its
annual
motion
passeth
in
an
hour
upon
the
circumference
of
the
grand
Orb
,
as
he
diligently
calculates
;
and
because
,
as
he
saith
,
by
the
judgment
of
Copernicus
,
Cum
terra
movetur
circumpositus
aër
,
motus
tamen
ejus
,
velocior
licet
ac
rapidior
celerrimo
quocunque
vento
,
à
nobis
non
sentiretur
,
sed
summa
tum
tranquilitas
reputaretur
,
nisi
alius
motus
accederet
.
Quid
est
verò
decipi
sensum
,
nisi
haec
esset
deceptio
?
[
Which
I
make
to
speak
to
this
sense
.
]
The
circumposed
air
is
moved
with
the
Earth
,
yet
its
motion
,
although
more
speedy
and
rapid
than
the
swiftest
wind
whatsoever
,
would
not
be
perceived
by
us
,
but
then
would
be
thought
a
great
tranquillity
,
unlesse
some
other
motion
should
happen
;
what
then
is
the
deception
of
the
sense
,
if
this
be
not
?
SALV
.
It
must
needs
be
that
this
Philosopher
thinketh
,
that
that
Earth
which
Copernicus
maketh
to
turn
round
,
together
with
the
ambient
air
along
the
circumference
of
the
great
Orb
,
is
not
that
whereon
we
inhabit
,
but
some
other
separated
from
this
;
for
that
this
of
ours
carrieth
us
also
along
with
it
with
the
same
velocity
,
The
air
alwayes
touching
us
with
the
same
part
of
it
cannot
make
us
feel
it
.
as
also
the
circumjacent
air
:
And
what
beating
of
the
air
can
we
feel
,
when
we
fly
vvith
equal
speed
from
that
vvhich
should
accost
us
?
This
Gentleman
forgot
,
that
vve
no
less
than
the
Earth
and
air
are
carried
about
,
and
that
consequently
vve
are
alvvays
touch'd
by
one
and
the
same
part
of
the
air
,
vvhich
yet
doth
not
make
us
feel
it
.
SIMP.
But
I
rather
think
that
he
did
not
so
think
;
hear
the
vvords
vvhich
immediatey
follovv
.
Praeterea
nos
quoque
rotamur
ex
circumductione
terrae
&c.
SALV
.
Now
I
can
no
longer
help
nor
excuse
him
;
do
you
plead
for
him
and
bring
him
off
,
Simplicius
.
SIMP.
I
cannot
thus
upon
the
sudden
think
of
an
excuse
that
pleaseth
me
.
SALV
.
Go
to
;
take
this
whole
night
to
think
on
it
,
and
defend
him
to
morrow
;
in
the
mean
time
let
us
hear
some
other
of
his
objections
.
SIMP.
He
prosecuteth
the
same
Objection
,
shewing
,
that
in
the
way
of
Copernicus
,
He
that
will
follow
Copernicus
,
must
deny
his
senses
.
a
man
must
deny
his
own
senses
.
For
that
this
principle
whereby
we
turn
round
with
the
Earth
,
either
is
intrinsick
to
us
,
or
external
;
that
is
,
a
rapture
of
that
Earth
;
and
if
it
be
this
second
,
we
not
feeling
any
such
rapture
,
it
must
be
confessed
that
the
sense
of
feeling
,
doth
not
feel
its
own
object
touching
it
,
nor
its
impression
on
the
sensible
part
:
but
if
the
principle
be
intrinsecal
,
we
shall
not
perceive
a
local
motion
that
is
derived
from
our selves
,
and
we
shall
never
discover
a
propension
perpetually
annexed
to
our selves
.
SALV
.
So
that
the
instance
of
this
Philosopher
lays
its
stress
upon
this
,
that
whether
the
principle
by
which
we
move
round
with
the
Earth
be
either
extern
,
or
intern
,
yet
however
we
must
perceive
it
,
and
not
perceiving
it
,
it
is
neither
the
one
nor
the
other
,
and
therefore
we
move
not
,
nor
consequently
the
Earth
.
Now
I
say
,
Our
motion
may
be
either
〈…〉
or
extern●
,
and
yet
we
never
perceive
or
feel
it
.
that
it
may
be
both
ways
,
and
yet
we
not
perceive
the
same
.
And
that
it
may
be
external
,
the
experiment
of
the
boat
superabundantly
satisfieth
me
;
I
say
,
superabundantly
,
because
it
being
in
our
power
at
all
times
to
make
it
move
,
and
also
to
make
it
stand
still
,
and
with
great
exactness
to
make
observation
,
whether
by
some
diversity
that
may
be
comprehended
by
the
sense
of
feeling
,
we
can
come
to
know
whether
it
moveth
or
no
,
seeing
that
as
yet
no
such
science
is
obtained
:
Will
it
then
be
any
matter
of
wonder
,
if
the
same
accident
is
unknown
to
us
on
the
Earth
,
the
which
may
have
carried
us
about
perpetually
,
and
we
,
without
our
being
ever
able
to
experiment
its
rest
?
The
motion
of
a
Boat
insensible
to
those
that
are
with
in
it
,
as
to
the
sense
of
feeling
.
You
,
Simplicius
,
as
I
believe
,
have
gone
by
boat
many
times
to
Padoua
,
and
if
you
will
confess
the
truth
,
you
never
felt
in
your self
the
participation
of
that
motion
,
unless
when
the
boat
running
a-ground
,
or
encountring
some
obstacle
,
did
stop
,
and
that
you
with
the
other
Passengers
being
taken
on
a
sudden
,
were
with
danger
over-set
.
It
would
be
necessary
that
the
Terrestrial
Globe
should
meet
with
some
rub
that
might
arrest
it
,
for
I
assure
you
,
that
then
you
would
discern
the
impulse
residing
in
you
,
when
it
should
toss
you
up
towards
the
Stars
.
It
's
true
,
that
by
the
other
senses
,
but
yet
assisted
by
Reason
,
The
boats
motion
is
perceptible
to
the
sight
joyn'd
with
reason
.
you
may
perceive
the
motion
of
the
boat
,
that
is
,
with
the
sight
,
in
that
you
see
the
trees
and
buildings
placed
on
the
shoar
,
which
being
separated
from
the
boat
,
seem
to
move
the
contrary
way
.
The
terrestrial
motion
collected
from
the
stars
.
But
if
you
would
by
such
an
experiment
receive
intire
satisfaction
in
this
business
of
the
Terrestrial
motion
,
look
on
the
stars
,
which
upon
this
reason
seem
to
move
the
contrary
way
.
As
to
the
wondering
that
we
should
not
feel
such
a
principle
,
supposing
it
to
be
internal
,
is
a
less
reasonable
conceit
;
for
if
we
do
not
feel
such
a
one
,
that
cometh
to
us
from
without
,
and
that
frequently
goeth
away
,
with
what
reason
can
we
expect
to
feel
it
,
if
it
immutably
and
continually
resides
in
us
?
Now
let
us
see
what
you
have
farther
to
allege
on
this
argument
.
SIMP.
Take
this
short
exclamation
.
Ex
hac
itaque
opinione
necesse
est
diffidere
nostris
sensibus
,
ut
penitùs
fallacibus
vel
stupidis
in
sensilibus
,
etiam
conjunctissimis
,
dijudicandis
.
Quam
ergò
veritatem
sperare
possumus
à
facultate
adeò
fallaci
ortum
trahentem
?
[
Which
I
render
thus
:
]
From
this
opinion
likewise
,
we
must
of
necessity
suspect
our
own
senses
,
as
wholly
fallible
,
or
stupid
in
judging
of
sensible
things
even
very
near
at
hand
.
What
truth
therefore
can
we
hope
for
,
to
be
derived
from
so
deceiveable
a
faculty
?
SALV
.
But
I
desire
not
to
deduce
precepts
more
profitable
,
or
more
certain
,
learning
to
be
more
circumspect
and
less
confident
about
that
which
at
first
blush
is
represented
to
us
by
the
senses
,
which
may
easily
deceive
us
.
And
I
would
not
have
this
Author
trouble
himself
in
attempting
to
make
us
comprehend
by
sense
,
that
this
motion
of
descending
Graves
is
simply
right
,
and
of
no
other
kind
;
nor
let
him
exclaim
that
a
thing
so
clear
,
manifest
,
and
obvious
should
be
brought
in
question
;
for
in
so
doing
,
he
maketh
others
believe
,
that
he
thinketh
those
that
deny
that
motion
to
be
absolutely
streight
,
but
rather
circular
,
the
stone
did
sensibly
see
it
to
move
in
an
arch
,
seeing
that
he
inviteth
their
senses
more
than
their
Reason
,
to
judg
of
that
effect
:
which
is
not
true
,
Simplicius
,
for
like
as
I
,
that
am
indifferent
in
all
these
opinions
,
and
onely
in
the
manner
of
a
Comedian
,
personate
Copernicus
in
these
our
representations
,
have
never
seen
,
nor
thought
that
I
have
seen
that
stone
fall
otherwise
than
perpendicularly
,
so
I
believe
,
that
to
the
eyes
of
all
others
it
seemed
to
do
the
same
.
Better
it
is
therefore
,
that
deposing
that
appearance
in
which
all
agree
,
we
make
use
of
our
Reason
,
either
to
confirm
the
reality
of
that
,
or
to
discover
its
fallacy
.
SAGR.
If
I
could
any
time
meet
with
this
Philosopher
,
who
yet
me
thinks
is
more
sublime
than
the
rest
of
the
followers
of
the
same
doctrines
,
I
would
in
token
of
my
affection
put
him
in
mind
of
an
accident
which
he
hath
doubtless
very
often
beheld
;
from
which
,
with
great
conformity
to
that
which
we
now
discourse
of
,
it
may
be
collected
how
easily
one
may
be
deceived
by
the
bare
appearance
,
or
,
if
you
will
,
representation
of
the
sense
.
And
the
accident
is
,
the
Moons
seeming
to
follow
those
that
walk
the
streets
in
the
night
,
with
a
pace
equal
to
theirs
,
whilst
they
see
it
go
gliding
along
the
Roofs
of
houses
,
upon
which
it
sheweth
just
like
a
cat
,
that
really
running
along
the
ridges
of
houses
,
leaveth
them
behind
.
An
appearance
that
,
did
not
reason
interpose
,
would
but
too
manifestly
delude
the
sight
.
SIMP.
Indeed
there
want
not
experiments
that
render
us
certain
of
the
fallacy
of
the
meer
senses
;
Arguments
against
the
Earths
motion
taken
,
ex
rerum
natura
.
therefore
suspending
such
sensations
for
the
present
,
let
us
hear
the
Arguments
that
follow
which
are
taken
,
as
he
saith
,
ex
rerum
natura
.
The
first
of
which
is
,
that
the
Earth
cannot
of
its
own
nature
move
with
three
motions
very
different
;
or
otherwise
we
must
deny
many
manifest
Axioms
.
Three
Axioms
that
are
supposed
manifest
.
The
first
whereof
is
,
that
Omnis
effectus
dependeat
ab
aliquâ
causà
;
[
i.
e.
]
that
every
effect
dependeth
on
some
cause
.
The
second
,
that
Nulla
res
seipsam
producat
;
[
i.
e.
]
that
nothing
produceth
it self
:
from
whence
it
follows
,
that
it
is
not
possible
that
the
move
and
moved
should
be
totally
the
same
thing
:
And
this
is
manifest
,
not
onely
in
things
that
are
moved
by
an
extrinsick
mover
;
but
it
is
gathered
also
from
the
principles
propounded
,
that
the
same
holdeth
true
in
the
natural
motion
dependent
on
an
intrinsick
principle
;
otherwise
,
being
that
the
mover
,
as
a
mover
,
is
the
cause
,
and
the
thing
moved
,
as
moved
,
is
the
effect
,
the
same
thing
would
totally
be
both
the
cause
and
effect
.
Therefore
a
body
doth
not
move
its
whole
self
,
that
is
,
so
as
that
all
moveth
,
and
all
is
moved
;
but
its
necessary
in
the
thing
moved
to
distinguish
in
some
manner
the
efficient
principle
of
the
motion
,
and
that
which
with
that
motion
is
moved
.
The
third
Axiom
is
,
that
in
rebus
quae
sensui
subjiciuntur
,
unum
,
quatenus
unum
,
unam
solam
rem
producat
;
i.
e.
That
in
things
subject
to
the
senses
,
one
,
as
it
is
one
,
produceth
but
onely
one
thing
:
That
is
,
the
soul
in
animals
produceth
its
true
divers
operations
,
as
the
sight
,
the
hearing
,
the
smell
,
generation
,
&c.
but
all
these
with
several
instruments
.
And
in
short
,
in
things
sensible
,
the
diversity
of
operations
,
is
observed
to
derive
it self
from
the
diversity
that
is
in
the
cause
.
A
simple
body
at
the
Earth
,
cannot
move
with
three
several
motions
.
Now
if
we
put
all
these
Axioms
together
,
it
will
be
a
thing
very
manifest
,
that
one
simple
body
,
as
is
the
Earth
,
cannot
of
its
own
nature
move
at
the
same
time
with
three
motions
,
very
divers
:
For
by
the
foregoing
suppositions
,
all
moveth
not
its
self
all
;
it
is
necessary
therefore
to
distinguish
in
it
three
principles
of
its
three
motions
;
otherwise
one
and
the
same
principle
would
produce
many
motions
;
but
if
it
contein
in
it
three
principles
of
natural
motions
,
besides
the
part
moved
,
it
shall
not
be
a
simple
body
,
but
compounded
of
three
principle
movers
,
The
Earth
cannot
move
with
any
of
the
motions
assigned
it
by
Copernicus
.
and
of
the
part
moved
.
If
therefore
the
Earth
be
a
simple
body
,
it
shall
not
move
with
three
motions
;
nay
more
,
it
will
not
move
with
any
of
those
which
Copernicus
ascribeth
to
it
,
it
being
to
move
but
with
one
alone
,
for
that
it
is
manifest
,
by
the
reasons
of
Aristotle
,
that
it
moveth
to
its
centre
,
as
its
parts
do
shew
,
which
descend
at
right
angles
to
the
Earths
Spherical
Surface
.
SALV
.
Many
things
might
be
said
,
and
considered
touching
the
connection
of
this
argument
;
Answers
to
the
arguments
contrary
to
the
Earths
motion
,
taken
ex
rerum
natura
.
but
in
regard
that
we
can
resolve
it
in
few
words
,
I
will
not
at
this
time
without
need
inlarge
upon
it
;
and
so
much
the
rather
,
because
the
same
Author
hath
furnished
me
with
an
answer
,
when
he
saith
that
from
one
sole
prinple
in
animals
,
there
are
produced
divers
operations
;
so
that
for
the
present
my
answer
shall
be
,
that
in
the
same
manner
the
Earth
from
one
onely
principle
deriveth
several
operations
.
SIMP.
But
this
answer
will
not
at
all
satisfie
the
Author
who
makes
the
objection
,
yea
,
it
is
totally
overthrown
by
that
which
immediately
after
he
addeth
for
a
greater
confirmation
of
his
argument
,
as
you
shall
hear
.
He
re-inforceth
his
argument
,
I
say
,
with
another
Axiome
,
A
fourth
Axiome
against
the
motion
of
the
Earth
which
is
this
;
That
natura
in
rebus
necessariis
nec
deficiat
,
nec
abundat
:
i.
e.
That
nature
in
things
necessary
is
neither
defective
,
nor
superfluous
.
Flexures
necessary
in
animals
for
the
diversity
of
their
motions
.
This
is
obvious
to
the
observers
of
natural
things
,
and
chiefly
of
animals
,
in
which
,
because
they
are
to
move
with
many
motions
,
Nature
hath
made
many
flexures
,
and
hath
thereunto
commodiously
knitted
the
parts
for
motion
,
as
to
the
knees
,
to
the
hips
,
for
the
inabling
of
living
creatures
to
go
,
and
run
at
their
pleasure
.
Moreover
in
man
he
hath
framed
many
flexions
,
and
joynts
,
in
the
elbow
,
and
hand
,
to
enable
them
to
perform
many
motions
.
Another
argument
against
the
threefold
motion
of
the
Earth
.
From
these
things
the
argument
is
taken
against
the
threefold
motion
of
the
Earth
.
[
Either
the
Body
,
that
is
one
,
and
continuate
,
without
any
manner
of
knittings
or
flexions
,
can
exercise
divers
motions
,
or
cannot
:
If
it
can
without
them
,
then
in
vain
hath
nature
framed
the
flexures
in
animals
;
which
is
contrary
to
the
Axiome
:
but
if
it
cannot
without
them
,
then
the
Earth
,
one
body
,
and
continuate
,
and
deprived
of
flexures
,
and
joynts
,
cannot
of
its
own
nature
move
with
plurality
of
motions
.
]
You
see
now
how
craftily
he
falls
upon
your
answer
,
as
if
he
had
foreseen
it
.
SALV
.
Are
you
serious
,
or
do
you
jest
?
SIMP.
I
speak
it
with
the
best
judgment
I
have
.
SALV
.
You
must
therefore
see
that
you
have
as
fortunate
an
hand
in
defending
the
reply
of
this
Philosopher
,
against
some
other
rejoynders
made
to
him
;
therefore
answer
for
him
,
I
pray
you
,
seeing
we
cannot
have
him
here
.
You
first
admit
it
for
true
,
that
Nature
hath
made
the
joynts
,
flexures
,
and
knuckles
of
living
creatures
,
to
the
intent
that
they
might
move
with
sundry
and
divers
motions
;
and
I
deny
this
proposition
;
and
say
,
that
these
flexions
are
made
,
that
the
animal
may
move
one
,
or
more
of
its
parts
,
The
Flexures
in
animals
are
not
made
for
the
diversity
of
motions
.
the
rest
remaining
immoved
:
and
I
say
,
that
as
to
the
species
and
differences
of
motions
those
are
of
one
kind
alone
,
to
wit
,
all
circular
,
and
for
this
cause
you
see
all
the
ends
of
the
moveable
bones
to
be
convex
or
concave
,
The
motions
of
animals
are
of
one
sort
.
and
of
these
some
are
spherical
,
as
are
those
that
are
to
move
every
way
,
as
in
the
shoulder-joynt
,
The
ends
of
the
bones
are
all
rotund
.
the
arme
of
the
Ensigne
doth
,
in
displaying
the
Colours
,
and
that
of
the
Falconer
in
bringing
his
Hawk
to
the
lure
;
and
such
is
the
flexure
of
the
elbow
,
upon
which
the
hand
turns
round
,
in
boring
with
an
augure
:
others
are
circular
onely
one
way
,
and
as
it
were
cylindrical
,
which
serve
for
the
members
that
bend
onely
in
one
fashion
,
It
is
demonstrated
,
that
the
ends
of
the
bones
are
of
necessity
to
be
rotund
.
as
the
joynts
of
the
fingers
one
above
another
,
&c.
But
without
more
particular
inductions
,
one
only
general
discourse
may
make
this
truth
understood
;
and
this
is
,
that
of
a
solid
body
that
moveth
,
one
of
its
extreams
standing
still
without
chanching
place
,
The
motions
of
animals
are
all
circular
.
the
motion
must
needs
be
circular
,
and
no
other
:
and
because
in
the
living
creatures
moving
,
one
of
its
members
doth
not
separate
from
the
other
its
conterminal
,
therefore
that
motion
is
of
necessity
circular
.
SIMP.
How
can
this
be
?
For
I
see
the
animal
move
with
an
hundred
motions
that
are
not
circular
,
and
very
different
from
one
another
,
as
to
run
,
to
skip
,
to
climbe
,
to
descend
,
to
swim
,
and
many
others
.
SALV
.
T
is
well
:
Secondary
motions
of
animals
dependent
on
the
first
.
but
these
are
secondary
motions
,
depending
on
the
preceding
motions
of
the
joynts
and
flexures
.
Upon
the
plying
of
the
legs
to
the
knees
,
and
the
thighs
to
the
hips
,
which
are
circular
motions
of
the
parts
,
is
produced
,
as
consequents
,
the
skip
,
or
running
,
which
are
motions
of
the
whole
body
,
and
these
may
possibly
not
be
circular
.
Now
because
one
part
of
the
terrestrial
Globe
is
not
required
to
move
upon
another
part
immoveable
,
The
Terrestriall
Globe
hath
noe
need
of
flexures
.
but
that
the
motion
is
to
be
of
the
whole
body
,
there
is
no
need
in
it
of
flexures
.
SIMP.
This
(
will
the
aduersary
rejoyn
)
might
be
,
if
the
motion
were
but
one
alone
,
but
they
being
three
,
and
those
very
different
from
each
other
,
it
is
not
possible
that
they
should
concur
in
an
[
](A61244-e54880-b)*
*
Without
joynts
articulate
body
.
SALV
.
I
verily
believe
that
this
would
be
the
answer
of
the
Philosopher
.
Against
which
I
make
opposition
another
way
;
and
ask
you
,
whether
you
think
that
by
way
of
joynts
and
flexures
one
may
adapt
the
terrestrial
Globe
to
the
participation
of
three
different
circular
motions
?
Do
you
not
answer
me
?
Seeing
you
are
speechlesse
,
I
will
undertake
to
answer
for
the
Philosopher
,
who
would
absolutely
reply
that
they
might
;
for
that
otherwise
it
would
have
been
superfluous
,
and
besides
the
purpose
to
have
proposed
to
consideration
,
that
nature
maketh
the
flexions
,
to
the
end
,
the
moveable
may
move
with
different
motions
;
and
that
therefore
the
terrestrial
Globe
having
no
flexures
,
it
cannot
have
those
three
motions
which
are
ascribed
to
it
.
For
if
he
had
thought
,
that
neither
by
help
of
flexures
,
it
could
be
rendered
apt
for
such
motions
,
he
would
have
freely
affirmed
,
that
the
Globe
could
not
move
with
three
motions
.
Now
granting
this
,
I
intreat
you
,
It
is
desired
to
know
,
by
means
of
what
flexures
and
joynts
the
Terrestrial
Globe
might
move
with
three
diverse
motions
.
and
by
you
,
if
it
were
possible
,
that
Philosopher
,
Author
of
the
Argument
,
to
be
so
courteous
as
to
teach
me
in
what
manner
those
flexures
should
be
accommodated
,
so
that
those
three
motions
might
commodiously
be
excercised
;
and
I
grant
you
four
or
six
moneths
time
to
think
of
an
answer
.
As
to
me
,
it
seemeth
that
one
principle
onely
may
cause
a
plurality
of
motions
in
the
Terrestrial
Globe
,
One
only
principle
may
cause
a
plurality
of
motions
in
the
Earth
.
just
in
the
same
manner
that
,
as
I
told
you
before
,
one
onely
principle
with
the
help
of
various
instruments
produceth
sundry
and
divers
motions
in
living
creatures
.
And
as
to
the
flexures
there
is
no
need
of
them
,
the
motions
being
of
the
whole
,
and
not
of
some
particular
parts
;
and
because
they
are
to
be
circular
,
the
meer
spherical
figure
is
the
most
perfect
articulation
or
flection
that
can
be
desired
.
SIMP.
The
most
that
ought
to
be
granted
upon
this
,
would
be
,
that
it
may
hold
true
in
one
single
motion
,
but
in
three
different
motions
,
in
my
opinion
,
and
that
of
the
Author
,
it
is
impossible
;
as
he
going
on
,
prosecuting
the
objection
,
writes
in
the
following
words
.
Let
us
suppose
,
with
Copernicus
,
that
the
Earth
moveth
of
its
own
faculty
,
and
upon
an
intrinsick
principle
from
West
to
East
in
the
plane
of
the
Ecliptick
;
and
again
,
that
it
also
by
an
intrinsick
principle
revolveth
about
its
centre
,
from
East
to
West
;
and
for
a
third
motion
,
that
it
of
its
own
inclination
deflecteth
from
North
to
South
,
and
so
back
again
.
It
being
a
continuate
body
,
and
not
knit
together
with
joints
and
flections
,
our
fancy
and
our
judgment
will
never
be
able
to
comprehend
,
that
one
and
the
same
natural
and
indistinct
principle
,
that
is
,
that
one
and
the
same
propension
,
should
actuate
it
at
the
same
instant
with
different
,
and
as
it
were
of
contrary
motions
.
I
cannot
believe
that
any
one
would
say
such
a
thing
,
unlesse
he
had
undertook
to
maintain
this
position
right
or
wrong
.
SALV
.
Stay
a
little
;
and
find
me
out
this
place
in
the
Book
.
Fingamus
modo
cum
Copernico
,
terram
aliqua
suâ
vi
,
&
ab
indito
principio
impelli
ab
Occasu
ad
Ortum
in
Eclipticae
plano
;
tum
rursus
revolvi
ab
indito
etiam
principio
,
circa
suimet
centrum
,
ab
Ortu
in
Occasum
;
A
grosse
error
of
the
opposer
of
Copernicus
.
tertio
deflecti
rursus
suopte
nutu
à
septentrione
in
Austrum
,
&
vicissim
.
I
had
thought
,
Simplicius
,
that
you
might
have
erred
in
reciting
the
words
of
the
Author
,
but
now
I
see
that
he
,
and
that
very
grossely
,
deceiveth
himself
;
and
to
my
grief
,
I
find
that
he
hath
set
himself
to
oppose
a
position
,
which
he
hath
not
well
understood
;
for
these
are
not
the
motions
which
Copernicus
assignes
to
the
Earth
.
Where
doth
he
find
that
Copernicus
maketh
the
annual
motion
by
the
Ecliptick
contrary
to
the
motion
about
its
own
centre
?
It
must
needs
be
that
he
never
read
his
Book
,
which
in
an
hundred
places
,
and
in
the
very
first
Chapters
affirmeth
those
motions
to
be
both
towards
the
same
parts
,
that
is
from
West
to
East
.
But
without
others
telling
him
,
ought
he
not
of
himself
to
comprehend
,
that
attributing
to
the
Earth
the
motions
that
are
taken
,
one
of
them
from
the
Sun
,
and
the
other
from
the
primum
mobile
,
they
must
of
necessity
both
move
one
and
the
same
way
.
SIMP.
Take
heed
that
you
do
not
erre
your self
,
A
subtil
and
withal
simple
argument
against
Copernicus
.
and
Copernicus
also
.
The
Diurnal
motion
of
the
primum
mobile
,
is
it
not
from
East
to
West
?
And
the
annual
motion
of
the
Sun
through
the
Ecliptick
,
is
it
not
on
the
contrary
from
West
to
East
?
How
then
can
you
make
these
motions
being
conferred
on
the
Earth
,
of
contraries
to
become
consistents
?
SAGR.
Certainly
,
Simplicius
hath
discovered
to
us
the
original
cause
of
error
of
this
Philosopher
;
and
in
all
probability
he
would
have
said
the
very
same
.
SALV
.
Now
if
it
be
in
our
power
,
let
us
at
least
recover
Simplicius
from
this
errour
,
who
seeing
the
Stars
in
their
rising
to
appear
above
the
Oriental
Horizon
,
will
make
it
no
difficult
thing
to
understand
,
〈…〉
that
in
case
that
motion
should
not
belong
to
the
Stars
,
it
would
be
necessary
to
confesse
,
that
the
Horizon
,
with
a
contrary
motion
would
go
down
;
and
that
consequently
the
Earth
would
reoolve
in
it self
a
contrary
way
to
that
wherewith
the
Stars
seem
to
move
,
that
is
from
West
to
East
,
which
is
according
to
the
order
of
the
Signes
of
the
Zodiack
.
As
,
in
the
next
place
,
to
the
other
motion
,
the
Sun
being
fixed
in
the
centre
of
the
Zodiack
,
and
the
Earth
moveable
about
its
circumference
,
to
make
the
Sun
seem
unto
us
to
move
about
the
said
Zodiack
,
according
to
the
order
of
the
Signes
,
it
is
necessary
,
that
the
Earth
move
according
to
the
same
order
,
to
the
end
that
the
Sun
may
seem
to
us
to
possesse
alwayes
that
degree
in
the
Zodiack
,
that
is
opposite
to
the
degree
in
which
we
find
the
Earth
;
and
thus
the
Earth
running
,
verbi
gratia
,
through
Aries
,
the
Sun
will
appear
to
run
thorow
Libra
;
and
the
Earth
passing
thorow
the
signe
Taurus
,
the
Sun
will
passe
thorow
Scorpio
,
and
so
the
Earth
going
thorow
Gemini
,
the
Sun
seemeth
to
go
thorow
Sagittarius
;
but
this
is
moving
both
the
same
way
,
that
is
according
to
the
order
of
the
signes
;
as
also
was
the
revolution
of
the
Earth
about
its
own
centre
.
SIMP.
I
understand
you
very
well
,
and
know
not
what
to
alledge
in
excuse
of
so
grosse
an
error
.
SALV
.
And
yet
,
Simplicius
,
there
is
one
yet
worse
then
this
;
and
it
is
,
that
he
makes
the
Earth
move
by
the
diurnal
motion
about
its
own
centre
from
East
to
West
;
and
perceives
not
that
if
this
were
so
,
the
motion
of
twenty
four
hours
appropriated
by
him
to
the
Universe
,
would
,
in
our
seeming
,
proceed
from
West
to
East
;
the
quite
contrary
to
that
which
we
behold
.
SIMP.
Oh
strange
!
Why
I
,
that
have
scarce
seen
the
first
elements
of
the
Sphere
,
would
not
,
I
am
confident
,
have
erred
so
horribly
.
SALV
.
Judg
now
what
pains
this
Antagonist
may
be
thought
to
have
taken
in
the
Books
of
Copernicus
,
By
another
gross
error
it
is
seen
that
the
Autagonist
had
but
little
studied
Copernicus
.
if
he
absolutely
invert
the
sense
of
this
grand
and
principal
Hypothesis
,
upon
which
is
founded
the
whole
summe
of
those
things
wherein
Copernicus
SAGR.
I
have
twice
or
thrice
observed
in
the
discourses
of
this
Authour
,
that
to
prove
that
a
thing
is
so
,
or
so
,
he
still
alledgeth
,
that
in
that
manner
it
is
conformable
with
our
understanding
;
or
that
otherwise
we
should
never
be
able
to
conceive
of
it
;
or
that
the
Criterium
of
Philosophy
would
be
overthrown
.
Never
first
〈…〉
of
them
.
As
if
that
nature
had
first
made
mens
brains
,
and
then
disposed
all
things
in
conformity
to
the
capacity
of
their
intellects
.
But
I
incline
rather
to
think
that
Nature
first
made
the
things
themselves
,
as
she
best
liked
,
and
afterwards
framed
the
reason
of
men
capable
of
conceiving
(
though
not
without
great
pains
)
some
part
of
her
secrets
.
SALV
.
I
am
of
the
same
opinion
.
But
tell
me
,
Simplicius
,
which
are
these
different
natures
,
to
which
,
contrary
to
experience
and
reason
,
Copernicus
assignes
the
same
motions
and
operations
.
SIMP.
They
are
these
.
The
Water
,
the
Air
,
(
which
doubtlesse
are
Natures
different
from
the
Earth
)
and
all
things
that
are
in
those
elements
comprised
,
shall
each
of
them
have
those
three
motions
,
which
Copernicus
pretends
to
be
in
the
Terrestriall
Globe
;
Copernicus
erroneously
assigneth
the
same
operations
to
different
natures
and
my
Authour
proceedeth
to
demonstrate
Geometrically
,
that
,
according
to
the
Copernican
Doctrine
,
a
cloud
that
is
suspended
in
the
Air
,
and
that
hangeth
a
long
time
over
our
heads
without
changing
place
,
must
of
necessity
have
all
those
three
motions
that
belong
to
the
Terrestrial
Globe
.
The
demonstration
is
this
,
which
you
may
read
your self
,
for
I
cannot
repeat
it
without
book
.
SALV
.
I
shall
not
stand
reading
of
it
,
nay
I
think
it
an
impertinency
in
him
to
have
inserted
it
,
for
I
am
certain
,
that
no
Copernican
will
deny
the
same
.
Therefore
admitting
him
what
he
would
demonstrate
,
let
us
speak
to
the
objection
,
which
in
my
judgment
hath
no
great
strength
to
conclude
any
thing
contrary
to
the
Copernican
Hypothesis
,
seeing
that
it
derogates
nothing
from
those
motions
,
and
those
operations
,
whereby
we
come
to
the
knowledge
of
the
natures
,
&c.
Answer
me
,
I
pray
you
,
Simplicius
:
Those
accidents
wherein
some
things
exactly
concur
,
can
they
serve
to
inform
us
of
the
different
natures
of
those
things
?
SIMP.
No
Sir
:
From
commune
accidents
one
cannot
know
different
natures
.
nay
rather
the
contrary
,
for
from
the
idendity
of
operations
and
of
accidents
nothing
can
be
inferred
,
but
an
idendity
of
natures
.
SALV
.
So
that
the
different
natures
of
the
Water
,
Earth
,
Air
,
and
other
things
conteined
in
these
Elements
,
is
not
by
you
argued
from
those
operations
,
wherein
all
these
Elements
and
their
affixes
agree
,
but
from
other
operations
;
is
it
so
?
SIMP.
The
very
same
.
SALV
.
So
that
he
who
should
leave
in
the
Elements
all
those
motions
,
operations
,
and
other
accidents
,
by
which
their
natures
are
distinguished
,
would
not
deprive
us
of
the
power
of
coming
to
the
knowledge
of
them
;
although
he
should
remove
those
operations
,
in
which
they
unitedly
concur
,
and
which
for
that
reason
are
of
no
use
for
the
distinguishing
of
those
natures
.
SIMP.
I
think
your
dissertation
to
be
very
good
.
SALV
.
But
that
the
Earth
,
Water
,
Air
,
are
of
a
nature
equally
constituted
immoveable
about
the
centre
,
is
it
not
the
opinion
of
your self
,
Aristotle
,
Prolomy
,
and
all
their
sectators
?
SIMP.
It
s
on
all
hands
granted
as
an
undeniable
truth
.
SALV
.
Then
from
this
common
natural
condition
of
quiescence
about
the
centre
,
there
is
no
argument
drawn
of
the
different
natures
of
these
Elements
,
and
things
elementary
,
but
that
knowledge
must
be
collected
from
other
qualities
not
common
;
and
therefore
whoso
should
deprive
the
Elements
of
this
common
rest
only
,
and
should
leave
unto
them
all
their
other
operations
,
would
not
in
the
least
block
up
the
way
that
leadeth
to
the
knowledge
of
their
essences
.
But
Copernicus
depriveth
them
onely
of
this
common
rest
,
and
changeth
the
same
into
a
common
motion
,
leaving
them
gravity
,
levity
,
the
motions
upwards
,
downwards
,
slower
,
The
concurrence
of
the
Elements
in
a
common
motion
importeth
no
more
or
lesse
,
than
their
concurrence
in
a
common
rest
.
faster
,
rarity
,
density
,
the
qualities
of
hot
,
cold
,
dry
,
moist
,
and
in
a
word
,
all
things
besides
.
Therefore
such
an
absurdity
,
as
this
Authour
imagineth
to
himself
,
is
no
Copernican
position
;
nor
doth
the
concurrence
in
an
identity
of
motion
import
any
more
or
less
,
than
the
concurrence
in
an
identity
of
rest
about
the
diversifying
,
or
not
diversifying
of
natures
.
Now
tell
us
,
if
there
be
any
argument
to
the
contrary
.
SIMP.
There
followeth
a
fourth
objection
,
taken
from
a
natural
observation
,
which
is
,
A
fourth
argument
against
Copernicus
.
That
bodies
of
the
same
kind
,
have
motions
that
agree
in
kinde
,
or
else
they
agree
in
rest
.
But
by
the
Copernican
Hypothesis
,
Bodies
of
the
same
kinde
have
motions
that
agree
in
kinde
.
bodies
that
agree
in
kinde
,
and
are
most
semblable
to
one
another
,
would
be
very
discrepant
,
yea
diametrically
repugnant
as
to
motion
;
for
that
Stars
so
like
to
one
another
,
would
be
neverthelesse
so
unlike
in
motion
,
as
that
six
Planets
would
perpetually
turn
round
;
but
the
Sun
and
all
the
fixeed
Stars
would
stand
perpetually
immoveable
.
SALV
.
The
forme
of
the
argument
appeareth
good
;
but
yet
I
believe
that
the
application
or
matter
is
defective
:
and
if
the
Authour
will
but
persist
in
his
assumption
,
the
consequence
shall
make
directly
against
him
.
The
Argument
runs
thus
;
Amongst
mundane
bodies
,
From
the
Earths
obscurity
,
and
the
splendour
of
the
Sun
,
and
fixed
Stars
,
is
argued
,
that
it
is
moveable
,
and
they
immoveable
.
six
there
are
that
do
perpetually
move
,
and
they
are
the
six
Planets
;
of
the
rest
,
that
is
,
of
the
Earth
,
Sun
,
and
fixed
Stars
,
it
is
disputable
which
of
them
moveth
,
and
which
stands
still
,
it
being
necessary
,
that
if
the
Earth
stand
still
,
the
Sun
and
fixed
Stars
do
move
;
and
it
being
also
possible
,
that
the
Sun
and
fixed
Stars
may
stand
immoveable
,
in
case
the
Earth
should
move
:
the
matter
of
fact
in
dispute
is
,
to
which
of
them
we
may
with
most
convenience
ascribe
motion
,
and
to
which
rest
.
Natural
reason
dictates
,
that
motion
ought
to
be
assigned
to
the
bodies
,
which
in
kind
and
essence
most
agree
with
those
bodies
which
do
undoubtedly
move
,
and
rest
to
those
which
most
dissent
from
them
;
and
in
regard
that
an
eternal
rest
and
perpetual
motion
are
most
different
,
it
is
manifest
,
that
the
nature
of
the
body
always
moveable
ought
to
be
most
different
from
the
body
alwayes
stable
.
Therefore
,
in
regard
that
we
are
dubious
of
motion
and
rest
,
let
us
enquire
,
whether
by
the
help
of
some
other
eminent
affection
,
we
may
discover
,
which
most
agreeth
with
the
bodies
certainly
moveable
,
either
the
Earth
,
or
the
Sun
and
fixed
Stars
.
But
see
how
Nature
,
in
favour
of
our
necessity
and
desire
,
presents
us
with
two
eminent
qualities
,
and
no
less
different
than
motion
and
rest
,
and
they
are
light
and
darkness
,
to
wit
,
the
being
by
nature
most
bright
,
and
the
being
obscure
,
and
wholly
deprived
of
light
:
the
bodies
therefore
adorned
with
an
internal
and
eternal
splendour
,
are
most
different
in
essence
from
those
deprived
of
light
:
The
Earth
is
deprived
of
light
,
the
Sun
is
most
splendid
in
it self
,
and
so
are
the
fixed
Stars
.
The
six
Planets
do
absolutely
want
light
,
as
the
Earth
;
therefore
their
essence
agreeth
with
the
Earth
,
and
differeth
from
the
Sun
and
fixed
Stars
.
Therefore
is
the
Earth
moveable
,
immoveable
the
Sunne
and
Starry
Sphere
.
SIMP.
But
the
Authour
will
not
grant
,
that
the
six
Planets
are
tenebrose
,
and
by
that
negative
will
he
abide
.
Or
he
will
argue
the
great
conformity
of
nature
between
the
six
Planets
,
and
the
Sun
,
and
Fixed
Stars
;
and
the
disparity
between
them
and
the
Earth
from
other
conditions
than
from
tenebrosity
and
light
;
yea
,
now
I
remember
in
the
fifth
objection
,
which
followeth
,
he
layeth
down
the
vast
difference
between
the
Earth
and
the
Coelestial
Bodies
,
A
fifth
argument
against
Copernicus
.
in
which
he
writeth
,
That
the
Copernican
Hypothesis
would
make
great
confusion
and
perturbation
in
the
Systeme
of
the
Vniverse
,
and
amongst
its
parts
:
As
for
instance
,
amongst
Coebodies
that
are
immutable
and
incorruptible
,
Another
difference
between
the
Earth
and
the
Coelestial
bodies
,
taken
from
purity
&
impurity
.
according
to
Aristotle
,
Tycho
,
and
others
;
amongst
bodies
,
I
say
,
of
such
nobility
,
by
the
confession
of
every
one
,
and
Copernicus
himself
,
who
affirmeth
them
to
be
ordinate
,
and
disposed
in
a
perfect
constitution
,
and
removeth
from
them
all
inconstancy
of
vertue
amongst
,
these
bodies
,
I
say
once
more
,
so
pure
,
that
is
to
say
,
amongst
Venus
,
Mars
,
&c.
to
place
the
very
sink
of
all
corruptible
matters
,
to
wit
,
the
Earth
,
Water
,
Air
,
and
all
mixt
bodies
.
But
how
much
properer
a
distribution
,
and
more
with
nature
,
yea
with
God
himself
,
the
Architect
,
is
it
,
to
sequester
the
pure
from
the
impute
,
the
mortal
from
the
immortal
,
as
other
Schools
teach
;
which
tell
us
that
these
impure
and
frail
matters
are
contained
within
the
angust
concave
of
the
Lunar
Orb
,
above
which
with
uninterrupted
Series
the
things
Celestial
distend
themselves
.
SALV
.
It
's
true
that
the
Copernican
Systeme
introduceth
distraction
in
the
universe
of
Aristotle
;
Copernicus
introduceth
confusion
in
the
Universe
of
Aristotle
.
but
we
speak
of
our
own
Universe
,
that
is
true
and
real
.
Again
if
this
Author
will
infer
the
disparity
of
essence
between
the
Earth
and
Celestial
bodies
from
the
incorruptibility
of
them
,
and
the
corruptibility
of
it
in
the
method
of
Aristotle
,
from
which
disparity
he
concludeth
motion
to
belong
to
the
Sun
and
fixed
Stars
,
and
the
immobility
of
the
Earth
,
The
Paralogisme
of
the
Author
of
Anti-Tycho
.
he
will
flatter
himself
with
a
Paralogisme
,
supposing
that
which
is
in
question
;
for
Aristotle
inferreth
the
incorruptibility
of
Celestial
bodies
from
motion
,
which
is
in
dispute
,
whether
it
belongeth
to
them
or
to
the
Earth
.
Of
the
vanity
of
these
Rhetorical
Illations
enough
hath
been
spoken
.
It
seemeth
a
folly
to
affirm
the
Earth
to
be
without
the
Heavens
.
And
what
can
be
more
fond
,
than
to
say
,
that
the
Earth
and
Elements
are
banished
and
sequestred
from
the
Celestial
Spheres
,
and
confined
within
the
Lunar
Orb
?
Is
,
not
then
the
Moons
Orb
one
of
the
Celestial
Spheres
,
and
according
to
consent
comprised
in
the
middle
of
all
the
rest
?
It
s
a
new
way
to
separate
the
pure
from
the
impure
,
and
the
sick
from
the
sound
,
to
assigne
the
infected
quarters
in
the
heart
of
the
City
:
I
had
thought
that
the
[
](A61244-e56410-b)*
*
Lazeretto
.
Pest-house
ought
to
have
been
removed
as
far
off
as
was
possible
.
Copernicus
admireth
the
disposition
of
the
parts
of
the
Universe
,
for
that
God
hath
constituted
the
grand
Lamp
,
which
is
to
give
light
all
over
his
Temple
in
the
centre
of
it
,
and
not
on
one
side
.
And
as
to
the
Earths
being
betwixt
Venus
and
Mars
,
we
will
but
hint
the
same
;
and
do
you
,
in
favour
of
this
Author
,
trie
to
remove
it
thence
.
But
let
us
not
[
](A61244-e56450-b)*
*
Intrecciare
,
to
twine
flowers
in
a
garland
.
mix
these
Rhetorical
Flowers
with
solid
Demonstrations
,
rather
let
us
leave
them
to
the
Orators
,
or
if
you
will
to
the
Poets
,
who
know
how
in
their
drolling
way
to
exalt
by
their
prayses
things
most
sordid
,
yea
and
sometimes
most
pernicious
.
And
if
any
thing
else
remain
,
let
us
dispatch
it
,
as
we
have
done
the
rest
.
SIMP.
There
is
the
sixth
and
last
argument
;
A
sixth
argument
against
Copernicus
,
taken
from
animals
,
who
have
need
of
rest
▪
though
their
motion
be
natural
.
wherein
he
maketh
it
a
very
improbale
thing
.
[
That
a
corruptible
and
dissipable
body
should
move
with
a
perpetual
and
regular
motion
;
and
this
be
confirmeth
with
the
example
of
living
creatures
,
which
moving
with
a
motion
natural
to
them
,
yet
grow
weary
,
and
have
need
of
repose
to
restore
their
strength
.
]
But
what
hath
this
motion
to
do
with
that
of
the
Earth
,
that
in
comparision
to
theirs
is
immense
?
Besides
,
to
make
it
move
with
three
motions
that
run
and
draw
several
wayes
:
Who
would
ever
assert
such
Paradoxes
,
unlesse
he
had
sworn
to
be
their
defender
?
Nor
doth
that
avail
in
this
case
,
which
Copernicus
alledgeth
,
that
by
reason
this
motion
is
natural
to
the
Earth
and
not
violent
,
it
worketh
contrary
effects
to
violent
motions
;
and
that
those
things
dissolve
and
cannot
long
subsist
,
to
which
impulse
is
conferred
,
but
those
so
made
by
nature
do
continue
in
their
perfect
disposure
;
this
answer
sufficeth
not
,
I
say
,
for
it
is
overthrown
by
that
of
ours
.
For
the
animal
is
a
natural
body
,
and
not
made
by
art
,
and
its
motion
is
natural
,
deriving
it self
from
the
soul
,
that
is
,
from
an
intrinsick
principle
;
and
that
motion
is
violent
,
whose
beginning
is
without
,
and
on
which
the
thing
moved
conferreth
nothing
;
however
,
if
the
animal
continueth
its
motion
any
long
time
,
it
grows
weary
,
and
also
dyeth
,
if
it
obstinately
strive
to
persist
therein
.
You
see
then
that
in
nature
we
meet
on
all
sides
with
notions
contrary
to
the
Copernican
Hypothesis
,
and
none
in
favour
of
it
.
And
for
that
I
have
nothing
more
wherein
to
take
the
part
of
this
Opponent
,
hear
what
he
produceth
against
Keplerus
(
with
whom
he
disputeth
)
upon
that
argument
,
which
the
said
Kepler
bringeth
against
those
who
think
it
an
inconvenient
,
nay
impossible
thing
,
to
augment
the
Starry
Sphere
immensely
,
as
the
Copernican
Hypothesis
requireth
.
Kepler
therefore
instanceth
,
saying
:
Difficilius
est
,
An
argument
from
Kepler
in
favour
of
Copernicus
.
accidens
praeter
modulum
subjecti
intendere
,
quàm
subjectum
sine
accidente
augere
.
Copernicus
ergo
verisimilius
facit
,
qui
auget
Orbem
Stellarum
fixarum
absque
motu
,
quam
Ptolomaeus
,
qui
anget
motum
fixarum
immensâ
velocitate
.
[
Which
makes
this
English
.
]
It
s
harder
to
stretch
the
accident
beyond
the
model
of
the
subject
than
to
augment
the
subject
without
the
accident
.
Copernicus
hath
more
probability
on
his
side
,
who
encreaseth
the
Orb
of
the
fixed
Stars
without
motion
,
than
Ptolomy
who
augmenteth
the
motion
of
the
fixed
Stars
to
an
immense
degree
of
velocity
.
Which
objection
the
Author
answereth
,
The
Author
of
the
Anti-Tycho
opposeth
Kepler
.
wondering
how
much
Kepler
deceived
himself
,
in
saying
,
that
in
the
Ptolomaick
Hypothesis
the
motion
encreaseth
beyond
the
model
of
the
subject
,
for
in
his
judgment
it
doth
not
encrease
,
save
onely
in
conformity
to
the
model
,
and
that
according
to
its
encreasement
,
the
velocity
of
the
motion
is
augmented
.
The
velocity
of
the
circular
motion
increaseth
,
according
to
the
encrease
of
the
diameter
of
the
circle
.
Which
he
proveth
by
supposing
a
machine
to
be
framed
,
that
maketh
one
revolution
in
twenty
four
hours
,
which
motion
shall
be
called
most
slow
;
afterwards
supposing
its
semidiameter
to
be
prolonged
,
as
far
as
to
the
distance
of
the
Sun
,
its
extreme
will
equal
the
velocity
of
the
Sun
;
and
it
being
continued
out
unto
the
Starry
Sphere
,
it
will
equal
the
velocity
of
the
fixed
Stars
,
though
in
the
circumference
of
the
machine
it
be
very
slow
.
Now
applying
this
consideration
of
the
machine
to
the
Starry
Sphere
,
let
us
imagine
any
point
in
its
semidiameter
,
as
neer
to
the
centre
as
is
the
semidiameter
of
the
machine
;
the
same
motion
that
in
the
Starry
Sphere
is
exceeding
swift
,
shall
in
that
point
be
exceeding
slow
;
But
the
great
magnitude
of
the
body
is
that
which
maketh
it
of
exceeding
slow
,
to
become
exceeding
swift
,
although
it
continueth
still
the
same
,
and
thus
the
velocity
encreaseth
,
not
beyond
the
model
of
the
subject
,
but
rather
according
to
it
,
and
to
its
magnitude
;
very
differently
from
the
imagination
of
Kepler
.
SALV
.
I
do
not
believe
that
this
Author
hath
entertained
so
mean
and
poor
a
conceit
of
Kepler
,
as
to
perswade
himself
that
he
did
not
understand
,
that
the
highest
term
of
a
line
drawn
from
the
centre
unto
the
Starry
Sphere
,
moveth
more
swiftly
than
a
point
of
the
same
line
taken
within
a
yard
or
two
of
the
centre
.
And
therefore
of
necessity
he
must
have
conceived
and
comprehended
that
the
mind
and
intention
of
Kepler
was
to
have
said
,
An
explanation
of
the
true
sense
of
Kepler
and
his
●●fence
.
that
it
is
lesse
inconvenient
to
encrease
an
immoveable
body
to
an
extraordinary
magnitude
,
than
to
ascribe
an
extraordinary
velocity
to
a
body
,
though
very
bigge
,
having
regard
to
the
model
,
that
is
to
the
gauge
,
and
to
the
example
of
other
natural
bodies
;
in
which
we
see
,
that
the
distance
from
the
centre
encreasing
,
the
velocity
diminisheth
;
that
is
,
that
the
periods
of
their
circulations
take
up
longer
times
.
The
greatnesse
and
smalnesse
of
the
body
make
a
differeuce
in
motion
and
not
in
rest
.
But
in
rest
which
is
not
capable
of
augmentation
or
diminution
,
the
grandure
or
smalnesse
of
the
body
maketh
no
difference
.
So
that
if
the
answer
of
the
Author
would
be
directed
against
the
argument
of
Kepler
,
it
is
necessary
,
that
that
Author
doth
hold
,
that
to
the
movent
principle
it
s
one
and
the
same
to
move
in
the
same
time
a
body
very
small
,
or
very
immense
,
in
regard
that
the
augmentation
of
velocity
inseparably
attends
the
augmentation
of
the
masse
.
The
order
of
nature
is
to
make
the
lesser
Orbs
to
circulate
in
shorter
times
,
and
the
bigger
in
longer
times
.
But
this
again
is
contrary
to
the
Architectonical
rule
of
nature
,
which
doth
in
the
lesser
Spheres
,
as
we
see
in
the
Planets
,
and
most
sensibly
in
the
Medicean
Stars
,
observe
to
make
the
lesser
Orbs
to
circulate
in
shorter
times
:
Whence
the
time
of
Saturns
revolution
is
longer
than
all
the
times
of
the
other
lesser
Spheres
,
it
being
thirty
years
;
now
the
passing
from
this
to
a
Sphere
very
much
bigger
,
and
to
make
it
move
in
24.
hours
,
may
very
well
be
said
to
exceed
the
rules
of
the
model
.
So
that
if
we
would
but
attentively
consider
it
,
the
Authors
answer
opposeth
not
the
intent
and
sense
of
the
argument
,
but
the
expressing
and
manner
of
delivering
of
it
;
where
again
the
Author
is
injurious
,
and
cannot
deny
but
that
he
artificially
dissembled
his
understanding
of
the
words
,
that
he
might
charge
Kepler
with
grosse
ignorance
;
but
the
imposture
was
so
very
dull
and
obvions
,
that
he
could
not
with
all
his
craft
alter
the
opinion
which
Kepler
hath
begot
of
his
Doctrine
in
the
minds
of
all
the
Learned
.
As
in
the
next
place
,
to
the
instance
against
the
perpetual
motion
of
the
Earth
,
taken
from
the
impossibility
of
its
moving
long
without
wearinesse
,
in
regard
that
living
creatures
themselves
,
which
yet
move
naturally
,
and
from
an
intern
principle
,
do
grow
weary
,
and
have
need
of
rest
to
relax
and
refresh
their
members
—
SAGR.
Methinks
I
hear
Kepler
answer
him
to
that
,
that
there
are
some
kinde
of
animals
which
refresh
themselves
after
wearinesse
,
by
rowling
on
the
Earth
;
and
that
therefore
there
is
no
need
to
fear
that
the
Terrestrial
Globe
should
tire
,
The
feigned
answer
of
Kepler
covered
with
an
artificial
Irony
.
nay
it
may
be
reasonably
affirmed
,
that
it
enjoyeth
a
perpetual
&
most
tranquil
repose
,
keeping
it self
in
an
eternal
rowling
.
SALV
.
You
are
too
tart
and
Satyrical
,
Sagredus
:
but
let
us
lay
aside
jests
,
whilst
we
are
treating
of
serious
things
.
SAGR.
Excuse
me
,
Salviatus
,
this
that
I
say
is
not
so
absolutely
besides
the
business
,
as
you
perhaps
make
it
;
for
a
motion
that
serveth
instead
of
rest
,
and
removeth
weariness
from
a
body
tired
with
travail
,
may
much
more
easily
serve
to
prevent
the
coming
of
that
weariness
,
Animals
would
not
grow
weary
of
their
motion
,
proceeding
as
that
which
is
assigned
to
the
terrestrial
Globe
.
like
as
preventive
remedies
are
more
easie
than
curative
.
And
I
hold
for
certain
,
that
if
the
motion
of
animals
should
proceed
in
the
same
manner
as
this
that
is
ascribed
to
the
Earth
,
they
would
never
grow
weary
;
Seeing
that
the
weariness
of
the
living
creature
,
deriveth
it self
,
in
my
opinion
,
from
the
imployment
of
but
one
part
alone
in
the
moving
of
its
self
,
The
cause
of
the
wearinesse
of
animals
.
and
all
the
rest
of
the
body
;
as
v.
g.
in
walking
,
the
thighs
and
the
legs
onely
are
imployed
for
carrying
themselves
and
all
the
rest
:
on
the
contrary
,
you
see
the
motion
of
the
heart
to
be
as
it
were
indefatigable
,
because
it
moveth
it self
alone
.
Besides
,
I
know
not
how
true
it
may
be
,
The
motion
of
an
animal
is
rather
to
be
called
violent
than
natural
.
that
the
motion
of
the
animal
is
natural
,
and
not
rather
violent
:
nay
,
I
believe
that
one
may
truly
say
,
that
the
soul
naturally
moveth
the
members
of
an
animal
with
a
motion
preternatural
,
for
if
the
motion
upwards
is
preternatural
to
grave
bodies
,
the
lifting
up
of
the
legs
,
and
the
thighs
,
which
are
grave
bodies
,
in
walking
,
cannot
be
done
without
violence
,
and
therefore
not
without
labour
to
the
mover
.
The
climbing
upwards
by
a
ladder
carrieth
the
grave
body
contrary
to
its
natural
inclination
upwards
,
from
whence
followeth
weariness
,
by
reason
of
the
bodies
natural
aversness
to
that
motion
:
but
in
moving
a
moveable
with
a
motion
,
to
which
it
hath
no
aversion
,
what
lassitude
,
The
strength
diminisheth
not
,
where
it
is
not
imployed
.
what
diminution
of
vertue
and
strength
need
we
fear
in
the
mover
?
and
how
should
the
forces
waste
,
where
they
are
not
at
all
imployed
?
SIMP.
They
are
the
contrary
motions
wherewith
the
Earth
is
pretended
to
move
,
against
which
the
Authour
produceth
his
argument
.
SAGR.
It
hath
been
said
already
,
that
they
are
no
wise
contraries
,
and
that
herein
the
Authour
is
extteamly
deceived
,
so
that
the
whole
strength
of
the
argument
recoileth
upon
the
Opponent
himself
,
The
argument
of
Chramontius
,
〈◊〉
upon
himself
.
whilst
he
will
make
the
First
Mover
to
hurry
along
with
it
all
the
inferiour
Spheres
,
contrary
to
the
motion
which
they
themselves
at
the
same
time
exercise
.
It
belongs
therefore
to
the
Primum
Mobile
to
grow
weary
,
which
besides
the
moving
of
its
self
is
made
to
carry
so
many
other
Spheres
,
and
which
also
strive
against
it
with
a
contrary
motion
.
So
that
the
ultimate
conclusion
that
the
Authour
inferred
,
saying
,
that
discoursing
of
the
effects
of
Nature
,
a
man
alwayes
meets
with
things
that
favour
the
opinion
of
Aristotle
and
Ptolomy
,
and
never
any
one
that
doth
not
interfer
with
Copernicus
,
stands
in
need
of
great
consideration
;
and
it
is
better
to
say
,
that
one
of
these
two
Hypotheses
being
true
,
and
the
other
necessarily
false
,
it
is
impossible
that
a
man
should
ever
be
able
to
finde
any
argument
,
experience
,
or
right
reason
,
in
favour
of
that
which
is
false
,
True
Propositions
meet
with
many
conclusive
arguments
,
so
do
not
the
false
.
like
as
to
the
truth
none
of
these
things
can
be
repugnant
.
Vast
difference
,
therefore
,
must
needs
be
found
between
the
reasons
and
arguments
produced
by
the
one
and
other
party
,
for
and
against
these
two
opinions
,
the
force
of
which
I
leave
you
your self
to
judge
of
,
Simplicius
.
SALV
.
But
you
,
Sagredus
,
being
transported
by
the
velocity
of
your
wit
,
have
taken
my
words
out
of
my
mouth
,
whilst
I
was
about
to
say
something
,
touching
this
last
argument
of
the
Author
;
and
although
you
have
more
then
sufficiently
refuted
him
,
yet
neverthelesse
I
will
adde
somewhat
,
which
then
ran
in
my
minde
.
He
proposeth
it
as
a
thing
very
unlikely
,
that
a
body
dissipable
and
corruptible
,
as
the
Earth
,
should
perpetually
move
with
a
regular
motion
,
especially
for
that
we
see
living
creatures
in
the
end
to
grow
weary
,
and
to
stand
in
need
of
rest
:
and
the
improbability
is
increased
,
in
that
the
said
motion
is
required
to
be
of
velocity
incomparable
and
immense
,
in
respect
to
that
of
animals
.
Now
,
I
cannot
see
why
the
velocity
of
the
Earth
should
,
at
present
,
trouble
it
;
so
long
as
that
of
the
starry
Sphere
so
very
much
bigger
doth
not
occasion
in
it
any
disturbance
more
considerable
,
than
that
which
the
velocity
of
a
machine
,
that
in
24
hours
maketh
but
one
sole
revolution
,
produceth
in
the
same
.
If
the
being
of
the
velocity
of
the
Earths
conversion
,
according
to
the
model
of
that
machine
,
inferreth
things
of
no
greater
moment
than
that
,
let
the
Author
cease
to
fear
the
Earths
growing
weary
;
for
that
not
one
of
the
most
feeble
and
slow-pac't
animals
,
no
not
a
Chamaeleon
would
tire
in
moving
no
more
than
[
](A61244-e57230-b)*
*
Cinque
〈◊〉
se●
braccia
Fiorentini
.
four
or
five
yards
in
24
hours
;
but
if
he
please
to
consider
the
velocity
to
be
no
longer
,
Weariness
more
to
be
feared
in
the
starry
Sphere
than
in
the
terrestriall
Globe
.
in
relation
to
the
model
of
the
machine
,
but
absolutely
,
and
inasmuch
as
the
moveable
in
24
hours
is
to
pass
a
very
great
space
,
he
ought
to
shew
himself
so
much
more
reserved
in
granting
it
to
the
starry
Sphere
,
which
with
a
velocity
incomparably
greater
than
that
of
the
Earth
is
to
carry
along
with
it
a
thousand
bodies
,
each
much
bigger
than
the
Terrestrial
Globe
.
Here
it
remains
for
us
to
see
the
proofs
,
whereby
the
Authour
concludes
the
new
stars
Anno
1572.
and
Anno
1604.
to
be
sublunary
,
and
not
coelestial
,
as
the
Astronomers
of
those
times
were
generally
perswaded
;
an
enterprize
very
great
certainly
;
but
I
have
considered
,
that
it
will
be
better
,
in
regard
the
Book
is
new
and
long
,
by
reason
of
its
many
calculations
,
that
between
this
evening
and
to
morrow
morning
I
make
them
as
plain
as
I
can
,
and
so
meeting
you
again
to
morrow
to
continue
our
wonted
conferences
,
give
you
a
brief
of
what
I
shall
observe
therein
;
and
if
we
have
time
left
,
we
will
say
something
of
the
Annual
motion
ascribed
to
the
Earth
.
In
the
mean
time
,
if
either
of
you
,
and
Simplicius
in
particular
,
hath
any
thing
to
say
more
,
touching
what
relates
to
the
Diurnal
motion
,
at
large
examined
by
me
,
we
have
a
little
time
still
left
to
treat
thereof
.
SIMP.
I
have
no
more
to
say
,
unlesse
it
be
this
,
that
the
discourses
that
this
day
have
falne
under
our
debate
,
have
appeared
to
me
fraught
with
very
acute
and
ingenious
notions
,
alledged
on
Copernicus
his
side
,
in
confirmation
of
the
motion
of
the
Earth
,
but
yet
I
find
not
my self
perswaded
to
believe
it
;
for
in
short
,
the
things
that
have
been
said
conclude
no
more
but
this
,
that
the
reasons
for
the
stability
of
the
Earth
are
not
necessary
;
but
all
the
while
no
demonstration
hath
been
produced
on
the
other
side
,
that
doth
necessarily
convince
and
prove
its
mobility
.
SALV
.
I
never
undertook
,
Simplicius
,
to
remove
you
from
that
your
opinion
;
much
less
dare
I
presume
to
determine
definitively
in
this
controversie
:
it
onely
was
,
and
still
shall
be
in
the
ensuing
disputations
my
intent
,
to
make
it
appear
to
you
,
that
those
who
have
thought
that
most
swift
motion
of
24
hours
doth
belong
to
the
Earth
alone
,
and
not
to
the
Universe
,
the
Earth
onely
excluded
,
were
not
induced
to
believe
,
that
so
it
might
and
ought
to
do
out
of
any
blind
perswasion
;
but
that
they
did
very
well
see
,
try
,
and
examine
the
reasons
on
the
contrary
side
,
and
also
not
slightly
answer
them
.
With
the
same
intention
,
if
it
stand
with
your
liking
,
and
that
of
Sagredus
,
we
may
passe
to
the
consideration
of
that
other
motion
;
first
,
by
Aristarchus
Samius
,
and
afterwards
by
Nicholaus
Copernicus
ascribed
to
the
said
Terrestrial
Globe
,
which
is
,
as
,
I
believe
,
you
have
heretofore
heard
,
made
under
the
Zodiack
within
the
space
of
a
year
about
the
Sun
,
immoveably
placed
in
the
centre
of
the
said
Zodiack
.
SIMP.
The
disquisition
is
so
great
,
and
so
noble
,
that
I
shall
gladly
hearken
to
the
discussion
thereof
,
perswading
my self
that
I
shall
hear
what
ever
can
be
said
of
that
matter
.
And
I
will
afterwards
by
my self
,
according
to
my
usual
custome
,
make
more
deliberate
reflexions
upon
what
hath
been
,
and
is
to
be
spoken
;
and
if
I
should
gain
no
more
but
this
,
it
will
be
no
small
benefit
that
I
shall
be
able
to
discourse
more
Logically
.
SAGR.
Therefore
,
that
we
may
no
further
weary
Salviatus
,
we
will
put
a
period
to
the
disputations
of
this
day
,
and
reassume
our
conference
to
morrow
in
the
usual
manner
,
with
hope
to
hear
very
pleasing
novelties
.
SIMP.
I
will
leave
with
you
the
Book
De
stellis
novis
,
and
carry
back
this
of
the
Conclusions
,
to
see
what
is
written
therein
against
the
Annual
motion
,
which
are
to
be
the
arguments
of
our
discourse
to
morrow
.
Place
this
Plate
at
the
end
of
the
Second
Dialogue
.
GALILAEUS
Galilaeus
Lyncaeus
,
HIS
SYSTEME
OF
THE
WORLD
.
The
Third
Dialogue
.
INTERLOCVTORS
.
SALVIATUS
,
SAGREDUS
,
and
SIMPLICIUS
.
SAGR.
THe
great
desire
wherewith
I
have
expected
your
coming
,
that
I
might
hear
the
novel
conceits
touching
the
annual
conversion
of
this
our
Globe
,
hath
made
me
think
the
houres
of
the
last
night
,
and
those
of
this
morning
very
tedious
,
although
I
spent
them
not
idly
,
but
lying
awake
I
imployed
a
good
part
thereof
in
ruminating
upon
our
yesterdayes
discourses
,
weighing
the
reasons
alledged
by
both
parties
,
in
favour
of
the
two
contrary
Hypotheses
,
that
of
Aristotle
and
Ptolomy
,
and
this
of
Aristarchus
,
and
Copernicus
.
And
really
methinks
,
that
which
ever
of
these
parties
have
been
deceived
,
they
are
worthy
of
excuse
,
so
specious
and
valid
in
appearance
are
the
reasons
that
may
have
perswaded
them
either
way
;
though
neverthelesse
we
do
for
the
most
part
close
with
those
produced
by
the
grave
Authours
first
above
mentioned
.
But
albeit
that
the
Peripatetick
Hypothesis
,
by
reason
of
its
antiquity
,
hath
had
many
followers
and
fautors
,
and
the
other
very
few
;
first
,
for
its
obscurity
,
and
next
,
for
its
novelty
,
yet
methinks
I
discover
amongst
those
many
,
and
particularly
amongst
the
modernes
some
,
who
for
the
support
of
the
opinion
by
them
esteemed
true
,
have
introduced
other
reasons
sufficiently
childish
,
I
could
say
ridiculous
.
SALV
.
I
have
met
with
the
like
,
and
so
much
worse
than
yours
,
Some
in
arguing
first
fix
in
their
minds
the
conclusion
beleeved
by
them
,
and
then
adapt
their
reasons
to
that
.
that
I
blush
to
rehearse
them
,
not
so
much
to
spare
the
fame
of
their
Authours
,
the
names
of
whom
might
be
perpetually
concealed
,
as
because
I
am
ashamed
so
much
to
stain
the
honour
of
mankinde
.
In
observing
of
these
men
,
I
have
found
that
some
there
are
who
preposterously
reasoning
,
first
stablish
the
conclusion
in
their
fancy
,
and
(
either
because
it
is
their
own
,
or
else
belongs
to
a
person
whom
they
much
confide
in
)
so
firmly
imprint
it
in
their
opinions
,
that
it
is
altogether
impossible
ever
wholly
to
efface
it
:
and
those
reasons
which
they
themselves
stumble
upon
,
or
which
they
hear
others
to
alledge
in
confirmation
of
the
conceit
entertained
,
though
never
so
simple
and
insipid
,
instantly
find
credit
and
applause
with
them
:
but
on
the
contrary
,
those
which
are
brought
against
their
opinion
,
though
ingenuous
and
concluding
,
they
receive
not
only
with
nauseating
,
but
with
disdain
and
bitter
indignation
,
yea
,
you
shall
have
one
of
these
so
inraged
,
as
that
he
will
not
be
backward
to
try
all
wayes
to
suppress
and
silence
their
adversaries
:
and
of
this
I
my self
have
had
some
experience
.
SAGR.
Indeed
these
men
deduce
not
the
conclusion
from
the
premises
,
nor
confirme
them
with
reasons
,
but
accomodate
,
or
to
say
better
,
discommodate
and
distort
the
premises
and
arguments
to
make
them
speak
in
favour
of
their
pre-assumed
and
pertinacious
conclusions
.
It
is
not
good
therefore
to
contract
familiarity
with
these
men
;
and
the
rather
,
for
that
their
conversation
is
not
only
unpleasant
,
but
also
dangerous
.
Yet
let
us
continue
our
conference
with
Simplicius
however
,
whom
I
have
known
this
long
while
for
a
man
of
great
ingenuity
;
and
altogether
void
of
malice
:
besides
he
is
well
verst
in
the
Peripatetick
Doctrine
;
so
that
I
may
assure
my self
,
that
what
shall
not
fall
within
the
reach
of
his
reason
for
the
support
of
the
Aristotelian
Hypothesis
,
will
not
easily
be
found
out
by
others
.
But
see
yonder
he
comes
,
quite
out
of
winde
,
whose
company
we
have
so
long
desired
:
we
were
just
now
speaking
against
the
small
hast
you
made
to
come
to
us
.
SIMP.
You
must
not
blame
me
,
but
Neptune
,
for
this
my
long
stay
;
which
in
the
ebbe
of
this
mornings
tide
hath
in
a
manner
drain'd
away
the
waters
,
for
the
Gondola
that
brought
me
,
being
entered
not
far
from
hence
into
a
certain
Channel
,
wanting
depth
,
where
I
was
stranded
,
and
forced
to
stay
there
more
than
a
full
hour
,
in
expecting
the
return
of
the
tide
:
and
there
waiting
in
this
manner
,
without
being
able
to
get
out
of
the
boat
,
which
on
a
sudden
ran
a
ground
,
The
motion
of
the
water
in
ebbing
and
flowing
not
interrupted
by
rest
.
I
observed
a
certain
accident
,
which
to
me
seemed
very
strange
;
and
it
was
this
,
that
in
the
waters
ebbing
I
saw
it
retreat
very
fast
by
several
small
rivolets
,
the
ouze
being
in
many
places
discovered
,
and
whilst
I
stood
looking
upon
this
effect
,
I
saw
this
motion
in
an
instant
to
cease
,
and
without
a
minutes
interval
the
same
water
to
begin
to
return
back
again
,
and
the
tide
from
ebbing
to
become
young
flood
,
without
standing
still
a
moment
:
an
effect
that
as
long
as
I
have
dwelt
in
Venice
,
I
never
took
notice
of
before
.
SAGR.
It
is
very
much
,
that
you
should
be
left
thus
on
ground
,
amongst
small
Channels
;
in
which
rivolets
,
as
having
very
little
declivity
,
the
rising
or
falling
of
the
main
sea
,
the
thickness
onely
of
a
paper
is
sufficient
to
make
the
water
to
ebbe
and
flow
for
good
long
spaces
of
time
:
like
as
in
some
creeks
of
the
Sea
,
its
flowing
four
or
six
[
](A61244-e57880-b)*
*
Pertiche
venetiani
.
yards
onely
,
maketh
the
water
to
overflow
the
adjacent
Marshes
for
some
hundreds
and
thousands
of
[
](A61244-e57890-b)*
*
Pertiche
venetiani
.
acres
.
SIMP.
This
I
know
very
well
,
but
I
should
have
thought
,
that
between
the
ultimate
terme
of
ebbing
,
and
the
first
beginnng
to
flow
,
there
should
have
interposed
some
considerable
interval
of
rest
.
SAGR.
This
will
appear
unto
you
,
if
you
cast
your
eye
upon
the
bank
or
piles
,
where
these
mutations
are
made
perpendicularly
,
but
not
that
there
is
any
real
time
of
cessation
.
SIMP.
I
did
think
,
that
because
these
two
motions
were
contrary
,
there
ought
to
be
in
the
midst
between
them
some
kind
of
rest
;
conformable
to
the
Doctrine
of
Aristotle
,
which
demonstrates
that
in
puncto
regressus
mediat
quies
.
SAGR.
I
very
well
remember
this
place
:
but
I
bear
in
minde
also
,
that
when
I
read
Philosophy
,
I
was
not
thorowly
satisfied
with
Aristotles
demonstration
;
but
that
I
had
many
experiments
on
the
contrary
,
which
I
could
still
rehearse
unto
you
,
but
I
am
unwilling
to
sally
out
into
any
other
digressions
,
we
being
met
here
to
discourse
of
the
proposed
mattes
,
if
it
be
possible
,
without
these
excursions
wherewith
we
have
interrupted
our
disputes
in
those
dayes
that
are
past
.
SIMP.
And
yet
we
may
with
convenience
,
if
not-interrupt
them
,
at
least
prolong
them
very
much
,
for
returning
yesterday
home
,
I
set
my self
to
read
the
Tractate
of
Conclusions
,
where
I
find
Demonstrations
against
this
annual
motion
ascribed
to
the
Earth
,
very
solid
;
and
because
I
would
not
trust
my
memory
with
the
punctual
relation
of
them
,
I
have
brought
back
the
Book
along
with
me
.
SAGR.
You
have
done
very
well
;
but
if
we
would
re-assume
our
Disputations
according
to
yesterdayes
appointment
,
it
is
requisite
that
we
first
hear
what
account
Salviatus
hath
to
give
us
of
the
Book
,
De
stellis
novis
,
and
then
without
interruption
we
may
proceed
to
the
Annual
motion
.
Now
what
say
you
,
Salviatus
touching
those
stars
?
Are
they
really
pull'd
down
from
Heaven
to
these
lower
regions
,
by
vertue
of
that
Authours
calculations
,
whom
Simplicius
mentioneth
?
SALV
.
I
set
my self
last
night
to
peruse
his
proceedings
,
and
I
have
this
morning
had
another
view
of
him
,
to
see
whether
that
which
he
seemed
over
night
to
affirm
,
were
really
his
sense
,
or
my
dreams
and
phantastical
nocturnal
imaginations
;
and
in
the
close
found
to
my
great
grief
that
those
things
were
really
written
and
printed
,
which
for
the
reputation-sake
of
this
Philosopher
I
was
unwilling
to
believe
.
It
is
in
my
judgment
impossible
,
but
that
he
should
perceive
the
vanity
of
his
undertaking
,
aswell
because
it
is
too
apert
,
as
because
I
remember
,
that
I
have
heard
him
mentioned
with
applause
by
the
Academick
our
Friend
:
it
seemeth
to
me
also
to
be
a
thing
very
unlikely
,
that
in
complacency
to
others
,
he
should
be
induced
to
set
so
low
a
value
upon
his
reputation
,
as
to
give
consent
to
the
publication
of
a
work
,
for
which
he
could
expect
no
other
than
the
censure
of
the
Learned
.
SAGR.
Yea
,
but
you
know
,
that
those
will
be
much
fewer
than
one
for
an
hundred
,
compared
to
those
that
shall
celebrate
and
extoll
him
above
the
greatest
wits
that
are
,
or
ever
have
been
in
the
world
:
He
is
one
that
hath
mentioned
the
Peripatetick
inalterability
of
Heaven
against
a
troop
of
Astronomers
,
and
that
to
their
greater
disgrace
hath
foiled
them
at
their
own
weapons
:
and
what
do
you
think
four
or
five
in
a
Countrey
that
discern
his
triflings
,
can
do
against
the
innumerable
multitude
,
that
,
not
being
able
to
discover
or
comprehend
them
,
suffer
themselves
to
be
taken
with
words
,
and
so
much
more
applaud
him
,
by
how
much
the
lesse
they
understand
him
?
You
may
adde
also
,
that
those
few
who
understand
,
scorn
to
give
an
answer
to
papers
so
trivial
and
unconcludent
;
and
that
upon
very
good
reasons
,
because
to
the
intelligent
there
is
no
need
thereof
,
and
to
those
that
do
not
understand
,
it
is
but
labour
lost
.
SALV
.
The
most
deserved
punishment
of
their
demerits
would
certainly
be
silence
,
if
there
were
not
other
reasons
,
for
which
it
is
haply
no
lesse
than
necessary
to
resent
their
timerity
:
one
of
which
is
,
that
we
Italians
thereby
incur
the
censure
of
Illiterates
,
and
attract
the
laughter
of
Forreigners
;
and
especially
to
such
who
are
separated
from
our
Religion
;
and
I
could
shew
you
many
of
those
of
no
small
eminency
,
who
scoff
at
our
Academick
,
and
the
many
Mathematicians
that
are
in
Italic
,
for
suffering
the
follies
of
such
a
[
](A61244-e58290-b)*
*
〈◊〉
.
Fabler
against
Astronomers
to
come
into
the
light
,
and
to
be
openly
maintained
without
contradiction
;
but
this
also
might
be
dispensed
with
,
in
respect
of
the
other
greater
occasions
of
laughter
,
wherewith
we
may
confront
them
depending
on
the
dissimulation
of
the
intelligent
,
touching
the
follies
of
these
opponents
of
the
Doctrines
that
they
well
enough
understand
.
SAGR.
I
desire
not
a
greater
proof
of
those
mens
petulancy
,
and
the
infelicity
of
a
Copernican
,
subject
to
be
opposed
by
such
as
understand
not
so
much
as
the
very
first
positions
,
upon
which
he
undertakes
the
quarrel
.
SALV
.
You
will
be
no
lesse
astonished
at
their
method
in
confuting
the
Astronomers
,
who
affirm
the
new
Stars
to
be
superiour
to
the
Orbs
of
the
Planets
;
and
peradventure
in
the
[
](A61244-e58390-b)†
†
He
taketh
〈◊〉
Firmament
〈◊〉
the
S●arry
Sphere
,
and
not
as
we
vulg●●ly
receive
the
word
.
Firmament
it self
.
SAGR.
But
how
could
you
in
so
short
a
time
examine
all
this
Book
,
which
is
so
great
a
Volume
,
and
must
needs
contain
very
many
demonstrations
?
SALV
.
I
have
confined
my self
to
these
his
first
confutations
,
in
which
with
twelve
demonstrations
founded
upon
the
observations
of
twelve
Astronomers
,
(
who
all
held
,
that
the
Star
,
Anno
1572.
which
appeared
in
Cassiopeia
,
was
in
the
Firmament
)
he
proveth
it
on
the
contrary
,
to
be
beneath
the
Moon
,
conferring
,
two
by
two
,
the
meridian
altitudes
,
proceeding
in
the
method
that
you
shall
understand
by
and
by
.
And
because
,
I
think
,
that
in
the
examination
of
this
his
first
progression
,
I
have
discovered
in
this
Authour
a
great
unlikelihood
of
his
ability
to
conclude
any
thing
against
the
Astronomers
,
in
favour
of
the
Peripatetick
Philosophers
,
and
that
their
opinion
is
more
and
more
concludently
confirmed
,
I
could
not
apply
my self
with
the
like
patience
in
examining
his
other
methods
,
but
have
given
a
very
slight
glance
upon
them
,
and
am
certain
,
that
the
defect
that
is
in
these
first
impugnations
,
is
likewise
in
the
rest
.
And
as
you
shall
see
,
by
experience
,
very
few
words
will
suffice
to
confute
this
whole
Book
,
though
compiled
with
so
great
a
number
of
laborious
calculations
,
The
method
observed
by
Clar.
in
confuting
the
Astronomers
,
and
by
Salviatus
in
confuting
him
.
as
here
you
see
.
Therefore
observe
my
proceedings
.
This
Authour
undertaketh
,
as
I
say
,
to
wound
his
adversaries
with
their
own
weapons
,
i.
e.
a
great
number
of
observations
made
by
themselves
,
to
wit
,
by
twelve
or
thirteen
Authours
in
number
,
and
upon
part
of
them
he
makes
his
supputations
,
and
concludeth
those
stars
to
have
been
below
the
Moon
.
Now
because
the
proceeding
by
interrogatories
very
much
pleaseth
me
,
in
regard
the
Authour
himself
is
not
here
,
let
Simplicius
answer
me
to
the
questions
that
I
shall
ask
him
,
as
he
thinks
he
himself
would
,
if
he
were
present
.
And
presupposing
that
we
speak
of
the
foresaid
Star
,
of
Anno
1572.
appearing
in
Cassiopeia
,
tell
me
,
Simplicius
,
whether
you
believe
that
it
might
be
in
the
same
time
placed
in
divers
places
,
that
is
,
amongst
the
Elements
,
aud
also
amongst
the
planetary
Orbs
,
and
also
above
these
amongst
the
fixed
Stars
,
and
yet
again
infinitely
more
high
.
SIMP.
There
is
no
doubt
,
but
that
it
ought
to
be
confessed
that
it
is
but
in
one
only
place
,
and
at
one
sole
and
determinate
distance
from
the
Earth
.
SALV
.
Therefore
if
the
observations
made
by
the
Astronomers
were
exact
,
and
the
calculations
made
by
this
Author
were
not
erroneous
,
it
were
easie
from
all
those
and
all
these
to
recollect
the
same
distances
alwayes
to
an
hair
,
is
not
this
true
?
SIMP.
My
reason
hitherto
tells
me
that
so
it
must
needs
be
;
nor
do
I
believe
that
the
Author
would
contradict
it
.
SALV
.
But
when
of
many
and
many
computations
that
have
been
made
,
there
should
not
be
so
much
as
two
onely
that
prove
true
,
what
would
you
think
of
them
?
SIMP.
I
would
think
that
they
were
all
false
,
either
through
the
fault
of
the
computist
,
or
through
the
defect
of
the
observators
,
and
at
the
most
that
could
be
said
,
I
would
say
,
that
but
onely
one
of
them
and
no
more
was
true
;
but
as
yet
I
know
not
which
to
choose
.
SALV
.
Would
you
then
from
false
fundamentals
deduce
and
establish
a
doubtful
conclusion
for
true
?
Certainly
no.
Now
the
calculations
of
this
Author
are
such
,
that
no
one
of
them
agrees
with
another
,
you
may
see
then
what
credit
is
to
be
given
to
them
.
SIMP.
Indeed
,
if
it
be
so
,
this
is
a
notable
failing
.
SAGR.
But
by
the
way
I
have
a
mind
to
help
Simplicius
,
and
the
Author
by
telling
Salviatus
,
that
his
arguments
would
hold
good
if
the
Author
had
undertook
to
go
about
to
find
out
exactly
the
distance
of
the
Star
from
the
Earth
,
which
I
do
not
think
to
be
his
intention
;
but
onely
to
demonstrate
that
from
those
observations
he
collected
that
the
Star
was
sublunary
.
So
that
if
from
those
observations
,
and
from
all
the
computations
made
thereon
,
the
height
of
the
Star
be
alwayes
collected
to
be
lesse
than
that
of
the
Moon
,
it
serves
the
Authors
turn
to
convince
all
those
Astronomers
of
most
impardonable
ignorance
,
that
through
the
defect
either
of
Geometry
or
Arithmetick
,
have
not
known
how
to
draw
true
conclusions
from
their
own
observations
themselves
.
SALV
.
It
will
be
convenient
therefore
that
I
turn
my self
to
you
,
Sagredus
,
who
so
cunningly
aphold
the
Doctrine
of
this
Author
.
And
to
see
whether
I
can
make
Simplicius
,
though
not
very
expert
in
calculations
,
and
demonstrations
to
apprehend
the
inconclusivenesse
at
least
of
the
demonstrations
of
this
Author
,
first
proposed
to
consideration
,
and
how
both
he
,
and
all
the
Astronomers
with
whom
he
contendeth
,
do
agree
that
the
new
Star
had
not
any
motion
of
its
own
,
and
onely
went
round
with
the
diurnal
motion
of
the
primum
mobile
;
but
dissent
about
the
placing
of
it
,
the
one
party
putting
it
in
the
Celestial
Region
,
that
is
above
the
Moon
,
and
haply
above
the
fixed
Stars
,
and
the
other
judging
it
to
be
neer
to
the
Earth
,
that
is
,
under
the
concave
of
the
Lunar
Orb.
And
because
the
situation
of
the
new
star
,
of
which
we
speak
,
was
towards
the
North
,
and
at
no
very
great
distance
from
the
Pole
,
so
that
to
us
Septentrionals
,
it
did
never
set
,
it
was
an
easie
matter
with
Astronomical
instruments
to
have
taken
its
several
meridian
altitudes
,
as
well
its
smallest
under
the
Pole
,
as
its
greatest
above
the
same
;
from
the
comparing
of
which
altitudes
,
made
in
several
places
of
the
Earth
,
situate
at
different
distances
from
the
North
,
that
is
,
different
from
one
another
in
relation
to
polar
altitudes
,
the
stars
distance
might
be
inferred
:
The
greatest
and
least
elevations
of
the
new
star
differ
not
from
each
other
more
than
the
polar
altitudes
,
the
said
star
being
in
the
Firmnment
.
For
if
it
was
in
the
Firmament
amongst
the
other
fixed
stars
,
its
meridian
altitudes
taken
in
divers
elevations
of
the
pole
,
ought
necessarily
to
differ
from
each
other
with
the
same
variations
that
are
found
amongst
those
elevations
themselves
;
that
is
,
for
example
,
if
the
elevation
of
the
star
above
the
horizon
was
30
degrees
,
taken
in
the
place
where
the
polar
altitude
was
v.
gr.
45
degrees
,
the
elevation
of
the
same
star
ought
to
have
been
encreased
4
or
5
degrees
in
those
more
Northernly
places
where
the
pole
was
higher
by
the
said
4
or
5
degrees
.
But
if
the
stars
distance
from
the
Earth
was
but
very
little
,
in
comparison
of
that
of
the
Firmament
;
its
meridian
altitudes
ought
approaching
to
the
North
to
encrease
considerably
more
than
the
polar
altitudes
;
and
by
that
greater
encrease
,
that
is
,
by
the
excesse
of
the
encrease
of
the
stars
elevation
,
above
the
encrease
of
the
polar
elevation
(
which
is
called
the
difference
of
Parallaxes
)
is
readily
calculated
with
a
cleer
and
sure
method
,
the
stars
distance
from
the
centre
of
the
Earth
.
Now
this
Author
taketh
the
observations
made
by
thirteen
Astronomers
in
sundry
elevations
of
the
pole
,
and
conferring
a
part
of
them
at
his
pleasure
,
he
computeth
by
twelve
collations
the
new
stars
height
to
have
been
alwayes
beneath
the
Moon
;
but
this
he
adventures
to
do
in
hopes
to
find
so
grosse
ignorance
in
all
those
,
into
whose
hands
his
book
might
come
,
that
to
speak
the
truth
,
it
hath
turn'd
my
stomack
;
and
I
wait
to
see
how
those
other
Astronomers
,
and
particularly
Kepler
,
against
whom
this
Author
principally
inveigheth
,
can
contein
themselves
in
silence
,
for
he
doth
not
use
to
hold
his
tongue
on
such
occasions
;
unlesse
he
did
possibly
think
the
enterprize
too
much
below
him
.
Now
to
give
you
to
understand
the
same
,
I
have
upon
this
paper
transcribed
the
conclusions
that
he
inferreth
from
his
twelve
indagations
;
the
first
of
which
is
upon
the
two
observations
:
-
Of
Maurolicus
and
Hainzelius
,
from
which
the
Star
is
collected
to
have
been
distant
from
the
centre
lesse
than
3
semidiameters
of
the
Earth
,
the
difference
of
Parallaxes
being
4
gr.
42
m.
30
sec.
3
semid
.
-
2.
And
is
calculated
on
the
observations
of
Hainzelius
,
with
Parall.
of
8.
m.
30
sec.
and
its
distance
from
the
centre
is
computed
to
be
more
than
25
semid
.
-
3.
And
upon
the
observations
of
Tycho
and
Hainzelius
,
with
Parall.
of
10
m.
and
the
distance
of
the
centre
is
collected
to
be
little
lesse
than
19
semid
.
-
4.
And
upon
the
observations
of
Tycho
and
the
Landgrave
,
with
Parall.
of
14
m.
the
distance
from
the
centre
is
made
to
be
about
10
semid
.
-
5.
And
upon
the
observations
of
Hainzelius
and
Gemma
,
with
Parall.
of
42
m.
30
sec.
whereby
the
distance
is
gathered
to
be
about
4
semid
.
-
6.
And
upon
the
observations
of
the
Landgrave
and
Camerarius
,
with
Parall.
of
8
m.
the
distance
is
concluded
to
be
about
4
semid
.
-
7.
And
upon
the
observations
of
Tycho
and
Hagecius
,
with
Parall.
of
6
m.
and
the
distance
is
made
31
semid
.
-
8.
And
upon
the
observations
of
Hagecius
and
Vrsinus
with
Parall.
of
43
m.
and
the
stars
distance
from
the
superficies
of
the
Earth
is
rendred
1/2
semid
.
-
9.
And
upon
the
observations
of
Landgravius
and
Buschius
,
with
Parall.
of
15
m.
and
the
distance
from
the
superficies
of
the
Earth
is
by
supputation
1/48
semid
.
-
10.
And
upon
the
observations
of
Maurolice
and
Munocius
,
with
Parall.
of
4
m.
30
sec.
and
the
compnted
distance
from
the
Earths
surface
is
1/5
semid
.
-
11.
And
upon
the
observations
of
Munocius
and
Gemma
,
with
Parall.
of
55
m.
and
the
distance
from
the
centre
is
rendred
13
semid
.
-
12.
And
upon
the
observations
of
Munosius
and
Vrsinus
with
Parall.
of
1
gr.
36
m.
and
the
distance
from
the
centre
cometh
forth
lesse
than
7
semid
.
These
are
twelve
indagations
made
by
the
Author
at
his
election
,
amongst
many
which
,
as
he
saith
,
might
be
made
by
combining
the
observations
of
these
thirteen
observators
.
The
which
twelve
we
may
believe
to
be
the
most
favourable
to
prove
his
intention
.
SAGR.
I
would
know
whether
amongst
the
so
many
other
indagations
pretermitted
by
the
Author
,
there
were
not
some
that
made
against
him
,
that
is
,
from
which
calculating
one
might
find
the
new
star
to
have
been
above
the
Moon
,
as
at
the
very
first
sight
I
think
we
may
reasonably
question
;
in
regard
I
see
these
already
produced
to
be
so
different
from
one
another
,
that
some
of
them
give
me
the
distance
of
the
said
star
from
the
Earth
,
4
,
6
,
10
,
100
,
a
thousand
,
and
an
hundred
thousand
times
bigger
one
than
another
;
so
that
I
may
well
suspect
that
amongst
those
that
he
did
not
calculate
,
there
was
some
one
in
fauour
of
the
adverse
party
.
And
I
guesse
this
to
be
the
more
probable
,
for
that
I
cannot
conceive
that
those
Astronomers
the
observators
could
want
the
knowledg
and
practice
of
rhese
computations
,
which
I
think
do
not
depend
upon
the
abstrucest
things
in
the
World
.
And
indeed
it
will
seem
to
me
a
thing
more
than
miraculous
,
if
whilst
in
these
twelve
investigations
onely
,
there
are
some
that
make
the
star
to
be
distant
from
the
Earth
but
a
few
miles
,
and
others
that
make
it
to
be
but
a
very
fmall
matter
below
the
Moon
,
there
are
none
to
be
found
that
in
favour
of
the
contrary
part
do
make
it
so
much
as
twenty
yards
above
the
Lunar
Orb.
And
that
which
shall
be
yet
again
more
extravagant
,
that
all
those
Astronomers
should
have
been
so
blind
as
not
to
have
discovered
that
their
so
apparent
mistake
.
SALV
.
Begin
now
to
prepare
your
ears
to
hear
with
infinite
admiration
to
what
excesses
of
confidence
of
ones
own
authority
and
others
folly
,
the
desire
of
contradicting
and
shewing
ones
self
wiser
than
others
,
transports
a
man
.
Amongst
the
indagations
omitted
by
the
Author
,
there
are
such
to
be
found
as
make
the
new
star
not
onely
above
the
Moon
,
but
above
the
fixed
stars
also
.
And
these
are
not
a
few
,
but
the
greater
part
,
as
you
shall
see
in
this
other
paper
,
where
I
have
set
them
down
.
SAGR.
But
what
saith
the
Author
to
these
?
It
may
be
he
did
not
think
of
them
?
SALV
.
He
hath
thought
of
them
but
too
much
:
but
saith
,
that
the
observations
upon
which
the
calculations
make
the
star
to
be
infinitely
remote
,
are
erroneous
,
and
that
they
cannot
be
combined
to
one
another
.
SIMP.
But
this
seemeth
to
me
a
very
lame
evasion
;
for
the
adverse
party
may
with
as
much
reason
reply
,
that
those
are
erroneous
wherewith
he
collecteth
the
star
to
have
been
in
the
Elementary
Region
.
SALV
.
Oh
Simplicius
,
if
I
could
but
make
you
comprehend
the
craft
,
though
no
great
craftinesse
of
this
Author
,
I
should
make
you
to
wonder
,
and
also
to
be
angry
to
see
how
that
he
palliating
his
sagacity
with
the
vail
of
the
simplicity
of
your self
;
and
the
rest
of
meer
Philosophers
,
would
insinuate
himself
into
your
good
opinion
,
by
tickling
your
ears
,
and
swelling
your
ambition
,
pretending
to
have
convinced
and
silenced
these
petty
Astronomers
,
who
went
about
to
assault
the
impregnable
inalterability
of
the
Peripatetick
Heaven
,
and
which
is
more
,
to
have
foild
and
conquered
them
with
their
own
arms
.
I
will
try
with
all
my
ability
to
do
the
same
;
and
in
the
mean
time
let
Sagredus
take
it
in
good
part
,
if
Simplicius
and
I
try
his
patience
,
perhaps
a
little
too
much
,
whilst
that
with
a
superfluous
circumlocution
(
superfluous
I
say
to
his
most
nimble
apprehension
)
I
go
about
to
make
out
a
thing
,
which
it
is
not
convenient
should
be
hid
and
unknown
unto
him
.
SAGR.
I
shall
not
onely
without
wearinesse
,
but
also
with
much
delight
hearken
to
your
discourses
;
and
so
ought
all
Peripatetick
Philosophers
,
to
the
end
they
may
know
how
much
they
are
oblieged
to
this
their
Protector
.
SALV
.
Tell
me
,
Simplicius
,
whether
you
do
well
comprehend
,
how
,
the
new
star
being
placed
in
the
meridian
circle
yonder
towards
the
North
,
the
same
to
one
that
from
the
South
should
go
towards
the
North
,
would
seem
to
rise
higher
and
higher
above
the
Horizon
,
as
much
as
the
Pole
,
although
it
should
have
been
scituate
amongst
the
fixed
stars
;
but
,
that
in
case
it
were
considerably
lower
,
that
is
nearer
to
the
Earth
,
it
would
appear
to
ascend
more
than
the
said
pole
,
and
still
more
by
how
much
its
vicinity
was
greater
?
SIMP.
I
think
that
I
do
very
well
conceive
the
same
;
in
token
whereof
I
will
try
if
I
can
make
a
mathematical
Scheme
of
it
,
and
in
this
great
circle
[
in
Fig.
1.
of
this
Dialogue
.
]
I
will
marke
the
pole
P
;
and
in
these
two
lower
circles
I
will
note
two
stars
beheld
from
one
place
on
the
Earth
,
which
let
be
A
;
and
let
the
two
stars
be
these
B
and
C
,
beheld
in
the
same
line
ABC
,
which
line
I
prolong
till
it
meet
with
a
fixed
star
in
D.
And
then
walking
along
the
Earth
,
till
I
come
to
the
term
E
,
the
two
stars
will
appear
to
me
separated
from
the
fixed
star
D
,
and
advanced
neerer
to
the
pole
P
,
and
the
lower
star
B
more
,
which
will
appear
to
me
in
G
,
and
the
star
C
lesse
,
which
will
appear
to
me
in
F
,
but
the
fixed
star
D
will
have
kept
the
same
distance
from
the
Pole
.
SALV
.
I
see
that
you
understand
the
businesse
very
well
.
I
believe
that
you
do
likewise
comprehend
,
that
,
in
regard
the
star
B
is
lower
than
C
,
the
angle
which
is
made
by
the
rayes
of
the
sight
,
which
departing
from
the
two
places
A
and
E
,
meet
in
C
,
to
wit
,
this
angle
ACE
,
is
more
narrow
,
or
if
we
will
say
more
acute
than
the
angle
constituted
in
B
,
by
the
rayes
AB
and
EB
.
SIMP.
This
I
likewise
understand
very
well
.
SALV
.
And
also
,
the
Earth
beine
very
little
and
almost
insensible
,
in
respect
of
the
Firmament
(
or
Starry
Sphere
;
)
and
consequently
the
space
AE
,
paced
on
the
Earth
,
being
very
small
in
comparison
of
the
immense
length
of
the
lines
EG
and
EF
,
passing
from
the
Earth
unto
the
Firmament
,
you
thereby
collect
that
the
star
C
might
rise
and
ascend
so
much
and
so
much
above
the
Earth
,
that
the
angle
therein
made
by
the
rayes
which
depart
from
the
said
stationary
points
A
and
E
,
might
become
most
acute
,
and
as
it
were
absolutely
null
and
insensible
.
SIMP.
And
this
also
is
most
manifest
to
sense
.
SALV
.
Now
you
know
Simplicius
that
Astronomers
and
Mathematicians
have
found
infallible
rules
by
way
of
Geometry
and
Arithmetick
,
to
be
able
by
help
of
the
quantity
of
these
angles
B
and
C
,
and
of
their
differences
,
with
the
additional
knowledg
of
the
distance
of
the
two
places
A
and
E
,
to
find
to
a
foot
the
remotenesse
of
sublime
bodies
;
provided
alwayes
that
the
aforesaid
distance
,
and
angles
be
exactly
taken
.
SIMP.
So
that
if
the
Rules
dependent
on
Geometry
and
Astronomy
be
true
,
all
the
fallacies
and
errours
that
might
be
met
with
in
attempting
to
investigate
those
altitudes
of
new
Stars
or
Comets
,
or
other
things
must
of
necessity
depend
on
the
distance
AE
,
and
on
the
angles
B
and
C
,
not
well
measured
.
And
thus
all
those
differences
which
are
found
in
these
twelve
workings
depend
,
not
on
the
defects
of
the
rules
of
the
Calculations
,
but
on
the
errours
committed
in
finding
out
those
angles
,
and
those
distances
,
by
means
of
the
Instrumental
Observations
.
SALV
.
True
;
and
of
this
there
is
no
doubt
to
be
made
.
Now
it
is
necessary
that
you
observe
intensely
,
how
in
removing
the
Star
from
B
to
C
,
whereupon
the
angle
alwayes
grows
more
acute
,
the
ray
EBG
goeth
farther
and
farther
off
from
the
ray
ABD
in
the
part
beneath
the
angle
,
as
you
may
see
in
the
line
ECF
,
whose
inferiour
part
EC
is
more
remote
from
the
part
AC
,
than
is
the
part
EB
,
but
it
can
never
happen
,
that
by
any
whatsoever
immense
recession
,
the
lines
AD
and
EF
should
totally
sever
from
each
other
,
they
being
finally
to
go
and
conjoyn
in
the
Star
:
and
onely
this
may
be
said
,
that
they
would
separate
,
and
reduce
themselves
to
parallels
,
if
so
be
the
recession
should
be
infinite
,
which
case
is
not
to
be
supposed
.
But
because
(
observe
well
)
the
distance
of
the
Firmament
,
in
relation
to
the
smallnesse
of
the
Earth
,
as
hath
been
said
,
is
to
be
accounted
,
as
if
it
were
infinite
;
therefore
the
angle
conteined
betwixt
the
two
rayes
,
that
being
drawn
from
the
points
A
and
E
,
go
to
determine
in
a
fixed
Star
,
is
esteemed
nothing
,
and
those
rayes
held
to
be
two
parallel
lines
;
and
therefore
it
is
concluded
,
that
then
only
may
the
New
Star
be
affirmed
to
have
been
in
the
Firmament
,
when
from
the
collating
of
the
Observations
made
in
divers
places
,
the
said
angle
is
,
by
calculation
,
gathered
to
be
insensible
,
and
the
lines
,
as
it
were
,
parallels
.
But
if
the
angle
be
of
a
considerable
quantity
,
the
New
Star
must
of
necessity
be
lower
than
those
fixed
;
and
also
than
the
Moon
,
in
case
the
angle
ABE
should
be
greater
than
that
which
would
be
made
in
the
Moons
centre
.
SIMP.
Then
the
remotenesse
of
the
Moon
is
not
so
great
,
that
a
like
angle
should
be
[
](A61244-e60170-b)*
*
〈◊〉
.
insensible
in
her
?
SALV
.
No
Sir
;
nay
it
is
sensible
,
not
onely
in
the
Moon
,
but
in
the
Sun
also
.
SIMP.
But
if
this
be
so
,
it
's
possible
that
the
said
angle
may
be
observed
in
the
New
Star
,
without
necessitating
it
to
be
inferiour
to
the
Sun
,
aswell
as
to
the
Moon
.
SALV
.
This
may
very
well
be
,
yea
,
and
is
in
the
present
case
,
as
you
shall
see
in
due
place
;
that
is
,
when
I
shall
have
made
plain
the
way
,
in
such
manner
that
you
also
,
though
not
very
perfect
in
Astronomical
calculations
,
may
clearly
see
,
and
,
as
it
were
,
with
your
hands
feel
how
that
this
Author
had
it
more
in
his
eye
to
write
in
complacency
of
the
Peripateticks
,
by
palliating
and
dissembling
sundry
things
,
than
to
establish
the
truth
,
by
producing
them
with
naked
sincerity
:
therefore
let
us
proceed
forwards
.
By
the
things
hitherto
spoken
,
I
suppose
that
you
comprehend
very
well
how
that
the
distance
of
the
new
Star
can
never
be
made
so
immense
,
that
the
angle
so
often
named
shall
wholly
disappear
,
and
that
the
two
rayes
of
the
Observators
at
the
places
A
and
E
,
shall
become
altogether
parallels
:
and
you
may
consequently
comprehend
to
the
full
,
that
if
the
calculations
should
collect
from
the
observations
,
that
that
angle
was
totally
null
,
or
that
the
lines
were
truly
parallels
,
we
should
be
certain
that
the
observations
were
at
least
in
some
small
particular
erroneous
:
But
,
if
the
calculations
should
give
us
the
said
lines
to
be
separated
not
only
to
equidistance
,
that
is
,
so
as
to
be
parallel
,
but
to
have
past
beyond
that
terme
,
and
to
be
dilated
more
above
than
below
,
then
must
it
be
resolutely
concluded
,
that
the
observations
were
made
with
lesse
accuratenesse
,
and
in
a
word
,
to
be
erroneous
;
as
leading
us
to
a
manifest
impossibility
.
In
the
next
place
,
you
must
believe
me
,
and
suppose
it
for
true
,
that
two
right
lines
which
depart
from
two
points
marked
upon
another
right
line
,
are
then
wider
above
than
below
,
when
the
angles
included
between
them
upon
that
right
line
are
greater
than
two
right
angles
;
and
if
these
angles
should
be
equal
to
two
right
angles
,
the
lines
would
be
parallels
;
but
if
they
were
less
than
two
right
angles
,
the
lines
would
be
concurrent
,
and
being
continued
out
would
undoubtedly
intersect
the
triangle
.
SIMP.
Without
taking
it
upon
trust
from
you
,
I
know
the
same
;
and
am
not
so
very
naked
of
Geometry
,
as
not
to
know
a
Proposition
,
which
I
have
had
occasion
of
reading
very
often
in
Aristotle
,
that
is
,
that
the
three
angles
of
all
triangles
are
equall
to
two
right
angles
:
so
that
if
I
take
in
my
Figure
the
triangle
ABE
,
it
being
supposed
that
the
line
EA
is
right
;
I
very
well
conceive
,
that
its
three
angles
A
,
E
,
B
,
are
equal
to
two
right
angles
;
and
that
consequently
the
two
angles
E
and
A
are
lesse
than
two
right
angles
,
so
much
as
is
the
angle
B.
Whereupon
widening
the
lines
AB
and
EB
(
still
keeping
them
from
moving
out
of
the
points
A
and
E
)
untill
that
the
angle
conteined
by
them
towards
the
parts
B
,
disappear
,
the
two
angles
beneath
shall
be
equal
to
two
right
angles
,
and
those
lines
shall
be
reduced
to
parallels
:
and
if
one
should
proceed
to
enlarge
them
yet
more
,
the
angles
at
the
points
E
and
A
would
become
greater
than
two
right
angles
.
SALV
.
You
are
an
Archimedes
,
and
have
freed
me
from
the
expence
of
more
words
in
declaring
to
you
,
that
whensoever
the
calculations
make
the
two
angles
A
and
E
to
be
greater
than
two
right
angles
,
the
observations
without
more
adoe
will
prove
erroneous
.
This
is
that
which
I
had
a
desire
that
you
should
perfectly
understand
,
and
which
I
doubted
that
I
was
not
able
so
to
make
out
,
as
that
a
meer
Peripatetick
Philosopher
might
attain
to
the
certain
knowledg
thereof
.
Now
let
us
go
on
to
what
remains
.
And
re-assuming
that
which
even
now
you
granted
me
,
namely
,
that
the
new
star
could
not
possibly
be
in
many
places
,
but
in
one
alone
,
when
ever
the
supputations
made
upon
the
observations
of
these
Astronomers
do
not
assign
it
the
same
place
,
its
necessary
that
it
be
an
errour
in
the
observations
,
that
is
,
either
in
taking
the
altitudes
of
the
pole
,
or
in
taking
the
elevations
of
the
star
,
or
in
the
one
or
other
working
.
Now
for
that
in
the
many
workings
made
with
the
combinations
two
by
two
,
there
are
very
few
of
the
observations
that
do
agree
to
place
the
star
in
the
same
situation
;
therefore
these
few
onely
may
happily
be
the
non-erroneous
,
but
the
others
are
all
absolutely
false
.
SAGR.
It
will
be
necessary
then
to
give
more
credit
to
these
few
alone
,
than
to
all
the
rest
together
,
and
because
you
say
,
that
these
which
accord
are
very
few
,
and
I
amongst
these
12
,
do
find
two
that
so
accord
,
which
both
make
the
distance
of
the
star
from
the
centre
of
the
Earth
4
semidiameters
,
which
are
these
,
the
fifth
and
sixth
,
therefore
it
is
more
probable
that
the
new
star
was
elementary
,
than
celestial
.
SALV
.
You
mistake
the
point
;
for
if
you
note
well
it
was
not
written
,
that
the
distance
was
exactly
4
semidiameters
,
but
about
4
semidiameters
;
and
yet
you
shall
see
that
those
two
distances
differed
from
each
other
many
hundreds
of
miles
.
Here
they
are
;
you
see
that
this
fifth
,
which
is
13389
Italian
miles
,
exceeds
the
sixth
,
which
is
13100
miles
,
by
almost
300
miles
.
SAGR.
Which
then
are
those
few
that
agree
in
placing
the
star
in
the
same
situation
?
SALV
.
They
are
,
to
the
disgrace
of
this
Author
five
workings
,
which
all
place
it
in
the
firmament
,
as
you
shall
see
in
this
note
,
where
I
have
set
down
many
other
combinations
.
But
I
will
grant
the
Author
more
than
peradventure
he
would
demand
of
me
,
which
is
in
sum
,
that
in
each
combination
of
the
observations
there
is
some
error
;
which
I
believe
to
be
absolutely
necessary
;
for
the
observations
being
four
in
number
that
serve
for
one
working
,
that
is
,
two
different
altitudes
of
the
Pole
,
and
two
different
elevations
of
the
star
,
made
by
different
obfervers
,
in
different
places
,
Astronomical
Instruments
are
very
subject
to
errour
.
with
different
instruments
,
who
ever
hath
any
small
knowledg
of
this
art
,
will
say
,
that
amongst
all
the
four
,
it
is
impossible
but
there
will
be
some
error
;
and
especially
since
we
see
that
in
taking
but
one
onely
altitude
of
the
Pole
,
with
the
same
instrument
,
in
the
same
place
,
by
the
same
observer
,
that
hath
repeated
the
observation
a
thousand
times
,
there
will
still
be
a
titubation
of
one
,
or
sometimes
of
many
minutes
,
as
in
this
same
book
you
may
see
in
several
places
.
These
things
presupposed
,
I
ask
you
Simplicius
whether
you
believe
that
this
Authour
held
these
thirteen
observators
for
wise
,
understanding
and
expert
men
in
using
those
instruments
,
or
else
for
inexpert
,
and
bunglers
?
SIMP.
It
must
needs
be
that
he
esteemed
them
very
acute
and
intelligent
;
for
if
he
had
thought
them
unskilful
in
the
businesse
,
he
might
have
omitted
his
sixth
book
as
inconclusive
,
as
being
founded
upon
suppositions
very
erroneous
;
and
might
take
us
for
excessively
simple
,
if
he
should
think
he
could
with
their
inexpertnesse
perswade
us
to
believe
a
false
position
of
his
for
truth
.
SALV
.
Therefore
these
observators
being
such
,
and
that
yet
notwithstanding
they
did
erre
,
and
so
consequently
needed
correction
,
that
so
one
might
from
their
observations
infer
the
best
hints
that
may
be
;
it
is
convenient
that
we
apply
unto
them
the
least
and
neerest
emendations
and
corrections
that
may
be
;
so
that
they
do
but
suffice
to
reduce
the
observations
from
impossibility
to
possibility
;
so
as
v.
gr
.
if
one
may
but
correct
a
manifest
errour
,
and
an
apparent
impossibility
of
one
of
their
observations
by
the
addition
or
substraction
of
two
or
three
minutes
,
and
with
that
amendment
to
reduce
it
to
possibility
,
a
man
ought
not
to
essay
to
adjust
it
by
the
addition
or
substraction
of
fifteen
,
twenty
,
or
fifty
.
SIMP.
I
think
the
Author
would
not
deny
this
:
for
granting
that
they
are
expert
and
judicious
men
,
it
ought
to
be
thought
that
they
did
rather
erre
little
than
much
.
SALV
.
Observe
again
;
The
places
where
the
new
Star
is
placed
,
are
some
of
them
manifestly
impossible
,
and
others
possible
.
Absolutely
impossible
it
is
,
that
it
should
be
an
infinite
space
superiour
to
the
fixed
Stars
,
for
there
is
no
such
place
in
the
world
;
and
if
there
were
,
the
Star
there
scituate
would
have
been
imperceptible
to
us
:
it
is
also
impossible
that
it
should
go
creeping
along
the
superficies
of
the
Earth
;
and
much
lesse
that
it
should
be
within
the
said
Terrestrial
Globe
.
Places
possible
are
these
that
be
in
controversie
,
it
not
interferring
vvith
our
understanding
,
that
a
visible
object
in
the
likenesse
of
a
Star
might
be
aswell
above
the
Moon
,
as
below
it
.
Now
whilst
one
goeth
about
to
compute
by
the
way
of
Observations
and
Calculations
made
with
the
utmost
certainty
that
humane
diligence
can
attain
unto
what
its
place
was
,
it
is
found
that
the
greatest
part
of
those
Calculations
make
it
more
than
infinitely
superiour
to
the
Firmament
,
others
make
it
very
neer
to
the
surface
of
the
Earth
,
and
some
also
under
the
same
;
and
of
the
rest
,
which
place
it
in
situations
not
impossible
,
none
of
them
agree
with
each
other
;
insomuch
that
it
must
be
confessed
,
hat
all
those
observations
are
necessarily
false
;
so
that
if
we
would
nevertheless
collect
some
fruit
from
so
many
laborious
calculations
,
we
must
have
recourse
to
the
corrections
,
amending
all
the
observations
.
SIMP.
But
the
Authour
will
say
,
that
of
the
observations
that
assign
to
the
Star
impossible
places
,
there
ought
no
account
to
be
made
,
as
being
extreamly
erroneous
and
false
;
and
those
onely
ought
to
be
accepted
,
that
constitute
it
in
places
not
impossible
:
and
amongst
these
a
man
ought
to
seek
,
by
help
of
the
most
probable
,
and
most
numerous
concurrences
,
not
if
the
particular
and
exact
situation
,
that
is
,
its
true
distance
from
the
centre
of
the
Earth
,
at
least
,
whether
it
was
amongst
the
Elements
,
or
else
amongst
the
Coelestial
bodies
.
SALV
.
The
discourse
which
you
now
make
,
is
the
self
same
that
the
Author
made
,
in
favour
of
his
cause
,
but
with
too
unreasonable
a
disadvantage
to
his
adversaries
;
and
this
is
that
principal
point
that
hath
made
me
excessively
to
wonder
at
the
too
great
confidence
that
he
expressed
to
have
,
no
less
of
his
own
authority
,
than
of
the
blindness
and
inadvertency
of
the
Astronomers
;
in
favour
of
whom
I
will
speak
,
and
you
shall
answer
for
the
Author
.
And
first
,
I
ask
you
,
whether
the
Astronomers
,
in
observing
with
their
Instruments
,
and
seeking
v.
gr
.
how
great
the
elevation
of
a
Star
is
above
the
Horizon
,
may
deviate
from
the
truth
,
aswell
in
making
it
too
great
,
as
too
little
;
that
is
,
may
erroneously
compute
,
that
it
is
sometime
higher
than
the
truth
,
and
sometimes
lower
;
or
else
whether
the
errour
must
needs
be
alwayes
of
one
kinde
,
to
wit
,
that
erring
they
alwayes
make
it
too
much
,
and
never
too
little
,
or
alwayes
too
little
,
and
never
too
much
?
SIMP.
I
doubt
not
,
but
that
it
is
as
easie
to
commit
an
errour
the
one
way
,
as
the
other
.
SALV
.
I
believe
the
Author
would
answer
the
same
.
Now
of
these
two
kinds
of
errours
,
which
are
contraries
,
and
into
which
the
observators
of
the
new
star
may
equally
have
fallen
,
applied
to
calculations
,
one
sort
will
make
the
star
higher
,
and
the
other
lower
than
really
it
is
.
And
because
we
have
already
agreed
,
that
all
the
observations
are
false
;
upon
what
ground
would
this
Author
have
us
to
accept
those
for
most
congruous
with
the
truth
,
that
shew
the
star
to
have
been
near
at
hand
,
than
the
others
that
shew
it
excessively
remote
?
SIMP.
By
what
I
have
,
as
yet
,
collected
of
the
Authors
mind
,
I
see
not
that
he
doth
refuse
those
observations
,
and
indagations
that
might
make
the
star
more
remote
than
the
Moon
,
and
also
than
the
Sun
,
but
only
those
that
make
it
remote
(
as
you
your self
have
said
)
more
than
an
infinite
distance
;
the
which
distance
,
because
you
also
do
refuse
it
as
impossible
,
he
also
passeth
over
,
as
being
convicted
of
infinite
falshood
;
as
also
those
observations
are
of
impossibility
.
Methinks
,
therefore
,
that
if
you
would
convince
the
Author
,
you
ought
to
produce
supputations
,
more
exact
,
or
more
in
number
,
or
of
more
diligent
observers
,
which
constitute
the
star
in
such
and
such
a
distance
above
the
Moon
,
or
above
the
Sun
,
and
to
be
brief
,
in
a
place
possible
for
it
to
be
in
,
like
as
he
produceth
these
twelve
,
which
all
place
the
star
beneath
the
Moon
in
places
that
have
a
being
in
the
world
,
and
where
it
is
possible
for
it
to
be
.
SALV
.
But
Simplicius
yours
and
the
Authors
Equivocation
lyeth
in
this
,
yours
in
one
respect
,
and
the
Authors
in
another
;
I
discover
by
your
speech
that
you
have
formed
a
conceit
to
your self
,
that
the
exorbitancies
that
are
commited
in
the
establishing
the
distance
of
the
Star
do
encrease
successively
,
according
to
the
proportion
of
the
errors
that
are
made
by
the
Instrument
,
in
taking
the
observations
,
and
that
by
conversion
,
from
the
greatness
of
the
exorbitancies
,
may
be
argued
the
greatnesse
of
the
error
;
and
that
thereforefore
hearing
it
to
be
infered
from
such
an
observation
,
that
the
distance
of
the
star
is
infinite
,
it
is
necessary
,
that
the
errour
in
observing
was
infinite
,
and
therefore
not
to
be
amended
,
and
as
such
to
be
refused
;
but
the
businesse
doth
not
succeed
in
that
manner
,
my
Simplicius
,
and
I
excuse
you
for
not
having
comprehended
the
matter
as
it
is
,
in
regard
of
your
small
experience
in
such
affairs
;
but
yet
cannot
I
under
that
cloak
palliate
the
error
of
the
Author
,
who
dissembling
the
knowledge
of
this
which
he
did
perswade
himself
that
we
in
good
earnest
did
not
understand
,
hath
hoped
to
make
use
of
our
ignorance
,
to
gain
the
better
credit
to
his
Doctrine
,
among
the
multitude
of
illiterate
men
.
Therefore
for
an
advertisement
to
those
who
are
more
credulous
then
intelligent
,
and
to
recover
you
from
error
,
know
that
its
possible
(
and
that
for
the
most
part
it
will
come
to
passe
)
that
an
observation
,
that
giveth
you
the
star
v.
gr
.
at
the
distance
of
Saturn
,
by
the
adition
or
substraction
of
but
one
sole
minute
from
the
elevation
taken
with
the
instrument
,
shall
make
it
to
become
infinitely
distant
;
and
therefore
of
possible
,
impossible
,
and
by
conversion
,
those
calculations
which
being
grounded
upon
those
observations
,
make
the
star
infinitely
remote
,
may
possibly
oftentimes
with
the
addition
or
subduction
of
one
sole
minute
,
reduce
it
to
a
possible
scituation
:
and
this
which
I
say
of
a
minute
,
may
also
happen
in
the
correction
of
half
a
minute
,
a
sixth
part
,
and
less
.
Now
fix
it
well
in
your
mind
,
that
in
the
highest
distances
,
that
is
v.
g.
the
height
of
Saturn
,
or
that
of
the
fixed
Stars
,
very
small
errors
made
by
the
Observator
,
with
the
instrument
,
render
the
scituation
determinate
and
possible
,
infinite
&
impossible
.
This
doth
not
so
evene
in
the
sublunary
distances
,
and
near
the
earth
,
where
it
may
happen
that
the
observation
by
which
the
Star
is
collected
to
be
remote
v.
g.
4.
Semidiameters
terrestrial
,
may
encrease
or
diminish
,
not
onely
one
minute
but
ten
,
and
an
hundred
,
and
many
more
,
without
being
rendred
by
the
calculation
either
infinitely
remote
,
or
so
much
as
superior
to
the
Moon
.
You
may
hence
comprehend
that
the
greatnesse
of
the
error
(
to
so
speak
)
instrumental
,
are
not
to
be
valued
by
the
event
of
the
calculation
,
but
by
the
quantity
it self
of
degrees
and
minutes
numbred
upon
the
instrument
,
and
these
observations
are
to
be
called
more
just
or
less
erroneous
,
which
with
the
addition
or
substraction
of
fewer
minutes
,
restore
the
star
to
a
possible
situation
;
and
amongst
the
possible
places
,
the
true
one
may
be
believed
to
have
been
that
,
about
which
a
greater
number
of
distances
concurre
upon
calculating
the
more
exact
observations
.
SIMP.
I
do
not
very
well
apprehend
this
which
you
say
:
nor
can
I
of
my self
conceive
how
it
can
be
,
that
in
greater
distances
,
greater
exorbitancies
can
arise
from
the
errour
of
one
minute
only
,
than
in
the
smaller
from
ten
or
an
hundred
;
and
therefore
would
gladly
understand
the
same
.
SALV
.
You
shall
see
it
,
if
not
Theorically
,
yet
at
least
Practically
,
by
this
short
assumption
,
that
I
have
made
of
all
the
combinations
,
and
of
part
of
the
workings
pretermitted
by
the
Author
,
which
I
have
calculated
upon
this
same
paper
.
SAGR.
You
must
then
from
yesterday
,
till
now
,
which
yet
is
not
above
eighteen
hours
,
have
done
nothing
but
compute
,
without
taking
either
food
or
sleep
.
SALV
.
I
have
refreshed
my self
both
those
wayes
;
but
truth
is
,
make
these
supputations
with
great
brevity
;
and
,
if
I
may
speak
the
truth
,
I
have
much
admired
,
that
this
Author
goeth
so
farre
about
,
and
introduceth
so
many
computations
no
wise
necessary
to
the
question
in
dispute
.
And
for
a
full
knowledge
of
this
,
and
also
to
the
end
it
may
soon
be
seen
,
how
that
from
the
observations
of
the
Astronomers
,
whereof
this
Author
makes
use
,
it
is
more
probably
gathered
,
that
the
new
star
might
have
been
above
the
Moon
,
and
also
above
all
the
Planets
,
yea
amongst
the
fixed
stars
,
and
yet
higher
still
than
they
,
I
have
transcribed
upon
this
paper
all
the
observations
set
down
by
the
said
Authour
,
which
were
made
by
thirteen
Astronomers
,
wherein
are
noted
the
Polar
altitude
,
and
the
altitudes
of
the
star
in
the
meridian
,
aswell
the
lesser
under
the
Pole
,
as
the
greater
and
higher
,
and
they
are
these
.
Tycho
.
|
gr
.
|
m.
|
|
Altitude
of
the
Pole
|
55
|
58
|
|
Altitude
of
the
Star
|
84
|
00
|
the
greatest
.
|
|
27
|
57
|
the
least
.
|
And
these
are
,
according
to
the
first
paper
:
but
according
to
the
second
,
the
greatest
is
—
|
27
|
45
|
|
Hainzelius
.
|
gr
.
|
m.
|
sec.
|
Altitude
of
the
Pole
|
48
|
22
|
|
Altitude
of
the
Star
|
76
|
34
|
|
|
76
|
33
|
45
|
|
76
|
35
|
|
|
20
|
09
|
40
|
|
20
|
09
|
30
|
|
20
|
09
|
20
|
Peucerus
and
Sculerus
.
|
gr
.
|
m.
|
Altitude
of
the
pole
|
51
|
54
|
Altitude
of
the
Star
|
79
|
56
|
|
23
|
33
|
Landgravius
.
|
gr
.
|
m.
|
Altitude
of
the
pole
|
51
|
18
|
Altitude
of
the
Star
|
79
|
30
|
Camerarius
.
|
gr
.
|
m.
|
Altitude
of
the
pole
|
52
|
24
|
Altitude
of
the
Star
|
80
|
30
|
|
80
|
27
|
|
80
|
26
|
|
24
|
28
|
|
24
|
20
|
|
24
|
17
|
Hagecius
|
gr
.
|
m.
|
Altitude
of
the
pole
|
48
|
22
|
Altitude
of
the
Star
|
20
|
15
|
Maurolycus
.
|
gr
.
|
m.
|
Altitude
of
the
pole
|
38
|
30
|
Altitude
of
the
Star
|
62
|
00
|
Munocius
.
|
gr
.
|
m.
|
Altitude
of
the
pole
|
39
|
30
|
Altitude
of
the
star
|
67
|
30
|
|
11
|
30
|
Vrsinus
.
|
gr
.
|
m.
|
Altitude
of
the
pole
|
49
|
24
|
Altitude
of
the
star
|
79
|
00
|
|
22
|
00
|
Reinholdus
.
|
gr
.
|
m.
|
Altitude
of
the
pole
|
51
|
18
|
Altitude
of
the
star
|
79
|
30
|
|
23
|
02
|
Buchius
.
|
gr
.
|
m.
|
Altitude
of
the
pole
|
51
|
10
|
Altitude
of
the
star
|
79
|
20
|
|
22
|
40
|
Gemma
.
|
gr
.
|
m.
|
Altitude
of
the
pole
|
50
|
50
|
Altitude
of
the
star
|
79
|
45
|
Now
to
see
my
whole
proceeding
,
we
may
begin
from
these
calculations
,
which
are
four
,
omitted
by
the
Author
,
perhaps
because
they
make
against
him
,
in
regard
they
place
the
star
above
the
moon
by
many
semidiameters
of
the
Earth
.
The
first
of
which
is
this
,
computed
upon
the
observations
of
the
Landgrave
of
Hassia
,
and
Tycho
;
which
are
,
even
by
the
Authors
concession
,
two
of
the
most
exact
observers
:
and
in
this
first
,
I
will
declare
the
order
that
I
hold
in
the
working
;
which
shall
serve
for
all
the
rest
,
in
that
they
are
all
made
by
the
same
rule
,
not
varying
in
any
thing
,
save
in
the
quantity
of
the
given
summes
,
that
is
,
in
the
number
of
the
degrees
of
the
Poles
altitude
,
and
of
the
new
Stars
elevation
above
the
Horizon
,
the
distance
of
which
from
the
centre
of
the
Earth
,
in
proportion
to
the
semidiameter
of
the
terrestrial
Globe
is
sought
,
touching
which
it
nothing
imports
in
this
case
,
to
know
how
many
miles
that
semidiameter
conteineth
;
whereupon
the
resolving
that
,
and
the
distance
of
places
where
the
observations
were
made
,
as
this
Author
doth
,
is
but
time
and
labour
lost
;
nor
do
I
know
why
he
hath
made
the
same
,
and
especially
why
at
the
last
he
goeth
about
to
reduce
the
miles
found
,
into
semidiameters
of
the
Terrestrial
Globe
.
SIMP.
Perhaps
he
doth
this
to
finde
with
such
small
measures
,
and
with
their
fractions
the
distance
of
the
Star
terminated
to
three
or
four
inches
;
for
we
that
do
not
understand
your
rules
of
Arithmetick
,
are
stupified
in
hearing
your
conclusions
;
as
for
instance
,
whilst
we
read
;
Therefore
the
new
Star
or
Comet
was
distant
from
the
Earths
centre
three
hundred
seventy
and
three
thousand
eight
hundred
and
seven
miles
;
and
moreover
,
two
hundred
and
eleven
,
four
thousand
ninety
sevenths
373807
21●/4097
,
and
upon
these
precise
punctualities
,
wherein
you
take
notice
of
such
small
matters
,
we
do
conceive
it
to
be
impossible
,
that
you
,
who
in
our
calculations
keep
an
account
of
an
inch
,
can
at
the
close
deceive
us
so
much
as
an
hundred
miles
.
SALV
.
This
your
reason
and
excuse
would
passe
for
currant
,
if
in
a
distance
of
thousands
of
miles
,
a
yard
over
or
under
were
of
any
great
moment
,
and
if
the
suppositions
that
we
take
for
true
,
were
so
certain
,
as
that
they
could
assure
us
of
producing
an
indubitable
truth
in
the
conclusion
;
but
here
you
see
in
the
twelve
workings
of
the
Author
,
the
distances
of
the
Star
,
which
from
them
one
may
conclude
to
have
been
different
from
each
other
,
(
and
therefore
wide
of
the
truth
)
for
many
hundreds
and
thousands
of
miles
:
now
whilst
that
I
am
more
than
certain
,
that
that
which
I
seek
must
needs
differ
from
the
truth
by
hundreds
of
miles
,
to
what
purppse
is
it
to
be
so
curious
in
our
calculations
,
for
fear
of
missing
the
quantity
of
an
inch
?
But
let
us
proceed
,
at
last
,
to
the
working
,
which
I
resolve
in
this
manner
.
Tycho
,
as
may
be
seen
in
that
same
note
observed
the
star
in
the
polar
altitude
of
55
degrees
and
58
mi.
pri
.
And
the
polar
altitude
of
the
Landgrave
was
51
degrees
and
18
mi.
pri
.
The
altitude
of
the
star
in
the
Meridian
taken
by
Tycho
was
27
degrees
45
mi.
pri
.
The
Landgrave
found
its
altitude
23
degrees
3
mi.
pri
.
The
which
altitudes
are
these
noted
here
,
as
you
see
.
|
|
gr
.
|
m.
|
|
gr
.
|
m.
|
Tycho
.
|
Pole
|
55
|
58
|
*
|
27
|
45
|
Landgr
.
|
Pole
|
51
|
18
|
*
|
23
|
3
|
This
done
,
substract
the
lesse
from
the
greater
,
and
there
remains
these
differences
here
underneath
.
|
gr
.
|
m.
|
|
4
|
40
|
|
4
|
42
|
Parall.
|
|
2
|
Where
the
difference
of
the
poles
altitudes
4
gr.
4
mi.
pr.
is
lesse
than
the
difference
of
the
altitudes
of
the
Star
4
gr.
42
mi.
pr.
and
therefore
we
have
the
difference
of
parallaxes
,
0
gr.
2
mi.
pri
.
These
things
being
found
,
take
the
Authours
own
figure
[
Fig.
2.
]
in
which
the
point
B
is
the
station
of
the
Landgrave
,
D
the
station
of
Tycho
,
C
the
place
of
the
star
,
A
the
centre
of
the
Earth
,
ABE
the
vertical
line
of
the
Landgrave
,
ADF
of
Tycho
,
and
the
angle
BCD
the
difference
of
Parallaxes
.
And
because
the
angle
BAD
,
conteined
between
the
vertical
lines
,
is
equal
to
the
difference
of
the
Polar
altitudes
,
it
shall
be
4gr
.
40m
.
which
I
note
here
apart
;
and
I
finde
the
chord
of
it
by
the
Table
of
Arches
and
Chords
,
and
set
it
down
neer
unto
it
,
which
is
8142
parts
,
of
which
the
semidiameter
AB
is
100000.
Next
,
I
finde
the
angle
BDC
with
ease
,
for
the
half
of
the
angle
BAD
,
which
is
2gr
.
20
m.
added
to
a
right
angle
,
giveth
the
angle
BDF
92gr
.
20
m.
to
which
adding
the
angle
CDF
,
which
is
the
distance
from
the
vertical
point
of
the
greatest
altitude
of
the
Star
,
which
here
is
62
gr.
15
m.
it
giveth
us
the
quantity
of
the
angle
BDC
,
154
grad.
45
min.
the
which
I
set
down
together
with
its
Sine
,
taken
out
of
the
Table
,
which
is
42657
,
and
under
this
I
note
the
angle
of
the
Parallax
BCD
0
gr.
2
m.
with
its
Sine
58.
And
because
in
the
Triangle
BCD
,
the
side
DB
is
to
the
side
BC
;
as
the
sine
of
the
opposite
angle
BCD
,
to
the
sine
of
the
opposite
angle
BDC
:
therefore
,
if
the
line
BD
were
58.
BC
would
be
42657.
And
because
the
Chord
DB
is
8142.
of
those
parts
whereof
the
semidiameter
BA
is
100000.
and
we
seek
to
know
how
many
of
those
parts
is
BC
;
therefore
we
will
say
,
by
the
Golden
Rule
,
if
when
BD
is
58.
BG
is
42657.
in
case
the
said
DB
were
8142.
how
much
would
BC
be
?
I
multiply
the
second
term
by
the
third
,
and
the
product
is
347313294.
which
ought
to
be
divided
by
the
first
,
namely
,
by
58.
and
the
quotient
shall
be
the
number
of
the
parts
of
the
line
BC
,
whereof
the
semidiameter
AB
is
100000.
And
to
know
how
many
semidiameters
BA
,
the
said
line
BC
doth
contein
,
it
will
be
necessary
anew
to
divide
the
said
quotient
so
found
by
100000.
and
we
shall
have
the
number
of
semidiameters
conteined
in
BC.
Now
the
number
347313294.
divided
by
58.
giveth
5988160¼
.
as
here
you
may
see
.
And
this
divided
by
100000.
the
product
is
59
88160/100000
But
we
may
much
abbreviate
the
operation
,
dividing
the
first
quotient
found
,
that
is
,
347313294.
by
the
product
of
the
multiplication
of
the
two
numbers
58.
and
100000.
that
is
,
And
this
way
also
there
will
come
forth
59
5113294/5●00●●●
And
so
many
semidiameters
are
contained
in
the
line
BC
,
to
which
one
being
added
for
the
line
AB
,
we
shall
have
little
lesse
than
61.
semidiameters
for
the
two
lines
ABC
;
and
therefore
the
right
distance
from
the
centre
A
,
to
the
Star
C
,
shall
be
more
than
60.
semidiameters
,
and
therefore
it
is
superiour
to
the
Moon
,
according
to
Ptolomy
,
more
than
27.
semidiameters
,
and
according
to
Copernicus
,
more
than
8.
supposing
that
the
distance
of
the
Moon
from
the
centre
of
the
Earth
by
Copernicus
his
account
is
what
the
Author
maketh
it
,
52
semidiameters
.
With
this
same
working
,
I
find
by
the
observations
of
Camerarius
,
and
of
Munosius
,
that
the
Star
was
situate
in
that
same
distance
,
to
wit
,
somewhat
more
than
60.
semidiameters
.
These
are
the
observations
,
and
these
following
next
after
them
the
calculations
.
The
next
working
is
made
upon
two
observations
of
Tycho
,
and
of
Munosius
,
from
which
the
Star
is
calculated
to
be
distant
from
the
Centre
of
the
Earth
478
Semidiameters
and
more
.
These
workings
following
make
the
Star
remote
from
the
Centre
,
more
than
358
Semidiameters
.
From
this
other
working
the
star
is
found
to
be
distant
from
the
centre
more
than
716.
semidiameters
.
These
as
you
see
are
five
workings
which
place
the
star
very
much
above
the
Moon
.
And
here
I
desire
you
to
consider
upon
that
particular
,
which
even
now
I
told
you
,
namely
,
that
in
great
distances
,
the
mutations
,
or
if
you
please
corrections
,
of
a
very
few
minutes
,
removeth
the
star
a
very
great
way
farther
off
.
As
for
example
,
in
the
first
of
these
workings
,
where
the
calculation
made
the
star
60.
semidiameters
remote
from
the
centre
,
with
the
Parallax
of
2.
minutes
;
he
that
would
maintain
that
it
was
in
the
Firmament
,
is
to
correct
in
the
observations
but
onely
two
minutes
,
nay
lesse
,
for
then
the
Parallax
ceaseth
,
or
becommeth
so
small
,
that
it
removeth
the
star
to
an
immense
distance
,
which
by
all
is
received
to
be
the
Firmament
.
In
the
second
indagation
,
or
working
,
the
correction
of
lesse
than
4
m.
prim.
d
th
the
same
.
In
the
third
,
and
fourth
,
like
as
in
the
first
,
two
minutes
onely
mount
the
star
even
above
the
Firmament
.
In
the
last
preceding
,
a
quarter
of
a
minute
,
that
is
15.
seconds
,
gives
us
the
same
.
But
it
doth
not
so
occur
in
the
sublunary
altitudes
;
for
if
you
fancy
to
your self
what
distance
you
most
like
,
and
go
about
to
correct
the
workings
made
by
the
Authour
,
and
adjust
them
so
as
that
they
all
answer
in
the
same
determinate
distance
,
you
will
find
how
much
greater
corrections
they
do
require
.
SAGR.
It
cannot
but
help
us
in
our
fuller
understanding
of
things
,
to
see
some
examples
of
this
which
you
speak
of
.
SALV
.
Do
you
assign
any
whatsoever
determinate
sublunary
distance
at
pleasure
in
which
to
constitute
the
star
,
for
with
small
ado
we
may
assertain
our selves
whether
corrections
like
to
these
,
which
we
see
do
suffice
to
reduce
it
amongst
the
fixed
stars
,
will
reduce
it
to
the
place
by
you
assigned
.
SAGR.
To
take
a
distance
that
may
favour
the
Authour
,
we
will
suppose
it
to
be
that
which
is
the
greatest
of
all
those
found
by
him
in
his
12
workings
;
for
whilst
it
is
in
controversie
between
him
and
Astronomers
,
and
that
they
affirm
the
star
to
have
been
superiour
to
the
Moon
,
and
he
that
it
was
inferiour
,
very
small
space
that
he
proveth
it
to
have
been
lower
,
giveth
him
the
victory
.
SALV
.
Let
us
therefore
take
the
seventh
working
wrought
upon
the
observations
of
Tycho
and
Thaddaeus
Hagecius
,
by
which
the
Authour
found
the
star
to
have
been
distant
from
the
centre
32.
semidiameters
,
which
situation
is
most
favourable
to
his
purpose
;
and
to
give
him
all
advantages
,
let
us
moreover
place
it
in
the
distance
most
disfavouring
the
Astronomers
,
which
is
to
situate
it
above
the
Firmament
.
That
therefore
being
supposed
,
let
us
seek
in
the
next
place
what
corrections
it
would
be
necessary
to
apply
to
his
other
11
workings
.
And
let
us
begin
at
the
first
calculated
upon
the
observations
of
Hainzelius
and
Mauroice
;
in
which
the
Authour
findeth
the
distance
from
the
centre
about
3.
semidiameters
with
the
Parallax
of
4
gr.
42
m.
30.
sec.
Let
us
see
whether
by
withdrawing
it
20.
minutes
onely
,
it
will
rise
to
the
height
of
32.
semidiameters
:
See
the
short
and
true
operation
.
Multiply
the
sine
of
the
angle
BDC
,
by
the
sine
of
the
chord
BD
,
and
divide
the
product
,
the
five
last
figures
being
cut
off
by
the
sine
of
the
Parallax
,
and
the
quotient
will
be
28.
semidiameters
,
and
an
half
,
so
that
though
you
make
a
correction
of
4
gr.
22
min.
30
sec.
taken
from
4
gr.
42
min.
30
sec.
it
shall
not
elevate
the
star
to
the
altitude
of
32.
semidiameters
,
which
correction
for
Simplicius
his
understanding
it
,
is
of
262.
minutes
,
and
an
half
.
In
the
second
operation
made
upon
the
observations
of
Hainzelius
,
and
Sculerus
,
with
the
Parallax
of
0
gr.
8
min.
30
sec.
the
star
is
found
in
the
height
of
25.
semidiameters
or
thereabouts
,
as
may
be
seen
in
the
subsequent
working
.
And
bringing
back
the
Parallax
0
gr.
8
m.
30
sec.
to
7
gr.
7
m.
whose
sine
is
204
,
the
star
elevateth
to
30
semidiameters
or
thereabouts
;
therefore
the
correction
of
0
gr.
1
mi.
30
sec.
doth
not
suffice
.
Now
let
us
see
what
correction
is
requisite
for
the
third
working
made
upon
the
observations
of
Hainzelius
and
Tycho
,
which
rendereth
the
star
about
19
semidiameters
high
,
with
the
Parallax
of
10
m.
pri
.
The
usual
angles
and
their
sines
,
and
chord
found
by
the
Authour
,
are
these
next
following
;
and
they
remove
the
star
(
as
also
in
the
Authours
working
)
19
semidiameters
from
the
centre
of
the
Earth
.
It
is
necessary
therefore
for
the
raising
of
it
,
to
diminish
the
Parallax
according
to
the
Rule
which
he
likewise
observeth
in
the
ninth
working
.
Let
us
therefore
suppose
the
Parallax
to
be
6
m.
prim
.
whose
sine
is
175
,
and
the
division
being
made
,
there
is
found
likewise
lesse
than
31
semidiameters
for
the
stars
distance
.
And
therefore
the
correction
of
4
min.
prim
.
is
too
little
to
serve
the
Authours
purpose
.
Let
us
come
to
the
fourth
working
,
and
the
rest
with
the
same
rule
,
and
with
the
chords
and
sines
found
out
by
the
Authour
himself
;
in
this
the
Parallax
is
14
m.
prim
.
and
the
height
found
lesse
than
10
semidiameters
,
and
diminishing
the
Parallax
from
14
min.
to
4
min.
yet
neverthelesse
you
see
that
the
star
doth
not
elevate
full
31
semidiameters
.
Therefore
10
min.
in
14
min.
doth
not
suffice
.
In
the
fifth
operation
of
the
Authour
we
have
the
sines
and
the
chord
as
you
see
,
and
the
Parallax
is
0
gr.
42
m.
30
sec.
which
rendereth
the
height
of
the
star
about
4
semidiameters
,
and
correcting
the
Parallax
,
with
reducing
it
from
0
gr.
42
m.
30
sec.
to
0
gr.
5
m.
onely
,
doth
not
suffice
to
raise
it
to
so
much
as
28
semidiameters
,
the
correction
therefore
of
0
gr.
37
m.
30
sec.
is
too
little
.
In
the
sixth
operation
the
chord
,
the
sines
and
Parallax
are
as
followeth
,
and
the
star
is
found
to
be
about
4.
semidiameters
;
let
us
see
whether
it
will
be
reduced
,
abating
the
Parallax
from
8
m.
to
1
m.
onely
;
Here
is
the
operation
,
and
the
star
raised
but
to
27.
semidiameters
or
thereabout
;
therefore
the
correction
of
7
m.
in
8
m.
doth
not
suffice
.
In
the
eighth
operation
the
chord
,
the
sines
,
and
the
Parallax
,
as
you
see
,
are
these
ensuing
,
and
hence
the
Authour
calculates
the
height
of
the
star
to
be
1.
semidiameter
and
an
half
,
with
the
Parallax
of
43.
min.
which
reduced
to
1
min.
yet
notwithstanding
giveth
the
star
lesse
remote
than
24.
semidiameters
,
the
correction
therefore
of
42.
min.
is
not
enough
.
Let
us
now
see
the
ninth
.
Here
is
the
chord
,
the
sines
and
the
Parallax
which
is
15
m.
From
whence
the
Authour
calculates
the
distance
of
the
star
from
the
superficies
of
the
Earth
to
be
lesse
than
a
[
](A61244-e65510-b)*
*
Here
the
Latine
version
is
erroneous
,
making
it
a
fortieth
part
of
,
&c.
seven
and
forteith
part
of
a
semidiameter
,
but
this
is
an
errour
in
the
calculation
,
for
it
cometh
forth
truly
,
as
we
shall
see
here
below
,
more
than
a
fifth
:
See
here
the
quotient
is
●90/4●●
,
which
is
more
than
one
fifth
.
That
which
the
Authour
presently
after
subjoyns
in
way
of
amending
the
observations
,
that
is
,
that
it
sufficeth
not
to
reduce
the
difference
of
Parallax
,
neither
to
a
minute
,
nor
yet
to
the
eighth
part
of
a
minute
is
true
.
But
I
say
,
that
neither
will
the
tenth
part
of
a
minute
reduce
the
height
of
the
star
to
32.
semidiameters
;
for
the
sine
of
the
tenth
part
of
a
minute
,
that
is
of
six
seconds
,
is
3
;
by
which
if
we
according
to
our
Rule
should
divide
90.
or
we
may
say
,
if
we
should
divide
9058672.
by
300000.
the
quotient
will
be
30
58671/100000
,
that
is
little
more
than
30.
semidiameters
and
an
half
.
The
tenth
giveth
the
altitude
of
the
star
one
fifth
of
a
semidiameter
,
with
these
angles
,
sines
,
and
Parallax
,
that
is
,
4
gr.
.
30
m.
which
I
see
that
being
reduced
from
4
gr.
30
min.
to
2
min.
yet
neverthelesse
it
elevates
not
the
star
to
29.
semidiameters
.
The
eleventh
rendereth
the
star
to
the
Authour
remote
about
13.
semidiameters
,
with
the
Parallax
of
55.
min.
let
us
see
,
reducing
it
to
20
min.
whether
it
will
exalt
the
star
:
See
here
the
calculation
elevates
it
to
little
lesse
than
33.
semidiameters
,
the
correction
therefore
is
little
lesse
than
35.
min.
in
55.
min.
The
twelfth
with
the
Parallax
of
1.
gr.
36.
min.
maketh
the
star
lesse
high
than
6.
semidiameters
,
reducing
the
Parallax
to
20
min.
it
carrieth
the
star
to
lesse
than
30.
semidiameters
distance
,
therefore
the
correction
of
1
gr.
16.
min.
sufficeth
not
.
These
are
the
Corrections
of
the
Parallaxes
of
the
ten
workings
of
the
Author
,
to
reduce
the
Star
to
the
altitude
of
32
Semidiameters
.
gr.
|
m.
|
sec.
|
|
gr
.
|
m.
|
sec.
|
04
|
22
|
30
|
in
|
04
|
42
|
30
|
00
|
04
|
00
|
in
|
00
|
10
|
00
|
00
|
10
|
00
|
in
|
00
|
14
|
00
|
00
|
37
|
00
|
in
|
00
|
42
|
30
|
00
|
07
|
00
|
in
|
00
|
18
|
00
|
00
|
42
|
00
|
in
|
00
|
43
|
00
|
00
|
14
|
50
|
in
|
00
|
15
|
00
|
04
|
28
|
00
|
in
|
04
|
30
|
00
|
00
|
35
|
00
|
in
|
00
|
55
|
00
|
01
|
16
|
00
|
in
|
01
|
36
|
00
|
From
hence
we
see
,
that
to
reduce
the
Star
to
32.
Semidiameters
in
altitude
,
it
is
requisite
from
the
sum
of
the
Parallaxes
836.
to
subtract
756.
and
to
reduce
them
to
80.
nor
yet
doth
that
correction
suffice
.
Here
we
see
also
,
(
as
I
have
noted
even
now
)
that
should
the
Authour
consent
to
assign
the
distance
of
32.
Semidiameters
for
the
true
height
of
the
Star
,
the
correction
of
those
his
10.
workings
,
(
I
say
10.
because
the
second
being
very
high
,
is
reduced
to
the
height
of
32.
Semidiameters
,
with
2.
minutes
correction
)
to
make
them
all
to
restore
the
said
Star
to
that
distance
,
would
require
such
a
reduction
of
Parallaxes
,
that
amongst
the
whole
number
of
substractions
they
should
make
more
than
756
m.
pr.
whereas
in
the
5.
calculated
by
me
,
which
do
place
the
Star
above
the
Moon
,
to
correct
them
in
such
sort
,
as
to
constitute
it
in
the
Firmament
,
the
correction
onely
of
10.
minutes
,
and
one
fourth
sufficeth
.
Now
adde
to
these
,
other
5.
workings
,
that
place
the
Star
precisely
in
the
Firmament
,
without
need
of
any
correction
at
all
,
and
we
shall
have
ten
workings
or
indagations
that
agree
to
place
it
in
the
Firmament
,
with
the
correction
onely
of
5.
of
them
(
as
hath
been
seen
)
but
10.
m.
and
15
sec.
Whereas
for
the
correction
of
those
10.
of
the
Authour
,
to
reduce
them
to
the
altitude
of
32.
semidiameters
,
there
will
need
the
emendations
of
756
minutes
in
836.
that
is
,
there
must
from
the
summe
836
be
substracted
756.
if
you
would
have
the
Star
elevated
to
the
altitude
of
32.
semidiameters
,
and
yet
that
correction
doth
not
fully
serve
.
The
workings
that
immediately
without
any
correction
free
the
Star
from
Parallaxes
,
and
therefore
place
it
in
the
Firmament
,
and
that
also
in
the
remotest
parts
of
it
,
and
in
a
word
,
as
high
as
the
Pole
it self
,
are
these
5.
noted
here
.
|
|
gr
.
|
m.
|
|
gr
.
|
m.
|
Camerar
.
|
Polar
altit
.
|
52
|
24
|
Altit
.
of
the
Star
|
80
|
26
|
Peucerus
|
51
|
54
|
79
|
56
|
|
|
0
|
30
|
|
0
|
30
|
|
|
gr
.
|
m.
|
|
gr
.
|
m.
|
Landgrav
.
|
Polar
altit
.
|
51
|
18
|
Altit
.
of
the
Star
|
79
|
30
|
Hainzel
.
|
48
|
22
|
76
|
34
|
|
|
2
|
56
|
|
2
|
56
|
|
|
gr
.
|
m.
|
|
gr
.
|
m.
|
Tycho
|
Polar
altit
.
|
55
|
58
|
Altit
.
of
the
Star
|
84
|
00
|
Peucerus
|
51
|
54
|
79
|
56
|
|
|
4
|
4
|
|
4
|
4
|
|
|
gr
.
|
m.
|
|
gr
.
|
m.
|
Reinhold
.
|
Polar
altit
.
|
51
|
18
|
Altit
.
of
the
Star
|
79
|
30
|
Hainzel
.
|
48
|
22
|
36
|
34
|
|
|
2
|
56
|
|
2
|
56
|
|
|
gr
.
|
m.
|
|
gr
.
|
m.
|
Camerar
.
|
Polar
altit
.
|
52
|
24
|
Altit
.
of
the
Star
|
24
|
17
|
Hagecius
|
48
|
22
|
20
|
15
|
|
|
4
|
2
|
|
4
|
2
|
Of
the
remaining
combinations
that
might
be
made
of
the
Observations
of
all
these
Astronomers
,
those
that
make
the
Stars
sublime
to
an
infinite
distance
,
are
many
in
number
,
namely
,
about
30.
more
than
those
who
give
the
Star
,
by
calculation
,
to
be
below
the
Moon
;
and
because
(
as
it
was
agreed
upon
between
us
)
it
is
to
be
believed
that
the
Observators
have
erred
rather
little
than
much
,
it
is
a
manifest
thing
that
the
corrections
to
be
applied
to
the
Observaations
,
which
make
the
star
of
an
infinite
altitude
,
to
reduce
it
lower
,
do
sooner
,
and
with
lesser
amendment
place
it
in
the
Firmament
,
than
beneath
the
Moon
;
so
that
all
these
applaud
the
opinion
of
those
who
put
it
amongst
the
fixed
Stars
.
You
may
adde
,
that
the
corrections
required
for
those
emendations
,
are
much
lesser
than
those
,
by
which
the
Star
from
an
unlikely
proximity
may
be
removed
to
the
height
more
favourable
for
this
Authour
,
as
by
the
foregoing
examples
hath
been
seen
;
amongst
which
impossible
proximities
,
there
are
three
that
seem
to
remove
the
Star
from
the
Earths
centre
,
a
lesse
distance
than
one
Semidiameter
,
making
it
,
as
it
were
,
to
turn
round
under
ground
,
and
these
are
those
combinations
,
wherein
the
Polar
altitude
of
one
of
the
Observators
being
greater
than
the
Polar
altitude
of
the
other
,
the
elevation
of
the
Star
taken
by
the
first
,
is
lesser
than
the
elation
of
the
Star
taken
by
the
latter
.
The
first
of
these
is
this
of
the
Landgrave
with
Gemma
,
where
the
Polar
altitude
of
the
Landgrave
51
gr.
18
min.
is
greater
than
the
Polar
altitude
of
Gemma
,
which
is
50
gr.
50
m.
But
the
altitude
of
the
Star
of
the
Landgrave
79
gr.
30
min.
is
lesser
than
that
of
the
Star
,
of
Gemma
79
gr.
45
min.
|
|
gr
.
|
m.
|
|
gr
.
|
m.
|
Landgrave
|
Polar
altit
.
|
51
|
18
|
Altit
.
of
the
Star
|
79
|
30
|
Gemma
|
50
|
50
|
79
|
45
|
The
other
two
are
these
below
.
|
|
gr
.
|
m.
|
|
gr
.
|
m.
|
Buschius
.
|
Polar
Altitude
|
51
|
10
|
Altit
.
of
the
Star
|
79
|
20
|
Gemma
.
|
50
|
50
|
79
|
45
|
Reinholdus
.
|
Polar
Altitude
|
51
|
18
|
Altit
.
of
the
Star
|
79
|
30
|
Gemma
.
|
50
|
50
|
79
|
45
|
From
what
I
have
hitherto
demonstrated
,
you
may
guesse
how
much
this
first
way
of
finding
out
the
distance
of
the
Star
,
and
proving
it
sublunary
introduced
by
the
Authour
,
maketh
against
himself
,
and
how
much
more
probably
and
clearly
the
distance
thereof
is
collected
to
have
been
amongst
the
more
remote
fixed
Stars
.
SIMP.
As
to
this
particular
,
I
think
that
the
inefficacy
of
the
Authors
demonstrations
is
very
plainly
discovered
;
But
I
see
that
all
this
was
comprised
in
but
a
few
leaves
of
his
Book
,
and
it
may
be
,
that
some
other
of
his
Arguments
are
more
conclusive
then
these
first
.
SALV
.
Rather
they
must
needs
be
lesse
valid
,
if
we
will
take
those
that
lead
the
way
for
a
proof
of
the
rest
:
For
(
as
it
is
clear
)
the
uncertainty
and
inconclusivenesse
of
those
,
is
manifestly
observed
to
derive
it self
from
the
errours
committed
in
the
instrumental
observations
,
upon
which
the
Polar
Altitude
,
and
height
of
the
Star
was
thought
to
have
been
justly
taken
,
all
in
effect
having
easily
erred
;
And
yet
to
find
the
Altitude
of
the
Pole
,
Astronomers
have
had
Ages
of
time
to
apply
themselves
to
it
,
at
their
leasure
:
and
the
Meridian
Altitudes
of
the
Star
are
easier
to
be
observed
,
as
being
most
terminate
,
and
yielding
the
Observator
some
time
to
continue
the
same
,
in
regard
they
change
not
sensibly
,
in
a
short
time
,
as
those
do
that
are
remote
from
the
Meridian
.
And
if
this
be
so
,
as
it
is
most
certain
,
what
credit
shall
we
give
to
Calculations
founded
upon
Observations
more
numerous
,
more
difficult
to
be
wrought
,
more
momentary
in
variation
,
and
we
may
add
,
with
Instruments
more
incommodious
and
erroneous
?
Upon
a
slight
perusal
of
the
ensuing
demonstrations
,
I
see
that
the
Computations
are
made
upon
Altitudes
of
the
Star
taken
in
different
Vertical
Circles
,
which
are
called
by
the
Arabick
name
,
Azimuths
;
in
which
observations
moveable
instruments
are
made
use
of
,
not
only
in
the
Vertical
Circles
,
but
in
the
Horizon
also
,
at
the
same
time
;
insomuch
that
it
is
requisite
in
the
same
moment
that
the
altitude
is
taken
,
to
have
observed
,
in
the
Horizon
,
the
distance
of
the
Virtical
point
in
which
the
Star
is
,
from
the
Meridian
;
Moreover
,
after
a
considerable
interval
of
time
,
the
operation
must
be
repeated
,
and
exact
account
kept
of
the
time
that
passed
,
trusting
either
to
Dials
,
or
to
other
observations
of
the
Stars
.
Such
an
Olio
of
Observations
doth
he
set
befo●●
you
,
comparing
them
with
such
another
made
by
another
observer
in
another
place
with
another
different
instrument
,
and
at
another
time
;
and
from
this
the
Authour
seeks
to
collect
what
would
have
been
,
the
Elevations
of
the
Star
,
and
Horizontal
Latitudes
happened
in
the
time
and
hour
of
the
other
first
observations
,
and
upon
such
a
coaequation
he
in
the
end
grounds
his
account
.
Now
I
refer
it
to
you
,
what
credit
is
to
be
given
to
that
which
is
deduced
from
such
like
workings
.
Moreover
,
I
doubt
not
in
the
least
,
but
that
if
any
one
would
torture
himself
with
such
tedious
computations
,
he
would
find
,
as
in
those
aforegoing
,
that
there
were
more
that
would
favour
the
adverse
party
,
than
the
Authour
:
But
I
think
it
not
worth
the
while
to
take
so
much
pains
in
a
thing
,
which
is
not
,
amongst
those
primary
ones
,
by
us
understood
.
SAGR.
I
am
of
your
Opinion
in
this
particular
:
But
this
businesse
being
environed
with
so
many
intricacies
,
uncertainties
,
and
errours
,
upon
what
confidence
have
so
many
Astronomers
positively
pronounced
the
new
Star
to
have
been
so
high
?
SALV
.
Upon
two
sorts
of
observations
most
plain
,
most
easie
,
and
most
certain
;
one
only
of
which
is
more
than
sufficient
to
assure
us
,
that
it
was
scituate
in
the
Firmament
,
or
at
least
by
a
great
distance
superiour
to
the
Moon
.
One
of
which
is
taken
from
the
equality
,
or
little
differing
inequality
of
its
distances
from
the
Pole
,
aswell
whilst
it
was
in
the
lowest
part
of
the
Meridian
,
as
when
it
was
in
the
uppermost
:
The
other
is
its
having
perpetually
kept
the
same
distances
from
certain
of
the
fixed
Stars
,
adjacent
to
it
,
and
particularly
from
the
eleventh
of
Cassiopea
,
no
more
remote
from
it
than
one
degree
and
an
half
;
from
which
two
particulars
is
undoubtedly
inferred
,
either
the
absolute
want
of
Parallax
,
or
such
a
smalnesse
thereof
,
that
it
doth
assure
us
with
very
expeditious
Calculations
of
its
great
distance
from
the
Earth
.
SAGR.
But
these
things
,
were
they
not
known
to
this
Author
?
and
if
he
saw
them
,
what
doth
he
say
unto
them
?
SALV
.
We
are
wont
to
say
,
of
one
that
having
no
reply
that
is
able
to
cover
his
fault
,
produceth
frivolous
excuses
,
cerca
di
attaccarsi
alle
funi
del
cielo
,
[
He
strives
to
take
hold
of
the
Cords
of
Heaven
;
]
but
this
Authour
runs
,
not
to
the
Cords
,
but
to
the
Spiders
Web
of
Heaven
;
as
you
shall
plainly
see
in
our
examination
of
these
two
particulars
even
now
hinted
.
And
first
,
that
which
sheweth
us
the
Polar
distances
of
the
Observators
one
by
one
,
I
have
noted
down
in
these
brief
Calculations
;
For
a
full
understanding
of
which
,
I
ought
first
to
advertise
you
,
that
when
ever
the
new
Star
,
or
other
Phaenomenon
is
near
to
the
earth
,
turning
with
a
Diurnal
motion
about
the
Pole
,
it
will
seem
to
be
farther
off
from
the
said
Pole
,
whilst
it
is
in
the
lower
part
of
the
Meridian
,
then
whilst
it
is
above
,
as
in
this
Figure
[
being
fig.
third
of
this
Dial.
]
may
be
seen
.
In
which
the
point
T.
denotes
the
centre
of
the
Earth
;
O.
the
place
of
the
Observator
;
the
Arch
VPC
the
Firmament
;
P.
the
Pole
.
The
Phaenomenon
,
[
or
appearance
]
moving
along
the
Circle
FS
.
is
seen
one
while
under
the
Pole
by
the
Ray
OFC.
and
another
while
above
,
according
to
the
Ray
OSD
.
so
that
the
places
seen
in
the
Firmament
are
D.
and
C.
but
the
true
places
in
respect
of
the
Centre
T
,
are
B
,
and
A
,
equidistant
from
the
Pole
.
Where
it
is
manifest
that
the
apparent
place
of
the
Phaenomenon
S
,
that
is
the
point
D
,
is
nearer
to
the
Pole
than
the
other
apparent
place
C
,
seen
along
the
Line
or
Ray
OFC
,
which
is
the
first
thing
to
be
noted
.
In
the
second
place
you
must
note
that
the
exces
of
the
apparent
inferiour
distance
from
the
Pole
,
over
and
above
the
apparent
superiour
distance
from
the
said
Pole
,
is
greater
than
the
Inferiour
Parallax
of
the
Phaenomenon
,
that
is
,
I
say
,
that
the
excesse
of
the
Arch
CP
,
(
the
apparent
inferior
distance
)
over
and
above
the
Arch
PD
,
(
the
apparent
superior
distance
)
is
greater
then
the
Arch
CA
,
(
that
is
the
inferiour
Paralax
.
)
Which
is
easily
proved
;
for
the
Arch
CP.
more
exceedeth
PD
,
then
PB
;
PB
,
being
bigger
than
PD
,
but
PB
.
is
equal
to
PA
,
and
the
excesse
of
CP
,
above
PA
,
is
the
arch
,
CA
,
therefore
the
excesse
of
the
arch
CP
above
the
arch
PD
,
is
greater
than
the
arch
CA
,
which
is
the
parallax
of
the
Phaenomenon
placed
in
F
,
which
was
to
be
demonstrated
.
And
to
give
all
advantages
to
the
Author
,
let
us
suppose
that
the
parallax
of
the
star
in
F
,
is
the
whole
excesse
of
the
arch
CP
(
that
is
of
the
inferiour
distance
from
the
pole
)
above
the
arch
PD
(
the
inferiour
distance
.
)
I
proceed
in
the
next
place
to
examine
that
which
the
observations
of
all
Astronomers
cited
by
the
Authour
giveth
us
,
amongst
which
,
there
is
not
one
that
maketh
not
against
himself
and
his
purpose
.
And
let
us
begin
with
these
of
Buschius
,
who
findeth
the
stars
distance
from
the
pole
,
when
it
was
superiour
,
to
be
28
gr.
10
m.
and
the
inferiour
to
be
28
gr.
30
m.
so
that
the
excesse
is
0
gr.
20
m.
which
let
us
take
(
in
favour
of
the
Author
)
as
if
it
all
were
the
parallax
of
the
star
in
F
,
that
is
the
angle
TFO
.
Then
the
distance
from
the
Vertex
[
or
Zenith
]
that
is
the
arch
CV
,
is
67
gr.
20
m.
These
two
things
being
found
,
prolong
the
line
CO
,
and
from
it
let
fall
the
perpendicular
TI
,
and
let
us
consider
the
triangle
TOI
,
of
which
the
angle
I
is
right
angle
,
and
the
angle
IOT
known
,
as
being
vertical
to
the
angle
VOC
,
the
distance
of
the
star
from
the
Vertex
,
Moreover
in
the
triangle
TIF
,
which
is
also
rectangular
,
there
is
known
the
angle
F
,
taken
by
the
parallax
.
Then
note
in
some
place
apart
the
two
angles
IOT
and
I
FT
,
and
of
them
take
the
sines
,
which
are
here
set
down
to
them
,
as
you
seen
.
And
because
in
the
triangle
IOT
,
the
sine
TI
is
92276.
of
those
parts
,
whereof
the
whole
sine
TO
is
100000
;
and
moreover
in
the
triangle
I
FT
,
the
sine
TI
is
582.
of
those
parts
,
whereof
the
whole
sine
TF
is
100000
,
to
find
how
many
TF
is
of
those
parts
,
whereof
TO
is
100000
;
we
will
say
by
the
Rule
of
three
:
If
TI
be
582.
TF
is
an
100000.
but
if
T
I
were
92276.
how
much
would
T
F
be
.
Let
us
multiply
92276.
by
100000.
and
the
product
will
be
9227600000.
and
this
must
be
divided
by
582.
and
the
quotient
will
be
15854982.
and
so
many
shall
there
be
in
TF
of
those
parts
,
of
which
there
are
in
TO
an
100000.
So
that
if
it
were
required
to
know
how
many
lines
TO
,
are
in
TF
,
we
would
divide
15854982
by
100000.
and
there
will
come
forth
158.
and
very
near
an
half
;
and
so
many
diameters
shall
be
the
distance
of
the
star
F
,
from
the
centre
T
,
and
to
abreviate
the
operation
,
we
seeing
,
that
the
product
of
the
multiplication
of
92276.
by
100000
,
ought
to
be
divided
first
by
582
,
and
then
the
quotient
of
that
division
by
100000.
we
may
without
multiplying
92276.
by
100000.
and
with
one
onely
division
of
the
sine
92276.
by
the
sine
582.
soon
obtain
the
same
solution
,
as
may
be
seen
there
below
;
where
92276.
divided
by
582.
giveth
us
the
said
158
1/2
,
or
thereabouts
.
Let
us
bear
in
mind
therefore
,
that
the
onely
division
of
the
sine
TI
,
as
the
sine
of
the
angle
TOI
by
the
sine
TI
,
as
the
sine
of
the
angle
I
FT
,
giveth
us
the
distance
sought
TF
,
in
so
many
diameters
TO
.
See
next
that
which
the
observations
of
Peucerus
giveth
us
,
in
which
the
inferiour
distance
from
the
Pole
is
28
gr.
21
m.
and
the
superiour
28
gr.
2
m.
the
difference
0
gr.
19
m.
and
the
distance
from
the
vertical
point
66
gr.
27
m.
from
which
particulars
is
gathered
the
stars
distance
from
the
centre
almost
166
semediameters
.
Here
take
what
Tycho
his
observation
holdeth
forth
to
us
,
interpreted
with
greatest
favour
to
the
adversary
;
to
wit
,
the
inferiour
distance
from
the
pole
is
28
gr.
13
m.
and
the
superiour
28
gr.
2
m.
omit●ing
the
difference
which
is
0
gr.
11
m.
as
if
all
were
one
Parallax
;
the
distance
from
the
vertical
point
62
gr.
15
m.
Behold
here
below
the
operation
,
and
the
distance
of
the
star
from
the
centre
found
to
be
976
9/16
semidiameters
.
The
observation
of
Reinholdus
,
which
is
the
next
ensuing
,
giveth
us
the
distance
of
the
Star
from
the
Centre
793.
Semidiameters
.
From
the
following
observation
of
the
Landgrave
,
the
distance
of
the
Star
from
the
Centre
is
made
to
be
1057
,
Semidiameters
.
Two
of
the
most
favourable
observations
for
the
Authour
being
taken
from
Camerarius
,
the
distance
of
the
Star
from
the
Centre
is
found
to
be
3143
Semidiameters
.
The
Observation
of
Munosius
giveth
no
Parallax
,
and
therefore
rendreth
the
new
Star
amongst
the
highest
of
the
fixed
.
That
of
Hainzelius
makes
it
infinitely
remote
,
but
with
the
correction
of
an
half
min.
prim
.
placeth
it
amongst
the
fixed
Stars
.
And
the
same
is
collected
from
Vrsinus
,
with
the
correction
of
12.
min.
prim
.
The
other
Astronomers
have
not
give
us
the
distance
above
and
below
the
Pole
,
so
that
nothing
can
be
concluded
from
them
.
By
this
time
you
see
,
that
all
the
observations
of
all
these
men
conspire
against
the
Author
,
in
placing
the
Star
in
the
Heavenly
and
highest
Regions
.
SAGR.
But
what
defence
hath
he
for
himself
against
so
manifest
contradictions
?
SALV
.
He
betakes
himself
to
one
of
those
weak
threads
which
I
speak
of
;
saying
that
the
Parallaxes
come
to
be
lessened
by
means
of
the
refractions
,
which
opperating
contrarily
sublimate
the
Phaenomenon
,
whereas
the
Parallaxes
abase
it
.
Now
of
what
little
stead
this
lamentable
refuge
is
,
judge
by
this
,
that
in
case
that
effect
of
the
refractions
were
of
such
an
efficacy
,
as
that
which
not
long
time
since
some
Astronomers
have
introduced
,
the
most
that
they
could
work
touching
the
elevating
a
Phaeuomenon
above
the
Horizon
more
than
truth
,
when
it
is
before
hand
23.
or
24.
Degrees
high
,
would
be
the
lessening
its
Parallax
about
3.
minutes
,
the
which
abatement
is
too
small
to
pull
down
the
Star
below
the
Moon
,
and
in
some
cases
is
lesse
than
the
advantage
given
him
by
us
in
admitting
that
the
excesse
of
the
inferiour
distance
from
the
Pole
above
the
Superiour
,
is
all
Parallax
,
the
which
advantage
is
far
more
clear
and
palpable
than
the
effect
of
Refracton
,
of
the
greatnesse
of
which
I
stand
in
doubt
,
and
not
without
reason
.
But
besides
,
I
demand
of
the
Author
,
whether
he
thinks
that
those
Astronomers
,
of
whose
observations
he
maketh
use
,
had
knowledge
of
these
effects
of
Refractions
,
and
considered
the
same
,
or
no
;
if
they
did
know
and
consider
them
,
it
is
reasonable
to
think
that
the
,
kept
account
of
them
in
assigning
the
true
Elevation
of
the
Star
,
making
in
those
degrees
of
Attitude
discovered
with
the
Instruments
,
such
abatements
as
were
convenient
on
the
account
of
the
alterations
made
by
the
Refractions
;
insomuch
that
the
distances
by
them
delivered
,
were
in
the
end
those
corrected
and
exact
,
and
not
the
apparent
and
false
ones
.
But
if
he
think
that
those
Authors
made
no
reflection
upon
the
said
Refractions
,
it
must
be
confessed
,
that
they
had
in
like
manner
erred
in
determining
all
those
things
which
cannot
be
perfectly
adjusted
without
allowance
for
the
Refractions
;
amongst
which
things
one
is
the
precise
investigation
of
the
Polar
Altitudes
,
which
are
commonly
taken
from
the
two
Meridian
Altitudes
of
some
of
the
fixed
Stars
that
are
constantly
visible
,
which
Altitudes
will
come
to
be
altered
by
Refraction
in
the
same
manner
,
just
as
those
of
the
new
Star
;
so
that
the
Polar
Altitude
that
is
deduced
from
them
,
will
prove
to
be
defective
,
and
to
partake
of
the
self
same
want
which
this
Author
assigns
to
the
Altitudes
ascribed
to
the
new
Star
,
to
wit
,
both
that
and
these
will
be
with
equal
falshood
placed
higher
than
really
they
are
.
But
any
such
errour
,
as
far
as
concerns
our
present
businesse
,
doth
no
prejudce
at
all
:
For
we
not
needing
to
know
any
more
,
but
onely
the
difference
between
the
two
distances
of
the
new
Star
from
the
Pole
at
such
time
as
it
was
inferiour
and
superiour
,
it
is
evident
that
such
distances
would
be
the
same
,
taking
the
alteration
of
Refraction
commonly
for
the
Star
and
for
the
Pole
,
or
for
them
when
commonly
amended
.
The
Authors
Argument
would
indeed
have
had
some
strength
,
though
very
small
,
if
he
had
assured
us
that
the
Altitude
of
the
Pole
had
been
once
precisely
assigned
,
and
corrected
from
the
errour
depending
on
refraction
,
from
which
again
the
Astronomers
had
not
kept
themselves
in
assigning
the
altitudes
of
the
new
Star
;
but
he
hath
not
ascertained
us
of
that
,
nor
perhaps
could
he
have
done
,
nor
haply
,
(
and
this
is
more
probable
)
was
that
caution
wanting
in
the
Observators
.
SAGR.
This
argument
is
in
my
judgment
sufficiently
answered
;
therefore
tell
me
how
he
dis-ingageth
himself
in
the
next
place
from
that
particular
of
the
Stars
having
constantly
kept
the
same
distance
from
the
fixed
Stars
circumjacent
to
it
.
SALV
.
He
betakes
himself
,
in
like
manner
,
to
two
threads
,
yet
more
unable
to
uphold
him
than
the
former
:
one
of
which
is
likewise
fastened
to
refraction
,
but
so
much
less
firmly
,
in
that
he
saith
,
that
refraction
operating
upon
the
new
Star
,
and
sublimating
it
higher
than
its
true
situation
,
maketh
the
seeming
distances
untain
to
be
distinguished
from
the
true
,
when
compared
to
the
circumposed
fixed
Stars
that
environ
it
.
Nor
can
I
sufficiently
admire
how
he
can
dissemble
his
knowing
how
that
the
same
refraction
will
work
alike
upon
the
new
Star
,
as
upon
the
antient
one
its
neighbour
,
elevating
both
equally
,
so
as
that
such
a
like
accident
altereth
not
the
space
betwixt
them
.
His
other
subterfuge
is
yet
more
unhappy
,
and
carryeth
with
it
much
of
ridiculous
,
it
being
founded
upon
the
errour
that
may
arise
in
the
instrumental
operation
it self
;
whilst
that
the
Observator
not
being
able
to
constitute
the
centre
of
the
eyes
pupil
in
the
centre
of
the
Sextant
(
an
Instrument
imployed
in
observing
the
distance
between
two
Stars
)
but
holding
it
elevated
above
that
centre
,
as
much
as
the
said
pupil
is
distant
from
I
know
not
what
bone
of
the
cheek
,
against
which
the
end
of
the
Instrument
resteth
,
there
is
formed
in
the
eye
an
angle
more
acute
than
that
which
is
made
by
the
sides
of
the
Instrument
;
which
angle
of
rayes
differeth
also
from
it self
,
at
such
time
as
a
man
looketh
upon
Stars
,
not
much
elevated
above
the
Horizon
,
and
the
same
being
afterwards
placed
at
a
great
height
;
that
angle
,
saith
he
,
is
made
different
,
while
the
Instrument
goeth
ascending
,
the
head
standing
still
:
but
if
in
mounting
the
Instrument
,
the
neck
should
bend
backwards
,
and
the
head
go
rising
,
together
with
the
Instrument
,
the
angle
would
then
continue
the
same
.
So
that
the
Authours
answer
supposeth
that
the
Observators
in
using
the
Instrument
have
not
raised
the
head
,
as
they
ought
to
have
done
;
a
thing
which
hath
nothing
of
likelihood
in
it
.
But
granting
that
so
it
had
been
,
I
leave
you
to
judge
what
difference
can
be
between
two
acute
angles
of
two
equicrural
triangles
,
the
sides
of
one
of
which
triangles
are
each
four
[
Italian
]
Braces
[
i.
e.
about
three
English
yards
]
and
those
of
the
other
,
four
braces
within
the
quantity
of
the
diameter
of
a
Pea
;
for
the
differences
cannot
be
absolutely
greater
between
the
length
of
the
two
visive
rayes
,
whilst
the
line
is
drawn
perpendicularly
from
the
centre
of
the
pupil
,
upon
the
plain
of
the
Rule
of
the
Sextant
(
which
line
is
no
bigger
than
the
breath
of
the
thumb
)
and
the
length
of
the
same
rayes
,
whilst
elevating
the
Sextant
,
without
raising
the
head
together
with
it
,
that
same
line
no
longer
falleth
perpendicularly
upon
the
said
plane
,
but
inclineth
,
making
the
angle
towards
the
circumference
something
acute
.
But
wholly
to
free
this
Authour
from
these
unhappy
lies
,
let
him
know
,
(
in
regard
it
appears
that
he
is
not
very
skilful
in
the
use
of
Astronomicall
Instruments
)
that
in
the
sides
of
the
Sextant
or
Quadrant
there
are
placed
two
[
](A61244-e70020-b)*
*
Traguardi
.
Sights
,
one
in
the
centre
,
and
the
other
at
the
other
at
the
opposite
end
,
which
are
raised
an
inch
or
more
above
the
plane
of
the
Rule
;
and
through
the
tops
of
those
sights
the
ray
of
the
eye
is
made
to
passe
,
which
eye
likewise
is
held
an
hands
breadth
or
two
,
or
it
may
be
more
,
from
the
Instrument
;
so
that
neither
the
pupil
,
nor
any
bone
of
the
cheek
,
nor
of
the
whole
body
toucheth
or
stayeth
it self
upon
the
Instrument
,
nor
much
lesse
is
the
Instrument
upheld
or
mounted
in
the
armes
,
especially
if
it
be
one
of
those
great
ones
,
as
is
usual
,
which
weighing
tens
,
hundreds
,
and
also
thousands
of
pounds
,
are
placed
upon
very
strong
feet
or
frames
:
so
that
the
whole
objection
vanisheth
.
These
are
the
subterfuges
of
this
Authour
,
which
,
though
they
were
all
of
steel
,
would
not
secure
him
the
hundredth
part
of
a
minute
;
and
with
these
he
conceits
to
make
us
believe
,
that
he
hath
compensated
that
difference
,
which
importeth
more
than
an
hundred
minutes
;
I
mean
,
that
of
the
not
observing
a
notable
difference
in
the
distances
between
one
of
the
fixed
stars
,
and
the
new
star
in
in
any
of
their
circulations
;
which
,
had
it
been
neer
to
the
Moon
,
it
ought
to
have
been
very
conspicuous
to
the
meer
sight
,
without
any
Instrument
,
especially
comparing
it
with
the
eleventh
of
Cassiopeia
,
its
neighbour
,
within
1
gr.
30
m.
which
ought
to
have
varied
from
it
more
than
two
diameters
of
the
moon
,
as
the
more
intelligent
Astronomers
of
those
times
do
well
note
.
SAGR.
Methinks
I
see
that
unfortunate
Husbandman
,
who
after
all
his
expected
crops
,
have
been
beaten
down
and
destroyed
by
a
storm
,
goeth
up
and
down
with
a
languishing
and
down-cast
look
,
gleaning
up
every
small
ear
that
would
not
suffice
to
keep
a
chicken
alive
one
sole
day
.
SALV
.
Truly
,
this
Authour
came
out
too
slenderly
provided
with
armes
against
the
assailants
of
the
Heavens
inalterability
,
and
with
too
brittle
a
chain
attempted
to
pull
down
the
new
star
of
Cassiopeia
from
the
highest
Regions
,
to
these
so
low
and
elementary
.
And
for
that
I
think
that
we
have
sufficiently
demonstrated
the
vast
difference
that
is
between
the
arguments
of
those
Astronomers
,
and
of
this
their
Antagonist
,
it
will
be
convenient
that
we
leave
this
particular
,
and
return
to
our
principal
matter
;
in
which
there
presents
it self
to
our
consideration
the
annual
motion
commonly
ascribed
to
the
Sun
,
but
by
Aristarchus
Samius
first
of
all
,
and
after
by
Copernicus
taken
from
the
Sun
,
and
transferred
upon
the
Earth
;
against
which
Hypothesis
,
methinks
I
see
Simplicius
to
come
strongly
provided
,
and
particularly
with
the
sword
and
buckler
of
the
little
Treatise
of
Conclusions
,
or
Disquisitions
Mathematical
,
the
oppugnations
of
which
it
would
be
good
to
begin
to
produce
.
SIMP.
I
will
,
if
you
so
please
,
reserve
them
to
the
last
,
as
those
that
are
of
latest
invention
.
SALV
.
It
will
therefore
be
necessary
,
that
in
conformity
to
the
method
hitherto
observed
,
you
do
orderly
,
one
by
one
,
propound
the
arguments
,
on
the
contrary
,
aswell
of
Aristotle
,
as
of
the
other
ancients
,
which
shall
be
my
task
also
,
that
so
nothing
may
escape
our
strict
consideration
and
examination
;
and
likewise
Sagredus
,
with
the
vivacity
of
his
wit
,
shall
interpose
his
thoughts
,
as
he
shall
finde
himself
inclined
.
SAGR.
I
will
do
it
with
my
wonted
freedome
;
and
your
commands
shall
oblige
you
to
excuse
me
in
so
doing
.
SALV
.
The
favour
will
challenge
thanks
,
and
not
an
excuse
.
But
now
let
Simplicius
begin
to
propose
those
doubts
which
disswade
him
from
believing
that
the
Earth
,
in
like
manner
,
as
the
other
planets
,
may
move
round
about
a
fixed
centre
.
SIMP.
The
first
and
greatest
difficulty
is
the
repugnance
and
incompatibility
that
is
between
being
in
the
centre
,
and
being
far
from
it
;
for
if
the
Terrestrial
Globe
were
to
move
in
a
year
by
the
circumference
of
a
circle
,
that
is
,
under
the
Zodiack
,
it
is
impossible
that
it
should
,
at
the
same
time
,
be
in
the
centre
of
the
Zodiack
;
but
that
the
Earth
is
in
the
said
centre
Aristotle
,
Ptolomy
,
and
others
have
many
wayes
proved
.
SALV
.
You
very
well
argue
,
and
there
is
no
question
but
that
one
that
would
make
the
Earth
to
move
in
the
circumference
of
a
circle
,
must
first
of
necessity
prove
,
that
it
is
not
in
the
centre
of
that
same
circle
;
it
now
followeth
,
that
we
enquire
,
whether
the
Earth
be
,
or
be
not
in
that
centre
,
about
which
,
I
say
,
that
it
turneth
,
and
you
say
that
it
is
fixed
;
and
before
we
speak
of
this
,
it
is
likewise
necessary
that
we
declare
our selves
,
whether
you
and
I
have
both
the
same
conceit
of
this
centre
,
or
no.
Therefore
tell
me
,
what
and
where
is
this
your
intended
centre
?
SIMP.
When
I
speak
of
the
centre
,
I
mean
that
of
the
Universe
,
that
of
the
World
,
that
of
the
Starry
Sphere
.
SALV
.
Although
I
might
very
rationally
put
it
in
dispute
,
whether
there
be
any
such
centre
in
nature
,
In
hath
not
been
hitherto
proved
by
any
,
whether
the
World
be
finite
or
infinite
.
or
no
;
being
that
neither
you
nor
any
one
else
hath
ever
proved
,
whether
the
World
be
finite
and
figurate
,
or
else
infinite
and
interminate
;
yet
nevertheless
granting
you
,
for
the
present
,
that
it
is
finite
,
and
of
a
terminate
Spherical
Figure
,
and
that
thereupon
it
hath
its
centre
;
it
will
be
requisite
to
see
how
credible
it
is
that
the
Earth
,
and
not
rather
some
other
body
,
doth
possesse
the
said
centre
.
SIMP.
That
the
world
is
finite
,
terminate
,
and
spherical
,
Aristotle
proveth
with
an
hundred
demonstrations
.
SALV
.
All
which
in
the
end
are
reduced
to
one
alone
,
The
Demonstrations
of
Aristotle
to
p●ove
that
the
Vniverse
is
finite
,
are
all
nullified
by
denying
it
to
be
moveable
.
and
that
one
to
none
at
all
;
for
if
I
deny
his
assumption
,
to
wit
,
that
the
Universe
is
moveable
,
all
his
demonstrations
come
to
nothing
,
for
he
onely
proveth
the
Universe
to
be
finite
and
terminate
,
for
that
it
is
moveable
.
But
that
we
may
not
multiply
disputes
,
let
it
be
granted
for
once
,
that
the
World
is
finite
,
spherical
,
and
hath
its
centre
.
And
seeing
that
that
centre
and
figure
is
argued
from
its
mobility
,
it
will
,
without
doubt
,
be
very
reasonable
,
if
from
the
circular
motions
of
mundane
bodies
we
proceed
to
the
particular
investigation
of
that
centres
proper
place
:
Aristotle
makes
that
point
to
be
the
centre
of
the
Universe
about
which
all
the
Celestial
Spheres
do
revolve
.
Nay
Aristotle
himself
hath
argued
and
determined
in
the
same
manner
,
making
that
same
to
be
the
centre
of
the
Universe
about
which
all
the
Coelelestial
Spheres
revolve
,
and
in
which
he
beleived
the
Terrestrial
Globe
to
have
been
placed
.
A
question
is
put
,
in
case
that
if
Aristotle
were
forced
to
receive
one
of
two
propositions
that
make
against
his
doctrine
,
which
he
would
admit
.
Now
tell
me
Simplicius
,
if
Aristotle
should
be
constrained
by
evident
experience
to
alter
in
part
this
his
disposure
and
order
of
the
Universe
,
and
confesse
himself
to
have
been
deceived
in
one
of
these
two
propositions
,
namely
,
either
in
placing
the
Earth
in
the
centre
,
or
in
saying
,
that
the
Coelestial
Spheres
do
move
about
that
centre
,
which
of
the
two
confessions
think
you
would
he
choose
?
SIMP.
I
believe
,
that
if
it
should
so
fall
out
,
the
Peripateticks
.
SALV
.
I
do
not
ask
the
Peripateticks
,
I
demand
of
Aristotle
,
for
as
to
those
,
I
know
very
well
what
they
would
reply
;
they
,
as
observant
and
humble
vassals
of
Aristotle
,
would
deny
all
the
experiments
and
all
the
observations
in
the
World
,
nay
,
would
also
refuse
to
see
them
,
that
they
might
not
be
forced
to
acknowledg
them
,
and
would
say
that
the
World
stands
as
Aristotle
writeth
,
and
not
as
nature
will
have
it
,
for
depriving
them
of
the
shield
of
his
Authority
,
with
what
do
you
think
they
would
appear
in
the
field
?
Tell
me
therefore
what
you
are
perswaded
Aristotle
himself
would
do
in
the
case
.
SIMP.
To
tell
you
the
truth
,
I
know
not
how
to
resolve
which
of
the
two
inconveniences
is
to
be
esteemed
the
lesser
.
SALV
.
Apply
not
I
pray
you
this
term
of
inconvenience
to
a
thing
which
possibly
may
of
necessity
be
so
.
It
was
an
inconvenience
to
place
the
Earth
in
the
centre
of
the
Coelestial
revolutions
;
but
seeing
you
know
not
to
which
part
he
would
incline
,
I
esteeming
him
to
be
a
man
of
great
judgment
,
let
us
examine
which
of
the
two
choices
is
the
more
rational
,
and
that
we
will
hold
that
Aristotle
would
have
received
.
Reassuming
therefore
our
discourse
from
the
beginning
,
we
suppose
with
the
good
liking
of
Aristotle
,
that
the
World
(
of
the
magnitude
of
which
we
have
no
sensible
notice
beyond
the
fixed
stars
)
as
being
of
a
spherical
figure
;
and
moveth
circularly
,
hath
necessarily
,
and
in
respect
of
its
figure
a
centre
;
and
we
being
moreover
certain
,
that
within
the
starry
Sphere
there
are
many
Orbs
,
the
one
within
another
,
with
their
stars
,
which
likewise
do
move
circulary
,
it
is
in
dispute
whether
it
is
most
reasonable
to
believe
and
to
say
that
these
conteined
Orbs
do
move
round
the
said
centre
of
the
World
,
or
else
about
some
other
centre
far
remote
from
that
?
Tell
me
now
Simplicius
what
you
think
concerning
this
particular
.
SIMP.
If
we
could
stay
upon
this
onely
supposition
,
It
s
more
rational
that
the
Orb
containing
,
and
the
parts
contained
,
do
move
all
about
one
centre
,
than
u●on
divers
.
and
that
we
were
sure
that
we
might
encounter
nothing
else
that
might
disturb
us
,
I
would
say
that
it
were
much
more
reasonable
to
affirm
that
the
Orb
containing
,
and
the
parts
contained
,
do
all
move
about
one
common
centre
,
than
about
divers
.
SALV
.
Now
if
it
were
true
that
the
centre
of
the
World
is
the
same
about
which
the
Orbs
of
mundane
bodies
,
If
the
centre
of
the
World
be
the
〈…〉
that
about
which
the
planets
move
,
the
Sun
and
not
the
Earth
is
placed
in
it
.
that
is
to
say
,
of
the
Planets
,
move
,
it
is
most
certain
that
it
is
not
the
Earth
,
but
the
Sun
rather
that
is
fixed
in
the
centre
of
the
World
.
So
that
as
to
this
first
simple
and
general
apprehension
,
the
middle
place
belongeth
to
the
Sun
,
and
the
Earth
is
as
far
remote
from
the
centre
,
as
it
is
from
that
same
Sun
.
SIMP.
But
from
whence
do
you
argue
that
not
the
Earth
,
but
the
Sun
is
in
the
centre
of
the
Planetary
revolutions
?
SALV
.
I
infer
the
same
from
most
evident
,
and
therefore
necessarily
concludent
observations
,
of
which
the
most
palpable
to
exclude
the
Earth
from
the
said
centre
,
Observations
from
whence
it
is
collected
that
the
Sun
and
not
the
Earth
is
in
the
centre
of
the
Celestial
revolutions
.
and
to
place
the
Sun
therein
,
are
,
the
seeing
all
the
Planets
one
while
neerer
and
another
while
farther
off
from
the
Earth
with
so
great
differences
,
that
for
example
,
Venus
when
it
is
at
the
farthest
,
is
six
times
more
remote
from
us
,
than
when
it
is
neerest
,
and
Mars
riseth
almost
eight
times
as
high
at
one
time
as
at
another
.
See
therefore
whether
Aristotle
was
not
somewhat
mistaken
in
thinking
that
it
was
at
all
times
equidistant
from
us
.
SIMP.
What
in
the
next
place
are
the
tokens
that
their
motions
are
about
the
Sun
?
SALV
.
It
is
argued
in
the
three
superiour
planets
Mars
,
Jupiter
,
and
Saturn
,
in
that
we
find
them
alwayes
neerest
to
the
Earth
when
they
are
in
opposition
to
the
Sun
,
and
farthest
off
when
they
are
towards
the
conjunction
,
and
this
approximatian
and
recession
importeth
thus
much
that
Mars
neer
at
hand
,
appeareth
very
neer
60
times
greater
than
when
it
is
remote
.
The
mutation
of
figure
in
Venus
argueth
its
motion
to
be
about
the
Sun
.
As
to
Venus
in
the
next
place
,
and
to
Mercury
,
we
are
certain
that
they
revolve
about
the
Sun
,
in
that
they
never
move
far
from
him
,
and
in
that
we
see
them
one
while
above
and
another
while
below
it
,
The
Moon
cannot
seperate
from
the
Earth
.
as
the
mutations
of
figure
in
Venus
necessarily
argueth
.
To●ching
the
Moon
it
is
certain
,
that
she
cannot
in
any
way
seperate
from
the
Earth
,
for
the
reasons
that
shall
be
more
distinctly
alledged
hereafter
.
SAGR.
I
expect
that
I
shall
hear
more
admirable
things
that
depend
upon
this
annual
motion
of
the
Earth
,
than
were
those
dependant
upon
the
diurnal
revolution
.
SALV
.
You
do
not
therein
erre
:
The
annual
motion
of
the
Earth
mixing
with
the
motions
of
the
other
Planets
produce
extravagant
appearances
.
For
as
to
the
operation
of
the
diurnal
motion
upon
the
Celestial
bodies
,
it
neither
was
,
nor
can
be
other
,
than
to
make
the
Universe
seem
to
run
precipitately
the
contrary
way
;
but
this
annual
motion
intermixing
with
the
particular
motions
of
all
the
planets
,
produceth
very
many
extravagancies
,
which
have
disarmed
and
non-plust
all
the
greatest
Scholars
in
the
World
.
But
returning
to
our
first
general
apprehensions
,
I
reply
that
the
centre
of
the
Celestial
conversions
of
the
●ive
planets
Saturn
,
Jupiter
,
Mars
,
Venus
and
Mercury
,
is
the
Sun
;
and
shall
be
likewise
the
centre
of
the
motion
of
the
Earth
,
if
we
do
but
succeed
in
our
attempt
of
placing
it
in
Heaven
.
And
as
for
the
Moon
,
this
hath
a
circular
motion
about
the
Earth
,
from
which
(
as
I
said
before
)
it
can
by
no
means
alienate
it self
,
but
yet
doth
it
not
cease
to
go
about
the
Sun
together
with
the
Ear●h
in
an
annual
motion
.
SIMP.
I
do
not
as
yet
very
well
apprehend
this
structure
,
but
it
may
be
,
that
with
making
a
few
draughts
thereof
,
one
may
better
and
more
easily
discourse
concerning
the
same
.
SALV
.
T
is
very
true
:
yea
for
your
greater
satisfaction
and
admiration
together
,
I
desire
you
,
that
you
would
take
the
pains
to
draw
the
same
;
and
to
see
that
although
you
think
you
do
not
apprehend
it
,
yet
you
very
perfectly
understand
it
;
And
onely
by
answering
to
my
interrogations
you
shall
designe
it
punctually
.
Take
therefore
a
sheet
of
paper
and
Compasses
;
The
Systeme
of
the
Universe
designed
from
the
appearances
.
And
let
this
white
paper
be
the
immense
expansion
of
the
Universe
;
in
which
you
are
to
distribute
and
dispose
its
parts
in
order
,
according
as
reason
shall
direct
you
.
And
first
,
in
regard
that
without
my
instruction
you
verily
believe
that
the
Earth
is
placed
in
this
Universe
,
therefore
note
a
point
at
pleasure
,
about
which
you
intend
it
to
to
be
placed
,
and
mark
it
with
some
characters
.
SIMP.
Let
this
mark
A
be
the
place
of
the
Terrestrial
Globe
.
SALV
.
Very
well
.
I
know
secondly
,
that
you
understand
perfectly
that
the
said
Earth
is
not
within
the
body
of
the
Sun
,
nor
so
much
as
contiguous
to
it
,
but
distant
for
some
space
from
the
same
,
and
therefore
assign
to
the
Sun
what
other
place
you
best
like
,
as
remote
from
the
Earth
as
you
please
,
and
mark
this
in
like
manner
.
SIMP.
Here
it
is
done
:
Let
the
place
of
the
Solar
body
be
O.
SALV
.
These
two
being
constituted
,
I
desire
that
we
may
think
of
accomodating
the
body
of
Venus
in
such
a
manner
that
its
state
and
motion
may
agree
with
what
sensible
experiments
do
shew
us
;
and
therefore
recall
to
mind
that
which
either
by
the
past
discourses
,
or
your
own
observations
you
have
learnt
to
befal
that
star
,
and
afterwards
assign
unto
it
that
state
which
you
think
agreeth
with
the
same
.
SIMP.
Supposing
those
Phaenomena
expressed
by
you
,
and
which
I
have
likewise
read
in
the
little
treatise
of
Conclusions
,
to
be
true
,
namely
,
that
that
star
never
recedes
from
the
Sun
beyond
such
a
determinate
space
of
40
degrees
or
thereabouts
,
so
as
that
it
never
cometh
either
to
apposition
with
the
Sun
,
or
so
much
as
to
quadrature
,
or
yet
to
the
sextile
aspect
;
and
more
than
that
,
Venus
very
great
towards
the
respective
conjunction
and
very
small
towards
the
maintine
.
supposing
that
it
sheweth
at
one
time
almost
40
times
greater
than
at
another
;
namely
,
very
great
,
when
being
retrograde
,
it
goeth
to
the
vespertine
conjnnction
of
the
Sun
,
and
very
small
when
with
a
motion
straight
forwards
,
it
goeth
to
the
matutine
conjunction
;
and
moreover
it
being
true
,
that
when
it
appeareth
bigge
it
shews
with
a
corniculate
figure
,
and
when
it
appeareth
little
,
it
seems
perfectly
round
,
these
appearances
,
I
say
,
being
true
,
I
do
not
see
how
one
can
choose
but
affirm
the
said
star
to
revolve
in
a
circle
about
the
Sun
,
Venus
necessarily
proved
to
move
about
the
Sun
.
for
that
the
said
circle
cannot
in
any
wise
be
said
to
encompasse
or
to
contain
the
Earth
within
it
,
nor
to
be
inferiour
to
the
Sun
,
that
is
between
it
and
the
Earth
,
nor
yet
superiour
to
the
Sun
.
That
circle
cannot
incompasse
the
Earth
,
because
Venus
would
then
sometimes
come
to
opposition
with
the
Sun
;
it
cannot
be
inferiour
,
for
then
Venus
in
both
its
conjunctions
with
the
Sun
would
seem
horned
;
nor
can
it
be
superiour
,
for
then
it
would
alwayes
appear
round
,
and
never
cornicular
;
and
therefore
for
receit
of
it
I
will
draw
the
circle
CH
,
about
the
Sun
,
without
encompassing
the
Earth
.
SALV
.
Having
placed
Venus
,
it
is
requisite
that
you
think
of
Mercury
,
which
,
as
you
know
,
alwayes
keeping
about
the
Sun
,
doth
recede
lesse
distance
from
it
than
Venus
;
therefore
consider
with
your self
,
what
place
is
most
convenient
to
assign
it
.
SIMP.
It
is
not
to
be
questioned
,
The
revolution
of
Mercury
concluded
to
be
about
the
Sun
,
within
the
Orb
of
Venus
.
but
that
this
Planet
imitating
Venus
,
the
most
commodious
place
for
it
will
be
,
a
lesser
circle
within
this
of
Venus
,
in
like
manner
about
the
Sun
,
being
that
of
its
greatest
vicinity
to
the
Sun
,
an
argument
,
an
evidence
sufficiently
proving
the
vigour
of
its
illumination
,
above
that
of
Venus
,
and
of
the
other
Planets
,
we
may
therefore
upon
these
considerations
draw
its
Circle
,
marking
it
with
the
Characters
BG
.
SALV
.
But
Mars
,
Mars
necessarily
includeth
within
its
Orb
the
Earth
,
and
also
the
Sun
.
Where
shall
we
place
it
?
SIMP.
Mars
,
Because
it
comes
to
an
opposition
with
the
Sun
,
its
Circle
must
of
necessity
encompass
the
Earth
;
But
I
see
that
it
must
necessarily
encompass
the
Sun
also
,
for
coming
to
conjunction
with
the
Sun
,
if
it
did
not
move
over
it
,
but
were
below
it
,
it
would
appear
horned
,
as
Venus
and
the
Moon
;
but
it
shews
alwayes
round
,
and
therefore
it
is
necessary
,
that
it
no
less
includeth
the
Sun
within
its
circle
than
the
Earth
.
Mars
at
its
opposition
to
the
Sun
shews
to
be
sixty
times
bigger
than
towards
the
conjunction
.
And
because
I
remember
that
you
did
say
,
that
when
it
is
in
opposition
with
the
Sun
,
it
seems
60
times
bigger
than
when
it
is
in
the
conjunction
,
me
thinks
that
a
Circle
about
the
Centre
of
the
Sun
,
and
that
taketh
in
the
earth
,
will
very
well
agree
with
these
Phaenomena
,
which
I
do
note
and
mark
DI
,
where
Mars
in
the
point
D
,
is
near
to
the
earth
,
and
opposite
to
the
Sun
;
but
when
it
is
in
the
point
I
,
it
is
at
Conjuction
with
the
Sun
,
but
very
far
from
the
Earth
.
And
because
the
same
appearances
are
observed
in
Jupiter
and
Saturn
,
Jupiter
and
Saturn
do
likewise
encompasse
the
Earth
,
and
the
Sun
.
although
with
much
lesser
difference
in
Jupiter
than
in
Mars
,
and
with
yet
lesse
in
Saturn
than
in
Jupiter
;
me
thinks
I
understand
that
we
should
very
commodiously
salve
all
the
Phaenomena
of
these
two
Planets
,
with
two
Circles
,
in
like
manner
,
drawn
about
the
Sun
,
and
this
first
for
Jupiter
,
marking
it
EL
,
and
another
above
that
for
Saturn
marked
FM
.
SALV
.
You
have
behaved
your self
bravely
hitherto
.
The
approximation
and
recession
of
the
three
superiour
Planets
,
importeth
double
the
Suns
distance
.
And
because
(
as
you
see
)
the
approach
and
recession
of
the
three
Superiour
Planets
is
measured
with
double
the
distance
between
the
Earth
and
Sun
,
this
maketh
greater
difference
in
Mars
than
in
Jupiter
,
the
Circle
DI
,
The
difference
of
the
apparent
magnitude
lesse
in
Saturn
,
than
in
Jupiter
,
and●
Jupiter
than
in
Mars
,
and
why
.
of
Mars
,
being
lesser
than
the
Circle
EL
,
of
Jupiter
,
and
likewise
because
this
EL
,
is
lesse
than
this
Circle
FM
,
of
Saturn
,
the
said
difference
is
also
yet
lesser
in
Saturn
than
in
Jupiter
,
and
that
punctually
answereth
the
Phaenomena
.
It
remains
now
that
you
assign
a
place
to
the
Moon
.
SIMP.
Following
the
same
Method
(
which
seems
to
me
very
conclusive
)
in
regard
we
see
that
the
Moon
cometh
to
conjunction
and
opposition
with
the
Sun
,
The
Moons
Orb
invironeth
the
Earth
,
but
not
the
Sun
.
it
is
necessary
to
say
,
that
its
circle
encompasseth
the
Earth
,
but
yet
doth
it
not
follow
,
that
it
must
environ
the
Sun
,
for
then
at
that
time
towards
its
conjunction
,
it
would
not
seem
horned
,
but
alwayes
round
and
full
of
Light
.
Moreover
it
could
never
make
,
as
it
often
doth
,
the
Eclipse
of
the
Sun
,
by
interposing
betwixt
it
and
us
;
It
is
necessary
therefore
to
assign
it
a
circle
about
the
Earth
,
which
should
be
this
NP
,
so
that
being
constituted
in
P
,
it
will
appear
from
the
Earth
A
,
to
be
in
conjunction
with
the
Sun
,
and
placed
in
N
,
it
appeareth
opposite
to
the
Sun
,
and
in
that
position
it
may
fall
under
the
Earths
shadow
,
and
be
obscured
.
SALV
.
Now
,
Simplicius
,
what
shall
we
do
with
the
fixed
stars
?
Shall
we
suppose
them
scattered
through
the
immense
abisses
of
the
Universe
,
at
different
distances
,
from
any
one
determinate
point
;
or
else
placed
in
a
superficies
spherically
distended
about
a
centre
of
its
own
,
so
that
each
of
them
may
be
equidistant
from
the
said
centre
?
SIMP.
I
would
rather
take
a
middle
way
;
The
probable
situation
of
the
fixed
stars
.
and
would
assign
them
an
Orb
described
about
a
determinate
centre
and
comprized
within
two
spherical
superficies
,
to
wit
,
one
very
high
,
and
concave
,
and
the
other
lower
,
Which
ought
to
be
accounted
the
sphere
of
the
Vniverse
.
and
convex
,
betwixt
which
I
would
constitute
the
innumerable
multitude
of
stars
,
but
yet
at
divers
altitudes
,
and
this
might
be
called
the
Sphere
of
the
Universe
,
conteining
within
it
the
Orbs
of
the
planets
already
by
us
described
.
SALV
.
But
now
we
have
all
this
while
,
Simplicius
,
disposed
the
mundane
bodies
exactly
,
according
to
the
order
of
Copernicus
,
and
we
have
done
it
with
your
hand
;
and
moreover
to
each
of
them
you
have
assigned
peculiar
motions
of
their
own
,
except
to
the
Sun
,
the
Earth
,
and
starry
Sphere
;
and
to
Mercury
with
Venus
,
you
have
ascribed
the
circular
motion
about
the
Sun
,
without
encompassing
the
Earth
;
about
the
same
Sun
you
make
the
three
superiour
Planets
Mars
,
Jupiter
,
and
Saturn
,
to
move
,
comprehending
the
Earth
within
their
circles
.
The
Moon
in
the
next
place
can
move
in
no
other
manner
than
about
the
Earth
,
without
taking
in
the
Sun
,
and
in
all
these
motions
you
agree
also
with
the
same
Copernicus
.
There
remains
now
three
things
to
be
decided
between
the
Sun
,
the
Earth
,
and
fixed
stars
,
namely
,
Rest
,
Rest
,
the
annual
motion
and
the
diurnal
ought
to
be
distributed
betwixt
the
Sun
,
Earth
,
and
Firmament
.
which
seemeth
to
belong
to
the
Earth
;
the
annual
motion
under
the
Zodiack
,
which
appeareth
to
pertain
to
the
Sun
;
and
the
diurnal
motion
,
which
seems
to
belong
to
the
Starry
Sphere
,
and
to
be
by
that
imparted
to
all
the
rest
of
the
Universe
,
the
Earth
excepted
,
And
it
being
true
that
all
the
Orbs
of
the
Planets
,
I
mean
of
Mercury
,
In
a
moveable
sphere
,
it
seemeth
more
reasonable
that
its
centre
be
stable
,
than
any
other
of
its
parts
.
Venus
,
Mars
,
Jupiter
,
and
Saturn
,
do
move
about
the
Sun
as
their
centre
;
rest
seemeth
with
so
much
more
reason
to
belong
to
the
said
Sun
,
than
to
the
Earth
,
in
as
much
as
in
a
moveable
Sphere
,
it
is
more
reasonable
that
the
centre
stand
still
,
than
any
other
place
remote
from
the
said
centre
;
to
the
Earth
therefore
,
which
is
constituted
in
the
midst
of
moveable
parts
of
the
Universe
,
I
mean
between
Venus
and
Mars
,
one
of
which
maketh
its
revolution
in
nine
moneths
,
and
the
other
in
two
years
,
may
the
motion
of
a
year
very
commodiously
be
assigned
,
leaving
rest
to
the
Sun
.
Granting
to
the
Earth
the
annual
,
it
must
of
necessity
also
have
the
diurnal
motion
assigned
to
it
.
And
if
that
be
so
,
it
followeth
of
necessary
consequence
,
that
likewise
the
diurnal
motion
belongeth
to
the
Earth
;
for
,
if
the
Sun
standing
still
,
the
Earth
should
not
revolve
about
its
self
,
but
have
onely
the
annual
motion
about
the
Sun
,
our
year
would
be
no
other
than
one
day
and
one
night
,
that
is
six
moneths
of
day
,
and
six
moneths
of
night
,
as
hath
already
been
said
.
You
may
consider
withal
how
commodiously
the
precipitate
motion
of
24
hours
is
taken
away
from
the
Universe
,
and
the
fixed
stars
that
are
so
many
Suns
,
are
made
in
conformity
to
our
Sun
to
enjoy
a
perpetual
rest
.
You
see
moreover
what
facility
one
meets
with
in
this
rough
draught
to
render
the
reason
of
so
great
appearances
in
the
Celestial
bodies
.
SAGR.
I
very
well
perceive
that
facility
,
but
as
you
from
this
simplicity
collect
great
probabilities
for
the
truth
of
that
System
,
others
haply
could
make
thence
contrary
deductions
;
doubting
,
not
without
reason
,
why
that
same
being
the
ancient
Systeme
of
Pythagoreans
,
and
so
well
accommodated
to
the
Phaenomena
,
hath
in
the
succession
of
so
many
thousand
years
had
so
few
followers
,
and
hath
been
even
by
Aristotle
himself
refuted
,
and
since
that
Copernicus
himself
hath
had
no
better
fortune
.
SALV
.
If
you
had
at
any
time
been
assaulted
,
as
I
have
been
,
many
and
many
a
time
,
with
the
relation
of
such
kind
of
frivolous
reasons
,
as
serve
to
make
the
vulgar
contumacious
,
and
difficult
to
be
perswaded
to
hearken
,
(
I
will
not
say
to
consent
)
to
this
novelty
,
I
believe
that
you
wonder
at
the
paucity
of
those
who
are
followers
of
that
opinion
would
be
much
diminished
.
Discourses
more
than
childish
,
serve
to
keep
fools
in
the
opinion
of
the
Earths
stability
.
But
small
regard
in
my
judgement
,
ought
to
be
had
of
such
thick
sculs
,
as
think
it
a
most
convincing
proof
to
confirm
,
and
steadfastly
settle
them
in
the
belief
of
the
earths
immobility
,
to
see
that
if
this
day
they
cannot
Dine
at
Constantinople
,
nor
Sup
in
Jappan
,
that
then
the
Earth
as
being
a
most
grave
body
cannot
clamber
above
the
Sun
,
and
then
slide
headlong
down
again
;
Of
such
as
these
I
say
,
whose
number
is
infinite
,
we
need
not
make
any
reckoning
,
nor
need
we
to
record
their
foolieries
,
or
to
strive
to
gain
to
our
side
as
our
partakers
in
subul
and
sublime
opinions
,
men
in
whose
definition
the
kind
onely
is
concerned
,
and
the
difference
is
wanting
.
Moreover
,
what
ground
do
you
think
you
could
be
able
to
gain
,
with
all
the
demonstrations
of
the
World
upon
brains
so
stupid
,
as
are
not
able
of
themselves
to
know
their
down
right
follies
?
But
my
admiration
,
Sagredus
,
is
very
different
from
yours
,
you
wonder
that
so
few
are
followers
of
the
Pythagorean
Opinion
;
and
I
am
amazed
how
there
could
be
any
yet
left
till
now
that
do
embrace
and
follow
it
:
A
declaration
of
the
improbability
of
Copernicus
his
opinion
.
Nor
can
I
sufficiently
admire
the
eminencie
of
those
mens
wits
that
have
received
and
held
it
to
be
true
,
and
with
the
sprightlinesse
of
their
judgements
offered
such
violence
to
their
own
sences
,
as
that
they
have
been
able
to
prefer
that
which
their
reason
dictated
to
them
,
to
that
which
sensible
experiments
represented
most
manifestly
on
the
contrary
.
That
the
reasons
against
the
Diurnal
virtiginous
revolution
of
the
Earth
by
you
already
examined
,
do
carry
great
probability
with
them
,
we
have
already
seen
;
as
also
that
the
Ptolomaicks
,
and
Aristotelicks
,
with
all
their
Sectators
did
receive
them
for
true
,
is
indeed
a
very
great
argument
of
their
efficacie
;
but
those
experiments
which
apertly
contradict
the
annual
motion
,
Reasons
and
discourse
in
Aristarcus
and
Copernicus
prevailed
over
manifest
sence
.
are
of
yet
so
much
more
manifestly
repugnant
,
that
(
I
say
it
again
)
I
cannot
find
any
bounds
for
my
admiration
,
how
that
reason
was
able
in
Aristarchus
and
Copernicus
,
to
commit
such
a
rape
upon
their
Sences
,
as
in
despight
thereof
,
to
make
her self
mistress
of
their
credulity
.
SAGR.
Are
we
then
to
have
still
more
of
these
strong
oppositions
against
this
annual
motion
?
SALV
.
We
are
,
and
they
be
so
evident
and
sensible
,
that
if
a
sence
more
sublime
and
excellent
than
those
common
and
vulgar
,
did
not
take
part
with
reason
,
I
much
fear
,
that
I
also
should
have
been
much
more
averse
to
the
Copernican
Systeem
than
I
have
been
since
the
time
that
a
clearer
lamp
than
ordinary
hath
enlightned
me
.
SAGR.
Now
therefore
Salviatus
,
let
us
come
to
joyn
battail
for
every
word
that
is
spent
on
any
thing
else
,
I
take
to
be
cast
away
.
SALV
.
I
am
ready
to
serve
you
.
You
have
already
seen
me
draw
the
form
of
the
Copernican
Systeme
;
Mars
makes
an
hot
assaults
upon
the
Coper●●can
Systeme
.
against
the
truth
of
which
Mars
himself
,
in
the
first
place
,
makes
an
hot
charge
;
who
,
in
case
it
were
true
,
that
its
distances
from
the
earth
should
so
much
vary
,
as
that
from
the
least
distance
to
the
greatest
,
there
were
twice
as
much
differences
,
as
from
the
earth
to
the
Sun
;
it
would
be
necessary
,
that
when
it
is
nearest
unto
us
,
its
discus
would
shew
more
than
60.
times
bigger
than
it
seems
,
when
it
is
farthest
from
us
;
nevertheless
that
diversity
of
apparent
magnitude
is
not
to
be
seen
,
nay
in
its
opposition
with
the
Sun
,
when
its
nearest
to
the
Earth
,
it
doth
not
shew
so
much
as
quadruple
and
quintuple
in
bigness
,
to
what
it
is
,
when
towards
the
conjunction
it
cometh
to
be
occulted
under
the
Suns
rayes
.
Another
and
greater
difficulty
doth
Venus
exhibit
;
For
if
revolving
about
the
Sun
,
as
Copernicus
affirmeth
,
The
Phaenomena
of
Venus
appear
contrary
to
the
Systeme
of
Copernicus
.
it
were
one
while
above
,
&
another
while
below
the
same
,
receding
and
approaching
to
us
so
much
as
the
Diameter
of
the
circle
described
would
be
,
at
such
time
as
it
should
be
below
the
Sun
,
and
nearest
to
us
,
its
discus
would
shew
little
less
than
40
times
bigger
than
when
it
is
above
the
Sun
,
near
to
its
other
conjunction
;
yet
neverthelesse
,
Another
difficulty
raised
by
Venus
against
Copernicus
.
the
difference
is
almost
imperceptible
Let
us
add
another
difficulty
,
that
in
case
the
body
of
Venus
be
of
it self
dark
,
and
onely
shineth
as
the
Moon
,
by
the
illumination
of
the
Sun
,
which
seemeth
most
reasonable
;
it
would
shew
forked
or
horned
at
such
time
as
it
is
under
the
Sun
,
as
the
Moon
doth
when
she
is
in
like
manner
near
the
Sun
;
an
accident
that
is
not
to
be
discovered
in
her
.
Venus
,
according
to
Copernicus
,
either
lucid
in
it self
,
or
else
of
a
transparent
substance
.
Whereupon
Copernicus
affirmeth
,
that
either
she
is
light
of
her self
,
or
else
that
her
substance
is
of
such
a
nature
,
that
it
can
imbue
the
Solar
light
,
and
transmit
the
same
through
all
its
whole
depth
,
so
as
to
be
able
to
appear
to
us
alwayes
shining
;
and
in
this
manner
Copernicus
excuseth
the
not
changing
figure
in
Venus
:
but
of
her
small
variation
of
Magnitude
,
Copernicus
speaketh
nothing
of
the
small
variation
of
bigness
in
Venus
and
in
Mars
.
he
maketh
no
mention
at
all
;
and
much
less
of
Mars
than
was
needful
;
I
believe
as
being
unable
so
well
as
he
desired
to
salve
a
Phaenomenon
so
contrary
to
his
Hypothesis
,
and
yet
being
convinced
by
so
many
other
occurrences
and
reasons
he
maintained
,
and
held
the
same
Hypothesis
to
be
true
.
Besides
these
things
,
to
make
the
Planets
,
together
with
the
Earth
,
to
move
above
the
Sun
as
the
Centre
of
their
conversions
,
and
the
Moon
onely
to
break
that
order
,
The
moon
much
disturbeth
the
order
of
the
other
Planets
.
and
to
have
a
motion
by
it self
about
the
earth
;
and
to
make
both
her
,
the
Earth
,
and
the
whole
Elementary
Sphere
,
to
move
all
together
about
the
Sun
in
a
year
,
this
seemeth
to
pervert
the
order
of
this
Systeme
,
which
rendreth
it
unlikely
and
false
.
These
are
those
difficulties
that
make
me
wonder
how
Aristarchus
and
Copernicus
,
who
must
needs
have
observed
them
,
not
having
been
able
for
all
that
to
salve
them
,
have
yet
notwithstanding
by
other
admirable
occurrences
been
induced
to
confide
so
much
in
that
which
reason
dictated
to
them
,
as
that
they
have
considently
affirmed
that
the
structure
of
the
Universe
could
have
no
other
figure
than
that
which
they
designed
to
themselves
.
There
are
also
several
other
very
serious
and
curious
doubts
,
not
so
easie
to
be
resolved
by
the
middle
sort
of
wits
,
but
yet
penetrated
and
declared
by
Coperninus
,
which
we
shall
defer
till
by
and
by
,
after
we
have
answered
to
other
objections
that
seem
to
make
against
this
opinion
.
Now
coming
to
the
declarations
and
answers
to
those
three
before
named
grand
Objections
,
I
say
,
that
the
two
first
not
onely
contradict
not
the
Copernican
Systeme
,
Answers
to
the
three
first
objections
against
the
Copernican
,
Systeme
.
but
greatly
and
absolutely
favour
it
;
For
both
Mars
and
Venus
seems
unequal
to
themselves
,
according
to
the
proportions
assigned
;
and
Venus
under
the
Sun
seemeth
horned
,
and
goeth
changing
figures
in
it self
exactly
like
the
Moon
.
SAGR.
But
how
came
this
to
be
concealed
from
Copernicus
,
and
revealed
to
you
?
SALV
.
These
things
cannot
be
comprehended
,
save
onely
by
the
sense
of
seeing
,
the
which
by
nature
was
not
granted
to
man
so
perfect
,
as
that
it
was
able
to
attain
to
the
discovery
of
such
differences
;
nay
even
the
very
instrument
of
sight
is
an
impediment
to
it self
:
But
since
that
it
hath
pleased
God
in
our
age
to
vouchsafe
to
humane
ingenuity
,
so
admirable
an
invention
of
perfecting
our
sight
,
by
multiplying
it
four
,
six
,
ten
,
twenty
,
thirty
,
and
fourty
times
,
infinite
objects
,
that
either
by
reason
of
their
distance
,
or
for
their
extream
smallnesse
were
invisible
unto
us
,
have
by
help
of
the
Telescope
been
rendered
visible
.
SAGR.
But
Venus
and
Mars
are
none
of
the
objects
invisible
for
their
distance
or
smallnesse
,
yea
,
we
do
discern
them
with
our
bare
natural
sight
;
why
then
do
we
not
distinguish
the
differences
of
their
magnitudes
and
figures
?
SALV
.
In
this
,
The
reason
whence
it
happens
that
Venus
and
Mars
do
not
appear
to
vary
magnitude
so
much
as
is
requisite
.
the
impediment
of
our
very
eye
it self
hath
a
great
share
,
as
but
even
now
I
hinted
,
by
which
the
resplendent
and
remote
objects
are
not
represented
to
us
simple
and
pure
;
but
gives
them
us
fringed
with
strange
and
adventitious
rayes
,
so
long
and
dense
,
that
their
naked
body
sheweth
to
us
agrandized
,
ten
twenty
,
an
hundred
,
yea
a
thousand
times
more
than
it
would
appear
,
if
the
capillitious
rayes
were
taken
away
.
SAGR.
Now
I
remember
that
I
have
read
something
on
this
subject
,
I
know
not
whether
in
the
Solar
Letters
,
or
in
the
Saggiatore
of
our
common
Friend
,
but
it
would
be
very
good
,
aswell
for
recalling
it
into
my
memory
,
as
for
the
information
of
Simplicius
,
who
it
may
be
never
saw
those
writings
,
that
you
would
declare
unto
us
more
distinctly
how
this
businesse
stands
,
the
knowledge
whereof
I
think
to
be
very
necessary
for
the
assisting
of
us
to
understand
that
of
which
we
now
speak
.
SIMP.
I
must
confesse
that
all
that
which
Salviatus
hath
spoken
is
new
unto
me
,
for
truth
is
,
I
never
have
had
the
curiosity
to
read
those
Books
,
nor
have
I
hitherto
given
any
great
credit
to
the
Telescope
newly
introduced
;
The
operations
of
the
Telescope
accounted
fallacies
by
the
Peripateticks
.
rather
treading
in
the
steps
of
other
Peripatetick
Philosophers
my
companions
,
I
have
thought
those
things
to
be
fallacies
and
delusions
of
the
Chrystals
,
which
others
have
so
much
admired
for
stupendious
operations
:
and
therefore
if
I
have
hitherto
been
in
an
errour
,
I
shall
be
glad
to
be
freed
from
it
,
and
allured
by
these
novelties
already
heard
from
you
,
I
shall
the
more
attentively
hearken
to
the
rest
.
SALV
.
The
confidence
that
these
men
have
in
their
own
apprehensivenesse
,
is
no
less
unreasonable
than
the
small
esteem
they
have
of
the
judgment
of
others
:
yet
it
s
much
that
should
esteem
themselves
able
to
judge
better
of
such
an
instrument
,
without
ever
having
made
trial
of
it
,
than
those
who
have
made
,
and
daily
do
make
a
thousand
experiments
of
the
same
:
But
I
pray
you
,
let
us
leave
this
kind
of
pertinacious
men
,
whom
we
cannot
so
much
as
tax
without
doing
them
too
great
honour
.
And
returning
to
our
purpose
,
Shining
objects
seem
environed
with
adventitious
rayes
.
I
say
,
that
resplendent
objects
,
whether
it
is
that
their
light
doth
refract
on
the
humidity
that
is
upon
the
pupils
,
or
that
it
doth
reflect
on
the
edges
of
the
eye-browes
,
diffusing
its
reflex
rayes
upon
the
said
pupils
,
or
whether
it
is
for
some
other
reason
,
they
do
appear
to
our
eye
,
as
if
they
were
environ'd
with
new
rayes
,
and
therefore
much
bigger
than
their
bodies
would
represent
themselves
to
us
,
were
they
divested
of
those
irradiations
.
The
reason
why
luminous
bodies
appear
enlarged
much
the
more
,
by
how
much
they
are
lesser
.
And
this
aggrandizement
is
made
with
a
greater
and
greater
proportion
,
by
how
much
those
lucid
objects
are
lesser
and
lesser
;
in
the
same
manner
for
all
the
world
,
as
if
we
should
suppose
that
the
augmentation
of
shining
locks
were
v.
g.
four
inches
,
which
addition
being
made
about
a
circle
that
hath
four
inches
diameter
would
increase
its
appearance
to
nine
times
its
former
bignesse
:
but
—
SIMP.
I
believe
you
would
have
said
three
times
;
for
adding
four
inches
to
this
side
,
and
four
inches
to
that
side
of
the
diameter
of
a
circle
,
which
is
likewise
four
inches
,
its
quantity
is
thereby
tripled
,
and
not
made
nine
times
bigger
.
SALV
.
A
little
more
Geometry
would
do
well
,
Superficial
figures
encreasing
proportion
double
to
their
lines
.
Simplicius
.
True
it
is
,
that
the
diameter
is
tripled
,
but
the
superficies
,
which
is
that
of
which
we
speak
,
increaseth
nine
times
:
for
you
must
know
,
Simplicius
,
that
the
superficies
of
circles
are
to
one
another
,
as
the
squares
of
their
diameters
;
and
a
circle
that
hath
four
inches
diameter
is
to
another
that
hath
twelve
,
as
the
square
of
four
to
the
square
of
twelve
;
that
is
,
as
16.
is
to
144.
and
therefore
it
shall
be
increased
nine
times
,
and
not
three
;
this
,
by
way
of
advertisement
to
Simplicius
.
And
proceeding
forwards
,
if
we
should
add
the
said
irradiation
of
four
inches
to
a
circle
that
hath
but
two
inches
of
diameter
onely
,
the
diameter
of
the
irradiation
or
Garland
would
be
ten
inches
,
and
the
superficial
content
of
the
circle
would
be
the
area
of
the
naked
body
,
as
100.
to
4.
for
those
are
the
squares
of
10.
and
of
2.
the
agrandizement
would
therefore
be
25.
times
so
much
;
and
lastly
,
the
four
inches
of
hair
or
fringe
,
added
to
a
small
circle
of
an
inch
in
diameter
,
the
same
would
be
increased
81.
times
;
and
so
continually
the
augmentations
are
made
with
a
proportion
greater
and
greater
,
according
as
the
real
objects
that
increase
,
are
lesser
and
lesser
.
SAGR.
The
doubt
which
puzzled
Simplicius
never
troubled
me
,
but
certain
other
things
indeed
there
are
,
of
which
I
desire
a
more
distinct
understanding
;
and
in
particular
,
I
would
know
upon
what
ground
you
affirm
that
the
said
agrandizement
is
alwayes
equal
in
all
visible
objects
.
Objects
the
more
vigorous
they
are
in
light
,
the
more
they
do
seem
to
increase
.
SALV
.
I
have
already
declared
the
same
in
part
,
when
I
said
,
that
onely
lucid
objects
so
increased
,
and
not
the
obscure
;
now
I
adde
what
remaines
,
that
of
the
resplendent
objects
those
that
are
of
a
more
bright
light
,
make
the
reflection
greater
and
more
resplendent
upon
our
pupil
;
whereupon
they
seem
to
augment
much
more
than
the
lesse
lucid
:
and
that
I
may
no
more
inlarge
my self
upon
this
particular
,
come
we
to
that
which
the
true
Mistris
of
Astronomy
,
Experience
,
teacheth
us
.
Let
us
this
evening
,
when
the
air
is
very
obscure
,
observe
the
star
of
Jupiter
;
we
shall
see
it
very
glittering
,
An
easie
experiment
that
sheweth
the
increase
in
the
stars
,
by
means
of
the
adventitious
rays
.
and
very
great
;
let
us
afterwards
look
through
a
tube
,
or
else
through
a
small
trunk
,
which
clutching
the
hand
close
,
and
accosting
it
to
the
eye
,
we
lean
between
the
palm
of
the
hands
and
the
fingers
,
or
else
by
an
hole
made
with
a
small
needle
in
a
paper
;
and
we
shall
see
the
said
star
divested
of
its
beams
,
but
so
small
,
that
we
shall
judge
it
lesse
,
even
than
a
sixtieth
part
of
its
great
glittering
light
seen
with
the
eye
at
liberty
:
we
may
afterwards
behold
the
Dog-stars
beautiful
and
bigger
than
any
of
the
other
fixed
stars
,
Jupiter
augments
lesse
than
the
Dog-star
.
which
seemeth
to
the
bare
eye
no
great
matter
lesse
than
Jupiter
;
but
taking
from
it
,
as
before
,
the
irradiation
,
its
Discus
will
shew
so
little
,
that
it
will
not
be
thought
the
twentieth
part
of
that
of
Jupiter
,
nay
,
he
that
hath
not
very
good
eyes
,
will
very
hardly
discern
it
;
from
whence
it
may
be
rationally
inferred
,
that
the
said
star
,
as
having
a
much
more
lively
light
than
Jupiter
,
maketh
its
irradiation
greater
than
Jupiter
doth
his
.
In
the
next
place
,
as
to
the
irradiation
of
the
Sun
and
Moon
,
The
Sun
and
Moon
increase
little
.
it
is
as
nothing
,
by
means
of
their
magnitude
,
which
possesseth
of
it self
alone
so
great
a
space
in
our
eye
,
that
it
leaveth
no
place
for
the
adventitious
rayes
;
so
that
their
faces
seem
close
clipt
,
and
terminate
.
We
may
assure
our selves
of
the
same
truth
by
another
experiment
which
I
have
often
made
triall
of
;
we
may
assure
ourselves
,
It
is
seen
by
manifest
experience
,
that
the
more
splendid
bodies
do
much
more
irradiate
than
the
lesse
lucid
.
I
say
,
that
bodies
shining
with
most
lively
light
do
irradiate
,
or
beam
forth
rayes
more
by
far
than
those
that
are
of
a
more
languishing
light
.
I
have
many
times
seen
Jupiter
and
Venus
together
twenty
or
thirty
degrees
distant
from
the
Sun
,
and
the
air
being
very
dark
,
Venus
appeared
eight
or
ten
times
bigger
than
Jupiter
,
being
both
beheld
by
the
eye
at
liberty
;
but
being
beheld
afterwards
with
the
Telescope
,
the
Discus
of
Jupiter
discovered
it self
to
be
four
or
more
times
greater
than
that
of
Venus
,
but
the
vivacity
of
the
splendour
of
Venus
was
incomparably
bigger
than
the
languishing
light
of
Jupiter
;
which
was
only
because
of
Jupiters
being
far
from
the
Sun
,
and
from
us
;
and
Venus
neer
to
us
,
and
to
the
Sun
.
These
things
premised
,
it
will
not
be
difficult
to
comprehend
,
how
Mars
,
when
it
is
in
opposition
to
the
Sun
,
and
therefore
neerer
to
the
Earth
by
seven
times
,
and
more
,
than
it
is
towards
the
conjunction
,
cometh
to
appear
scarce
four
or
five
times
bigger
in
that
state
than
in
this
,
when
as
it
should
appear
more
than
fifty
times
so
much
;
of
which
the
only
irradiation
is
the
cause
;
for
if
we
divest
it
of
the
adventitious
rayes
,
we
shall
find
it
exactly
augmented
with
the
due
proportion
:
but
to
take
away
the
capillitious
border
,
The
Telescope
is
the
best
means
to
take
away
the
irradiations
of
the
Stars
.
the
Telescope
is
the
best
and
only
means
,
which
inlarging
its
Discus
nine
hundred
or
a
thousand
times
,
makes
it
to
be
seen
naked
and
terminate
,
as
that
of
the
Moon
,
Another
second
reason
of
the
small
apparent
increase
of
Venus
.
and
different
from
it self
in
the
two
positions
,
according
to
its
due
proportions
to
an
hair
.
Again
,
as
to
Venus
,
that
in
its
vespertine
conjunction
,
when
it
is
below
the
Sun
,
ought
to
shew
almost
fourty
times
bigger
than
in
the
other
matutine
conjunction
,
and
yet
doth
not
appear
so
much
as
doubled
;
it
happeneth
,
besides
the
effect
of
the
irradiation
,
that
it
is
horned
;
and
its
crescents
,
besides
that
they
are
sharp
,
they
do
receive
the
Suns
light
obliquely
,
and
therefore
emit
but
a
faint
splendour
;
so
that
as
being
little
and
weak
,
its
irradiation
becometh
the
lesse
ample
and
vivacious
,
than
when
it
appeareth
to
us
with
its
Hemisphere
all
shining
:
but
now
the
Telescope
manifestly
shews
its
hornes
to
have
been
as
terminate
and
distinct
as
those
of
the
Moon
,
and
appear
,
as
it
were
,
with
a
great
circle
,
and
in
a
proportion
those
well
neer
fourty
times
greater
than
its
same
Discus
,
at
such
time
as
it
is
superiour
to
the
Sun
in
its
ultimate
matutine
apparition
.
SAGR.
Oh
,
Nicholas
Copernicus
,
how
great
would
have
been
thy
joy
to
have
seen
this
part
of
thy
Systeme
,
confirmed
with
so
manifest
experiments
!
SALV
.
T
is
true
.
Copernicus
perswaded
by
reasons
contrary
to
sensible
experiments
.
But
how
much
lesse
the
fame
of
his
sublime
wit
amongst
the
intelligent
?
when
as
it
is
seen
,
as
I
also
said
before
,
that
he
did
constantly
continue
to
affirm
(
being
perswaded
thereto
by
reason
)
that
which
sensible
experiments
seemed
to
contradict
;
for
I
cannot
cease
to
wonder
that
he
should
constantly
persist
in
saying
,
that
Venus
revolveth
about
the
Sun
,
and
is
more
than
six
times
farther
from
us
at
one
time
,
than
at
another
;
and
also
seemeth
to
be
alwayes
of
an
equal
bigness
,
although
it
ought
to
shew
forty
times
bigger
when
nearest
to
us
,
than
when
farthest
off
.
SAGR.
But
in
Jupiter
,
Saturn
and
Mercury
,
I
believe
that
the
differences
of
their
apparent
magnitudes
,
should
seem
punctually
to
answer
to
their
different
distances
.
SALV
.
In
the
two
Superiour
ones
,
I
have
made
precise
observation
yearly
for
this
twenty
two
years
last
past
:
Mercury
admitteth
not
of
clear
observations
.
In
Mercury
there
can
be
no
observation
of
moment
made
,
by
reason
it
suffers
not
it self
to
be
seen
,
save
onely
in
its
greatest
dig●ssieons
from
the
Sun
,
in
which
its
distances
from
the
earth
are
insensibly
unequal
,
and
those
differences
consequently
not
to
be
observed
;
as
also
its
mutations
of
figures
which
must
absolutely
happen
in
it
,
as
in
Venus
.
And
if
we
do
see
it
,
it
must
of
necessity
appear
in
form
of
a
Semicircle
,
as
Venus
likewise
doth
in
her
greatest
digressions
;
but
its
discns
is
so
very
small
,
and
its
splendor
so
very
great
,
by
reason
of
its
vicinity
to
the
Sun
,
that
the
virtue
of
the
Telescope
doth
not
suffice
to
clip
its
tresses
or
adventitious
rayes
,
The
difficulties
removed
that
arise
from
the
Earths
moving
about
the
Sun
,
not
solitarily
,
but
in
consort
with
the
Moon
.
so
as
to
make
them
appear
shaved
round
about
.
It
remains
,
that
we
remove
that
which
seemed
a
great
inconvenience
in
the
motion
of
the
Earth
,
namely
that
all
the
Planets
moving
about
the
Sun
,
it
alone
,
not
solitary
as
the
rest
,
but
in
company
with
the
Moon
,
and
the
whole
Elementary
Sphear
,
should
move
round
about
the
Sun
in
a
year
;
and
that
the
said
Moon
withal
should
move
every
moneth
about
the
earth
.
Here
it
is
necessary
once
again
to
exclaim
and
extol
the
admirable
perspicacity
of
Copernicus
,
and
withal
to
condole
his
misfortune
,
in
that
he
is
not
now
alive
in
our
dayes
,
when
for
removing
of
the
seeming
absurdity
of
the
Earth
and
Moons
motion
in
consort
we
see
Jupiter
,
as
if
it
were
another
Earth
,
not
in
consort
with
the
Moon
,
but
accompanied
by
four
Moons
to
rovolve
about
the
Sun
in
12.
years
together
,
with
what
ever
things
the
Orbs
of
the
four
Medicaean
Stars
can
contain
within
them
.
SALV
.
Why
do
you
call
the
four
jovial
Planets
,
Moons
?
SAGR.
Such
they
would
seem
to
be
to
one
that
standing
in
Jupiter
should
behold
them
;
The
Medicean
Stars
areas
it
were
four
Moons
about
Jupiter
.
for
they
are
of
themselves
dark
,
and
receive
their
light
from
the
Sun
,
which
is
manifest
from
their
being
eclipsed
,
when
they
enter
into
the
cone
of
Jupiters
shadow
:
and
because
onely
those
their
Hemispheres
,
that
look
towards
the
Sun
are
illuminated
,
to
us
that
are
without
their
Orbs
,
and
nearer
to
the
Sun
,
they
seem
alwayes
lucid
,
but
to
one
that
should
be
in
Jupiter
,
they
would
shew
all
illuminated
,
at
such
time
as
they
were
in
the
upper
parts
of
their
circles
;
but
in
the
parts
inferiour
,
that
is
between
Jupiter
and
the
Sun
,
they
would
from
Jupiter
be
observed
to
be
horned
;
and
in
a
word
they
would
,
to
the
observators
standing
in
Jupiter
,
make
the
self
same
changes
of
Figure
,
that
to
us
upon
the
Earth
,
the
Moon
doth
make
.
You
see
now
how
these
three
things
,
which
at
first
seemed
dissonant
,
do
admirably
accord
with
the
Copernican
Systeme
.
Here
also
by
the
way
may
Simplicius
see
,
with
what
probability
one
may
conclude
,
that
the
Sun
and
not
the
Earth
,
is
in
the
Centre
of
the
Planetary
conversions
.
And
since
the
Earth
is
now
placed
amongst
mundane
Bodies
,
that
undoubtedly
move
about
the
Sun
,
to
wit
,
above
Mercury
and
Venus
,
and
below
Saturn
,
Jupiter
,
and
Mars
;
shall
it
not
be
in
like
manner
probable
,
and
perhaps
necessary
to
grant
,
that
it
also
moveth
round
?
SIMP.
These
accidents
are
so
notable
and
conspicuous
,
that
it
is
not
possible
,
but
that
Ptolomy
and
others
his
Sectators
,
should
have
had
knowledge
of
them
,
and
having
so
,
it
is
likewise
necessary
,
that
they
have
found
a
way
to
render
reasons
of
such
,
and
so
sensible
appearances
that
were
sufficient
,
and
also
congruous
and
probable
,
seeing
that
they
have
for
so
long
a
time
been
received
by
such
numbers
of
learned
men
.
SALV
.
You
argue
very
well
;
The
Principal
scope
of
Astronomers
,
is
to
give
a
reason
of
appearances
.
but
you
know
that
the
principal
scope
of
Astronomers
,
is
to
render
only
reason
for
the
appearances
in
the
Caelestial
Bodies
,
and
to
them
,
and
to
the
motions
of
the
Stars
,
to
accomodate
such
structures
and
compositions
of
Circles
,
that
the
motions
following
those
calculations
,
answer
to
the
said
appearances
,
little
scrupling
to
admit
of
some
exorbitances
,
that
indeed
upon
other
accounts
they
would
much
stick
at
.
And
Copernicus
himself
writes
,
Copernicus
restored
Astronomy
upon
the
suppositions
of
Ptolomy
.
that
he
had
in
his
first
studies
restored
the
Science
of
Astronomy
upon
the
very
suppositions
of
Ptolomy
,
and
in
such
manner
corrected
the
motions
of
the
Planets
,
that
the
computations
did
very
exactly
agree
with
the
Phaenomena
,
and
the
Phaenomena
with
the
supputations
,
in
case
that
he
took
the
Planets
severally
one
by
one
.
But
he
addeth
,
that
in
going
about
to
put
together
all
the
structures
of
the
particular
Fabricks
,
there
resulted
thence
a
Monster
and
Chimaera
,
composed
of
members
most
disproportionate
to
one
another
,
and
altogether
incompatible
;
So
that
although
it
satisfied
an
Astronomer
meerly
Arithmetical
,
yet
did
it
not
afford
satisfaction
or
content
to
the
Astronomer
Phylosophical
.
What
moved
Copernicus
to
establish
his
Systeme
.
And
because
he
very
well
understood
,
that
if
one
might
salve
the
Caelestial
appearances
with
false
assumptions
in
nature
,
it
might
with
much
more
ease
be
done
by
true
suppositions
,
he
set
himself
diligently
to
search
whether
any
amongst
the
antient
men
of
fame
,
had
ascribed
to
the
World
any
other
structure
,
than
that
commonly
received
by
Ptolomy
;
and
finding
that
some
Pythagoreans
had
in
particular
assigned
the
Diurnal
conversion
to
the
Earth
,
and
others
the
annual
motion
also
,
he
began
to
compare
the
appearances
,
and
particularities
of
the
Planets
motions
,
with
these
two
new
suppositions
,
all
which
things
jumpt
exactly
with
his
purpose
;
and
seeing
the
whole
correspond
,
with
admirable
facility
to
its
parts
,
he
imbraced
this
new
Systeme
,
and
it
took
up
his
rest
.
SIMP.
But
what
great
exorbitancies
are
there
in
the
Ptolomaick
Systeme
,
for
which
there
are
not
greater
to
be
found
in
this
of
Copernicus
?
SALV
.
In
the
Ptolomaick
Hypothesis
there
are
diseases
,
Inconveniencies
that
are
in
the
Systeme
of
Ptolomy
.
and
in
the
Copernican
their
cures
.
And
first
will
not
all
the
Sects
of
Phylosophers
,
account
it
a
great
inconvenience
,
that
a
body
naturally
moveable
in
circumgyration
,
should
move
irregularly
upon
its
own
Centre
,
and
regularly
upon
another
point
?
And
yet
there
are
such
deformed
motions
as
these
in
the
Ptolomaean
Hypothesis
,
but
in
the
Copernican
all
move
evenly
about
their
own
Centres
.
In
the
Ptolomaick
,
it
is
necessary
to
assign
to
the
Caelestial
bodies
,
contrary
motions
,
and
to
make
them
all
to
move
,
from
East
to
West
,
and
at
the
same
time
,
from
West
to
East
;
But
in
the
Copernican
,
all
the
Caelestial
revolutions
are
towards
one
onely
way
,
from
West
to
East
.
But
what
shall
we
say
of
the
apparent
motion
of
the
Planets
,
so
irregular
,
that
they
not
only
go
one
while
swift
,
and
another
while
slow
,
but
sometimes
wholly
seace
to
move
;
and
then
after
a
long
time
return
back
again
?
To
salve
which
appearances
Ptolomie
introduceth
very
great
Epicicles
,
accommodating
them
one
by
one
to
each
Planet
,
with
some
rules
of
incongruous
motions
,
which
are
all
with
one
single
motion
of
the
Earth
taken
away
.
And
would
not
you
,
Simplicius
,
call
it
a
great
absurditie
,
if
in
the
Ptolomaick
Hypothesis
,
in
which
the
particular
Planets
,
have
their
peculiar
Orbs
assigned
them
one
above
another
,
one
must
be
frequently
forced
to
say
,
that
Mars
,
constituted
above
the
Sphaere
of
the
Sun
,
doth
so
descend
,
that
breaking
the
Solar
Orb
,
it
goeth
under
it
,
and
approacheth
nearer
to
the
Earth
,
than
to
the
Body
of
the
Sun
,
and
by
and
by
immeasurably
ascendeth
above
the
same
?
And
yet
this
,
and
other
exorbitancies
are
remedied
by
the
sole
and
single
annual
motion
of
the
Earth
.
SAGR.
I
would
gladly
be
bettter
informed
how
these
stations
,
and
retrograde
and
direct
motions
,
which
did
ever
seem
to
me
great
improbalities
,
do
accord
in
this
Copernican
Systeme
.
SALV
.
You
see
,
Gentlemen
,
with
what
facility
and
simplicity
the
annual
motion
,
The
annual
motion
of
the
Earth
most
apt
to
render
a
reason
of
the
exorbitances
of
the
five
Planets
.
were
it
appertaining
to
the
Earth
,
is
accommodated
to
render
a
reason
of
the
apparent
exorbitances
,
that
are
observed
in
the
motions
of
the
five
Planets
,
Saturn
,
Jupiter
,
Mars
,
Venus
and
Mercury
,
taking
them
all
away
,
and
reducing
them
to
equal
and
regular
motions
.
The
Sun
it self
testifieth
the
annual
motion
to
belong
to
the
Earth
.
And
of
this
admirable
effect
,
Nicholas
Copernicus
,
hath
been
the
first
that
hath
made
the
reason
plain
unto
us
.
But
of
another
effect
,
no
lesse
admirable
than
this
,
and
that
with
a
knot
,
perhaps
more
difficult
to
unknit
,
bindeth
the
wit
of
man
,
to
admit
this
annual
conversion
,
and
to
leave
it
to
our
Terrestrial
Globe
;
a
new
and
unthought
of
conjecture
ariseth
from
the
Sun
it self
,
which
sheweth
that
it
is
unwilling
to
be
singular
in
shifting
,
of
this
attestation
of
so
eminent
a
conclusion
,
rather
as
a
testimony
beyond
all
exception
,
it
hath
desired
to
be
heard
apart
.
Hearken
then
to
this
great
and
new
wonder
.
The
first
discoverer
and
observer
of
the
Solar
spots
,
The
Lyncaean
Academick
the
first
discoverer
of
the
Solar
spots
,
and
all
the
other
celestial
novelties
.
as
also
of
all
the
other
Coelestial
novelties
,
was
our
Academick
Lincaeus
;
and
he
discovered
them
anno
1610.
being
at
that
time
Reader
of
the
Mathematicks
,
in
the
Colledge
of
Padua
,
and
there
,
and
in
Venice
,
The
history
of
the
proceedings
of
the
Academian
for
a
long
time
about
the
observation
of
the
Solar
spots
.
he
discoursed
thereof
with
several
persons
,
of
which
some
are
yet
living
:
And
the
year
following
,
he
shewed
them
in
Rome
to
many
great
personages
,
as
he
relates
in
the
first
of
his
Letters
to
Marcus
Velserus
,
[
](A61244-e75340-b)*
*
Duumviro
.
Sheriffe
of
Augusta
.
He
was
the
first
that
against
the
opinions
of
the
too
timorous
and
too
jealous
assertors
of
the
Heavens
inalterability
,
affirmed
those
spots
to
be
matters
,
that
in
short
times
were
produced
and
dissolved
:
for
as
to
place
,
they
were
contiguous
to
the
body
of
the
Sun
,
and
revolved
about
the
same
;
or
else
being
carried
about
by
the
said
Solar
body
,
which
revolveth
in
it selfe
about
its
own
Centre
,
in
the
space
almost
of
a
moneth
,
do
finish
their
course
in
that
time
;
which
motion
he
judged
at
first
to
have
been
made
by
the
Sun
about
an
Axis
erected
upon
the
plane
of
the
Ecliptick
;
in
regard
that
the
arches
described
by
the
said
spots
upon
the
Discus
of
the
Sun
appear
unto
our
eye
right
lines
,
and
parallels
to
the
plane
of
the
Ecliptick
:
which
therefore
come
to
be
altered
,
in
part
,
with
some
accidental
,
wandring
,
and
irregular
motions
,
to
which
they
are
subject
,
and
whereby
tumultuarily
,
and
without
any
order
they
successively
change
situations
amongst
themselves
,
one
while
crouding
close
together
,
another
while
dissevering
,
and
some
dividing
themselves
into
many
and
very
much
changing
figures
,
which
,
for
the
most
part
,
are
very
unusual
.
And
albeit
those
so
inconstant
mutations
did
somewhat
alter
the
primary
periodick
course
of
the
said
spots
,
yet
did
they
not
alter
the
opinion
of
our
friend
,
so
as
to
make
him
believe
,
that
they
were
any
essential
and
fixed
cause
of
those
deviations
,
but
he
continued
to
hold
,
that
all
the
apparent
alterations
derived
themselves
from
those
accidental
mutations
:
in
like
manner
,
just
as
it
would
happen
to
one
that
should
from
far
distant
Regions
observe
the
motion
of
our
Clouds
;
which
would
be
discovered
to
move
with
a
most
swift
,
great
,
and
constant
motion
,
carried
round
by
the
diurnal
Vertigo
of
the
Earth
(
if
haply
that
motion
belong
to
the
same
)
in
twenty
four
hours
,
by
circles
parallel
to
the
Equinoctial
,
but
yet
altered
,
in
part
,
by
the
accidental
motions
caused
by
the
winds
,
which
drive
them
,
at
all
adventures
,
towards
different
quarters
of
the
World
.
While
this
was
in
agitation
,
it
came
to
pass
that
Velserus
sent
him
two
Letters
,
written
by
a
certain
person
,
under
the
feigned
name
of
[
](A61244-e75390-b)*
*
This
Authors
true
name
is
Christopher
Scheinerus
a
Jesuit
,
and
his
Book
here
meant
is
intituled
,
Apelles
post
tabulam
.
Apelles
,
upon
the
subject
of
these
Spots
,
requesting
him
,
with
importunity
,
to
declare
his
thoughts
freely
upon
those
Letters
,
and
withall
to
let
him
know
what
his
opinion
was
touching
the
essence
of
those
spots
;
which
his
request
he
satisfied
in
3
Letters
,
shewing
first
of
all
howvain
the
conjectures
of
Apelles
were
;
&
discovering
,
secondly
,
his
own
opinions
;
withal
foretelling
to
him
,
that
Apelles
would
undoubtedly
be
better
advised
in
time
,
and
turn
to
his
opinion
,
as
it
afterwards
came
to
pass
.
And
because
that
our
Academian
(
as
it
was
also
the
judgment
of
many
others
that
were
intelligent
in
Natures
secrets
)
thought
he
had
in
those
three
Letters
investigated
and
demonstrated
,
if
not
all
that
could
be
desired
,
or
required
by
humane
curiosity
,
at
least
all
that
could
be
attained
by
humane
reason
in
such
a
matter
,
he
,
for
some
time
(
being
bufied
in
other
studies
)
intermitted
his
continual
observations
,
and
onely
in
complacency
to
some
friend
,
joyned
with
him
,
in
making
now
and
then
an
abrupt
observation
:
till
that
he
,
and
after
some
years
,
we
,
being
then
at
my
[
](A61244-e75450-b)*
*
La
mia
villa
delle
S●lue
.
Country-seat
,
met
with
one
of
the
solitary
Solar
spots
very
big
,
and
thick
,
invited
withal
by
a
clear
and
constant
serenity
of
the
Heavens
,
he
,
at
my
request
,
made
observations
of
the
whole
progresse
of
the
said
spot
,
carefully
marking
upon
a
sheet
of
paper
the
places
that
it
was
in
every
day
at
the
time
of
the
Suns
coming
into
the
Meridian
;
and
we
having
found
that
its
course
was
not
in
a
right
line
,
but
somewhat
incurvated
,
we
came
to
resolve
,
at
last
,
to
make
other
observations
from
time
to
time
;
to
which
undertaking
we
were
strongly
induced
by
a
conceit
,
that
accidentally
came
into
the
minde
of
my
Guest
,
which
he
imparted
to
me
in
these
or
the
like
words
.
In
my
opinion
,
Philip
,
there
is
a
way
opened
to
a
business
of
very
great
consequence
.
For
if
the
Axis
about
which
the
Sun
turneth
be
not
erect
perpendicularly
to
the
plane
of
the
Ecliptick
,
A
conceipt
that
came
suddenly
into
the
minde
of
the
Academian
Lyncaeus
concerning
the
great
consequence
that
followed
upon
the
motion
of
the
Solar
spots
.
but
is
inclined
upon
the
same
,
as
its
crooked
course
,
but
even
now
observed
,
makes
me
believe
,
we
shall
be
able
to
make
such
conjectures
of
the
states
of
the
Sun
and
Earth
,
as
neither
so
solid
or
so
rational
have
been
hitherto
deduced
from
any
other
accident
whatsoever
.
I
being
awakened
at
so
great
a
promise
,
importun'd
him
to
make
a
free
discovery
of
his
conceit
unto
me
.
And
he
continued
his
discourse
to
this
purpose
.
Extravagant
mutations
to
be
observed
in
the
motions
of
the
spots
,
foreseen
by
the
Academick
,
in
case
the
Earth
had
the
annual
motion
.
If
the
Earths
motion
were
along
the
Ecliptique
about
the
Sun
;
and
the
Sun
were
constituted
in
the
centre
of
the
said
Ecliptick
,
and
therein
revolved
in
its
self
,
not
about
the
Axis
of
the
said
Ecliptique
(
which
would
be
the
Axis
of
the
Earths
annual
motion
)
but
upon
one
inclined
,
it
must
needs
follow
,
that
strange
changes
will
represent
themselves
to
us
in
the
apparent
motions
of
the
Solar
spots
,
although
the
said
Axis
of
the
Sun
should
be
supposed
to
persist
perpetually
and
immutably
in
the
same
inclination
,
and
in
one
and
the
same
direction
towards
the
self-same
point
of
the
Universe
.
Therefore
the
Terrestrial
Globe
in
the
annual
motion
moving
round
it
,
it
will
first
follow
,
that
to
us
,
carried
about
by
the
same
,
the
courses
of
the
spots
shall
sometimes
seem
to
be
made
in
right
lines
,
but
this
only
twice
a
year
,
and
at
all
other
times
shall
appear
to
be
made
by
arches
insensibly
incurvated
.
Secondly
,
the
curvity
of
those
arches
for
one
half
of
the
year
,
will
shew
inclined
the
contrary
way
to
what
they
will
appear
in
the
other
half
;
that
is
,
for
six
moneths
the
convexity
of
the
arches
shall
be
towards
the
upper
part
of
the
Solar
Discus
,
and
for
the
other
six
moneths
towards
the
inferiour
.
Thirdly
,
the
spots
beginning
to
appear
,
and
(
if
I
may
so
speak
)
to
rise
to
our
eye
from
the
left
side
of
the
Solar
Discus
,
and
going
to
hide
themselves
and
to
set
in
the
right
side
,
the
Oriental
termes
,
that
is
,
of
their
first
appearings
for
six
moneths
,
shall
be
lower
than
the
opposite
termes
of
their
occultations
;
and
for
other
six
moneths
it
shall
happen
contrarily
,
to
wit
,
that
the
said
spots
rising
from
more
elevated
points
,
and
from
them
descending
,
they
shall
,
in
their
courses
,
go
and
hide
themselves
in
lower
points
;
and
onely
for
two
dayes
in
all
the
year
shall
those
termes
of
risings
and
settings
be
equilibrated
:
after
which
freely
beginning
by
small
degrees
the
inclination
of
the
courses
of
the
spots
,
and
day
by
day
growing
bigger
,
in
three
moneths
,
it
shall
arrive
at
its
greatest
obliquity
,
and
from
thence
beginning
to
diminish
,
in
such
another
time
it
shall
reduce
it self
to
the
other
Aequilibrium
.
It
shall
happen
,
for
a
fourth
wonder
,
that
the
course
of
the
greatest
obliquity
shall
be
the
same
with
the
course
made
by
the
right
line
,
and
in
the
day
of
the
Libration
the
arch
of
the
course
shall
seem
more
than
ever
incurvated
.
Again
,
in
the
other
times
,
according
as
the
pendency
shall
successively
diminish
,
and
make
it
approach
towards
the
Aequilibrium
,
the
incurvation
of
the
arches
of
the
courses
on
the
contrary
shall
,
by
degrees
,
increase
.
SAGR.
I
confesse
,
Salviatus
,
that
to
interrupt
you
in
your
Discourse
is
ill
manners
,
but
I
esteem
it
no
lesse
rudeness
to
permit
you
to
run
on
any
farther
in
words
,
whilst
they
are
,
as
the
saying
is
,
cast
into
the
air
:
for
,
to
speak
freely
,
I
know
not
how
to
form
any
distinct
conceit
of
so
much
as
one
of
these
conclusions
,
that
you
have
pronounced
;
but
because
,
as
I
thus
generally
and
confusedly
apprehend
them
,
they
hold
forth
things
of
admirable
consequence
,
I
would
gladly
,
some
way
or
other
,
be
made
to
understand
the
same
.
SALV
.
The
same
that
befalls
you
,
befell
me
also
,
whilst
my
Guest
transported
me
with
bare
words
;
who
afterwards
assisted
my
capacity
,
The
first
Accident
to
be
observed
in
the
motion
of
the
Solar
spots
;
and
consequently
all
the
rest
explained
.
by
describing
the
businesse
upon
a
material
Instrument
,
which
was
no
other
than
a
simple
Sphere
,
making
use
of
some
of
its
circles
,
but
to
a
different
purpose
from
that
,
to
which
they
are
commonly
applied
.
Now
I
will
supply
the
defect
of
the
Sphere
,
by
drawing
the
same
upon
a
piece
of
paper
,
as
need
shall
require
.
And
to
represent
the
first
accident
by
me
propounded
,
which
was
,
that
the
courses
or
journeys
of
the
spots
,
twice
a
year
,
and
no
more
,
might
be
seen
to
be
made
in
right
lines
,
let
us
suppose
this
point
O
[
in
Fig.
4.
]
to
be
the
centre
of
the
grand
Orb
,
or
,
if
you
will
,
of
the
Ecliptick
,
and
likewise
also
of
the
Globe
of
the
Sun
it self
;
of
which
,
by
reason
of
the
great
distance
that
is
between
it
and
the
Earth
,
we
that
live
upon
the
Earth
,
may
suppose
that
we
see
the
one
half
:
we
will
therefore
describe
this
circle
ABCD
about
the
said
centre
O
,
which
representeth
unto
us
the
extream
term
that
divideth
and
separates
the
Hemisphere
of
the
Sun
that
is
apparent
to
us
,
from
the
other
that
is
occult
.
And
because
that
our
eye
,
no
lesse
than
the
centre
of
the
Earth
,
is
understood
to
be
in
the
plane
of
the
Ecliptick
,
in
which
is
likewise
the
centre
of
the
Sun
,
therefore
,
if
we
should
fancy
to
our selves
the
body
of
the
Sun
to
be
cut
thorow
by
the
said
plane
,
the
section
will
appear
to
our
eye
a
right
line
,
which
let
be
BOD
,
and
upon
that
a
perpendicular
being
let
fall
AOC
,
it
shall
be
the
Axis
of
the
said
Ecliptick
,
and
of
the
annual
motion
of
the
Terrestrial
Globe
.
Let
us
next
suppose
the
Solar
body
(
without
changing
centre
)
to
revolve
in
it self
,
not
about
the
Axis
AOC
(
which
is
the
erect
Axis
upon
the
plane
of
the
Ecliptick
)
but
about
one
somewhat
inclined
,
which
let
be
this
EOI
,
the
which
fixed
and
unchangeable
Axis
maintaineth
it self
perpetually
in
the
same
inclination
and
direction
towards
the
same
points
of
the
Firmament
,
and
of
the
Universe
.
And
because
,
in
the
revolutions
of
the
Solar
Globe
,
each
point
of
its
superficies
(
the
Poles
excepted
)
describeth
the
circumference
of
a
circle
,
either
bigger
or
lesser
,
according
as
it
is
more
or
lesse
remote
from
the
said
Poles
,
let
us
take
the
point
F
,
equally
distant
from
them
,
and
draw
the
diameter
FOG
,
which
shall
be
perpendicular
to
the
Axis
EI
,
and
shall
be
the
diameter
of
the
grand
circle
described
about
the
Poles
EI.
Supposing
not
that
the
Earth
,
and
we
with
her
be
in
such
a
place
of
the
Ecliptick
,
that
the
Hemisphere
of
the
Sun
to
us
apparent
is
determin'd
or
bounded
by
the
circle
ABCD
,
which
passing
(
as
it
alwayes
doth
)
by
the
Poles
AC
,
passeth
also
by
EI.
It
is
manifest
,
that
the
grand
circle
,
whose
diameter
is
FG
,
shall
be
erect
to
the
circle
ABCD
,
to
which
the
ray
that
from
our
eye
falleth
upon
the
centre
O
,
is
perpendicular
;
so
that
the
said
ray
falleth
upon
the
plane
of
the
circle
,
whose
diameter
is
FG
,
and
therefore
its
circumference
will
appear
to
us
a
right
line
,
and
the
self
same
with
FG
,
whereupon
if
there
should
be
in
the
point
F
,
a
spot
,
it
comming
afterwards
to
be
carried
about
by
the
Solar
conversion
,
would
,
upon
the
surface
of
the
Sun
,
trace
out
the
circumference
of
that
circle
,
which
seems
to
us
a
right
line
.
It
s
course
or
passage
will
therefore
seem
straight
.
And
straight
also
will
the
motion
of
the
other
spots
appear
,
which
in
the
said
revolution
shall
describe
lesser
circles
,
as
being
all
parallel
to
the
greater
,
and
to
our
eye
placed
at
an
immense
distance
from
them
.
Now
,
if
you
do
but
consider
,
how
that
after
the
Earth
shall
in
six
moneths
have
run
thorow
half
the
grand
Orb
,
and
shall
be
situate
opposite
to
that
Hemisphere
of
the
Sun
,
which
is
now
occult
unto
us
,
so
as
that
the
boundary
of
the
part
that
then
shall
be
seen
,
may
be
the
self
same
ABCD
,
which
also
shall
passe
by
the
Poles
EI
;
you
shall
understand
that
the
same
will
evene
in
the
courses
of
the
spots
,
as
before
,
to
wit
,
that
all
will
appear
to
be
made
by
right
lines
.
But
because
that
that
accident
takes
not
place
,
save
onely
when
the
teminator
or
boundary
passeth
by
the
Poles
EI
,
and
the
said
terminator
from
moment
to
moment
,
by
meanes
of
the
Earths
annual
motion
,
continually
altereth
,
therefore
its
passage
by
the
fixed
Poles
EI
,
shall
be
momentary
,
and
consequently
momentary
shall
be
the
time
,
in
which
the
motions
of
those
spots
shall
appear
straight
.
From
what
hath
been
hitherto
spoken
one
may
comprehend
also
how
that
the
apparition
and
beginning
of
the
motion
of
the
spots
from
the
part
F
,
proceeding
towards
G
,
their
passages
or
courses
are
from
the
left
hand
,
ascending
towards
the
right
;
but
the
Earth
being
placed
in
the
part
diametrically
opposite
the
appearance
of
the
spots
about
G
,
shall
still
be
to
the
left
hand
of
the
beholder
,
but
the
passage
shall
be
descending
towards
the
right
hand
F.
Let
us
now
describe
the
Earth
to
be
situate
one
fourth
part
farther
distant
from
its
present
state
,
and
let
us
draw
,
as
in
the
other
figure
,
the
terminator
ABCD
,
[
as
in
Fig.
5.
]
and
the
Axis
,
as
before
AC
,
by
which
the
plane
of
our
Meridian
would
passe
,
in
which
plane
should
also
be
the
Axis
of
the
Suns
revolution
,
with
its
Poles
,
one
towards
us
,
that
is
,
in
the
apparent
Hemisphere
,
which
Pole
we
will
represent
by
the
point
E
,
and
the
other
shall
fall
in
the
occult
Hemisphere
,
and
I
mark
it
I.
Inclining
therefore
the
Axis
EI
,
with
the
superiour
part
E
,
towards
us
,
the
great
circle
described
by
the
Suns
conversion
,
shall
be
this
BFDG
,
whose
half
by
us
seen
,
namely
BFD
,
shall
no
longer
seem
unto
us
a
right
line
,
by
reason
the
Poles
EI
are
not
in
the
circumference
ABCD
,
but
shall
appear
incurvated
,
and
with
its
convexity
towards
the
inferiour
part
C.
And
it
is
manifest
,
that
the
same
will
appear
in
all
the
lesser
circles
parallel
to
the
same
BFD
.
It
is
to
be
understood
also
,
that
when
the
Earth
shall
be
diametrically
opposite
to
this
state
,
so
that
it
seeth
the
other
Hemisphere
of
the
Sun
,
which
now
is
hid
,
it
shall
of
the
said
great
circle
behold
the
part
DGB
incurved
,
with
its
convexity
towards
the
superiour
part
A
;
and
the
courses
of
the
spots
in
these
constitutions
shall
be
first
,
by
the
arch
BFD
,
and
afterwards
by
the
other
DGB
,
and
the
first
apparitions
and
ultimate
occultations
made
about
the
points
B
and
D
,
shall
be
equilibrated
,
and
not
those
that
are
more
or
lesse
elevated
than
these
.
But
if
we
constitute
the
Earth
in
such
a
place
of
the
Ecliptick
,
that
neither
the
boundary
ABCD
,
nor
the
Meridian
AC
,
passeth
by
the
Poles
of
the
Axis
EI
,
as
I
will
shew
you
anon
,
drawing
this
other
Figure
[
viz.
Fig.
6.
]
wherein
the
apparent
or
visible
Pole
E
falleth
between
the
arch
of
the
terminator
AB
,
and
the
section
of
the
Meridian
AC
;
the
diameter
of
the
great
circle
shall
be
FOG
,
and
the
apparent
semicircle
FNG
,
and
the
occult
semicircle
GSF
,
the
one
incurvated
with
its
convexity
N
towards
the
inferiour
part
,
and
the
other
also
bending
with
its
convexity
S
towards
the
upper
part
of
the
Sun
.
The
ingressions
and
exitions
of
the
spots
,
that
is
,
the
termes
F
and
G
shall
not
be
librated
,
as
the
two
others
B
and
D
;
but
F
shall
be
lower
,
and
G
higher
:
but
yet
with
lesser
difference
than
in
the
first
Figure
.
The
arch
also
FNG
shall
be
incurvated
,
but
not
so
much
as
the
precedent
BFD
;
so
that
in
this
position
the
passages
or
motions
of
the
spots
shall
be
ascendent
from
the
left
side
F
,
towards
the
right
G
,
and
shall
be
made
by
curved
lines
.
And
imagining
the
Earth
to
be
constituted
in
the
position
diametrically
opposite
;
so
that
the
Hemisphere
of
the
Sun
,
which
was
before
the
occult
,
may
be
the
apparent
,
and
terminated
by
the
same
boundary
ABCD
,
it
will
be
manifestly
discerned
,
that
the
course
of
the
spots
shall
be
by
the
arch
GSF
,
beginning
from
the
upper
point
G
,
which
shall
then
be
likewise
from
the
left
hand
of
the
beholder
,
and
going
to
determine
,
descending
towards
the
right
,
in
the
point
F.
What
I
have
hitherto
said
,
being
understood
,
I
believe
that
there
remains
no
difficulty
in
conceiving
how
from
the
passing
of
the
terminator
of
the
Solar
Hemispheres
by
the
Poles
of
the
Suns
conversion
,
or
neer
or
far
from
the
same
,
do
arise
all
the
differences
in
the
apparent
courses
of
the
spots
;
so
that
by
how
much
the
more
those
Poles
shall
be
remote
from
the
said
terminator
,
by
so
much
the
more
shall
those
courses
be
incurvated
,
and
lesse
oblique
;
whereupon
at
the
same
distance
,
that
is
,
when
those
Poles
are
in
the
section
of
the
Meridian
,
the
incurvation
is
reduced
to
the
greatest
,
but
the
obliquity
to
the
least
,
that
is
to
Aequilibrium
,
as
the
second
of
these
three
last
figures
[
viz.
Fig.
5.
]
demonstrateth
.
On
the
contrary
,
when
the
Poles
are
in
the
terminator
,
as
the
first
of
these
three
figures
[
viz.
Fig.
4.
]
sheweth
the
inclination
is
at
the
greatest
,
but
the
incurvation
at
the
least
,
and
reduced
to
rectitude
.
The
terminator
departing
from
the
Poles
,
the
curvity
begins
to
grow
sensible
,
the
obliquity
all
the
way
encreasing
,
and
the
inclination
growing
lesser
.
These
are
those
admirable
and
extravagant
mutations
,
that
my
Guest
told
me
would
from
time
to
time
appear
in
the
progresses
of
the
Solar
spots
,
if
so
be
it
should
be
true
that
the
annual
motion
belonged
to
the
Earth
,
and
that
the
Sun
being
constituted
in
the
centre
of
the
Ecliptick
,
were
revolved
in
it self
upon
an
Axis
,
not
erect
,
but
inclined
to
the
Plane
of
the
said
Ecliptick
.
SAGR.
I
do
now
very
well
apprehend
these
consequences
,
and
believe
that
they
will
be
better
imprinted
in
my
fancy
,
when
I
shall
come
to
reflect
upon
them
,
accommodating
a
Globe
to
those
inclinations
,
and
then
beholding
them
from
several
places
.
It
now
remains
that
you
tell
us
what
followed
afterwards
touching
the
event
of
these
imaginary
consequences
.
SALV
.
It
came
to
passe
thereupon
,
The
events
being
observed
,
were
answerable
to
the
predictions
.
that
continuing
many
several
moneths
to
make
most
accurate
observations
,
noting
down
with
great
exactnesse
the
courses
or
transitions
of
sundry
spots
at
divers
times
of
the
year
,
we
found
the
events
punctually
to
correspond
to
the
predictions
.
SAGR.
Simplicius
,
if
this
which
Salviatus
saith
be
true
;
(
nor
can
we
distrust
him
upon
his
word
)
the
Ptolomeans
and
Aristoteleans
had
need
of
solid
arguments
,
strong
conjectures
,
and
well
grounded
experiments
to
counterpoise
an
objection
of
so
much
weight
,
and
to
support
their
opinion
from
its
final
overthrow
.
SIMP.
Fair
and
softly
good
Sir
,
for
haply
you
may
not
yet
be
got
▪
so
far
as
you
perswade
your self
you
are
gone
.
And
though
I
am
not
an
absolute
master
of
the
subject
of
that
narration
given
us
by
Salviatus
;
Though
the
annual
motion
assigned
to
the
Earth
answerth
to
the
Phaenomena
of
the
solar
spots
,
yet
doth
it
not
follow
by
conversion
that
from
the
Phaenomena
of
the
spots
one
may
inf●r
the
annual
motion
to
belong
to
the
Earth
.
yet
do
I
not
find
that
my
Logick
,
whilst
I
have
a
regard
to
form
,
teacheth
me
,
that
that
kind
of
argumentation
affords
me
any
necessary
reason
to
conclude
in
favour
of
the
Copernican
Hypothesis
,
that
is
,
of
the
stability
of
the
Sun
in
the
centre
of
the
Zodiack
,
and
of
the
mobility
of
the
Earth
under
its
circumference
.
For
although
it
be
true
,
that
the
said
conversion
of
the
Sun
,
and
cirnition
of
the
Earth
being
granted
,
there
be
a
necessity
of
discerning
such
and
such
strange
extravagancies
as
these
in
the
spots
of
the
Sun
,
yet
doth
it
not
follow
that
arguing
per
conversum
,
from
finding
such
like
unusual
accidents
in
the
Sun
,
one
must
of
necssity
conclude
the
Earth
to
move
by
the
circumference
,
and
the
Sun
to
be
placed
in
the
centre
of
the
Zodiack
.
For
who
shall
assertain
me
that
the
like
irregularities
may
not
as
well
be
visible
in
the
Sun
,
it
being
moveable
by
the
Ecliptick
,
to
the
inhabitants
of
the
Earth
,
it
being
also
immoveable
in
the
centre
of
the
same
?
Unlesse
you
demonstrate
to
me
,
that
there
can
be
no
reason
given
for
that
appearance
,
when
the
Sun
is
made
moveable
,
and
the
Earth
stable
,
I
will
not
alter
my
opinion
and
belief
that
the
Sun
moveth
,
and
the
Earth
standeth
still
.
SAGR.
Simplicius
behaveth
himself
very
bravely
,
and
argueth
very
subtilly
in
defence
of
the
cause
of
Aristotle
and
Ptolomy
;
and
if
I
may
speak
the
truth
,
mythinks
that
the
conversation
of
Salviatus
,
though
it
have
been
but
of
small
continuance
,
hath
much
farthered
him
in
discoursing
silogistically
.
An
effect
which
I
know
to
be
wrought
in
others
as
well
as
him
.
But
as
to
finding
and
judging
whether
competent
reason
may
be
rendered
of
the
apparent
exorbitancies
and
irregularities
in
the
motions
of
the
spots
,
supposing
the
Earth
to
be
immoveable
,
and
the
Sun
moveable
,
I
shall
expect
that
Salviatus
manifest
his
opinion
to
us
,
for
it
is
very
probable
that
he
he
hath
considered
of
the
same
,
and
collected
together
whatever
may
be
said
upon
the
point
.
SALV
.
I
have
often
thought
thereon
,
and
also
discoursed
thereof
with
my
Friend
and
Guest
afore-named
;
and
touching
what
is
to
be
produced
by
Philosophers
and
Astronomers
,
in
defence
of
the
ancient
Systeme
,
we
are
on
one
hand
certain
,
certain
I
say
,
The
Pure
Peripatetick
Philosophers
will
laugh
at
the
spots
and
their
Phaenomena
,
as
illusions
of
the
Chrystals
in
the
Telescope
.
that
the
true
and
pure
Peripateticks
laughing
at
such
as
employ
themselves
in
such
,
to
their
thinking
,
insipid
fooleries
,
will
censure
all
these
Phaenomena
to
be
vain
illusions
of
the
Christals
;
and
in
this
manner
will
with
little
trouble
free
themselves
from
the
obligation
of
studying
any
more
upon
the
same
.
Again
,
as
to
the
Astronomical
Philosophers
,
after
we
have
with
some
diligence
weighed
that
which
may
be
alledged
as
a
mean
between
those
two
others
,
we
have
not
been
able
to
find
out
an
answer
that
sufficeth
to
satisfie
at
once
the
course
of
the
spots
,
and
the
discourse
of
the
Mind
.
I
will
explain
unto
you
so
much
as
I
remember
thereof
,
that
so
you
may
judge
thereon
as
seems
best
unto
you
.
Supposing
that
the
apparent
motions
of
the
Solar
spots
are
the
same
with
those
that
have
been
above
declared
,
and
supposing
the
Earth
to
be
immoveable
in
the
centre
of
the
Ecliptick
,
in
whose
circumference
let
the
center
of
the
Sun
be
placed
;
it
is
necessary
that
of
all
the
differences
that
are
seen
in
those
motions
,
the
causes
do
reside
in
the
motions
that
are
in
the
body
of
the
Sun
:
Which
in
the
first
place
must
necessarily
revolve
in
it self
(
i.
e.
about
its
own
axis
)
carrying
the
spots
along
therewith
;
If
the
Earth
be
immoveable
in
the
centre
of
the
Zodiack
,
there
must
be
ascribed
to
the
Sun
four
several
motions
,
as
is
declared
at
length
.
which
spots
have
been
supposed
,
yea
and
proved
to
adhere
to
the
Solar
superficies
.
It
must
secondly
be
confest
,
that
the
Axis
of
the
Solar
conversion
is
not
parallel
to
the
Axis
of
the
Ecliptick
,
that
is
as
much
as
to
say
,
that
it
is
not
perpendicularly
erected
upon
the
Plane
of
the
Ecliptick
,
because
if
it
were
so
,
the
courses
and
exitions
of
those
spots
would
seem
to
be
made
by
right
lines
parallel
to
the
Ecliptick
.
The
said
Axis
therefore
is
inclining
,
in
regard
the
said
courses
are
for
the
most
part
made
by
curve
lines
.
It
will
be
necessary
in
the
third
place
to
grant
that
the
inclination
of
this
Axis
is
not
fixed
,
and
continually
extended
towards
one
and
the
same
point
of
the
Universe
,
but
rather
that
it
doth
alwayes
from
moment
to
moment
go
changing
its
direction
;
for
if
the
pendency
should
always
look
towards
the
self
same
point
,
the
courses
of
the
spots
would
never
change
appearance
;
but
appearing
at
one
time
either
right
or
curved
,
bending
upwards
or
downwards
,
ascending
or
descending
,
they
would
appear
the
same
at
all
times
.
It
is
therefore
necessary
to
say
,
that
the
said
Axis
is
convertible
;
and
is
sometimes
found
to
be
in
the
Plane
of
the
circle
that
is
extreme
,
terminate
,
or
of
the
visible
Hemisphere
,
I
mean
at
such
time
as
the
courses
of
the
spots
seem
to
be
made
in
right
lines
,
and
more
than
ever
pendent
,
which
happeneth
twice
a
year
;
and
at
other
times
found
to
be
in
the
Plane
of
the
Meridian
of
the
Observator
,
in
such
sort
that
one
of
its
Poles
falleth
in
the
visible
Hemisphere
of
the
Sun
,
and
the
other
in
the
occult
;
and
both
of
them
remote
from
the
extreme
points
,
or
we
may
say
,
from
the
poles
of
another
Axis
of
the
Sun
,
which
is
parallel
to
the
Axis
of
the
Ecliptick
;
(
which
second
Axis
must
necessarily
be
assigned
to
the
Solar
Globe
)
remote
,
I
say
,
as
far
as
the
inclination
of
the
Axis
of
the
revolution
of
the
spots
doth
import
;
and
moreover
that
the
Pole
falling
in
the
apparent
Hemisphere
,
is
one
while
in
the
superiour
,
another
while
in
the
inferiour
part
thereof
;
for
that
it
must
be
so
,
the
courses
themselves
do
manifestly
evince
at
such
time
as
they
are
equilibrated
,
and
in
their
greatest
curvity
,
one
while
with
their
convexity
towards
the
upper
part
,
and
another
while
towards
the
lower
part
of
the
Solar
Discus
.
And
because
those
positions
are
in
continuall
alteration
,
making
the
inclinations
and
incurvations
now
greater
,
now
lesser
,
and
sometimes
reduce
themselves
,
the
first
sort
to
perfect
libration
,
and
the
second
to
perfect
perpendicularity
,
it
is
necessary
to
assert
that
the
self
same
Axis
of
the
monethly
revolution
of
the
spots
hath
a
particular
revolution
of
its
own
,
whereby
its
Poles
describe
two
circles
about
the
Poles
of
another
Axis
,
which
for
that
reason
ought
(
as
I
have
said
)
to
be
assigned
to
the
Sun
,
the
semidiameter
of
which
circles
answereth
to
the
quantity
of
the
inclination
of
the
said
Axis
.
And
it
is
necessary
,
that
the
time
of
its
Period
be
a
year
;
for
that
such
is
the
time
in
which
all
the
appearances
and
differences
in
the
courses
of
the
spots
do
return
.
And
that
the
revolution
of
this
Axis
,
is
made
about
the
Poles
of
the
other
Axis
parallel
to
that
of
the
Ecliptick
,
&
not
about
other
points
,
the
greatest
inclinations
and
greatest
incurvations
,
which
are
always
of
the
same
bigness
,
do
clearly
prove
.
So
that
finally
,
to
maintain
the
Earth
fixed
in
the
centre
,
it
will
be
necessary
to
assign
to
the
Sun
,
two
motions
about
its
own
centre
,
upon
two
several
Axes
,
one
of
which
finisheth
its
conversion
in
a
year
,
and
the
other
in
lesse
than
a
moneth
;
which
assumption
seemeth
,
to
my
understanding
,
very
hard
,
and
almost
impossible
;
and
this
dependeth
on
the
necessity
of
ascribing
to
the
said
Solar
body
two
other
motions
about
the
Earth
upon
different
Axes
,
describing
with
one
the
Ecliptick
in
a
year
,
and
with
the
other
forming
spirals
,
or
circles
parallel
to
the
Equinoctial
one
every
day
:
whereupon
that
third
motion
which
ought
to
be
assigned
to
the
Solar
Clobe
about
its
own
centre
(
I
mean
not
that
almost
monethly
,
which
carrieth
the
spots
about
,
but
I
speak
of
that
other
which
ought
to
passe
thorow
the
Axis
and
Poles
of
this
monethly
one
)
ought
not
,
for
any
reason
that
I
see
,
to
finish
its
Period
rather
in
a
year
,
as
depending
on
the
annual
motion
by
the
Ecliptick
,
than
in
twenty
four
hours
,
as
depending
on
the
diurnal
motion
upon
the
Poles
of
the
Equinoctial
.
I
know
,
that
what
I
now
speak
is
very
obscure
,
but
I
shall
make
it
plain
unto
you
,
when
we
come
to
speak
of
the
third
motion
annual
,
assigned
by
Copernicus
,
to
the
Earth
.
Now
if
these
four
motions
,
so
incongruous
with
each
other
,
(
all
which
it
would
be
necessary
to
assign
to
the
self
same
body
of
the
Sun
)
may
be
reduced
to
one
sole
and
simple
motion
,
assigned
the
Sun
upon
an
Axis
that
never
changeth
position
,
and
that
without
innovating
any
thing
in
the
motions
for
so
many
other
causes
assigned
to
the
Terrestrial
Globe
,
may
so
easily
salve
so
many
extravagant
appearances
in
the
motions
of
the
Solar
spots
,
it
seemeth
really
that
such
an
Hypothesis
ought
not
to
be
rejected
.
This
,
Simplicius
,
is
all
that
came
into
the
minds
of
our
friend
,
and
my self
,
that
could
be
alledged
in
explanation
of
this
Phaenomenon
by
the
Copernicans
,
and
by
the
Ptolomaeans
,
in
defence
of
their
opinions
.
Do
you
inferre
from
thence
what
your
judgment
perswades
you
.
SIMP.
I
acknowledge
my self
unable
to
interpose
in
so
important
a
decision
:
And
,
as
to
my
particular
thoughts
,
I
will
stand
neutral
;
and
yet
neverthelesse
I
hope
that
a
time
will
come
,
when
our
minds
being
illumin'd
by
more
lofty
contemplations
than
these
our
humane
reasonings
,
we
shall
be
awakened
and
freed
from
that
mist
which
now
is
so
great
an
hinderance
to
our
sight
.
SAGR.
Excellent
and
pious
is
the
counsel
taken
by
Simplicius
,
and
worthy
to
be
entertained
and
followed
by
all
,
as
that
which
being
derived
from
the
highest
wisdome
and
supreamest
authority
,
may
onely
,
with
security
be
received
.
But
yet
so
far
as
humane
reason
is
permitted
to
penetrate
,
confining
my self
within
the
bounds
of
conjectures
,
and
probable
reasons
,
I
will
say
a
little
more
resolutely
than
Simplicius
doth
,
that
amongst
all
the
ingenuous
subtilties
I
ever
heard
,
I
have
never
met
with
any
thing
of
greater
admiration
to
my
intellect
,
nor
that
hath
more
absolutely
captivated
my
judgment
,
(
alwayes
excepting
pure
Geometrical
and
Arithmetical
Demonstrations
)
than
these
two
conjectures
taken
,
the
one
from
the
stations
and
retrogradations
of
the
five
Planets
,
and
the
other
from
these
irregularities
of
the
motions
of
the
Solar
spots
:
and
because
they
seem
to
me
so
easily
and
clearly
to
assign
the
true
reason
of
so
extravagant
appearances
,
shewing
as
if
they
were
but
one
sole
simple
motion
,
mixed
with
so
many
others
,
simple
likewise
,
but
different
from
each
other
,
without
introducing
any
difficulty
,
rather
with
obviating
those
that
accompany
the
other
Hypothesis
;
I
am
thinking
that
I
may
rationally
conclude
,
that
those
who
contumaciously
withstand
this
Doctrine
,
either
never
heard
,
or
never
understood
,
these
so
convincing
arguments
.
SALV
.
I
will
not
ascribe
unto
them
the
title
either
of
convincing
,
or
non-convincing
;
in
regard
my
intention
is
not
,
as
I
have
several
times
told
you
,
to
resolve
any
thing
upon
so
high
a
question
,
but
onely
to
propose
those
natural
and
Astronomicall
reasons
,
which
,
for
the
one
and
other
Systeme
,
may
be
produced
by
me
,
leaving
the
determination
to
others
;
which
determination
cannot
at
last
,
but
be
very
manifest
:
for
one
of
the
two
positions
being
of
necessity
to
be
true
,
and
the
other
of
necessity
to
be
false
,
it
is
a
thing
impossible
that
(
alwayes
confining
our selves
within
the
limits
of
humane
doctrine
)
the
reasons
alledged
for
the
true
Hypothesis
should
not
manifest
themselves
as
concludent
as
those
for
the
contrary
vain
and
ineffectual
.
SAGR.
It
will
be
time
therefore
,
that
we
hear
the
objections
of
the
little
Book
of
[
](A61244-e76330-b)*
*
I
should
have
told
you
,
that
the
true
name
of
this
concealed
Authour
is
Christopher
Scheinerus
,
and
its
title
Disquisitiones
Mathematica
.
Conclusions
,
or
Disquisitions
which
Simplicius
did
bring
with
him
.
SIMP.
Here
is
the
Book
,
and
this
is
the
place
where
the
Author
first
briefly
describeth
the
Systeme
of
the
world
,
according
to
the
Hypothesis
of
Copernicus
,
saying
,
Terram
igitur
unà
cum
Luna
,
totoque
hoc
elementari
mundo
Copernicus
,
&c.
SALV
.
Forbear
a
little
,
Simplicius
,
for
methinks
that
this
Authour
,
in
this
first
entrance
,
shews
himself
to
be
but
very
ill
verst
in
the
Hypothesis
which
he
goeth
about
to
confute
,
in
regard
,
he
saith
that
Copernicus
maketh
the
Earth
,
together
with
the
Moon
,
to
describe
the
[
](A61244-e76480-b)*
*
i.
e.
the
Ecliptick
grand
Orb
in
a
year
moving
from
East
to
West
;
a
thing
that
as
it
is
false
and
impossible
,
so
was
it
never
affirmed
by
Copernicus
,
who
rather
maketh
it
to
move
the
contrary
way
,
I
mean
from
West
to
East
,
that
is
,
according
to
the
order
of
the
Signes
;
whereupon
we
come
to
think
the
same
to
be
the
annual
motion
of
the
Sun
,
constituted
immoveable
in
the
centre
of
the
Zodiack
.
See
the
too
adventurous
confidence
of
this
man
;
to
undertake
the
confutation
of
anothers
Doctrine
,
and
yet
to
be
ignorant
of
the
primary
fundamentals
;
upon
which
his
adversary
layeth
the
greatest
and
most
important
part
of
all
the
Fabrick
.
This
is
a
bad
beginning
to
gain
himself
credit
with
his
Reader
;
but
let
us
go
on
.
SIMP.
Having
explained
the
Universal
Systeme
,
he
beginneth
to
propound
his
objections
against
this
annual
motion
:
and
the
first
are
these
,
which
he
citeth
Ironically
,
and
in
derision
of
Copernicus
,
Instances
of
a
certain
Book
Ironically
propounded
against
Copernicus
.
and
of
his
followers
,
writing
that
in
this
phantastical
Hypothesis
of
the
World
one
must
necessarily
maintain
very
grosse
absurdities
;
namely
,
that
the
Sun
,
Venus
,
and
Mercury
are
below
the
Earth
;
and
that
grave
matters
go
naturally
upwards
,
and
the
light
downwards
;
and
that
Christ
,
our
Lord
and
Redeemer
,
ascended
into
Hell
,
and
descended
into
Heaven
,
when
he
approached
towards
the
Sun
,
and
that
when
Joshuah
commanded
the
Sun
to
stand
still
,
the
Earth
stood
still
,
or
the
Sun
moved
a
contrary
way
to
that
of
the
Earth
;
and
that
when
the
Sun
is
in
Cancer
,
the
Earth
runneth
through
Capricorn
;
and
that
the
Hyemal
(
or
Winter
)
Signes
make
the
Summer
,
and
the
Aestival
Winter
;
and
that
the
Stars
do
not
rise
and
set
to
the
Earth
,
but
the
Earth
to
the
Stars
;
and
that
the
East
beginneth
in
the
West
,
and
the
West
in
the
East
;
and
,
in
a
word
,
that
almost
the
whole
course
of
the
World
is
inverted
.
SALV
.
Every
thing
pleaseth
me
,
except
it
be
his
having
intermixed
places
out
of
the
sacred
Scriptures
(
alwayes
venerable
,
and
to
be
rever'd
)
amongst
these
,
but
two
scurrilous
fooleries
,
and
attempting
to
wound
with
holy
Weapons
,
those
who
Philosophating
in
jest
,
and
for
divertisement
,
neither
affirm
nor
deny
,
but
,
some
presupposals
and
positions
being
assumed
,
do
familiarly
argue
.
SIMP.
Truth
is
,
he
hath
displeased
me
also
,
and
that
not
a
little
;
and
especially
,
by
adding
presently
after
that
,
howbeit
,
the
Copernichists
answer
,
though
but
very
impertinently
to
these
and
such
like
other
reasons
,
yet
can
they
not
reconcile
nor
answer
those
things
that
follow
.
SALV
.
This
is
worse
than
all
the
rest
;
for
he
pretendeth
to
have
things
more
efficacious
and
concludent
than
the
Authorities
of
the
sacred
Leaves
;
But
I
pray
you
,
let
us
reverence
them
,
and
passe
on
to
natural
and
humane
reasons
:
and
yet
if
he
give
us
amongst
his
natural
arguments
,
things
of
no
more
solidity
,
than
those
hitherto
alleadged
,
we
may
wholly
decline
this
undertaking
,
for
I
as
to
my
own
parricular
,
do
not
think
it
fit
to
spend
words
in
answering
such
trifling
impertinencies
.
And
as
to
what
he
saith
,
that
the
Copernicans
answer
to
these
objections
,
it
is
most
false
,
nor
may
it
be
thought
,
that
any
man
should
set
him self
to
wast
his
time
so
unprofitably
.
SIMP.
I
concur
with
you
in
the
same
judgement
;
Supposing
the
annual
motion
to
belong
to
the
Earth
,
it
followeth
,
that
one
fixed
Star
,
is
bigger
than
the
whole
grand
Orb.
therefore
let
us
hear
the
other
instances
that
he
brings
,
as
much
stronger
.
And
observe
here
,
how
he
with
very
exact
computations
concludeth
,
that
if
the
grand
Orb
of
the
Earth
,
or
the
ecliptick
,
in
which
Copernicus
maketh
it
to
run
in
a
year
round
the
Sun
,
should
be
as
it
were
,
insensible
,
in
respect
of
the
immensitie
of
the
Starry
Sphaere
,
according
as
the
said
Copernicus
,
saith
it
is
to
be
supposed
,
it
would
be
necessary
to
grant
and
confirm
,
that
the
fixed
Stars
were
remote
from
us
,
an
unconceivable
distance
,
and
that
the
lesser
of
them
,
were
bigger
than
the
whole
grand
Orb
aforesaid
,
and
some
other
much
bigger
than
the
whole
Sphaere
of
Saturn
;
Masses
certainly
too
excessively
vast
,
unimaginable
,
and
incredible
.
SALV
.
I
have
heretofore
seen
such
another
objection
brought
by
Tycho
against
Copernicus
,
Tycho
his
Argument
grounded
upon
a
false
Hypothesis
.
and
this
is
not
the
first
time
that
I
have
discovered
the
fallacy
,
or
,
to
say
better
,
the
fallacies
of
this
Argumemtation
,
founded
upon
a
most
false
Hypothesis
,
and
upon
a
Proposition
of
the
said
Copernicus
,
Litigious
Lawyers
that
are
extertained
in
an
ill
cause
,
keep
close
to
s●me
ex●ression
fallen
from
the
adverse
party
at
unawares
.
understood
by
his
adversaries
,
with
too
punctual
a
nicity
,
according
to
the
practise
of
those
pleaders
,
who
finding
the
flaw
to
be
in
the
very
merit
of
their
cause
,
keep
to
some
one
word
,
fallen
unawares
from
the
contrary
partie
,
and
fly
out
into
loud
and
tedious
descants
upon
that
.
But
for
your
better
information
;
Copernicus
having
declared
those
admirable
consequences
which
are
derived
from
the
Earths
annual
motion
,
to
the
other
Planets
,
that
is
to
say
,
of
the
[
](A61244-e76930-b)*
*
Or
progressions
.
directions
and
retrogradations
of
the
three
uppermost
in
particular
;
The
apparent
diversity
of
motion
in
the
Planets
,
is
insensible
in
the
fixed
Stars
.
he
subjoyneth
,
that
this
apparent
mutation
(
which
is
discerned
more
in
Mars
than
in
Jupiter
,
by
reason
Jupiter
is
more
remote
,
and
yet
lesse
in
Saturn
,
by
reason
it
is
more
remote
than
Jupiter
)
in
the
fixed
Stars
,
did
remain
imperceptible
,
by
reason
of
their
immense
remotenesse
from
us
,
in
comparison
of
the
distances
of
Jupiter
or
Saturn
.
Here
the
Adversaries
of
this
opinion
rise
up
,
and
supposing
that
fore-named
imperceptibility
of
Copernicus
,
as
if
it
had
been
taken
by
him
,
for
a
real
and
absolute
thing
of
nothing
,
and
adding
,
that
a
fixed
Star
of
one
of
the
lesser
magnitudes
,
is
notwithstanding
perceptible
,
seeing
that
it
cometh
under
the
sence
of
seeing
,
they
go
on
to
calculate
with
the
intervention
of
other
false
assumptions
,
and
concluding
that
it
is
necessary
by
the
Copernican
Doctrine
,
to
admit
,
that
a
fixed
Star
is
much
bigger
than
the
whole
grand
Orb.
Supposing
that
a
fixed
Star
of
the
sixth
magnitude
is
no
bigger
than
the
Sun
,
the
diversitie
which
is
so
great
in
the
Planets
,
in
the
fixed
Stars
is
almost
insensible
.
Now
to
discover
the
vanity
of
this
their
whole
proceeding
,
I
shall
shew
that
a
fixed
Star
of
the
sixth
magnitude
,
being
supposed
to
be
no
bigger
than
the
Sun
,
one
may
thence
conclude
with
true
demonstrations
,
that
the
distance
of
the
said
fixed
Stars
from
us
,
cometh
to
be
so
great
,
that
the
annual
motion
of
the
Earth
,
which
causeth
so
great
and
notable
variations
in
the
Planets
,
appears
scarce
observable
in
them
;
and
at
the
same
time
,
I
will
distinctly
shew
the
gross
fallacies
,
in
the
assumptions
of
Copernicus
his
Adversaries
.
And
first
of
all
,
The
distance
of
the
Sun
,
containeth
1208
Semid
.
of
the
Earth
.
I
suppose
with
the
said
Copernicus
,
and
also
with
his
opposers
,
that
the
Semidiameter
of
the
grand
Orb
,
which
is
the
distance
of
the
Earth
from
the
Sun
,
containeth
1208
Semidiameters
of
the
said
Earth
.
Secondly
,
I
premise
with
the
allowance
aforesaid
,
and
of
truth
,
that
the
[
](A61244-e77100-b)*
*
The
Diameter
of
the
Sun
,
half
a
degree
.
apparent
diameter
of
the
Sun
in
its
mean
distance
,
to
be
about
half
a
degree
,
that
is
,
30.
min.
prim
.
which
are
1800.
seconds
,
that
is
,
108000.
thirds
.
And
because
the
apparent
Diameter
of
a
fixed
Star
of
the
first
magnitude
,
The
Diameter
of
a
fixed
Star
,
of
the
first
magnitude
,
and
of
one
of
the
sixth
.
is
no
more
than
5.
seconds
,
that
is
,
300.
thirds
,
and
the
Diameter
of
a
fixed
Star
of
the
sixth
magnitude
,
50.
thirds
,
(
and
herein
is
the
greatest
errour
of
the
Anti-Copernicans
)
Therefore
the
Diameter
of
the
Sun
,
The
apparent
Diameter
of
the
Sun
,
how
much
it
is
bigger
than
that
of
a
fixed
star
.
containeth
the
Diameter
of
a
fixed
Star
of
the
sixth
magnitude
2160.
times
.
And
therefore
if
a
fixed
Star
of
the
sixth
magnitude
,
were
supposed
to
be
really
equal
to
the
Sun
,
and
not
bigger
,
which
is
the
same
as
to
say
,
if
the
Sun
were
so
far
removed
,
that
its
Diameter
should
seem
to
be
one
of
the
2160.
parts
of
what
it
now
appeareth
,
its
distance
ought
of
necessity
to
be
2160.
times
greater
than
now
in
effect
it
is
,
which
is
as
much
as
to
say
,
that
the
distance
of
the
fixed
Stars
of
the
sixth
magnitude
,
is
2160.
Semidiameters
of
the
grand
Orb.
The
distance
of
a
fixed
star
of
the
sixth
magnitude
,
how
much
it
is
,
the
star
being
supposed
to
be
equal
to
the
Sun
.
And
because
the
distance
of
the
Sun
from
the
Earth
,
contains
by
common
consent
1208.
Semidiameters
of
the
said
Earth
,
and
the
distance
of
the
fixed
Stars
(
as
hath
been
said
)
2160.
Semediameters
of
the
grand
Orb
,
therefore
the
Semidiameter
of
the
Earth
is
much
greater
(
that
is
almost
double
)
in
comparison
of
the
grand
Orb
,
than
the
Semidiameter
of
the
grand
Orb
,
in
relation
to
the
distance
of
the
Starry
Sphaere
;
In
the
fixed
stars
the
diversitie
of
aspect
,
caused
by
the
grand
Orb
,
is
little
more
then
that
caused
by
the
Earth
in
the
Sun
.
and
therefore
the
variation
of
aspect
in
the
fixed
Stars
,
caused
by
the
Diameter
of
the
grand
Orb
,
can
be
but
little
more
observable
,
than
that
which
is
observed
in
the
Sun
,
occasioned
by
the
Semidiameter
of
the
Earth
.
SAGR.
This
is
a
great
fall
for
the
first
step
.
SALV
.
It
is
doubtlesse
an
errour
;
for
a
fixed
Star
of
the
sixth
magnitude
,
A
star
of
the
sixth
magnitude
,
supposed
by
Tycho
and
the
Authour
of
the
Book
of
Conclusions
,
an
hundred
and
six
milions
of
times
bigger
than
needs
.
which
by
the
computation
of
this
Authour
,
ought
,
for
the
upholding
the
proposition
of
Copernicus
,
to
be
as
big
as
the
whole
grand
Orb
,
onely
by
supposing
it
equal
to
the
Sun
,
which
Sun
is
lesse
by
far
,
than
the
hundred
and
six
millionth
part
of
the
said
grand
Orb
,
maketh
the
starry
Sphaere
so
great
and
high
as
sufficeth
to
overthrow
the
instance
brought
against
the
said
Copernicus
.
SAGR.
Favour
me
with
this
computation
.
SALV
.
The
supputation
is
easie
and
short
.
The
Diameter
of
the
Sun
,
The
computation
of
the
magnitude
of
the
fixed
Stars
,
in
respect
to
the
grand
Orb.
is
eleven
semidiameters
of
the
Earth
,
and
the
Diameter
of
the
grand
Orb
,
contains
2416.
of
those
same
semidiameters
,
by
the
ascent
of
both
parties
;
so
that
the
Diameter
of
the
said
Orb
,
contains
the
Suns
Diameter
220.
times
very
near
.
And
because
the
Spheres
are
to
one
another
,
as
the
Cubes
of
their
Diameters
,
let
us
make
the
Cube
of
220.
which
is
106480000.
and
we
shall
have
the
grand
Orb
,
an
hundred
and
six
millions
,
four
hundred
and
eighty
thousand
times
bigger
than
the
Sun
,
to
which
grand
Orb
,
a
star
of
the
sixth
magnitude
,
ought
to
be
equal
,
according
to
the
assertion
of
this
Authour
.
SAGR.
The
errour
then
of
these
men
,
consisteth
in
being
extreamly
mistaken
,
in
taking
the
apparent
Diameter
of
the
fixed
Stars
.
SALV
.
This
is
one
,
but
not
the
onely
errour
of
them
;
and
indeed
,
A
common
errour
of
all
the
Astronomers
,
touching
the
magnitude
of
the
stars
.
I
do
very
much
admire
how
so
many
Astronomers
,
and
those
very
famous
,
as
are
Alfagranus
,
Albategnus
,
Tebizius
,
and
much
more
modernly
the
Tycho's
and
Clavins's
,
and
in
sum
,
all
the
predecessors
of
our
Academian
,
should
have
been
so
grosly
mistaken
,
in
determining
the
magnitudes
of
all
the
Stars
,
as
well
fixed
as
moveable
,
the
two
Luminaries
excepted
out
of
that
number
;
and
that
they
have
not
taken
any
heed
to
the
adventitious
irradiations
that
deceitfully
represent
them
an
hundred
and
more
times
bigger
,
than
when
they
are
beheld
,
without
those
capillious
rayes
,
nor
can
this
their
inadvertency
be
excused
,
in
regard
that
it
was
in
their
power
to
have
beheld
them
at
their
pleasure
without
those
tresses
,
which
is
done
,
by
looking
upon
them
at
their
first
appearance
in
the
evening
,
Venus
renders
the
errour
of
Astronomers
in
determining
the
magnitudes
of
stars
inexcusable
.
or
their
last
occultation
in
the
comming
on
of
day
;
and
if
none
of
the
rest
,
yet
Venus
,
which
oft
times
is
seen
at
noon
day
,
so
small
,
that
one
must
sharpen
the
sight
in
discerning
it
;
and
again
,
in
the
following
night
,
seemeth
a
great
flake
of
light
,
might
advertise
them
of
their
fallacy
;
for
I
will
not
believe
that
they
thought
the
true
Discus
to
be
that
which
is
seen
in
the
obscurest
darknesses
,
and
not
that
which
is
discerned
in
the
luminous
Medium
:
for
our
lights
,
which
seen
by
night
afar
off
appear
great
,
and
neer
at
hand
shew
their
true
lustre
to
be
terminate
and
small
,
might
have
easily
have
made
them
cautious
;
nay
,
if
I
may
freely
speak
my
thoughts
,
I
absolutely
believe
that
none
of
them
,
no
not
Tycho
himself
,
so
accurate
in
handling
Astronomical
Instruments
,
and
that
so
great
and
accurate
,
without
sparing
very
great
cost
in
their
construction
,
did
ever
go
about
to
take
and
measure
the
apparent
diameter
of
any
Star
,
the
Sun
and
Moon
excepted
;
but
I
think
,
that
arbitrarily
,
and
as
we
say
,
with
the
eye
,
some
one
of
the
more
antient
of
them
pronounced
the
thing
to
be
so
and
so
,
and
that
all
that
followed
him
afterwards
,
without
more
ado
,
kept
close
to
what
the
first
had
said
;
for
if
any
one
of
them
had
applied
himself
to
have
made
some
new
proof
of
the
same
,
he
would
doubtlesse
have
discovered
the
fraud
.
SAGR.
But
if
they
wanted
the
Telescope
,
and
you
have
already
said
,
that
our
Friend
with
that
same
Instrument
came
to
the
knowledge
of
the
truth
,
they
ought
to
be
excused
,
and
not
accused
of
ignorance
.
SALV
.
This
would
hold
good
,
if
without
the
Telescope
the
businesse
could
not
be
effected
.
It
s
true
,
that
this
Instrument
by
shewing
the
Discus
of
the
Star
naked
,
and
magnified
an
hundred
or
a
thousand
times
,
rendereth
the
operation
much
more
easie
,
but
the
same
thing
may
be
done
,
although
not
altogether
so
exactly
,
without
the
Instrument
,
and
I
have
many
times
done
the
same
,
and
my
method
therein
was
this
.
I
have
caused
a
rope
to
be
hanged
towards
some
Star
,
A
way
to
measure
the
apparent
diameter
of
a
star
.
and
I
have
made
use
of
the
Constellation
,
called
the
Harp
,
which
riseth
between
the
North
and
[
](A61244-e77630-b)*
*
Rendred
in
Latine
Corum
,
that
is
to
say
,
North-west
.
North-east
,
and
then
by
going
towards
,
and
from
the
said
rope
,
interposed
between
me
and
the
Star
,
I
have
found
the
place
from
whence
the
thicknesse
of
the
rope
hath
just
hid
the
Star
from
me
:
this
done
,
I
have
taken
the
distance
from
the
eye
to
the
rope
,
which
was
one
of
the
sides
including
the
angle
that
was
composed
in
the
eye
,
and
[
](A61244-e77650-b)*
*
i.
e.
Is
subtended
by
.
which
insisteth
upon
the
thicknesse
of
the
rope
,
and
which
is
like
,
yea
the
same
with
the
angle
in
the
Starry
Sphere
,
that
insisteth
upon
the
diameter
of
the
Star
,
and
by
the
proportion
of
the
ropes
thicknesse
to
the
distance
from
the
eye
to
the
rope
,
by
the
table
of
Arches
and
Chords
,
I
have
immediately
found
the
quantity
of
the
angle
;
using
all
the
while
the
wonted
caution
that
is
observed
in
taking
angles
so
acute
,
not
to
forme
the
concourse
of
the
visive
rayes
in
the
centre
of
the
eye
,
where
they
are
onely
refracted
,
but
beyond
the
eye
,
where
really
the
pupils
greatnesse
maketh
them
to
concur
.
SAGR.
I
apprehend
this
your
cautelous
procedure
,
albeit
I
have
a
kind
of
haesitancy
touching
the
same
,
but
that
which
most
puzzleth
me
is
,
that
in
this
operation
,
if
it
be
made
in
the
dark
of
night
,
methinks
that
you
measure
the
diameter
of
the
irradiated
Discus
,
and
not
the
true
and
naked
face
of
the
Star
.
SALV
.
Not
so
,
Sir
,
for
the
rope
in
covering
the
naked
body
of
the
Star
,
taketh
away
the
rayes
,
which
belong
not
to
it
,
but
to
our
eye
,
of
which
it
is
deprived
so
soon
as
the
true
Discus
thereof
is
hid
;
and
in
making
the
observation
,
you
shall
see
,
how
unexpectedly
a
little
cord
will
cover
that
reasonable
big
body
of
light
,
which
seemed
impossible
to
be
hid
,
unlesse
it
were
with
a
much
broader
Screene
:
to
measure
,
in
the
next
place
,
and
exactly
to
find
out
,
how
many
of
those
thicknesses
of
the
rope
interpose
in
the
distance
between
the
said
rope
and
the
eye
,
I
take
not
onely
one
diameter
of
the
rope
,
but
laying
many
pieces
of
the
same
together
upon
a
Table
,
so
that
they
touch
,
I
take
with
a
pair
of
Compasses
the
whole
space
occupied
by
fifteen
,
or
twenty
of
them
,
and
with
that
measure
I
commensurate
the
distance
before
with
another
smaller
cord
taken
from
the
rope
to
the
concourse
of
the
visive
rayes
.
And
with
this
sufficiently-exact
operation
I
finde
the
apparent
diameter
of
a
fixed
Star
of
the
first
magnitude
,
commonly
esteemed
to
be
2
min.
pri
.
and
also
3
min.
prim
.
by
Tycho
in
his
Astronomical
Letters
,
The
diameter
of
a
fixed
star
of
the
first
magnitude
not
more
than
five
sec.
min.
cap.
167.
to
be
no
more
than
5
seconds
,
which
is
one
of
the
24.
or
36.
parts
of
what
they
have
held
it
:
see
now
upon
what
grosse
errours
their
Doctrines
are
founded
.
SAGR.
I
see
and
comprehend
this
very
well
,
but
before
we
passe
any
further
,
I
would
propound
the
doubt
that
ariseth
in
me
in
the
finding
the
concourse
[
or
intersection
]
of
the
visual
rayes
beyond
the
eye
,
when
observation
is
made
of
objects
comprehended
between
very
acute
angles
;
and
my
scruple
proceeds
from
thinking
,
that
the
said
concourse
may
be
sometimes
more
remote
,
and
sometimes
lesse
;
and
this
not
so
much
,
by
meanes
of
the
greater
or
lesser
magnitude
of
the
object
that
is
beheld
,
as
because
that
in
observing
objects
of
the
same
bignesse
,
it
seems
to
me
that
the
concourse
of
the
rayes
,
for
certain
other
respects
ought
to
be
made
more
and
lesse
remote
from
the
eye
.
SALV
.
I
see
already
,
whither
the
apprehension
of
Sagredus
,
a
most
diligent
observer
of
Natures
secrets
,
tendeth
;
and
I
would
lay
any
wager
,
The
circle
of
the
pupil
of
the
eye
enlargeth
and
contracteth
.
that
amongst
the
thousands
that
have
observed
Cats
to
contract
and
inlarge
the
pupils
of
their
eyes
very
much
,
there
are
not
two
,
nor
haply
one
that
hath
observed
the
like
effect
to
be
wrought
by
the
pupils
of
men
in
seeing
,
whilst
the
medium
is
much
or
little
illumin'd
,
and
that
in
the
open
light
the
circlet
of
the
pupil
diminisheth
considerably
:
so
that
in
looking
upon
the
face
or
Discus
of
the
Sun
,
it
is
reduced
to
a
smallnesse
lesser
than
a
grain
of
[
](A61244-e77920-b)*
*
Panicum
,
a
small
grain
like
to
Mill
,
I
take
it
to
be
the
same
with
that
called
Bird
Seed
.
Panick
,
and
in
beholding
objects
that
do
not
shine
,
and
are
in
a
lesse
luminous
medium
,
it
is
inlarged
to
the
bignesse
of
a
Lintel
or
more
;
and
in
summe
this
expansion
and
contraction
differeth
in
more
than
decuple
proportion
:
From
whence
it
is
manifest
,
that
when
the
pupil
is
much
dilated
,
it
is
necessary
that
the
angle
of
the
rayes
concourse
be
more
remote
from
the
eye
;
which
happeneth
in
beholding
objects
little
luminated
.
This
is
a
Doctrine
which
Sagredus
hath
,
just
now
,
given
me
the
hint
of
,
whereby
,
if
we
were
to
make
a
very
exact
observation
,
and
of
great
consequence
,
we
are
advertized
to
make
the
observation
of
that
concourse
in
the
act
of
the
same
,
or
just
such
another
operation
;
but
in
this
our
case
,
wherein
we
are
to
shew
the
errour
of
Astronomers
,
this
accuratenesse
is
not
necessary
:
for
though
we
should
,
in
favour
of
the
contrary
party
,
suppose
the
said
concourse
to
be
made
upon
the
pupil
it self
,
it
would
import
little
,
their
mistake
being
so
great
.
I
am
not
certain
,
Sagredus
,
that
this
would
have
been
your
objection
.
SAGR.
It
is
the
very
same
,
and
I
am
glad
that
it
was
not
altogether
without
reason
,
as
your
concurrence
in
the
same
assureth
me
;
but
yet
upon
this
occasion
I
would
willingly
hear
what
way
may
be
taken
to
finde
out
the
distance
of
the
concourse
of
the
visual
rayes
.
SALV
.
The
method
is
very
easie
,
and
this
it
is
,
I
take
two
long
[
](A61244-e78050-b)*
*
Strisce
.
How
to
find
the
distance
of
the
rays
concourse
from
the
pupil
.
labels
of
paper
,
one
black
,
and
the
other
white
,
and
make
the
black
half
as
broad
as
the
white
;
then
I
stick
up
the
white
against
a
wall
,
and
far
from
that
I
place
the
other
upon
a
stick
,
or
other
support
,
at
a
distance
of
fifteen
or
twenty
yards
,
and
receding
from
this
,
second
another
such
a
space
in
the
same
right
line
,
it
is
very
manifest
,
that
at
the
said
distance
the
right
lines
will
concur
,
that
departing
from
the
termes
of
the
breadth
of
the
white
piece
,
shall
passe
close
by
the
edges
of
the
other
label
placed
in
the
mid-way
;
whence
it
followeth
,
that
in
case
the
eye
were
placed
in
the
point
of
the
said
concourse
or
intersection
,
the
black
slip
of
paper
in
the
midst
would
precisely
hide
the
opposite
blank
,
if
the
sight
were
made
in
one
onely
point
;
but
if
we
should
find
,
that
the
edges
of
the
white
cartel
appear
discovered
,
it
shall
be
a
necessary
argument
that
the
visual
rayes
do
not
issue
from
one
sole
point
.
And
to
make
the
white
label
to
be
hid
by
the
black
,
it
will
be
requisite
to
draw
neerer
with
the
eye
:
Therefore
,
having
approached
so
neer
,
that
the
intermediate
label
covereth
the
other
,
and
noted
how
much
the
required
approximation
was
,
the
quantity
of
that
approach
shall
be
the
certain
measure
,
how
much
the
true
concourse
of
the
visive
rayes
,
is
remote
from
the
eye
in
the
said
operation
,
and
we
shall
moreover
have
the
diameter
of
the
pupil
,
or
of
that
circlet
from
whence
the
visive
rayes
proceed
:
for
it
shall
be
to
the
breadth
of
the
black
paper
,
as
is
the
distance
from
the
concourse
of
the
lines
,
that
are
produced
by
the
edges
of
the
papers
to
the
place
where
the
eye
standeth
,
when
it
first
seeth
the
remote
paper
to
be
hid
by
the
intermediate
one
,
as
that
distance
is
,
I
say
,
to
the
distance
that
is
between
those
two
papers
.
And
therefore
when
we
would
,
with
exactnesse
,
measure
the
apparent
diameter
of
a
Star
,
having
made
the
observation
in
manner
,
as
aforesaid
,
it
would
be
necessary
to
compare
the
diameter
of
the
rope
to
the
diameter
of
the
pupil
;
and
having
found
v.
g.
the
diameter
of
the
rope
to
be
quadruple
to
that
of
the
pupil
,
and
the
distance
of
the
eye
from
the
rope
to
be
,
for
example
,
thirty
yards
,
we
would
say
,
that
the
true
concourse
of
the
lines
produced
from
the
ends
or
extremities
of
the
diameter
of
the
star
,
by
the
extremities
of
the
diameter
of
the
rope
,
doth
fall
out
to
be
fourty
yards
remote
from
the
said
rope
,
for
so
we
shall
have
observed
,
as
we
ought
,
the
proportion
between
the
distance
of
the
rope
from
the
concourse
of
the
said
lines
,
and
the
distance
from
the
said
concourse
to
the
place
of
the
eye
,
which
ought
to
be
the
same
that
is
between
the
diameter
of
the
rope
,
and
diameter
of
the
pupil
.
SAGR.
I
have
perfectly
understood
the
whole
businesse
,
and
therefore
let
us
hear
what
Simplicius
hath
to
alledge
in
defence
of
the
Anti-Copernicans
.
SIMP.
Albeit
that
grand
and
altogether
incredible
inconvenience
insisted
upon
by
these
adversaries
of
Copernicus
be
much
moderated
and
abated
by
the
discourse
of
Salviatus
,
yet
do
I
not
think
it
weakened
so
,
as
that
it
hath
not
strength
enough
left
to
foil
this
same
opinion
.
For
,
if
I
have
rightly
apprehended
the
chief
and
ultimate
conclusion
,
in
case
,
the
stars
of
the
sixth
magnitude
were
supposed
to
be
as
big
as
the
Sun
,
(
which
yet
I
can
hardly
think
)
yet
it
would
still
be
true
,
that
the
grand
Orb
[
or
Ecliptick
]
would
occasion
a
mutation
and
variation
in
the
starry
Sphere
,
like
to
that
which
the
semidiameter
of
the
Earth
produceth
in
the
Sun
,
which
yet
is
observable
;
so
that
neither
that
,
no
nor
a
lesse
mutation
being
discerned
in
the
fixed
Stars
,
methinks
that
by
this
means
the
annual
motion
of
the
Earth
is
destroyed
and
overthrown
.
SALV
.
You
might
very
well
so
conclude
,
Simplicius
,
if
we
had
nothing
else
to
say
in
behalf
of
Copernicus
:
but
we
have
many
things
to
alledge
that
yet
have
not
been
mentioned
;
and
as
to
that
your
reply
,
nothing
hindereth
,
but
that
we
may
suppose
the
distance
of
the
fixed
Stars
to
be
yet
much
greater
than
that
which
hath
been
allowed
them
,
and
you
your self
,
and
whoever
else
will
not
derogate
from
the
propositions
admitted
by
Piolomy's
sectators
,
must
needs
grant
it
as
a
thing
most
requisite
to
suppose
the
Starry
Sphere
to
be
very
much
bigger
yet
than
that
which
even
now
we
said
that
it
ought
to
be
esteemed
.
All
Astronomers
agree
that
the
greater
magnitudes
of
the
Orbes
is
the
cause
of
the
tardity
of
the
conversions
.
For
all
Astronomers
agreeing
in
this
,
that
the
cause
of
the
greater
tardity
of
the
Revolutions
of
the
Planets
is
,
the
majority
of
their
Spheres
,
and
that
therefore
Saturn
is
more
slow
than
Jupiter
,
and
Jupiter
than
the
Sun
,
for
that
the
first
is
to
describe
a
greater
circle
than
the
second
,
and
that
than
this
later
,
&c.
considering
that
Saturn
v.
g.
the
altitude
of
whose
Orb
is
nine
times
higher
than
that
of
the
Sun
,
and
that
for
that
cause
the
time
of
one
Revolution
of
Saturn
,
is
thirty
times
longer
than
that
of
a
conversion
of
the
Sun
,
in
regard
that
according
to
the
Doctrine
of
Ptolomy
,
one
conversion
of
the
starry
Sphere
is
finished
in
36000.
years
,
whereas
that
of
Saturn
is
consummate
in
thirty
,
and
that
of
the
Sun
in
one
,
By
another
supposition
taken
from
Astronomers
,
the
distance
of
the
fixed
Stars
is
calculated
to
be
10800
semidiameters
of
the
grand
Orb.
arguing
with
a
like
proportion
,
and
saying
,
if
the
Orb
of
Saturn
,
by
reason
it
is
nine
times
bigger
than
that
of
the
Sun
,
revolves
in
a
time
thirty
times
longer
,
by
conversion
,
how
great
ought
that
Orb
to
be
,
which
revolves
36000.
times
more
slowly
?
it
shall
be
found
that
the
distance
of
the
starry
Sphere
ought
to
be
10800
semidiameters
of
the
grand
Orb
,
which
should
be
full
five
times
bigger
than
that
,
which
even
now
we
computed
it
to
be
,
in
case
that
a
fixed
Star
of
the
sixth
magnitude
were
equal
to
the
Sun
.
Now
see
how
much
lesser
yet
;
upon
this
account
,
the
variation
occasioned
in
the
said
Stars
,
by
the
annual
motion
of
the
Earth
,
ought
to
appear
.
And
if
at
the
same
rate
we
would
argue
the
distance
of
the
starry
Sphere
from
Jupiter
,
By
the
proportion
of
Jupiter
and
of
Mars
,
the
starry
Sphere
is
found
to
be
yet
more
remo●e
.
and
from
Mars
,
that
would
give
it
us
to
be
15000.
and
this
27000
semidiameters
of
the
grand
Orb
,
to
wit
,
the
first
seven
,
and
the
second
twelve
times
bigger
than
what
the
magnitude
of
the
fixed
Star
,
supposed
equal
to
the
Sun
,
did
make
it
.
SIMP.
Methinks
that
to
this
might
be
answered
,
that
the
motion
of
the
starry
Sphere
hath
,
since
Ptolomy
,
been
observed
not
to
be
so
slow
as
he
accounted
it
;
yea
,
if
I
mistake
not
,
I
have
heard
that
Copernicus
himself
made
the
Observation
.
SALV
.
You
say
very
well
;
but
you
alledge
nothing
in
that
which
may
favour
the
cause
of
the
Ptolomaeans
in
the
least
,
who
did
never
yet
reject
the
motion
of
36000.
years
in
the
starry
Sphere
,
for
that
the
said
tardity
would
make
it
too
vast
and
immense
.
For
if
that
the
said
immensity
was
not
to
be
supposed
in
Nature
,
they
ought
before
now
to
to
have
denied
a
conversion
so
slow
as
that
it
could
not
with
good
proportion
adapt
it self
,
save
onely
to
a
Sphere
of
monstrous
magnitude
.
SAGR.
Pray
you
,
Salviatus
,
let
us
lose
no
more
time
in
proceeding
,
by
the
way
of
these
proportions
with
people
that
are
apt
to
admit
things
most
dis-proportionate
;
so
that
its
impossible
to
win
any
thing
upon
them
this
way
:
and
what
more
disproportionate
proportion
can
be
imagined
than
that
which
these
men
swallow
down
,
and
admit
,
in
that
writing
,
that
there
cannot
be
a
more
convenient
way
to
dispose
the
Coelestial
Spheres
,
in
order
,
than
to
regulate
them
by
the
differences
of
the
times
of
their
periods
,
placing
from
one
degree
to
another
the
more
slow
above
the
more
swift
,
when
they
have
constituted
the
Starry
Sphere
higher
than
the
rest
,
as
being
the
slowest
,
they
frame
another
higher
still
than
that
,
and
consequently
greater
,
and
make
it
revolve
in
twenty
four
hours
,
whilst
the
next
below
,
it
moves
not
round
under
36000.
years
?
SALV
.
I
could
wish
,
Simplicius
,
that
suspending
for
a
time
the
affection
rhat
you
bear
to
the
followers
of
your
opinion
,
you
would
sincerely
tell
me
,
whether
you
think
that
they
do
in
their
minds
comprehend
that
magnitude
,
which
they
reject
afterwards
as
uncapable
for
its
immensity
to
be
ascribed
to
the
Universe
.
For
I
,
Imme●se
magnitudes
and
numbers
are
incomprehensible
by
our
understanding
.
as
to
my
own
part
,
think
that
they
do
not
;
But
believe
,
that
like
as
in
the
apprehension
of
numbers
,
when
once
a
man
begins
to
passe
those
millions
of
millions
,
the
imagination
is
confounded
,
and
can
no
longer
form
a
conceipt
of
the
same
,
so
it
happens
also
in
comprehending
immense
magnitudes
and
distances
;
so
that
there
intervenes
to
the
comprehension
an
effect
like
to
that
which
befalleth
the
sense
;
For
whilest
that
in
a
serene
night
I
look
towards
the
Stars
,
I
judge
,
according
to
sense
,
that
their
distance
is
but
a
few
miles
,
and
that
the
fixed
Stars
are
not
a
jot
more
remote
than
Jupiter
or
Saturn
,
nay
than
the
Moon
.
But
without
more
ado
,
consider
the
controversies
that
have
past
between
the
Astronomers
and
Peripatetick
Philosophers
,
upon
occasion
of
the
new
Stars
of
Cassiopeia
and
of
Sagittary
,
the
Astronomers
placing
them
amongst
the
fixed
Stars
,
and
the
Philosophers
believing
them
to
be
below
the
Moon
.
So
unable
is
our
sense
to
distinguish
great
distances
from
the
greatest
,
though
these
be
in
reality
many
thousand
times
greater
than
those
.
In
a
word
,
I
ask
of
thee
,
O
foolish
man
!
Doth
thy
imagination
comprehend
that
vast
magnitude
of
the
Universe
,
wh●ch
thou
afterwards
judgest
to
be
too
immense
?
If
thou
comprehendest
it
;
wilt
thou
hold
that
thy
apprehension
extendeth
it self
farther
than
the
Divine
Power
?
wilt
thou
say
,
that
thou
canst
imagine
greater
things
than
those
which
God
can
bring
to
passe
?
But
if
thou
apprehendest
it
not
,
why
wilt
thou
passe
thy
verdict
upon
things
beyond
thy
comprehension
?
SIMP.
All
this
is
very
well
,
nor
can
it
be
denied
,
but
that
Heaven
may
in
greatnesse
surpasse
our
imagination
,
as
also
that
God
might
have
created
it
thousands
of
times
vaster
than
now
it
is
;
but
we
ought
not
to
grant
any
thing
to
have
been
made
in
vain
,
and
to
be
idle
in
the
Universe
.
Now
,
in
that
we
see
this
admirable
order
of
the
Planets
,
disposed
about
the
Earth
in
distances
proportionate
for
producing
their
effects
for
our
advantage
,
to
what
purpose
is
it
to
interpose
afterwards
between
the
sublime
Orb
of
Saturn
and
the
starry
Sphere
,
a
vast
vacancy
,
without
any
star
that
is
superfluous
,
and
to
no
purpose
?
To
what
end
?
For
whose
profit
and
advantage
?
SALV
.
Methinks
we
arrogate
too
much
to
our selves
,
Simplicius
,
whilst
we
will
have
it
,
that
the
onely
care
of
us
,
is
the
adaequate
work
,
and
bound
,
beyond
which
the
Divine
Wisdome
and
Power
doth
,
or
disposeth
of
nothing
.
But
I
will
not
consent
,
that
we
should
so
much
shorten
its
hand
,
but
desire
that
we
may
content
our selves
with
an
assurance
that
God
and
Nature
are
so
imployed
in
the
governing
of
humane
affairs
,
God
&
Nature
do
imploy
themselves
in
caring
for
men
,
as
if
they
minded
nothing
else
.
that
they
could
not
more
apply
themselves
thereto
,
although
they
had
no
other
care
than
onely
that
of
mankind
;
and
this
,
I
think
,
I
am
able
to
make
out
by
a
most
pertinent
and
most
noble
example
,
taken
from
the
operation
of
the
Suns
light
,
which
whilest
it
attracteth
these
vapours
,
An
example
of
Gods
care
of
mankind
taken
from
the
Sun
.
or
scorcheth
that
plant
,
it
attracteth
,
it
scorcheth
them
,
as
if
it
had
no
more
to
do
;
yea
,
in
ripening
that
bunch
of
grapes
,
nay
that
one
single
grape
,
it
doth
apply
it self
so
,
that
it
could
not
be
more
intense
,
if
the
sum
of
all
its
business
had
been
the
only
maturation
of
that
grape
.
Now
if
this
grape
receiveth
all
that
it
is
possible
for
it
to
receive
from
the
Sun
,
not
suffering
the
least
injury
by
the
Suns
production
of
a
thousand
other
effects
at
the
same
time
;
it
would
be
either
envy
or
folly
to
blame
that
grape
,
if
it
should
think
or
wish
that
the
Sun
would
onely
appropriate
its
rayes
to
its
advantage
.
I
am
confident
that
nothing
is
omitted
by
the
Divine
Providence
,
of
what
concernes
the
government
of
humane
affairs
;
but
that
there
may
not
be
other
things
in
the
Universe
,
that
depend
upon
the
same
infinite
Wisdome
,
I
cannot
,
of
my self
,
by
what
my
reason
holds
forth
to
me
,
bring
my self
to
believe
.
However
,
if
it
were
not
so
,
yet
should
I
not
forbear
to
believe
the
reasons
laid
before
me
by
some
more
sublime
intelligence
.
In
the
mean
time
,
if
one
should
tell
me
,
that
an
immense
space
interposed
between
the
Orbs
of
the
Planets
and
the
Starry
Sphere
,
deprived
of
stars
and
idle
,
would
be
vain
and
uselesse
,
as
likewise
that
so
great
an
immensity
for
receipt
of
the
fixed
stars
,
as
exceeds
our
utmost
comprehension
would
be
superfluous
,
I
would
reply
,
that
it
is
rashnesse
to
go
about
to
make
our
shallow
reason
judg
of
the
Works
of
God
,
and
to
call
vain
and
superfluous
,
whatsoever
thing
in
the
Universe
is
not
subservient
to
us
.
SAGR.
Say
rather
,
It
is
great
rashnesse
to
censure
that
to
be
superfluous
in
h●ll
verse
,
which
we
do
not
perceive
to
be
made
for
us
.
and
I
believe
you
would
say
better
,
that
we
know
not
what
is
subservient
to
us
;
and
I
hold
it
one
of
the
greatest
vanities
,
yea
follies
,
that
can
be
in
the
World
,
to
say
,
because
I
know
not
of
what
use
Jupiter
or
Saturn
are
to
me
,
that
therefore
these
Planets
are
superfluous
,
yea
more
,
that
there
are
no
such
things
in
rerum
natura
;
when
as
,
oh
foolish
man
!
I
know
not
so
much
as
to
what
purpose
the
arteries
,
the
gristles
,
the
spleen
,
the
gall
do
serve
;
nay
I
should
not
know
that
I
have
a
gall
,
spleen
,
or
kidneys
,
if
in
many
desected
Corps
,
they
were
not
shewn
unto
me
;
and
then
onely
shall
I
be
able
to
know
what
the
spleen
worketh
in
me
,
when
it
comes
to
be
taken
from
me
.
To
be
able
to
know
what
this
or
that
Coelestial
body
worketh
in
me
(
seeing
you
will
have
it
that
all
their
influences
direct
themselves
to
us
)
it
would
be
requisite
to
remove
that
body
for
some
time
;
By
depriving
Heaven
of
some
star
,
one
might
come
to
know
what
influence
it
hath
upon
us
.
and
then
whatsoever
effect
I
should
find
wanting
in
me
,
I
would
say
that
it
depended
on
that
star
.
Moreover
,
who
will
presume
to
say
that
the
space
which
they
call
too
vast
and
uselesse
between
Saturn
and
the
fixed
stars
,
is
void
of
other
mundane
bodies
?
Must
it
be
so
,
Many
things
may
be
in
Heaven
,
that
are
invisible
to
us
.
because
we
do
not
see
them
?
Then
the
four
Medicean
Planets
,
and
the
companions
of
Saturn
came
first
into
Heaven
,
when
we
began
to
see
them
,
and
not
before
?
And
by
this
rule
the
innumerable
other
fixed
stars
had
no
existence
before
that
men
did
look
on
them
?
and
the
cloudy
constellations
called
Nebulosae
were
at
first
only
white
flakes
,
but
afterwards
with
the
Telescope
we
made
them
to
become
constellations
of
many
lucid
and
bright
stars
.
Oh
presumptious
,
rather
oh
rash
ignorance
of
man
!
SALV
.
It
's
to
no
purpose
Sagredus
,
to
sally
out
any
more
into
these
unprofitable
exaggerations
:
Let
us
pursue
our
intended
designe
of
examining
the
validity
of
the
reasons
alledged
on
either
side
,
without
determining
any
thing
,
remitting
the
judgment
thereof
when
we
have
done
,
to
such
as
are
more
knowing
.
Returning
therefore
to
our
natural
and
humane
disquisitions
,
I
say
,
Great
,
small
,
immense
,
&c.
are
relative
terms
.
that
great
,
little
,
immense
,
small
,
&c.
are
not
absolute
,
but
relative
terms
,
so
that
the
self
same
thing
compared
with
divers
others
,
may
one
while
be
called
immense
,
and
another
while
imperceptible
,
not
to
say
small
.
This
being
so
,
I
demand
in
relation
to
what
the
Starry
Sphere
of
Copernicus
may
be
called
over
vast
.
In
my
judgment
it
cannot
be
compared
,
or
said
to
be
such
,
unlesse
it
be
in
relation
to
some
other
thing
of
the
same
kind
;
Vanity
of
those
mens
discourse
who
judg
the
starry
sphere
too
vast
in
the
Copernican
Hypothesis
.
now
let
us
take
the
very
least
of
the
same
kind
,
which
shall
be
the
Lunar
Orb
;
and
if
the
Starry
Orb
may
be
so
censured
to
be
too
big
in
respect
to
that
of
the
Moon
,
every
other
magnitude
that
with
like
or
greater
proportion
exceedeth
another
of
the
same
kind
,
ought
to
be
adjudged
too
vast
,
and
for
the
same
reason
to
be
denied
that
they
are
to
be
found
in
the
World
;
and
thus
an
Elephant
,
and
a
Whale
,
shall
without
more
ado
be
condemned
for
Chymaera's
,
and
Poetical
fictions
,
because
that
the
one
as
being
too
vast
in
relation
to
an
Ant
,
which
is
a
Terrestrial
animal
,
and
the
other
in
respect
to
the
[
](A61244-e78940-b)*
*
Spelloncola
,
which
is
here
put
for
the
l●ast
of
Fishes
.
Gudgeon
,
which
is
a
Fish
,
and
are
certainly
seen
to
be
in
rerum
natura
,
would
be
too
immeasurable
;
for
without
all
dispute
,
the
Elephant
and
Whale
exceed
the
Ant
and
Gudgeon
in
a
much
greater
proportion
than
the
Starry
Sphere
doth
that
of
the
Moon
,
although
we
should
fancy
the
said
Sphere
to
be
as
big
as
the
Copernican
Systeme
maketh
it
.
The
space
assigned
to
a
fixed
star
,
is
much
lesse
than
that
of
a
Planet
.
Moreover
,
how
hugely
big
is
the
Sphere
of
Jupiter
,
or
that
of
Saturn
,
designed
for
a
receptacle
but
for
one
single
star
;
and
that
very
small
in
comparison
of
one
of
the
fixed
?
Certainly
if
we
should
assign
to
every
one
of
the
fixed
stars
for
its
receptacle
so
great
a
part
of
the
Worlds
space
,
it
would
be
necessary
to
make
the
Orb
wherein
such
innumerable
multitudes
of
them
reside
,
very
many
thousands
of
times
bigger
than
that
which
serveth
the
purpose
of
Copernicus
.
A
star
is
called
in
respect
of
the
space
that
environs
it
.
Besides
,
do
not
you
call
a
fixed
star
very
small
,
I
mean
even
one
of
the
most
apparent
,
and
not
one
of
those
which
shun
our
sight
;
and
do
we
not
call
them
so
in
respect
of
the
vast
space
circumfused
?
Now
if
the
whole
Starry
Sphere
were
one
entire
lucid
body
;
The
whole
starry
sphere
behold
from
a
great
distance
might
appear
as
small
as
one
single
star
.
who
is
there
,
that
doth
not
know
that
in
an
infinite
space
there
might
be
assigned
a
distance
so
great
,
as
that
the
said
lucid
Sphere
might
from
thence
shew
as
little
,
yea
lesse
than
a
fixed
star
,
now
appeareth
beheld
from
the
Earth
?
From
thence
therefore
we
should
then
judg
that
self
same
thing
to
be
little
,
which
now
from
hence
we
esteem
to
be
immeasurably
great
.
SAGR.
Great
in
my
judgment
,
is
the
folly
of
those
who
would
have
had
God
to
have
made
the
World
more
proportinal
to
the
narrow
capacities
of
their
reason
,
than
to
his
immense
,
rather
infinite
power
.
SIMP.
All
this
that
you
say
is
very
true
;
but
that
upon
which
the
adversary
makes
a
scruple
,
is
,
to
grant
that
a
fixed
star
should
be
not
onely
equal
to
,
but
so
much
bigger
than
the
Sun
;
when
as
they
both
are
particular
bodies
situate
within
the
Starry
Orb
:
And
indeed
in
my
opinion
this
Authour
very
pertinently
questioneth
and
asketh
:
To
what
end
,
and
for
whose
sake
are
such
huge
machines
made
?
Instances
of
the
Authour
of
the
Conclusions
by
way
of
interogation
.
Were
they
produced
for
the
Earth
,
for
an
inconsiderable
point
?
And
why
so
remote
?
To
the
end
they
might
seem
so
very
small
,
and
might
have
no
influence
at
all
upon
the
Earth
?
To
what
purpose
is
such
a
needlesse
monstrous
[
](A61244-e79140-b)*
*
Or
Gulph
.
immensity
between
them
and
Saturn
?
All
those
assertions
fall
to
the
ground
that
are
not
upheld
by
probable
reasons
.
SALV
.
I
conceive
by
the
questions
which
this
person
asketh
,
that
one
may
collect
,
Answers
to
the
interrogatories
of
the
said
Authour
.
that
in
case
the
Heavens
,
the
Stars
,
and
the
quantity
of
their
distances
and
magnitudes
which
he
hath
hitherto
held
,
be
let
alone
,
(
although
he
never
certainly
fancied
to
himself
any
conceivable
magnitude
thereof
)
he
perfectly
discerns
and
comprehends
the
benefits
that
flow
from
thence
to
the
Earth
,
which
is
no
longer
an
inconsiderable
thing
;
nor
are
they
any
longer
so
remote
as
to
appeare
so
very
small
,
but
big
enough
to
be
able
to
operate
on
the
Earth
;
and
that
the
distance
between
them
and
Saturn
is
very
well
proportioned
,
and
that
he
,
for
all
these
things
,
hath
very
probable
reasons
;
of
which
I
would
gladly
have
heard
some
one
:
The
Authour
of
the
Conclusions
confound
and
contradicts
himself
in
his
interrogations
.
but
being
that
in
these
few
words
he
confounds
and
contradicts
himself
,
it
maketh
me
think
that
he
is
very
poor
and
ill
furnished
with
those
probable
reasons
,
and
that
those
which
he
calls
reasons
,
are
rather
fallacies
,
or
dreams
of
an
over-weening
fancy
.
For
I
ask
of
him
,
whether
these
Celestial
bodies
truly
operate
on
the
Earth
,
Interrogatories
put
to
the
Authour
of
the
Conclusions
,
by
which
the
weaknesse
of
his
is
made
appear
.
and
whether
for
the
working
of
those
effects
they
were
produced
of
such
and
such
magnitudes
,
and
disposed
at
such
and
such
distances
,
or
else
whether
they
have
nothing
at
all
to
do
with
Terrene
mattets
.
If
they
have
nothing
to
do
with
the
Earth
;
it
is
a
great
folly
for
us
that
are
Earth-born
,
to
offer
to
make
our selves
arbitrators
of
their
magnitudes
,
and
regulators
of
their
local
dispositions
,
seeing
that
we
are
altogether
ignorant
of
their
whole
businesse
and
concerns
;
but
if
he
shall
say
that
they
do
operate
,
and
that
they
are
directed
to
this
end
,
he
doth
affirm
the
same
thing
which
a
little
before
he
denied
,
and
praiseth
that
which
even
now
he
condemned
,
in
that
he
said
,
that
the
Celestial
bodies
situate
so
far
remote
as
that
they
appear
very
small
,
cannot
have
any
influence
at
all
upon
the
Earth
.
But
,
good
Sir
,
in
the
Starry
Sphere
pre-established
at
its
present
distance
,
and
which
you
did
acknowledg
to
be
in
your
judgment
,
well
proportioned
to
have
an
influence
upon
these
Terrene
bodies
,
many
stars
appear
very
small
,
and
an
hundred
times
as
many
more
are
wholly
invisible
unto
us
(
which
is
an
appearing
yet
lesse
than
very
small
)
therefore
it
is
necessary
that
(
contradicting
your self
)
you
do
now
deny
their
operation
upon
the
Earth
;
or
else
that
(
still
contradicting
your self
)
you
grant
that
their
appearing
very
small
doth
not
in
the
least
lessen
their
influence
;
or
else
that
(
and
this
shall
be
a
more
sincere
and
modest
concession
)
you
acknowledg
and
freely
confesse
,
that
our
passing
judgment
upon
their
magnitudes
and
distances
is
a
vanity
,
not
to
say
presumption
or
rashnesse
.
SIMP.
Truth
is
,
I
my self
did
also
,
in
reading
this
passage
perceive
the
manifest
contradiction
,
in
saying
,
that
the
Stars
(
if
one
may
so
speak
)
of
Copernicus
appearing
so
very
small
,
could
not
operate
on
the
Earth
,
and
not
perceiving
that
he
had
granted
an
influence
upon
the
Earth
to
those
of
Ptolomy
,
and
his
sectators
,
which
appear
not
only
very
small
,
but
are
,
for
the
most
part
,
very
invisible
.
SALV
.
But
I
proceed
to
another
consideration
:
What
is
the
reason
,
doth
he
say
,
why
the
stars
appear
so
little
?
Is
it
haply
,
because
they
seem
so
to
us
?
That
remote
objects
appeare
so
small
,
is
the
defect
of
the
eye
,
as
is
demonstrated
.
Doth
not
he
know
,
that
this
commeth
from
the
Instrument
that
we
imploy
in
beholding
them
,
to
wit
,
from
our
eye
?
And
that
this
is
true
,
by
changing
Instrument
,
we
shall
see
them
bigger
and
bigger
,
as
much
as
we
will
.
And
who
knows
but
that
to
the
Earth
,
which
beholdeth
them
without
eyes
,
they
may
not
shew
very
great
,
and
such
as
in
reality
they
are
?
But
it
's
time
that
,
omitting
these
trifles
,
we
come
to
things
of
more
moment
;
and
therefore
I
having
already
demonstrated
these
two
things
:
First
,
how
far
off
the
Firmament
ought
to
be
placed
to
make
,
that
the
grand
Orb
causeth
no
greater
difference
than
that
which
the
Terrestrial
Orb
occasioneth
in
the
remotenesse
of
the
Sun
;
And
next
,
how
likewise
to
make
that
a
star
of
the
Firmament
appear
to
us
of
the
same
bignesse
,
as
now
we
see
it
,
it
is
not
necessary
to
suppose
it
bigger
than
the
Sun
;
I
would
know
whether
Tycho
,
or
any
of
his
adherents
hath
ever
attempted
to
find
out
,
by
any
means
,
whether
any
appearance
be
to
be
discovered
in
the
starry
Sphere
,
upon
which
one
may
the
more
resolutely
deny
or
admit
the
annual
motion
of
the
Earth
.
SAGR.
I
would
answer
for
them
,
that
there
is
not
,
no
nor
is
there
any
need
there
should
;
Tycho
nor
his
followers
ever
attempted
to
see
whether
there
are
any
appearances
in
the
Firmament
for
or
against
the
annual
m●tion
.
seeing
that
it
is
Copernicus
himself
that
saith
,
that
no
such
diversity
is
there
:
and
they
,
arguing
ad
hominem
,
admit
him
the
same
;
and
upon
this
assumption
they
demonstrate
the
improbability
that
followeth
thereupon
,
namely
,
that
it
would
be
necessary
to
make
the
Sphere
so
immense
,
that
a
fixed
star
,
to
appear
unto
us
as
great
as
it
now
seems
,
ought
of
necessity
to
be
of
so
immense
a
magnitude
,
as
that
it
would
exceed
the
bignesse
of
the
whole
grand
Orb
,
a
thing
,
which
notwithstanding
,
as
they
say
,
is
altogether
incredible
.
SALV
.
I
am
of
the
same
judgment
,
and
verily
believe
that
they
argue
contra
hominem
,
studying
more
to
defend
another
man
,
than
desiring
to
come
to
the
knowledge
of
the
truth
.
And
I
do
not
only
believe
,
Astronomers
,
perhaps
,
have
not
known
what
appearances
ought
to
follow
upon
the
annual
motion
of
the
Earth
.
that
none
of
them
ever
applied
themselves
to
make
any
such
observation
,
but
I
am
also
uncertain
,
whether
any
of
them
do
know
what
alteration
the
Earths
annual
motion
ought
to
produce
in
the
fixed
stars
,
in
case
the
starry
Sphere
were
not
so
far
distant
,
as
that
in
them
the
said
diversity
,
by
reason
of
its
minuity
dis-appeareth
;
for
their
surceasing
that
inquisition
,
and
referring
themselves
to
the
meer
assertion
of
Copernicus
,
may
very
well
serve
to
convict
a
man
,
but
not
to
acquit
him
of
the
fact
:
Copernicus
understood
not
some
things
for
want
of
Instruments
.
For
its
possible
that
such
a
diversity
may
be
,
and
yet
not
have
been
sought
for
;
or
that
either
by
reason
of
its
minuity
,
or
for
want
of
exact
Instruments
it
was
not
discovered
by
Copernicus
;
for
though
it
were
so
,
this
would
not
be
the
first
thing
,
that
he
either
for
want
of
Instruments
,
or
for
some
other
defect
hath
not
known
;
and
yet
he
proceeding
upon
other
solid
and
rational
conjectures
,
affirmeth
that
,
which
the
things
by
him
not
discovered
do
seem
to
contradict
:
for
,
as
hath
been
said
already
,
without
the
Telescope
,
neither
could
Mars
be
discerned
to
increase
60.
times
;
nor
Venus
40.
more
in
that
than
in
this
position
;
yea
,
their
differences
appear
much
lesse
than
really
they
are
and
yet
neverthelesse
it
is
certainly
discovered
at
length
,
that
those
mutations
are
the
same
,
to
an
hair
that
the
Copernican
Systeme
required
.
Tycho
and
others
argue
against
the
annual
motion
,
from
the
invariable
elevation
of
the
Pole
.
Now
it
would
be
very
well
,
if
with
the
greatest
accuratenesse
possible
one
should
enquire
whether
such
a
mutation
as
ought
to
be
discoverable
in
the
fixed
stars
,
supposing
the
annual
motion
of
the
Earth
,
would
be
observed
really
and
in
effect
,
a
thing
which
I
verily
believe
hath
never
as
yet
been
done
by
any
;
done
,
said
I
?
no
,
nor
haply
(
as
I
said
before
)
by
many
well
understood
how
it
ought
to
be
done
.
Nor
speak
I
this
at
randome
,
for
I
have
heretofore
seen
a
certain
Manuscript
of
one
of
these
Anti-Copernicans
,
which
said
,
that
there
would
necessarily
follow
,
in
case
that
opinion
were
true
,
a
continual
rising
and
falling
of
the
Pole
from
six
moneths
to
six
moneths
,
according
as
the
Earth
in
such
a
time
,
by
such
a
space
as
is
the
diameter
of
the
grand
Orb
,
retireth
one
while
towards
the
North
,
and
another
while
towards
the
South
;
and
yet
it
seemed
to
him
reasonable
,
yea
necessary
,
that
we
,
following
the
Earth
,
when
we
were
towards
the
North
should
have
the
Pole
more
elevated
than
when
we
are
towards
the
South
.
In
this
very
error
did
one
fall
that
was
otherwise
a
very
skilful
Mathematician
,
&
a
follower
of
Copernic
.
as
Tycho
relateth
in
his
[
](A61244-e79570-b)*
*
Christophorus
Rothmannus
.
Progymnasma
.
pag.
684.
which
said
,
that
he
had
observed
the
Polar
altitude
to
vary
,
and
to
differ
in
Summer
from
what
it
is
in
Winter
:
and
because
Tycho
denieth
the
merit
of
the
cause
,
but
findeth
no
fault
with
the
method
of
it
;
that
is
,
denieth
that
there
is
any
mutation
to
be
seen
in
the
altitude
of
the
Pole
,
but
doth
not
blame
the
inquisition
,
for
not
being
adapted
to
the
finding
of
what
is
sought
,
he
thereby
sheweth
,
that
he
also
esteeemed
the
Polar
altitude
varied
,
or
not
varied
every
six
moneths
,
to
be
a
good
testimony
to
disprove
or
inferre
the
annual
motion
of
the
Earth
.
SIMP.
In
truth
,
Salviatus
,
my
opinion
also
tells
me
,
that
the
same
must
necessarily
ensue
:
for
I
do
not
think
that
you
will
deny
me
,
but
that
if
we
walk
only
60.
miles
towards
the
North
,
the
Pole
will
rise
unto
us
a
degree
higher
,
and
that
if
we
move
60.
miles
farther
Northwards
,
the
Pole
will
be
elevated
to
us
a
degree
more
,
&c.
Now
if
the
approaching
or
receding
60.
miles
onely
,
make
so
notable
a
change
in
the
Polar
altitudes
,
what
alteration
would
follow
,
if
the
Earth
and
we
with
it
,
should
be
transported
,
I
will
not
say
60.
miles
,
but
60.
thousand
miles
that
way
.
SALV
.
It
would
follow
(
if
it
should
proceed
in
the
same
proportion
)
that
the
Pole
shall
be
elevated
a
thousand
degrees
.
See
,
Simplicius
,
what
a
long
rooted
opinion
can
do
.
Yea
,
by
reason
you
have
fixed
it
in
your
mind
for
so
many
years
,
that
it
is
Heaven
,
that
revolveth
in
twenty
four
hours
,
and
not
the
Earth
,
and
that
consequently
the
Poles
of
that
Revolution
are
in
Heaven
,
and
not
in
the
Terrestrial
Globe
,
cannot
now
,
in
an
hours
time
shake
off
this
habituated
conceipt
,
and
take
up
the
contrary
,
fancying
to
your self
,
that
the
Earth
is
that
which
moveth
,
only
for
so
long
time
as
may
suffice
to
conceive
of
what
would
follow
,
thereupon
should
that
lye
be
a
truth
.
If
the
Earth
Simplicius
,
be
that
which
moveth
in
its
self
in
twenty
four
hours
,
in
it
are
the
Poles
,
in
it
is
the
Axis
,
in
it
is
the
Equinoctial
,
that
is
,
the
grand
Circle
,
described
by
the
point
,
equidistant
from
the
Poles
,
in
it
are
the
infinite
Parallels
bigger
and
lesser
described
by
the
points
of
the
superficies
more
and
lesse
distant
from
the
Poles
,
in
it
are
all
these
things
,
and
not
in
the
starry
Sphere
,
which
,
as
being
immoveable
,
wants
them
all
,
and
can
only
by
the
imagination
be
conceived
to
be
therein
,
prolonging
the
Axis
of
the
Earth
so
far
,
till
that
determining
,
it
shall
mark
out
two
points
placed
right
over
our
Poles
,
and
the
plane
of
the
Equinoctial
being
extended
,
it
shall
describe
in
Heaven
a
circle
like
it self
.
Now
if
the
true
Axis
,
the
true
Poles
,
the
true
Equinoctial
,
do
not
change
in
the
Earth
so
long
as
you
continue
in
the
same
place
of
the
Earth
,
and
though
the
Earth
be
transported
,
as
you
do
please
,
yet
you
shall
not
change
your
habitude
either
to
the
Poles
,
or
to
the
circles
,
or
to
any
other
Earthly
thing
;
and
this
because
,
that
that
transposition
being
common
to
you
and
to
all
Terrestrial
things
;
Motion
〈◊〉
it
is
common
is
as
if
it
never
were
.
and
that
motion
where
it
is
common
,
is
as
if
it
never
were
;
and
as
you
change
not
habitude
to
the
Terrestrial
Poles
(
habitude
I
say
,
whether
that
they
rise
,
or
descend
)
so
neither
shall
you
change
position
to
the
Poles
imagined
in
Heaven
;
alwayes
provided
that
by
Celestial
Poles
we
understand
(
as
hath
been
already
defined
)
those
two
points
that
come
to
be
marked
out
by
the
prolongation
of
the
Terrestrial
Axis
unto
that
length
.
T
is
true
those
points
in
Heaven
do
change
,
when
the
Earths
transportment
is
made
after
such
a
manner
,
that
its
Axis
cometh
to
passe
by
other
and
other
points
of
the
immoveable
Celestial
Sphere
,
but
our
habitude
thereunto
changeth
not
,
so
as
that
the
second
should
be
more
elevated
to
us
than
the
first
.
If
any
one
will
have
one
of
the
points
of
the
Firmament
,
which
do
answer
to
the
Poles
of
the
Earth
to
ascend
,
and
the
other
to
descend
,
he
must
walk
along
the
Earth
towards
the
one
,
receding
from
the
other
,
for
the
transportment
of
the
Earth
,
and
with
it
us
our selves
,
(
as
I
told
you
before
)
operates
nothing
at
all
.
SAGR.
Permit
me
,
I
beseech
you
Salviatus
,
to
make
this
a
little
more
clear
by
an
example
,
which
although
grosse
,
is
acommodated
to
this
purpose
.
An
example
fitted
to
prove
that
the
altitude
of
the
Pole
ought
not
to
vary
by
means
of
the
Earths
annual
motion
.
Suppose
your self
,
Simplicius
,
to
be
aboard
a
Ship
,
and
that
standing
in
the
Poope
,
or
Hin-deck
;
you
have
directed
a
Quadrant
,
or
some
other
Astronomical
Instrument
,
towards
the
top
of
the
Top-gallant-Mast
,
as
if
you
would
take
its
height
,
which
suppose
it
were
v.
gr.
40.
degrees
,
there
is
no
doubt
,
but
that
if
you
walk
along
the
[
](A61244-e79770-b)*
*
Corsia
,
the
bank
or
bench
on
which
slaves
sit
in
a
Gally
.
Hatches
towards
the
Mast
25.
or
30.
paces
;
and
then
again
direct
the
said
Instrument
to
the
same
Top-Gallant-Top
.
You
shall
find
its
elevation
to
be
greater
,
and
to
be
encreased
v.
gr.
10.
degrees
;
but
if
instead
of
walking
those
25.
or
30.
paces
towards
the
Mast
,
you
stand
still
at
the
Sterne
,
and
make
the
whole
Ship
to
move
thitherwards
,
do
you
believe
that
by
reason
of
the
25.
or
30.
paces
that
it
had
past
,
the
elevation
of
the
Top-Gallant-Top
would
shew
10.
degrees
encreased
?
SIMP.
I
believe
and
know
that
it
would
not
gain
an
hairs
breadth
in
the
passing
of
30.
paces
,
nor
of
a
thousand
,
no
nor
of
an
hundred
thousand
miles
;
but
yet
I
believe
withal
that
looking
through
the
sights
at
the
Top
and
Top-Gallant
,
if
I
should
find
a
fixed
Star
that
was
in
the
same
elevation
,
I
believe
I
say
,
that
,
holding
still
the
Quadrant
,
after
I
had
sailed
towards
the
star
60.
miles
,
the
eye
would
meet
with
the
top
of
the
said
Mast
,
as
before
,
but
not
with
the
star
,
which
would
be
elevated
to
me
one
degree
.
SAGR.
Then
you
do
not
think
that
the
sight
would
fall
upon
that
point
of
the
Starry
Sphere
,
that
answereth
to
the
direction
of
the
Top-Gallant
Top
?
SIMP.
No
:
For
the
point
would
be
changed
,
and
would
be
beneath
the
star
first
observed
.
SAGR.
You
are
in
the
right
.
Now
like
as
that
which
in
this
example
answereth
to
the
elevation
of
the
Top-Gallant-Top
,
is
not
the
star
,
but
the
point
of
the
Firmament
that
lyeth
in
a
right
line
with
the
eye
,
and
the
said
top
of
the
Mast
,
so
in
the
case
exemplified
,
that
which
in
the
Firmament
answers
to
the
Pole
of
the
Earth
,
is
not
a
star
,
or
other
fixed
thing
in
the
Firmament
;
but
is
that
point
in
which
the
Axis
of
the
Earth
continued
streight
out
,
till
it
cometh
thither
doth
determine
,
which
point
is
not
fixed
,
but
obeyeth
the
mutations
that
the
Pole
of
the
Earth
doth
make
.
Upon
the
annual
motion
of
the
Earth
,
alteration
may
ensue
in
some
fixed
star
,
not
in
the
Pole
.
And
therefore
Tycho
,
or
who
ever
else
that
did
alledg
this
objection
,
ought
to
have
said
that
upon
that
same
motion
of
the
Earth
,
were
it
true
,
one
might
observe
some
difference
in
the
elevation
and
depression
(
not
of
the
Pole
,
but
)
of
some
fixed
star
toward
that
part
which
answereth
to
our
Pole
.
SIMP.
I
already
very
well
understand
the
mistake
by
them
committed
;
but
yet
therefore
(
which
to
me
seems
very
great
)
of
the
argument
brought
on
the
contrary
is
not
lessened
,
supposing
relation
to
be
had
to
the
variation
of
the
stars
,
and
not
of
the
Pole
;
for
if
the
moving
of
the
Ship
but
60.
miles
,
make
a
fixed
star
rise
to
me
one
degree
,
shall
I
not
find
alike
,
yea
and
very
much
greater
mutation
,
if
the
Ship
should
sail
towards
the
said
star
for
so
much
space
as
is
the
Diameter
of
the
Grand
Orb
,
which
you
affirm
to
be
double
the
distance
that
is
between
the
Earth
and
Sun
?
SAGR.
Herein
Simplicius
,
there
is
another
fallacy
,
which
,
truth
is
,
The
equivoke
of
those
who
believe
that
in
the
annual
motion
great
mutations
are
to
be
made
about
the
elevation
of
a
fixed
star
,
is
confuted
.
you
understand
,
but
do
not
upon
the
sudden
think
of
the
same
,
but
I
will
try
to
bring
it
to
your
remembrance
:
Tell
me
therefore
;
if
when
after
you
have
directed
the
Quadrant
to
a
fixed
star
,
and
found
v.
g.
its
elevation
to
be
40.
degrees
,
you
should
without
stirring
from
the
place
,
incline
the
side
of
the
Quadrant
,
so
as
that
the
star
might
remain
elevated
above
that
direction
,
would
you
thereupon
say
that
the
star
had
acquired
greater
elevation
?
SIMP.
Certainly
no
:
For
the
mutation
was
made
in
the
Instrument
and
not
in
the
Observer
,
that
did
change
place
,
moving
towards
the
same
.
SAGR.
But
if
you
sail
or
walk
along
the
surface
of
the
Terrestrial
Globe
,
will
you
say
that
there
is
no
alteration
made
in
the
said
Quadrant
,
but
that
the
same
elevation
is
still
retained
in
respect
of
the
Heavens
,
so
long
as
you
your self
do
not
incline
it
,
but
let
it
stand
at
its
first
constitution
?
SIMP.
Give
me
leave
to
think
of
it
.
I
would
say
without
more
ado
,
that
it
would
not
retain
the
same
,
in
regard
the
progresse
I
make
is
not
in
plano
,
but
about
the
circumference
of
the
Terrestrial
Globe
,
which
at
every
step
changeth
inclination
in
respect
to
Heaven
,
and
consequently
maketh
the
same
change
in
the
Instrument
which
is
erected
upon
the
same
.
SAGR.
You
say
very
well
:
And
you
know
withal
,
that
by
how
much
the
bigger
that
circle
shall
be
upon
which
you
move
,
so
many
more
miles
you
are
to
walk
,
to
make
the
said
star
to
rise
that
same
degree
higher
;
and
that
finally
if
the
motion
towards
the
star
should
be
in
a
right
line
,
you
ought
to
move
yet
farther
,
than
if
it
were
about
the
circumference
of
never
so
great
a
circle
?
SALV
.
True
:
The
right
line
,
and
circumference
of
an
infinite
circle
,
are
the
same
thing
.
For
in
short
the
circumference
of
an
infinite
circle
,
and
a
right
line
are
the
same
thing
.
SAGR.
But
this
I
do
not
understand
,
nor
as
I
believe
,
doth
Simplicius
apprehend
the
same
;
and
it
must
needs
be
concealed
from
us
under
some
mistery
,
for
we
know
that
Salviatus
never
speaks
at
random
,
nor
proposeth
any
Paradox
,
which
doth
not
break
forth
into
some
conceit
,
not
trivial
in
the
least
.
Therefore
in
due
time
and
place
I
will
put
you
in
mind
to
demonstrate
this
,
that
the
right
line
is
the
same
with
the
circumference
of
an
infinite
circle
,
but
at
present
I
am
unwilling
that
we
should
interrupt
the
discourse
in
hand
.
Returning
then
to
the
case
,
I
propose
to
the
consideration
of
Simplicius
,
how
the
accession
and
recession
that
the
Earth
makes
from
the
said
fixed
star
which
is
neer
the
Pole
can
be
made
as
it
were
by
a
right
line
,
for
such
is
the
Diameter
of
the
Grand
Orb
,
so
that
the
attempting
to
regulate
the
elevation
and
depression
of
the
Polar
star
by
the
motion
along
the
said
Diameter
,
as
if
it
were
by
the
motion
about
the
little
circle
of
the
Earth
,
is
a
great
argument
of
but
little
judgment
.
SIMP.
But
we
continue
still
unsatisfied
,
in
regard
that
the
said
small
mutation
that
should
be
therein
,
would
not
be
discerned
;
and
if
this
be
null
,
then
must
the
annual
motion
about
the
Grand
Orb
ascribed
to
the
Earth
,
be
null
also
.
SAGR.
Here
now
I
give
Salviatus
leave
to
go
on
,
who
as
I
believe
will
not
overpasse
the
elevation
and
depression
of
the
Polar
star
or
any
other
of
those
that
are
fixed
as
null
,
although
not
discovered
by
any
one
,
and
affirmed
by
Copernicus
himself
to
be
,
I
will
not
say
null
,
but
unobservable
by
reason
of
its
minuity
.
SALV
.
I
have
already
said
above
,
that
I
do
not
think
that
any
one
did
ever
set
himself
to
observe
,
Enquiry
is
made
what
mutations
,
&
in
what
stars
,
are
to
be
discovered
,
by
means
of
the
annual
motion
of
the
Earth
.
whether
in
different
times
of
the
year
there
is
any
mutation
to
be
seen
in
the
fixed
stars
,
that
may
have
a
dependance
on
the
annual
motion
of
the
Earth
,
and
added
withal
,
that
I
doubted
least
haply
some
might
never
have
understood
what
those
mutations
are
,
and
amongst
what
stars
they
should
be
discerned
;
therefore
it
would
be
necessary
that
we
in
the
next
place
narrowly
examine
this
particular
.
Astronomers
having
omitted
to
instance
what
alterations
those
are
that
may
be
derived
from
the
annual
motion
of
the
Earth
,
do
thereby
testifie
that
they
never
rightly
understood
the
same
.
My
having
onely
found
written
in
general
terms
that
the
annual
motion
of
the
Earth
about
the
Grand
Orb
,
ought
not
to
be
admitted
,
because
it
is
not
probable
but
that
by
means
of
the
same
there
would
be
discoverd
some
apparent
mutation
in
the
fixed
stars
,
and
not
hearing
say
what
those
apparent
mutations
ought
to
be
in
particular
,
and
in
what
stars
,
maketh
me
very
reasonably
to
infer
that
they
who
rely
upon
that
general
position
,
have
not
understood
,
no
nor
possibly
endeavoured
to
understand
,
how
the
businesse
of
these
mutations
goeth
,
nor
what
things
those
are
which
they
say
ought
to
be
seen
.
The
mutations
of
the
fixed
stars
ought
to
be
in
some
greater
,
in
others
lesser
,
and
in
others
nothing
at
all
.
And
to
this
judgment
I
am
the
rather
induced
;
knowing
that
the
annual
motion
ascribed
by
Copernicus
to
the
Earth
,
if
it
should
appear
sensible
in
the
Starry
Sphere
,
is
not
to
make
apparent
mutations
equal
in
respect
to
all
the
stars
,
but
those
appearances
ought
to
be
made
in
some
greater
,
in
others
lesser
,
and
in
others
yet
lesser
;
and
lastly
,
in
others
absolutely
nothing
at
all
,
by
reason
of
the
vast
magnitude
that
the
circle
of
this
annual
motion
is
supposed
to
be
of
.
As
for
the
mutations
that
should
b●
seen
,
they
are
of
two
kinds
,
one
is
the
said
stars
changing
apparent
magnitude
,
and
the
other
their
variation
of
altitudes
in
the
Meridian
.
Upon
which
necessarily
followeth
the
mutation
of
risings
and
settings
,
and
of
their
distances
from
the
Zenith
,
&c.
SAGR.
Methinks
I
see
preparing
for
me
such
a
skean
of
these
revolutions
,
that
I
wish
it
may
never
be
my
task
to
dis-intangle
them
,
for
to
confesse
my
infirmity
to
Salviatus
,
I
have
sometimes
thought
thereon
,
but
could
never
find
the
[
](A61244-e80500-b)*
*
Bandola
that
end
of
a
skeen
wherewith
housewives
fasten
their
hankes
of
yarn
,
thread
or
silk
.
Lay-band
of
it
,
and
I
speak
not
so
much
of
this
which
pertains
to
the
fixed
stars
,
as
of
another
more
terrible
labour
which
you
bring
to
my
remembrance
by
maintaining
these
Meridian
Altitudes
,
Ortive
Latitudes
and
distances
from
the
Vertex
,
&c.
The
grand
difficulty
in
Copernicus
his
Doctrine
,
is
that
which
concerns
the
Phaenomena
of
the
Sun
and
fixed
stars
.
And
that
which
puzzleth
my
brains
,
ariseth
from
what
I
am
now
about
to
tell
you
.
Copernicus
supposeth
the
Starry
Sphere
immoveable
,
and
the
Sun
in
the
centre
thereof
immoveable
also
.
Therefore
every
mutation
which
seemeth
unto
us
to
be
made
in
the
Sun
or
in
the
fixed
stars
,
must
of
necessity
befall
the
Earth
and
be
ous
.
But
the
Sun
riseth
and
declineth
in
our
Meridian
by
a
very
great
arch
of
almost
47.
degrees
,
and
by
arches
yet
greater
and
greatet
,
varieth
its
Ortive
and
Occidual
Latitudes
in
the
oblique
Horizons
.
Now
how
can
the
Earth
ever
incline
and
elevate
so
notably
to
the
Sun
,
and
nothing
at
all
to
the
fixed
stars
,
or
so
little
,
that
it
is
not
to
be
perceived
?
This
is
that
knot
which
could
never
get
thorow
my
[
](A61244-e80570-b)*
*
Pettine
,
it
is
the
stay
in
a
Weavets
Loom
,
that
permitteth
no
knot
or
snarle
to
passe
it
,
called
by
them
the
Combe
of
the
Loom
.
Loom-Combe
;
and
if
you
shall
untie
it
,
I
shall
hold
you
for
more
than
an
Alexander
.
SALV
.
These
are
scruples
worthy
of
the
ingenuity
of
Sagredus
,
and
this
doubt
is
so
intricate
,
that
even
Copernicus
himself
almost
despaired
of
being
able
to
explain
the
same
,
so
as
to
render
it
intelligible
,
which
we
see
as
well
by
his
own
confession
of
its
obscurity
,
as
also
by
his
,
at
two
several
times
,
taking
two
different
wayes
to
make
it
out
.
And
,
I
ingenuously
confesse
that
I
understood
not
his
explanation
,
till
such
time
as
another
method
more
plain
and
manifest
,
had
rendred
it
intelligible
;
and
yet
neither
was
that
done
without
a
long
and
laborious
application
of
my
thoughts
to
the
same
.
SIMP.
Aristotle
saw
the
same
scruple
,
Aristotles
argument
against
the
Ancients
,
who
held
that
the
Earth
was
a
Planet
.
and
makes
use
thereof
to
oppose
certain
of
the
Ancients
,
who
held
that
the
Earth
was
a
Planet
;
against
whom
he
argueth
,
that
if
it
were
so
,
it
would
follow
that
it
also
,
as
the
rest
of
the
Planets
,
should
have
a
plurality
of
motions
,
from
whence
would
follow
these
variations
in
the
risings
and
settings
of
the
fixed
stars
,
and
likewise
in
the
Meridian
Altitudes
.
And
in
regard
that
he
propoundeth
the
difficulty
,
and
doth
not
answer
it
,
it
must
needs
be
,
if
not
impossible
,
at
least
very
difficult
to
be
resolved
.
SALV
.
The
stresse
and
strength
of
the
knot
rendereth
the
solution
thereof
more
commendable
and
admirable
;
but
I
do
not
promise
you
the
same
at
this
time
,
and
pray
you
to
dispense
with
me
therein
till
too
morrow
,
and
for
the
present
we
will
go
considering
and
explaining
those
mutations
and
differences
that
by
means
of
the
annual
motion
ought
to
be
discerned
in
the
fixed
stars
,
like
as
even
now
we
said
,
for
the
explication
whereof
certain
preparatory
points
offer
themselves
,
which
may
facilitate
the
answer
to
the
grand
objection
.
Now
reassuming
the
two
motions
ascribed
to
the
Earth
(
two
I
say
,
for
the
third
is
no
motion
,
as
in
its
place
I
will
declare
)
that
is
the
annual
and
diurnal
,
The
annual
motion
made
by
the
centre
of
the
Earth
under
the
Ecliptick
and
the
diurnal
motion
made
by
the
Earth
about
its
own
centre
.
the
first
is
to
be
understood
to
be
made
by
the
centre
of
the
Earth
in
or
about
the
circumference
of
the
grand
Orb
,
that
is
of
a
very
great
circle
described
in
the
plain
of
the
fixed
and
immutable
Ecliptick
;
the
other
,
namely
the
diurnal
,
is
made
by
the
Globe
of
the
Earth
in
it self
about
its
own
centre
,
and
own
Axis
,
not
erect
,
but
inclined
to
the
Plane
of
the
Ecliptick
,
with
the
inclination
of
23.
degrees
and
an
half
,
or
thereabouts
,
the
which
inclination
is
maintained
all
the
year
about
,
and
that
which
ought
especially
to
be
observed
,
is
alwayes
situate
towards
the
same
point
of
Heaven
:
The
axis
of
the
Earth
continueth
alwayes
parallel
to
it self
,
and
describeth
a
Cylindraical
superficies
,
inclining
to
the
grand
Orb.
in
so
much
that
the
Axis
of
the
diurnal
motion
doth
alwayes
remain
parallel
to
it self
;
so
that
if
we
imagine
that
same
Axis
to
be
continued
out
until
it
reach
the
fixed
stars
,
whilst
the
centre
of
the
Earth
is
encircling
the
whole
Ecliptick
in
a
year
,
the
said
Axis
describeth
the
superficies
of
an
oblique
Cylinder
,
which
hath
for
one
of
its
bases
the
said
annual
circle
,
and
for
the
other
a
like
circle
imaginarily
described
by
its
extremity
,
or
,
(
if
you
will
)
Pole
,
amongst
the
fixed
stars
.
And
this
same
cylinder
is
oblique
to
the
Plane
of
the
Ecliptick
,
according
to
the
inclination
of
the
Axis
that
describeth
it
,
which
we
have
said
to
be
23
degrees
and
an
half
,
the
which
continuing
perpetually
the
same
(
save
onely
,
that
in
many
thousands
of
years
it
maketh
some
very
small
mutation
,
which
nothing
importeth
in
our
present
businesse
)
causeth
that
the
Terrestrial
Globe
doth
never
more
incline
or
elevate
,
The
Orb
of
the
Earth
never
inclineth
,
but
is
immutably
the
same
.
but
still
conserveth
the
same
state
without
mutation
.
From
whence
ensueth
,
that
as
to
what
pertaineth
to
the
mutations
to
be
observed
in
the
fixed
stars
dependant
on
the
sole
annual
motion
,
the
same
shall
happen
to
any
point
whatsoever
of
the
Earths
surface
,
as
befalleth
unto
the
centre
of
the
Earth
it self
;
and
therefore
in
the
present
explanations
we
will
make
use
of
the
centre
,
as
if
it
were
any
whatsoever
point
of
the
superficies
.
And
for
a
more
facile
understanding
of
the
whole
,
The
fixed
stars
placed
in
the
Ecliptick
never
elevate
nor
descend
,
on
account
of
the
annual
motion
,
but
yet
approach
and
recede
.
let
us
design
the
same
in
lineal
figures
:
And
first
of
all
let
us
describe
in
the
Plane
of
the
Ecliptick
the
circle
ANBO
[
in
Fig.
7.
]
and
let
us
understand
the
points
A
and
B
,
to
be
the
extreams
towards
the
North
and
South
;
that
is
,
the
beginning
of
[
or
entrance
into
]
Cancer
or
Capricorn
,
and
let
us
prolong
the
Diameter
AB
,
indeterminately
by
D
and
C
towards
the
Starry
Sphere
.
I
say
now
in
the
first
place
,
that
none
of
the
fixed
stars
placed
in
the
Ecliptick
,
shall
ever
vary
elevation
,
by
reason
of
any
whatsoever
mutation
made
by
the
Earth
along
the
said
Plane
of
the
Ecliptick
,
but
shall
alwayes
appear
in
the
same
superficies
,
although
the
Earth
shall
approach
and
recede
as
great
a
space
as
is
that
of
the
diameter
of
the
Grand
Orb
,
as
may
plainly
be
seen
in
the
said
figure
.
For
whether
the
Earth
be
in
the
point
A
or
in
B
,
the
star
C
alwayes
appeareth
in
the
same
line
ABC
;
although
the
distance
BC
,
be
lesse
than
AC
,
by
the
whole
diameter
AB
.
The
most
therefore
that
can
be
discovered
in
the
star
C
,
and
in
any
other
placed
in
the
Ecliptick
,
is
the
augmented
or
diminished
apparent
magnitude
,
by
reason
of
the
approximation
or
recession
of
the
Earth
.
SAGR.
Stay
a
while
I
pray
you
,
for
I
meet
with
a
certain
scruple
,
which
much
troubleth
me
,
and
it
is
this
:
That
the
star
C
may
be
seen
by
the
same
line
ABC
,
as
wel
when
the
Earth
is
in
A
,
as
when
it
is
in
B
,
I
understand
very
well
,
as
also
furthermore
I
apprehend
that
the
same
would
happen
in
all
the
points
of
the
line
AB
,
Objections
against
the
Earths
annual
motion
taken
from
the
fixed
stars
placed
in
the
Ecliptick
.
so
long
as
the
Earth
should
passe
from
A
to
B
by
the
said
line
;
but
it
passing
thither
,
as
is
to
be
supposed
,
by
the
arch
ANB
,
it
is
manifest
that
when
it
shall
be
in
the
point
N
,
and
in
any
other
except
those
two
A
and
B
,
the
said
star
shall
no
longer
be
observed
in
the
line
AB
;
but
in
others
.
So
that
,
if
the
appearing
under
several
lines
ought
to
cause
apparent
mutations
,
some
difference
must
needs
appear
in
this
case
.
Nay
more
,
I
will
speak
it
with
that
Philosophical
freedom
,
which
ought
to
be
allowed
amongst
Philosophick
friends
,
methinks
that
you
,
contradicting
your self
,
deny
that
now
,
which
but
even
now
to
our
admiration
,
you
proved
to
be
really
true
,
and
considerable
;
I
mean
that
which
happeneth
in
the
Planets
,
and
particularly
in
the
three
superiour
ones
,
that
being
constantly
in
the
Ecliptick
,
or
very
near
unto
it
,
do
not
onely
shew
themselves
one
while
near
unto
us
,
and
another
while
remote
,
but
so
deformed
in
their
regular
motions
,
that
they
seem
sometimes
immoveable
,
and
sometimes
many
degrees
retrograde
;
and
all
upon
no
other
occasion
than
the
annual
motion
of
the
Earth
.
SALV
.
Though
by
a
thousand
accidents
I
have
been
heretofore
assured
of
the
wittinesse
of
Sagredus
,
yet
I
had
a
desire
by
this
one
experiment
more
to
ascertain
me
of
what
I
may
expect
from
his
ingenuity
,
and
all
this
for
my
own
interest
,
for
in
case
my
Propositions
stand
but
proof
against
the
hammer
and
furnace
of
his
judgment
,
I
shall
be
confident
that
they
will
abide
the
[
](A61244-e80890-b)*
*
Or
will
prove
of
good
alloy
.
test
of
all
Touch-stones
.
I
say
therefore
that
I
had
purposely
dissembled
this
objection
,
but
yet
not
with
any
intent
to
deceive
you
,
and
to
put
any
falshood
upon
you
,
as
it
might
have
happened
if
the
objection
by
me
disguised
,
and
by
you
over-lookt
,
had
been
the
same
in
effect
as
it
seemed
to
be
in
appearance
,
that
is
,
really
valid
and
conclusive
;
but
it
is
not
so
;
nay
I
rather
suspect
that
to
try
me
,
you
make
as
if
you
did
not
see
its
nullity
.
But
I
will
herein
be
too
hard
for
you
,
and
force
from
your
tongue
,
that
which
you
would
so
artificially
conceal
;
and
therefore
tell
me
,
what
that
thing
should
be
,
whereby
you
come
to
know
the
station
and
retrogradation
of
the
Planets
,
which
is
derived
from
the
annual
motion
,
aud
which
is
so
great
,
that
at
least
some
foot-steps
of
such
an
effect
ought
to
appear
in
the
stars
of
the
Ecliptick
?
SAGR.
This
demand
of
yours
containeth
two
questions
,
to
which
it
is
necessary
that
I
make
reply
;
the
first
relates
to
the
imputation
which
you
lay
upon
me
of
a
Dissembler
;
the
other
concerneth
that
which
may
appear
in
the
stars
,
&c.
As
to
the
first
,
I
will
say
with
your
permission
,
that
it
is
not
true
,
that
I
have
dissembled
my
knowing
the
nullity
of
that
objection
;
and
to
assure
you
of
the
same
,
I
now
tell
you
that
I
very
well
understand
the
nullity
thereof
.
SALV
.
But
yet
I
do
not
understand
how
it
can
be
,
that
you
spake
not
friendly
,
when
you
said
you
did
not
know
that
same
fallacy
which
you
now
confesse
that
you
know
very
well
.
SAGR.
The
very
confession
of
knowing
it
may
assure
you
that
I
did
not
dissemble
,
when
I
said
that
I
did
not
understand
it
;
for
if
I
had
had
a
mind
,
and
would
dissemble
,
who
could
hinder
me
from
continuing
in
the
same
simulation
,
and
denying
still
that
I
understand
the
fallacy
?
I
say
therefore
that
I
understood
not
the
same
,
at
that
time
,
but
that
I
do
now
at
this
present
apprehend
it
,
for
that
you
have
prompted
my
intellect
,
first
by
telling
me
resolutely
that
it
is
null
,
and
then
by
beginning
to
question
me
so
at
large
what
thing
that
might
be
,
whereby
I
might
come
to
know
the
station
and
retrogradation
of
the
Planets
;
The
station
,
direction
and
retrogradation
of
the
Planets
is
known
,
in
relation
to
the
fixed
stars
.
and
because
this
is
known
by
comparing
them
with
the
fixed
stars
,
in
relation
to
which
,
they
are
seen
to
vary
their
motions
,
one
while
towards
the
West
,
and
another
towards
the
East
,
and
sometimes
to
abide
immoveable
;
and
because
there
is
not
any
thing
above
the
Starry
Sphere
,
immensely
more
remote
from
us
,
and
visible
unto
us
,
wherewith
we
may
compare
our
fixed
stars
,
therefore
we
cannot
discover
in
the
fixed
stars
any
foot-steps
of
what
appeareth
to
us
in
the
Planets
.
This
I
believe
is
the
substance
of
that
which
you
would
force
from
me
.
SALV
.
It
is
so
,
An
Indice
is
the
fixed
stars
like
to
that
which
is
〈◊〉
in
the
Plane●s
,
is
an
argument
of
the
Earths
annual
motion
.
with
the
addition
moreover
of
your
admirable
ingenuity
;
and
if
with
half
a
word
I
did
open
your
eyes
,
you
by
the
like
have
remembred
me
that
it
is
not
altogether
impossible
,
but
that
sometime
or
other
something
observable
may
be
found
amongst
the
fixed
stars
,
by
which
it
may
be
gathered
wherein
the
annual
conversion
resides
,
so
as
that
they
also
no
lesse
than
the
Planets
and
Sun
it self
,
may
appear
in
judgment
to
bear
witnesse
of
that
motion
,
in
favour
of
the
Earth
;
for
I
do
not
think
that
the
sta●s
are
spread
in
a
spherical
superficies
equally
remote
from
a
common
centre
,
but
hold
,
that
their
distances
from
us
are
so
various
,
that
some
of
them
may
be
twice
and
thrice
as
remote
as
others
;
so
that
if
with
the
Telescope
one
should
observe
a
very
small
star
neer
to
one
of
the
bigger
,
and
which
therefore
was
very
exceeding
high
,
it
might
happen
,
that
some
sensible
mutation
might
fall
out
between
them
,
correspondent
to
that
of
the
superiour
Planets
.
And
so
much
shall
serve
to
have
spoken
at
this
time
touching
the
stars
placed
in
the
Ecliptick
.
The
fixed
stars
without
the
Ecliptick
elevate
and
descend
more
or
lesse
,
according
to
their
distance
from
the
said
Ecliptick
▪
Let
us
now
come
to
the
fixed
stars
,
placed
out
of
the
Ecliptick
,
and
let
us
suppose
a
great
circle
erect
upon
[
i.
e.
at
right
angles
to
]
the
Plane
of
the
[
](A61244-e81080-b)*
*
i.
e.
of
the
Ecliptick
.
same
;
and
let
it
,
for
example
,
be
a
circle
that
in
the
Starry
Sphere
answers
to
the
Solstitial
Colure
,
and
let
us
mark
it
CEH
[
in
Fig.
8.
]
which
shall
happen
to
be
withal
a
Meridian
,
and
in
it
we
will
take
a
star
without
the
Ecliptick
,
which
let
be
E.
Now
this
star
will
indeed
vary
its
elevation
upon
the
Earths
motion
;
for
from
the
Earth
in
A
it
shall
be
seen
according
to
the
ray
AE
,
with
the
elevation
of
the
angle
EAC
;
but
from
the
Earth
placed
in
B
,
it
shall
be
seen
according
to
the
ray
BE
,
with
the
elevation
of
the
angle
EBC
,
bigger
than
the
other
EAC
,
that
being
extern
,
and
this
intern
and
opposite
in
the
triangle
EAB
,
the
distance
therefore
of
the
star
E
from
the
Ecliptick
,
shall
appear
changed
;
and
likewise
its
altitude
in
the
Meridian
shall
become
greater
in
the
position
B
,
than
in
the
place
A
,
according
as
the
angle
EBC
exceeds
the
angle
EAC
,
which
excesse
is
the
quantity
of
the
angle
AEB
:
For
in
the
triangle
EAB
,
the
side
AB
being
continued
to
C
,
the
exteriour
angle
EBC
(
as
being
equal
to
the
two
interiour
and
opposite
E
and
A
)
exceedeth
the
said
angle
A
,
by
the
quantity
of
the
angle
E.
And
if
we
should
take
another
star
in
the
same
Meridian
,
more
remote
from
the
Ecliptick
,
as
for
instance
the
star
H
,
the
diversity
in
it
shall
be
greater
by
being
observed
from
the
two
stations
A
and
B
,
according
as
the
angle
AHB
is
greater
than
the
other
E
;
which
angle
shall
encrease
continually
according
as
the
observed
star
shall
be
farther
and
farther
from
the
Ecliptick
,
till
that
at
last
the
greatest
mutation
will
appear
in
that
star
that
should
be
placed
in
the
very
Pole
of
the
Ecliptick
.
As
for
a
full
understanding
thereof
we
thus
demonstrate
.
Suppose
the
diameter
of
the
Grand
Orb
to
be
AB
,
whose
centre
[
in
the
same
Figure
]
is
G
,
and
let
it
be
supposed
to
be
continued
out
as
far
as
the
Starry
Sphere
in
the
points
D
and
C
,
and
from
the
centre
G
let
there
be
erected
the
Axis
of
the
Ecliptick
GF
,
prolonged
till
it
arrive
at
the
said
Sphere
,
in
which
a
Meridian
DFC
is
supposed
to
be
described
,
that
shall
be
perpendicular
to
the
Plane
of
the
Ecliptick
;
and
in
the
arch
FC
any
points
H
and
E
,
are
imagined
to
be
taken
,
as
places
of
fixed
stars
:
Let
the
lines
FA
,
FB
,
AH
,
HG
,
HB
,
AE
,
GE
,
BE
,
be
conjoyned
.
And
let
the
angle
of
difference
,
or
,
if
you
will
,
the
Parallax
of
the
star
placed
in
the
Pole
F
,
be
AFB
,
and
let
that
of
the
star
placed
in
H
,
be
the
angle
AHB
,
and
let
that
of
the
star
in
E
,
be
the
angle
AEB
.
I
say
,
that
the
angle
of
difference
of
the
Polar
star
F
,
is
the
greatest
,
and
that
of
the
rest
,
those
that
are
nearer
to
the
greatest
are
bigger
than
the
more
remote
;
that
is
to
say
,
that
the
angle
F
is
bigger
than
the
angle
H
,
and
this
bigger
than
the
angle
E.
Now
about
the
triangle
FAB
,
let
us
suppose
a
circle
to
be
described
.
And
because
the
angle
F
is
acute
,
(
by
reason
that
its
base
AB
is
lesse
than
the
diameter
DC
,
of
the
semicircle
DFC
)
it
shall
be
placed
in
the
greater
portion
of
the
circumscribed
circle
cut
by
the
base
AB
.
And
because
the
said
AB
is
divided
in
the
midst
,
and
at
right
angles
by
FG
,
the
centre
of
the
circumscribed
circle
shall
be
in
the
line
FG
,
which
let
be
the
point
I
;
and
because
that
of
such
lines
as
are
drawn
from
the
point
G
,
which
is
not
the
centre
,
unto
the
circumference
of
the
circumscribed
circle
,
the
biggest
is
that
which
passeth
by
the
centre
,
GF
shall
be
bigger
than
any
other
that
is
drawn
from
the
point
G
,
to
the
circumference
of
the
said
circle
;
and
therefore
that
circumference
will
cut
the
line
GH
(
which
is
equal
to
the
line
GF
)
and
cutting
GH
,
it
will
also
cut
AH
.
Let
it
cut
it
in
L
,
and
conjoyn
the
line
LB
.
These
two
angles
,
therefore
,
AFB
and
ALB
shall
be
equal
,
as
being
in
the
same
portion
of
the
circle
circumscribed
.
But
ALB
external
,
is
bigger
than
the
internal
H
;
therefore
the
angle
F
is
bigger
than
the
angle
H.
And
by
the
same
method
we
might
demonstrate
the
angle
H
to
be
bigger
than
the
angle
E
,
because
that
of
the
circle
described
about
the
triangle
AHB
,
the
centre
is
in
the
perpendicular
GF
,
to
which
the
line
GH
is
nearer
than
the
line
GE
,
and
therefore
the
circumference
of
it
cutteth
GE
,
and
also
AE
,
whereupon
the
proposition
is
manifest
.
We
will
conclude
from
hence
,
that
the
difference
of
appearance
,
(
which
with
the
proper
term
of
art
,
we
might
call
the
Parallax
of
the
fixed
stars
)
is
greater
,
or
lesse
,
according
as
the
Stars
observed
are
more
or
lesse
adjacent
to
the
Pole
of
the
Ecliptick
,
so
that
,
in
conclusion
of
those
Stars
that
are
in
the
Ecliptick
it self
,
the
said
diversity
is
reduced
to
nothing
.
In
the
next
place
,
The
Earth
approacheth
or
recedeth
from
the
fixed
stars
of
the
Ecliptick
,
the
quantity
of
the
Diameter
of
the
Grand
Orb.
as
to
the
Earths
accession
by
that
motion
to
,
or
recession
from
the
Stars
,
it
appeareth
to
,
and
recedeth
from
those
that
are
in
the
Ecliptick
,
the
quantity
of
the
whole
diameter
of
the
grand
Orb
,
as
we
did
see
even
now
,
but
that
accession
or
recession
to
,
or
from
the
stars
about
the
Pole
of
the
Ecliptick
,
is
almost
nothing
;
and
in
going
to
and
from
others
,
this
difference
groweth
greater
,
according
as
they
are
neerer
to
the
Ecliptick
.
We
may
,
The
stars
nearer
to
us
make
greater
differences
than
the
more
remote
.
in
the
third
place
,
know
,
that
the
said
difference
of
Aspect
groweth
greater
or
lesser
,
according
as
the
Star
observed
shall
be
neerer
to
us
,
or
farther
from
us
.
For
if
we
draw
another
Meridian
,
lesse
distant
from
the
Earth
;
as
for
example
,
this
DFI
[
in
Fig.
7.
]
a
Star
placed
in
F
,
and
seen
by
the
same
ray
AFE
,
the
Earth
being
in
A
,
would
,
in
case
it
should
be
observed
from
the
Earth
in
B
,
appear
according
to
the
ray
BF
,
and
would
make
the
angle
of
difference
,
namely
,
BFA
,
bigger
than
the
former
AEB
,
being
the
exteriour
angle
of
the
triangle
BFE
.
SAGR.
With
great
delight
,
and
also
benefit
have
I
heard
your
discourse
;
The
Epilogue
of
the
Phaenomena
of
the
fixed
stars
caused
by
the
annual
motion
of
the
Earth
.
and
that
I
may
be
certain
,
whether
I
have
rightly
understood
the
same
,
I
shall
give
you
the
summe
of
the
Conclusions
in
a
few
words
.
As
I
take
it
,
you
have
explained
to
us
the
different
appearances
,
that
by
means
of
the
Earths
annual
motion
,
may
be
by
us
observed
in
the
fixed
stars
to
be
of
two
kinds
:
The
one
is
,
that
of
their
apparent
magnitudes
varied
,
according
as
we
,
transported
by
the
Earth
,
approach
or
recede
from
the
same
:
The
other
(
which
likewise
dependeth
on
the
same
accession
and
recession
)
their
appearing
unto
us
in
the
same
Meridian
,
one
while
more
elevated
,
and
another
while
lesse
.
Moreover
,
you
tell
us
(
and
I
understand
it
very
well
)
that
the
one
and
other
of
these
mutations
are
not
made
alike
in
all
the
stars
,
but
in
some
greater
,
and
in
others
lesser
,
and
in
others
not
at
all
.
The
accession
and
recession
whereby
the
same
star
ought
to
appear
,
one
while
bigger
,
and
another
while
lesser
,
is
insensible
,
and
almost
nothing
in
the
stars
neer
unto
the
pole
of
the
Ecliptick
,
but
is
greatest
in
the
stars
placed
in
the
Ecliptick
it self
,
and
indifferent
in
the
intermediate
:
the
contrary
happens
in
the
other
difference
,
that
is
,
the
elevation
or
depression
of
the
stars
placed
in
the
Ecliptick
is
nothing
at
all
,
greatest
in
those
neerest
to
the
Pole
of
the
said
Ecliptick
,
and
indifferent
in
the
intermediate
.
Besides
,
both
these
differences
are
more
sensible
in
the
Stars
neerest
to
us
,
in
the
more
remote
lesse
sensible
,
and
in
those
that
are
very
far
distant
wholly
disappear
.
This
is
,
as
to
what
concerns
my self
;
it
remaineth
now
,
as
I
conceive
,
that
something
be
said
for
the
satisfaction
of
Simplicius
,
who
,
as
I
believe
,
will
not
easily
be
made
to
over-passe
those
differences
,
as
insensible
that
are
derived
from
a
motion
of
the
Earth
so
vast
,
and
from
a
mutation
that
transports
the
Earth
into
places
twice
as
far
distant
from
us
as
the
Sun
.
SIMP.
Truth
is
,
to
speak
freely
,
I
am
very
loth
to
confesse
,
that
the
distance
of
the
fixed
Stars
ought
to
be
such
,
that
in
them
the
fore-mentioned
differences
should
be
wholly
imperceptible
.
SALV
.
Do
not
throw
your self
into
absolute
despair
,
Simplicius
,
for
there
may
perhaps
yet
some
qualification
be
found
for
your
difficulties
.
And
first
,
that
the
apparent
magnitude
of
the
stars
is
not
seen
to
make
any
sensible
alteration
,
ought
not
to
be
judged
by
you
a
thing
improbable
,
in
regard
you
see
the
guesses
of
men
in
this
particular
to
be
so
grossely
erroneous
,
especially
in
looking
upon
splendid
objects
;
and
you
your self
beholding
v.
g.
a
lighted
Torch
at
the
distance
of
200
paces
,
In
objects
far
remote
,
and
luminous
,
a
small
approach
or
recession
is
imperceptible
.
if
it
approach
nearer
to
you
3.
or
4.
yards
,
do
you
think
that
it
will
shew
any
whit
encreased
in
magnitude
?
I
for
my
part
should
not
perceive
it
certainly
,
although
it
should
approach
20.
or
30.
yards
nearer
;
nay
it
hath
sometimes
happened
that
in
seeing
such
a
light
at
that
distance
I
know
not
how
to
resolve
whether
it
came
towards
me
,
or
retreated
from
me
,
when
as
it
did
in
reality
approach
nearer
to
me
.
But
what
need
I
speak
of
this
?
If
the
self
same
accession
and
recession
(
I
speak
of
a
distance
twice
as
great
as
that
from
the
Sun
to
us
)
in
the
star
of
Saturn
is
almost
totally
imperceptible
,
and
in
Jupiter
not
very
observable
,
what
shall
we
think
of
the
fixed
stars
,
which
I
believe
you
will
not
scruple
to
place
twice
as
far
off
as
Saturn
?
In
Mars
,
which
for
that
it
is
nearer
to
us
—
SIMP.
Pray
Sir
,
put
your self
to
no
farther
trouble
in
this
particular
,
for
I
already
conceive
that
what
hath
been
spoken
touching
the
unaltered
apparent
magnitude
of
the
fixed
stars
may
very
well
come
to
passe
,
but
what
shall
we
say
of
the
other
difficulty
that
proceeds
from
not
perceiving
any
variation
in
the
mutation
of
aspect
?
SALV
.
We
will
say
that
which
peradventure
may
satisfie
you
also
in
this
particular
.
And
to
make
short
,
would
you
not
be
satisfied
if
there
should
be
discovered
in
the
stars
face
mutations
that
you
think
ought
to
be
discovered
,
in
case
the
annual
motion
belonged
to
the
Earth
?
SIMP.
I
should
so
doubtlesse
,
as
to
what
concerns
this
particular
.
SALV
.
I
could
wish
you
would
say
that
in
case
such
a
difference
were
discovered
,
If
in
the
fixed
stars
one
should
discover
any
annual
mutation
,
the
motion
of
the
Earth
would
be
undeniable
.
nothing
more
would
remain
behind
,
that
might
render
the
mobility
of
the
Earth
questionable
.
But
although
yet
that
should
not
sensibly
appear
▪
yet
is
not
its
mobility
removed
,
nor
its
immobility
necessarily
proved
,
it
being
possible
,
(
as
Copernicus
affirmeth
)
that
the
immense
distance
of
the
Starry
Sphere
rendereth
such
very
small
Phaenomena
unobservable
;
the
which
as
already
hath
been
said
,
may
possibly
not
have
been
hitherto
so
much
as
sought
for
,
or
if
sought
for
,
yet
not
sought
for
in
such
a
way
as
they
ought
,
It
is
proved
what
small
credit
is
to
be
given
to
Astronomical
Instruments
in
minute
observations
.
to
wit
,
with
that
exactnesse
which
to
so
minute
a
punctuality
would
be
necessary
;
which
exactnesse
is
very
difficult
to
obtain
,
as
well
by
reason
of
the
deficiency
of
Astronomical
Instruments
,
subject
to
many
alterations
,
as
also
through
the
fault
of
those
that
manage
them
with
less
diligence
then
is
requisite
.
A
necessary
argument
how
little
credit
is
to
be
given
to
those
observations
may
be
deduced
from
the
differences
which
we
find
amongst
Astronomers
in
assigning
the
places
,
I
will
not
say
,
of
the
new
Stars
or
Comets
,
but
of
the
fixed
stars
themselves
,
even
to
the
altitudes
of
the
very
Poles
,
in
which
,
most
an
end
,
they
are
found
to
differ
from
one
another
many
minutes
.
And
to
speak
the
truth
,
who
can
in
a
Quadrant
,
or
Sextant
,
that
at
most
shall
have
its
side
[
](A61244-e81500-b)*
*
Braccia
Italian
.
3.
or
4.
yards
long
,
ascertain
himself
in
the
incidence
of
the
perpendicular
,
or
in
the
direction
of
the
sights
,
not
to
erre
two
or
three
minutes
,
which
in
its
circumference
shall
not
amount
to
the
breadth
of
a
grain
of
[
](A61244-e81510-b)*
*
Or
Mi●
.
Mylet
?
Besides
that
,
it
is
almost
impossible
,
that
the
Instrument
should
be
made
,
and
kept
with
absolute
exactnesse
.
Ptolomey
sheweth
his
distrust
of
a
Spherical
Instrument
composed
by
Archimedes
hismelf
to
take
the
Suns
ingression
into
the
Aequinoctial
.
Ptolomy
did
not
trust
to
an
Instrument
made
by
Archimedes
.
SIMP.
But
if
the
Instruments
be
so
suspitious
,
Instruments
of
Tycho
made
with
great
expence
.
and
the
observations
so
dubious
,
how
can
we
ever
come
to
any
certainty
of
things
,
or
free
our selves
from
mistakes
?
I
have
heard
strange
things
of
the
Instruments
of
Tycho
made
with
extraordinary
cost
,
and
of
his
singular
diligence
in
observations
.
SALV
.
All
this
I
grant
you
;
but
neither
one
nor
other
of
these
is
sufficient
to
ascertain
us
in
a
businesse
of
this
importance
.
I
desire
that
we
may
make
use
of
Instruments
greater
by
far
,
What
Instruments
are
apt
for
most
exact
observation
.
and
by
far
certainer
than
those
of
Tycho
,
made
with
a
very
small
charge
;
the
sides
of
which
are
of
4.
6.
20.
30.
and
50.
miles
,
so
as
that
a
degree
is
a
mile
broad
,
a
minute
prim
.
50
[
](A61244-e81690-b)*
*
Italian
braces
.
yards
,
a
second
but
little
lesse
than
a
yard
,
and
in
short
we
may
without
a
farthing
expence
procure
them
of
what
bignesse
we
please
.
I
being
in
a
Countrey
Seat
of
mine
near
to
Florence
,
An
exquisite
observation
of
the
approach
and
departure
of
the
Sun
from
the
Summer
Solstice
.
did
plainly
observe
the
Suns
arrival
at
,
and
departure
from
the
Summer
Solstice
,
whilst
one
Evening
at
the
time
of
its
going
down
it
appeared
upon
the
top
of
a
Rock
on
the
Mountains
of
Pietrapana
,
about
60.
miles
from
thence
,
leaving
discovered
of
it
a
small
streak
or
filament
▪
towards
the
North
,
whose
breadth
was
not
the
hundredth
part
of
its
Diameter
;
and
the
following
Evening
at
the
like
setting
,
it
shew'd
such
another
part
of
it
,
but
notably
more
small
,
a
necessary
argument
,
that
it
had
begun
to
recede
from
the
Tropick
;
and
the
regression
of
the
Sun
from
the
first
to
the
second
observation
,
doth
not
import
doubtlesse
a
second
minute
in
the
East
.
A
place
accommodated
for
the
observation
of
the
fixed
stars
,
as
to
what
concers
the
annual
motion
of
the
Earth
.
The
observation
made
afterwards
with
an
exquisite
Telescope
,
and
that
multiplyeth
the
Discus
of
the
Sun
more
than
a
thousand
times
,
would
prove
easie
,
and
with
all
delightful
.
Now
with
such
an
Instrument
as
this
,
I
would
have
observations
to
be
made
in
the
fixed
stars
,
making
use
of
some
of
those
wherein
the
mutation
ought
to
appear
more
conspicuous
,
such
as
are
(
as
hath
already
been
declared
)
the
more
remote
from
the
Ecliptick
,
amongst
which
the
Harp
a
very
great
star
,
and
near
to
the
Pole
of
the
Ecliptick
,
would
be
very
proper
in
Countries
far
North
,
proceeding
according
to
the
manner
that
I
shall
shew
by
and
by
,
but
in
the
use
of
another
star
;
and
I
have
already
fancied
to
my self
a
place
very
well
adapted
for
such
an
observation
.
The
place
is
an
open
Plane
,
upon
which
towards
the
North
there
riseth
a
very
eminent
Mountain
,
in
the
apex
or
top
whereof
is
built
a
little
Chappel
,
situate
East
and
West
,
so
as
that
the
ridg
of
its
Roof
may
intersect
at
right
angles
,
the
meridian
of
some
building
standing
in
the
Plane
.
I
will
place
a
beam
parallel
to
the
said
ridg
,
or
top
of
the
Roof
,
and
distant
from
it
a
yard
or
thereabouts
.
This
being
placed
,
I
will
seek
in
the
Plain
the
place
from
whence
one
of
the
stars
of
Charls's
Waine
,
in
passing
by
the
Meridian
,
cometh
to
hide
it self
behind
the
beam
so
placed
,
or
in
case
the
beam
should
not
be
so
big
as
to
hide
the
star
,
I
will
finde
a
station
where
one
may
see
the
said
beam
to
cut
the
said
star
into
two
equal
parts
;
an
effect
that
with
an
*
exquisite
Telescope
may
be
perfectly
discerned
.
And
if
in
the
place
where
the
said
accident
is
discovered
,
there
were
some
building
,
it
will
be
the
more
commodious
;
but
if
not
,
I
will
cause
a
Pole
to
be
stuck
very
fast
in
the
ground
,
with
some
standing
mark
to
direct
where
to
place
the
eye
anew
,
when
ever
I
have
a
mind
to
repeat
the
observation
.
The
first
of
which
observations
I
will
make
about
the
Summer
Solstice
,
to
continue
afterwards
from
Moneth
to
Moneth
,
or
when
I
shall
so
please
,
to
the
other
Solstice
;
with
which
observation
one
may
discover
the
elevation
and
depression
of
the
star
,
though
it
be
very
small
.
And
if
in
that
operation
it
shall
happen
,
that
any
mutation
shall
discover
it self
,
what
and
how
great
benefit
will
it
bring
to
Astronomy
?
Seeing
that
thereby
,
besides
our
being
assured
of
the
annual
motion
,
we
may
come
to
know
the
grandure
and
distance
of
the
same
star
.
SAGR.
I
very
well
comprehend
your
whole
proceedings
;
and
the
operation
seems
to
me
so
easie
,
and
so
commodious
for
the
purpose
,
that
it
may
very
rationally
be
thought
,
that
either
Copernicus
himself
,
or
some
other
Astronomer
had
made
trial
of
it
.
SALV
.
But
I
judg
the
quite
contrary
,
for
it
is
not
probable
,
that
if
any
one
had
experimented
it
,
he
would
not
have
mentioned
the
event
,
whether
it
fell
out
in
favour
of
this
,
or
that
opinion
;
besides
that
,
no
man
that
I
can
find
,
either
for
this
,
or
any
other
end
,
did
ever
go
about
to
make
such
an
Observation
;
which
also
without
an
exact
Telescope
could
but
badly
be
effected
.
SIMP.
I
am
fully
satisfied
with
what
you
say
.
But
seeing
that
it
is
a
great
while
to
night
,
if
you
desire
that
I
shall
passe
the
same
quietly
,
let
it
not
be
a
trouble
to
you
to
explain
unto
us
those
Problems
,
the
declaration
whereof
you
did
even
now
request
might
be
deferred
until
too
morrow
.
Be
pleased
to
grant
us
your
promised
indulgence
,
and
,
laying
aside
all
other
discourses
,
proceed
to
shew
us
,
that
the
motions
which
Copernicus
assigns
to
the
Earth
being
taken
for
granted
,
and
supposing
the
Sun
and
fixed
stars
immoveable
,
there
may
follow
the
same
accidents
touching
the
elevations
and
depressions
of
the
Sun
,
touching
the
mutations
of
the
Seasons
,
and
the
inequality
of
dayes
and
nights
,
&c.
in
the
self
same
manner
,
just
as
they
are
with
facility
apprehended
in
the
Ptolomaick
Systeme
.
SALV
.
I
neither
ought
,
nor
can
deny
any
thing
that
Sagredus
shall
request
:
And
the
delay
by
me
desired
was
to
no
other
end
,
save
only
that
I
might
have
time
once
again
to
methodize
those
prefatory
points
,
in
my
fancy
,
that
serve
for
a
large
and
plain
declaration
of
the
manner
how
the
forenamed
accidents
follow
,
as
well
in
the
Copernican
position
,
as
in
the
Ptolomaick
:
nay
,
with
much
greater
facility
and
simplicity
in
that
than
in
this
.
The
Copernican
Systeme
difficult
to
be
understood
,
but
easie
to
be
effected
.
Whence
one
may
manifestly
conceive
that
Hypothesis
to
be
as
easie
to
be
effected
by
nature
,
as
difficult
to
be
apprehended
by
the
understanding
:
yet
neverthelesse
,
I
hope
by
making
use
of
another
kind
of
explanation
,
Necessary
prepositions
for
the
better
conceiving
of
the
consequences
of
the
Earths
motion
.
than
that
used
by
Copernicus
,
to
render
likewise
the
apprehending
of
it
somewhat
lesse
obscure
.
Which
that
I
may
do
,
I
will
propose
certain
suppositions
of
themselves
known
and
manifest
,
and
they
shall
be
these
that
follow
.
First
,
I
suppose
that
the
Earth
is
a
spherical
body
,
turning
round
upon
its
own
Axis
and
Poles
,
and
that
each
point
assigned
in
its
superficies
,
describeth
the
circumference
of
a
circle
,
greater
or
lesser
,
according
as
the
point
assigned
shall
be
neerer
or
farther
from
the
Poles
:
And
that
of
these
circles
the
greatest
is
that
which
is
described
by
a
point
equidistant
from
the
said
Poles
;
and
all
these
circles
are
parallel
to
each
other
;
and
Parallels
we
will
call
them
.
Secondly
,
The
Earth
being
of
a
Spherical
Figure
,
and
of
an
opacous
substance
,
it
is
continually
illuminated
by
the
Sun
,
according
to
the
half
of
its
surface
,
the
other
half
remaining
obscure
,
and
the
boundary
that
distinguisheth
the
illuminated
part
from
the
dark
being
a
grand
circle
,
we
will
call
that
circle
the
terminator
of
the
light
.
Thirdly
,
If
the
Circle
that
is
terminator
of
the
light
should
passe
by
the
Poles
of
the
Earth
,
it
would
cut
(
being
a
grand
and
principal
circle
)
all
the
parallels
into
equal
parts
;
but
not
passing
by
the
Poles
,
it
would
cut
them
all
in
parts
unequal
,
except
only
the
circle
in
the
middle
,
which
,
as
being
a
grand
circle
will
be
cut
into
equal
parts
.
Fourthly
,
The
Earth
turning
round
upon
its
own
Poles
,
the
quantities
of
dayes
and
nights
are
termined
by
the
arches
of
the
Parallels
,
intersected
by
the
circle
,
that
is
,
the
terminator
of
the
light
,
and
the
arch
that
is
scituate
in
the
illuminated
Hemisphere
prescribeth
the
length
of
the
day
,
and
the
remainer
is
the
quantity
of
the
night
.
These
things
being
presupposed
,
A
plain
Scheme
representing
the
Copernican
Hypothesis
,
and
its
consequences
.
for
the
more
clear
understanding
of
that
which
remaines
to
be
said
,
we
will
lay
it
down
in
a
Figure
.
And
first
,
we
will
draw
the
circumference
of
a
circle
,
that
shall
represent
unto
us
that
of
the
grand
Orb
described
in
the
plain
of
the
Ecliptick
,
and
this
we
will
divide
into
four
equal
parts
with
the
two
diameters
Capricorn
Cancer
,
and
Libra
Aries
,
which
,
at
the
same
time
,
shall
represent
unto
us
the
four
Cardinal
points
,
that
is
,
the
two
Solstices
,
and
the
two
Equinoctials
;
and
in
the
centre
of
that
circle
we
will
place
the
Sun
O
,
fixed
and
immoveable
.
SAGR.
To
me
,
as
far
as
concerneth
sense
,
there
appeareth
no
small
difference
betwixt
the
simplicity
and
facility
of
operating
effects
by
the
means
assigned
in
this
new
constitution
,
and
the
multiplicity
,
confusion
,
and
difficulty
,
that
is
found
in
the
ancient
and
commonly
received
Hypothesis
.
For
if
the
Universe
were
disposed
according
to
this
multiplicity
,
it
would
be
necessary
to
renounce
many
Maximes
in
Philosophy
commonly
received
by
Philosophers
,
Axiomes
commonly
admitted
by
all
Philosophers
.
as
for
instance
,
That
Nature
doth
not
multiply
things
without
necessity
;
and
,
That
She
makes
use
of
the
most
facile
and
simple
means
in
producing
her
effects
;
and
,
That
She
doth
nothing
in
vain
,
and
the
like
.
I
do
confesse
that
I
never
heard
any
thing
more
admirable
than
this
,
nor
can
I
believe
that
Humane
Understanding
ever
penetrated
a
more
sublime
speculation
.
I
know
not
what
Simplicius
may
think
of
it
.
SIMP.
These
(
if
I
may
speak
my
judgment
freely
)
do
seem
to
me
some
of
those
Geometrical
subtilties
which
Aristotle
finds
fault
with
in
Plato
,
Aristotle
taxeth
Plato
for
being
too
studious
of
Geometry
.
when
he
accuseth
him
that
by
his
too
much
studying
of
Geometry
he
forsook
solid
Philosophy
;
and
I
have
known
and
heard
very
great
Peripatetick
Philosophers
to
disswade
their
Scholars
from
the
Study
of
the
Mathematicks
,
as
those
that
render
the
wit
cavilous
,
and
unable
to
philosophate
well
;
an
Institute
diametrically
contrary
to
that
of
Plato
,
who
admitted
one
to
Philosophy
,
unlesse
he
was
first
well
entered
in
Geometry
.
SALV
.
I
commend
the
policy
of
these
your
Peripateticks
,
Peripatetick
Philosophers
condemn
the
Study
of
Geometry
,
and
why
.
in
dehorting
their
Disciples
from
the
Study
of
Geometry
,
for
that
there
is
not
art
more
commodious
for
detecting
their
fallacies
;
but
see
how
they
differ
from
the
Mathematical
Philosophers
,
who
much
more
willingly
converse
with
those
that
are
well
verst
in
the
commune
Peripatetick
Philosophy
,
than
with
those
that
are
destitute
of
that
knowledg
,
who
for
want
thereof
cannot
distinguish
between
doctrine
and
doctrine
.
But
passing
by
this
,
tell
me
I
beseech
you
,
what
are
those
extravagancies
and
those
too
affected
subtilties
that
make
you
think
this
Copernican
Systeme
the
lesse
plausible
?
SIMP.
To
tell
you
true
,
I
do
not
very
well
know
;
perhaps
,
because
I
have
not
so
much
as
learnt
the
reasons
that
are
by
Ptolomy
produced
,
of
those
effects
,
I
mean
of
those
stations
,
retrogradations
,
accessions
,
recessions
of
the
Planets
;
lengthenings
and
shortnings
of
dayes
,
changes
of
seasons
,
&c.
But
omitting
the
consequences
that
depend
on
the
first
suppositions
,
I
find
in
the
suppositions
themselves
no
small
difficulties
;
which
suppositions
,
if
once
they
be
overthrown
,
they
draw
along
with
them
the
ruine
of
the
whole
fabrick
.
Now
forasmuch
as
because
the
whole
module
of
Copernicus
seemeth
in
my
opinion
to
be
built
upon
infirm
foundations
,
in
that
it
relyeth
upon
the
mobility
of
the
earth
,
if
this
should
happen
to
be
disproved
,
there
would
be
no
need
of
farther
dispute
.
And
to
disprove
this
,
the
Axiom
of
Aristotle
is
in
my
judgement
most
sufficient
,
That
of
one
simple
body
,
one
sole
simple
motion
can
be
natural
:
but
here
in
this
case
,
to
the
Earth
,
Four
several
motions
assigned
to
the
Earth
.
a
simple
body
,
there
are
assigned
3.
if
not
4.
motions
,
and
all
very
different
from
each
other
.
For
besides
the
right
motion
,
as
a
grave
body
towards
its
centre
,
which
cannot
be
denied
it
,
there
is
assigned
to
it
a
circular
motion
in
a
great
circle
about
the
Sun
in
a
year
,
and
a
vertiginous
conversion
about
its
own
centre
in
twenty
four
hours
.
And
that
in
the
next
place
which
is
more
exorbitant
,
&
which
happly
for
that
reason
you
pass
over
in
silence
,
there
is
ascribed
to
it
another
revolution
about
its
own
centre
,
contrary
to
the
former
of
twenty
four
hours
,
and
which
finisheth
its
period
in
a
year
.
In
this
my
understanding
apprehendeth
a
very
great
contradiction
.
SALV
.
As
to
the
motion
of
descent
,
The
motion
of
descent
belongs
not
to
the
terrestrial
Globe
,
but
to
its
parts
.
it
hath
already
been
concluded
not
to
belong
to
the
Terrestrial
Globe
which
did
never
move
with
any
such
motion
,
nor
never
shall
do
;
but
is
(
if
there
be
such
a
thing
)
that
propension
of
its
parts
to
reunite
themselves
to
their
whole
.
As
,
in
the
next
place
,
to
the
Annual
motion
,
and
the
Diurnal
,
The
annual
and
diurnal
motion
are
compatible
in
the
Earth
.
these
being
both
made
towards
one
way
,
are
very
compatible
,
in
the
same
manner
just
as
if
we
should
let
a
Ball
trundle
downwards
upon
a
declining
superficies
,
it
would
in
its
descent
along
the
same
spontaneously
revolve
in
it self
.
As
to
the
third
motion
assigned
it
by
Copernicus
,
namely
about
it self
in
a
year
,
onely
to
keep
its
Axis
inclined
and
directed
towards
the
same
part
of
the
Firmament
,
I
will
tell
you
a
thing
worthy
of
great
consideration
:
namely
ut
tantum
abest
(
although
it
be
made
contrary
to
the
other
annual
)
it
is
so
far
from
having
any
repugnance
or
difficulty
in
it
,
Every
pensil
and
librated
,
body
carryed
round
in
the
circumference
of
a
circle
,
acquireth
of
it self
a
motion
in
it self
contrary
to
that
.
that
naturally
and
without
any
moving
cause
,
it
agreeth
to
any
whatsoever
suspended
and
librated
body
,
which
if
it
shall
be
carried
round
in
the
circumference
of
a
circle
,
immediate
of
it self
,
it
acquireth
a
conversion
about
its
own
centre
,
contrary
to
that
which
carrieth
it
about
,
and
of
such
velocity
,
that
they
both
finish
one
revolution
in
the
same
time
precisely
.
You
may
see
this
admirable
,
and
to
our
purpose
accommodate
experience
,
An
Experiment
which
sensibly
shews
that
two
contrary
motions
may
naturally
agree
in
the
same
moveable
.
if
putting
in
a
Bason
of
water
a
Ball
that
will
swim
;
and
holding
the
Bason
in
your
hand
,
you
turn
round
upon
your
toe
,
for
you
shall
immediatly
see
the
Ball
begin
to
revolve
in
it self
with
a
motion
,
contrary
to
that
of
the
Bason
,
and
it
shall
finish
its
revolution
,
when
that
of
the
Bason
it
shall
finish
.
Now
what
other
is
the
Earth
than
a
pensil
Globe
librated
in
tenuous
and
yielding
aire
,
which
being
carried
about
in
a
year
along
the
circumference
of
a
great
circle
,
The
third
motion
ascribed
to
the
Earth
is
rather
a
resting
immoveable
.
must
needs
acquire
,
without
any
other
mover
,
a
revolution
about
its
own
centre
,
annual
,
and
yet
contrary
to
the
other
motion
in
like
manner
annual
?
You
shall
see
this
effect
I
say
,
but
if
afterwards
you
more
narrowly
consider
it
,
you
shall
find
this
to
be
no
real
thing
,
but
a
meer
appearance
;
and
that
which
you
think
to
be
a
revolution
in
it self
,
you
will
find
to
be
a
not
moving
at
all
,
but
a
continuing
altogether
immoveable
in
respect
of
all
that
which
without
you
,
and
without
the
vessel
is
immoveable
:
for
if
in
that
Ball
you
shall
make
some
mark
,
and
consider
to
what
part
of
the
Room
where
you
are
,
or
of
the
Field
,
or
of
Heaven
it
is
situate
,
you
shall
see
that
mark
in
yours
,
and
the
vessels
revolution
to
look
alwayes
towards
that
same
part
;
but
comparing
it
to
the
vessel
and
to
your self
that
are
moveable
,
it
will
appear
to
go
altering
its
direction
,
and
with
a
motion
contrary
to
yours
,
and
that
of
the
vessel
,
to
go
seeking
all
the
points
of
its
circumgyration
;
so
that
with
more
reason
you
and
the
bason
may
be
said
to
turn
round
the
immoveable
Ball
,
than
that
it
moveth
round
in
the
bason
.
In
the
same
manner
the
Earth
suspended
and
librated
in
the
circumference
of
the
Grand
Orbe
,
and
scituate
in
such
sort
that
one
of
its
notes
,
as
for
example
,
its
North
Pole
,
looketh
towards
such
a
Star
or
other
part
of
the
Firmament
,
it
always
keepeth
directed
towards
the
same
,
although
carried
round
by
the
annual
motion
about
the
circumference
of
the
said
Grand
Orbe
.
This
alone
is
sufficient
to
make
the
Wonder
cease
,
and
to
remove
all
difficulties
.
But
what
will
Simplicius
say
,
if
to
this
non-indigence
of
the
co-operating
cause
we
should
adde
an
admirable
intrinsick
vertue
●f
the
Terrestrial
Globe
,
An
admirable
intern
vertue
of
the
terrestrial
Globe
of
alwayes
beholding
the
same
part
of
Heaven
.
of
looking
with
its
determinate
parts
towards
determinate
parts
of
the
Firmament
,
I
speak
of
the
Magnetick
vertue
constantly
participated
by
any
whatsoever
piece
of
Loade-stone
.
And
if
every
minute
particle
of
that
S●one
have
in
it
such
a
vertue
,
The
terrestrial
Globe
made
of
Loade-stone
.
who
will
question
but
that
the
same
more
powerfully
resides
in
this
whole
Terrestrial
Globe
,
abounding
in
that
Magnetick
matter
,
and
which
happily
it self
,
as
to
its
internal
and
primary
substance
,
is
nothing
else
but
a
huge
masse
of
Loade-stone
.
SIMP.
Then
you
are
one
of
those
it
seems
that
hold
the
Magnetick
Phylosophy
William
[
](A61244-e82580-b)*
*
An
eminent
Doctor
of
Physick
,
our
Countreyman
,
born
at
Colchester
,
and
famous
for
this
his
learned
Treatise
,
published
about
60
years
since
at
London
,
The
Magnetick
Philosophy
of
William
Gilbert
.
Gilbert
.
SALV
.
I
am
for
certain
,
and
think
that
all
those
that
have
seriously
read
his
Book
,
and
tried
his
experiments
,
will
bear
me
company
therein
;
nor
should
I
despair
,
that
what
hath
befallen
me
in
this
case
,
might
possibly
happen
to
you
also
,
if
so
be
a
curiosity
,
like
to
mine
,
and
a
notice
that
infinite
things
in
Nature
are
still
conceal'd
from
the
wits
of
mankind
,
by
delivering
you
from
being
captivated
by
this
or
that
particular
writer
in
natural
things
,
should
but
slacken
the
reines
of
your
Reason
,
and
mollifie
the
contumacy
and
tenaceousnesse
of
your
sense
;
so
as
that
they
would
not
refuse
to
hearken
sometimes
to
novelties
never
before
spoken
of
.
The
Pusillanimity
of
Popular
Wits
.
But
(
permit
me
to
use
this
phrase
)
the
pusillanimity
of
vulgar
Wits
is
come
to
that
passe
,
that
not
only
like
blind
men
,
they
make
a
gift
,
nay
tribute
of
their
own
assent
to
whatsoever
they
find
written
by
those
Authours
,
which
in
the
infancy
of
their
Studies
were
laid
before
them
,
as
authentick
by
their
Tutors
,
but
refuse
to
hear
(
not
to
say
examine
)
any
new
Proposition
or
Probleme
,
although
it
not
only
never
hath
been
confuted
,
but
not
so
much
as
examined
or
considered
by
their
Authours
.
Amongst
which
,
one
is
this
,
of
investigating
what
is
the
true
,
proper
,
primary
,
interne
,
and
general
matter
and
substance
of
this
our
Terrestrial
Globe
;
For
although
it
never
came
into
the
mind
either
of
Aristotle
,
or
of
any
one
else
,
before
William
Gilbert
to
think
that
it
might
be
a
Magnet
,
so
far
are
Aristotle
and
the
rest
from
confuting
this
opinion
,
yet
neverthelesse
I
have
met
with
many
,
that
at
the
very
first
mention
of
it
,
as
a
Horse
at
his
own
shadow
,
have
start
back
,
and
refused
to
discourse
thereof
,
and
censured
the
conceipt
for
a
vain
Chymaera
,
yea
,
for
a
solemn
madnesse
:
and
its
possible
the
Book
of
Gilbert
had
never
come
to
my
hands
,
if
a
Peripatetick
Philosopher
,
of
great
fame
,
as
I
believe
,
to
free
his
Library
from
its
contagion
,
had
not
given
it
me
.
SIMP.
I
,
who
ingenuously
confesse
my self
to
be
one
of
those
vulgar
Wits
,
and
never
till
within
these
few
dayes
that
I
have
been
admitted
to
a
share
in
your
conferences
,
could
I
pretend
to
have
in
the
least
withdrawn
from
those
trite
and
popular
paths
,
yet
,
for
all
that
,
I
think
I
have
advantaged
my self
so
much
,
as
that
I
could
without
much
trouble
or
difficulty
,
master
the
roughnesses
of
these
novel
and
fantastical
opinions
.
SALV
.
If
that
which
Gilbert
writeth
be
true
,
then
is
it
no
opinion
,
but
the
subject
of
Science
;
nor
is
it
new
,
but
as
antient
as
the
Earth
it self
;
nor
can
it
(
being
true
)
be
rugged
or
difficult
,
but
plain
and
easie
;
and
when
you
please
I
shall
make
you
feel
the
same
in
your
hand
,
for
that
you
of
your self
fancy
it
to
be
a
Ghost
,
and
stand
in
fear
of
that
which
hath
nothing
in
it
of
dreadfull
,
like
as
a
little
child
doth
fear
the
Hobgoblin
,
without
knowing
any
more
of
it
,
save
the
name
;
as
that
which
besides
the
name
is
nothing
.
SIMP.
I
should
be
glad
to
be
informed
,
and
reclaimed
from
an
errour
.
SALV
.
Answer
me
then
to
the
questions
that
I
shall
ask
you
.
And
first
of
all
,
Tell
me
whether
you
believe
,
that
this
our
Globe
,
which
we
inhabit
and
call
Earth
,
consisteth
of
one
sole
and
simple
matter
,
or
else
that
it
is
an
aggregate
of
matters
different
from
each
other
.
SIMP.
I
see
it
to
be
composed
of
substances
and
bodies
very
different
;
The
Terrestrial
Globe
composed
of
sundry
matters
.
and
first
,
for
the
greatest
parts
of
the
composition
,
I
see
the
Water
and
the
Earth
,
which
extreamly
differ
from
one
another
.
SALV
.
Let
us
,
for
this
once
,
lay
aside
the
Seas
and
other
Waters
,
and
let
us
consider
the
solid
parts
,
and
tell
me
,
if
you
think
them
one
and
the
same
thing
,
or
else
different
.
SIMP.
As
to
appearance
,
I
see
that
they
are
different
things
,
there
being
very
great
heaps
of
unfruitful
sands
,
and
others
of
fruitful
soiles
;
There
are
infinite
sharp
and
steril
mountains
,
full
of
hard
stones
and
quarries
of
several
kinds
,
as
Porphyre
,
Alablaster
,
Jasper
,
and
a
thousand
other
kinds
of
Marbles
:
There
are
vast
Minerals
of
so
many
kinds
of
metals
;
and
in
a
word
,
such
varieties
of
matters
,
that
a
whole
day
would
not
suffice
only
to
enumerate
them
.
SALV
.
Now
of
all
these
different
matters
,
do
you
think
,
that
in
the
composition
of
this
grand
masse
,
there
do
concur
portions
,
or
else
that
amongst
them
all
there
is
one
part
that
far
exceeds
the
rest
,
and
is
as
it
were
the
matter
and
substance
of
the
immense
lump
?
SIMP.
I
believe
that
the
Stones
,
Marbles
,
Metals
,
Gems
,
and
the
so
many
other
several
matters
are
as
it
were
Jewels
,
and
exteriour
and
superficial
Ornaments
of
the
primary
Globe
,
which
in
grosse
,
as
I
believe
,
doth
without
compare
exceed
all
these
things
put
together
.
SALV
.
And
this
principal
and
vast
masse
,
of
which
those
things
above
named
are
as
it
were
excressences
and
ornaments
,
of
what
matter
do
you
think
that
it
is
composed
?
SIMP.
I
think
that
it
is
the
simple
,
or
lesse
impure
element
of
Earth
.
SALV
.
But
what
do
you
understand
by
Earth
?
Is
it
haply
that
which
is
dispersed
all
over
the
fields
,
which
is
broke
up
with
Mattocks
and
Ploughs
,
wherein
we
sowe
corne
,
and
plant
fruits
,
and
in
which
great
boscages
grow
up
,
without
the
help
of
culture
,
and
which
is
,
in
a
word
,
the
habitation
of
all
animals
,
and
the
womb
of
all
vegetables
?
SIMP.
T
is
this
that
I
would
affirm
to
be
the
substance
of
this
our
Globe
.
SALV
.
But
in
this
you
do
,
in
my
judgment
,
affirm
that
which
is
not
right
:
for
this
Earth
which
is
broke
up
,
is
sowed
,
and
is
fertile
,
is
but
one
part
,
and
that
very
small
of
the
surface
of
the
Globe
,
which
doth
not
go
very
deep
,
yea
,
its
depth
is
very
small
,
in
comparison
of
the
distance
to
the
centre
:
and
experience
sheweth
us
,
that
one
shall
not
dig
very
low
,
but
one
shall
finde
matters
very
different
from
this
exteriour
scurf
,
more
solid
,
and
not
good
for
the
production
of
vegetables
.
Besides
the
interne
parts
,
as
being
compressed
by
very
huge
weights
that
lie
upon
them
,
are
,
in
all
probability
,
slived
,
and
made
as
hard
as
any
hard
rock
.
One
may
adde
to
this
,
that
fecundity
would
be
in
vain
conferred
upon
those
matters
which
never
were
designed
to
bear
fruit
,
but
to
rest
eternally
buried
in
the
profound
and
dark
abysses
of
the
Earth
.
SIMP.
But
who
shall
assure
us
,
that
the
parts
more
inward
and
near
to
the
centre
are
unfruitful
?
They
also
may
,
perhaps
,
have
their
productions
of
things
unknown
to
us
?
SALV
.
You
may
aswell
be
assured
thereof
,
as
any
man
else
,
as
being
very
capable
to
comprehend
,
that
if
the
integral
bodies
of
the
Universe
be
produced
onely
for
the
benefit
of
Mankind
,
this
above
all
the
rest
ought
to
be
destin'd
to
the
sole
conveniences
of
us
its
inhabitants
.
But
what
benefit
can
we
draw
from
matters
so
hid
and
remote
from
us
,
as
that
we
shall
never
be
able
to
make
use
of
them
?
The
interne
parts
of
the
terrestrial
Globe
must
of
necessity
be
solid
.
Therefore
the
interne
substance
of
this
our
Globe
cannot
be
a
matter
frangible
,
dissipable
,
and
non-coherent
,
like
this
superficial
part
which
we
call
[
](A61244-e83230-b)*
*
Or
MOULD
.
EARTH
:
but
it
must
,
of
necessity
,
be
a
most
dense
and
solid
body
,
and
in
a
word
,
a
most
hard
stone
.
And
,
if
it
ought
to
be
so
,
what
reason
is
there
that
should
make
you
more
scrupulous
to
believe
that
it
is
a
Loadstone
than
a
Porphiry
,
a
Jasper
,
or
other
hard
Marble
?
Happily
if
Gilbert
had
written
,
that
this
Globe
is
all
compounded
within
of
[
](A61244-e83250-b)*
*
Of
which
with
the
Latin
translatour
,
I
must
once
more
professe
my self
ignorant
.
Pietra
Serena
,
or
of
Chalcedon
,
the
paradox
woul●
have
seemed
to
you
lesse
exorbitant
?
SIMP.
That
the
parts
of
this
Globe
more
intern
are
more
compressed
,
and
so
more
slived
together
and
solid
,
and
more
and
more
so
,
according
as
they
lie
lower
,
I
do
grant
,
and
so
likewise
doth
Aristotle
,
but
that
they
degenerate
and
become
other
than
Earth
,
of
the
same
sort
with
this
of
the
superficial
parts
,
I
see
nothing
that
obliegeth
me
to
believe
.
SALV
.
I
undertook
not
this
discourse
with
an
intent
to
prove
demonstratively
that
the
primary
and
real
substance
of
this
our
Globe
is
Load-stone
;
but
onely
to
shew
that
no
reason
could
be
given
why
one
should
be
more
unwilling
to
grant
that
it
is
of
Load-stone
,
Our
Globe
would
have
been
called
stone
,
in
stead
of
Earth
,
of
that
name
had
been
giuen
it
in
the
beginning
.
than
of
some
other
matter
.
And
if
you
will
but
seriously
consider
,
you
shall
find
that
it
is
not
improbable
,
that
one
sole
,
pure
,
and
arbitrary
name
,
hath
moved
men
to
think
that
it
consists
of
Earth
;
and
that
is
their
having
made
use
commonly
from
the
beginning
of
this
word
Earth
,
as
well
to
signifie
that
matter
which
is
plowed
and
sowed
,
as
to
name
this
our
Globe
.
The
denomination
of
which
if
it
had
been
taken
from
stone
,
as
that
it
might
as
well
have
been
taken
from
that
as
from
the
Earth
;
the
saying
that
its
primary
substance
was
stone
,
would
doubtlesse
have
found
no
scruple
or
opposition
in
any
man
.
And
is
so
much
the
more
probable
,
in
that
I
verily
believe
,
that
if
one
could
but
pare
off
the
scurf
of
this
great
Globe
,
taking
away
but
one
full
thousand
or
two
thousand
yards
;
and
afterwards
seperate
the
Stones
from
the
Earth
,
the
accumulation
of
the
stones
would
be
very
much
biger
than
that
of
the
fertile
Mould
.
But
as
for
the
reasons
which
concludently
prove
de
facto
,
that
is
our
Globe
is
a
Magnet
,
I
have
mentioned
none
of
them
,
nor
is
this
a
time
to
alledg
them
,
and
the
rather
,
for
that
to
your
benefit
you
may
read
them
in
Gilbert
;
onely
to
encourage
you
to
the
perusal
of
them
,
I
will
set
before
you
,
in
a
similitude
of
my
own
,
The
method
of
Gilbert
in
his
Philosophy
.
the
method
that
he
observed
in
his
Philosophy
.
I
know
you
understand
very
well
how
much
the
knowledg
of
the
accidents
is
subservient
to
the
investigation
of
the
substance
and
essence
of
things
;
therefore
I
desire
that
you
would
take
pains
to
informe
your self
well
of
many
accidents
and
properties
that
are
found
in
the
Magnet
,
Many
properties
in
the
Magnet
.
and
in
no
other
stone
,
or
body
;
as
for
instance
of
attracting
Iron
,
of
conferring
upon
it
by
its
sole
presence
the
same
virtue
,
of
communicating
likewise
to
it
the
property
of
looking
towards
the
Poles
,
as
it
also
doth
it self
;
and
moreover
endeavour
to
know
by
trial
,
that
it
containeth
in
it
a
virtue
of
conferring
upon
the
magnetick
needle
not
onely
the
direction
under
a
Meridian
towards
the
Poles
,
with
an
Horizontal
motion
,
(
a
property
a
long
time
ago
known
)
but
a
new
found
accident
,
of
declining
(
being
ballanced
under
the
Meridian
before
marked
upon
a
little
spherical
Magnet
)
of
declining
I
say
to
determinate
marks
more
or
lesse
,
according
as
that
needle
is
held
nearer
or
farther
from
the
Pole
,
till
that
upon
the
Pole
it self
it
erecteth
perpendicularly
,
whereas
in
the
middle
parts
it
is
parallel
to
the
Axis
.
Furthermore
procure
a
proof
to
be
made
,
whether
the
virtue
of
attracting
Iron
,
residing
much
more
vigorously
about
the
Poles
,
than
about
the
middle
parts
,
this
force
be
not
notably
more
vigorous
in
one
Pole
than
in
the
other
,
and
that
in
all
pieces
of
Magnet
;
the
stronger
of
which
Poles
is
that
which
looketh
towards
the
South
.
Observe
,
in
the
next
place
,
that
in
a
little
Magnet
this
South
and
more
vigorous
Pole
,
becometh
weaker
,
when
ever
it
is
to
take
up
an
iron
in
presence
of
the
North
Pole
of
another
much
bigger
Magnet
:
and
not
to
make
any
tedious
discourse
of
it
,
assertain
your self
,
by
experience
,
of
these
and
many
other
properties
described
by
Gilbert
,
which
are
all
so
peculiar
to
the
Magnet
,
as
that
none
of
them
agree
with
any
other
matter
.
〈…〉
Tell
me
now
,
Simplicius
,
if
there
were
laid
before
you
a
thousand
pieces
of
several
matters
,
but
all
covered
and
concealed
in
a
cloth
,
under
which
it
is
hid
,
and
you
were
required
,
without
uncovering
them
,
〈…〉
a
guesse
,
by
external
signes
,
at
the
matter
of
each
of
them
,
and
that
in
making
trial
,
you
should
hit
upon
one
that
should
openly
shew
it self
to
have
all
the
properties
by
you
already
acknowledged
to
reside
onely
in
the
Magnet
,
and
in
no
other
matter
,
what
judgment
would
you
make
of
the
essence
of
such
a
body
?
Would
you
say
,
that
it
might
be
a
piece
of
Ebony
,
or
Alablaster
,
o●
Tin
.
SIMP.
I
would
say
,
without
the
least
haesitation
,
that
it
was
a
piece
of
Load-stone
.
SALV
.
If
it
be
so
,
say
resolutely
,
that
under
this
cover
and
scurf
of
Earth
,
stones
,
metals
,
water
,
&c.
there
is
hid
a
great
Magnet
,
forasmuch
as
about
the
same
there
may
be
seen
by
any
one
that
will
heedfully
observe
the
same
,
all
those
very
accidents
that
agree
with
a
true
and
visible
Globe
of
Magnet
;
but
if
no
more
were
to
be
seen
than
that
of
the
Declinatory
Needle
,
which
being
carried
about
the
Earth
,
more
and
more
inclineth
,
as
it
approacheth
to
the
North
Pole
,
and
declineth
lesse
towards
the
Equinoctial
,
under
which
it
finally
is
brought
to
an
Aequilibrium
,
it
might
serve
to
perswade
even
the
most
scrupulous
judgment
.
I
forbear
to
mention
that
other
admirable
effect
,
which
is
sensibly
observed
in
every
piece
of
Magnet
,
of
which
,
to
us
inhabitants
of
the
Northern
Hemisphere
,
the
Meridional
Pole
of
the
said
Magnet
is
more
vigorous
than
the
other
;
and
the
difference
is
found
greater
,
by
how
much
one
recedeth
from
the
Equinoctial
;
and
under
the
Equinoctial
both
the
parts
are
of
equal
strength
,
but
notably
weaker
.
But
,
in
the
Meridional
Regions
,
far
distant
from
the
Equinoctial
,
it
changeth
nature
,
and
that
part
which
to
us
was
more
weak
,
acquireth
more
strength
than
the
other
:
and
all
this
I
confer
with
that
which
we
see
to
be
done
by
a
small
piece
of
Magnet
,
in
the
presence
of
a
great
one
,
the
vertue
of
which
superating
the
lesser
,
maketh
it
to
become
obedient
to
it
,
and
according
as
it
is
held
,
either
on
this
or
on
that
side
the
Equinoctial
of
the
great
one
,
maketh
the
self
same
mutations
,
which
I
have
said
are
made
by
every
Magnet
,
carried
on
this
side
,
or
that
side
of
the
Equinoctiall
of
the
Earth
.
SAGR.
I
was
perswaded
,
at
the
very
first
reading
of
the
Book
of
Gilbertus
;
and
having
met
with
a
most
excellent
piece
of
Magnet
,
The
Magnet
armed
takes
up
much
more
Iron
,
than
when
armed
.
I
,
for
a
long
time
,
made
many
Observations
,
and
all
worthy
of
extream
wonder
;
but
above
all
,
that
seemeth
to
me
very
stupendious
of
increasing
the
faculty
of
taking
up
Iron
so
much
by
arming
it
,
like
as
the
said
Authour
teacheth
;
and
with
arming
that
piece
of
mine
,
I
multiplied
its
force
in
octuple
proportion
;
and
whereas
unarmed
it
scarce
took
up
nine
ounces
of
Iron
,
it
being
armed
did
take
up
above
six
pounds
:
And
,
it
may
be
,
you
have
seen
this
Loadstone
in
the
[
](A61244-e83560-b)*
*
Or
Closet
of
rarities
.
Gallery
of
your
Most
Serene
Grand
Duke
(
to
whom
I
presented
it
)
upholding
two
little
Anchors
of
Iron
.
SALV
.
I
saw
it
many
times
,
and
with
great
admiration
,
till
that
a
little
piece
of
the
like
stone
gave
me
greater
cause
of
wonder
,
that
is
in
the
keeping
of
our
Academick
,
which
being
no
more
than
of
six
ounces
weight
,
and
sustaining
,
when
unarmed
,
hardly
two
ounces
,
doth
,
when
armed
,
take
up
160.
ounces
,
so
as
that
it
is
of
80.
times
more
force
armed
than
unarmed
,
and
takes
up
a
weight
26.
times
greater
than
its
own
;
a
much
greater
wonder
than
Gilbert
could
ever
meet
with
,
who
writeth
,
that
he
could
never
get
any
Loadstone
that
could
reach
to
take
up
four
times
its
own
weight
.
SAGR.
In
my
opinion
,
this
Stone
offers
to
the
wit
of
man
a
large
Field
to
Phylosophate
in
;
and
I
have
many
times
thought
with
my self
,
how
it
can
be
that
it
conferreth
on
that
Iron
,
which
armeth
it
,
a
strength
so
superiour
to
its
own
;
and
finally
,
I
finde
nothing
that
giveth
me
satisfaction
herein
;
nor
do
I
find
any
thing
extraordinary
in
that
which
Gilbert
writes
about
this
particular
;
I
know
not
whether
the
same
may
have
befallen
you
.
SALV
.
I
extreamly
praise
,
admire
,
and
envy
this
Authour
,
for
that
a
conceit
so
stupendious
should
come
into
his
minde
,
touching
a
thing
handled
by
infinite
sublime
wits
,
and
hit
upon
by
none
of
them
:
I
think
him
moreover
worthy
of
extraordinary
applause
for
the
many
new
and
true
Observations
that
he
made
,
to
the
disgrace
of
so
many
fabulous
Authours
,
that
write
not
only
what
they
do
not
know
,
but
what
ever
they
hear
spoken
by
the
foolish
vulgar
,
never
seeking
to
assure
themselves
of
the
same
by
experience
,
perhaps
,
because
they
are
unwilling
to
diminish
the
bulk
of
their
Books
.
That
which
I
could
have
desired
in
Gilbert
,
is
,
that
he
had
been
a
little
greater
Mathematician
,
and
particularly
well
grounded
in
Geometry
,
the
practice
whereof
would
have
rendered
him
less
resolute
in
accepting
those
reasons
for
true
Demonstrations
,
which
he
produceth
for
true
causes
of
the
true
conclusions
observed
by
himself
.
Which
reasons
(
freely
speaking
)
do
not
knit
and
bind
so
fast
,
as
those
undoubtedly
ought
to
do
,
in
that
of
natural
,
necessary
,
and
lasting
conclusions
may
be
alledged
.
And
I
doubt
not
,
but
that
in
processe
of
time
this
new
Science
will
be
perfected
with
new
observations
,
and
,
which
is
more
,
with
true
and
necessary
Demonstrations
.
The
first
observers
and
inventers
of
things
ought
to
be
admired
.
Nor
ought
the
glory
of
the
first
Inventor
to
be
thereby
diminished
;
nor
do
I
lesse
esteem
,
but
rather
more
admire
,
the
Inventor
of
the
Harp
(
although
it
may
be
supposed
that
the
Instrument
at
first
was
but
rudely
framed
,
and
more
rudely
fingered
)
than
an
hundred
other
Artists
,
that
in
the
insuing
Ages
reduced
that
profession
to
great
perfection
.
And
methinks
,
that
Antiquity
had
very
good
reason
to
enumerate
the
first
Inventors
of
the
Noble
Arts
amongst
the
Gods
;
seeing
that
the
common
wits
have
so
little
curiosity
,
and
are
so
little
regardful
of
rare
and
elegant
things
,
that
though
they
see
and
hear
them
exercitated
by
the
exquisite
professors
of
them
,
yet
are
they
not
thereby
perswaded
to
a
desire
of
learning
them
.
Now
judge
,
whether
Capacities
of
this
kind
would
ever
have
attempted
to
have
found
out
the
making
of
the
Harp
,
or
the
invention
of
Musick
,
upon
the
hint
of
the
whistling
noise
of
the
dry
sinews
of
a
Tortois
,
or
from
the
striking
of
four
Hammers
.
The
application
to
great
inventions
moved
by
small
hints
,
and
the
thinking
that
under
a
primary
and
childish
appearance
admirable
Arts
may
lie
hid
,
is
not
the
part
of
a
trivial
,
but
of
a
super-humane
spirit
.
Now
answering
to
your
demands
,
I
say
,
that
I
also
have
long
thought
upon
what
might
possibly
be
the
cause
of
this
so
tenacious
and
potent
union
,
that
we
see
to
be
made
between
the
one
Iron
that
armeth
the
Magnet
,
and
the
other
that
conjoyns
it self
unto
it
.
And
first
,
The
true
cause
of
the
multiplication
of
vertue
in
the
Magnet
,
by
means
of
the
arming
.
we
are
certain
,
that
the
vertue
and
strength
of
the
stone
doth
not
augment
by
being
armed
,
for
it
neither
attracts
at
greater
distance
,
nor
doth
it
hold
an
Iron
the
faster
,
if
between
it
,
and
the
arming
or
cap
,
a
very
fine
paper
,
or
a
leaf
of
beaten
gold
,
be
interposed
;
nay
,
with
that
interposition
,
the
naked
stone
takes
up
more
Iron
than
the
armed
.
There
is
therefore
no
alteration
in
the
vertue
,
and
yet
there
is
an
innovation
in
the
effect
.
And
because
its
necessary
,
Of
a
new
effect
its
necessary
that
the
cause
be
likewise
new
.
that
a
new
effect
have
a
new
cause
,
if
it
be
inquired
what
novelty
is
introduced
in
the
act
of
taking
up
with
the
cap
or
arming
,
there
is
no
mutation
to
be
discovered
,
but
in
the
different
contact
;
for
whereas
before
Iron
toucht
Loadstone
,
now
Iron
toucheth
Iron
.
Therefore
it
is
necessary
to
conclude
,
It
is
proved
,
that
Iron
consists
of
parts
more
subtil
,
pure
,
and
compact
than
the
magnet
.
that
the
diversity
of
contacts
is
the
cause
of
the
diversity
of
effects
.
And
for
the
difference
of
contacts
it
cannot
,
as
I
see
,
be
derived
from
any
thing
else
,
save
from
that
the
substance
of
the
Iron
is
of
parts
more
subtil
,
more
pure
,
and
more
compacted
than
those
of
the
Magnet
,
which
are
more
grosse
,
impure
,
and
rare
.
From
whence
it
followeth
,
that
the
superficies
of
two
Irons
that
are
to
touch
,
by
being
exquisitely
plained
,
filed
,
and
burnished
,
do
so
exactly
conjoyn
,
that
all
the
infinite
points
of
the
one
meet
with
the
infinite
points
of
the
other
;
so
that
the
filaments
,
if
I
may
so
say
,
that
collegate
the
two
Irons
,
are
many
more
than
those
that
collegate
the
Magnet
to
the
Iron
,
by
reason
that
the
substance
of
the
Magnet
is
more
porous
,
and
lesse
compact
,
which
maketh
that
all
the
points
and
filaments
of
the
Loadstone
do
not
close
with
that
which
it
unites
unto
.
In
the
next
place
,
that
the
substance
of
Iron
(
especially
the
well
refined
,
as
namely
,
the
purest
steel
)
is
of
parts
much
more
dense
,
subtil
,
and
pure
than
the
matter
of
the
Loadstone
,
is
seen
,
in
that
one
may
bring
its
edge
to
an
extraordinary
sharpnesse
,
such
as
is
that
of
the
Rasor
,
which
can
never
be
in
any
great
measure
effected
in
a
piece
of
Magnet
.
A
sensible
proof
of
the
impurity
of
the
Magnet
.
Then
,
as
for
the
impurity
of
the
Magnet
,
and
its
being
mixed
with
other
qualities
of
stone
,
it
is
first
sensibly
discovered
by
the
colour
of
some
little
spots
,
for
the
most
part
white
;
and
next
by
presenting
a
needle
to
it
,
hanging
in
a
thread
,
which
upon
those
stonynesses
cannot
find
repose
,
but
being
attracted
by
the
parts
circumfused
,
seemeth
to
fly
from
[
](A61244-e83760-b)*
*
The
Author
hereby
meaneth
that
the
stone
doth
not
all
consist
of
magnetick
matter
,
but
that
the
whiter
specks
being
weak
,
those
other
parts
of
the
Loadstone
of
a
more
dark
&
constant
colour
,
contain
all
that
vertue
wherewith
bodies
are
attracted
.
those
,
and
to
leap
upon
the
Magnet
contiguous
to
them
:
and
as
some
of
those
Heterogeneal
parts
are
for
their
magnitude
very
visible
,
so
we
may
believe
,
that
there
are
others
,
in
great
abundance
,
which
,
for
their
smallnesse
,
are
imperceptible
,
that
are
disseminated
throughout
the
whole
masse
.
That
which
I
say
,
(
namely
,
that
the
multitude
of
contacts
that
are
made
between
Iron
and
Iron
,
is
the
cause
of
the
so
solid
conjunction
)
is
confirmed
by
an
experiment
,
which
is
this
,
that
if
we
present
the
sharpned
point
of
a
needle
to
the
cap
of
a
Magnet
,
it
will
stick
no
faster
to
it
,
than
to
the
same
stone
unarmed
:
which
can
proceed
from
no
other
cause
,
than
from
the
equality
of
the
contacts
that
are
both
of
one
sole
point
.
But
what
then
?
Let
a
[
](A61244-e83790-b)*
*
A
common
sewing
needle
.
Needle
be
taken
and
placed
upon
a
Magnet
,
so
that
one
of
its
extremities
hang
somewhat
over
,
and
to
that
present
a
Nail
;
to
which
the
Needle
will
instantly
cleave
,
insomuch
that
withdrawing
the
Nail
,
the
Needle
will
stand
in
suspense
,
and
with
its
two
ends
touching
the
Magnet
and
the
Iron
;
and
withdrawing
the
Nail
yet
a
little
further
,
the
Needle
will
forsake
the
Magnet
;
provided
that
the
eye
of
the
Needle
be
towards
the
Nail
,
and
the
point
towards
the
Magnet
;
but
if
the
eye
be
towards
the
Loadstone
,
in
withdrawing
the
Nail
the
Needle
will
cleave
to
the
Magnet
;
and
this
,
in
my
judgment
,
for
no
other
reason
,
save
onely
that
the
Needle
,
by
reason
it
is
bigger
towards
the
eye
,
toucheth
in
much
more
points
than
its
sharp
point
doth
.
SAGR.
Your
whole
discourse
hath
been
in
my
judgment
very
concluding
,
and
this
experiment
of
the
Needle
hath
made
me
think
it
little
inferiour
to
a
Mathematical
Demonstration
;
and
I
ingenuously
confesse
,
that
in
all
the
Magnetick
Philosophy
,
I
never
heard
or
read
any
thing
,
that
with
such
strong
reasons
gave
account
of
its
so
many
admirable
accidents
,
of
which
,
if
the
causes
were
with
the
same
perspicuity
laid
open
,
I
know
not
what
sweeter
food
our
Intellects
could
desire
.
SALV
.
In
seeking
the
reasons
of
conclusions
unknown
unto
us
,
it
is
requisite
to
have
the
good
fortune
to
direct
the
discourse
from
the
very
beginning
towards
the
way
of
truth
;
in
which
if
any
one
walk
,
it
will
easily
happen
,
that
one
shall
meet
with
several
other
Propositions
known
to
be
true
,
either
by
disputes
or
experiments
,
from
the
certainty
of
which
the
truth
of
ours
acquireth
strength
and
evidence
;
as
it
did
in
every
respect
happen
to
me
in
the
present
Probleme
,
for
being
desirous
to
assure
my self
,
by
some
other
accident
,
whether
the
reason
of
the
Proposition
,
by
me
found
,
were
true
;
namely
,
whether
the
substance
of
the
Magnet
were
really
much
lesse
continuate
than
that
of
Iron
or
of
Steel
,
I
made
the
Artists
that
work
in
the
Gallery
of
my
Lord
the
Grand
Duke
,
to
smooth
one
side
of
that
piece
of
Magnet
,
which
formerly
was
yours
,
and
then
to
polish
and
burnish
it
;
upon
which
to
my
satisfaction
I
found
what
I
desired
.
For
I
discovered
many
specks
of
colour
different
from
the
rest
,
but
as
splendid
and
bright
,
as
any
of
the
harder
sort
of
stones
;
the
rest
of
the
Magnet
was
polite
,
but
to
the
tact
onely
,
not
being
in
the
least
splendid
;
but
rather
as
if
it
were
smeered
over
with
foot
;
and
this
was
the
substance
of
the
Load-stone
,
and
the
shining
part
was
the
fragments
of
other
stones
intermixt
therewith
,
as
was
sensibly
made
known
by
presenting
the
face
thereof
to
filings
of
Iron
,
the
which
in
great
number
leapt
to
the
Load-stone
,
but
not
so
much
as
one
grain
did
stick
to
the
said
spots
,
which
were
many
,
some
as
big
as
the
fourth
part
of
the
nail
of
a
mans
finger
,
others
somewhat
lesser
,
the
least
of
all
very
many
,
and
those
that
were
scarce
visible
almost
innumerable
.
So
that
I
did
assure
my self
,
that
my
conjecture
was
true
,
when
I
first
thought
that
the
substance
of
the
Magnet
was
not
close
and
compact
,
but
porous
,
or
to
say
better
,
spongy
;
but
with
this
difference
,
that
whereas
the
sponge
in
its
cavities
and
little
cels
conteineth
Air
or
Water
,
the
Magnet
hath
its
pores
full
of
hard
and
heavy
stone
,
as
appears
by
the
exquisite
lustre
which
those
specks
receive
.
Whereupon
,
as
I
have
said
from
the
beginning
,
applying
the
surface
of
the
Iron
to
the
superficies
of
the
Magnet
the
minute
particles
of
the
Iron
,
though
perhaps
more
continuate
than
these
of
any
other
body
(
as
its
shining
more
than
any
other
matter
doth
shew
)
do
not
all
,
nay
but
very
few
of
them
incounter
pure
Magnet
;
and
the
contacts
being
few
,
the
union
is
but
weak
.
But
because
the
cap
of
the
Load-stone
,
besides
the
contact
of
a
great
part
of
its
superficies
,
invests
its
self
also
with
the
virtue
of
the
parts
adjoyning
,
although
they
touch
not
;
that
side
of
it
being
exactly
smoothed
to
which
the
other
face
,
in
like
manner
well
polisht
of
the
Iron
to
be
attracted
,
is
applyed
,
the
contract
is
made
by
innumerable
minute
particles
,
if
not
haply
by
the
infinite
points
of
both
the
superficies
,
whereupon
the
union
becometh
very
strong
.
This
observation
of
smoothing
the
surfaces
of
the
Irons
that
are
to
touch
,
came
not
into
the
thoughts
of
Gilbert
,
for
he
makes
the
Irons
convex
,
so
that
their
contact
is
very
small
;
and
thereupon
it
cometh
to
passe
that
the
tenacity
,
wherewith
those
Irons
conjoyn
,
is
much
lesser
.
SAGR.
I
am
,
as
I
told
you
before
,
little
lesse
satisfied
with
this
reason
,
that
if
it
were
a
pure
Geometrical
Demonstration
;
and
because
we
speak
of
a
Physical
Problem
,
I
believe
that
also
Simplicius
will
find
himself
satisfied
as
far
as
natural
science
admits
,
in
which
he
knows
that
Geometrical
evidence
is
not
to
be
required
.
SIMP.
I
think
indeed
,
Sympathy
and
Antipathy
,
terms
used
by
Philosophers
to
give
a
reason
easily
of
many
natural
effests
▪
that
Salviatus
with
a
fine
circumlocution
hath
so
manifestly
displayed
the
cause
of
this
effect
,
that
any
indifferent
wit
,
though
not
verst
in
the
Sciences
,
may
apprehend
the
same
;
but
we
,
confining
our selves
to
the
terms
of
Art
,
reduce
the
cause
of
these
and
other
the
like
natural
effects
to
Sympathy
,
which
is
a
certain
agreemet
and
mutual
appetite
which
ariseth
between
things
that
are
semblable
to
one
another
in
qualities
;
as
likewise
on
the
contrary
that
hatred
&
enmity
for
which
other
things
shun
&
abhor
one
another
we
call
Antipathy
.
SAGR.
And
thus
with
these
two
words
men
come
to
render
reasons
of
a
great
number
of
accidents
and
effects
which
we
see
not
without
admiration
to
be
produced
in
nature
.
But
this
kind
of
philosophating
seems
to
me
to
have
great
sympathy
with
a
certain
way
of
Painting
that
a
Friend
of
mine
used
,
A
pleasant
example
declaring
the
invalidity
of
some
Phylosophical
argumentations
.
who
writ
upon
the
Tele
or
Canvasse
in
chalk
,
here
I
will
have
the
Fountain
with
Diana
and
her
Nimphs
,
there
certain
Hariers
,
in
this
corner
I
will
have
a
Hunts-man
with
the
Head
of
a
Stag
,
the
rest
shall
be
Lanes
,
Woods
,
and
Hills
;
and
left
the
remainder
for
the
Painter
to
set
forth
with
Colours
;
and
thus
he
perswaded
himself
that
he
had
painted
the
Story
of
Acteon
,
when
as
he
had
contributed
thereto
nothing
of
his
own
more
than
the
names
.
But
whether
are
we
wandred
with
so
long
a
digression
,
contrary
to
our
former
resolutions
?
I
have
almost
forgot
what
the
point
was
that
we
were
upon
when
we
fell
into
this
magnetick
discourse
▪
and
yet
I
had
something
in
my
mind
that
I
intended
to
have
spoken
upon
that
subject
.
SALV
.
We
were
about
to
demonstrate
that
third
motion
ascribed
by
Copernicus
to
the
Earth
to
be
no
motion
but
a
quiescence
and
maintaining
of
it self
immutably
directed
with
its
determinate
parts
towards
the
same
&
determinate
parts
of
the
Universe
,
that
is
a
perpetual
conservation
of
the
Axis
of
its
diurnal
revolution
parallel
to
it self
,
and
looking
towards
such
and
such
fixed
stars
;
which
most
constant
position
we
said
did
naturally
agree
with
every
librated
body
suspended
in
a
fluid
and
yielding
medium
,
which
although
carried
about
,
yet
did
it
not
change
directionin
respect
of
things
external
,
but
onely
seemed
to
revolve
in
its
self
,
in
respect
of
that
which
carryed
it
round
,
and
to
the
vessel
in
which
it
was
transported
.
And
then
we
added
to
this
simple
and
natural
accident
the
magnetick
virtue
,
whereby
the
self
Terrestrial
Globe
might
so
much
the
more
constantly
keep
it
immutable
,
—
SAGR.
Now
I
remember
the
whole
businesse
;
and
that
which
then
came
into
my
minde
,
&
which
I
would
have
intimated
,
was
a
certain
consideration
touching
the
scruple
and
objection
of
Simplicius
,
which
he
propounded
against
the
mobility
of
the
Earth
,
taken
from
the
multiplicity
of
motions
,
The
several
natural
motions
of
the
Magnet
.
impossible
to
be
assigned
to
a
simple
body
,
of
which
but
one
sole
and
simple
motion
,
according
to
the
doctrine
of
Aristotle
,
can
be
natural
;
and
that
which
I
would
have
proposed
to
consideration
,
was
the
Magnet
,
to
which
we
manifestly
see
three
motions
naturally
to
agree
:
one
towards
the
centre
of
the
Earth
,
as
a
Grave
;
the
second
is
the
circular
Horizontal
Motion
,
whereby
it
restores
and
conserves
its
Axis
towards
determinate
parts
of
the
Universe
;
and
the
third
is
this
,
newly
discovered
by
Gilbert
,
of
inclining
its
Axis
,
being
in
the
plane
of
a
Meridian
towards
the
surface
of
the
Earth
,
and
this
more
and
lesse
,
according
as
it
shall
be
distant
from
the
Equinoctial
,
under
which
it
is
parallel
to
the
Axis
of
the
Earth
.
Besides
these
three
,
it
is
not
perhaps
improbable
,
but
that
it
may
have
a
fourth
,
of
revolving
upon
its
own
Axis
,
in
case
it
were
librated
and
suspended
in
the
air
or
other
fluid
and
yielding
Medium
,
so
that
all
external
and
accidental
impediments
were
removed
,
and
this
opinion
Gilbert
himself
seemeth
also
to
applaud
.
So
that
,
Simplicius
,
you
see
how
tottering
the
Axiome
of
Aristotle
is
.
SIMP.
This
doth
●ot
only
not
make
against
the
Maxime
,
but
not
so
much
as
look
towards
it
:
for
that
he
speaketh
of
a
simple
body
,
and
of
that
which
may
naturally
consist
therewith
;
but
you
propose
that
which
befalleth
a
mixt
body
;
nor
do
you
tell
us
of
any
thing
that
is
new
to
the
doctrine
of
Aristotle
,
for
that
he
likewise
granteth
to
mixt
bodies
compound
motions
by
—
SAGR.
Stay
a
little
,
Simplicius
,
&
answer
me
to
the
questions
I
shall
ask
you
.
Aristole
grants
a
compound
motion
to
mixt
bodies
.
You
say
that
the
Load-stone
is
no
simple
body
,
now
I
desire
you
to
tell
me
what
those
simple
bodies
are
,
that
mingle
in
composing
the
Load-stone
.
SIMP.
I
know
not
how
to
tell
you
th'
ingredients
nor
simples
precisely
,
but
it
sufficeth
that
they
are
things
elementary
.
SALV
.
So
much
sufficeth
me
also
.
And
of
these
simple
elementary
bodies
,
what
are
the
natural
motions
?
SIMP.
They
are
the
two
right
and
simple
motions
,
sursum
and
deorsum
.
SAGR.
Tell
me
in
the
next
place
?
Do
you
believe
that
the
motion
,
that
shall
remain
natural
to
that
same
mixed
body
,
should
be
one
that
may
result
from
the
composition
of
the
two
simple
natural
motions
of
the
simple
bodies
compounding
,
or
that
it
may
be
a
motion
impossible
to
be
composed
of
them
.
The
motion
of
mixt
bodies
ought
to
be
such
as
may
result
from
the
composition
of
the
motions
of
the
simple
bodies
compounding
.
SIMP.
I
believe
that
it
shall
move
with
the
motion
resulting
from
the
composition
of
the
motions
of
the
simple
bodies
compounding
,
and
that
with
a
motion
impossible
to
be
composed
of
these
,
it
is
impossible
that
it
should
move
.
SAGR.
But
,
Simplicius
,
with
two
right
and
simple
motions
,
you
shall
never
be
able
to
compose
a
circular
motion
,
With
two
right
motions
one
cannot
compose
circular
motions
.
such
as
are
the
two
,
or
three
circular
motions
that
the
magnet
hath
:
you
see
then
into
what
absurdities
evil
grounded
Principles
,
or
,
to
say
better
,
Philosophers
are
forced
to
confesse
that
the
Magnet
is
compounded
of
coelestial
substances
,
and
of
elementary
.
the
ill-inferred
consequences
of
good
Principles
carry
a
man
;
for
you
are
now
forced
to
say
,
that
the
Magnet
is
a
mixture
compounded
of
substances
elementary
and
coelestial
,
if
you
will
maintain
that
the
straight
motion
is
a
peculiar
to
the
Elements
,
and
the
circular
to
the
coelestial
bodies
.
Therefore
if
you
will
more
safely
argue
,
you
must
say
,
that
of
the
integral
bodies
of
the
Universe
,
those
that
are
by
nature
moveable
,
do
all
move
circularly
,
and
that
therefore
the
Magnet
,
as
a
part
of
the
true
primary
,
The
errour
of
those
who
call
the
Magnet
a
mixt
body
,
and
the
terrestrial
Globe
a
simble
body
.
and
integral
substance
of
our
Globe
,
pertaketh
of
the
same
qualities
with
it
.
And
take
notice
of
this
your
fallacy
,
in
calling
the
Magnet
a
mixt
body
,
and
the
Terrestrial
Globe
a
simple
body
,
which
is
sensibly
perceived
to
be
a
thousand
times
more
compound
:
for
,
besides
that
it
containeth
an
hundred
an
hundred
matters
,
exceeding
different
from
one
another
,
it
containeth
great
abundance
of
this
which
you
call
mixt
,
I
mean
of
the
Load-stone
.
This
seems
to
me
just
as
if
one
should
call
bread
a
mixt
body
,
and
[
](A61244-e84590-b)*
*
Ogliopotrida
a
Spanish
dish
of
many
ingredients
boild
together
.
Pannada
a
simple
body
,
in
which
there
is
put
no
small
quantity
of
bread
,
besides
many
other
things
edible
.
This
seemeth
to
me
a
very
admirable
thing
,
amongst
others
of
the
Peripateticks
,
The
Discourses
of
Peripateticks
,
full
of
errours
and
contradictions
.
who
grant
(
nor
can
it
be
denied
)
that
our
Terrestrial
Globe
is
,
de
facto
,
a
compound
of
infinite
different
matters
;
and
grant
farther
that
of
compound
bodies
the
motion
ought
to
be
compound
:
now
the
motions
that
admit
of
composition
are
the
right
and
circular
:
For
the
two
right
motions
,
as
being
contrary
,
are
incompatible
together
,
they
affirm
,
that
the
pure
Element
of
Earth
is
no
where
to
be
found
;
they
confesse
,
that
it
never
hath
been
moved
with
a
local
motion
;
and
yet
they
will
introduce
in
Nature
that
body
which
is
not
to
be
found
,
and
make
it
move
with
that
motion
which
it
never
exercised
,
nor
never
shall
do
,
and
to
that
body
which
hath
,
and
ever
had
a
being
,
they
deny
that
motion
,
which
before
they
granted
,
ought
naturally
to
agree
therewith
.
SALV
.
I
beseech
you
,
Sagredus
,
let
us
not
weary
our selves
any
more
about
these
particulars
,
and
the
rather
,
because
you
know
that
our
purpose
was
not
to
determine
resolutely
,
or
to
accept
for
true
,
this
or
that
opinion
,
but
only
to
propose
for
our
divertisement
such
reasons
,
and
answers
as
may
be
alledged
on
the
one
side
,
or
on
the
other
;
and
Simplicius
maketh
this
answer
,
in
defence
of
his
Peripateticks
,
therefore
let
us
leave
the
judgment
in
suspense
,
and
remit
the
determination
into
the
hands
of
such
as
are
more
known
than
we
.
And
because
I
think
that
we
have
,
with
sufficient
prolixity
,
in
these
three
dayes
,
discoursed
upon
the
Systeme
of
the
Universe
,
it
will
now
be
seasonable
,
that
we
proceed
to
the
grand
accident
,
from
whence
our
Disputations
took
beginning
,
I
mean
,
of
the
ebbing
and
flowing
of
the
Sea
,
the
cause
whereof
may
,
in
all
probability
,
be
referred
to
the
motion
of
the
Earth
.
But
that
,
if
you
so
please
,
we
will
reserve
till
to
morrow
.
In
the
mean
time
,
that
I
may
not
forget
it
,
I
will
speak
to
one
particular
,
to
which
I
could
have
wished
,
that
Gilbert
had
not
lent
an
ear
;
An
improbable
effect
admired
by
Gilbertus
in
the
Loadstone
.
I
mean
that
of
admitting
,
that
in
case
a
little
Sphere
of
Loadstone
might
be
exactly
librated
,
it
would
revolve
in
it self
;
because
there
is
no
reason
why
it
should
do
so
;
For
if
the
whole
Terrestrial
Globe
hath
a
natural
faculty
of
revolving
about
its
own
centre
in
twenty
four
hours
,
and
that
all
its
parts
ought
to
have
the
same
,
I
mean
,
that
faculty
of
turning
round
together
with
their
whole
,
about
its
centre
in
twenty
four
hours
;
they
already
have
the
same
in
effect
,
whilst
that
,
being
upon
the
Earth
,
they
turn
round
along
with
it
:
And
the
assigning
them
a
revolution
about
their
particular
centres
,
would
be
to
ascribe
unto
them
a
second
motion
much
different
from
the
first
:
for
so
they
would
have
two
,
namely
,
the
revolving
in
twenty
four
hours
about
the
centre
of
their
whole
;
and
the
turning
about
their
own
:
now
this
second
is
arbitrary
,
nor
is
there
any
reason
for
the
introducing
of
it
:
If
by
plucking
away
a
piece
of
Loadstone
from
the
whole
natural
masse
,
it
were
deprived
of
the
faculty
of
following
it
,
as
it
did
,
whilst
it
was
united
thereto
,
so
that
it
is
thereby
deprived
of
the
revolution
about
the
universal
centre
of
the
Terrestrial
Globe
,
it
might
haply
,
with
somewhat
greater
probability
be
thought
by
some
,
that
the
said
Magnet
was
to
appropriate
to
it self
a
new
conversion
about
its
particular
centre
;
but
if
it
do
no
lesse
,
when
separated
,
than
when
conjoyned
,
continue
always
to
pursue
its
first
,
eternal
,
and
natural
course
,
to
what
purpose
should
we
go
about
to
obtrude
upon
it
another
new
one
?
SAGR.
I
understand
you
very
well
,
and
this
puts
me
in
mind
of
a
Discourse
very
like
to
this
for
the
vanity
of
it
,
The
vain
argumentation
of
some
to
prove
the
Element
of
Water
to
be
of
a
Spherical
superficies
.
falling
from
certain
Writers
upon
the
Sphere
,
and
I
think
,
if
I
well
remember
,
amongst
others
from
Sacrobosco
,
who
,
to
shew
how
the
Element
of
Water
,
doth
,
together
with
the
Earth
,
make
a
compleat
Spherical
Figure
,
and
so
between
them
both
compose
this
our
Globe
,
writeth
,
that
the
seeing
the
small
*
particles
of
water
shape
themselves
into
rotundity
,
as
in
the
drops
,
and
in
the
dew
daily
apparent
upon
the
leaves
of
several
herbs
,
is
a
strong
argument
;
and
because
,
according
to
the
trite
Axiome
,
there
is
the
same
reason
for
the
whole
,
as
for
the
parts
,
the
parts
affecting
that
same
figure
,
it
is
necessary
that
the
same
is
proper
to
the
whole
Element
:
and
truth
is
,
methinks
it
is
a
great
oversight
that
these
men
should
not
perceive
so
apparent
a
vanity
,
and
consider
that
if
their
argument
had
run
right
,
it
would
have
followed
,
that
not
only
the
small
drops
,
but
that
any
whatsoever
greater
quantity
of
water
separated
from
the
whole
Element
,
should
be
reduced
into
a
Globe
:
Which
is
not
seen
to
happen
;
though
indeed
the
Senses
may
see
,
and
the
Understanding
perceive
that
the
Element
of
Water
loving
to
form
it self
into
a
Spherical
Figure
about
the
common
centre
of
gravity
,
to
which
all
grave
bodies
tend
(
that
is
,
the
centre
of
the
Terrestrial
Globe
)
it
therein
is
followed
by
all
its
parts
,
according
to
the
Axiome
;
so
that
all
the
surfaces
of
Seas
,
Lakes
,
Pools
,
and
in
a
word
,
of
all
the
parts
of
Waters
conteined
in
vessels
,
distend
themselves
into
a
Spherical
Figure
,
but
that
Figure
is
an
arch
of
that
Sphere
that
hath
for
its
centre
the
centre
of
the
Terrestrial
Globe
,
and
do
not
make
particular
Spheres
of
themselves
.
SALV
.
The
errour
indeed
is
childish
;
and
if
it
had
been
onely
the
single
mistake
of
Sacrobosco
,
I
would
easily
have
allowed
him
in
it
;
but
to
pardon
it
also
to
his
Commentators
,
and
to
other
famous
men
,
and
even
to
Ptolomy
himselfe
;
this
I
cannot
do
,
without
blushing
for
their
reputation
.
But
it
is
high
time
to
take
leave
,
it
now
being
very
late
,
and
we
being
to
meet
again
to
morrow
,
at
the
usual
hour
,
to
bring
all
the
foregoing
Discourses
to
a
final
conclusion
.
Place
this
Plate
at
the
end
of
the
third
Dialogue
GALILAEUS
Gailaeus
Lyncaeus
,
HIS
SYSTEME
OF
THE
WORLD
.
The
Fourth
Dialogue
.
INTERLOCVTORS
.
SALVIATUS
,
SAGREDUS
,
&
SIMPLICIUS
.
SAGR.
I
know
not
whether
your
return
to
our
accustomed
conferences
hath
really
been
later
than
usual
,
or
whether
the
desire
of
hearing
the
thoughts
of
Salviatus
,
touching
a
matter
so
curious
,
hath
made
me
think
it
so
:
But
I
have
tarried
a
long
hour
at
this
window
,
expecting
every
moment
when
the
Gondola
would
appear
that
I
sent
to
fetch
you
.
SALV
.
I
verily
believe
that
your
imagination
more
than
our
tarriance
hath
prolonged
the
time
:
Nature
in
sport
maketh
the
ebbing
and
flowing
of
the
Sea
,
to
approve
the
Earth●
mobility
.
and
to
make
no
longer
demurre
,
it
would
be
well
,
if
without
interposing
more
words
,
we
came
to
the
matter
it self
;
and
did
shew
,
that
nature
hath
permitted
(
whether
the
business
in
rei
veritate
be
so
,
or
else
to
play
and
sport
with
our
Fancies
)
hath
,
The
tide
,
and
mobility
of
the
Earth
mutually
confirm
each
other
.
I
say
,
hath
permitted
that
the
motions
for
every
other
respect
,
except
to
resolve
the
ebbing
and
flowing
of
the
Sea
,
assigned
long
since
to
the
earth
,
should
be
found
now
at
last
to
answer
exactly
to
the
cause
thereof
;
and
,
as
it
were
,
All
terrene
effects
,
indifferently
confirm
the
motion
or
rest
of
the
Earth
,
except
the
ebbing
and
flowing
of
the
Sea
.
with
mutual
a
emulation
,
the
said
ebbing
and
flowing
to
appear
in
confirmation
of
the
Terrestrial
motion
:
the
judices
whereof
have
hitherto
been
taken
from
the
coelestial
Phaenomena
,
in
regard
that
of
those
things
that
happen
on
Earth
,
not
any
one
was
of
force
to
prove
one
opinion
more
than
another
,
as
we
already
have
at
large
proved
,
by
shewing
that
all
the
terrene
occurrences
upon
which
the
stability
of
the
Earth
and
mobility
of
the
Sun
and
Firmament
is
commonly
inferred
,
are
to
seem
to
us
performed
in
the
same
manner
,
though
we
supposed
the
mobility
of
the
Earth
,
and
the
immobility
of
them
.
The
Element
of
Water
onely
,
as
being
most
vast
,
and
which
is
not
annexed
and
concatenated
to
the
Terrestrial
Globe
as
all
its
other
solid
parts
are
;
yea
,
rather
which
by
reason
of
its
fluidity
remaineth
apart
sui
juris
,
and
free
,
is
to
be
ranked
amongst
those
sublunary
things
,
from
which
we
may
collect
some
hinte
and
intimation
of
what
the
Earth
doth
in
relation
to
motion
and
rest
.
After
I
had
many
and
many
a
time
examined
with
my self
the
effects
and
accidents
,
partly
seen
and
partly
understood
from
others
,
that
are
to
be
observed
in
the
motions
of
waters
:
and
moreover
read
and
heard
the
great
vanities
produced
by
many
,
as
the
causes
of
those
accidents
,
The
first
general
conclusion
of
the
impossibility
of
the
ebbing
and
flowing
the
immobility
of
the
terrestrial
Globe
being
granted
.
I
have
been
induced
upon
no
slight
reasons
to
omit
these
two
conclusions
(
having
made
withal
the
necessary
presupposals
)
that
in
case
the
terrestrial
Globe
be
immoveable
,
the
flux
and
reflux
of
the
Sea
cannot
be
natural
;
and
that
,
in
case
those
motions
be
conferred
upon
the
said
Globe
,
which
have
been
long
since
assigned
to
it
,
it
is
necessary
that
the
Sea
be
subject
to
ebbing
and
flowing
,
according
to
all
that
which
we
observe
to
happen
in
the
same
.
SAGR.
The
Proposition
is
very
considerable
,
as
well
for
it self
as
for
what
followeth
upon
the
same
by
way
of
consequence
,
so
that
I
shall
the
more
intensly
hearken
to
the
explanation
and
confirmation
of
it
.
SALV
.
Because
in
natural
questions
,
The
knowledge
of
the
effests
contributes
to
the
investigation
of
the
causes
.
of
which
number
this
which
we
have
in
hand
is
one
,
the
knowledge
of
the
effects
is
a
means
to
guide
us
to
the
investigation
and
discovery
of
the
causes
,
and
without
which
we
should
walk
in
the
dark
,
nay
with
more
uncertainty
,
for
that
we
know
not
whither
we
would
go
,
whereas
the
blind
,
at
least
,
know
where
they
desire
to
arrive
;
therefore
first
of
all
it
is
necessary
to
know
the
effects
whereof
we
enquire
the
causes
:
of
which
effects
you
,
Sagredus
,
ought
more
abundantly
and
more
certainly
to
be
informed
than
I
am
,
as
one
,
that
besides
your
being
born
,
and
having
,
for
a
long
time
,
dwelt
in
Venice
,
where
the
Tides
are
very
notable
for
their
greatnesse
,
have
also
sailed
into
Syria
,
and
,
as
an
ingenuous
and
apprehensive
wit
,
must
needs
have
made
many
Observations
upon
this
subject
:
whereas
I
,
that
could
onely
for
a
time
,
and
that
very
short
,
observe
what
happened
in
these
extream
parts
of
the
Adriatick
Gulph
,
and
in
our
Seas
below
about
the
Tyrrhene
shores
,
must
needs
take
many
things
upon
the
relation
of
others
,
who
,
for
the
most
part
,
not
very
well
agreeing
,
and
consequently
being
very
uncertain
,
contribute
more
of
confusion
than
confirmation
to
our
speculations
.
Neverthelesse
,
from
those
that
we
are
sure
of
,
and
which
are
the
principal
,
I
think
I
am
able
to
attain
to
the
true
and
primary
causes
;
not
that
I
pretend
to
be
able
to
produce
all
the
proper
and
adequate
reasons
of
those
effects
that
are
new
unto
me
,
and
which
consequently
I
could
never
have
thought
upon
.
And
that
which
I
have
to
say
,
I
propose
only
,
as
a
key
that
openeth
the
door
to
a
path
never
yet
trodden
by
any
,
in
certain
hope
,
that
some
wits
more
speculative
than
mine
,
will
make
a
further
progresse
herin
,
and
penetrate
much
farther
than
I
shall
have
done
in
this
my
first
Discovery
:
And
although
that
in
other
Seas
,
remote
from
us
,
there
may
●appen
several
accidents
,
which
do
not
happen
in
our
Mediterranean
Sea
,
yet
doth
not
this
invalidate
the
reason
and
cause
that
I
shall
produce
,
if
so
be
that
it
verifie
and
fully
resolve
the
accidents
which
evene
in
our
Sea
:
for
that
in
conclusion
there
can
be
but
one
true
and
primary
cause
of
the
effects
that
are
of
the
same
kind
.
I
will
relate
unto
you
,
therefore
,
the
effects
that
I
know
to
be
true
,
and
assigne
the
causes
thereof
that
I
think
to
be
true
,
and
you
also
,
Gentlemen
,
shall
produce
such
others
as
are
known
to
you
,
besides
mine
,
and
then
we
will
try
whether
the
cause
,
by
me
alledged
,
may
satisfie
them
also
.
Three
Periods
of
ebbings
and
flowings
,
diurnal
,
monethly
,
and
annual
.
I
therefore
affirm
the
periods
that
are
observed
in
the
fluxes
and
refluxes
of
the
Sea-waters
to
be
three
:
the
first
and
principal
is
this
great
and
most
obvious
one
;
namely
,
the
diurnal
,
according
to
which
the
intervals
of
some
hours
with
the
waters
flow
and
ebbe
;
and
these
intervals
are
,
for
the
most
part
,
in
the
Mediterrane
from
six
hours
to
six
hours
,
or
thereabouts
,
that
is
,
they
for
six
hours
flow
,
and
for
six
hours
ebbe
.
The
second
period
is
monethly
,
and
it
seemes
to
take
its
origen
from
the
motion
of
the
Moon
,
not
that
it
introduceth
other
motions
,
but
only
altereth
the
greatnesse
of
those
before
mentioned
,
with
a
notable
difference
,
according
as
it
shall
wax
or
wane
,
or
come
to
the
Quadrature
with
the
Sun
.
The
third
Period
is
annual
,
and
is
seen
to
depend
on
the
Sunne
,
and
onely
altereth
the
diurnal
motions
,
by
making
them
different
in
the
times
of
the
Solstices
,
as
to
greatnesse
,
from
what
they
are
in
the
Equinoxes
.
We
will
speak
(
in
the
first
place
,
of
the
diurnal
motion
,
as
being
the
principal
,
and
upon
which
the
Moon
and
Sun
seem
to
exercise
their
power
secondarily
,
Varieties
that
●appen
in
the
diur●●●
period
.
in
their
monethly
and
annual
alterations
.
Three
differences
are
observable
in
these
horary
mutations
;
for
in
some
places
the
waters
rise
and
fall
,
without
making
any
progressive
motion
;
in
others
,
without
rising
or
falling
they
run
one
while
towards
the
East
,
and
recur
another
while
towards
the
West
;
and
in
others
they
vary
the
heights
and
course
also
,
as
happeneth
here
in
Venice
,
where
the
Tides
in
coming
in
rise
,
and
in
going
out
fall
;
and
this
they
do
in
the
extermities
of
the
lengths
of
Gulphs
that
distend
from
West
to
East
,
and
terminate
in
open
shores
,
up
along
which
shores
the
Tide
at
time
of
flood
hath
room
to
extend
it self
:
but
if
the
course
of
the
Tide
were
intercepted
by
Cliffes
and
Banks
of
great
height
and
steepnesse
,
there
it
will
flow
and
ebbe
without
any
progressive
motion
.
Again
,
it
runs
to
and
again
,
without
changing
height
in
the
middle
parts
of
the
Mediterrane
,
as
notably
happeneth
in
the
[
](A61244-e85250-b)*
*
A
Strair
,
so
called
.
Faro
de
Messina
,
between
Scylla
and
Carybdis
,
where
the
Currents
,
by
reason
of
the
narrownesse
of
the
Channel
,
are
very
swift
;
but
in
the
more
open
Seas
,
and
about
the
Isles
that
stand
farther
into
the
Mediterranean
Sea
,
as
the
Baleares
,
Corsica
,
Sardignia
,
[
](A61244-e85300-b)*
*
Or
Ilva
.
Elba
,
Sicily
towards
the
Affrican
Coasts
,
Malta
,
[
](A61244-e85340-b)*
*
Or
Crets
.
Candia
,
&c.
the
changes
of
watermark
are
very
small
;
but
the
currents
indeed
are
very
notable
,
and
especially
when
the
Sea
is
pent
between
Islands
,
or
between
them
and
the
Continent
.
Now
these
onely
true
and
certain
effects
,
were
there
no
more
to
be
observed
,
do
,
in
my
judgment
,
very
probably
perswade
any
man
,
that
will
contain
himself
within
the
bounds
of
natural
causes
,
to
grant
the
mobility
of
the
Earth
:
for
to
make
the
vessel
(
as
it
may
be
called
)
of
the
Mediterrane
stand
still
,
and
to
make
the
water
contained
therein
to
do
,
as
it
doth
,
exceeds
my
imagination
,
and
perhaps
every
mans
else
,
who
will
but
pierce
beyond
the
rinde
in
these
kind
of
inquiries
.
SIMP.
These
accidents
,
Salviatus
,
begin
not
now
,
they
are
most
ancient
,
and
have
been
observed
by
very
many
,
and
several
have
attempted
to
assigne
,
some
one
,
some
another
cause
for
the
same
:
and
there
dwelleth
not
many
miles
from
hence
a
famous
Peripatetick
,
The
cause
of
the
ebbing
and
flowing
alledged
by
a
certain
modern
Philosopher
.
that
alledgeth
a
cause
for
the
same
newly
fished
out
of
a
certain
Text
of
Aristotle
,
not
well
understood
by
his
Expositors
,
from
which
Text
he
collecteth
,
that
the
true
cause
of
these
motions
doth
only
proceed
from
the
different
profundities
of
Seas
〈…〉
waters
of
greatest
depth
being
greater
in
abundance
,
and
therefore
more
grave
,
drive
back
the
Waters
of
lesse
depth
,
which
being
afterwards
raised
,
desire
to
descend
,
and
from
this
continual
colluctation
or
contest
proceeds
the
ebbing
and
flowing
.
The
cause
of
the
ebbing
and
flowing
ascribed
to
the
Moon
by
a
certain
Prelate
.
Again
those
that
referre
the
same
to
the
Moon
are
many
,
saying
that
she
hath
particular
Domination
over
the
Water
;
and
at
last
a
certain
Prelate
hath
published
a
little
Treatise
,
wher●in
he
saith
that
the
Moon
wandering
too
and
fro
in
the
Heavens
attracteth
and
draweth
towards
it
a
Masse
of
Water
,
which
goeth
continually
following
it
,
so
that
it
is
full
Sea
alwayes
in
that
part
which
lyeth
under
the
Moon
;
and
because
,
that
though
she
be
under
the
Horizon
,
yet
neverthelesse
the
Tide
returneth
,
he
saith
that
no
more
can
be
said
for
the
salving
of
that
particular
,
save
onely
,
that
the
Moon
doth
not
onely
naturally
retain
this
faculty
in
her self
;
but
in
this
case
hath
power
to
confer
it
upon
that
degree
of
the
Zodiack
that
is
opposite
unto
it
.
Others
,
Hieronymus
Borrius
and
other
Peripateticks
refer
it
to
the
temperate
heat
of
the
Moon
,
as
I
believe
you
know
,
do
say
that
the
Moon
is
able
with
her
temperate
heat
to
rarefie
the
Water
,
which
being
rarefied
,
doth
thereupon
flow
.
Nor
hath
there
been
wanting
some
that
—
SAGR.
I
pray
you
Simplicius
let
us
hear
no
more
of
them
,
for
I
do
not
think
it
is
worth
the
while
to
wast
time
in
relating
them
,
or
to
spend
our
breath
in
confuting
them
;
and
for
your
part
,
if
you
gave
your
assent
to
any
of
these
or
the
like
foole●ies
,
you
did
a
great
injury
to
your
judgment
,
which
neverthelesse
I
acknowledg
to
be
very
piercing
.
SALV
.
But
I
that
am
a
little
more
flegmatick
than
you
,
Answers
to
the
vanities
alledged
as
causes
of
the
ebbing
and
flowing
.
Sagredus
,
will
spend
a
few
words
in
favour
of
Simplicius
,
if
haply
he
thinks
that
any
probability
is
to
be
found
in
those
things
that
he
hath
related
.
I
say
therefore
:
The
Waters
,
Simplicius
,
that
have
their
exteriour
superficies
higher
,
repel
those
that
are
inferiour
to
them
,
and
lower
;
but
so
do
not
those
Waters
that
are
of
greatest
profundity
;
and
the
higher
having
once
driven
back
the
lower
,
they
in
a
short
time
grow
quiet
and
[
](A61244-e85580-b)*
*
Or
rather
smooth
.
level
.
This
your
Peripatetick
must
needs
be
of
an
opinion
,
that
all
the
Lakes
in
the
World
that
are
in
a
calme
,
and
that
all
the
Seas
where
the
ebbing
and
flowing
is
insensible
,
are
level
in
their
bottoms
;
but
I
was
so
simple
,
that
I
perswaded
my self
that
had
we
no
other
plummet
to
sound
with
,
The
Isles
are
tokens
of
the
unevennesse
of
the
bottomes
of
Seas
.
the
Isles
that
advance
so
high
above
Water
,
had
been
a
sufficient
evidence
of
the
unevennesse
of
their
bottomes
.
To
that
Prelate
I
could
say
that
the
Moon
runneth
every
day
along
the
whole
Mediterrane
,
and
yet
its
Waters
do
not
rise
thereupon
,
save
onely
in
the
very
extream
bounds
of
it
Eastward
,
and
here
to
us
at
Venice
.
And
for
those
that
make
the
Moons
temperate
heat
able
to
make
the
Water
swell
,
bid
them
put
fire
under
a
Kettle
full
of
Water
,
and
hold
their
right
hand
therein
till
that
the
Water
by
reason
of
the
heat
do
rise
but
one
sole
inch
,
and
then
let
them
take
it
out
,
and
write
off
the
tumefaction
of
the
Sea
.
Or
at
least
desire
them
to
shew
you
how
the
Moon
doth
to
rarefie
a
certain
part
of
the
Waters
,
and
not
the
remainder
;
as
for
instance
,
these
here
of
Venice
,
and
not
those
of
Ancona
,
Naples
,
Genova
:
the
truth
is
Poetick
Wits
are
of
two
kinds
,
Poetick
wits
of
two
kinds
.
some
are
ready
and
apt
to
invent
Fables
,
and
others
disposed
and
inclined
to
believe
them
.
SIMP.
I
believe
that
no
man
believeth
Fables
,
so
long
as
he
knows
them
to
be
so
;
and
of
the
opinions
concerning
the
causes
of
ebbing
and
flowing
,
which
are
many
,
because
I
know
that
of
one
single
effect
there
is
but
one
single
cause
that
is
true
and
primary
,
I
understand
very
well
,
and
am
certain
that
but
one
alone
at
the
most
can
be
true
,
and
for
all
the
rest
I
am
sure
that
they
are
fabulous
,
and
false
;
and
its
possible
that
the
true
one
may
not
be
among
those
that
have
been
hitherto
produced
;
nay
I
verily
believe
that
it
is
not
,
for
it
would
be
very
strange
that
the
truth
should
have
so
little
light
,
Truth
hath
not
so
little
light
as
not
to
be
discovered
amidst
the
umbrages
of
falshoods
.
as
that
it
should
not
be
visible
amongst
the
umbrages
of
so
many
falshoods
.
But
this
I
shall
say
with
the
liberty
that
is
permitted
amongst
us
,
that
the
introduction
of
the
Earths
motion
,
and
the
making
it
the
cause
of
the
ebbing
and
flowing
of
Tides
,
seemeth
to
me
as
yet
a
conjecture
no
lesse
fabulous
than
the
rest
of
those
that
I
have
heard
;
and
if
there
should
not
be
proposed
to
me
reasons
more
conformable
to
natural
matters
,
I
would
without
any
more
ado
proceed
to
believe
this
to
be
a
supernatural
effect
,
and
therefore
miraculous
,
and
unsearchable
to
the
understandings
of
men
,
as
infinite
others
there
are
,
that
immediately
depend
on
the
Omnipotent
hand
of
God
.
SAGR.
You
argue
very
prudently
,
Aristotle
holdeth
those
effects
to
be
miraculous
,
of
which
the
causes
are
unknown
.
and
according
to
the
Doctrine
of
Aristotle
,
who
you
know
in
the
beginning
of
his
mechanical
questions
referreth
those
things
to
a
Miracle
,
the
causes
whereof
are
occult
.
But
that
the
cause
of
the
ebbing
and
flowing
is
one
of
those
that
are
not
to
be
found
out
,
I
believe
you
have
no
greater
proof
than
onely
that
you
see
,
that
amongst
all
those
that
have
hitherto
been
produced
for
true
causes
thereof
,
there
is
not
one
wherewith
,
working
by
what
artifice
you
will
,
we
are
able
to
represent
such
an
effect
;
in
regard
that
neither
with
the
light
of
the
Moon
nor
of
the
Sun
,
nor
with
temperate
heats
,
nor
with
different
profundities
,
shall
one
ever
artificially
make
the
Water
conteined
in
an
immoveable
Vessel
to
run
one
way
or
another
,
and
to
ebbe
and
flow
in
one
place
,
and
not
in
another
.
But
if
without
any
other
artifice
,
but
with
the
onely
moving
of
the
Vessel
,
I
am
able
punctually
to
represent
all
those
mutations
that
are
observed
in
the
Sea
Water
,
why
will
you
refuse
this
reason
and
run
to
a
Miracle
?
SIMP.
I
will
run
to
a
Miracle
still
,
if
you
do
not
with
some
other
natural
causes
,
besides
that
of
the
motion
of
the
Vessels
of
the
Sea-water
disswade
me
from
it
;
for
I
know
that
those
Vessels
move
not
,
in
regard
that
all
the
entire
Terrestrial
Globe
is
naturally
immoveable
.
SALV
.
But
do
not
you
think
,
that
the
Terrestrial
Globe
might
supernaturally
,
that
is
,
by
the
absolute
power
of
God
,
be
made
moveable
?
SIMP.
Who
doubts
it
?
SALV
.
Then
Simplicius
,
seeing
that
to
make
the
flux
and
reflux
of
the
Sea
,
it
is
necessary
to
introduce
a
Miracle
,
let
us
suppose
the
Earth
to
move
miraculously
,
upon
the
motion
of
which
the
Sea
moveth
naturally
:
and
this
effect
shall
be
also
the
more
simple
,
and
I
may
say
natural
,
amongst
the
miraculous
operations
,
in
that
the
making
a
Globe
to
move
round
,
of
which
kind
we
see
many
others
to
move
,
is
lesse
difficult
than
to
make
an
immense
masse
of
water
go
forwards
and
backwards
,
in
one
place
more
swiftly
,
and
in
another
lesse
,
and
to
rise
and
fall
in
some
places
more
;
in
some
lesse
,
and
in
some
not
at
all
:
and
to
work
all
these
different
effects
in
one
and
the
same
Vessel
that
containeth
it
:
besides
,
that
these
are
several
Miracles
,
and
that
is
but
one
onely
.
And
here
it
may
be
added
,
that
the
Miracle
of
making
the
water
to
move
is
accompanied
with
another
,
namely
,
the
holding
of
the
Earth
stedfast
against
impetuosities
of
the
water
,
able
to
make
it
swage
sometimes
one
way
,
and
sometimes
another
,
if
it
were
not
miraculously
kept
to
rights
.
SAGR.
God
Simplicius
,
let
us
for
the
present
suspend
our
judgement
about
sentencing
the
new
opinion
to
be
vain
that
Salviatus
is
about
to
explicate
unto
us
,
nor
let
us
so
hastily
flye
out
into
passion
like
the
scolding
overgrown
Haggs
:
and
as
for
the
Miracle
,
we
may
as
well
recurre
to
it
when
we
have
done
hearing
the
Discourses
contained
within
the
bounds
of
natural
causes
:
though
to
speak
freely
,
all
the
Works
of
nature
,
or
rather
of
God
,
are
in
my
judgement
miraculous
.
SALV
.
And
I
am
of
the
same
opinion
;
nor
doth
my
saying
,
that
the
motion
of
the
Earth
is
the
Natural
cause
of
the
ebbing
and
flowing
,
hinder
,
but
that
the
said
motion
of
the
Earth
may
be
miraculous
.
Now
reassuming
our
Argument
,
I
apply
,
and
once
again
affirm
,
that
it
hath
been
hitherto
unknown
how
it
might
be
that
the
Waters
contained
in
our
Mediterranean
Straights
should
make
those
motions
,
as
we
see
it
doth
,
if
so
be
the
said
Straight
,
or
containing
Vessel
were
immoveable
.
And
that
which
makes
the
difficulty
,
and
rendreth
this
matter
inextricable
,
are
the
things
which
I
am
about
to
speak
of
,
and
which
are
daily
observed
.
Therefore
lend
me
your
attention
.
We
are
here
in
Venice
,
where
at
this
time
the
Waters
are
low
,
the
Sea
calm
,
It
is
proved
impossible
that
there
should
naturally
be
any
ebbing
and
flowing
,
the
Earth
being
immoveable
.
the
Air
tranquil
;
suppose
it
to
be
young
flood
,
and
that
in
the
term
of
five
or
six
hours
the
water
do
rise
ten
[
](A61244-e85990-b)*
*
Palms
.
hand
breadths
and
more
;
that
rise
is
not
made
by
the
first
water
,
which
was
said
to
be
rarefied
,
but
it
is
done
by
the
accession
of
new
Water
:
Water
of
the
same
sort
with
the
former
,
of
the
same
brackishness
,
of
the
same
density
,
of
the
same
weight
:
Ships
,
Simplicius
,
float
therein
as
in
the
former
,
without
drawing
an
hairs
breadth
more
water
;
a
Barrel
of
this
second
doth
not
weigh
one
single
grain
more
or
less
than
such
another
quantity
of
the
other
,
and
retaineth
the
same
coldness
without
the
least
alteration
:
And
it
is
,
in
a
word
,
Water
newly
and
visibly
entred
by
the
Channels
and
Mouth
of
the
[
](A61244-e86010-b)†
†
Lio
is
a
fair
Port
in
the
Venetian
Gulph
,
lying
N.
E.
from
the
City
.
Lio.
Consider
now
,
how
and
from
whence
it
came
thither
.
Are
there
happly
hereabouts
any
Gulphs
or
Whirle-pools
in
the
bottom
of
the
Sea
,
by
which
the
Earth
drinketh
in
and
spueth
out
the
Water
,
breathing
as
it
were
a
great
and
monstruous
Whale
?
But
if
this
be
so
,
how
comes
it
that
the
Water
doth
not
flow
in
the
space
of
six
hours
in
Ancona
,
in
*
Ragusa
,
in
Corfu
,
where
the
Tide
is
very
small
,
and
happly
unobservable
?
Who
will
invent
a
way
to
pour
new
Water
into
an
immoveable
Vessel
,
and
to
make
that
it
rise
onely
in
one
determinate
part
of
it
,
and
in
other
places
not
?
Will
you
say
,
that
this
new
Water
is
borrowed
from
the
Ocean
,
being
brought
in
by
the
Straight
of
Gibraltar
?
This
will
not
remove
the
doubt
aforesaid
,
but
will
beget
a
greater
.
And
first
tell
me
what
ought
to
be
the
current
of
that
Water
,
that
entering
at
the
Straights
mouth
,
is
carried
in
six
hours
to
the
remotest
Creeks
of
the
Mediterrane
,
at
a
distance
of
two
or
three
thousand
Miles
,
and
that
returneth
the
same
space
again
in
a
like
time
at
its
going
back
?
What
would
Ships
do
that
lye
out
at
Sea
?
What
would
become
of
those
that
should
be
in
the
Straights-mough
in
a
continual
precipice
of
a
vast
accumulation
of
Waters
,
that
entering
in
at
a
Channel
but
eight
Miles
broad
,
is
to
give
admittance
to
so
much
Water
as
in
six
hours
over-floweth
a
tract
of
many
hundred
Miles
broad
,
&
thousands
in
length
?
What
Tygre
,
what
Falcon
runneth
or
flyeth
with
so
much
swiftness
?
With
the
swiftness
,
I
say
,
of
above
400
Miles
an
hour
.
The
currents
run
(
nor
can
it
be
denied
)
the
long-wayes
of
the
Gulph
,
but
so
slowly
,
as
that
a
Boat
with
Oars
will
out-go
them
,
though
indeed
not
without
defalking
for
their
wanderings
.
Moreover
,
if
this
Water
come
in
at
the
Straight
,
the
other
doubt
yet
remaineth
,
namely
,
how
it
cometh
to
flow
here
so
high
in
a
place
so
remote
,
without
first
rising
a
like
or
greater
height
in
the
parts
more
adjacent
?
In
a
word
,
I
cannot
think
that
either
obstinacy
,
or
sharpness
of
wit
can
ever
find
an
answer
to
these
Objections
,
nor
consequently
to
maintain
the
stability
of
the
Earth
against
them
,
keeping
within
the
bounds
of
Nature
.
SAGR.
I
have
all
the
while
perfectly
apprehended
you
in
this
;
and
I
stand
greedily
attending
to
hear
in
what
manner
these
wonders
may
occur
without
obstruction
from
the
motion
already
assigned
to
the
Earth
.
SALV
.
These
effects
being
to
ensue
in
consequence
of
the
motions
that
naturally
agree
with
the
Earth
,
it
is
necessary
that
they
not
onely
meet
with
no
impediment
or
obstacle
,
but
that
they
do
follow
easily
,
&
not
onely
that
they
follow
with
facility
,
but
with
necessity
,
so
as
that
it
is
impossible
that
it
should
succeed
otherwise
,
for
such
is
the
property
&
condition
of
things
natural
&
true
.
Having
therefore
shewen
the
impossibility
of
rendring
a
reason
of
the
motions
discerned
in
the
Waters
,
True
and
natural
effects
follow
without
difficulty
.
&
at
the
same
time
to
maintain
the
immobility
of
the
vessel
that
containeth
them
we
may
proceed
to
enquire
,
whether
the
mobility
of
the
Container
may
produce
the
required
effect
,
in
the
manner
that
it
is
observed
to
evene
.
Two
kinds
of
motions
may
be
conferred
upon
a
Vessel
,
whereby
the
Water
therein
contained
,
Two
sorts
of
motions
of
the
containing
Vessel
,
may
make
the
contained
water
to
rise
and
fall
.
may
acquire
a
faculty
of
fluctuating
in
it
,
one
while
towards
one
side
,
and
another
while
towards
another
;
and
there
one
while
to
ebbe
,
and
another
while
to
flow
.
The
first
is
,
when
first
one
,
and
then
another
of
those
sides
is
declined
,
for
then
the
Water
running
towards
the
inclining
side
,
will
alternately
be
higher
and
lower
,
sometimes
on
one
side
,
and
sometimes
on
another
.
But
because
that
this
rising
and
abating
is
no
other
than
a
recession
and
accession
to
the
centre
of
the
Earth
,
such
a
motion
cannot
be
ascribed
to
the
Cavities
of
the
said
Earth
,
that
are
the
Vessels
which
contain
the
Waters
;
the
parts
of
which
Vessel
cannot
by
any
whatsoever
motion
assigned
to
the
Earth
,
The
Cavities
of
the
Earth
cannot
approach
or
go
farther
from
the
centre
of
the
same
.
be
made
to
approach
or
recede
from
the
centre
of
the
same
:
The
other
sort
of
motion
is
,
when
the
Vessel
moveth
(
without
inclining
in
the
least
)
with
a
progressive
motion
,
not
uniform
,
but
that
changeth
velocity
,
by
sometimes
accellerating
,
and
other
times
retarding
:
from
which
disparity
it
would
follow
,
The
progpessive
and
uneven
motion
may
make
the
water
contained
in
a
Vessel
to
run
to
and
fro
.
that
the
VVater
contained
in
the
Vessel
its
true
,
but
not
fixed
fast
to
it
,
as
its
other
solid
parts
,
but
by
reason
of
its
fluidity
,
as
if
it
were
separated
and
at
liberty
,
and
not
obliged
to
follow
all
the
mutations
of
its
Container
,
in
the
retardation
of
the
Vessel
,
it
keeping
part
of
the
impetus
before
conceived
,
would
run
towards
the
the
preceding
part
,
whereupon
it
would
of
necessity
come
to
rise
;
and
on
the
contrary
,
if
new
velocity
should
be
added
to
the
Vessel
,
with
retaining
parts
of
its
tardity
,
staying
somewhat
behind
,
before
it
could
habituate
it self
to
the
new
impetus
,
it
would
hang
back
towards
the
following
part
,
where
it
would
come
to
rise
something
.
The
which
effects
we
may
plainly
declare
and
make
out
to
the
Sense
by
the
example
of
one
of
those
same
Barks
yonder
,
which
continually
come
from
[
](A61244-e86210-b)*
*
A
Town
lying
S.
E.
of
Venice
Lizza-Fusina
,
laden
with
fresh
water
,
for
the
service
of
the
City
.
Let
us
therefore
fancy
one
of
those
Barks
,
to
come
from
thence
with
moderate
velocity
along
the
Lake
,
carrying
the
water
gently
,
of
which
it
is
full
:
and
then
either
by
running
a
ground
,
or
by
some
other
impediment
that
it
shall
meet
with
,
let
it
be
notably
retarded
.
The
water
therein
contained
shall
not
,
by
that
means
,
lose
,
as
the
Bark
doth
,
its
pre-conceived
impetus
,
but
retaining
the
same
,
shall
run
forwards
towards
the
prow
,
where
it
shall
rise
notably
,
falling
as
much
a
stern
.
But
if
,
on
the
contrary
,
the
said
Bark
,
in
the
midst
of
its
smooth
course
,
shall
have
a
new
velocity
,
with
notable
augmentation
added
to
it
,
the
water
contained
before
it
can
habituate
it self
thereto
,
continuing
in
its
tardity
,
shall
stay
behinde
,
namely
a
stern
,
where
of
consequence
it
shall
mount
,
and
abate
for
the
same
at
the
prow
.
This
effect
is
undoubted
and
manifest
,
and
may
hourly
be
experimented
;
in
which
I
desire
that
for
the
present
three
particulars
may
be
noted
.
The
first
is
,
that
to
make
the
water
to
rise
on
one
side
of
the
vessel
,
there
is
no
need
of
new
water
,
nor
that
it
run
thither
,
forsaking
the
other
side
.
The
second
is
,
that
the
water
in
the
middle
doth
not
rise
or
fall
notably
,
unlesse
the
course
of
the
Bark
were
not
before
that
very
swift
,
and
the
shock
or
other
arrest
that
held
it
exceeding
strong
and
sudden
,
in
which
case
its
possible
,
that
not
only
all
the
water
might
run
forwards
,
but
that
the
greater
part
thereof
might
issue
forth
of
the
Bark
:
and
the
same
also
would
ensue
,
whilst
that
being
under
sail
in
a
smooth
course
,
a
most
violent
impetus
should
,
upon
an
instant
,
overtake
it
:
But
when
to
its
calme
motion
there
is
added
a
moderate
retardation
or
incitation
,
the
middle
parts
(
as
I
said
)
unobservedly
rise
and
fall
:
and
the
other
parts
,
according
as
they
are
neerer
to
the
middle
,
rise
the
lesse
;
and
the
more
remote
,
more
.
The
third
is
,
that
whereas
the
parts
about
the
midst
do
make
little
alteration
in
rising
and
falling
,
in
respect
of
the
waters
of
the
sides
;
on
the
contrary
,
they
run
forwards
and
backwards
very
much
,
in
comparison
of
the
extreams
.
Now
,
my
Masters
,
that
which
the
Bark
doth
,
in
respect
of
the
water
by
it
contained
,
and
that
which
the
water
contained
doth
,
in
respect
of
the
Bark
its
container
,
is
the
self-same
,
to
an
hair
,
with
that
which
the
Mediterranean
Vessel
doth
,
in
respect
of
the
waters
in
it
contained
,
and
that
which
the
waters
contained
do
,
in
respect
of
the
Mediterranean
Vessel
their
container
.
The
parts
of
the
terrestrial
Globe
accelerate
and
regard
in
their
motion
.
It
followeth
now
that
we
demonstrate
how
,
and
in
what
manner
it
is
true
,
that
the
Mediterrane
,
and
all
the
other
Straits
;
and
in
a
word
,
all
the
parts
of
the
Earth
do
all
move
,
with
a
motion
notably
uneven
,
though
no
motion
that
is
not
regular
and
uniforme
,
is
thereby
assigned
to
all
the
said
Globe
taken
collectively
.
SIMP.
This
Proposition
,
at
first
sight
to
me
,
that
am
neither
Geometrician
nor
Astronomer
,
hath
the
appearance
of
a
very
great
Paradox
;
and
if
it
should
be
true
,
that
the
motion
of
the
whole
,
being
regular
,
that
of
the
parts
,
which
are
all
united
to
their
whole
,
may
be
irregular
,
the
Paradox
will
overthrow
the
Axiome
that
affirmeth
,
Eandem
esse
rationem
totius
&
partium
.
SALV
.
I
will
demonstrate
my
Paradox
,
and
leave
it
to
your
care
,
Simplicius
,
to
defend
the
Axiome
from
it
,
or
else
to
reconcile
them
;
and
my
demonstration
shall
be
short
and
familiar
,
depending
on
the
things
largely
handled
in
our
precedent
conferences
,
without
introducing
the
least
syllable
,
in
favour
of
the
flux
and
reflux
.
We
have
said
,
Demonstrations
how
the
parts
of
the
terrestriall
Globe
accelerate
and
retard
.
that
the
motions
assigned
to
the
Terrestrial
Globe
are
two
,
the
first
Annual
,
made
by
its
centre
about
the
circumference
of
the
Grand
Orb
,
under
the
Ecliptick
,
according
to
the
order
of
the
Signes
,
that
is
,
from
West
to
East
;
the
other
made
by
the
said
Globe
revolving
about
its
own
centre
in
twenty
four
hours
;
and
this
likewise
from
West
to
East
:
though
about
an
Axis
somewhat
inclined
,
and
not
equidistant
from
that
of
the
Annual
conversion
.
From
the
mixture
of
these
two
motions
,
each
of
it self
uniform
,
I
say
,
that
there
doth
result
an
uneven
and
deformed
motion
in
the
parts
of
the
Earth
.
Which
,
that
it
may
the
more
easily
be
understood
,
I
will
explain
,
by
drawing
a
Scheme
thereof
.
And
first
,
about
the
centre
A
[
in
Fig.
1.
of
this
Dialogue
]
I
will
describe
the
circumference
of
the
Grand
Orb
B
C
,
The
parts
of
a
Circle
regularly
moved
about
its
own
centre
move
in
divers
times
with
contrary
motions
.
in
which
any
point
being
taken
,
as
B
,
about
it
as
a
centre
we
will
describe
this
lesser
circle
D
E
F
G
,
representing
the
Terrestrial
Globe
;
the
which
we
will
suppose
to
run
thorow
the
whole
circumference
of
the
Grand
Orb
,
with
its
centre
B
,
from
the
West
towards
the
East
,
that
is
,
from
the
part
B
towards
C
;
and
moreover
we
will
suppose
the
Terrestrial
Globe
to
turn
about
its
own
centre
B
likewise
from
West
to
East
,
that
is
,
according
to
the
succession
of
the
points
D
E
F
G
,
in
the
space
of
twenty
four
hours
.
But
here
we
ought
carefully
to
note
,
that
a
circle
turning
round
upon
its
own
centre
,
each
part
of
it
must
,
at
different
times
,
move
with
contrary
motions
:
the
which
is
manifest
,
considering
that
whilst
the
parts
of
the
circumference
,
about
the
point
D
move
to
the
left
hand
,
that
is
,
towards
E
,
the
opposite
parts
that
are
about
F
,
approach
to
the
right
hand
,
that
is
,
towards
G
;
so
that
when
the
parts
D
shall
be
in
F
,
their
motion
shall
be
contrary
to
what
it
was
before
.
when
it
was
in
D.
Furthermore
,
the
same
time
that
the
parts
E
descend
,
if
I
may
so
speak
,
towards
F
,
those
in
G
ascend
towards
D.
It
being
therefore
presupposed
,
that
there
are
such
contrarieties
of
motions
in
the
parts
of
the
Terrestrial
Surface
,
The
mixture
of
the
two
motions
annnal
and
diurnal
,
causeth
the
inequality
in
the
motion
of
the
parts
of
the
terrestrial
Globe
.
whilst
it
turneth
round
upon
its
own
centre
,
it
is
necessary
,
that
in
conjoyning
this
Diurnal
Motion
,
with
the
other
Annual
,
there
do
result
an
absolute
motion
for
the
parts
of
the
said
Terrestrial
Superficies
,
one
while
very
accelerate
,
and
another
while
as
slow
again
.
The
which
is
manifest
,
considering
first
the
parts
about
D
,
the
absolute
motion
of
which
shall
be
extream
swift
,
as
that
which
proceedeth
from
two
motions
made
both
one
way
,
namely
,
towards
the
left
hand
;
the
first
of
which
is
part
of
the
Annual
Motion
,
common
to
all
the
parts
of
the
Globe
,
the
other
is
that
of
the
said
point
D.
,
carried
likewise
to
the
left
,
by
the
Diurnal
Revolution
;
so
that
,
in
this
case
,
the
Diurnal
motion
increaseth
and
accelerateth
the
Annual
.
The
contrary
to
which
happeneth
in
the
opposite
part
F
,
which
,
whilst
it
is
by
the
common
annual
motion
carried
,
together
with
the
whole
Globe
,
towards
the
left
,
it
happeneth
to
be
carried
by
the
Diurnal
conversion
also
towards
the
right
:
so
that
the
Diurnal
motion
by
that
means
detracteth
from
the
Annual
,
whereupon
the
absolute
motion
,
resulting
from
the
composition
of
both
the
other
,
is
much
retarded
.
Again
,
about
the
points
E
and
G
,
the
absolute
motion
becometh
in
a
manner
equal
to
the
simple
Annual
one
,
in
regard
that
little
or
nothing
increaseth
or
diminisheth
it
,
as
not
tending
either
to
the
left
hand
,
or
to
the
right
,
but
downwards
and
upwards
.
We
will
conclude
therefore
,
that
like
as
it
is
true
,
that
the
motion
of
the
whole
Globe
,
and
of
each
of
its
parts
,
would
be
equal
and
uniforme
,
in
case
they
did
move
with
one
single
motion
,
whether
it
were
the
meer
Annual
,
or
the
single
Diurnal
Revolution
,
so
it
is
requisite
,
that
mixing
those
two
motions
together
,
there
do
result
thence
for
the
parts
of
the
said
Globe
irregular
motions
,
one
while
accelerated
,
and
another
while
retarded
,
by
means
of
the
additions
or
substractions
of
the
Diurnal
conversion
from
the
annual
circulation
.
So
that
,
if
it
be
true
(
and
most
true
it
is
,
as
experience
proves
)
that
the
acceleration
and
retardation
of
the
motion
of
the
Vessel
,
makes
water
contained
therein
to
run
to
and
again
the
long
wayes
of
it
,
and
to
rise
and
fall
in
its
extreames
,
who
will
make
scruple
of
granting
,
that
the
said
effect
may
,
nay
ought
to
succeed
in
the
Sea-waters
,
contained
within
their
Vessels
,
subject
to
such
like
alterations
,
and
especially
in
those
that
distend
themselves
long-wayes
from
West
to
East
,
which
is
the
course
that
the
motion
of
those
same
Vessels
steereth
?
The
most
potent
and
primary
cause
of
the
ebbing
and
flowing
.
Now
this
is
the
most
potent
and
primary
cause
of
the
ebbing
and
flowing
,
without
the
which
no
such
effect
would
ensue
.
But
because
the
particular
accidents
are
many
and
various
,
that
in
several
places
and
times
are
observed
,
which
must
of
necessity
have
dependance
on
other
different
concomitant
causes
,
although
they
ought
all
to
have
connexion
with
the
primary
;
therefore
it
is
convenient
that
we
propound
and
examine
the
several
accidents
that
may
be
the
causes
of
such
different
effects
.
The
first
of
which
is
,
Sundry
accidents
that
happen
in
the
ebbings
&
flowings
The
first
accident
.
that
when
ever
the
water
,
by
means
of
a
notable
retardation
or
acceleration
of
the
motion
of
the
Vessel
,
its
container
,
shall
have
acquired
a
cause
of
running
towards
this
or
that
extream
,
The
Water
raised
in
one
end
of
the
Vessel
returneth
of
its
self
to
Aequilibrium
.
and
shall
be
raised
in
the
one
,
and
abated
in
the
other
,
it
shall
not
neverthelesse
continue
,
for
any
time
in
that
state
,
when
once
the
primary
cause
is
ceased
:
but
by
vertue
of
its
own
gravity
and
natural
inclination
to
level
and
grow
,
even
it
shall
speedily
return
backwards
of
its
own
accord
,
and
,
as
being
grave
and
fluid
,
shall
not
only
move
towards
Aequilibrium
;
but
being
impelled
by
its
own
impetus
,
shall
go
beyond
it
,
rising
in
the
part
,
where
before
it
was
lowest
;
nor
shall
it
stay
here
,
but
returning
backwards
anew
,
with
more
reiterated
reciprocations
of
its
undulations
,
it
shall
give
us
to
know
,
that
it
will
not
from
a
velocity
of
motion
,
once
conceived
,
reduce
it self
,
in
an
instant
,
to
the
privation
thereof
,
and
to
the
state
of
rest
,
but
will
successively
,
by
decreasing
a
little
and
a
little
,
reduce
it self
unto
the
same
,
just
in
the
same
manner
as
we
see
a
weight
hanging
at
a
cord
,
after
it
hath
been
once
removed
from
its
state
of
rest
,
that
is
,
from
its
perpendicularity
,
of
its
own
accord
,
to
return
thither
and
settle
it self
,
but
not
till
such
time
as
it
shall
have
often
past
to
one
side
,
and
to
the
other
,
with
its
reciprocall
vibrations
.
The
second
accident
to
be
observed
is
,
In
the
shorter
Vessels
the
undulations
of
waters
are
more
frequent
.
that
the
before-declared
reciprocations
of
motion
come
to
be
made
and
repeated
with
greater
or
lesser
frequency
,
that
is
,
under
shorter
or
longer
times
,
according
to
the
different
lengths
of
the
Vessels
containing
the
waters
;
so
that
in
the
shorter
spaces
the
reciprocations
are
more
frequent
,
and
in
the
longer
more
rare
:
just
as
in
the
former
example
of
pendent
bodies
,
the
vibrations
of
those
that
are
hanged
to
longer
cords
are
seen
to
be
lesse
frequent
,
than
those
of
them
that
hang
at
shorter
strings
.
And
here
,
The
greater
profundity
maketh
the
undulations
of
waters
more
frequent
.
for
a
third
observation
,
it
is
to
be
noted
,
that
not
onely
the
greater
or
lesser
length
of
the
Vessel
is
a
cause
that
the
water
maketh
its
reciprocations
under
different
times
;
but
the
greater
or
lesser
profundity
worketh
the
same
effect
.
And
it
happeneth
,
that
of
waters
contained
in
receptacles
of
equall
length
,
but
of
unequal
depth
,
that
which
shall
be
the
deepest
,
maketh
its
undulations
under
shorter
times
,
and
the
reciprocations
of
the
shallower
waters
are
lesse
frequent
.
Fourthly
,
there
are
two
effects
worthy
to
be
noted
,
and
diligently
observed
,
which
the
water
worketh
in
those
its
vibrations
;
the
one
is
its
rising
and
falling
alternately
towards
the
one
and
other
extremity
;
Water
riseth
&
falleth
in
the
extream
parts
of
the
Vessel
,
and
runneth
to
and
fro
in
the
midst
.
the
other
is
its
moving
and
running
,
to
so
speak
,
Horizontally
forwards
and
backwards
.
Which
two
different
motions
differently
reside
in
divers
parts
of
the
Water
:
for
its
extream
parts
are
those
which
most
eminently
rise
and
fall
;
those
in
the
middle
never
absolutely
moving
upwards
,
and
downwards
;
of
the
rest
successively
those
that
are
neerest
to
the
extreams
rise
and
fall
proportionally
more
than
the
remote
:
but
on
the
contrary
,
touching
the
other
progressive
motion
forwards
and
backwards
,
the
middle
parts
move
notably
,
going
and
returning
,
and
the
waters
that
are
in
the
extream
parts
gain
no
ground
at
all
;
save
onely
in
case
that
in
their
rising
they
overflow
their
banks
,
and
break
forth
of
their
first
channel
and
receptacle
;
but
where
there
is
the
obstacle
of
banks
to
keep
them
in
,
they
onely
rise
and
fall
;
which
yet
hindereth
not
the
waters
in
the
middle
from
fluctuating
to
and
again
;
which
likewise
the
other
parts
do
in
proportion
,
undulating
more
or
lesse
,
according
as
they
are
neerer
or
more
remote
from
the
middle
.
The
fifth
particular
accident
ought
the
more
attentively
to
be
considered
,
An
accident
of
the
Earths
motions
impossible
to
be
reduced
to
practice
by
art
.
in
that
it
is
impossible
to
represent
the
effect
thereof
by
an
experiment
or
example
;
and
the
accident
is
this
.
In
the
vessels
by
us
framed
with
art
,
and
moved
,
as
the
above-named
Bark
,
one
while
more
,
and
another
while
lesse
swiftly
,
the
acceleration
and
retardation
is
imparted
in
the
same
manner
to
all
the
vessel
,
and
to
every
part
of
it
;
so
that
whilst
v.
g.
the
Bark
forbeareth
to
move
,
the
parts
precedent
retard
no
more
than
the
subsequent
,
but
all
equally
partake
of
the
same
retardment
;
and
the
self-same
holds
true
of
the
acceleration
,
namely
,
that
conferring
on
the
Bark
a
new
cause
of
greater
velocity
,
the
Prow
and
Poop
both
accelerate
in
one
and
the
same
manner
.
But
in
huge
great
vessels
,
such
as
are
the
very
long
bottomes
of
Seas
,
albeit
they
also
are
no
other
than
certain
cavities
made
in
the
solidity
of
the
Terrestrial
Globe
,
it
alwayes
admirably
happeneth
,
that
their
extreams
do
not
unitedly
equall
,
and
at
the
same
moments
of
time
increase
and
diminish
their
motion
,
but
it
happeneth
that
when
one
of
its
extreames
hath
,
by
vertue
of
the
commixtion
of
the
two
Motions
,
Diurnal
,
and
Annual
,
greatly
retarded
its
velocity
,
the
other
extream
is
animated
with
an
extream
swift
motion
.
Which
for
the
better
understanding
of
it
we
will
explain
,
reassuming
a
Scheme
like
to
the
former
;
in
which
if
we
do
but
suppose
a
tract
of
Sea
to
be
long
,
v.
g.
a
fourth
part
,
as
is
the
arch
B
C
[
in
Fig.
2.
]
because
the
parts
B
are
,
as
hath
been
already
declared
,
very
swift
in
motion
,
by
reason
of
the
union
of
the
two
motions
diurnal
and
annual
,
towards
one
and
the
same
way
,
but
the
part
C
at
the
same
time
is
retarded
in
its
motion
,
as
being
deprived
of
the
progression
dependant
on
the
diurnal
motion
:
If
we
suppose
,
I
say
,
a
tract
of
Sea
as
long
as
the
arch
B
C
,
we
have
already
seen
,
that
its
extreams
shall
move
in
the
same
time
with
great
inequality
.
And
extreamly
different
would
the
velocities
of
a
tract
of
Sea
be
that
is
in
length
a
semicircle
,
and
placed
in
the
position
B
C
D
,
in
regard
that
the
extream
B
would
be
in
a
most
accelerate
motion
,
and
the
other
D
,
in
a
most
slow
one
;
and
the
intermediate
parts
towards
C
,
would
be
in
a
moderate
motion
.
And
according
as
the
said
tracts
of
Sea
shall
be
shorter
,
they
shall
lesse
participate
of
this
extravagant
accident
,
of
being
in
some
hours
of
the
day
with
their
parts
diversly
affected
by
velocity
and
tardity
of
motion
.
So
that
,
if
,
as
in
the
first
case
,
we
see
by
experience
that
the
acceleration
and
retardation
,
though
equally
imparted
to
all
the
parts
of
the
conteining
Vessel
,
is
the
cause
that
the
water
contained
fluctuates
too
and
again
,
what
may
we
think
would
happen
in
a
Vessel
so
admirably
disposed
,
that
retardation
and
acceleration
of
motion
is
very
unequally
contributed
to
its
parts
?
Certainly
we
must
needs
grant
that
greater
and
more
wonderful
causes
of
the
commotions
in
the
Water
ought
to
be
looked
for
.
And
though
it
may
seem
impossible
to
some
,
that
in
artificial
Machines
and
Vessels
we
should
be
able
to
experiment
the
effects
of
such
an
accident
;
yet
neverthelesse
it
is
not
absolutely
impossible
to
be
done
;
and
I
have
by
me
the
model
of
an
Engine
,
in
which
the
effect
of
these
admirable
commixtions
of
motions
may
be
particularly
observed
.
But
as
to
what
concerns
our
present
purpose
,
that
which
you
may
have
hitherto
comprehended
with
your
imagination
may
suffice
.
SAGR.
I
for
my
own
particular
very
well
conceive
that
this
admirable
accident
ought
necessarily
to
evene
in
the
Straights
of
Seas
,
and
especially
in
those
that
distend
themselves
for
a
great
length
from
VVest
to
East
;
namely
according
to
the
course
of
the
motions
of
the
Terrestrial
Globe
;
and
as
it
is
in
a
certain
manner
unthought
of
,
and
without
a
president
among
the
motions
possible
to
be
made
by
us
,
so
it
is
not
hard
for
me
to
believe
,
that
effects
may
be
derived
from
the
same
,
which
are
not
to
be
imitated
by
our
artificial
experiments
.
SALV
.
These
things
being
declared
,
it
is
time
that
we
proceed
to
examine
the
particular
accidents
,
which
,
together
with
their
diversities
,
are
observed
by
experience
in
the
ebbing
and
flowing
of
the
waters
.
Reasons
renewed
of
the
particnlar
accidents
observed
in
the
ebbings
and
flowings
.
And
first
we
need
not
think
it
hard
to
guesse
whence
it
happeneth
,
that
in
Lakes
,
Pooles
,
and
also
in
the
lesser
Seas
there
is
no
notable
flux
and
reflux
;
the
which
hath
two
very
solid
reasons
.
The
one
is
,
that
by
reason
of
the
shortnesse
of
the
Vessel
,
Second
causes
why
in
small
Seas
and
in
Lakes
there
are
no
ebbings
and
flowings
.
in
its
acquiring
in
several
hours
of
the
day
several
degrees
of
velocity
,
they
are
with
very
little
difference
acquired
by
all
its
parts
;
for
as
well
the
precedent
as
the
subsequent
,
that
is
to
say
,
both
the
Eastern
and
VVestern
parts
,
do
accelerate
and
retard
almost
in
the
same
manner
;
and
withal
making
that
alteration
by
little
and
little
,
and
not
by
giving
the
motion
of
the
conteining
Vessel
a
sudden
check
,
and
retardment
,
or
a
sudden
and
great
impulse
or
acceleration
;
both
it
and
all
its
parts
,
come
to
be
gently
and
equally
impressed
with
the
same
degrees
of
velocity
;
from
which
uniformity
it
followeth
,
that
also
the
conteined
water
with
but
small
resistance
and
opposition
,
receiveth
the
same
impressions
,
and
by
consequence
doth
give
but
very
obscure
signes
of
its
rising
or
falling
,
or
of
its
running
towards
one
part
or
another
.
The
which
effect
is
likewise
manifestly
to
be
seen
in
the
little
artificial
Vessels
,
wherein
the
contained
water
doth
receive
the
self
same
impressions
of
velocity
;
when
ever
the
acceleration
and
retardation
is
made
by
gentle
and
uniform
proportion
.
But
in
the
Straights
and
Bays
that
for
a
great
length
distend
themselves
from
East
to
West
,
the
acceleration
and
retardation
is
more
notable
and
more
uneven
,
for
that
one
of
its
extreams
shall
be
much
retarded
in
motion
,
and
the
other
shall
at
the
same
time
move
very
swiftly
:
The
reciprocal
libration
or
levelling
of
the
water
proceeding
from
the
impetus
that
it
had
conceived
from
the
motion
of
its
container
.
The
which
libration
,
as
hath
been
noted
,
hath
its
undulations
very
frequent
in
small
Vessels
;
from
whence
ensues
,
that
though
there
do
reside
in
the
Terrestrial
motions
the
cause
of
conferring
on
the
waters
a
motion
onely
from
twelve
hours
to
twelve
hours
,
for
that
the
motion
of
the
conteining
Vessels
do
extreamly
accelerate
and
extreamly
retard
but
once
every
day
,
and
no
more
;
yet
neverthelesse
this
same
second
cause
depending
on
the
gravity
of
the
water
which
striveth
to
reduce
it self
to
equilibration
,
and
that
according
to
the
shortnesse
of
the
Vessel
hath
its
reciprocations
of
one
,
two
,
three
,
or
more
hours
,
this
intermixing
with
the
first
,
which
also
it self
in
small
Vessels
is
very
little
,
it
becommeth
upon
the
whole
altogether
insensible
.
For
the
primary
cause
,
which
hath
the
periods
of
twelve
hours
,
having
not
made
and
end
of
imprinting
the
precedent
commotion
,
it
is
overtaken
and
opposed
by
the
other
second
,
dependant
on
the
waters
own
weight
,
which
according
to
the
brevity
and
profundity
of
the
Vessel
,
hath
the
time
of
its
undulations
of
one
,
two
,
three
,
four
,
or
more
hours
;
and
this
contending
with
the
other
former
one
,
disturbeth
and
removeth
it
,
not
permitting
it
to
come
to
the
height
,
no
nor
to
the
half
of
its
motion
;
and
by
this
contestation
the
evidence
of
the
ebbing
and
flowing
is
wholly
annihilated
,
or
at
least
very
much
obscured
.
I
passe
by
the
continual
alteration
of
the
air
,
which
disquieting
the
water
,
permits
us
not
to
come
to
a
certainty
,
whether
any
,
though
but
small
,
encrease
or
abatement
of
half
an
inch
,
or
losse
,
do
reside
in
the
Straights
,
or
receptacles
of
water
not
above
a
degree
or
two
in
length
.
I
come
in
the
second
place
to
resolve
the
question
,
The
reason
given
,
why
the
ebbings
and
flowings
,
for
the
most
part
,
are
every
six
hours
.
why
,
there
not
residing
any
vertue
in
the
primary
principle
of
commoving
the
waters
,
save
onely
every
twelve
hours
,
that
is
to
say
,
once
by
the
greatest
velocity
,
and
once
by
the
greatest
tardity
of
motion
;
the
ebbings
and
flowings
should
yet
neverthelesse
appear
to
be
every
six
hours
.
To
which
is
answered
,
that
this
determination
cannot
any
wayes
be
taken
from
the
primary
cause
onely
;
but
there
is
a
necessity
of
introducing
the
secondary
causes
,
as
namely
the
greater
or
lesse
length
of
the
Vessels
,
and
the
greater
or
lesse
depth
of
the
waters
in
them
conteined
.
Which
causes
although
they
have
not
any
operation
in
the
motions
of
the
waters
,
those
operations
belonging
to
the
sole
primary
cause
,
without
which
no
ebbing
or
flowing
would
happen
,
yet
neverthelesse
they
have
a
principal
share
in
determining
the
times
or
periods
of
the
reciprocations
,
and
herein
their
influence
is
so
powerful
,
that
the
primary
cause
must
of
force
give
way
unto
them
.
The
period
of
six
hours
therefore
is
no
more
proper
or
natural
than
those
of
other
intervals
of
times
,
though
indeed
its
the
most
observed
,
as
agreeing
with
our
Mediterrane
,
which
was
the
onely
Sea
that
for
many
Ages
was
navigated
:
though
neither
is
that
period
observed
in
all
its
parts
;
for
that
in
some
more
angust
places
,
such
as
are
the
Hellespont
,
and
the
Aegean
Sea
,
the
periods
are
much
shorter
,
and
also
very
divers
amongst
themselves
;
for
which
diversities
,
and
their
causes
incomprehensible
to
Aristotle
,
some
say
,
that
after
he
had
a
long
time
observed
it
upon
some
cliffes
of
Negropont
,
being
brought
to
desperation
,
he
threw
himself
into
the
adjoyning
Euripus
,
and
voluntarily
drowned
himself
.
In
the
third
place
we
have
the
reason
ready
at
hand
,
The
cause
why
some
Seas
,
though
very
long
,
suffer
no
ebbing
and
flowing
.
whence
it
commeth
to
passe
,
that
some
Seas
,
although
very
long
,
as
is
the
Red
Sea
,
are
almost
altogether
exempt
from
Tides
,
which
happeneth
because
their
length
extendeth
not
from
East
to
West
,
but
rather
transversly
from
the
Southeast
to
the
Northwest
;
but
the
motions
of
the
Earth
going
from
West
to
East
;
the
impulses
of
the
water
,
by
that
means
,
alwayes
happen
to
fall
in
the
Meridians
,
and
do
not
move
from
parallel
to
parallel
;
insomuch
that
in
the
Seas
that
extend
themselves
athwart
towards
the
Poles
,
and
that
the
contrary
way
are
narrow
,
there
is
no
cause
of
ebbing
and
flowing
,
save
onely
by
the
participation
of
another
Sea
,
wherewith
it
hath
communication
,
that
is
subject
to
great
commotions
.
In
the
fourth
place
we
shall
very
easily
find
out
the
reason
why
the
fluxes
and
refluxes
are
greatest
,
Ebbings
and
flowings
why
greatest
in
the
extremities
of
Gulphs
,
and
least
in
the
middle
parts
.
as
to
the
waters
rising
and
falling
in
the
utmost
extremities
of
Gulphs
,
and
least
in
the
intermediate
parts
;
as
daily
experience
sheweth
here
in
Venice
,
lying
in
the
farther
end
of
the
Adriatick
Sea
,
where
that
difference
commonly
amounts
to
five
or
six
feet
;
but
in
the
places
of
the
Mediterrane
,
far
distant
from
the
extreams
,
that
mutation
is
very
small
,
as
in
the
Isles
of
Corsica
and
Sardinnia
,
and
in
the
Strands
of
Rome
and
Ligorne
,
where
it
exceeds
not
half
a
foot
;
we
shall
understand
also
,
why
on
the
contrary
,
where
the
risings
and
fallings
are
small
,
the
courses
and
recourses
are
great
:
I
say
it
is
an
easie
thing
to
understand
the
causes
of
these
accidents
,
seeing
that
we
meet
with
many
manifest
occurrences
of
the
same
nature
in
every
kind
of
Vessel
by
us
artificially
composed
,
in
which
the
same
effects
are
observed
naturally
to
follow
upon
our
moving
it
unevenly
,
that
is
,
one
while
faster
,
and
another
while
flower
.
Moreover
,
Why
in
narrow
places
the
course
of
the
waters
is
more
swift
than
in
larger
.
considering
in
the
fifth
place
,
that
the
same
quantity
of
Water
being
moved
,
though
but
gently
,
in
a
spatious
Channel
,
comming
afterwards
to
go
through
a
narrow
passage
,
will
of
necessity
run
,
with
great
violence
,
we
shall
not
finde
it
hard
to
comprehend
the
cause
of
the
great
Currents
that
are
made
in
the
narrow
Channel
that
separateth
Calabria
from
Sicilia
:
for
that
all
the
Waters
that
,
by
the
spaciousnesse
of
the
Isle
,
and
by
the
Ionick
Gulph
,
happens
to
be
pent
in
the
Eastern
part
of
the
Sea
,
though
it
do
in
that
,
by
reason
of
its
largeness
,
gently
descend
towards
the
West
,
yet
neverthelesse
,
in
that
it
is
pent
up
in
the
Bosphorus
,
it
floweth
with
great
violence
between
Scilla
and
Caribdis
,
and
maketh
a
great
agitation
.
Like
to
which
,
and
much
greater
,
is
said
to
be
betwixt
Africa
and
the
great
Isle
of
St.
Lorenzo
,
where
the
Waters
of
the
two
vast
Seas
,
Indian
and
Ethiopick
,
that
lie
round
it
,
must
needs
be
straightned
into
a
lesse
Channel
between
the
said
Isle
and
the
Ethiopian
Coast.
And
the
Currents
must
needs
be
very
great
in
the
Straights
of
Megallanes
,
which
joyne
together
the
vast
Oceans
of
Ethiopia
,
and
Del
Zur
,
called
also
the
Pacifick
Sea
.
It
follows
now
,
in
the
sixth
place
,
A
discussion
of
〈…〉
●abstruce
〈…〉
obse●ved
〈…〉
ebbing
and
●●●wing
.
that
to
render
a
reason
of
some
more
abstruse
and
incredible
accidents
,
which
are
observed
upon
this
occasion
,
we
make
a
considerable
reflection
upon
the
two
principal
causes
of
ebbings
and
flowings
,
afterwards
compounding
and
mixing
them
together
.
The
first
and
simplest
of
which
is
(
as
hath
often
been
said
)
the
determinate
acceleration
and
retardation
of
the
parts
of
the
Earth
,
from
whence
the
Waters
have
a
determinate
period
put
to
their
decursions
towards
the
East
,
and
return
towards
the
West
,
in
the
time
of
twenty
four
hours
.
The
other
is
that
which
dependeth
on
the
proper
gravity
of
the
Water
,
which
being
once
commoved
by
the
primary
cause
,
seeketh
,
in
the
next
place
,
to
reduce
it self
to
Aequilibrium
,
with
iterated
reciprocations
;
which
are
not
determined
by
one
sole
and
prefixed
time
;
but
have
as
many
varieties
of
times
as
are
the
different
lengths
and
profundities
of
the
receptacles
,
and
Straights
of
Seas
;
and
by
what
dependeth
on
this
second
principle
,
they
would
ebbe
and
flow
,
some
in
one
hour
,
others
in
two
,
in
four
,
in
six
,
in
eight
,
in
ten
,
&c.
Now
if
we
begin
to
put
together
the
first
cause
,
which
hath
its
set
Period
from
twelve
hours
to
twelve
hours
,
with
some
one
of
the
secondary
,
that
hath
its
Period
verb.
grat
.
from
five
hours
to
five
hours
,
it
would
come
to
passe
,
that
at
sometimes
the
primary
cause
and
secondary
would
accord
to
make
impulses
both
one
the
same
way
;
and
in
this
concurrency
,
and
(
as
one
may
call
it
)
unanimous
conspiration
the
flowings
shall
be
great
.
At
other
times
it
happening
that
the
primary
impulse
doth
,
in
a
certain
manner
,
oppose
that
which
the
secondary
Period
would
make
,
and
in
this
contest
one
of
the
Principles
being
taken
away
,
that
which
the
other
would
give
,
will
weaken
the
commotion
of
the
Waters
,
and
the
Sea
will
return
to
a
very
tranquil
State
,
and
almost
immoveable
.
And
at
other
times
,
according
as
the
two
aforesaid
Principles
shall
neither
altogether
contest
,
nor
altogether
concur
,
there
shall
be
other
kinds
of
alterations
made
in
the
increase
and
diminution
of
the
ebbing
and
flowing
.
It
may
likewise
fall
out
that
two
Seas
,
considerably
great
and
which
communicate
by
some
narrow
Channel
,
may
chance
to
have
,
by
reason
of
the
mixtion
of
the
two
Principles
of
motion
,
one
cause
to
flow
at
the
time
that
the
other
hath
cause
to
move
a
contrary
way
;
in
which
case
in
the
Channel
,
whereby
they
disimbogue
themselves
into
each
other
,
there
do
extraordinary
conturbations
insue
,
with
opposite
and
vortick
motions
,
and
most
dangerous
boilings
and
breakings
,
as
frequent
relations
and
experiences
do
assure
us
.
From
such
like
discordant
motions
,
dependent
not
onely
on
the
different
positions
and
longitudes
,
but
very
much
also
upon
the
different
profundities
of
the
Seas
,
which
have
the
said
intercourse
there
do
happen
at
sometimes
different
commotions
in
the
Waters
,
irregular
,
and
that
can
be
reduced
to
no
rules
of
observation
,
the
reasons
of
which
have
much
troubled
,
and
alwayes
do
trouble
Mariners
,
for
that
they
meet
with
them
without
seeing
either
impulse
of
winds
,
or
other
eminent
aereal
alteration
that
might
occasion
the
same
;
of
which
disturbance
of
the
Air
we
ought
to
make
great
account
in
other
accidents
,
and
to
take
it
for
a
third
and
accidental
cause
,
able
to
alter
very
much
the
observation
of
the
effects
depending
on
the
secondary
and
more
essential
causes
.
And
it
is
not
to
be
doubted
,
but
that
impetuous
windes
,
continuing
to
blow
,
for
example
,
from
the
East
,
they
shall
retein
the
Waters
and
prohibit
the
reflux
or
ebbing
;
whereupon
the
second
and
third
reply
of
the
flux
or
tide
overtaking
the
former
,
at
the
hours
prefixed
,
they
will
swell
very
high
;
and
being
thus
born
up
for
some
dayes
,
by
the
strength
of
the
Winds
,
they
shall
rise
more
than
usual
,
making
extraordinary
inundations
.
We
ought
also
,
(
and
this
shall
serve
for
a
seventh
Probleme
)
to
take
notice
of
another
cause
of
motion
dependant
on
the
great
abundance
of
the
Waters
of
great
Rivers
that
discharge
themselves
into
Seas
of
no
great
capacity
,
The
cause
why
,
in
some
narrow
Channels
,
we
see
the
Sea-waters
run
alwayes
one
way
.
whereupon
in
the
Straits
or
Bosphori
that
communicate
with
those
Seas
,
the
Waters
are
seen
to
run
always
one
way
:
as
it
happeneth
in
the
Thracian
Bosphorus
below
Constantinople
,
where
the
water
alwayes
runneth
from
the
Black-Sea
,
towards
the
Propontis
:
For
in
the
said
Black-Sea
by
reason
of
its
shortnesse
,
the
principal
causes
of
ebbing
and
flowing
are
but
of
small
force
.
But
,
on
the
contrary
,
very
great
Rivers
falling
into
the
same
,
those
huge
defluxions
of
water
being
to
passe
and
disgorge
themselves
by
the
the
straight
,
the
[
](A61244-e87150-b)*
*
Or
current
.
course
is
there
very
notable
and
alwayes
towards
the
South
.
Where
moreover
we
ought
to
take
notice
,
that
the
said
Straight
or
Channel
,
albeit
very
narrow
,
is
not
subject
to
perturbations
,
as
the
Straight
of
Scilla
and
Carybdis
;
for
that
that
hath
the
Black-Sea
above
towards
the
North
,
and
the
Propontis
,
the
Aegean
,
and
the
Mediterranean
Seas
joyned
unto
it
,
though
by
a
long
tract
towards
the
South
;
but
now
,
as
we
have
observed
,
the
Seas
,
though
of
never
so
great
length
,
lying
North
and
South
,
are
not
much
subject
to
ebbings
and
flowings
;
but
because
the
Sicilian
Straight
is
situate
between
the
parts
of
the
Mediterrane
distended
for
a
long
tract
or
distance
from
West
to
East
,
that
is
,
according
to
the
course
of
the
fluxes
and
refluxes
;
therefore
in
this
the
agitations
are
very
great
;
and
would
be
much
more
violent
between
Hercules
Pillars
,
in
case
the
Straight
of
Gibraltar
did
open
lesse
;
and
those
of
the
Straight
of
Magellanes
are
reported
to
be
extraordinary
violent
.
This
is
what
,
for
the
present
,
cometh
into
my
mind
to
say
unto
you
about
the
causes
of
this
first
period
diurnal
of
the
Tide
,
and
its
various
accidents
,
touching
which
,
if
you
have
any
thing
to
offer
,
you
may
let
us
hear
it
,
that
so
we
may
afterwards
proceed
to
the
other
two
periods
,
monethly
and
annual
.
SIMP.
In
my
opinion
,
it
cannot
be
denied
,
but
that
your
discourse
carrieth
with
it
much
of
probability
,
arguing
,
as
we
say
,
ex
suppositione
,
namely
,
granting
that
the
Earth
moveth
with
the
two
motions
assigned
it
by
Copernicus
:
The
Hypothesis
of
the
Earths
mobility
taken
in
favour
of
the
Tide
,
opposed
.
but
if
that
motion
be
disproved
,
all
that
you
have
said
is
vain
,
and
insignificant
:
and
for
the
disproval
of
that
Hypothesis
,
it
is
very
manifestly
hinted
by
your
Discourse
it self
.
You
,
with
the
supposition
of
the
two
Terrestrial
motions
,
give
a
reason
of
the
ebbing
and
flowing
;
and
then
again
,
arguing
circularly
,
from
the
ebbing
and
flowing
,
draw
the
reason
and
confirmation
of
those
very
motions
;
and
so
proceeding
to
a
more
specious
Discourse
,
you
say
that
the
Water
,
as
being
a
fluid
body
,
and
not
tenaciously
annexed
to
the
Earth
,
is
not
constrained
punctually
to
obey
every
of
its
motions
,
from
which
you
afterwards
infer
its
ebbing
and
flowing
,
Now
I
,
according
to
your
own
method
,
argue
the
quite
contrary
,
and
say
;
the
Air
is
much
more
tenuous
,
and
fluid
than
the
Water
,
and
lesse
annexed
to
the
Earths
superficies
,
to
which
the
Water
,
if
it
be
for
nothing
else
,
yet
by
reason
of
its
gravity
that
presseth
down
upon
the
same
more
than
the
light
Air
,
adhereth
;
therefore
the
Air
is
much
obliged
to
follow
the
motions
of
the
Earth
:
and
therefore
were
it
so
,
that
the
Earth
did
move
in
that
manner
,
we
the
inhabitants
of
it
,
and
carried
round
with
like
velocity
by
it
,
ought
perpetually
to
feel
a
Winde
from
the
East
that
beateth
upon
us
with
intolerable
force
.
And
that
so
it
ought
to
fall
out
,
quotidian
experience
assureth
us
:
for
if
with
onely
riding
post
,
at
the
speed
of
eight
or
ten
miles
an
hour
in
the
tranquil
Air
,
the
incountering
of
it
with
our
face
seemeth
to
us
a
Winde
that
doth
not
lightly
blow
upon
us
,
what
should
we
expect
from
our
rapid
course
of
800.
or
a
thousand
miles
an
hour
,
against
the
Air
,
that
is
,
free
from
that
motion
?
And
yet
,
notwithstanding
we
cannot
perceive
any
thing
of
that
nature
.
SALV
.
To
this
objection
that
hath
much
of
likelihood
in
it
,
The
answer
to
the
objections
made
against
the
motion
of
the
Terrestrial
Globe
.
I
reply
,
that
its
true
,
the
Air
is
of
greater
tenuity
and
levity
;
and
,
by
reason
of
its
levity
,
lesse
adherent
to
the
Earth
than
Water
so
much
more
grave
and
[
](A61244-e87380-b)*
*
Corpulenta
bulky
;
but
yet
the
consequence
is
false
that
you
infer
from
these
qualities
;
namely
,
that
upon
account
of
that
its
levity
,
tenuity
,
and
lesse
adherence
to
the
Earth
,
it
should
be
more
exempt
than
the
Water
from
following
the
Terrestrial
Motions
;
so
as
that
to
us
,
who
absolutely
pertake
of
of
them
,
the
said
exemption
should
be
sensible
and
manifest
;
nay
,
it
happeneth
quite
contrary
;
for
,
if
you
well
remember
,
the
cause
of
the
ebbing
and
flowing
of
the
Water
assigned
by
us
,
consisteth
in
the
Waters
not
following
the
unevennesse
of
the
motion
of
its
Vessel
,
but
retaining
the
impetus
conceived
before
,
without
diminishing
or
increasing
it
according
to
the
precise
rate
of
its
diminishing
or
increasing
in
its
Vessel
.
Because
therefore
that
in
the
conservation
and
retention
of
the
impetus
before
conceived
,
The
Water
more
apt
to
conserve
an
impetus
conceived
,
then
the
Air.
the
disobedience
to
a
new
augmentation
or
diminution
of
motion
consisteth
,
that
moveable
that
shall
be
most
apt
for
such
a
retention
,
shall
be
also
most
commodious
to
demonstrate
the
effect
that
followeth
in
consequence
of
that
retention
.
Now
how
much
the
Water
is
disposed
to
maintain
such
a
conceived
agitation
;
though
the
causes
cease
that
impress
the
same
,
the
experience
of
the
Seas
extreamly
disturbed
by
impetuous
Winds
sheweth
us
;
the
Billows
of
which
,
though
the
Air
be
grown
calm
,
and
the
Wind
laid
,
for
a
long
time
after
continue
in
motion
:
As
the
Sacred
Poet
pleasantly
sings
,
Qual
l'alto
Egeo
,
&c.
—
And
that
long
continuing
rough
after
a
storm
,
Light
bodies
easier
to
be
moved
than
heavy
,
but
less
apt
to
conserve
the
motion
.
dependeth
on
the
gravity
of
the
water
:
For
,
as
I
have
elsewhere
said
,
light
bodies
are
much
easier
to
be
moved
than
the
more
grave
,
but
yet
are
so
much
the
less
apt
to
conserve
the
motion
imparted
,
when
once
the
moving
cause
ceaseth
.
Whence
it
comes
that
the
Aire
,
as
being
of
it self
very
light
and
thin
,
is
easily
mov'd
by
any
very
small
force
,
yet
it
is
withall
very
unable
to
hold
on
its
motion
,
the
Mover
once
ceasing
.
Therefore
,
as
to
the
Aire
which
environs
the
Terrestrial
Globe
,
I
would
fay
,
that
by
reason
of
its
adherence
,
it
is
no
lesse
carried
about
therewith
then
the
Water
;
and
especially
that
part
which
is
contained
in
its
vessels
;
which
vessels
are
the
valleys
enclosed
with
Mountains
.
It
s
more
rational
that
the
Air
be
commoved
by
the
rugged
surface
of
the
Earth
▪
than
by
the
Celestial
motion
.
And
we
may
with
much
more
reason
affirm
that
this
same
part
of
the
Air
is
carried
round
,
and
born
forwards
by
the
rugged
parts
of
the
Earth
,
than
that
the
higher
is
whirl'd
about
by
the
motion
of
the
Heavens
,
as
ye
Peripateticks
maintain
.
What
hath
been
hitherto
spoken
,
seems
to
me
a
sufficient
answer
to
the
allegation
of
Simplitius
;
The
revolution
of
the
Earth
confirmed
by
a
new
argument
taken
from
the
Air.
yet
nevertheless
with
a
new
instance
and
solution
,
founded
upon
an
admirable
experiment
,
I
will
superabundantly
satisfie
him
,
and
confirm
to
Sagredus
the
mobility
of
the
Earth
.
I
have
told
you
that
the
Air
,
and
in
particular
that
part
of
it
which
ascendeth
not
above
the
tops
of
the
highest
Mountains
,
is
carried
round
by
the
uneven
parts
of
the
Earths
surface
:
from
whence
it
should
seem
,
that
it
must
of
consequence
come
to
passe
,
that
in
case
the
superficies
of
the
Earth
were
not
uneven
,
but
smooth
and
plain
,
no
cause
would
remain
for
drawing
the
Air
along
with
it
,
or
at
least
for
revolving
it
with
so
much
uniformity
.
Now
the
surface
of
this
our
Globe
,
is
not
all
craggy
and
rugged
,
but
there
are
exceeding
great
tracts
very
even
,
to
wit
,
the
surfaces
of
very
vast
Seas
,
which
being
also
far
remote
from
the
continuate
ledges
of
Mountains
which
environ
it
,
seem
to
have
no
faculty
of
carrying
the
super-ambient
Air
along
therewith
:
and
not
carrying
it
about
,
we
may
perceive
what
will
of
consequence
ensue
in
those
places
.
SIMP.
I
was
about
to
propose
the
very
same
difficulty
,
which
I
think
is
of
great
validity
.
SALV
.
You
say
very
well
Simplicius
,
for
from
the
not
finding
in
the
Air
that
which
of
consequence
would
follow
,
did
this
our
Globe
move
round
;
you
argue
its
immoveablenesse
.
But
in
case
that
this
which
you
think
ought
of
necessary
consequence
to
be
found
,
be
indeed
by
experience
proved
to
be
so
;
will
you
accept
it
for
a
sufficient
testimony
and
an
argument
for
the
mobility
of
the
said
Globe
?
SIMP.
In
this
case
it
is
not
requisite
to
argue
with
me
alone
,
for
if
it
should
so
fall
out
,
and
that
I
could
not
comprehend
the
cause
thereof
,
yet
haply
it
might
be
known
by
others
.
SALV
.
So
that
by
playing
with
you
,
a
man
shall
never
get
,
but
be
alwayes
on
the
losing
hand
;
and
therefore
it
would
be
better
to
give
over
:
Nevertheless
,
that
we
may
not
cheat
our
third
man
we
will
play
on
.
We
said
even
now
,
and
with
some
addition
we
reitterate
it
,
that
the
Ayr
as
if
it
were
a
thin
and
fluid
body
,
and
not
solidly
conjoyned
with
the
Earth
,
seem'd
not
to
be
necessitated
to
obey
its
motion
;
unlesse
so
far
as
the
cragginess
of
the
terrestrial
superficies
,
transports
and
carries
with
it
a
part
thereof
contigious
thereunto
;
which
doth
not
by
any
great
space
exceed
the
greatest
altitude
of
Mountains
:
the
which
portion
of
Air
ought
to
be
so
much
less
repugnant
to
the
terrestrial
conversion
,
by
how
much
it
is
repleat
with
vapours
,
The
vaporous
parts
of
the
earth
,
partake
of
its
motions
.
fumes
,
and
exhalations
,
matters
all
participating
of
terrene
qualities
,
and
consequently
apt
of
their
own
nature
to
the
same
motions
.
But
where
there
are
wanting
the
causes
of
motion
,
that
is
,
where
the
surface
of
the
Globe
hath
great
levels
,
and
where
there
is
less
mixture
of
the
terrene
vapours
,
there
the
cause
whereby
the
ambient
Air
is
constrained
to
give
entire
obedience
to
the
terrestrial
conversion
will
cease
in
part
;
so
that
in
such
places
,
whilst
the
Earth
revolveth
towards
the
East
,
there
will
be
continually
a
wind
perceived
which
will
beat
upon
us
,
blowing
from
the
East
towards
the
West
:
and
such
gales
will
be
the
more
sensible
,
where
the
revolution
of
the
Globe
is
most
swift
;
which
will
be
in
places
more
remote
from
the
Poles
,
and
approaching
to
the
greatest
Circle
of
the
diurnal
conversion
.
But
now
de
facto
experience
much
confirmeth
this
Phylosophical
argumentation
;
for
in
the
spatious
Seas
,
and
in
their
parts
most
remote
from
Land
,
and
situate
under
the
Torrid
Zone
,
that
is
bounded
by
the
Tropicks
,
where
there
are
none
of
those
same
terrestrial
evaporations
,
Constant
gales
within
the
Tropicks
blow
towards
the
VVest
.
we
finde
a
perpetual
gale
move
from
the
East
with
so
constant
a
blast
,
that
ships
by
favour
thereof
sail
prosperously
to
the
West-India's
.
And
from
the
same
coasting
along
the
Mexican
shore
,
they
with
the
same
felicity
pass
the
Pacifick
Ocean
towards
the
India's
;
which
to
us
are
East
,
but
to
them
are
West
.
The
course
to
the
VVest
-
India's
easie
,
the
return
difficult
.
Whereas
on
the
contrary
the
Course
from
thence
towards
the
East
is
difficult
and
uncertain
,
and
not
to
be
made
by
the
same
Rhumb
,
but
must
vere
more
to
Land-ward
,
to
recover
other
Winds
,
which
we
may
call
accidentary
and
tumultuary
,
produced
from
other
Principles
,
as
those
that
inhabit
the
continent
find
by
experience
.
Of
which
productions
of
Winds
,
the
Causes
are
many
and
different
,
which
shall
not
at
this
time
be
mentioned
.
Winds
from
Land
make
rough
the
Seas
.
And
these
accidentary
Winds
are
those
which
blow
indifferently
from
all
parts
of
the
Earth
,
and
make
rough
the
Seas
remote
from
the
Equinoctial
,
and
environed
by
the
rugged
Surface
of
the
Earth
;
which
is
as
much
as
to
say
environ'd
with
those
perturbations
of
Air
,
that
confound
that
primary
Gale
.
The
which
,
in
case
these
accidental
impediments
were
removed
,
would
be
continually
felt
,
and
especially
upon
the
Sea
.
Now
see
how
the
effect
of
the
Water
and
Air
seem
wonderfully
to
accord
with
the
Celestial
observations
,
to
confirm
the
mobility
of
our
Terrestrial
Globe
.
SAGR.
I
also
for
a
final
close
will
relate
to
you
one
particular
,
Another
observation
taken
from
the
Air
in
confirmation
of
the
motion
of
the
Earth
.
which
as
I
believe
is
unknown
unto
you
,
and
which
likewise
may
serve
to
confirm
the
same
conclusion
:
You
Salviatus
alledged
,
That
Accident
which
Sailers
meet
with
between
the
Tropicks
;
I
mean
that
perpetual
Gale
of
Winde
that
beats
upon
them
from
the
East
,
of
which
I
have
an
account
from
those
that
have
many
times
made
the
Voyage
:
And
moreover
(
which
is
very
observable
)
I
understand
that
the
Mariners
do
not
call
it
a
Wind
,
but
by
another
[
](A61244-e87820-b)*
*
Which
Wind
with
our
English
Mariners
is
called
the
Trade-wind
.
name
,
which
I
do
not
now
remember
,
taken
haply
from
its
so
fixed
and
constant
Tenor
;
which
when
they
have
met
with
,
they
tie
up
their
shrouds
and
other
cordage
belonging
to
the
Sails
,
and
without
any
more
need
of
touching
them
,
though
they
be
in
a
sleep
,
they
can
continue
their
course
.
Now
this
constant
Trade-wind
was
known
to
be
such
by
its
continual
blowing
without
interruptions
;
for
if
it
were
interrupted
by
other
Windes
,
it
would
not
have
been
acknowledged
for
a
singular
Effect
,
and
different
from
the
rest
:
from
which
I
will
infer
,
That
it
may
be
that
also
our
Mediterranean
Sea
doth
partake
of
the
like
accident
;
but
it
is
not
observed
,
as
being
frequently
altered
by
the
confluence
of
other
windes
.
And
this
I
say
,
not
without
good
grounds
,
yea
upon
very
probable
conjectures
whch
came
unto
my
knowledge
,
from
that
which
tendred
it self
to
my
notice
on
occasion
of
the
voyage
that
I
made
into
Syria
,
going
Consul
for
this
Nation
to
Aleppo
,
The
voiages
in
the
Mediterrane
from
East
to
West
are
made
in
shorter
times
than
from
West
to
East
.
and
this
it
is
:
That
keeping
a
particular
account
and
memorial
of
the
dayes
of
the
departure
and
arrival
of
the
Ships
in
the
Ports
of
Alexandria
,
of
Alexandretta
,
and
this
of
Venice
;
in
comparing
sundry
of
them
,
which
I
did
for
my
curiosity
,
I
found
that
in
exactness
of
account
the
returns
hither
,
that
is
the
voiages
from
East
to
West
along
the
Mediterrane
,
are
made
in
less
time
then
the
contrary
courses
by
25.
in
the
Hundred
:
So
that
we
see
that
one
with
another
,
the
Eastern
windes
are
stronger
then
the
Western
.
SALV
.
I
am
very
glad
I
know
this
particular
,
which
doth
not
a
little
make
for
the
confirmation
of
the
Earths
mobility
.
And
although
it
may
be
alledged
,
That
all
the
Water
of
the
Mediterrane
runs
perpetually
towards
the
Straits-mouth
,
as
being
to
disimbogue
into
the
Ocean
,
the
waters
of
as
many
Rivers
,
as
do
discharge
themselves
into
the
same
;
I
do
not
think
that
that
current
can
be
so
great
,
as
to
be
able
of
it self
alone
to
make
so
notable
a
difference
:
which
is
also
manifest
by
observing
that
the
water
in
the
Pharo
of
Sicily
runneth
back
again
no
less
towards
the
East
,
than
it
runneth
forwards
towards
the
West
.
SAGR.
I
,
that
have
not
as
Simplicius
,
an
inclination
to
satisfie
any
one
besides
my self
,
am
satisfied
with
what
hath
been
said
as
to
this
first
particular
:
Therefore
Salviatus
,
when
you
think
it
sit
to
proceed
forward
,
I
am
prepared
to
hear
you
.
SALV
.
I
shall
do
as
you
command
me
,
but
yet
I
would
fain
hear
the
opinion
also
of
Simplicius
,
from
whose
judgement
I
can
argue
how
much
I
may
promise
to
my self
touching
these
discourses
from
the
Peripatetick
Schools
,
if
ever
they
should
come
to
their
ears
.
SIMP.
I
desire
not
that
my
opinion
should
serve
or
stand
for
a
measure
,
whereby
you
should
judge
of
others
thoughts
;
for
as
I
have
often
said
,
I
am
inconsiderable
in
these
kinde
of
studies
,
and
such
things
may
come
into
the
mindes
of
those
that
are
entered
into
the
deepest
passages
of
Philosophy
,
as
I
could
never
think
of
;
as
having
(
according
to
the
Proverb
)
scarce
kist
her
Maid
:
yet
nevertheless
,
to
give
you
my
sudden
thoughts
,
I
shall
tell
you
,
That
of
those
effects
by
you
recounted
,
and
particularly
the
last
,
there
may
in
my
judgement
very
sufficient
Reasons
be
given
without
the
Earths
mobility
,
by
the
mobility
of
the
Heavens
onely
;
never
introducing
any
novelty
more
,
than
the
inversion
of
that
which
you
your self
propose
unto
us
.
It
hath
been
received
by
the
Peripatetick
Schools
,
It
is
demonstrated
inverting
the
argument
,
that
the
perpetual
motion
of
the
Air
from
East
to
West
cometh
from
the
motion
of
Heaven
▪
that
the
Element
of
Fire
,
and
also
a
great
part
of
the
Aire
is
carried
about
according
to
the
Diurnal
conversion
from
East
to
West
,
by
the
contact
of
the
Concave
of
the
Lunar
Orb
,
as
by
the
Vessel
their
container
.
Now
without
going
out
of
your
track
,
I
will
that
we
determine
the
Quantity
of
the
Aire
which
partaketh
of
that
motion
to
distend
so
low
as
to
the
Tops
of
the
highest
Hills
,
It
is
demonstrated
inverting
the
argument
,
that
the
perpetual
motion
of
the
Air
from
East
to
VVest
,
cometh
from
the
motion
of
Heaven
.
and
that
likewise
they
would
reach
to
the
Earth
,
if
those
Mountains
did
not
impede
them
,
which
agreeth
with
what
you
say
:
For
as
you
affirm
,
the
Air
,
which
is
invironed
by
ledges
of
Mountains
,
to
be
carried
about
by
the
asperity
of
the
moveable
Earth
;
we
on
the
contrary
say
,
That
the
whole
Element
of
Air
is
carried
about
by
the
motion
of
Heaven
,
that
part
only
excepted
which
lyeth
below
those
bodies
,
which
is
hindred
by
the
asperity
of
the
immoveable
Earth
.
And
whereas
you
said
,
That
in
case
that
asperity
should
be
removed
,
the
Air
would
also
cease
to
be
whirld
about
;
we
may
say
,
That
the
said
asperity
being
removed
,
the
whole
Aire
would
continue
its
motion
.
Whereupon
,
because
the
surfaces
of
spacious
Seas
are
smooth
,
and
even
;
the
Airs
motion
shall
continue
upon
those
,
alwaies
blowing
from
the
East
:
And
this
is
more
sensibly
perceived
in
Climates
lying
under
the
Line
,
and
within
the
Tropicks
,
where
the
motion
of
Heaven
is
swifter
;
and
like
as
that
Celestial
motion
is
able
to
bear
before
it
all
the
Air
that
is
at
liberty
,
so
we
may
very
rationally
affirm
that
it
contributeth
the
same
motion
to
the
Water
moveable
,
as
being
fluid
and
not
connected
to
the
immobility
of
the
Earth
:
The
motion
of
the
VVater
dependeth
on
the
motion
of
Heaven
.
And
with
so
much
the
more
confidence
may
we
affirm
the
same
,
in
that
by
your
confession
,
that
motion
ought
to
be
very
small
in
resect
of
the
efficient
Cause
;
which
begirting
in
a
natural
day
the
whole
Terrestrial
Globe
,
passeth
many
hundreds
of
miles
an
hour
,
and
especially
towards
the
Equinoctial
;
whereas
in
the
currents
of
the
open
Sea
,
it
moveth
but
very
few
miles
an
hour
.
And
thus
the
voiages
towards
the
West
shall
come
to
be
commodious
and
expeditious
,
not
onely
by
reason
of
the
perpetual
Eastern
Gale
,
but
of
the
course
also
of
the
Waters
;
from
which
course
also
perhaps
the
Ebbing
and
Flowing
may
come
,
by
reason
of
the
different
scituation
of
the
Terrestrial
Shores
:
The
flux
and
reflux
may
depend
on
the
diurnal
motion
of
Heaven
.
against
which
the
Water
coming
to
beat
,
may
also
return
backwards
with
a
contrary
motion
,
like
as
experience
sheweth
us
in
the
course
of
Rivers
;
for
according
as
the
Water
in
the
unevenness
of
the
Banks
,
meeteth
with
some
parts
that
stand
out
,
or
make
with
their
Meanders
some
Reach
or
Bay
,
here
the
Water
turneth
again
,
and
is
seen
to
retreat
back
a
considerable
space
.
Upon
this
I
hold
,
That
of
those
effects
from
which
you
argue
the
Earths
mobility
,
and
alledge
it
as
a
cause
of
them
,
there
may
be
assigned
a
cause
sufficiently
valid
,
retaining
the
Earth
stedfast
,
and
restoring
the
mobility
of
Heaven
.
SALV
.
It
cannot
be
denied
,
but
that
your
discourse
is
ingenious
,
&
hath
much
of
probability
,
I
mean
probability
in
appearance
,
but
not
in
reality
&
existence
:
It
consisteth
of
two
parts
:
In
the
first
it
assignes
a
reason
of
the
continual
motion
of
the
Eastern
Winde
,
and
also
of
a
like
motion
in
the
Water
.
In
the
second
,
It
would
draw
from
the
same
Sourse
the
cause
of
the
Ebbing
and
Flowing
.
The
first
part
hath
(
as
I
have
said
)
some
appearance
of
probability
,
but
yet
extreamly
less
then
that
which
we
take
from
the
Terrestrial
motion
.
The
second
is
not
onely
wholly
improbable
,
but
altogether
impossible
and
false
.
A
reason
of
the
continual
motion
of
the
Air
and
VVater
may
be
given
,
making
the
Earth
moveable
,
then
by
making
it
immoveable
.
And
coming
to
the
first
,
whereas
it
is
said
that
the
Concave
of
the
Moon
carrieth
about
the
element
of
Fire
,
and
the
whole
Air
,
even
to
the
tops
of
the
higher
Mountains
.
I
answer
first
,
that
it
is
dubious
whether
there
be
any
element
of
Fire
:
But
suppose
there
be
,
it
is
much
doubted
of
the
Orbe
of
the
Moon
,
as
also
of
all
the
rest
;
that
is
,
Whether
there
be
any
such
solid
bodies
and
vast
,
or
elss
,
Whether
beyond
the
Air
there
be
extended
a
continuate
expansion
of
a
substance
of
much
more
tenuity
and
purity
than
our
Air
,
up
and
down
which
the
Planets
go
wandring
,
as
now
at
last
a
good
part
of
those
very
Phylosophers
begin
to
think
:
It
s
improbable
that
the
element
of
Fire
should
be
carried
round
by
the
Concave
of
the
Moon
.
But
be
it
in
this
or
in
that
manner
,
there
is
no
reason
for
which
the
Fire
,
by
a
simple
contract
to
a
superficies
,
which
you
your self
grant
to
be
smooth
and
terse
,
should
be
according
to
its
whole
depth
carried
round
in
a
motion
different
from
its
natural
inclination
;
as
hath
been
defusely
proved
,
and
with
sensible
reasons
demonstrated
by
[
](A61244-e88180-b)†
†
A
Treatise
of
our
Author
formerly
cited
.
Il
Saggiatore
:
Besides
the
other
improbability
of
the
said
motions
transfusing
it self
from
the
subtilest
Fire
throughout
the
Air
,
much
more
dense
;
and
from
that
also
again
to
the
Water
.
But
that
a
body
of
rugged
and
mountainous
surface
,
by
revolving
in
it self
,
should
carry
with
it
the
Air
contiguous
to
it
,
and
against
which
its
promontaries
beat
,
is
not
onely
probable
but
necessary
,
and
experience
thereof
may
be
daily
seen
;
though
without
seeing
it
,
I
believe
that
there
is
no
judgement
that
doubts
thereof
.
As
to
the
other
part
,
supposing
that
the
motion
of
Heaven
did
carry
round
the
Air
,
and
also
the
Water
;
yet
would
that
motion
for
all
that
have
nothing
to
do
with
the
Ebbing
and
Flowing
.
For
being
that
from
one
onely
and
uniform
cause
,
there
can
follow
but
one
sole
and
uniform
effect
;
The
Ebbing
and
Flowing
cannot
depend
on
the
motion
of
Heaven
.
that
which
should
be
discovered
in
the
Water
,
would
be
a
continuate
and
uniform
course
from
East
to
West
;
and
in
that
a
Sea
onely
,
which
running
compass
environeth
the
whole
Globe
.
But
in
determinate
Seas
,
such
as
is
the
Mediterrane
shut
up
in
the
East
,
there
could
be
no
such
motion
.
For
if
its
Water
might
be
driven
by
the
course
of
Heaven
towards
the
West
,
it
would
have
been
dry
many
ages
since
:
Besides
that
our
Water
runneth
not
onely
towards
the
West
,
But
returneth
backwards
towards
the
East
,
and
that
in
ordinal
Periods
:
And
whereas
you
say
by
the
example
of
Rivers
,
that
though
the
course
of
the
Sea
were
Originally
that
onely
from
East
to
West
,
yet
nevertheless
the
different
Position
of
the
Shores
may
make
part
of
the
Water
regurgitate
,
and
return
backwards
:
I
grant
it
you
,
but
it
is
necessary
that
you
take
notice
my
Simplicius
,
that
where
the
Water
upon
that
account
returneth
backwards
,
it
doth
so
there
perpetually
;
and
where
it
runneth
straight
forwards
,
it
runneth
there
alwayes
in
the
same
manner
;
for
so
the
example
of
the
Rivers
shewes
you
.
But
in
the
case
of
the
ebbing
and
flowing
,
you
must
finde
and
give
us
some
reason
why
it
doth
in
the
self
same
place
run
one
while
one
way
,
and
another
while
another
;
Effects
that
being
contrary
&
irregular
,
can
never
be
deduced
from
any
uniform
and
constant
Cause
:
And
this
Argument
,
that
overthrows
the
Hypothesis
of
the
motion
contributed
to
the
Sea
from
the
Heavens
diurnal
motion
,
doth
also
confute
that
Position
of
those
who
would
admit
the
sole
diurnal
motion
of
the
Earth
,
and
believe
that
they
are
able
with
that
alone
to
give
a
reason
of
the
Flux
and
Reflux
:
Of
which
effect
since
it
is
irregular
,
the
cause
must
of
necessity
be
irregular
and
alterable
.
SIMP.
I
have
nothing
to
reply
,
neither
of
my
own
,
by
reason
of
the
weakness
of
my
understanding
;
nor
of
that
of
others
,
for
that
the
Opinion
is
so
new
:
But
I
could
believe
that
if
it
were
spread
amongst
the
Schools
,
there
would
not
want
Phylosophers
able
to
oppose
it
.
SAGR.
Expect
such
an
occasion
;
and
we
in
the
mean
time
if
it
seem
good
to
Salviatus
,
will
proceed
forward
.
SALV
.
All
that
which
hath
been
said
hitherto
,
pertaineth
to
the
diurnal
period
of
the
ebbing
and
flowing
;
of
which
we
have
in
the
first
place
demonstrated
in
general
the
primary
and
universal
Cause
,
without
which
,
no
such
effect
would
follow
:
Afterw●●ds
passing
to
the
particular
Accidents
,
various
,
and
in
a
certain
sort
irregular
,
that
are
observed
therein
:
We
have
handled
the
secondary
and
concommitant
Causes
upon
which
they
depend
.
Now
follow
the
two
other
Periods
,
Monethly
,
and
Annual
,
which
do
not
bring
with
them
new
and
different
Accidents
,
other
than
those
already
considered
in
the
diurnal
Period
;
but
they
operate
on
the
same
Accidents
,
by
rendring
them
greater
and
lesser
in
several
parts
of
the
Lunar
Moneth
,
and
in
several
times
of
the
Solar
Year
;
as
if
that
the
Moon
and
Sun
did
each
conceive
it self
apart
in
operating
and
producing
of
those
Effects
;
a
thing
that
totally
clasheth
with
my
understanding
,
which
seeing
how
that
this
of
Seas
is
a
local
and
sensible
motion
,
made
in
an
immense
mass
of
Water
,
it
cannot
be
brought
to
subscribe
to
Lights
,
to
temperate
Heats
,
to
predominacies
by
occult
Qualities
,
and
to
such
like
vain
Imaginations
,
that
are
so
far
from
being
,
or
being
possible
to
be
Causes
of
the
Tide
;
that
on
the
contrary
,
the
Tide
is
the
cause
of
them
,
that
is
,
of
bringing
them
into
the
brains
more
apt
for
loquacity
and
ostentation
,
than
for
the
speculation
and
discovering
of
the
more
abstruse
secrets
of
Nature
;
which
kind
of
people
,
before
they
can
be
brought
to
pronounce
that
wise
,
ingenious
,
and
modest
sentence
,
I
know
it
not
,
suffer
to
escape
from
their
mouths
and
pens
all
manner
of
extravagancies
.
And
the
onely
observing
,
that
the
same
Moon
,
and
the
same
Sun
operate
not
with
their
light
with
their
motion
,
with
great
heat
,
or
with
temperate
,
on
the
lesser
reeeptacl●s
of
Water
,
but
that
to
effect
their
flowing
by
heat
,
they
must
be
reduced
to
little
lesse
than
boiling
,
and
in
short
,
we
not
being
able
artificially
to
imitate
any
way
the
motions
of
the
Tide
,
save
only
by
the
motion
of
the
Vessel
,
ought
it
not
to
satisfie
every
one
,
that
all
the
other
things
alledged
,
as
causes
of
those
effects
,
are
vaine
fancies
,
and
altogether
estranged
from
the
Truth
.
I
say
,
The
alterations
in
the
effects
argue
alteration
in
the
cause
.
therefore
,
that
if
it
be
true
,
that
of
one
effect
there
is
but
one
sole
primary
cause
,
and
that
between
the
cause
and
effect
,
there
is
a
firm
and
constant
connection
;
it
is
necessary
that
whensoever
there
is
seen
a
firm
and
constant
alteration
in
the
effect
,
there
be
a
firm
and
constant
alteration
in
the
cause
.
And
because
the
alterations
that
happen
in
the
ebbing
and
flowing
in
several
parts
of
the
Year
and
Moneths
,
have
their
periods
firm
and
constant
,
it
is
necessary
to
say
,
that
a
regular
alteration
in
those
same
times
happeneth
in
the
primary
cause
of
the
ebbings
and
flowings
.
The
causes
as
large
assigned
of
the
Periods
Monethly
and
Annual
of
the
ebbings
and
flowings
.
And
as
for
the
alteration
that
in
those
times
happens
in
the
ebbings
and
flowings
consisteth
onely
in
their
greatness
;
that
is
,
in
the
Waters
rising
and
falling
more
or
lesse
,
and
in
running
with
greater
or
lesse
impetus
;
therefore
it
is
necessary
,
that
that
which
is
the
primary
cause
of
the
ebbing
and
flowing
,
doth
in
those
same
determinate
times
increase
and
diminish
its
force
.
But
we
have
already
concluded
upon
the
inequality
and
irregularity
of
the
motion
of
the
Vessels
containing
the
Water
to
be
the
primary
cause
of
the
ebbings
and
flowings
.
Therefore
it
is
necessary
,
that
that
irregularity
,
from
time
to
time
,
correspondently
grow
more
irregular
,
that
is
,
grow
greater
and
lesser
.
Now
it
is
requisite
,
that
we
call
to
minde
,
that
the
irregularity
,
that
is
,
the
different
velocity
of
the
motions
of
the
Vessels
,
to
wit
,
of
the
parts
of
the
Terrestrial
Superficies
,
dependeth
on
their
moving
with
a
compound
motion
,
resulting
from
the
commixtion
of
the
two
motions
,
Annual
and
Diurnal
,
proper
to
the
whole
Terrestrial
Globe
;
of
which
the
Diurnal
conversion
,
by
one
while
adding
to
,
and
another
while
substracting
from
,
the
Annual
motion
,
is
that
which
produceth
the
irregularity
in
the
compound
motion
;
so
that
,
in
the
additions
and
substractions
,
that
the
Diurnal
revolution
maketh
from
the
Annual
motion
,
consisteth
the
original
cause
of
the
irregular
motion
of
the
Vessels
,
The
monethly
and
annual
alterations
of
the
tide
can
depend
upon
nothing
,
save
on
the
alteration
of
the
additions
&
substractions
of
the
diurnal
period
from
the
annual
.
and
consequently
of
the
Ebbing
and
Flowing
:
insomuch
that
if
these
additions
and
substractions
should
alwayes
proceed
in
the
same
proportion
,
in
respect
of
the
Annual
motion
,
the
cause
of
the
Ebbing
and
Flowing
would
indeed
continue
,
but
yet
so
as
that
they
would
perpetually
return
in
the
self
same
manner
:
But
we
are
to
finde
out
the
cause
of
making
the
same
Ebbings
and
Flowings
in
divers
times
greater
and
lesser
:
Therefore
we
must
(
if
we
will
retain
the
identity
of
the
cause
)
find
the
alteration
in
these
additions
and
substractions
,
that
make
them
more
&
less
potent
,
in
producing
those
effects
which
depend
thereupon
.
But
I
see
not
how
that
potency
and
impotence
can
be
introduced
,
unlesse
by
making
the
same
additions
and
substractions
,
one
while
greater
,
and
another
while
lesser
;
so
that
the
acceleration
and
the
retardment
of
the
compound
motion
,
may
be
made
,
sometimes
in
greater
,
and
sometimes
in
lesser
proportion
.
SAGR.
I
feel
my self
very
gently
led
,
as
it
were
,
by
the
hand
,
and
though
I
finde
no
rubs
in
the
way
,
yet
neverthelesse
,
like
a
blind
man
,
I
see
not
whether
your
Clue
leadeth
me
,
nor
can
I
imagine
where
such
a
Journey
will
end
.
SALV
.
Though
there
be
a
great
difference
between
my
slow
pac't
Philosophy
,
and
your
more
nimble
Reason
,
yet
neverthelesse
,
in
this
particular
which
we
are
now
upon
,
I
do
not
much
wonder
,
if
the
apprehensivenesse
of
your
wit
be
a
little
obscured
by
the
dark
and
thick
mist
that
hides
the
mark
,
at
which
we
aime
:
and
that
which
lesseneth
my
admiration
is
,
the
remembrance
of
the
many
hours
,
many
dayes
,
yea
more
,
many
nights
that
I
have
consumed
in
this
contemplation
,
and
of
the
many
times
that
,
despairing
to
bring
it
to
a
period
,
I
have
,
for
an
incouragement
of
my self
,
indeavoured
to
believe
,
by
the
example
of
the
unfortunate
Orlando
,
that
that
might
not
possibly
be
true
,
which
yet
the
testimony
of
so
many
credible
men
set
before
my
eyes
:
wonder
not
,
therefore
,
if
this
once
,
contrary
to
your
custome
,
you
do
not
foresee
what
I
intend
:
and
if
you
will
needs
admire
,
I
believe
that
the
event
,
as
far
as
I
can
judge
unexpected
,
will
make
you
cease
your
wonderment
.
SAGR.
I
thank
God
,
that
he
did
not
permit
that
desperation
of
yours
to
end
in
the
Exit
that
is
fabled
of
the
miserable
Orlando
,
nor
in
that
which
haply
is
no
lesse
fabulously
related
of
Aristotle
,
,
that
so
neither
my self
nor
others
should
be
deprived
of
the
discovery
of
a
thing
,
as
abstruse
as
it
was
desirable
:
I
beseech
you
,
therefore
,
to
satisfie
my
eager
appetite
as
soon
as
you
can
.
SALV
.
I
am
ready
to
serve
you
:
We
were
upon
an
inquiry
in
what
manner
the
additions
and
substractions
of
the
Terrestriall
conversion
from
the
Annual
motion
,
could
be
made
,
one
while
in
a
greater
,
and
another
while
in
a
lesser
proportion
;
which
diversity
,
and
no
other
thing
,
could
be
assigned
for
the
cause
of
the
alterations
,
Monethly
and
Annual
,
that
are
seen
in
the
greatnesse
of
the
Ebbings
and
Flowings
.
I
will
now
consider
how
this
proportion
of
the
additions
and
substractions
of
the
Diurnal
Revolution
,
Three
wayes
of
altering
the
proportion
of
the
additions
of
the
diurnal
Revolution
to
the
annual
motion
.
and
Annual
motion
may
grow
greater
and
lesser
three
several
wayes
.
One
is
by
increasing
and
diminishing
the
velocity
of
the
Annual
motion
,
retaining
the
additions
and
substractions
made
by
the
Diurnal
conversion
in
the
same
greatnesse
,
because
the
Annual
motion
being
about
three
times
greater
,
that
is
,
more
velocious
than
the
Diurnal
motion
(
considered
likewise
in
the
Grand
Circle
)
if
we
increase
it
anew
,
the
additions
and
substractions
of
the
Diurnal
motion
will
occasion
lesse
alteration
therein
:
but
,
on
the
other
side
,
making
it
more
slow
,
it
will
be
altered
in
greater
proportion
,
by
that
same
diurnal
motion
,
just
as
the
adding
or
substracting
four
degrees
of
velocity
from
one
that
moveth
with
twenty
degrees
,
altereth
his
course
lesse
,
than
those
very
four
degrees
would
do
,
added
or
substracted
from
one
that
should
move
onely
with
ten
degrees
.
The
second
way
would
be
,
by
making
the
additions
and
substractions
greater
and
lesser
,
retaining
the
annual
motion
in
the
same
velocity
;
which
is
as
easie
to
be
understood
,
as
it
is
manifest
,
that
a
velocity
v.
gr
.
of
20
degr.
is
more
altered
by
the
addition
or
substraction
of
10.
deg.
than
by
the
addition
or
substraction
of
4.
The
third
way
would
be
,
in
case
these
two
were
joyned
together
,
diminishing
the
annual
motion
,
&
increasing
the
diurnal
additions
and
substractions
.
Hitherto
,
as
you
see
,
it
was
no
hard
matter
to
attain
,
but
yet
it
proved
to
me
very
hard
to
find
by
what
means
this
might
be
effected
in
Nature
.
That
which
to
us
is
hard
to
be
understood
,
is
with
Nature
easie
to
be
effected
.
Yet
in
the
end
,
I
finde
that
she
doth
admirably
make
use
thereof
,
and
in
wayes
almost
incredible
:
I
mean
,
admirable
and
incredible
to
us
,
but
not
to
her
,
who
worketh
even
those
very
things
,
which
,
to
our
capacity
,
are
of
infinite
wonder
,
with
extraordinary
facility
and
simplicity
:
and
that
which
it
is
hard
for
us
to
understand
,
is
easie
for
her
to
effect
.
Now
to
proceed
,
having
shewn
that
the
proportion
between
the
additions
and
substractions
of
the
Diurnal
conversion
and
Annual
motion
may
be
made
greater
and
lesser
,
two
wayes
,
(
and
I
say
two
,
because
the
third
is
comprized
in
the
two
first
)
I
adde
,
that
Nature
maketh
use
of
them
both
:
and
farthermore
,
I
subjoyn
,
that
if
she
did
make
use
but
of
one
alone
,
it
would
be
necessary
to
take
away
one
of
the
two
Periodical
alterations
.
If
the
Diurnal
motion
should
not
alter
,
the
annual
Period
would
cease
That
of
the
Monethly
Period
would
cease
,
if
the
annual
motion
should
not
alter
.
And
in
case
the
additions
and
substractions
of
the
diurnal
revolution
should
continually
be
equal
,
the
alterations
of
the
annual
Period
would
fail
.
SAGR.
It
seems
then
,
that
the
Monethly
alteration
of
ebbings
and
flowings
dependeth
on
the
alteration
of
the
annual
motion
of
the
Earth
?
And
the
annual
alteration
of
those
ebbings
and
flowings
do
,
it
seems
,
depend
on
the
additions
and
substractions
of
the
diurnal
conversion
?
And
here
now
I
finde
my self
worse
puzzled
than
before
,
and
more
out
of
hope
of
being
able
to
comprehend
how
this
intricacy
may
be
,
which
is
more
inextricable
,
in
my
judgment
,
than
the
Gordian
knot
.
And
I
envy
Simplicius
,
from
whose
silence
I
argue
that
he
doth
apprehend
the
whole
businesse
,
and
is
acquit
of
that
confusion
which
greatly
puzzleth
my
brains
.
SIMP.
I
believe
verily
,
Sagredus
,
that
you
are
put
to
a
a
stand
;
and
I
believe
that
I
know
also
the
cause
of
your
confusion
,
which
,
if
I
mistake
not
,
riseth
from
your
understanding
part
of
those
particulars
but
even
now
alledged
by
Salviatus
,
and
but
a
part
.
It
is
true
likewise
that
I
find
my self
free
from
the
like
confusion
;
but
not
for
that
cause
as
you
think
,
to
wit
,
because
I
apprehend
the
whole
,
nay
it
happens
upon
the
quite
contrary
account
;
namely
,
from
my
not
comprehending
any
thing
,
and
confusion
is
in
the
plurality
of
things
,
and
not
in
nothing
.
SAGR.
You
see
Salviatus
,
how
a
few
checks
given
to
Simplicius
in
the
dayes
preceding
,
have
rendered
him
gentle
,
and
brought
him
from
the
capriol
to
the
amble
.
But
I
beseech
you
without
farther
delay
,
put
us
both
out
of
suspence
.
SALV
.
I
will
endeavour
it
to
the
utmost
of
my
harsh
way
of
expressing
my self
,
the
obtusenesse
of
which
,
the
acutenesse
of
your
wit
shall
supply
.
The
accidents
of
which
we
are
to
enquire
the
causes
are
two
:
The
first
respecteth
the
varieties
that
happen
in
the
ebbings
and
flowings
in
the
Monethly
Period
;
and
the
othr
relateth
to
the
Annual
.
We
will
first
speak
of
the
Monethly
,
and
then
treat
of
the
Annual
;
and
it
is
convenient
that
we
resolve
them
all
according
to
the
Fundamentals
and
Hypothesis
already
laid
down
,
without
introducing
any
novelty
either
in
Astronomy
,
or
in
the
Universe
,
in
favour
of
the
ebbings
and
flowings
;
therefore
let
us
demonstrate
that
of
all
the
several
accidents
in
them
observed
,
the
causes
reside
in
the
things
already
known
,
The
true
Hypothesis
may
dispatch
its
revolutions
in
a
shorter
time
,
in
lesser
circles
than
in
greater
;
the
which
is
proved
by
two
examples
.
and
received
for
true
and
undoubted
.
I
say
therefore
,
that
it
is
a
truly
natural
,
yea
necessary
thing
,
that
one
and
the
same
moveable
made
to
move
round
by
the
same
moving
virtue
in
a
longer
time
,
do
make
its
course
by
a
greater
circle
,
rather
than
by
a
lesser
;
and
this
is
a
truth
received
by
all
,
and
confirmed
by
all
experiments
,
The
first
example
.
of
which
we
will
produce
a
few
.
In
the
wheel-clocks
,
and
particularly
in
the
great
ones
,
to
moderate
the
time
,
the
Artificers
that
make
them
accomodate
a
certain
voluble
staffe
horozontally
,
and
at
each
end
of
it
they
fasten
two
Weights
of
Lead
,
and
when
the
time
goeth
too
slow
,
by
the
onely
removing
those
Leads
a
little
nearer
to
the
centre
of
the
staffe
,
they
render
its
vibrations
more
frequent
;
and
on
the
contrary
to
retard
it
,
it
is
but
drawing
those
Weights
more
towards
the
ends
;
for
so
the
vibrations
are
made
more
seldome
,
and
consequently
the
intervals
of
the
hours
are
prolonged
.
Here
the
movent
vertue
is
the
same
,
The
second
example
.
namely
the
counterpoise
,
the
moveables
are
those
same
Weights
of
lead
,
and
their
vibrations
are
more
frequent
when
they
are
neerer
to
the
centre
,
that
is
,
when
they
move
by
lesser
circles
.
Hanging
equal
Weights
at
unequal
cords
,
and
being
removed
from
their
perpendicularity
,
letting
them
go
;
we
shall
see
those
that
are
pendent
at
the
shorter
cords
,
to
make
their
vibrations
under
shorter
times
,
as
those
that
move
by
lesser
circles
.
Again
,
let
such
a
kind
of
Weight
be
fastened
to
a
cord
,
which
cord
let
play
upon
a
staple
fastened
in
the
Seeling
,
and
do
you
hold
the
other
end
of
the
cord
in
your
hand
,
and
having
given
the
motion
to
the
pendent
Weight
,
whilst
it
is
making
its
vibrations
,
pull
the
end
of
the
cord
that
you
hold
in
your
hand
,
so
that
the
Weight
may
rise
higher
and
higher
:
In
its
rising
you
shall
see
the
frequency
of
its
vibrations
encrease
,
in
regard
that
they
are
made
successively
by
lesser
and
lesser
circies
.
Two
particular
notable
accidents
in
the
penduli
and
their
vibrations
.
And
here
I
desire
you
to
take
notice
of
two
particulars
worthy
to
be
observed
.
One
is
that
the
vibrations
of
one
of
those
plummets
are
made
with
such
a
necessity
under
such
determinate
times
,
that
it
is
altogether
impossible
to
cause
them
to
be
made
under
other
times
,
unlesse
it
be
by
prolonging
,
or
abreviating
the
cord
;
of
which
you
may
also
at
this
very
instant
ascertain
your selves
by
experience
,
tying
a
stone
to
a
pack-threed
,
and
holding
the
other
end
in
your
hand
,
trying
whether
you
can
ever
by
any
artifice
be
able
to
swing
it
this
way
and
that
way
in
other
than
one
determinate
time
,
unlesse
by
lengthening
of
shortening
the
string
,
which
you
will
find
to
be
absolutely
impossible
.
The
other
particular
truly
admirable
is
,
that
the
self
same
pendulum
makes
its
vibrations
with
one
and
the
same
frequency
,
or
very
little
,
and
as
it
were
insensibly
different
,
whether
they
be
made
by
very
great
,
or
very
small
arches
of
the
self-same
circumference
.
I
mean
that
whether
we
remove
the
pendulum
from
perpendicularity
one
,
two
,
or
three
degrees
onely
,
or
whether
we
remove
it
70.
80.
nay
to
an
entire
quadrant
,
it
being
let
go
,
will
in
the
one
case
and
in
the
other
make
its
vibrations
with
the
same
frequency
,
as
well
the
former
where
it
is
to
move
by
an
arch
of
but
four
or
six
degrees
,
as
the
second
,
where
it
is
to
passe
arches
of
160.
or
more
degrees
.
Which
may
the
better
be
seen
,
by
hanging
two
weights
at
two
strings
of
equal
length
,
and
then
removing
them
from
perpendicularity
,
one
a
little
way
,
and
the
other
very
far
;
the
which
being
set
at
liberty
,
will
go
&
return
under
the
same
times
,
the
one
by
arches
very
small
,
&
the
other
by
very
great
ones
,
from
whence
followeth
the
conclusion
of
an
admirable
Problem
;
Admirable
Problems
of
moveables
descending
by
the
Quadrant
of
a
Circle
,
and
of
those
descending
by
all
the
cords
of
the
whole
Circle
.
which
is
,
That
a
Quadrant
of
a
Circle
being
given
(
take
a
little
diagram
of
the
same
,
[
in
Fig.
3.
]
)
as
for
instance
:
AB
erect
to
the
Horizon
,
so
as
that
it
rest
upon
the
plain
touching
in
the
point
B.
and
an
Arch
being
made
with
a
Hoop
well
plained
and
smoothed
in
the
concave
part
,
bending
it
according
to
the
curvity
of
the
Circumference
ADB
.
So
that
a
Bullet
very
round
and
smooth
may
freely
run
to
and
again
within
it
(
the
rim
of
a
Sieve
is
very
proper
for
the
experiment
)
I
say
,
that
the
Bullet
being
put
in
any
what
ever
place
,
neer
or
far
from
the
lowest
term
B.
As
for
instance
,
putting
it
in
the
point
C
,
or
here
in
D
,
or
in
E
;
and
then
let
go
,
it
will
in
equal
times
,
or
insensibly
different
arrive
at
the
term
B
,
departing
from
C
,
or
from
D
,
or
from
E
,
or
from
whatever
other
place
;
an
accident
truly
wonderfull
.
We
may
add
another
accident
no
less
strange
than
this
,
which
is
,
That
moreover
by
all
the
cords
drawn
from
the
point
B
to
the
points
C
,
D
,
E
;
and
to
any
other
whatsoever
,
taken
not
onely
in
the
Quadrant
BA
,
but
in
all
the
whole
circumference
of
the
Circle
the
said
moveable
shall
descend
in
times
absolutely
equal
;
insomuch
that
it
shall
be
no
longer
in
descending
by
the
whole
Diameter
erect
perpendicularly
upon
the
point
B
,
then
it
shall
in
descending
by
B.
C.
although
it
do
sublend
but
one
sole
degree
,
or
a
lesser
Arch.
Let
us
add
the
other
wonder
,
which
is
,
That
the
motions
of
the
falling
bodies
made
by
the
Arches
of
the
Quadrant
AB
;
are
made
in
shorter
times
than
those
that
are
made
by
the
cords
of
those
same
Arches
;
so
that
the
swiftest
motion
,
and
made
by
a
moveable
in
the
shortest
time
,
to
arrive
from
the
point
A
,
to
the
term
B
,
shall
be
that
which
is
made
,
not
by
the
right
line
A
,
B
,
(
although
it
be
the
shortest
of
all
those
that
can
de
drawn
between
the
points
A.
B.
)
but
by
the
circumference
ADB
.
And
any
point
being
taken
in
the
said
Arch
;
as
for
example
:
The
point
D.
and
two
cords
drawn
AD
,
and
D.
B.
the
moveable
departing
from
the
qoint
A
,
shall
in
a
less
time
come
to
B
,
moving
by
the
two
cords
AD
and
DB.
than
by
the
sole
cord
A
,
B.
But
the
shortest
of
all
the
times
shall
be
that
of
the
fall
by
the
Arch
ADB
.
And
the
self
same
accidents
are
to
be
understood
of
all
the
other
lesser
Arches
taken
from
the
lowermost
term
B.
upwards
.
SAGR.
No
more
,
no
more
;
for
you
so
confund
and
fill
me
with
Wonders
,
and
distract
my
thoughts
so
many
several
wayes
,
that
I
fear
I
shall
have
but
a
small
part
of
it
left
free
and
disingaged
,
to
apply
to
the
principal
matter
that
is
treated
of
,
and
which
of
it self
is
but
even
too
obscure
and
intricate
:
So
that
I
intreat
you
to
vouchsafe
me
,
having
once
dispatcht
the
business
of
the
ebbings
and
flowings
,
to
do
this
honour
to
my
house
(
and
yours
)
some
other
dayes
,
and
to
discourse
upon
the
so
many
other
Problems
that
we
have
left
in
suspence
;
and
which
perhaps
are
no
less
curious
and
admirable
,
than
this
that
hath
been
discussed
these
dayes
past
,
and
that
now
ought
to
draw
to
a
conclusion
.
SALV
.
I
shall
be
ready
to
serve
you
,
but
we
must
make
more
than
one
or
two
Sessions
;
if
besides
the
other
questions
reserved
to
be
handled
apart
,
we
would
discusse
those
many
that
pertain
to
the
local
motion
,
as
well
of
natural
moveables
,
as
of
the
rejected
:
an
Argument
largely
treated
of
by
our
Lyncean
Accademick
.
But
turning
to
our
first
purpose
,
where
we
were
about
to
declare
,
That
the
bodies
moving
circularly
by
a
movent
virtue
,
which
continually
remaineth
the
same
,
the
times
of
the
circulation
were
prefixt
and
determined
,
and
impossible
to
be
made
longer
or
shorter
,
having
given
examples
,
and
produced
experiments
thereof
,
sensible
,
and
feasible
,
we
may
confirm
the
same
truth
by
the
experiences
of
the
Celestial
motions
of
the
Planets
;
in
which
we
see
the
same
rule
observed
;
for
those
that
move
by
greater
Circles
,
confirm
longer
times
in
passing
them
.
A
most
pertinent
observation
of
this
we
have
from
the
Medicaean
Planets
,
which
in
short
times
make
their
revolutions
about
Jupiter
:
Insomuch
that
it
is
not
to
be
questioned
,
nay
we
may
hold
it
for
sure
and
certain
,
that
if
for
example
,
the
Moon
continuing
to
be
moved
by
the
same
movent
faculty
,
should
retire
by
little
and
little
in
lesser
Circles
,
it
would
acquire
a
power
of
abreviating
the
times
of
its
Periods
,
according
to
that
Pendulum
,
of
which
in
the
course
of
its
vibrations
,
we
by
degrees
shortned
the
cord
,
that
is
contracted
the
Semidiameter
of
the
circumferences
by
it
passed
.
Know
now
that
this
that
I
have
alledged
an
example
of
it
in
the
Moon
,
is
seen
and
verified
essentially
in
fact
.
Let
us
call
to
mind
,
that
it
hath
been
already
concluded
by
us
,
together
with
Copernicus
,
The
Earths
annual
motion
by
the
Ecliptick
,
unequal
by
means
of
the
Moons
motion
,
That
it
is
not
possible
to
separate
the
Moon
from
the
Earth
,
about
which
it
without
dispute
revolveth
in
a
Moneth
:
Let
us
remember
also
that
the
Terrestrial
Globe
,
accompanyed
alwayes
by
the
Moon
,
goeth
along
the
circumference
of
the
Grand
Orb
about
the
Sun
in
a
year
,
in
which
time
the
Moon
revolveth
about
the
Earth
almost
thirteen
times
;
from
which
revolution
it
followeth
,
that
the
said
Moon
sometimes
is
found
near
the
Sun
;
that
is
,
when
it
is
between
the
Sun
and
the
Earth
,
and
sometimes
much
more
remote
,
that
is
,
when
the
Earth
is
situate
between
the
Moon
and
Sun
;
neer
,
in
a
word
,
at
the
time
of
its
conjunction
and
change
;
remote
,
in
its
Full
and
Opposition
;
and
the
greatest
vicinity
differ
the
quantity
of
the
Diameter
of
the
Lunar
Orb.
Now
if
it
be
true
that
the
virtue
which
moveth
the
Earth
and
Moon
,
about
the
Sun
,
be
alwayes
maintained
in
the
same
vigour
;
and
if
it
be
true
that
the
same
moveable
moved
by
the
same
virtue
,
but
in
circles
unequal
,
do
in
shorter
times
passe
like
arches
of
lesser
circles
,
it
must
needs
be
granted
,
that
the
Moon
when
it
is
at
a
lesse
distance
from
the
Sun
,
that
is
in
the
time
of
conjunction
,
passeth
greater
arches
of
the
Grand
Orb
,
than
when
it
is
at
a
greater
distance
,
that
is
in
its
Opppsition
and
Full.
And
this
Lunar
inequality
must
of
necessity
be
imparted
to
the
Earth
also
;
for
if
we
shall
suppose
a
right
line
produced
from
the
centre
of
the
Sun
by
the
centre
of
the
Terrestrial
Globe
,
and
prolonged
as
far
as
the
Orb
of
the
Moon
,
this
shall
be
the
semidiameter
of
the
Grand
Orb
,
in
which
the
Earth
,
in
case
it
were
alone
,
would
move
uniformly
,
but
if
in
the
same
semidiameter
we
should
place
another
body
to
be
carried
about
,
placing
it
one
while
between
the
Earth
and
Sun
,
and
another
while
beyond
the
Earth
,
at
a
greater
distance
from
the
Sun
,
it
is
necessary
,
that
in
this
second
case
the
motion
common
to
both
,
according
to
the
circumference
of
the
great
Orb
by
means
of
the
distance
of
the
Moon
,
do
prove
a
little
slower
than
in
the
other
case
,
when
the
Moon
is
between
the
Earth
and
Sun
,
that
is
at
a
lesser
distance
.
So
that
in
this
businesse
the
very
same
happeneth
that
befals
in
the
time
of
the
clock
;
that
lead
which
is
placed
one
while
farther
from
the
centre
,
to
make
the
vibrations
of
the
staffe
or
ballance
lesse
frequent
,
and
another
while
nearer
,
to
make
them
thicker
,
representing
the
Moon
.
Hence
it
may
be
manifest
,
that
the
annual
motion
of
the
Earth
in
the
Grand
Orb
,
and
under
the
Ecliptick
,
is
not
uniform
,
and
that
its
irregularity
proceedeth
from
the
Moon
,
and
hath
its
Monethly
Periods
and
Returns
.
And
because
it
hath
been
concluded
,
that
the
Monethly
and
Annual
Periodick
alterations
of
the
ebbings
and
flowings
,
cannot
be
deduced
from
any
other
cause
than
from
the
altered
proportion
between
the
annual
motion
and
the
additions
and
substractions
of
the
diurnal
conversion
;
and
that
those
alterations
might
be
made
two
wayes
,
that
is
by
altering
the
annual
motion
,
keeping
the
quantity
of
the
additions
unaltered
,
or
by
changing
of
the
bignesse
of
these
,
reteining
the
uniformity
of
annual
motion
.
We
have
already
found
the
first
of
these
,
depending
on
the
irregularity
of
the
annual
motion
occasioned
by
the
Moon
,
and
which
hath
its
Monethly
Periods
.
It
is
therefore
necessary
,
that
upon
that
account
the
ebbings
and
flowings
have
a
Monethly
Period
in
which
they
do
grow
greater
and
lesser
.
Now
you
see
that
the
cause
of
the
Monethly
Period
resideth
in
the
annual
motion
;
and
withal
you
see
how
much
the
Moon
is
concerned
in
this
business
,
and
how
it
is
therewith
interrupted
apart
,
without
having
any
thing
to
do
with
either
,
with
Seas
or
Waters
.
SAGR.
If
one
that
never
had
seen
any
kinde
of
Stairs
or
Lader
,
were
shewed
a
very
high
Tower
,
and
asked
if
ever
he
hoped
to
climb
to
the
top
of
it
,
I
verily
believe
that
he
would
answer
he
did
not
,
not
conceiving
how
one
should
come
thither
any
way
except
by
flying
;
but
shewing
him
a
stone
of
but
a
foot
high
,
and
asking
him
whether
he
thought
he
could
get
to
the
top
of
that
,
I
am
certain
that
he
would
answer
he
could
;
and
farther
,
that
he
would
not
deny
,
but
that
it
was
not
onely
one
,
but
ten
,
twenty
,
and
an
hundred
times
easier
to
climb
that
:
But
now
if
he
should
be
shewed
the
Stairs
,
by
means
whereof
,
with
the
facility
by
him
granted
,
it
is
possible
to
get
thither
,
whither
he
a
little
before
had
affirmed
it
was
impossible
to
ascend
,
I
do
think
that
laughing
at
himself
he
would
confess
his
dulness
of
apprehension
.
Thus
,
Salviatus
,
have
you
step
by
step
so
gently
lead
me
,
that
,
not
without
wonder
,
I
finde
that
I
am
got
with
small
pains
to
that
height
which
I
despaired
of
arriving
at
.
'T
is
true
;
that
the
Stair-case
having
been
dark
,
I
did
not
perceive
that
I
was
got
nearer
to
,
or
arrived
at
the
top
,
till
that
coming
into
the
open
Air
I
discovered
a
great
Sea
,
and
spacious
Country
:
And
as
in
ascending
one
step
,
there
is
no
labour
;
so
each
of
your
propositions
by
it self
seemed
to
me
so
plain
,
that
thinking
I
heard
but
little
or
nothing
that
was
new
unto
me
,
I
conceived
that
my
benefit
thereby
had
been
little
or
none
at
all
:
Whereupon
I
was
the
more
amazed
at
the
unexpected
exit
of
this
discourse
,
that
hath
guided
me
to
the
knowledge
of
a
thing
which
I
held
impossible
to
be
demonstrated
.
One
doubt
onely
remains
,
from
which
I
desire
to
be
freed
,
and
this
it
is
;
Whether
that
if
the
motion
of
the
Earth
together
with
that
of
the
Moon
under
the
Zodiack
are
irregular
motions
,
those
irregularities
ought
to
have
been
observed
and
taken
notice
of
by
Astronomers
,
which
I
do
not
know
that
they
are
:
Therefore
I
pray
you
,
who
are
better
acquainted
with
these
things
than
I
,
to
free
me
from
this
doubt
,
and
tell
me
how
the
●ase
stands
.
SALV
.
You
ask
a
rational
question
,
and
answering
to
the
Objection
,
Many
things
may
remain
as
yet
unobserved
in
Astronomy
.
I
say
;
That
although
Astronomy
in
the
courses
of
many
ages
hath
made
a
great
progress
in
discovering
the
constitution
and
motions
of
the
Celestial
bodies
,
yet
is
it
not
hitherto
arrived
at
that
height
,
but
that
very
many
things
remain
undecided
,
and
haply
many
others
also
undiscovered
.
It
is
to
be
supposed
that
the
first
observers
of
Heaven
knew
no
more
but
one
motion
common
to
all
the
Stars
,
as
is
this
diurnal
one
:
yet
I
believe
that
in
few
dayes
they
perceived
that
the
Moon
was
inconstant
in
keeping
company
with
the
other
Stars
;
but
yet
withal
,
that
many
years
past
,
before
that
they
distinguished
all
the
Planets
:
And
in
particular
,
Saturn
for
its
slowness
,
and
Mercury
for
its
rareness
of
appearing
were
amongst
those
that
were
last
observed
.
I
conceit
that
Saturn
by
its
slowness
,
and
Mercury
by
reason
of
its
seldom
appearing
,
were
the
last
that
were
observed
to
be
wandring
and
errant
.
It
is
to
be
thought
that
many
more
years
run
out
before
the
statio●s
and
retrogradations
of
the
three
superiour
Planets
were
known
,
as
also
their
approximations
and
recessions
from
the
Earth
,
necessary
occasions
of
introducing
the
Eccentrix
and
Epicicles
,
things
unknown
even
to
Aristotle
,
for
that
he
makes
no
mention
thereof
.
Mercury
,
and
Venus
,
with
their
admirable
apparitions
;
how
long
did
they
keep
Astronomers
in
suspence
,
before
that
they
could
resolve
(
not
to
speak
of
any
other
of
their
qualities
)
upon
their
situation
?
Insomuch
that
the
very
order
onely
of
the
Mundane
bodies
,
and
the
integral
structure
of
the
parts
of
the
Universe
by
us
known
,
hath
been
doubted
of
untill
the
time
of
Copernicus
,
who
hath
at
last
given
us
notice
of
the
true
constitution
,
and
real
systeme
,
according
to
which
those
parts
are
disposed
;
so
that
at
length
we
are
certain
that
Mercury
,
Venus
,
and
the
other
Planets
do
revolve
about
the
Sun
;
and
that
the
Moon
revolveth
about
the
Earth
.
But
how
each
Planet
governeth
it self
in
its
particular
revolution
,
Particular
structures
of
the
Orbs
of
the
Planets
not
yet
well
resolved
.
and
how
precisely
the
structure
of
its
Orb
is
framed
;
which
is
that
which
is
vulgarly
called
the
Theory
of
the
Planets
,
we
cannot
as
yet
undoubtedly
resolve
.
Mars
,
that
hath
so
much
puzled
our
Modern
Astronomers
,
is
a
proof
of
this
:
And
to
the
Moon
her self
there
have
been
assigned
several
Theories
,
after
that
the
said
Copernicus
had
much
altered
it
from
that
of
Ptolomy
.
And
to
descend
to
our
particular
case
,
that
is
to
say
,
to
the
apparent
motion
of
the
Sun
and
Moon
;
touching
the
former
,
there
hath
been
observed
a
certain
great
irregularity
,
whereby
it
passeth
the
two
semicircles
of
the
Ecliptick
,
The
Sun
passeth
one
half
of
the
Zodiack
nine
days
sooner
than
the
other
.
divided
by
the
points
of
the
Equinoxes
in
very
different
times
;
in
passing
one
of
which
,
it
spendeth
about
nine
dayes
more
than
in
passing
the
other
;
a
difference
,
as
you
see
,
very
great
and
notable
.
But
if
in
passing
small
arches
,
such
for
example
as
are
the
twelve
Signs
,
he
maintain
a
most
regular
motion
,
or
else
proceed
with
paces
,
one
while
a
little
more
swift
,
and
another
more
slow
,
as
it
is
necessary
that
it
do
,
in
case
the
annual
motion
belong
to
the
Sun
onely
in
appearance
,
but
in
reality
to
the
Earth
in
company
with
the
Moon
,
it
is
what
hath
not
hitherto
been
observed
,
The
Moons
motion
principally
sought
in
the
account
of
Eclipses
.
nor
it
may
be
,
sought
.
Touching
the
Moon
in
the
next
place
,
whose
restitutions
have
been
principally
lookt
into
an
account
of
the
Eclipses
,
for
which
it
is
sufficient
to
have
an
exact
knowledge
of
its
motion
about
the
Earth
,
it
hath
not
been
likewise
with
a
perfect
curiosity
inquired
,
what
it●
course
is
thorow
the
particular
arches
of
the
Zodiack
.
That
therefore
the
Earth
and
Moon
in
running
through
the
Zodiack
,
that
is
round
the
Grand
Orb
,
do
somewhat
accellerate
at
the
Moons
change
,
and
retard
at
its
full
,
ought
not
to
be
doubted
;
for
that
the
said
difference
is
not
manifest
,
which
cometh
to
be
unobserved
upon
two
accounts
;
First
,
Because
it
hath
not
been
lookt
for
.
Secondly
,
Because
that
its
possible
it
may
not
be
very
great
.
Nor
is
there
any
need
that
it
should
be
great
,
for
the
producing
the
effect
that
we
see
in
the
alteration
of
the
greatness
of
ebbings
and
flowings
.
Ebbings
and
flowings
are
petty
things
in
comparison
of
the
vastness
of
Seas
and
of
the
velocity
of
the
motion
of
the
Terrestrial
Globe
.
For
not
onely
those
alterations
,
but
the
Tides
themselves
are
but
small
matters
in
respect
of
the
grandure
of
the
subjects
on
which
they
work
;
albeit
that
to
us
,
and
to
our
littleness
they
seem
great
.
For
the
addition
or
subduction
of
one
degree
of
velocity
where
there
are
naturally
700
,
or
1000
,
can
be
called
no
great
alteration
,
either
in
that
which
conferreth
it
,
or
in
that
Which
receiveth
it
:
the
Water
of
our
Mediterrane
carried
about
by
the
diurnal
revolution
,
maketh
about
700
miles
an
hour
,
(
which
is
the
motion
common
to
the
Earth
and
to
it
,
and
therefore
not
perceptible
to
us
)
&
that
which
we
sensibly
discern
to
be
made
in
the
streams
or
currents
,
is
not
at
the
rate
of
full
one
mile
an
hour
,
(
I
speak
of
the
main
Seas
,
and
not
of
the
Straights
)
and
this
is
that
which
altereth
the
first
,
naturall
,
and
grand
motion
;
and
this
motion
is
very
great
in
respect
of
us
,
and
of
Ships
:
for
a
Vessel
that
in
a
standing
Water
by
the
help
of
Oares
can
make
v.
g.
three
miles
an
hour
,
in
that
same
current
will
row
twice
as
far
with
the
stream
as
against
it
:
A
notable
difference
in
the
motion
of
the
Boat
,
though
but
very
small
in
the
motion
of
the
Sea
,
which
is
altered
but
its
seven
hundredth
part
.
The
like
I
say
of
its
rising
,
and
falling
one
,
two
,
or
three
feet
;
and
scarcely
four
or
five
in
the
utmost
bounds
of
a
streight
,
two
thousand
,
or
more
miles
long
,
and
where
there
are
depths
of
hundreds
of
feet
;
this
alteration
is
much
less
than
if
in
one
of
the
Boats
that
bring
us
fresh
Water
,
the
said
Water
upon
the
arrest
of
the
Boat
should
rise
at
the
Prow
the
thickness
of
a
leaf
.
I
conclude
therefore
that
very
small
alterations
in
respect
of
the
immense
greatness
,
and
extraordinary
velocity
of
the
Seas
,
is
sufficient
to
make
therein
great
mutations
in
relation
to
our
smallness
,
and
to
our
accidents
.
SAGR.
I
am
fully
satisfied
as
to
this
particular
;
it
remains
to
declare
unto
us
how
those
additions
and
substractions
derived
from
the
diurnal
Vertigo
are
made
one
while
greater
,
and
another
while
lesser
;
from
which
alterations
you
hinted
that
the
annual
period
of
the
augmentations
and
diminutions
of
the
ebbings
and
flowings
did
depend
.
SALV
.
I
will
use
my
utmost
endeavours
to
render
my self
intelligible
,
The
causes
of
the
inequality
of
the
additions
and
substractions
of
the
diurnal
conversion
from
the
annual
motion
.
but
the
difficulty
of
the
accident
it self
,
and
the
great
attention
of
mind
requisite
for
the
comprehending
of
it
,
constrains
me
to
be
obscure
.
The
unequalities
of
the
additions
and
substractions
,
that
the
diurnal
motion
maketh
to
or
from
the
annual
dependeth
upon
the
inclination
of
the
Axis
of
the
diurnal
motion
upon
the
plane
of
the
Grand
Orb
,
or
,
if
you
please
,
of
the
Ecliptick
;
by
means
of
which
inclination
the
Equinoctial
intersecteth
the
said
Ecliptick
,
remaining
inclined
and
oblique
upon
the
same
according
to
the
said
inclination
of
Axis
.
And
the
quantity
of
the
additions
importeth
as
much
as
the
whole
diameter
of
the
said
Equinoctial
,
the
Earths
centre
being
at
the
same
time
in
the
Solstitial
points
;
but
being
out
of
them
it
importeth
lesse
and
lesse
,
according
as
the
said
centre
successively
approacheth
to
the
points
of
the
Equinoxes
,
where
those
additions
are
lesser
than
in
any
other
places
.
This
is
the
whole
businesse
,
but
wrapt
up
in
the
obscurity
that
you
see
.
SAGR.
Rather
in
that
which
I
do
no
not
see
;
for
hitherto
I
comprehend
nothing
at
all
.
SALV
.
I
have
already
foretold
it
.
Neverthelesse
we
will
try
whether
by
drawing
a
Diagram
thereof
,
we
can
give
some
small
light
to
the
same
;
though
indeed
it
might
better
be
set
forth
by
solid
bodies
than
by
bare
Schemes
;
yet
we
will
help
our selves
with
Perspective
and
fore-shortning
.
Let
us
draw
therefore
,
as
before
,
the
circumference
of
the
Grand
Orb
,
[
as
in
Fig.
4.
]
in
which
the
point
A
is
understood
to
be
one
of
the
Solstitials
,
and
the
diameter
AP
the
common
Section
of
the
Solstitial
Colure
,
and
of
the
plane
of
the
Grand
Orb
or
Ecliptick
;
and
in
that
same
point
A
let
us
suppose
the
centre
of
the
Terrestrial
Globe
to
be
placed
,
the
Axis
of
which
CAB
,
inclined
upon
the
Plane
of
the
Grand
Orb
,
falleth
on
the
plane
of
the
said
Colure
that
passeth
thorow
both
the
Axis
of
the
Equinoctial
,
and
of
the
Ecliptick
.
And
for
to
prevent
confusion
,
let
us
only
draw
the
Equinoctial
circle
,
marking
it
with
these
characters
DGEF
,
the
common
section
of
which
,
with
the
plane
of
the
grand
Orb
,
let
be
the
line
DE
,
so
that
half
of
the
said
Equinoctial
DFE
will
remain
inclined
below
the
plane
of
the
Grand
Orb
,
and
the
other
half
DGE
elevated
above
.
Let
now
the
Revolution
of
the
said
Equinoctial
be
made
,
according
to
the
order
of
the
points
DGEF
,
and
the
motion
of
the
centre
from
A
towards
E.
And
because
the
centre
of
the
Earth
being
in
A
,
the
Axis
CB
(
which
is
erect
upon
the
diameter
of
the
Equinoctial
DE
)
falleth
,
as
hath
been
said
,
in
the
Solstitial
Colure
,
the
common
Section
of
which
and
of
the
Grand
Orb
,
is
the
diameter
PA
,
the
said
line
PA
shall
be
perpendicular
to
the
same
DE
,
by
reason
that
the
Colure
is
erect
upon
the
grand
Orb
;
and
therefore
the
said
DE
,
shall
be
the
Tangent
of
the
grand
Orb
in
the
point
A.
So
that
in
this
Position
the
motion
of
the
Centre
by
the
arch
AE
;
that
is
,
of
one
degree
every
day
differeth
very
little
;
yea
,
is
as
if
it
were
made
by
the
Tangent
DAE
.
And
because
by
means
of
the
diurnal
motion
the
point
D
,
carried
about
by
G
,
unto
E
,
encreaseth
the
motion
of
the
Centre
moved
almost
in
the
same
line
DE
,
as
much
as
the
whole
diameter
DE
amounts
unto
;
and
on
the
other
side
diminisheth
as
much
,
moving
about
the
other
semicircle
EFD
.
The
additions
and
subductions
in
this
place
therefore
,
that
is
in
the
time
of
the
solstice
,
shall
be
measured
by
the
whole
diameter
DE.
Let
us
in
the
next
place
enquire
,
Whether
they
be
of
the
same
bigness
in
the
times
of
the
Equinoxes
;
and
transporting
the
Centre
of
the
Earth
to
the
point
I
,
distant
a
Quadrant
of
a
Circle
from
the
point
A.
Let
us
suppose
the
said
Equinoctial
to
be
GEFD
,
its
common
section
with
the
grand
Orb
DE
,
the
Axis
with
the
same
inclination
CB
;
but
the
Tangent
of
the
grand
Orb
in
the
point
I
shall
be
no
longer
DE
,
but
another
which
shall
cut
that
at
right
Angles
;
and
let
it
be
this
marked
HIL
,
according
to
which
the
motion
of
the
Centre
I
,
shall
make
its
progress
,
proceeding
along
the
circumference
of
this
grand
Orb.
Now
in
this
state
the
Additions
and
Substractions
are
no
longer
measured
by
the
diameter
DE
,
as
before
was
done
;
because
that
diameter
not
distending
it self
according
to
the
line
of
the
annual
motion
HL
,
rather
cutting
it
at
right
angles
,
those
terms
DE
,
do
neither
add
nor
substract
any
thing
;
but
the
Additions
and
Substractons
are
to
be
taken
from
that
diameter
that
falleth
in
the
plane
that
is
errect
upon
the
plane
of
the
grand
Orb
,
and
that
intersects
it
according
to
the
line
HL
;
which
diameter
in
this
case
shall
be
this
GF
and
the
Adjective
,
if
I
may
so
say
,
shall
be
that
made
by
the
point
G
,
about
the
semicircle
GEF
,
and
the
Ablative
shall
be
the
rest
made
by
the
other
semicircle
FDG
.
Now
this
diameter
,
as
not
being
in
the
same
line
HL
of
the
annual
motion
,
but
rather
cutting
it
,
as
we
see
in
the
point
I
,
the
term
G
being
elevated
above
,
and
E
depressed
below
the
plane
of
the
grand
Orb
,
doth
not
determine
the
Additions
and
Substractions
according
to
its
whole
length
,
but
the
quantity
of
those
first
ought
to
be
taken
from
the
part
of
the
line
HL
,
that
is
intercepted
between
the
perpendiculars
drawn
upon
it
from
the
terms
GF
;
namely
,
these
two
GS
,
and
FV
:
So
that
the
measure
of
the
additions
is
the
line
SV
lesser
then
GF
,
or
then
DE
;
which
was
the
measure
of
the
additions
in
the
Solstice
A.
And
so
successively
,
according
as
the
centre
of
the
Earth
shall
be
constituted
in
other
points
of
the
Quadrant
AI
,
drawing
the
Tangents
in
the
said
points
,
and
the
perpendiculars
upon
the
same
falling
from
the
terms
of
the
diameters
of
the
Equinoctial
drawn
from
the
errect
planes
by
the
said
Tangents
to
the
plane
of
the
grand
Orb
;
the
parts
of
the
said
Tangents
(
which
shall
continually
be
lesser
towards
the
Equinoctials
,
and
greater
towards
the
Solstices
)
shall
give
us
the
quantities
of
the
additions
and
substractions
.
How
much
in
the
next
place
the
least
additions
differ
from
the
greatest
,
is
easie
to
be
known
,
because
there
is
the
same
difference
betwixt
them
,
as
between
the
whole
Axis
or
Diameter
of
the
Sphere
,
and
the
part
thereof
that
lyeth
between
the
Polar-Circles
;
the
which
is
less
than
the
whole
diameter
by
very
near
a
twelfth
part
,
supposing
yet
that
we
speak
of
the
additions
and
substractions
made
in
the
Equinoctial
;
but
in
the
other
Parallels
they
are
lesser
,
according
as
their
diameters
do
diminish
.
This
is
all
that
I
have
to
say
upon
this
Argument
,
and
all
perhaps
that
can
fall
under
the
comprehension
of
our
knowledge
,
which
,
as
you
well
know
,
may
not
entertain
any
conclusions
,
save
onely
those
that
are
firm
and
constant
,
such
as
are
the
three
kinds
of
Periods
of
the
ebbings
and
flowings
;
for
that
they
depend
on
causes
that
are
invariabl●
,
simple
,
and
eternal
.
But
because
that
secondary
and
particular
causes
,
able
to
make
many
alterations
,
intermix
with
these
that
are
the
primary
and
universal
;
and
these
secondary
causes
being
part
of
them
inconstant
,
and
not
to
be
observed
;
as
for
example
,
The
alteration
of
Winds
,
and
part
(
though
terminate
and
fixed
)
unobserved
for
their
multiplicity
,
as
are
the
lengths
of
the
Straights
,
their
various
inclinations
towards
this
or
that
part
,
the
so
many
and
so
different
depths
of
the
Waters
,
who
shall
be
able
,
unless
after
very
long
observations
,
and
very
certain
relations
,
to
frame
so
expeditious
Histories
thereof
,
as
that
they
may
serve
for
Hypotheses
,
and
certain
suppositions
to
such
as
will
by
their
combinations
give
adequate
reasons
of
all
the
appearances
,
and
as
I
may
say
,
Anomalie
,
and
particular
irregularities
that
may
be
discovered
in
the
motions
of
the
Waters
?
I
will
content
my self
with
advertising
you
,
that
the
accidental
causes
are
in
nature
,
and
are
able
to
produce
many
alterations
;
for
the
more
minute
observations
,
I
remit
them
to
be
made
by
those
that
frequent
several
Seas
:
and
onely
by
way
of
a
conclusion
to
this
our
conference
,
I
will
propose
to
be
considered
,
how
that
the
precise
times
of
the
fluxes
and
refluxes
do
not
onely
happen
to
be
altered
by
the
length
of
Straights
,
and
by
the
difference
of
depths
;
but
I
believe
that
a
notable
alteration
may
also
proceed
from
the
comparing
together
of
sundry
tarcts
of
Sea
,
different
in
greatness
;
and
in
position
,
or
,
if
you
will
,
inclination
;
which
difference
happeneth
exactly
here
in
the
Adriatick
Gulph
,
lesse
by
far
than
the
rest
of
the
Mediterrane
,
and
placed
in
so
different
an
inclination
,
that
whereas
that
hath
its
bounds
that
incloseth
it
on
the
Eastern
part
,
as
are
the
Coasts
of
Syria
,
this
is
shut
up
in
its
more
Westerly
part
:
and
because
the
ebbings
and
flowings
are
much
greater
towards
the
extremities
,
yea
,
because
the
Seas
risings
and
fallings
are
there
onely
greatest
,
it
may
probably
happen
that
the
times
of
Flood
at
Venice
may
be
the
time
of
low
Water
in
the
other
Sea
,
which
,
as
being
much
greater
,
and
distended
more
directly
from
West
to
East
,
cometh
in
a
certain
sort
to
have
dominion
over
the
Adriatick
:
and
therefore
it
would
be
no
wonder
,
in
case
the
effects
depending
on
the
primary
causes
,
should
not
hold
true
in
the
times
that
they
ought
,
and
that
correspond
to
the
periods
in
the
Adriatick
,
as
it
doth
in
the
rest
of
the
Mediterrane
.
But
these
Particularities
require
long
Observations
,
which
I
neither
have
made
as
yet
,
nor
shall
I
ever
be
able
to
make
the
same
for
the
future
.
SAGR.
You
have
,
in
my
opinion
,
done
enough
in
opening
us
the
way
to
so
lofty
a
speculation
,
of
which
,
if
you
had
given
us
no
more
than
that
first
general
Proposition
that
seemeth
to
me
to
admit
of
no
reply
,
where
you
declare
very
rationally
,
that
the
Vessels
containing
the
Sea-waters
continuing
stedfast
,
it
would
be
impossible
,
according
to
the
common
course
of
Nature
,
that
those
motions
should
follow
in
them
which
we
see
do
follow
;
and
that
,
on
the
other
side
,
granting
the
motions
ascribed
,
for
other
respects
,
by
Copernicus
to
the
Terrestrial
Globe
,
these
same
alterations
ought
to
ensue
in
the
Seas
,
if
I
say
you
had
told
us
no
more
,
this
alone
in
my
judgment
,
so
far
exceeds
the
vanities
introduced
by
so
many
others
,
that
my
meer
looking
on
them
makes
me
nauseate
them
,
and
I
very
much
admire
,
that
among
men
of
sublime
wit
,
of
which
nevertheless
there
are
not
a
few
,
not
one
hath
ever
considered
the
incompatibility
that
is
between
the
reciprocal
motion
of
the
Water
contained
,
and
the
immobility
of
the
Vessel
containing
,
which
contradiction
seemeth
to
me
now
so
manifest
.
SALV
.
It
is
more
to
be
admired
,
One
single
motion
of
the
terrestrial
Globe
sufficeth
not
to
produce
the
Ebbing
&
Flowing
that
it
having
come
into
the
thoughts
of
some
to
refer
the
cause
of
the
Tide
to
the
motion
of
the
Earth
,
therein
shewing
a
more
than
common
apprehension
,
they
should
,
in
afterwards
driving
home
the
motion
close
with
no
side
;
and
all
,
because
they
did
not
see
that
one
simple
and
uniform
motion
,
as
v.
gr
.
the
sole
diurnal
motion
of
the
Terrestrial
Globe
,
doth
not
suffice
,
but
that
there
is
required
an
uneven
motion
,
one
while
accelerated
,
and
another
while
retarded
:
for
when
the
motion
of
the
Vessels
are
uniforme
,
the
waters
contained
will
habituate
themselves
thereto
,
without
ever
making
any
alteration
.
To
say
also
(
as
it
is
related
of
an
ancient
Mathematician
)
that
the
motion
of
the
Earth
meeting
with
the
motion
of
the
Lunar
Orb
,
The
opinion
of
Seleucus
the
Mathematician
censured
.
the
concurrence
of
them
occasioneth
the
Ebbing
and
Flowing
,
is
an
absolute
vanity
,
not
onely
because
it
is
not
exprest
,
nor
seen
how
it
should
so
happen
,
but
the
falsity
is
obvious
,
for
that
the
Revolution
of
the
Earth
is
not
contrary
to
the
motion
of
the
Moon
,
but
is
towards
the
same
way
.
So
that
all
that
hath
been
hitherto
said
,
and
imagined
by
others
,
is
,
in
my
judgment
,
altogether
invalid
.
But
amongst
all
the
famous
men
that
have
philosophated
upon
this
admirable
effect
of
Nature
,
Kepler
is
with
respect
blamed
.
I
more
wonder
at
Kepler
than
any
of
the
rest
,
who
being
of
a
free
and
piercing
wit
,
and
having
the
motion
ascribed
to
the
Earth
,
before
him
,
hath
for
all
that
given
his
ear
and
assent
to
the
Moons
predominancy
over
the
Water
,
and
to
occult
properties
,
and
such
like
trifles
.
SAGR.
I
am
of
opinion
,
that
to
these
more
spaculative
persons
the
same
happened
,
that
at
present
befalls
me
,
namely
,
the
not
understanding
the
intricate
commixtion
of
the
three
Periods
Annual
,
Monethly
,
and
Diurnal
;
And
how
their
causes
should
seem
to
depend
on
the
Sun
,
and
on
the
Moon
,
without
the
Suns
or
Moons
having
any
thing
to
do
with
the
Water
;
a
businesse
,
for
the
full
understanding
of
which
I
stand
in
need
of
a
little
longer
time
to
consider
thereof
,
which
the
novelty
and
difficulty
of
it
hath
hitherto
hindred
me
from
doing
:
but
I
despair
not
,
but
that
when
I
return
in
my
solitude
and
silence
to
ruminate
that
which
remaineth
in
my
fancy
,
not
very
well
digested
,
I
shall
make
it
my
own
.
We
have
now
,
from
these
four
dayes
Discourse
,
great
attestations
,
in
favour
of
the
Copernican
Systeme
,
amongst
which
these
three
taken
:
the
first
,
from
the
Stations
and
Retrogradations
of
the
Planets
,
and
from
their
approaches
,
and
recessions
from
the
Earth
;
the
second
,
from
the
Suns
revolving
in
it self
,
and
from
what
is
observed
in
its
spots
;
the
third
,
from
the
Ebbing
and
Flowing
of
the
Sea
do
shew
very
rational
and
concluding
.
SALV
.
To
which
also
haply
,
in
short
,
one
might
adde
a
fourth
,
and
peradventure
a
fifth
;
a
fourth
,
I
say
,
taken
from
the
fixed
stars
,
seeing
that
in
them
,
upon
exact
observations
,
those
minute
mutations
appear
,
that
Copernicus
thought
to
have
been
insensible
.
There
starts
up
,
at
this
instant
,
a
fifth
novelty
,
from
which
one
may
argue
mobility
in
the
Terrestrial
Globe
,
by
means
of
that
which
the
most
Illustrious
Signore
Caesare
,
Sig.
Caesare
Marsilius
observeth
the
Meridian
to
be
moveable
.
of
the
noble
Family
of
the
Marsilii
of
Bologna
,
and
a
Lyncean
Academick
,
discovereth
with
much
ingenuity
,
who
in
a
very
learned
Tract
of
his
,
sheweth
very
particularly
how
that
he
had
observed
a
continual
mutation
,
though
very
slow
in
the
Meridian
line
,
of
which
Treatise
,
at
length
,
with
amazement
,
perused
by
me
,
I
hope
he
will
communicate
Copies
to
all
those
that
are
Students
of
Natures
Wonders
.
SAGR.
This
is
not
the
first
time
that
I
have
heard
speak
of
the
exquisite
Learning
of
this
Gentleman
,
and
of
his
shewing
himself
a
zealous
Patron
of
all
the
Learned
,
and
if
this
,
or
any
other
of
his
Works
shall
come
to
appear
in
publique
,
we
may
be
aforehand
assured
,
that
they
will
be
received
,
as
things
of
great
value
.
SALV
.
Now
because
it
is
time
to
put
an
end
to
our
Discourses
,
it
remaineth
,
that
I
intreat
you
,
that
if
,
at
more
leasure
going
over
the
things
again
that
have
been
alledged
you
meet
with
any
doubts
,
or
scruples
not
well
resolved
,
you
will
excuse
my
oversight
,
as
well
for
the
novelty
of
the
Notion
,
as
for
the
weaknesse
of
my
wit
,
as
also
for
the
grandure
of
the
Subject
,
as
also
finally
,
because
I
do
not
,
nor
have
pretended
to
that
assent
from
others
,
which
I
my self
do
not
give
to
this
conceit
,
which
I
could
very
easily
grant
to
be
a
Chymaera
,
and
a
meer
paradox
;
and
you
Sagredus
,
although
in
the
Discourses
past
you
have
many
times
,
with
great
applause
,
declared
,
that
you
were
pleased
with
some
of
my
conjectures
,
yet
do
I
believe
,
that
that
was
in
part
more
occasioned
by
the
novelty
than
by
the
certainty
of
them
,
but
much
more
by
your
courtesie
,
which
did
think
and
desire
,
by
its
assent
,
to
procure
me
that
content
which
we
naturally
use
to
take
in
the
approbation
and
applause
of
our
own
matters
:
and
as
your
civility
hath
obliged
me
to
you
;
so
am
I
also
pleased
with
the
ingenuity
of
Simplicius
.
Nay
,
his
constancy
in
maintaining
the
Doctrine
of
his
Master
,
with
so
much
strength
&
undauntedness
,
hath
made
me
much
to
love
him
.
And
as
I
am
to
give
you
thanks
,
Sagredus
,
for
your
courteous
affection
;
so
of
Simplicius
,
I
ask
pardon
,
if
I
have
sometimes
moved
him
with
my
too
bold
and
resolute
speaking
:
and
let
him
be
assured
that
I
have
not
done
the
same
out
of
any
inducement
of
sinister
affection
,
but
onely
to
give
him
occasion
to
set
before
us
more
lofty
fancies
that
might
make
me
the
more
knowing
.
SIMP.
There
is
no
reason
why
you
should
make
all
these
excuses
,
that
are
needlesse
,
and
especially
to
me
,
that
being
accustomed
to
be
at
Conferences
and
publique
Disputes
,
have
an
hundred
times
seen
the
Disputants
not
onely
to
grow
hot
and
angry
at
one
another
,
but
likewise
to
break
forth
into
injurious
words
,
and
sometimes
to
come
very
neer
to
blows
.
As
for
the
past
Discourses
,
and
particulatly
in
this
last
,
of
the
reason
of
the
Ebbing
and
Flowing
of
the
Sea
,
I
do
not
,
to
speak
the
truth
,
very
well
apprehend
the
same
,
but
by
that
slight
Idea
,
what
ever
it
be
,
that
I
have
formed
thereof
to
my self
,
I
confesse
that
your
conceit
seemeth
to
me
far
more
ingenuous
than
any
of
all
those
that
I
ever
heard
besides
,
but
yet
neverthelesse
I
esteem
it
not
true
and
concluding
:
but
keeping
alwayes
before
the
eyes
of
my
mind
a
solid
Doctrine
that
I
have
learn't
from
a
most
learned
and
ingenuous
person
,
and
with
which
it
is
necessary
to
sit
down
;
I
know
that
both
you
being
asked
,
Whether
God
,
by
his
infinite
Power
and
Wisdome
might
confer
upon
the
Element
of
Water
the
reciprocal
motion
which
we
observe
in
the
same
in
any
other
way
,
than
by
making
the
containing
Vessel
to
move
;
I
know
,
I
say
,
that
you
will
answer
,
that
he
might
,
and
knew
how
to
have
done
the
same
many
wayes
,
and
those
unimaginable
to
our
shallow
understanding
:
upon
which
I
forthwith
conclude
,
that
this
being
granted
,
it
would
be
an
extravagant
boldnesse
for
any
one
to
goe
about
to
limit
and
confine
the
Divine
Power
and
Wisdome
to
some
one
particular
conjecture
of
his
own
.
SALV
.
This
of
yours
is
admirable
,
and
truly
Angelical
Doctrine
,
to
which
very
exactly
that
other
accords
,
in
like
manner
divine
,
which
whilst
it
giveth
us
leave
to
dispute
,
touching
the
constitution
of
the
World
,
addeth
withall
(
perhaps
to
the
end
,
that
the
exercise
of
the
minds
of
men
might
neither
be
discouraged
,
nor
made
bold
)
that
we
cannot
find
out
the
works
made
by
his
hands
.
Let
therefore
the
Disquisition
permitted
and
ordain'd
us
by
God
,
assist
us
in
the
knowing
,
and
so
much
more
admiring
his
greatnesse
,
by
how
much
lesse
we
finde
our selves
too
dull
to
penetrate
the
profound
Abysses
of
his
infinite
Wisdome
.
SAGR.
And
this
may
serve
for
a
final
close
of
our
four
dayes
Disputations
,
after
which
,
if
it
seem
good
to
Salviatus
,
to
take
some
time
to
rest
himself
,
our
curiosity
must
,
of
necessity
,
grant
him
the
same
,
yet
upon
condition
,
that
when
it
is
lesse
incommodious
for
him
,
he
will
return
and
satisfie
my
desire
in
particular
concerning
the
Problemes
that
remain
to
be
discust
,
and
that
I
have
set
down
to
be
propounded
at
one
or
two
other
Conferences
,
according
to
our
agreement
:
and
above
all
,
I
shall
very
impatiently
wait
to
hear
the
Elements
of
the
new
Science
of
our
Academick
about
the
natural
and
violent
local
Motions
.
And
in
the
mean
time
,
we
may
,
according
to
our
custome
,
spend
an
hour
in
taking
the
Air
in
the
Gondola
that
waiteth
for
us
.
FINIS
.
Place
this
Plate
at
the
end
of
the
fourth
Dialogue