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Robert
Hues
Jo.
Isa.
PONTANUS
John
Chilmead
J.
B.
Andrew
Kemb
Leontius
Mechanicus
Eratosthenes
,
Hipparchus
,
Polybius
Pytheas
,
Euthemeres
,
Antiphanes
Megasthenes
,
Nearchus
Marinus
Tyrius
Sir
Hugh
Willoughby
Richard
Chanceler
Stephen
Borough
Arthur
Pet
Charles
Jackman
Sebastian
Cabot
Mr.
Martin
Frobisher
M
John
Davis
Sir
Humphrey
Gilbert
Sir
Walter
Rawleigh
Sir
Richard
Greenvile
M.
Thomas
Harriot
Sir
Francis
Drake
Mr.
Thomas
Candish
Sir
John
Mandivel
India
,
China
,
Tartary
THere
are
two
kinds
of
Instruments
,
by
which
Artificers
haue
conceived
,
that
the
figure
of
this
so
beautifull
,
and
various
fabricke
of
the
whole
Universe
,
might
most
aptly
bee
expressed
,
and
,
as
it
were
,
at
once
presented
to
the
view
.
The
one
,
exhibiting
this
Idea
in
a
round
solid
,
is
called
a
The
other
,
expressing
the
same
in
a
plaine
,
they
tearme
a
Both
of
which
,
having
been
long
since
invented
by
the
Ancients
,
have
yet
even
to
our
times
,
in
a
continued
succession
,
received
still
more
ripenesse
and
perfection
.
The
Sphaere
or
and
the
use
thereof
,
is
reported
by
to
have
been
first
found
out
by
whence
afterward
sprung
the
Fable
,
of
his
bearing
up
the
Heavens
with
his
shoulders
.
Others
attribute
the
invention
of
the
same
to
And
it
was
afterward
brought
to
perfection
by
(
of
whom
makes
mention
but
most
of
all
,
by
according
to
whose
rules
,
and
observations
especially
,
succeeding
times
composed
their
affirmes
.
And
now
there
hath
been
much
perfection
added
to
the
same
,
in
these
our
later
times
,
by
the
industry
,
and
diligence
as
it
may
appear
by
those
Globes
,
that
were
set
forth
at
so
that
now
there
seemes
not
to
bee
any
thing
that
may
be
added
to
them
.
The
indeed
is
a
fine
invention
,
and
hath
in
it
wonderfull
variety
of
workm●…nship
,
if
so
bee
,
that
the
composition
of
it
be
rightly
deduced
out
of
Geometricall
,
and
Opticall
principles
:
and
it
wants
not
it's
great
delightfullnesse
,
and
beauty
also
.
But
yet
that
Other
,
being
tbe
more
ancient
,
hath
also
the
priority
in
Nature
,
and
is
of
the
most
convenient
forme
;
and
therefore
more
aptly
accommodated
for
the
understanding
and
fancy
,
(
not
to
speak
any
thing
of
the
beauty
,
and
gracefulnesse
of
it
)
for
it
representeth
the
things
themselves
,
in
proper
genuiue
figurs
.
For
as
concerning
the
figure
of
the
Heavens
,
whether
it
were
round
,
was
scarcely
e-ever
questioned
by
any
.
So
likewise
,
touching
the
figure
of
the
Earth
,
notwithstanding
many
,
and
sundry
opinions
have
,
been
broached
among
the
ancient
Philosophers
,
some
of
them
contending
for
a
plain
,
others
an
hollow
,
others
a
Cubic
all
,
and
some
a
Pyramidall
forme
:
yet
this
opinion
of
it's
Roundnesse
,
with
greatest
consent
of
reason
,
at
length
prevailed
,
the
rest
being
all
exploded
.
Now
wee
affirme
it
to
be
round
,
yet
so
,
as
that
wee
also
admit
of
it's
inequalities
,
by
reason
of
those
so
great
eminences
of
hills
,
and
depression
of
vallies
.
as
hee
is
cited
by
in
his
first
book
,
saith
,
that
the
fashion
of
the
Earth
is
like
that
of
a
Globe
,
not
so
exactly
round
as
an
artificiall
Globe
is
,
but
that
it
hath
certain
inequalities
.
The
earth
cannot
be
said
to
be
of
an
exact
orbicular
forme
,
by
reason
of
somany
high
hilles
,
and
low
plaines
:
as
rightly
observes
.
And
also
in
his
first
book
of
his
saith
,
that
the
Earth
and
the
water
together
,
make
up
one
sphaericall
body
,
not
of
so
exact
a
forme
,
as
that
of
the
Heavens
,
although
not
much
unlike
it
.
This
assertion
of
the
roundnesse
of
the
Earth
,
with
the
intervening
Sea
,
is
confirmed
also
by
these
reasons
.
For
first
,
that
it
is
round
from
East
to
West
is
proved
by
the
Sun
,
Moon
,
and
the
other
Stars
,
which
are
seen
to
rise
,
and
set
.
first
with
those
that
inhabit
more
Eastwardly
,
and
afterward
with
them
that
are
farther
West
.
The
Sun
riseth
with
the
that
dwell
in
the
Easterne
parts
,
foure
hours
soonner
then
it
doth
with
those
that
dwell
in
more
Westward
:
as
affirmes
.
The
same
is
also
proved
by
the
observing
of
Eclipses
,
especially
those
of
the
Moon
;
which
although
they
happen
at
the
same
time
,
are
not
yet
observed
in
all
places
at
the
same
houre
of
the
day
or
night
,
but
the
hour
of
their
appearing
is
later
with
them
,
that
inhabite
Eastward
,
then
it
is
with
the
more
Westerne
people
.
An
Eclipse
of
the
Moon
,
which
To
have
been
seen
in
(
a
town
in
at
the
fift
houre
of
the
night
;
the
same
was
observed
at
at
the
second
houre
.
In
like
manner
an
Eclipse
of
the
Sun
,
which
was
observed
in
to
be
betwixt
of
the
Clock
;
was
seen
by
a
Captain
in
as
it
is
related
by
Now
that
it
is
also
of
a
sphaericall
figure
from
North
to
South
,
may
be
clearly
demonstrated
by
the
risings
,
settings
,
elevations
and
depressions
of
the
Stars
,
and
Poles
.
The
bright
Star
that
shines
so
resplendently
,
in
the
upper
part
of
the
sterne
of
the
Ship
,
and
is
called
by
the
is
scarcely
to
bee
seen
at
all
in
unlesse
it
bee
from
some
eminent
high
place
:
yet
the
same
is
seen
very
plainly
in
as
being
elevated
above
the
Horizon
,
about
the
fourth
part
of
a
signe
:
as
affirms
in
the
end
of
his
book
,
For
I
read
it
not
as
it
is
commonly
notwithst
anding
,
that
both
the
Greek
text
,
and
also
the
Latine
translation
are
against
it
.
Another
argument
may
bee
taken
,
from
the
figure
of
the
shadow
,
in
the
Eclipse
of
the
Moon
,
caused
by
the
interposition
of
the
Earths
opacous
body
:
Which
shadow
being
Sphaericall
,
cannot
proceed
from
any
other
then
a
round
Globous
body
:
as
it
is
demonstrated
unto
us
out
of
Opticall
principles
.
But
this
one
reason
is
beyond
all
exception
:
that
those
that
make
toward
the
Land
at
the
Sea
,
shal
first
of
all
descry
the
tops
of
the
hilles
onely
,
a●…d
afterwards
,
as
they
draw
nearer
to
shore
,
they
see
the
lower
parts
of
the
same
,
by
little
and
little
:
Which
cannot
proceed
from
any
other
cause
,
then
the
gibbosity
of
the
Earths
superficies
.
As
for
those
other
opinions
of
the
hollow
,
Cubicall
,
Pyramidall
,
and
plaine
figure
of
the
Earth
,
you
have
them
all
largely
examined
both
in
and
almost
in
all
our
ordinary
Authours
of
the
Sphaere
:
together
with
the
reasons
why
they
are
rejected
.
Yet
that
old
conceit
of
the
plainnesse
of
the
Earths
superficies
,
is
again
now
at
last
,
set
forth
in
a
new
dresse
,
and
thrust
upon
us
by
who
by
some
few
eold
arguments
,
and
misunderstood
experiments
,
endeavours
to
confirme
his
own
,
and
consequently
to
overthrow
that
other
received
opinion
of
the
sphaericall
figure
of
the
Earth
.
I
shall
onely
lightly
touch
at
his
chiefest
arguments
;
my
present
purpose
and
intention
,
suffering
mce
not
to
insist
long
on
the
confutation
of
them
.
And
f●…rst
of
all
,
the
great
beight
of
Hills
,
and
the
depression
of
vallies
,
so
much
disagreeing
from
the
evennesse
of
the
plain
parts
of
the
Earth
,
scem
to
make
very
much
against
the
roundnesse
of
the
Earth
.
Who
can
hear
with
patience
,
saith
hee
,
that
those
huge
high
mountains
of
or
the
mountaine
which
lies
under
the
Pole
,
and
is
the
highest
in
the
world
,
should
yet
be
thought
to
have
the
same
superficies
with
●…he
Sealying
beneath
it
?
This
therefore
being
the
chiefest
reason
,
that
m●…y
seem
to
overthrow
the
opinion
of
the
Earth
,
and
Seas
making
up
one
sphaericall
body
;
let
us
examine
it
a
little
more
nearly
,
and
consider
,
how
great
this
inequality
may
bee
,
that
seems
to
make
so
much
against
the
evennessc
of
this
Yerrestitall
Globe
.
Many
strange
,
and
almost
incredible
things
are
reported
by
of
the
unusuall
height
of
an
Hill
in
and
of
as
also
of
another
of
the
same
name
in
and
of
the
monntaine
And
among
the
rest
,
one
of
the
most
miraculous
things
which
they
have
observed
of
the
mountain
is
,
that
whereas
it
is
situate
in
it
casts
a
shadow
into
the
market
place
at
a
Town
in
the
Island
from
whence
is
distant
miles
.
But
for
as
much
as
lies
Westward
from
as
may
appeare
out
of
Tables
,
no
marvail
that
it
casts
so
large
a
shadow
:
seeing
that
wee
may
observe
by
dayly
experience
,
that
as
well
when
the
Sunriseth
,
as
when
it
sets
,
the
shadowes
are
always
extraordinary
long
.
But
that
which
report
of
the
same
mountain
,
I
should
rather
account
among
the
rest
of
their
fabulous
Stories
;
where
as
they
affirm
it
to
be
so
high
,
that
it
is
thought
to
be
above
that
region
of
the
aire
whence
the
rain
is
wont
to
fall
.
And
this
opinion
(
say
they
)
was
first
grounded
upon
a
report
that
there
goes
,
that
the
ashes
which
are
left
upon
the
Altars
on
the
top
of
this
hill
,
are
never
washed
away
,
but
are
found
remaining
in
heapes
upon
the
same
.
To
this
may
be
added
another
testimony
,
out
of
the
Excerpts
of
the
seventh
booke
of
where
it
is
said
,
that
those
that
inhabite
the
top
of
this
mountain
,
do
see
the
Sun
three
hours
sooner
,
then
those
that
live
neare
the
Sea
side
.
The
height
of
the
mount●…in
is
in
like
manner
celebrated
by
the
top
whereof
is
enlightned
by
the
Suns
b●…ames
,
the
third
part
of
the
night
both
morning
and
evening
.
No
lesle
fabulous
is
that
which
is
reported
by
from
whose
top
the
Sun
rising
is
discovered
about
the
fourth
watch
of
the
night
:
which
is
also
related
by
of
that
other
But
that
all
these
relations
are
no
other
then
meer
fables
,
is
acutely
and
solidly
proved
by
out
of
the
ve●…y
principles
●…f
Geometry
.
As
for
that
which
writes
,
that
pill●…
called
by
the
Greeks
are
celebrated
by
for
their
miraculous
height
is
plainly
absurd
and
ridiculous
.
For
these
a●…ise
not
above
an
hundred
Ells
in
height
,
which
is
but
a
furlong
:
whereas
the
are
reported
by
to
equall
that
height
;
and
some
trees
in
are
found
to
exceed
it
:
if
wee
may
credit
the
relations
of
those
Writers
,
who
in
the
same
affirm
,
that
there
grows
a
tree
by
the
river
that
casteth
a
shadow
at
noon
,
five
furlongs
long
.
Those
fabulous
narrations
of
the
Ancients
,
are
seconded
by
as
vaine
reports
of
our
modern
times
.
And
first
of
all
writes
,
from
other
mens
relation
,
that
one
of
the
Islands
,
riseth
in
height
fifteen
leagues
,
which
amount
to
above
sixtie
miles
.
But
not
content
with
this
measure
,
stretchth
it
to
seventie
miles
.
There
are
other
hills
in
like
manner
cryed
up
for
their
great
height
;
as
namely
the
mountain
and
another
in
the
Isle
among
the
Islands
▪
but
yet
both
these
fall
short
of
What
credit
the
relations
may
des●…rve
,
we
will
now
examine
.
And
first
for
it
is
reported
by
many
writers
to
be
of
so
great
a
height
,
that
it
is
probable
the
whole
World
affoards
not
a
more
eminent
place
;
n●…t
ex●…pting
the
mountaine
it
sel●…
;
which
whether
ever
any
other
mortall
man
hath
seen
,
besides
that
Monke
of
(
who
by
his
skill
in
Magicke
conveighed
himself
into
the
utmost
Northerne
regions
,
and
tooke
a
view
of
all
the
places
about
the
Pole
,
(
as
the
Story
hath
it
)
is
more
then
I
am
able
to
determine
.
Yet
that
this
Isle
cannot
be
so
high
as
would
have
it
,
wee
may
be
the
more
bold
to
believe
,
because
that
the
tops
of
it
are
scarcely
ever
free
from
snow
:
so
that
you
shall
have
them
coverd
all
over
with
snow
all
the
year
long
,
save
onely
one
,
or
,
at
the
most
,
two
months
in
the
midst
of
summer
:
as
may
appear
out
of
the
Writers
.
Now
that
any
s●…ow
is
generated
miles
above
the
plain
superficies
of
the
Earth
and
Water
,
is
more
then
they
will
ever
perswade
us
:
seeing
that
the
highest
vapour●…
never
rise
above
miles
above
the
earth
,
according
to
his
measure
;
but
according
to
they
ascend
not
above
miles
.
Notwithstanding
and
some
other
profest
Mathematicians
,
are
bold
to
raise
them
up
to
miles
;
but
with
no
sma●…
stain
of
their
name
,
have
they
mixed
those
trifles
with
their
other
writings
.
reports
that
the
tops
of
the
mountain
reacheth
very
near
as
high
as
the
circle
of
the
Moon
:
but
he
betrayeth
his
own
errour
,
in
that
he
confesseth
that
the
top
of
it
is
covered
with
snow
,
and
shineth
with
fires
in
the
night
.
Not
unlike
to
this
,
are
those
thi●…gs
which
are
reported
of
the
some
mountain
,
and
it's
height
,
by
and
his
scholiast
whence
it
is
called
in
Authours
,
the
pillar
that
bears
up
the
Heavens
▪
But
to
let
passe
these
vain
prodigious
relations
:
let
us
come
to
those
things
that
seem
to
carry
a
greater
shew
of
truth
.
found
by
Dioptricall
instruments
,
and
measuring
the
distances
betwixt
the
places
of
his
observation
,
that
a
perpendicular
,
drawn
from
the
top
of
the
highest
mountain
,
down
to
the
lowest
bottome
or
vally
,
did
not
exceed
ten
furlongs
.
saith
that
there
is
no
hill
found
to
be
above
fifteen
furlong●…
in
height
:
and
so
high
as
this
,
was
that
vast
steep
rock
in
which
is
called
mentioned
by
in
the
booke
of
his
The
topps
of
the
mountatns
are
raiscd
to
a
greater
height
by
then
ever
it
is
possible
for
any
hill
to
reach
.
Yet
if
wee
may
believs
being
employed
by
the
Kings
command
,
in
the
same
businesse
,
found
that
the
height
of
which
is
the
highest
of
all
,
exceeded
not
pases
,
which
is
but
ten
furlongs
.
But
to
proceed
yet
a
little
further
,
least
wee
should
seem
too
sparing
herein
,
and
to
restrain
them
within
narrower
limits
then
wee
ought
:
we
will
adde
to
the
height
of
hills
,
the
depth
also
of
the
Sea
.
Of
which
the
illustrious
in
his
Exercitation
against
writeth
thus
.
The
depth
of
the
Sea
(
saith
he
)
is
not
very
great
:
for
it
seldome
exceeds
pase●…
,
in
most
places
it
is
not
pases
,
and
in
many
places
not
above
six
,
in
few
places
,
it
reacheth
pases
,
and
very
seld●…me
,
or
never
exceeds
this
number
.
But
because
that
falls
very
far
short
of
the
truth
,
as
is
testified
by
the
daily
experience
of
those
that
passe
the
Se●…s
:
let
us
make
the
depth
of
the
Sea
equall
to
the
height
of
mountains
:
so
that
suppose
the
depth
thereof
to
bee
ten
furlongs
,
which
is
the
measure
of
the
Sea
,
in
the
deepest
places
,
as
affirms
.
Or
if
you
please
,
let
it
be
fifteen
furlongs
,
as
cited
by
will
have
(
For
in
his
interpretation
of
deales
not
fairly
with
his
Author
,
where
he
makes
him
assign
thirty
furlongs
to
bee
the
measure
of
the
Seas
depth
.
)
These
grounds
being
thus
laid
,
let
us
now
see
what
proportion
the
height
of
hills
may
bear
to
the
Diameter
of
the
whole
Earth
:
that
so
we
may
hence
gather
,
that
the
extubcrancy
of
hills
are
able
to
detract
little
or
nothing
from
the
roundnesse
of
the
Earth
;
but
that
this
excrescency
will
bee
but
like
a
little
knob
or
dust
upon
a
ball
,
as
saith
For
if
wee
suppose
the
circumference
of
the
whole
earth
to
bee
furlongs
,
according
to
account
,
(
neither
did
ever
any
of
the
Ancients
assigne
a
lesse
measure
then
this
;
as
witnesseth
:
)
the
Diameter
thereof
will
bee
,
(
according
to
the
proportion
betwixt
a
circle
and
it's
Diameter
found
out
by
furl●…ng
.
If
then
we
grant
the
highest
Hills
to
bee
ten
furlongs
high
,
according
to
they
will
beare
the
same
proportion
to
the
Diameter
of
the
Earth
,
●…hat
is
,
betwixt
one
and
mistakes
himself
when
he
saith
,
that
the
Diameter
of
the
Earth
to
the
perpendicular
of
ten
furlongs
is
as
to
one
for
this
is
the
proportien
it
beareth
to
the
whole
circumference
,
and
not
the
Diameter
.
Or
suppose
the
topps
of
the
●…ighest
hills
to
ascend
to
the
perpendicular
of
●…ifteene
furlongs
,
as
would
have
it
:
●…he
proportion
then
will
be
of
one
to
Or
if
●…ouplease
,
let
it
bee
thirtie
furlongs
,
of
which
●…height
is
a
certain
rock
in
spoken
●…f
by
in
the
eleventh
Booke
of
his
(
notwithstanding
is
of
o●…inion
,
that
a
perpendicular
drawn
from
the
top
of
the
highest
hill
,
to
the
bottome
of
the
dee●…est
Sea
,
exceeds
not
this
measure
:
)
the
proportion
will
be
no
greater
,
then
of
one
to
Or
let
us
extend
it
yet
farther
,
if
you
will
,
to
foure
miles
,
or
thirty-two
furlongs
,
(
of
which
●…eight
the
mountain
is
repor●…ed
by
to
be
,
)
the
proportion
will
yet
bee
somewhat
lesse
then
of
one
to
I
am
therefore
so
farre
from
giving
any
credit
to
his
relation
of
being
seventy●…wo
miles
high
,
(
unlesse
it
bee
measured
by
ma●…y
oblique
and
crooked
turnings
and
windings
:
●…n
which
manner
measureth
the
height
of
●…he
also
to
bee
fifteen
miles
;
)
as
that
I
●…annot
assent
to
who
would
have
the
topps
of
the
highest
hills
to
reach
●…o
eight
miles
,
or
eighty
furlongs
,
as
I
think
:
neither
yet
to
who
in
his
affirmes
the
mountain
to
be
six
miles
in
height
:
and
I
can
scarcely
yeeld
to
the
samc
when
as
he
speakes
of
other
Hills
four
miles
in
height
.
And
whosoever
should
affirm
any
Hill
to
bee
higher
then
this
,
though
it
were
himself
,
I
would
bardly
believe
him
.
Thus
much
of
the
height
o●…
hills
,
which
s●…emed
to
derogate
from
the
roundnesse
of
the
Terrestriall
Globe
.
proceeds
,
and
goes
about
to
prove
that
the
water
also
is
not
round
or
sphaericall
.
And
he
b●…rroweth
his
argument
from
the
observations
of
those
that
conveigh
or
levell
waters
,
who
finde
by
their
Dioptricall
Instruments
;
that
water●…
have
all
an
equall
and
plaine
superficies
,
except
th●…y
be
troubled
by
the
violence
of
winds
.
On
the
contrary
side
,
affirmes
,
that
the
superficies
of
the
Sea
is
in
some
places
higher
,
then
it
is
in
other
.
And
hee
also
produceth
,
as
assertors
of
his
ignorance
,
those
Water-levellers
,
wbo
being
employed
by
ab●…ut
the
entring
away
of
the
or
neck
of
land
betwixt
returned
him
answer
;
that
they
found
by
their
In●…ruments
,
that
that
part
of
the
Se●…
which
was
on
side
,
was
higher
then
it
was
at
The
like
is
also
storied
of
one
of
the
Kings
of
who
going
about
to
make
a
passage
out
of
the
into
the
gulfe
,
is
said
to
have
desisted
from
his
purpose
,
because
hee
found
that
the
superficies
of
the
gulfe
was
higher
then
was
the
as
it
is
reported
by
in
the
end
of
his
first
Booke
of
The
like
is
also
said
in
the
same
place
,
by
the
same
Authour
,
to
have
happened
afterward
to
Now
whether
tbe
imployed
by
deserve
more
cre●…it
,
then
those
whom
nameth
;
I
shall
no●…●…uch
trouble
my selfe
to
examine
.
Yet
in●…igheth
against
for
attributing
any
●…ch
eminencies
,
and
depressions
to
the
superficies
〈◊〉
the
Sea
.
And
his
doctrine
is
,
●…at
every
humid
body
,
standing
still
and
with●…t
disturbance
,
hath
a
Sphericall
superficies
,
whose
●…enter
is
the
same
with
that
of
the
Earth
.
So
that
●…ee
have
just
cause
to
reject
the
opinions
,
both
of
●…hose
that
contend
that
the
superficies
of
the
Sea
is
●…aine
;
as
also
of
those
that
will
have
it
to
bee
in
●…me
places
higher
tben
in
other
.
Although
we●…●…annot
,
in
reason
,
but
confesse
,
that
so
small
a
por●…on
of
the
whole
Terrestiall
his
agreement
,
which
he
alledgeth
from
●…he
experience
of
Water-conveighers
,
to
be
of
no
●…eight
at
all
.
But
hee
goes
on
,
and
labours
to
prove
his
●…ssertion
from
the
elevation
and
depression
,
rising
●…d
setting
of
the
Poles
,
and
Stars
,
which
are
●…served
daily
,
by
those
that
traverse
the
Seas
:
●…ll
which
,
hee
saith
,
may
come
to
passe
,
al●…ough
the
surface
of
the
water
were
plaine
.
For
〈◊〉
any
Star
be
observed
,
that
is
in
the
verticall
●…int
of
any
place
;
which
way
soever
you
tra●…ell
from
that
place
,
the
same
Star
will
seem
〈◊〉
bee
depressed
,
and
abate
something
of
it's
ele●…ation
,
though
it
were
on
a
plaine
superficies
.
●…ut
there
is
something
more
in
it
then
takes
notice
of
.
For
if
wee
go●…
an
equall
measure
of
miles
either
towards
the
North
,
or
toward
the
South
;
the
elevation
or
depression
of
the
Star
,
will
alwayes
bee
found
to
bee
equall
:
which
that
it
can
possibly
bee
so
in
a
plaine
superficies
;
is
more
then
hee
will
ever
bee
able
to
demonstrate
.
If
wee
take
any
Star
situate
near
the
AEquator
,
the
same
when
yo●…
have
removed
thence
English
miles
,
will
bee
elevated
about
a
degree
higher
,
above
the
Horizon
,
whether
the
Star
bee
directly
over
your
head
,
or
whether
you
depart
thence
,
that
so
it
may
bee
depressed
from
your
Zenith
,
for
or
any
other
number
of
degrees
.
Which
that
it
cannot
thus
bee
;
on
a
plaine
superficies
,
may
be
demonstrated
out
of
the
principles
of
Geometry
.
But
yet
mee
thinks
,
this
one
thing
might
have
perswaded
(
being
so
well
versed
in
the
Histories
of
the
Navigations
,
as
his
writings
sufficiently
testifie
)
that
the
superficies
of
the
Sea
is
not
plaine
;
because
that
the
Ship
called
the
losing
from
and
directing
his
course
towards
the
South-west
parts
,
passed
through
the
Straights
,
called
since
by
his
name
,
and
so
touching
upon
the
haveing
compassed
the
whole
World
about
,
returned
again
into
And
here
I
shall
not
need
to
maintain
the
famous
Voyages
of
our
owne
Countrie-men
,
not
so
well
known
perhaps
abroad
;
which
yet
convince
and
the
same
errour
.
A●…d
thus
have
wee
lightly
touched
the
chiefe
foundations
that
his
cause
is
built
upon
:
but
as
for
●…ose
ill
understood
experiments
,
which
he
brings
〈◊〉
the
confirmation
of
the
same
.
I
shall
let
them
●…sse
,
for
that
they
seem
rather
to
subvert
his
opi●…n
then
confirme
it
.
Thus
having
proved
the
of
the
Earth
〈◊〉
be
of
a
Sphaericall
figure
,
seeing
that
the
E●…inency
of
the
highest
Hills
hath
scarcely
the
●…e
proportion
to
the
Semidiameter
of
the
●…rth
,
that
there
is
betwixt
●…hich
how
small
it
is
,
any
one
may
easily
per●…ive
:
I
hold
it
very
superfluous
to
goe
about
to
●…ove
,
that
a
is
of
a
figure
most
proper
and
●…t
to
expresse
,
and
represent
the
fashion
of
the
Hea●…ns
and
earth
,
as
being
most
agreeable
to
Nature
,
●…siest
to
be
understood
,
and
also
very
beautifull
〈◊〉
behold
.
Now
in
materiall
besides
the
true
●…d
exact
description
of
places
,
which
indeed
is
●…e
chiefest
matter
to
bee
considered
;
there
are
●…o
things
especially
required
.
The
first
where●…
is
the
magnitude
and
capacity
of
them
;
that
〈◊〉
there
may
bee
convenient
space
for
the
de●…ription
of
each
particular
place
or
region
:
the
●…cond
is
the
lightnesse
of
them
,
that
so
their
●…ight
be
not
cumbersome
.
in
his
eleventh
,
●…ok
,
would
have
a
to
have
ten
foot
〈◊〉
Diameter
,
that
so
it
might
in
some
rea●…nable
manner
admit
the
description
of
particu●…r
places
.
But
this
bulk
is
too
vast
,
to
bee
●…nveniently
dealt
withall
.
And
in
this
regard
,
〈◊〉
think
that
those
of
which
I
intend
〈◊〉
speake
in
this
ensuing
discourse
,
may
justly
bee
perferred
before
all
other
,
that
have
been●…
set
forth
before
them
;
as
being
more
capacious
then
any
other
:
for
they
are
in
Diameter
two
foot
,
and
two
inches
:
whereas
(
which
are
bigger
then
any
other
ever
set
forth
before
him
,
)
are
scarcely
sixteen
inches
Diameter
.
The
proportion
therefore
of
the
superficies
of
these
will
be
as
and
somewhat
more
,
Every
Countrey
therefore
in
those
will
bee
above
twice
as
large
as
it
is
in
so
that
each
particular
place
may
the
more
easily
bee
described
.
And
this
I
would
have
to
bee
understood
of
those
great
made
by
concerning
the
use
of
which
especially
,
wee
have
written
this
discourse
.
For
he
hath
set
forth
other
smaller
also
,
which
as
they
are
of
a
lesser
bulk●…
and
magnitude
,
so
are
they
of
a
cheaper
price
:
that
so
the
meaner
Students
might
herein
also
bee
provided
for
.
Now
concerning
th●…
Geographicall
part
of
them
,
seeing
it
is
taken
out
of
the
newest
Charts
and
descriptions
;
I
am
bold
to
think
them
more
perfect
then
any
other
:
how
ever
they
want
not
their
errours
.
And
I
think
it
may
bee
the
Authors
glorie
to
have
performed
thus
much
in
the
edition
of
these
One
thing
by
the
way
you
are
to
take
notice
of
:
which
is
,
that
the
descriptions
of
particular
places
are
to
bee
sought
for
else
where
;
for
this
is
not
to
bee
expected
in
a
And
for
these
descriptions
of
particular
Countries
,
you
may
have
recourse
to
the
Geographicall
tables
of
whose
diligence
and
industry
in
this
Regard
seemes
to
exceed
all
other
before
him
.
To
him
,
therefore
we
referre
you
.
Tvcho
Brabe
Second
Atlas
O.
F.
Sibi
&
posteris
.
F.
F.
First
moveable
Armillary
Sphaere
Now
concerning
those
spoken
of
by
our
Author
,
the
same
have
been
since
,
accurately
corrected
,
according
to
observations
,
and
set
forth
both
in
a
great
,
and
lesser
form●…
by
and
are
still
made
,
and
sold
by
his
Son
.
And
because
that
in
this
ensuing
discourse
of
there
is
often
mention
made
of
a
and
other
the
like
Geometricall
tearmes
:
I
have
thought
good
to
set
down
the
severall
definitions
of
the
same
.
is
that
which
hath
no
parts
:
or
a
thing
supposed
to
be
Indivisible
,
or
that
cannot
be
divided
into
parts
.
is
a
supposed
length
without
breadth
;
whose
extreames
or
bounds
are
t●…
Points
.
is
the
shortest
of
all
Lines
,
drawn
from
any
two
of
the
same
Points
.
are
Lines
equidistant
from
each
other
:
which
though
they
should
be
protended
infinitely
▪
would
never
meet
in
one
point
,
but
keep
still
the
same
distance
mutally
.
is
a
right
Line
,
falling
directly
on
a
Right
Line
,
and
making
on
each
side
that
Point
where
they
touch
,
two
equall
Right
Angles
.
is
a
Longitude
,
having
onely
Latitude
:
whose
tearmes
and
limits
are
two
Lines
.
is
that
which
is
comprehended
within
one
,
or
many
bands
:
under
one
bound
is
comprehended
a
Circle
:
and
all
other
Figures
under
many
.
or
Limit
,
is
that
which
is
the
end
of
any
thing
.
is
a
plaine
Figure
,
comprehended
under
one
round
line
:
in
the
midst
whereof
there
is
a
P●…int
,
from
whence
all
Lines
drawn
to
the
Circumference
are
equall
.
of
a
Circle
,
is
that
point
in
the
midst
,
from
which
all
equall
lines
are
drawn
to
the
Circumference
.
of
a
Circle
,
is
a
Right
line
passing
through
the
Center
,
terminated
at
each
end
with
the
Circumference
,
and
dividing
the
Circle
into
two
equall
Parts
.
is
the
halfe
of
a
Circle
,
contained
within
the
Diameter
,
and
halfe
the
Circumference
.
is
a
portion
of
a
Circle
,
comprehended
within
a
Right
line
,
and
any
part
of
the
Circumference
.
and
is
alwayes
either
greater
or
lesser
then
a
Semicircle
.
is
,
when
two
lines
are
extended
upon
the
same
superficies
,
so
that
they
touch
one
another
in
a
Point
,
but
not
directy
.
is
that
which
is
produced
of
a
Right
line
,
falling
upon
a
Right
line
,
and
making
two
equal
Angles
,
on
each
side
the
Point
,
where
they
touch
each
other
:
As
the
Lines
A
,
B
,
C.
is
that
which
is
Greater
then
a
Right
Angle
,
as
the
Angle
A
,
C
,
D.
is
that
which
is
lesse
then
a
Right
:
as
the
Angle
A
,
C
,
B.
is
that
which
is
comprehended
under
more
then
two
plaine
Angles
,
which
are
not
in
the
same
superficies
and
meeting
all
in
one
point
:
as
are
the
Angles
of
a
Cube
,
or
Die
.
is
a
Figure
Quadrangular
,
having
equall
sides
,
but
not
equall
Angles
.
is
a
Figure
having
neither
equal
sides
,
nor
equall
Angles
:
yet
the
Opposite
sides
and
Angles
are
equall
.
is
that
which
hath
length
,
breadth
,
and
thickness
;
as
a
Cube
or
Die
:
and
the
Limits
or
Extreames
of
it
are
superficies
.
is
that
Diameter
,
aboue
which
the
Sphaere
or
Globe
is
turned
.
of
a
Sphaere
,
are
the
Extreames
,
or
ends
of
the
Diameter
,
and
are
terminated
in
the
superficies
of
the
Sphaere
.
is
defined
by
to
be
,
when
the
Diameter
of
a
semicircle
remaining
fixed
,
the
Semicircle
is
turned
about
,
till
it
returne
again
to
the
place
,
whence
it
began
to
move
at
first
.
A
Globe
is
also
called
a
Sphaere
:
onely
with
this
distinction
,
that
a
Sphere
is
properly
such
an
one
,
as
consists
only
of
circles
or
little
hoopes
of
brasse
,
or
like
matter
,
and
is
not
a
solid
body
,
as
is
a
Globe
:
the
Latines
call
it
Armillaris
.
Now
those
Circles
whereof
it
is
made
,
although
we
are
not
to
cone
eive
that
there
are
any
such
reallones
in
the
Heavens
,
yet
they
have
been
invented
by
Artificers
,
to
the
end
,
that
by
meanes
of
the
same
,
the
doctrine
of
the
true
motions
of
the
Coelestiall
bodies
might
the
more
easily
bee
apprehended
.
And
what
is
said
of
the
and
the
other
Circles
,
is
also
to
bee
understood
of
the
other
Orbs
themselves
,
and
their
Hypotheses
.
For
as
concerning
the
objection
made
long
since
by
and
lately
by
touching
the
facility
the
ancient
had
in
searching
out
the
courses
of
the
Stars
:
I
think
it
not
amisse
to
let
you
see
what
the
Noble
opinion
is
herein
,
and
what
answer
hee
,
once
upon
occasion
gave
himselfe
,
proposing
the
same
unto
him
:
as
wee
find
it
related
by
himself
in
his
book
of
Astronomicall
Epistles
pag.
60.
And
thus
it
is
.
Where
as
that
famous
Philosopher
of
our
times
,
was
of
opinion
,
that
the
Science
of
Astronomy
might
bee
framed
by
some
certain
wayes
of
computation
,
with
this
is
nothing
else
but
a
meere
ground-lesse
conjecture
.
Which
con●…eit
of
his
,
he
proposed
indeed
to
mee
about
sixteen
●…eares
since
,
when
as
wee
were
together
at
wishing
mee
withall
,
that
when
as
I
had
●…nce
reduced
the
course
of
the
Stars
into
some
●…xact
order
,
by
the
now
in
use
;
I
●…ould
then
try
what
might
be
done
without
them
.
And
that
this
might
possibly
be
effected
,
he
brought
this
for
his
reason
,
because
that
hee
had
read
,
that
the
had
antiently
a
most
easie
and
facile
way
and
method
in
their
Astronomy
.
And
therefore
,
seeing
that
this
way
of
computation
by
is
very
intricate
and
difficult
;
it
must
needs
follow
,
that
they
had
a
more
plaine
and
compendious
way
to
the
knowledge
of
the
course
of
the
Starres
,
and
that
without
them
But
I
opposed
him
herein
,
shewing
withall
,
that
it
was
altogether
impossible
that
the
Caelestiall
Apparen●…es
should
bee
reduced
into
any
certain
order
or
science
,
so
as
to
bee
understood
,
without
the
help●…
of
And
that
this
facility
of
the
was
onely
in
the
AEquators
of
the
Planets
,
whereby
they
freed
themselves
from
all
tedious
supputation
;
Whereas
,
the
ease
and
facile
use
of
the
was
not
as
yet
brought
to
light
.
But
for
as
much
as
hee
(
thought
otherwise
a
man
of
an
excellent
apprehension
and
wit
,
and
a
great
lover
of
the
truth
)
seemed
not
to
bee
so
throughly
acquainted
with
the
hidden
secrets
of
this
intricate
Science
,
and
considered
not
that
the
course
of
the
Heavenly
bodi●…s
did
not
keepe
a
constant
period
at
any
set
time
:
I
neither
could
nor
indeed
desired
to
get
any
thing
of
him
,
in
this
matter
.
He
hath
many
Sectaries
at
this
day
,
who
have
a
strong
faith
of
the
possibility
of
this
thing
:
but
such
they
are
,
that
neither
understand
the
matter
themselves
,
nor
will
ever
be
able
to
bring
it
to
any
effect
.
For
seeing
that
all
things
consist
in
number
,
weight
,
and
measure
:
without
these
,
there
is
no●…
any
thing
in
this
visible
world
that
can
be
explained
or
understood
.
Now
the
office
of
these
is
only
to
shew
the
measure
of
the
apparent
motion
of
the
Heavenly
bodies
,
by
circles
and
other
figures
:
which
are
again
resolved
into
numbers
by
Arithmeticke
without
which
,
whosoever
shal
think
to
attaine
to
the
knowledge
of
the
motion
of
the
Stars
:
he
may
be
said
to
invoke
Fortune
,
(
as
the
Proverb
is
:
)
and
dreames
of
some
strange
incorporeall
,
and
more
then
Seraphicall
way
,
above
the
reach
of
humane
capacity
.
In
the
midst
among
these
Signes
are
there
described
certain
Characters
,
to
denote
the
particular
Planet
,
to
whose
dominion
each
Sig●…
doth
appertain
.
Next
to
this
there
is
another
Section
,
wherein
are
set
down
the
severall
day●…
of
every
week
:
after
that
,
followeth
the
number
of
the
dayes
of
every
Moneth
,
throughout
th●…
whole
yeare
.
Besides
this
number
of
the
day●…s
,
each
of
them
hath
in
their
severall
orders
some
one
of
these
three
letters
affixed
,
signifying
the
which
tearmes
the
Ancient
used
in
their
accounts
,
to
sign●…
fie
the
dayes
of
every
Moneth
.
For
they
did
〈◊〉
reckon
as
wee
doe
now
,
from
the
first
day
of
every
Month
to
the
of
the
same
;
but
their
account
was
according
to
the
So
that
the
first
of
each
Month
w●…
the
and
the
rest
of
the
dayes
of
the
same
month
were
not
reckoned
forward
,
but
after
a
retrograde
manner
.
As
for
example
:
The
last
day
of
with
us
is
the
They
called
the
second
of
the
and
the
of
the
same
month
,
the
third
of
the
Thus
reckoning
backward
till
they
came
to
the
which
was
the
foureteenth
of
and
the
nineteenth
of
the
The
like
order
they
observed
in
the
also
.
Now
what
months
have
more
or
fewer
may
be
found
upon
the
as
we
have
said
:
and
as
may
be
gathered
also
out
of
these
old
verses
.
sex
Nonas
Romane
Calendar
Dionysius
Exigum
〈◊〉
is
The
true
Horizon
is
either
Rational
or
Sensible
.
The
Rationall
or
Intelligible
Horizo●…
divide
th
the
Sphaere
into
two
equall
parts
exactly
;
and
these
are
called
the
upper
and
the
lower
Hemisphaeres
.
The
sensible
or
apparent
Horizon
,
is
s●…
called
,
because
it
only
seemes
to
divide
the
Heavens
into
two
equall
parts
,
or
Hemisphaeres
:
whereas
indeed
it
doth
not
divide
it
so
exactly
,
but
only
seemeth
so
to
doe
.
The
Rationall
Horizon
,
is
also
called
the
artificiall
,
because
that
it
was
brought
in
,
for
the
use
of
Astronomy
.
The
use
of
the
Horizon
is
manifold
.
First
,
it
divides
the
Heavens
into
two
Hemisphaeres
.
Secondly
,
it
sheweth
what
Starres
never
set
,
and
so
what
never
rise
from
under
the
Earth
;
and
so
,
likewise
what
Stars
do
both
rise
and
set
.
Thirdly
,
it
shewes
the
cause
of
the
equality
,
and
in
equality
of
the
artificiall
dayes
and
nights
.
Fourthly
,
it
condueeth
to
the
finding
out
of
the
latitude
of
any
place
.
Fifthly
,
it
is
the
cause
of
the
Rectitude
and
obliquity
of
the
Sphare
;
whereof
we
have
occasion
to
speak
more
largely
hereafter
.
The
us●…s
of
the
are
these
,
especially
It
determineth
the
paynt
of
mid-day
,
and
midnight
:
whence
the
Astronomers
begin
the
day
alwayes
from
the
Circle
..
in
the
is
observed
the
or
v●…rticall
point
of
places
,
whence
afterward
the
distances
of
Stars
and
Parallel
circles
are
gathered
.
The
Longitude
and
Latitude
of
places
are
taken
from
hence
.
It
shewes
the
greatest
elevation
of
the
Sun
,
and
other
Starrs
:
which
elevation
is
called
their
By
the
elevdtion
of
the
Sun
,
when
hee
is
in
the
AEquinoctiall
point
,
may
be
found
out
the
eleuation
of
thé
Pole
,
and
habitude
or
position
of
the
Sphaere
.
For
the
quarter
of
a
circle
being
90.
degrees
,
if
then
we
substract
the
Altitude
of
the
Sun
in
the
AEquinoctiall
from
90.
degrees
,
the
remainder
sheweth
the
elevation
of
the
Pole
.
As
for
example
,
The
elevation
of
the
Sun
at
noon
,
when
it
is
in
the
AEquinoxe
,
is
about
degrees
with
us
here
at
which
being
deducted
out
of
there
remaines
Which
is
the
elevation
of
the
Pole
with
us
.
So
at
the
AEquinoctiall
altitude
of
the
Sun
is
about
degrees
;
which
being
substracted
from
degrees
,
which
is
a
Quadrant
,
there
remaines
for
the
elevation
of
the
Pole
.
Index
Horarius
The
use
of
this
is
to
denote
the
houres
of
the
riseing
and
setting
of
the
Sun
and
other
Starrs
,
which
must
be
practised
after
this
manner
.
First
,
you
must
set
the
Globe
to
your
elevation
or
Pole
,
and
then
apply
the
degree
of
the
signe
,
in
which
the
Sun
at
the
time
is
,
to
the
Meridian
,
and
the
to
the
twelfth
houre
which
is
uppermost
.
And
so
having
thus
done
,
you
must
turne
the
Globe
about
,
till
the
degree
wherein
the
Sun
is
,
come
to
the
Eastern
side
of
the
Horizon
;
which
done
,
the
will
point
out
the
houre
of
his
riseing
,
and
if
you
turne
it
about
to
the
West
side
,
you
shall
in
like
manner
have
the
houre
of
his
setting
.
There
is
also
belonging
to
the
Meridian
a
being
made
of
a
long
thin
plate
of
steele
or
brasse
,
and
fashioned
crooked
,
so
that
it
may
be
apply'd
to
the
conuexs
Superficies
of
the
Globe
,
and
having
the
fourth
part
of
the
circle
in
length
.
And
this
is
made
in
such
a
sort
,
as
that
it
may
be
fastened
on
the
and
so
be
applyed
to
the
of
any
place
whatsoever
,
being
divided
from
one
end
to
the
other
into
equall
parts
or
degrees
There
is
besides
at
the
foot
of
the
Globe
,
a
Mariners
compasse
placed
:
which
serves
to
shew
,
how
to
place
the
Globe
rightly
,
according
to
the
Foure
winds
or
quarters
of
the
world
.
The
use
of
the
consists
chiefly
in
these
things
.
First
,
it
sheweth
the
time
of
the
which
are
alwayes
when
the
Sun
falies
upon
the
circle
.
And
this
is
,
when
as
the
Sun
enters
into
the
first
degree
of
according
to
that
of
The
Sun
in
plac'd
,
each
yeare
The
day
and
night
are
equall
every
where
.
Secondly
●…he
AEquator
divides
the
Heauens
into
two
equall
parts
,
or
Hemisphaeres
.
whereof
one
is
called
the
Septeutrionall
or
Northern
Hemisphaere
:
the
other
,
the
Meridionall
or
Southerne
.
Thirdly
,
it
sheweth
the
ascension
and
descension
of
the
parts
of
the
Zodiack
:
whence
the
length
of
the
Artificiall
day
and
night
,
for
any
position
of
Sphaere
,
may
be
known
.
Fou●…thly
〈◊〉
shewes
what
Starrs
,
and
parts
of
the
Eclipticke
have
any
Declination
.
Anaximander
Milesius
Cleostretus
Tenedius
Thales
Milesius
was
the
first
that
calculated
the
time
of
the
AEquinoxe
and
Eclipses
:
and
he
flourished
about
the
yeares
of
the
Creation
,
which
was
about
yeares
before
lived
about
yeares
before
in
the
yeare
of
the
Creation
,
He
was
the
Son
of
and
was
a
man
of
excellent
knowledg
in
Astronomy
.
He
also
first
invented
the
Moones
Circle
of
yeares
:
whose
first
new
Moon
fell
upon
the
day
of
the
month
which
is
the
same
with
our
being
on
a
Friday
writes
of
him
thus
There
are
(
saith
he
(
besides
,
many
other
great
yeares
:
as
the
yeare
which
invented
and
consisted
of
common
yeares
&c.
was
by
nation
an
and
he
lived
yeares
before
Christ
The
whole
latitude
of
the
Zodiaqu●…
is
divided
into
two
parts
by
the
which
is
the
circle
,
or
Circumference
under
which
the
Sun
steeres
his
course
continually
.
whence
it
is
called
in
Latine
,
the
Sun●…
high
way
.
And
in
a
Circle
divideing
the
in
the
middest
.
And
it
is
called
the
because
the
Eclipses
of
the
never
haeppen
,
but
when
they
are
either
in
conjunction
or
opposition
under
this
line
,
or
very
near
the
same
.
Vitruvius
,
Pliny
,
Thco●…
Alexandrinus
,
Censorinus
,
The
office
and
use
of
the
in
that
,
it
is
a
rule
or
measure
of
the
proper
motion
of
the
Planets
.
By
the
helpe
of
the
the
true
place
,
of
all
the
Starrs
are
sound
:
besides
it
may
be
knowne
in
what
signe
any
fixed
Starr
or
Planet
may
be
said
to
be
.
It
sheweth
the
Latitude
of
the
Planets
and
fixed
Starrs
,
All
Eclipses
happen
when
the
Sun
and
Moon
are
under
the
Ecliptique
.
The
obliquity
of
the
Ecliptique
is
the
cause
of
the
inequality
of
the
artificial
dayes
and
nights
.
Julius
Caesar
Jacobus
Christmannus
Ptolomy
,
Almagest
.
lib.
Julius
Caesar
Julius
Caesar
Theodorus
Gaza
Thebit
Ben
Chorah
March
.
Arzachel
Joseph
Scaliger
Jacobus
Christmannus
Equinoctiall
Colure
Solsticiall
Colure
The
office
of
the
Colures
in
general
is
.
First
to
show
the
foure
principall
points
of
the
Zodiack
,
in
which
,
by
reason
of
the
motion
of
the
Sun
,
there
are
caused
the
great
changes
of
the
Seasons
of
the
year
.
Of
which
points
,
two
are
in
the
AEquator
,
at
determining
the
place
of
the
which
constitute
the
Solsticiall
Colure
.
Secondly
,
To
distinguish
the
AEquator
Zodiack
and
the
whole
Sphaere
of
the
Heavens
into
foure
equall
parts
.
The
use
of
which
is
principally
seen
in
examining
the
ascensions
of
the
Signes
.
These
Colures
differ
from
each
other
,
in
that
the
passeth
through
the
Poles
of
the
world
,
and
also
of
the
Zodiack
:
but
the
AEquinoctiall
Colure
passeth
through
the
Poles
of
the
world
only
.
What
the
opinion
of
was
,
concerning
the
procession
of
AEquinoctial
points
thus
diversly
thought
on
by
you
have
expressed
in
an
epistle
of
his
●…o
there
having
been
not
long
before
a
disputation
holden
concerning
some
certain
Mathematicall
question
,
at
the
intreaty
of
some
of
the
chiefest
of
the
States
of
the
Low
Countries
;
among
which
number
was
chosen
also
,
as
an
Arbitrator
:
which
Epistle
of
his
,
was
afterwards
Printed
,
amongst
some
other
of
his
Epistles
at
What
the
Illustrious
also
thought
concerning
this
point
,
you
have
in
his
But
I
will
first
set
down
opinion
:
and
afterward
adde
and
some
others
also
I
received
(
saith
he
)
●…eur
second
letters
,
the
next
day
aster
your
former
.
In
which
you
make
mention
of
one
that
undertakes
●…o
discourse
of
the
Magneticall
direction
of
the
Needle
.
Many
indeed
have
endeavoured
in
this
matter
,
and
doc
daily
endeavour
,
being
thereto
incouraged
by
the
rewards
proposed
by
the
Illustrious
States
.
To
whose
hands
some
have
delivered
up
their
opinions
in
writing
:
and
Arbitrators
forthwith
have
been
called
about
it
.
O●…
which
number
,
it
was
my
chance
to
bee
chosen
f●…
one
:
there
being
indeed
amongst
them
many
excellent
,
both
Mathematicians
and
〈◊〉
But
those
that
professed
the
Mathematicks
,
were
altogether
unexperienced
in
Nauticall
affaires
:
an●…
the
Navigators
were
as
ignorant
of
Astronom●…call
.
Besides
these
Authors
of
whom
wee
were
〈◊〉
passe
our
judgments
,
performed
nothing
worth
〈◊〉
great
expectation
.
Neither
hath
that
who
wrote
a
Book
three
yeares
since
,
of
the
produced
anything
answereable
to
th●…
great
opinion
was
raised
of
it
.
I
my selfe
hav●…
often
proposed
,
to
these
Mathematicians
that
professe
in
this
place
,
a
thing
which
it
seemes
can
never
sinke
into
their
heads
:
insomuch
that
they
entertained
it
with
scorne
and
laughter
.
was
the
first
that
brought
in
that
merry
conceit
of
the
eight
sphaeres
moveing
toward
th●…
East
:
and
so
perswaded
that
the
fix●…d
Stars
in
the
eighth
sphaere
moved
all
in
the
same
order
,
situation
,
and
distance
from
each
other
,
toward
the
East
.
Which
so
confirmed
,
that
it
had
been
a
hainous
matter
for
posterity
to
have
doubted
of
the
same
.
And
first
of
all
within
the
memory
of
our
Fathers
,
that
great
restorer
of
Astronomy
,
perceived
the
weaknesse
of
this
conceit
of
and
withall
observed
,
that
the
eight
Sphaere
did
not
move
toward
the
East
,
but
that
the
AEquinoctiall
points
went
forward
in●…o
the
precedent
Signes
:
and
this
he
calls
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
But
this
observation
of
his
,
hee
onely
nakedly
proposed
,
without
any
demonstration
at
all
.
But
I
have
observed
,
that
the
Starrs
have
not
(
as
dreame
)
gone
on
to
the
subsequent
parts
:
and
that
the
or
Polar
Star
was
at
the
same
distanoe
from
Pole
in
his
time
,
as
it
is
at
this
day
.
For
proof
of
which
assertion
I
have
collected
many
instances
.
which
being
granted
,
the
procession
of
the
AEquinoctiall
point
must
necessarily
follow
.
For
one
of
these
two
must
needes
be
granted
;
to
wit
,
either
of
the
motion
of
the
eighth
Sphaere
toward
the
east
,
or
else
the
progresse
of
the
AEquinoctiall
points
into
the
precedent
Signes
.
Now
that
the
first
is
not
to
be
admitted
appeares
manifestly
,
because
that
the
fixed
Starrs
have
not
〈◊〉
all
●…hanged
their
situation
in
respect
of
the
Pol●…
,
since
his
time
.
Therefore
the
other
must
needs
be
granted
.
The
AEquinoctiall
points
therefore
,
have
gone
forward
to
the
ant●…cedent
Signes
.
Which
proposition
notwithstanding
the
great
had
no
way
to
demonstrate
,
〈◊〉
out
of
the
by
which
that
other
motion
might
as
well
bee
defended
▪
as
●…his
.
Wee
therefore
now
have
this
But
what
is
it
?
Even
nothing
else
,
b●…
the
motion
of
the
AEquinoctiall
points
into
the
precedent
Signes
.
Now
if
the
AEquinoctiall
points
be●…
moveable
;
and
the
AEquinoctiall
C●…cle
b●…e
de●…cribed
by
these
points
;
the
AEquinoctiall
Circle
●…hen
must
needs
be
moveable
also
:
which
is
as
true
,
as
truth
it selfe
.
And
if
the
AEquinoctiall
circle
be
moveable
;
his
Pole
must
be
moveable
also
;
and
so
the
Poles
of
the
AEquinoctiall
must
be
divers
from
the
Poles
of
the
world
.
for
the
Pole
of
the
World
is
immoveable
;
but
this
moveable
.
Besides
,
all
the
Meridian
circles
do
passe
through
the
Poles
of
the
AEquinoctiall
:
and
in
the
superficies
of
stone
Dialls
,
the
Meridian
line
,
which
is
drawn
for
the
placing
of
the
Sun
Diall
,
is
understood
to
passe
through
the
Poles
of
the
AEquinoctiall
;
which
is
confest
by
all
men
,
and
is
most
true
.
But
because
the
Poles
of
the
AEquinoctiall
are
moveable
,
the
Meridian
line
.
that
passeth
through
the
same
,
must
bee
moveable
also
.
And
therefore
it
necessarily
followeth
,
that
after
some
certain
number
of
yeares
,
there
wil
be
no
further
use
of
these
Meridian
lines
in
the
designing
of
the
hours
in
Dialls
;
but
a
new
Meridian
line
must
be
taken
,
and
the
situation
of
the
Diall
altered
,
though
not
the
Diall
it self
.
We
may
therefore
conclude
,
that
the
Sun
Dialls
,
after
some
certain
time
,
will
prove
false
,
unlesse
the
Meridian
line
be
rectified
.
This
is
demonstrated
of
the
very
principles
of
the
Mathematitcks
.
But
besides
this
,
we
have
some
notable
instances
out
of
the
Ancients
,
which
do
manefestly
evince
,
that
after
some
tearm
of
yeares
,
Sun
Dialls
doe
not
agree
to
their
first
designations
:
all
which
I
have
diligently
collected
.
These
things
thus
demonstrated
,
I
proposed
them
to
these
Mathematicians
,
that
,
because
the
whole
businesses
of
the
Magneticall
Needle
had
dependance
upon
these
Meridians
,
they
would
consider
,
whether
or
no
,
this
doctrine
,
by
me
first
proposed
,
might
open
the
way
to
the
matter
in
hand
,
&c.
Thus
far
Let
us
now
heare
That
the
reason
(
saith
he
)
of
the
inaequality
observed
in
the
motion
of
the
fixed
Starrs
,
or
as
calls
it
,
the
Anticipation
of
the
AEquinoctiall
points
(
which
is
a
very
subtile
and
ingenious
speculation
of
his
owne
,
that
so
he
might
reconcile
and
maintain
the
inventions
of
all
that
went
before
him
)
that
this
conceit
,
I
say
,
doth
not
yeares
obseruations
of
the
Starr
called
since
his
first
observing
the
same
;
doe
manifestly
prove
.
For
in
this
space
of
time
,
the
reciprocation
of
the
AEquinoctiall
points
,
or
promotion
of
the
Starrs
,
is
swifter
,
by
much
,
then
he
conceiued
it
would
have
been
.
So
that
,
whereas
now
they
ought
to
have
finished
but
one
degree
in
an
hundred
years
space
,
or
thereabout
,
they
finished
the
same
in
the
quantity
of
the
yeares
being
not
so
slow
as
hee
imagined
it
to
be
:
as
appeares
plainly
by
that
wee
have
delivered
in
the
former
Chapter
.
For
these
two
things
do
mutually
cohere
together
in
that
when
the
quantity
of
the
yeare
is
greatest
,
the
motion
of
tho
fixed
Starrs
should
then
bee
slowest
.
But
these
things
the
accurate
observat●…
ons
of
these
present
yeares
doe
manifestly
elude
,
for
as
much
as
they
doe
not
answer
his
periodicall
restitutions
.
Thus
these
two
great
lights
of
our
times
,
to
whom
wee
may
adde
the
opinion
of
our
Country-man
who
in
his
will
have
the
praecession
of
the
AEquinoctiall
points
to
depend
upon
the
Magneticall
mot●…n
of
the
Poles
of
the
Earth
▪
And
this
is
that
as
far
as
I
can
gather
,
whom
mentions
in
his
fore-cited
Epistle
:
Vnto
whom
I
refer
you
for
satisfaction
in
this
point
,
in
his
Thales
Milesius
Franciscus
Baroccius
Polar
Starr
In
the
Torrid
Zone
the
whole
Zodiack
passeth
over
it
,
and
therefore
the
there
are
seen
to
appear
above
the
Northward
from
Ocele
Ocele
〈◊〉
distant
from
in
the
of
that
Constellation
,
is
distant
degrees
▪
Johannes
Wernerus
Peter
Nonius
The
use
of
those
tropickes
is
,
First
,
to
shew
when
the
Sun
,
in
an
oblique
Sphaere
,
is
neerest
the
verticall
point
of
any
place
,
and
so
likewise
when
the
farthest
off
.
Secondly
,
they
shew
,
when
the
Sun
,
in
his
Diurnall
motion
,
maketh
the
longest
or
shortest
dayes
in
the
yeare
.
Thirdly
,
they
are
▪
as
it
were
,
the
limits
and
bounds
,
wherein
the
Sun
finisheth
his
yearly
course
.
Fourthly
,
they
distinguish
the
Torrid
Zone
in
the
heavens
,
from
the
two
temperate
Zones
.
Strabo
,
Proclus
Leontius
Mechanicus
Machomethes
Aratensis
Johan
.
Wernerus
This
distance
of
the
Tropickes
from
the
AEquator
,
is
caused
by
the
Suns
greatest
declination
,
as
the
Astronomers
call
it
.
which
greatest
declination
of
the
Sun
hath
been
,
at
divers
times
,
found
to
be
variable
.
For
begining
as
sar
backward
,
as
possibly
we
can
,
and
so
driving
it
down
by
the
Olympiads
,
and
the
yeare
of
even
to
these
present
times
,
according
to
calculation
.
wee
find
it
to
bee
thus
,
both
in
the
degree
and
minute
,
as
is
here
expressed
in
this
ensuing
Table
.
To
which
we
may
adde
these
words
out
of
Book
of
new
Star
which
appeared
where
he
saith
,
that
by
certain
observations
it
hath
been
found
,
that
both
the
Suns
greatest
declination
,
as
also
the
other
Intermediat
by
the
same
reason
are
alter'd
,
as
it
is
testified
by
the
whole
current
of
the
most
skilfull
Artists
,
in
a
continuall
succession
of
time
:
so
that
time
,
&
some
certain
yeares
before
him
,
it
was
found
to
be
gr
▪
but
it
doth
not
appear
by
any
certain
testimony
to
have
been
ever
greater
.
Whence
may
be
collected
,
that
whome
we
have
set
in
the
first
place
,
who
assignes
gr.
speakes
with
the
largest
,
and
as
it
were
,
at
randome
,
and
(
as
our
learned
Authour
hath
also
observed
of
not
so
accurately
as
he
should
have
.
Strabo
,
Proclus
,
Cleomedes
The
Arctique
,
and
Antarctique
circles
do
shew
,
The
Poles
of
the
Zodiaque
and
their
distance
from
the
Poles
of
the
world
,
They
doe
distinguish
the
frigid
from
the
Temperate
,
and
with
the
Tropiques
and
AEquator
they
helpe
to
divide
the
whole
Heaven
into
five
parts
or
regions
which
they
call
Arabians
Azimuth
Concerning
the
moveableness
or
mutability
of
the
Arctique
,
and
Antarctique
Circles
,
reports
himself
to
be
the
first
that
observed
it
,
out
of
the
Ancient
Greek
Authors
:
as
you
may
see
in
his
Comentaries
upon
revised
,
and
published
by
himself
a
little
before
his
death
.
Neither
doth
he
think
that
any
ancient
Latine
Author
within
yeares
after
those
Greek
Writers
,
nor
scarcely
any
before
time
,
can
be
found
to
have
determined
them
to
be
immoveable
.
But
because
there
are
many
excellent
things
to
be
met
withall
in
that
pssage
of
his
,
and
that
he
sets
down
the
same
by
way
of
demonstration
;
I
have
thought
it
not
impertinent
,
seeing
our
Author
hath
given
a
touch
at
it
,
to
set
down
opin●…n
in
his
own
words
:
as
you
have
them
upon
those
verses
of
He
proceeds
after
this
manner
Let
there
be
described
(
saith
he
)
Parallel
circles
to
the
AEquinoctiall
,
and
these
will
be
the
same
that
alwayes
appearing
.
Now
among
all
those
,
That
which
toucheth
the
Horizon
in
the
point
of
intersection
of
the
Horizon
and
Meridian
,
will
be
the
greatest
of
those
that
alwayes
appeare
,
and
so
conseqvently
,
the
Circle
of
that
place
:
now
because
the
Horizons
are
moveable
,
the
Arctique
Circles
must
also
be
moveable
.
So
in
the
Climat
wherein
lies
,
the
elevation
of
the
Pole
being
thirty
six
degrees
,
determines
the
Artique
Circle
also
to
be
so
many
degrees
from
the
Pole
▪
in
like
manner
in
another
Climate
,
it
will
bee
diverse
,
according
to
the
diversity
of
the
elevation
of
the
Pole
.
Thus
(
saith
he
)
the
greatest
of
the
Circle
alwaies
appearing
is
distant
from
the
Pole
thirty
seven
degrees
:
but
that
in
thirie
sixe
degrees
:
and
look
how
great
the
Altitude
of
the
place
is
,
the
same
must
the
distance
necessarily
be
,
betwixi
the
Pole
and
that
point
,
by
which
the
Artique
circle
is
described
.
And
therefore
the
Ancient
Greekes
alwayes
defined
the
Arctique
circle
to
be
The
most
Northerne
point
that
their
Horizon
,
or
place
of
habitation
had
.
So
that
the
Artique
circle
is
nothing
else
,
but
the
pointe
of
their
habitation
which
toucheth
the
Horizon
.
For
in
describing
,
they
have
both
one
common
point
.
Only
in
this
they
differ
,
that
the
center
of
the
Arctique
circle
is
the
Pole
of
the
world
;
but
the
center
of
the
Horizon
is
the
Verticall
circle
,
or
of
the
place
As
for
example
is
the
Horizon
the
Artique
circle
the
Meridian
the
point
of
Intersection
of
the
Horizon
with
the
Meridian
;
in
which
place
also
the
Artique
and
Horizon
in
describing
doe
mutually
touch
each
other
.
the
Pole
the
Zenith
of
the
place
the
opposite
point
of
the
diameter
of
the
Actique
circle
,
Now
if
the
elevation
of
the
Pole
bee
full
degrees
,
as
it
is
at
then
the
point
will
be
the
same
with
that
is
to
say
,
the
opposite
part
of
the
Arctique
cir●…le
will
touch
the
Zenith
of
the
place
.
Ent
if
the
elevation
of
the
Pole
be
lesse
then
degrees
,
the
Zenith
will
then
fall
without
the
circle
:
but
if
it
be
greater
,
it
will
fall
within
.
S●…
that
by
this
meanes
it
will
come
to
passe
,
that
the
nearer
wee
are
to
the
AEquator
,
the
lesser
these
circles
will
bee
:
and
contrarywise
,
the
farther
we
live
off
the
AEquator
,
the
greater
they
are
:
But
under
the
AEquinoctiall
it self
,
that
is
in
a
right
position
of
Sphaere
,
there
is
no
Artique
circle
at
all
:
writes
,
that
those
that
inhabit
now
call
have
a
Tropick
for
their
Arctique
circle
.
Whether
therefore
this
Circle
fal
within
or
without
the
Tropicke
,
the
distance
of
it
from
the
poi●…t
,
Will
be
as
great
,
as
is
the
difference
betwixt
the
elevation
of
the
Pole
,
and
the
elevation
of
the
Equinoctiall
above
the
Horizon
of
the
place
.
As
for
Example
:
The
elevation
of
the
Pole
at
degrees
,
therefore
the
AEquinoctiall
is
elevated
above
the
Horizon
m.
and
the
difference
is
m.
And
therefore
the
or
verticall
point
of
m.
without
the
circumference
of
its
Arcticke
circle
.
So
this
distance
which
those
that
inhabite
gr.
as
having
their
Pole
elevated
m.
So
that
the
Trepick
with
them
toucheth
the
very
point
of
intersection
of
the
Meridian
and
Horizon
.
And
therefore
,
designes
the
Artick
circle
to
be
.
A
circle
that
alwayes
appeareth
,
and
toucheth
upon
the
skirts
of
the
Horizon
,
yet
never
goeth
under
it
.
By
these
words
hee
meaneth
the
intersection
of
the
Horizon
and
Meridian
in
the
most
Northerly
point
These
grounds
being
thus
laid
,
we
see
that
as
many
habitations
as
there
are
,
so
many
Arctick
circles
there
are
also
,
and
the
same
not
fixed
and
unchangeable
,
but
different
according
to
the
diversity
of
paces
.
So
that
,
by
this
we
may
plainly
●…erceive
the
errour
of
our
moderne
Artificers
,
who
,
in
their
Artificiall
Globes
,
describe
this
circle
contrary
to
the
doctrine
and
practise
of
the
Ancients
,
drawing
it
on
the
Poles
of
the
Ecliptique
above
the
Pole
of
the
world
.
Fur
such
an
Arctick
circle
there
cannot
be
,
but
only
to
those
that
inhabit
by
the
Nile
:
for
with
them
,
the
Pole
is
elevated
m.
These
things
considered
,
the
Arctick
circle
ought
not
to
have
any
place
in
the
Materiall
unlesse
it
be
made
for
the
inclination
of
some
certain
place
:
otherwise
there
can
be
no
such
Arcticke
circle
.
These
things
,
when
I
first
proposed
in
where
were
many
,
both
learned
and
unlearned
,
Noble
and
Paedants
,
it
cannot
be
imagined
with
with
what
scorne
and
hissing
they
entertained
them
.
And
at
length
,
when
my
constancy
would
not
give
place
to
their
stubborne
ignorance
;
I
thought
I
should
have
been
beaten
among
them
.
Yet
at
last
,
having
nothing
to
defend
themselves
with
,
they
said
,
that
,
however
it
were
,
these
circles
were
usefull
for
the
distinction
of
the
Zones
.
At
which
answere
of
theires
,
I
had
much
adoe
to
forbeare
laughing
.
For
this
division
of
the
world
into
Zones
,
is
quite
cashiered
in
these
our
times
,
when
as
the
whole
world
hath
at
length
been
fully
discovered
by
the
Navigations
of
the
And
for
this
purpose
,
to
confute
these
Mathematicians
,
I
alledged
these
words
of
therefore
did
not
,
(
saith
he
)
in
making
certain
Zones
,
which
are
to
be
limited
by
the
Arcticke
circles
:
two
of
which
line
under
the
said
Arctiques
,
and
other
terminated
betwixt
the
Arctiques
,
and
the
Tropiques
.
For
this
is
a
Maxime
:
That
determinate
things
cannot
bee
bound
by
uncertain
and
indeterminate
limits
.
This
their
Philosophy
therefore
is
vaine
and
frivelous
.
But
yet
their
impudence
ends
not
so
.
For
you
shall
hardly
meet
with
any
of
those
Mathematicians
,
that
will
not
presently
conclude
him
madd
,
that
should
but
dare
to
descend
any
whit
from
the
doctrine
of
in
the
point
of
these
circles
.
Yet
one
of
them
,
not
long
since
,
being
as
it
seemes
,
advised
thereto
by
the
former
edition
of
confesseth
by
the
way
,
and
as
it
were
unwillingly
,
that
the
Ancients
made
other
use
of
the
Arcticke
circle
s
;
then
wee
now
doe
.
And
yet
he
would
not
be
thought
to
have
learned
this
of
me
:
notwithstanding
these
kind
of
fellows
are
the
most
ignorant
in
matters
of
Antiquity
,
in
the
world
.
Who
should
be
the
first
broacher
of
this
ridiculous
conceit
,
I
cannot
guesse
,
otherwise
,
then
that
it
must
needs
bee
some
latine
Writer
,
and
thaet
yeares
later
then
any
of
the
Greeke
Authors
.
And
I
know
not
whether
any
other
taught
this
doctrine
before
ceartainely
he
is
the
most
ancient
I
can
readily
think
on
.
As
therefore
our
men
are
in
an
errour
,
in
making
the
Arcticke
to
bee
an
Immutable
circle
,
so
likewise
are
the
Ancients
,
and
those
among
us
that
follow
them
,
to
be
blamed
,
for
making
this
circle
to
be
Parallel
to
the
other
three
:
whereas
the
Parallel
circles
in
a
Sphaere
have
the
same
Pole
with
the
Sphere
it self
.
But
the
Pole
of
the
Arctique
is
the
same
alwayes
with
the
Pole
of
the
World
:
whereas
the
Pole
of
the
other
three
altereth
,
as
do
the
Tropicall
,
and
Equinoctiall
points
.
For
the
AEquinoctiall
and
Tropicall
points
doe
anticipate
their
places
in
the
Zodiaque
:
insomuch
,
that
in
a
certain
tearme
of
yeares
,
they
are
removed
forward
a
degree
.
Now
the
AEquinoctiall
,
and
Tropicall
circles
,
are
no
other
then
what
are
described
by
those
points
,
which
in
themselves
are
moveable
.
Therefore
are
their
Poles
also
moveable
.
But
wee
shall
suffer
for
these
things
too
,
I
doubt
not
,
untill
that
length
of
time
shall
have
beaten
this
into
the
heads
of
such
men
,
with
whom
strength
of
reason
is
able
to
prevaile
nothing
at
all
:
And
this
is
the
opinion
of
and
the
Ancients
,
concerning
the
Artique
circles
:
which
a
learned
man
,
in
his
hath
lately
examined
,
and
indeavonred
to
confute
the
Arctique
circle
(
saith
he
)
is
thus
described
by
The
Arctique
circle
is
the
greatest
of
all
those
circles
that
are
alwayes
in
sight
,
and
it
toucheth
the
Horizon
in
one
point
,
and
is
seen
also
above
the
earth
.
And
the
Antarctique
he
defines
thus
.
The
Antartique
is
a
circle
equall
and
Parallel
to
the
Arctique
,
and
lies
wholy
hid
under
the
earth
.
These
circles
therefore
,
in
the
opinion
of
are
moveable
,
andare
described
by
a
point
that
toucheth
the
Horizon
about
the
Pole
that
is
nearest
to
it
:
and
they
are
also
changed
,
with
the
Horizon
,
as
often
as
a
man
moveth
either
Northward
or
Southward
.
So
that
the
nearer
they
are
to
the
Pole
,
the
lesser
they
are
:
and
so
contrariwise
,
the
farther
off
they
are
from
the
same
,
the●…
are
so
much
the
greater
:
and
consequently
it
followes
,
because
they
have
no
fixed
place
,
that
therefore
they
cannot
be
described
upon
a
Sphaere
or
But
from
hence
there
ariseth
three
inconveniencies
.
First
,
that
these
Arctiques
described
by
are
not
of
any
use
in
distinguishing
the
Frigid
Zone
from
the
Temperate
,
by
reason
of
their
uncertain
situation
,
and
mutability
.
The
next
is
,
that
with
those
that
inbabite
within
twenty
three
degrees
and
an
halfe
of
the
Pole
,
(
which
is
as
much
as
the
Suns
greatest
declination
from
the
AEquator
)
the
Arctique
circle
will
bee
the
same
with
the
Tropique
of
and
the
Antartique
with
that
of
So
that
they
will
have
but
two
lesser
circles
or
Parallels
,
which
will
make
but
three
Zones
in
all
,
two
cold
ones
;
and
a
torrid
.
For
in
this
confusion
of
the
circles
,
there
will
be
no
distinction
betwixt
the
cold
,
and
the
temperate
Zones
,
And
which
is
more
,
they
that
dwell
under
the
AEquator
.
will
have
no
Arctiques
at
all
.
Lastly
there
are
certain
accidents
proper
to
,
certain
Climates
,
which
cannot
he
assigned
them
,
unlesse
there
bee
fixed
and
certain
limets
set
to
distinguish
the
cold
Zones
from
the
temperate
.
As
for
example
,
If
it
be
enquired
,
what
properties
are
incident
to
those
that
inhabite
betwixt
the
Tropique
of
and
the
Arctique
circle
:
and
what
to
those
under
the
Arctique
circle
it self
:
and
lastly
,
what
betwixt
the
Arctique
circle
and
the
Pole
of
the
World
.
To
these
questions
there
can
be
no
answere
made
without
these
fixed
Arctique
circles
.
Besides
this
,
it
would
take
away
much
light
and
futhera●…ce
,
both
from
Geographicall
Maps
,
and
Astronomicall
instruments
,
if
these
Arctique
circles
might
not
bee
described
in
them
:
Which
could
not
possibly
bee
described
in
them
,
but
that
they
might
change
evermore
with
the
Horizon
.
These
and
the
like
inconveniences
are
easily
avoided
,
by
placeing
the
Arctique
circle
,
as
usually
it
is
,
on
the
Poles
of
the
Zodiaque
.
Neither
am
I
any
way
swayed
with
the
Authority
of
adhering
to
his
Doctrine
of
the
mutability
of
the
Arctique
Circle
:
although
I
am
n●…t
ignorant
,
how
rare
a
thing
it
is
▪
for
such
Judgment
,
matched
with
so
great
knowledg
,
to
fall
into
an
errour
.
And
as
for
that
testimony
which
they
bring
out
of
that
it
is
sufficient
,
if
there
be
Arctique
circles
in
the
temperate
Climes
,
and
that
those
that
have
any
,
have
not
all
the
same
:
this
is
(
to
use
own
words
)
nothing
to
the
argument
in
hand
,
and
concludes
nothing
.
For
then
they
should
be
of
no
use
at
all
.
I
cannot
therefore
assent
to
a
man
,
whose
Tenent
is
dissonant
both
from
the
nature
of
the
thing
,
and
reason
it self
.
But
to
return
at
length
to
who
,
seeing
that
he
acknowledgeth
that
there
are
five
Zones
:
two
of
which
are
terminated
betwixt
the
Poles
,
and
the
Arctique
and
the
Antarctique
circles
:
and
other
two
bordering
upon
the
same
,
which
are
the
two
temperate
Zones
,
and
are
bounded
on
one
side
by
the
Arctique
,
and
the
other
,
by
the
Tropickes
:
betwixt
both
which
lieth
the
Torrid
Zone
.
he
himself
seems
tacitely
to
approve
these
Immoueable
Artiques
,
without
which
there
can
be
no
set
constant
limits
of
the
Frigid
and
temperate
Zones
.
Now
concerning
the
opinion
that
the
Ancientes
had
of
those
Zones
,
namely
,
that
some
of
them
were
inhabited
through
extream
cold
,
and
some
through
parching
heat
;
notwithstanding
these
are
discovered
at
length
to
be
but
vaine
dreames
,
by
the
late
Sea-voyages
both
of
the
and
our
owne
Countrimen
:
yet
can
it
not
be
denyed
,
but
that
in
each
of
them
there
are
certain
speciall
and
peculiar
Occurrences
.
So
that
,
if
,
but
for
doctrine
sake
.
it
were
good
that
these
circles
should
not
bee
taken
away
,
neither
are
wee
to
despise
it
,
if
by
the
industry
of
later
times
,
any
thing
hath
been
added
to
the
inventions
of
the
Ancients
,
which
may
any
whit
bee
usefull
for
the
instruction
of
learners
,
or
may
any
way
conduce
so
the
clearing
of
things
,
in
themselves
obscure
and
intricate
.
That
in
a
right
Sphaere
all
the
Stars
do
both
rise
and
set
that
is
,
are
all
generally
seene
above
the
Horizon
,
and
in
like
manner
doe
also
all
set
by
turnes
;
so
likewise
that
boath
the
Poles
,
both
Arctique
and
Ant●…rctique
may
be
seen
at
once
:
hath
hitherto
been
the
received
opinion
both
of
and
generally
,
of
all
other
Writers
:
whichour
Author
also
here
followeth
.
Yet
if
wee
do
but
examine
the
matter
more
nearely
,
we
shall
find
this
to
agree
not
so
much
with
the
Sensible
,
as
with
the
Rationall
or
Intelligible
Horizon
.
For
as
much
as
eve●…
in
a
Right
Sphaere
,
the
fight
can
hardly
reach
both
the
Poles
,
by
reason
of
the
extuberancy
of
the
earth
.
Which
is
also
confirmed
by
the
Testimony
of
who
in
his
history
of
his
voyage
into
the
New
world
,
whether
thus
.
Under
the
AEquinoctiall
(
saith
he
)
not
only
both
the
Poles
are
invisible
,
and
do
not
appear
,
but
neither
one
nor
other
can
be
seene
,
till
a
man
hath
passed
on
two
degrees
from
the
AEquator
.
But
whether
this
assertion
of
his
,
or
the
contrary
of
some
of
our
Countrymen
,
who
have
also
sailed
through
those
parts
,
be
to
be
accounted
the
more
accurate
and
trne
,
I
leave
to
other
to
determine
,
The
position
or
siauation
of
a
Sphaere
is
rightly
distinguished
by
our
Author
,
into
three
●…inds
,
to
wit
,
Parallel
,
Right
,
and
Oblique
.
Notwithstanding
acknowledg
onely
two
:
and
they
are
,
Right
,
and
Oblique
▪
For
if
it
be
demanded
,
(
saith
what
manner
of
Sphaere
they
may
be
said
to
have
,
that
inhabite
under
the
Poles
:
we
must
make
answer
,
an
Oblique
.
But
both
are
herein
deceived
.
For
those
that
have
such
a
position
of
Sphaere
,
as
that
they
dwell
under
the
Pole
,
the
AEquator
with
them
doth
not
make
Oblique
Angles
with
the
Horizon
:
because
the
Horizon
and
AEquator
there
,
make
both
but
one
circle
.
This
kind
of
Sphaere
therefore
may
more
rightly
be
called
a
Parallel
,
or
Neutrall
Sphaere
:
because
that
it's
Verticall
point
falleth
upon
the
Pole
of
the
Sphaere
.
hath
given
it
the
aptest
appellation
of
all
,
in
his
Notes
,
upon
upon
these
Verses
Where
he
saith
,
that
every
Sphaere
may
be
said
,
either
to
lye
,
sit
,
or
stand
.
So
that
the
first
position
of
Sphaere
is
,
as
of
lying
all
along
,
which
is
that
of
a
Right
Sphaere
,
where
the
Horizon
makes
right
Angles
with
the
AEquinoctiall
.
The
seeond
is
of
sitting
,
The
third
is
of
standing
and
is
like
a
Mill.
for
in
this
Position
,
the
AEquinoctiall
,
supplying
the
office
of
the
Horizon
,
and
as
it
were
,
turned
round
about
,
is
just
like
a
Hand-mill
,
both
in
habit
,
and
manner
of
turning
about
,
But
we
cannot
so
properly
call
it
a
Right
Sphaere
because
of
the
right
Angles
that
it
makes
with
the
AEquinoctiall
,
as
passing
through
it's
Poles
:
because
that
that
appellation
seemes
to
suit
more
fitly
with
a
standing
Sphaere
,
in
which
the
AEquinoctiall
is
the
same
with
the
Horizon
and
Arctique
circle
.
Lastly
there
is
but
one
Right
,
or
Lying
Sphaere
because
there
is
but
one
AEquinoctiall
:
and
there
are
but
two
standing
Sphaeres
;
because
there
be
but
two
Poles
.
But
there
is
great
variety
and
diversitis
of
Oblique
;
or
sitting
Sphaeres
,
as
may
manifestly
appear
to
any
man
;
and
as
our
Author
hath
declared
at
large
,
Theon
Alexandrinus
Torrid
Zone
(
Nicolaus
Lyranus
,
Thomas
Aquinas
,
Whereas
our
Author
accuseth
of
inconstancy
,
in
that
in
his
hee
accounteth
it
a
fahle
,
rather
then
any
true
,
history
whatsoever
is
reported
of
the
in
hahitants
under
the
AEquator
:
where
as
in
his
he
seemeth
to
contradict
the
same
:
I
think
that
also
is
not
free
from
the
like
fault
.
For
whereas
in
his
having
discoursed
of
the
M●…gnitude
of
the
Isle
(
which
is
now
thought
to
be
and
lyeth
directly
under
the
line
,
)
out
of
he
presently
adds
,
that
besides
the
testimony
of
the
Antients
,
the
had
better
knowledg
of
the
same
,
in
the
time
of
the
Em●…eror
there
being
Embassadors
sent
from
thence
to
who
among
other
things
,
should
relate
,
that
with
them
Gold
,
&
Silver
was
in
high
account
,
and
that
they
had
greater
wealth
then
the
themselves
;
but
yet
that
the
had
greater
use
of
riches
,
then
they
.
Which
words
of
with
many
other
there
at
large
set
down
by
him
,
if
they
be
but
compared
with
what
himself
elsewhere
writeth
,
in
his
he
will
be
found
manifestly
to
contradict
himself
.
For
disputing
in
this
place
,
and
inquireing
,
how
great
a
part
of
the
earth
is
inhabited
:
(
saith
he
Three
parts
of
the
world
the
Heaveus
have
robbed
us
of
;
to
wit
,
the
Torrid
,
or
middle
Zone
,
●…bat
is
,
whatsoever
lieth
betwixt
the
two
Tropiques
:
and
the
two
outmost
or
Frigid
Zones
:
that
is
to
say
,
whatever
ground
lieth
betwixt
either
Pole
,
and
the
Arctique
and
Antarctique
circles
.
According
to
that
which
the
Poët
sung
of
old
:
For
this
is
that
which
meaneth
:
that
those
two
outwardmost
are
not
habitable
,
by
reason
of
extremity
of
●…old
,
nor
the
other
,
through
too
violent
heat
.
But
that
which
is
more
to
be
wondred
at
in
so
great
an
Author
,
(
who
not
withstanding
indifferently
took
up
aswel
the
common
popular
fables
,
as
the
extravagant
fixions
of
the
Poëts
also
)
is
that
which
he
very
confidently
relates
out
of
how
that
one
taking
Ship
in
the
gulf
,
came
as
farr
as
the
two
Isles
upon
the
confines
of
Which
voyage
if
we
should
but
throughly
examine
,
wil
be
found
to
be
as
much
,
〈◊〉
that
all
the
and
our
Countrymen
at
this
day
performe
in
their
Sea
voyage
to
the
East
when
as
touching
upon
the
hope
,
they
twice
crosse
the
line
,
and
passe
through
the
whole
Torrid
Zone
.
Not
to
speak
any
thing
of
that
which
he
writes
in
his
first
book
,
twenty
third
Chapter
,
Namely
,
that
there
is
never
a
yeare
,
that
doth
not
suck
out
of
the
Empire
,
at
the
least
Sestercies
,
by
sending
in
such
commodities
,
as
they
sell
to
the
for
an
hundred
times
as
much
as
they
are
worth
in
And
that
there
is
yearly
Traffique
by
Shippe
through
the
Red
Sea
,
betwixt
them
and
the
who
are
saine
,
for
their
safer
passage
,
to
defend
themselves
from
Pirats
,
by
going
provided
with
bands
of
Archers
.
And
here
,
all
that
can
be
said
in
defence
,
is
,
tha●…those
things
which
he
relates
in
this
second
book
,
were
written
by
him
long
before
the
rest
which
followeh
:
and
that
at
that
time
,
these
voyages
were
not
so
frequently
undertaken
,
or
the
passages
so
well
known
unto
the
especially
,
for
that
in
the
bookes
following
,
as
namely
the
sixth
book
Chapters
he
saith
,
that
the
whole
course
of
the
voyage
from
began
but
then
first
to
be
discovered
,
when
as
he
was
writing
the
same
:
and
that
having
not
long
before
begun
a
description
of
reckoned
up
therein
great
rivers
,
and
Nations
,
to
be
contained
within
the
same
.
The
principall
cause
of
the
habitablenesse
and
fortility
of
the
parts
under
the
Torrid
Zone
,
i●…
,
in
that
the
Sun
shineth
upon
them
but
houres
:
so
that
the
nights
beeing
alwayes
as
long
as
the
daies
,
the
coldnesse
of
the
one
doth
very
much
attemperate
the
excessive
heat
of
the
other
.
In
like
manner
,
that
both
the
Frigid
Zones
are
habitable
,
is
to
be
attributed
to
the
Sun
,
which
in
his
course
,
through
the
six
Northern
signes
of
the
Zodiaque
,
never
sets
in
six
months
space
so
those
that
live
under
degrees
of
latitude
:
so
that
by
his
continuall
presene●…
the
extream
rigidity
of
the
Clime
i●…
mitigated
,
and
the
cold
,
by
this
meanes
,
dispelled
.
Zone
is
therefore
two
,
fold
either
Northern
or
Southern
.
The
Northern
is
comprehended
betwixt
the
Tropique
of
and
the
Artik
circle
:
and
●…s
called
because
that
in
it
the
Sun
beames
,
at
noon
,
are
alwayes
cast
to
that
part
only
that
byoth
toward
the
●…ole
Articks
The
Southern
containeth
all
that
space
of
ground
that
lieth
betwixt
the
Tropique
of
and
u●…e
Antarctique
circle
,
And
it
is
call●…d
because
the
Noon
shadowes
are
proje●…ed
toward
the
South
Pole
only
.
The
properties
of
these
severall
Zones
are
these
that
follow
.
First
,
they
that
inhabit
the
midst
of
the
Torrid
Zone
,
are
in
a
Right
Sphaere
:
for
with
them
,
both
the
Poles
of
the
world
lie
in
their
Horizon
:
and
their
Zenith
or
Verticall
point
falleth
in
the
AEquinoctiall
Circle
.
So
that
their
peculiar
Accidents
are
these
.
First
,
All
the
S●…arres
do
rise
and
set
in
an
equall
space
of
time
,
except
the
Arctique
and
Antarctique
Poles
:
as
we
have
demonstrated
out
of
in
our
notes
upon
the
third
Chapter
.
Secondly
,
They
have
a
perpetuall
AEquinoxe
.
Thirdly
,
They
have
the
Sun
verticall
unto
them
twice
in
a
yeare
,
namely
,
when
hee
entered
into
♈
and
♎
Fourthly
,
In
the
Suns
periodicall
motion
through
the
Zodiaque
,
look
how
much
he
goeth
Southward
from
their
Zenith
,
in
his
returne
hee
declines
as
farr
northward
from
the
same
.
Fi●…thly
,
They
have
soure
Solstices
;
two
when
the
Sun
is
in
their
Zenith
and
AEquinocti●…ll
points
:
and
two
Collaterall
,
when
he
is
in
the
Solsticiall
points
.
Sixthly
,
They
have
two
summers
every
yeare
,
when
the
Sun
is
in
the
AEquinoctioll
points
:
and
two
,
as
it
were
,
Winters
,
when
the
Sun
declineth
to
either
Tropiqu'
.
Seventhly
,
They
have
five
different
kindes
of
shadows
:
to
wit
,
Eastward
,
Westward
,
Northward
,
Southward
,
and
Perpendicular
.
And
therefore
the
Inhabitants
of
this
Zone
are
called
that
is
to
say
,
having
their
shadowes
cast
on
both
sides
:
The
properties
os
those
that
inhabit
toward
the
utmost
border
of
the
Torrid
Zone
,
and
being
os
the
Northern
Temperate
,
whi●…h
have
an
Oblique
Sphaere
,
(
for
the
Arctique
Pole
with
them
is
elevated
twenty
three
degrees
and
an
halfe
,
and
their
Zenith
fall
th
on
the
Troqi●…ue
of
are
these
following
.
Fi●…st
,
All
those
Starrs
that
are
comprehended
within
the
compasse
of
the
Arctique
Circle
,
are
alwaies
above
the
Horizon
:
and
contrariwise
,
those
within
the
Circuite
of
the
Acctique
alwayes
lye
hid
.
But
if
the
intermediate
Starrs
,
those
that
are
Northward
from
the
AEqnator
,
or
a
longer
time
above
the
Horizon
,
then
they
are
under
it
:
in
like
manner
,
as
the
other
that
decline
more
Southward
,
their
Nocturnall
Arch
is
greater
then
the
Diurnall
:
onely
those
in
the
line
itself
,
do
rise
and
set
in
an
equall
space
of
time
.
Secondly
,
Their
Artificiall
dayes
and
nights
are
unequall
.
Thirdly
,
The
Sun
is
in
their
Zenith
but
once
in
the
yeare
,
and
that
is
in
the
beginning
of
so
that
it
never
ascends
more
Northward
,
but
at
all
other
times
is
Southward
to
them
.
Fourthly
,
They
have
two
Solstices
:
one
,
when
the
Sun
is
in
the
begining
of
which
is
their
Verticall
point
:
and
the
other
when
the
Sun
entereth
into
the
begining
of
at
which
time
the
Sun
hath
the
least
elevation
.
Fifthly
,
They
have
also
but
one
Summer
and
one
Winter
.
They
have
foure
differences
of
shadows
,
namely
,
Eastern
,
Western
,
Northern
,
and
Perpendicular
.
And
here
is
the
beginning
of
the
They
that
dwell
on
the
Oblique
Sphaere
,
so
that
the
Arctique
Pole
is
elevated
with
them
above
degrees
,
an
an
halfe
,
but
lesse
then
degrees
,
and
an
half
:
their
Zenith
or
Verticall
point
alwayes
falleth
betwixt
the
Tropique
of
and
the
Arctique
Circle
:
whence
they
have
these
properties
.
First
,
Very
many
Stars
with
them
are
never
observed
to
set
:
for
the
higher
the
Pole
is
elevated
,
the
more
Stars
there
are
which
alwaies
appear
;
and
so
,
in
like
manner
,
there
are
as
many
in
the
opposite
Haemisphaere
that
never
rise
.
Secondly
,
Their
Artificiall
dates
and
nights
are
equall
.
Thirdly
,
The
Sun
is
never
in
their
Verticall
point
:
but
is
alwayes
at
Noon
Southward
from
them
.
Fourthly
,
They
have
one
Summer
,
and
one
Winter
,
and
two
Solstices
.
Fifthly
,
They
have
also
three
different
kinds
of
shadows
,
as
namely
,
Eastward
,
Westward
,
and
Northward
.
Whence
they
are
called
Those
that
inhabit
about
the
end
of
the
Northern
temperate
Zone
,
have
the
Pole
Arctique
elevated
with
them
degrees
and
an
halfe
:
so
that
their
Zenith
falleth
on
the
Arctique
circle
:
whence
they
have
these
properties
of
Sphere
.
All
the
Starrs
that
lye
within
the
Tropique
of
and
the
Pole
Arctique
are
of
perpetuall
Apparition
:
and
contrarywise
,
those
that
are
comprehended
within
the
Opposite
circle
,
are
never
seen
to
rise
.
When
the
Sun
is
in
the
begining
of
the
Artificial
day
is
with
them
twenty
foure
hours
in
length
:
and
so
likewise
when
the
Sun
entreth
into
the
nights
are
as
long
The
Sun
,
at
noon
,
is
alwayes
Southward
to
them
:
but
when
he
is
in
the
begining
of
and
is
near
the
very
Horizon
,
he
then
seemes
,
in
a
manner
,
to
be
Northward
.
They
have
two
Solstices
,
and
one
Summer
,
and
one
Winter
.
They
have
foure
differences
of
shadows
:
as
namely
,
Eastern
,
Western
,
Southern
and
Northern
also
,
especially
when
the
Sun
entereth
into
the
begining
of
About
these
parts
the
end
,
and
the
Those
that
inhabit
about
the
middle
of
the
Northern
Frigid
Zone
,
have
a
Parallel
or
standing
Sphaere
:
for
the
AEquinoctiall
is
their
Horizon
,
whence
they
have
consequently
these
properties
No
Starrs
either
rise
ar
set
at
all
:
but
whatsoever
are
circumscribed
within
the
AEquinoctiall
circle
and
the
very
Pole
,
are
carried
about
in
circles
Parallel
both
to
the
AEquinoctiall
and
Horizon
.
For
the
space
os
months
they
haue
one
continued
day
,
the
Sun
in
this
space
finishing
his
course
through
the
Northern
signes
of
the
Zodiaque
,
and
so
likewise
while
he
is
in
the
opposite
meridionall
signes
,
they
have
a
night
of
the
same
length
.
They
have
but
one
Solstice
,
and
that
is
,
when
the
Sun
entereth
into
the
begining
of
They
have
one
Winter
and
one
Summer
,
or
rather
instead
of
a
Summer
they
have
some
certain
small
remission
of
the
extremity
of
cold
.
Their
shadows
are
carried
round
about
them
in
à
circle
toward
every
part
of
the
world
:
whence
they
are
called
that
is
to
say
,
having
their
shadows
carried
round
about
in
a
circular
forme
.
These
are
the
properties
of
the
Northerne
Zones
;
which
if
they
be
referred
to
the
opposite
meridionall
parts
also
,
you
have
their
properties
likewise
.
For
whatsoever
is
said
of
one
Hemisphaere
,
the
same
is
also
to
be
understood
of
the
other
opposite
Hemisphaere
,
only
in
a
contrary
sense
.
For
when
these
that
dwell
in
the
Septentrionall
Hemisphaere
,
have
their
longest
day
,
the
opposite
inhabitants
in
the
meridionall
part
of
the
world
have
their
shortest
:
and
when
they
have
their
Summer
,
with
those
it
is
then
winter
,
&c.
And
the
same
is
also
to
be
understood
of
the
other
Accidents
also
,
concerning
their
shadows
,
the
rising
and
setting
of
the
Starrs
,
and
the
li●…e
.
Perioeci
,
Antoeci
Coelestiall
Globe
Almagest
,
lib.
The
Starrs
are
divided
into
Planets
,
or
wandring
Starrs
,
and
fixed
:
not
as
if
these
were
indeed
fixed
in
one
certain
place
,
and
altogether
without
motion
,
and
the
other
only
moveable
and
erraticall
:
but
these
appellations
are
onely
given
then
comparatively
;
in
which
sence
also
they
are
to
be
understood
.
For
seeing
that
the
fixed
Starrs
were
observed
alwayes
to
keep
the
same
places
in
the
eighth
Sphaere
,
and
the
same
distance
from
each
other
:
notwithstanding
that
they
are
alwayes
in
continuall
motion
,
caused
by
the
vertue
of
the
first
Moveable
,
which
carrieth
them
about
in
the
space
of
twenty
foure
hours
.
But
the
Planets
,
besides
this
motion
,
have
a
proper
motion
of
their
owne
,
so
that
they
keep
neither
their
the
same
distance
from
the
fixed
Starrs
,
nor
yet
the
same
aspect
to
each
other
:
for
these
reasons
were
the
one
called
Fixed
,
and
the
other
Planets
.
For
otherwise
if
the
Planets
be
considered
severally
,
each
one
by
himselfe
,
there
is
nothing
more
certain
then
their
periodicall
motion
.
So
that
alluding
hereto
,
would
have
the
Planets
to
bee
called
Julius
Higinus
,
Stella
Solis
The
Mother
of
the
Gods
:
)
Pythagoras
Samius
m
Alphonsus
m.
Ptolomy
m.
Alphonsus
sec.
Copernicus
Julius
Scaliger
Besides
the
Eccentricities
of
the
Planets
,
it
is
worth
our
paines
also
to
observe
their
Magnitudes
:
And
this
consists
especially
in
the
knowledge
of
their
Diameters
,
and
what
proportion
they
beare
to
each
other
.
For
the
Diameter
of
a
Planet
,
compared
to
the
Diameters
,
of
the
Earth
,
is
after
this
,
manner
following
.
The
Diameter
of
the
Sun
compared
to
the
Diameter
of
the
Moon
,
beareth
the
same
proportion
,
that
is
betwixt
And
now
that
which
is
said
may
be
demonstrated
by
an
example
:
let
us
suppose
the
Diameter
of
the
Sun
,
in
proportion
,
to
the
Diameter
of
the
Earth
,
to
be
(
as
is
already
shewed
)
as
The
Cube
therefore
of
the
Sun
is
and
the
Cube
of
the
Earth
.
Now
these
Diameters
being
multiplied
cubically
and
thae
greater
Cube
divided
by
the
lesse
,
the
difference
of
their
severaell
will
appear
.
For
if
you
multiply
there
ariseth
which
number
being
multiplyed
again
by
the
whole
will
be
So
likewise
multiply
cubically
,
that
is
to
say
,
by
it selfe
,
and
there
riseth
which
being
again
multiplied
by
ariseth
to
Now
divide
the
greater
Cube
and
the
product
will
be
which
is
the
difference
of
the
of
the
Sun
and
the
Earth
.
Ptolomy
,
Copernicus
Ptolomy
Alfraganus
Berenices
Haire
Antinous
.
Germanicus
Coesar
Festus
Avienus
Rufus
Julius
Higinus
The
man
that
holdeth
it
South
Crown
Theon
,
Aratus
Julius
Higinus
Julius
Higinus
Greekes
.
Pliny
Timochares
,
Aratus
That
which
is
written
of
is
not
to
be
understood
any
further
,
then
touching
the
distinction
of
the
Starrs
of
the
first
,
second
,
and
third
magnitude
.
For
so
in
his
Commentaries
upon
the
(
saith
he
)
wrote
of
the
Signes
,
and
reckoned
up
how
many
bright
Stars
,
how
many
of
the
second
degree
of
light
,
and
how
many
obscure
Stars
there
were
in
each
constellation
,
For
otherwise
,
that
the
Stars
were
known
by
the
same
names
yeares
before
may
be
proved
cut
of
who
in
his
saith
thus
It
is
not
(
saith
hee
)
yeares
yet
,
since
Greece
first
began
to
number
the
Starrs
,
and
to
give
them
certain
Appellations
,
Now
we
know
,
was
put
to
death
by
the
command
of
in
the
yeare
after
lived
not
above
yeares
before
in
the
time
of
also
whom
reporteth
to
have
married
daughter
,
mentioneth
these
names
if
wee
may
trust
St.
translation
in
this
case
,
cap.
Who
maketh
(
saith
he
and
the
Starrs
in
the
remo●…st
parts
of
the
South
.
So
likewise
the
Prophet
Seeke
ye
him
that
made
the
Now
it
is
probable
,
that
there
were
two
kinds
of
men
,
that
reduced
the
Starrs
into
constellations
:
and
these
might
probably
be
Husbandmen
,
and
Mariners
.
The
Husbandmen
perhaps
might
make
these
,
to
wit
:
the
in
the
the
young
the
little
all
which
,
are
names
used
also
by
Of
the
Mariners
,
the
and
the
like
names
seem
to
have
been
invented
,
according
to
that
of
in
the
first
of
his
Georgickes
.
T.
May.
And
now
to
whom
do
those
other
new
Constellations
above
the
Antartick
Pole
,
we
their
now
so
well
known
names
but
to
the
Sea-faring
men
?
Neither
are
those
men
at
all
to
be
regarded
,
that
condemne
these
usual
names
of
the
Starrs
,
and
Constellations
,
as
unfit
to
be
used
by
Christian
men
.
For
seeing
they
are
now
used
,
without
the
least
shew
of
superstirion
,
and
that
there
is
very
great
necessity
of
these
Appellations
,
in
as
much
as
without
them
there
could
be
no
agreement
or
accord
in
these
Arts
and
cience
(
for
these
very
names
are
used
all
the
world
over
,
where
ever
the
same
Arts
are
taught
or
professed
)
I
see
no
reason
but
that
we
may
lawfully
use
these
names
,
til
such
time
as
,
the
true
names
,
wherewith
the
great
Creator
of
all
things
,
at
the
first
called
every
Star
as
witnesseth
in
the
be
made
known
unto
us
.
As
concerning
the
practise
of
the
who
rejected
these
humane
figures
,
having
substituted
in
their
places
the
forme
of
Beasts
:
you
may
read
in
his
Commentaries
upon
Now
as
we
have
already
shewed
,
how
by
comparing
the
Diameters
of
the
Planets
,
with
the
Diameter
of
the
Earth
,
their
magnitude
may
bee
known
:
in
like
manner
also
,
may
the
magnitude
of
the
fixed
Sttarrs
be
found
out
:
as
may
be
seene
by
this
scheme
.
More
over
concerning
those
other
fixed
Starrs
about
the
Southern
Pole
,
which
were
unknown
to
and
the
Ancients
,
and
now
of
late
yeares
discovered
by
the
wee
shall
set
down
their
names
also
in
their
due
place
.
Jacobus
Christmannus
Arabique
Epitome
Ptolomies
Almagest
Prutenicke
Tables
Erasmus
Reinholt
You
may
also
see
in
his
Commentary
upon
And
above
all
the
rest
who
in
his
book
of
the
New
Starrs
that
appeared
in
the
yeare
hath
proposed
tables
of
the
longitude
and
latitude
of
all
the
fixed
Starrs
that
can
conveniently
be
seen
in
these
Climates
,
according
to
his
owne
most
accurate
observations
:
as
you
may
see
in
the
aforenamed
book
,
and
so
forward
Erosmus
Reinholt
Victorinus
Strigelius
Ursa
Minor
Dub
Alasgar
lesser
Bear
Vrsa
Major
Great
Beare
Dub
Alacher
Alfonsines
,
Aliare
Scaliger
,
Aliath
Arabians
,
Beneth
As
Phoenicians
Phicares
Alsamech
,
Alramech
Somech
haramach
There
is
mention
made
of
also
in
cap.
9.
verse
.
9.
according
both
to
translation
,
and
also
the
Greeke
translation
of
the
70.
as
we
have
noted
already
.
But
in
the
Hebrew
text
it self
,
it
is
called
from
the
root
which
signifieth
in
his
observeth
that
is
also
called
sometimes
Orion
:
according
to
that
of
In
Which
signification
in
his
notes
upon
his
Asterismes
,
thinkes
it
is
here
to
be
taken
.
Sometimes
also
the
whole
Constellation
of
is
called
from
the
Greek
word
a
Bear
,
and
which
is
the
same
that
a
Keeper
:
as
observes
.
Now
that
the
Hebrewes
call
by
a
word
signifying
a
congregating
,
or
gathering
together
,
the
reason
I
take
to
be
,
because
he
hath
the
great
Bear
joyned
to
him
.
For
this
Star
standeth
behind
the
taile
of
the
great
Bear
,
whence
it
seemeth
to
have
it's
name
,
the
keeper
of
the
Bear
,
whence
Corona
Borea
Arabians
,
Aclilaschemali
Alcheti
hale
rechabateb
Nesses
:
Marsic
,
Reclinatorium
Falling
Vulture
Deneb
Adigege
And
here
,
in
this
place
,
it
is
worth
our
noting
that
there
was
a
new
Star
observed
in
the
breast
of
the
Swan
,
in
the
yeare
one
which
set
many
Mathematicians
on
work
and
among
therest
,
besides
Engineer
to
the
Emperor
and
others
also
,
who
had
some
time
been
Scholler
,
put
forth
a
Mathematicall
Tract
of
it
.
when
it
had
now
continued
in
the
same
place
of
that
constellation
for
the
space
of
years
,
being
a
Starr
about
the
third
Magnitude
.
Dha●…
Aleursi
Scheder
,
Scaliger
Seder
There
was
another
new
Star
also
appared
in
being
as
great
as
a
Starr
of
the
first
Magnitude
,
in
the
year
and
it
lasted
Months
.
Of
which
Star
there
were
divers
opinions
amongst
Astronomers
:
yet
they
all
agreed
in
this
,
that
it
was
placed
in
the
seat
of
in
the
very
Skie
,
and
in
and
those
that
had
observed
it
more
accurately
)
&
among
the
rest
,
the
noble
Brahe
,
who
also
wrote
a
large
Volume
of
the
same
,
full
of
most
accurate
observations
did
a●…
of
them
unanmiously
confess
that
they
could
not
perceive
that
it
had
any
at
●…all
,
nor
yet
distinguish
any
difference
betwixt
its
True
and
Apparant
place
;
and
also
added
,
that
it
alwayes
kept
the
same
situation
in
the
Eight
Sphaere
whence
they
manifestly
are
refuted
,
who
deny
that
there
hath
ever
any
new
Starr
risen
in
the
heavens
since
the
first
Creation
:
among
which
is
as
may
appeare
in
his
testifieth
)
was
observed
by
to
have
been
generated
in
the
very
Skie
it self
in
his
time
.
For
where
as
the
same
thinkes
,
that
the
Star
which
appeared
at
our
Nativity
,
was
either
some
Comet
,
or
else
some
one
of
the
Ordinary
Starrs
,
whichr
at
that
time
kept
an
extraordinary
course
in
its
motion
:
the
first
of
these
cannot
be
granted
;
because
it
is
expresly
called
a
star
:
neither
is
the
second
of
any
force
becaase
,
it
is
not
probable
,
that
the
who
were
so
skilfull
in
the
knowledg
of
the
Starrs
,
should
be
so
much
deceived
as
to
mistake
an
old
star
that
had
only
changed
its
place
,
for
a
new
one
.
Neither
yet
do
we
believe
this
to
be
the
same
that
is
said
to
have
observed
in
his
time
,
or
this
other
,
which
,
as
we
have
said
.
was
seen
but
rather
that
it
was
a
different
star
from
both
.
For
further
satisfaction
whereof
,
I
refer
my
reader
to
Perseus
,
Chamil
Ras
Algol
Ras
Algol
Rosch
hassatan
Memassich
Alhanam
Hoedi
Kids
Scaliger
,
Sadateni
Cleostratus
Tenedius
Higixus
reporteth
Aquila
Alhhakkab
flying
Vulture
There
was
also
discovered
a
new
Starr
in
the
foot
of
the
Serpent
.
bearer
,
which
might
have
been
reckoned
among
the
Stars
of
the
third
magnitude
.
It
began
first
to
appeare
about
in
the
yeare
aforesaid
,
and
about
the
yeare
following
,
being
it
vanished
out
of
fight
wrote
a
Book
of
this
Star
also
,
unto
whom
you
may
have
recourse
for
further
satisfaction
.
Kasam
Alfar●…
Aifaro●…
Alath●…m
Seat
Alfras
,
Br●…hium
equi
Enif
Alfaras
Almara
Al●…sela
〈◊〉
,
quae
non
est
experi●…
〈◊〉
Scaliger
,
Mizar
Among
all
these
constellations
in
the
Northerne
Hemisphaere
,
which
are
in
all
there
are
but
three
Stars
onely
of
the
first
Magnitude
.
The
first
of
which
is
that
in
the
left
shoulder
of
or
the
Waggoner
,
called
in
Latine
The
second
is
the
bright
Star
in
the
and
the
third
is
betwixt
the
legs
of
Now
the
whole
number
of
Stars
in
this
part
of
the
Heavens
,
reckoning
in
these
also
which
are
of
the
magnitude
,
with
the
obscure
and
cloudy
ones
also
,
ariseth
to
Hain
Altor
Hero
Mechanicus
Thales
Milesius
words
in
that
place
do
not
seeme
to
carry
any
such
sense
simply
,
seeing
that
he
addes
the
same
also
of
the
Bear
.
His
words
are
these
in
his
Where
speaking
of
certain
Embassadours
that
came
from
the
Isle
he
saith
They
wondered
to
see
the
Beare
.
and
the
seven
Stars
withus
,
〈◊〉
if
they
had
b●…
〈◊〉
in
a
new
world
.
And
●…tainely
if
bee
situated
under
the
very
Li●…e
,
this
then
,
for
that
very
reason
we
alledged
before
on
the
〈◊〉
of
had
been
no
such
strange
●…ter
,
is
it
had
been
spoken
of
the
only
.
Neither
had
written
any
so
absurd
●…on
,
if
he
had
said
thus
.
In
the
meane
time
I
could
wish
,
that
Authors
would
〈◊〉
nothing
in
their
bookes
,
without
〈◊〉
examination
:
although
I
am
not
ignorant
,
that
it
is
not
strange
to
find
fa●…ring
,
〈◊〉
and
then
,
in
these
kind
of
things
.
〈◊〉
〈◊〉
Scaliger
Cale
Alased
Deneb
Alased
Virgo
,
Hazimeth
Al●…acel
Mizan
Aliemin
Libra
dextravel
meridionalis
Zubeneschi
mali
Denob
Algedi
Among
all
the
Constellations
reckoed
up
by
the
Author
in
this
and
the
precedent
chapters
,
there
are
only
found
Stars
of
the
first
Magnitude
.
The
first
of
which
,
is
the
the
second
the
third
the
fourth
and
the
fifth
and
last
,
is
a
star
about
the
month
of
the
south
Fish
.
The
rest
are
all
either
of
the
Magnitude
,
beside
some
certain
cloudy
ones
;
which
are
reckoned
in
all
to
be
Monkar
Elkaitos
Boten
Elkaitos
Deneb
Elkaitos
Ied
Algeuze
Bed
Elgeuze
Bet
Elgeuze
Alfonsines
Bellatrix
Rigel
Algeuze
In
the
there
is
mention
made
of
as
we
said
before
.
Now
the
word
in
the
Originall
is
which
signifieth
Madnesse
;
Rage
,
and
Instability
:
and
it
is
so
called
perchance
,
because
that
when
this
Constellation
riseth
with
the
Sun
,
it
causeth
great
store
of
tempestuous
weather
in
all
places
:
whence
it
is
stled
by
the
Poëts
,
Now
we
must
note
,
that
this
word
in
Hebrew
,
(
which
is
rendred
and
others
)
doth
answere
to
the
Arabique
word
which
signifieth
likewise
a
Bold
or
Furious
fellow
as
our
Author
saith
.
In
like
manner
there
is
mention
made
of
again
in
the
Canst
thou
bind
the
sweet
inflences
of
the
Pleiades
,
or
loose
the
bands
of
Orion
?
notwithstanding
,
Interpreters
do
not
all
agree
in
rendering
this
plaee
.
Look
also
in
the
Prophet
calls
this
River
these
verses
of
his
The
other
part
relates
of
fruitfull
Nile
,
Whose
swelling
streames
enrich
the
Pharian
I
le
.
also
hath
an
elegant
of
the
same
in
his
where
be
speakes
thus
relating
it
,
as
of
a
River
that
should
spring
out
in
the
Heavens
,
from
under
Alcheleb
Alachbar
Alsahare
aliemalija
Scera
,
Scaliger
Alcheleb
Alasgar
Alsahare
alsemalija
There
is
extant
a
noble
witty
Epigram
in
of
the
Coelestiall
,
Terestriall
and
Marine
Dogs
;
which
may
have
reference
to
this
place
also
,
if
so
be
that
,
it
be
presented
in
it's
proper
meaning
after
this
manner
.
At
once
a
Hare
came
lightly
tripping
o're
The
sandy
banks
of
the
Trinacrian
shore
:
A
Dog
fish
caught
her
.
Where
at
she
replies
.
Land
,
Stars
,
and
all
are
still
mine
enemies
In
which
place
in
the
second
verse
,
signifieth
a
Yet
this
place
hitherto
hath
commonly
gon
thus
,
&c.
without
any
sense
at
all
.
Now
the
Poët
in
this
place
useth
this
word
in
●…ation
of
who
first
of
all
Latine
Authors
,
rendred
as
manifestly
appeareth
out
of
his
translation
of
into
Latine
verse
Ar●…as
Montanus
Benjamin
Tudelensis
Geogra
.
lib.
Crow
,
Algorab
Almugamra
:
Bassus
Corona
Australis
Alachil
Algenubi
Ahaut
algenubi
in
Phom
Ahut
A●…megest
.
lib.
This
part
of
the
Heavens
hath
in
it
Stars
of
the
first
Magnitude
,
whereof
the
first
is
in
the
right
shoulder
of
the
second
,
in
his
left
scot:
the
third
,
in
the
end
of
the
River
the
fourth
,
in
the
mouth
of
the
great
Dog
,
which
they
call
the
sifih
,
in
the
thigh
of
the
Little
Dog
,
called
the
sixth
,
is
in
the
ship
and
the
seventh
is
in
the
right
foot
of
the
To
which
we
may
add
of
the
second
magnitude
.
of
the
third
of
the
fourth
of
the
fifth
of
the
sixth
and
one
cloudy
one
.
All
which
are
in
the
generall
,
Now
the
whole
Firmament
,
reckoning
in
the
Northern
and
Southern
Hemi
phaeres
together
with
th
Zodiaque
,
co●…taineth
in
all
Stars
,
which
make
up
Aste●…ismes
or
Constellations
.
Neither
did
either
before
him
,
know
any
more
then
these
.
Notwithstanding
as
our
Author
hath
advertised
before
in
the
second
Chapter
,
made
the
number
of
Stars
and
Constellations
a
great
deal
larger
But
of
this
wee
shall
spe●…k
more
in
the
end
of
the
next
Chapter
.
And
concerning
those
Constellations
,
which
have
been
more
lately
observed
about
the
South
Pole
by
the
and
by
them
named
,
we
intend
to
speak
something
in
the
end
of
t●…o
Chapter
following
.
Lynceus
:
Promontorium
Sacrum
Posidonius
.
Alsraganus
Franciscus
Patricius
Senensis
Americus
Vespuccius
Andreas
Corsalius
Auditum
admissi
risum
teneatis
Andreas
Corsalius
Magellanes
Clouds
The
names
of
the
Constellations
of
the
Southerne
Hemisphaere
as
they
have
been
now
lately
observed
,
and
named
by
the
and
others
,
are
these
.
The
situated
in
the
very
Pole
of
the
Ecliptique
;
the
Pye
.
All
which
are
accurate●…y
portraited
in
the
Globes
set
fourth
by
Among
all
these
there
are
no
Stars
,
of
the
first
Magnitude
,
hut
of
the
seven
:
of
the
six
:
of
the
thirty
five
:
of
the
fifty
six
;
of
the
eleven
:
with
six
unsormed
,
and
two
clowdy
Stars
,
besides
the
two
cloudes
themselves
.
Now
,
the
whole
number
of
the
Stats
in
this
Southerne
part
,
beside-the
cloudy
ones
,
is
which
being
added
to
the
whole
sum
will
b●…e
Of
which
were
reckoned
before
,
by
our
●…uthor
,
out
of
onely
there
is
a
scruple
cast
in
our
way
by
those
words
of
in
his
And
this
opinion
(
sa●…th
he
)
is
seconded
also
by
the
vast
n●…sse
and
immensity
of
the
Heavens
which
is
distinguished
into
Signes
,
all
which
are
the
resemblances
either
of
living
creatures
,
or
other
things
,
according
as
they
have
been
reduced
into
method
and
order
by
the
skilfull
in
those
Arts.
Among
which
Constellations
.
They
have
observed
Stars
,
all
which
are
not
able
either
in
their
effects
or
magnitude
,
Where
wee
see
that
●…ee
accounteth
the
whole
number
of
the
Stars
to
be
after
him
acknawledged
only
So
likewise
he
reckoneth
the
Signes
or
Ast●…rismes
to
be
be
in
all
which
yet
in
account
,
are
but
in
his
Comentaries
upon
that
he
might
untie
this
knot
,
reads
these
words
of
Where
,
for
seventy
two
,
he
would
have
it
to
be
wanting
two
:
which
is
the
j●…st
number
reckoned
by
But
yet
the
same
doubt
still
remaines
in
the
ensuing
words
,
where
he
maketh
the
whole
number
of
the
Stars
to
be
I
find
also
two
other
Signes
added
to
the
former
Southern
Constellati●…ns
,
which
are
a●…d
the
The
first
of
which
containeth
in
it
,
Stars
:
of
which
there
are
two
in
the
back
of
it
,
of
the
second
magnitude
,
which
they
call
the
or
bri●…gers
of
good
newes
:
and
those
in
the
right
wing
are
consecrated
to
the
Deity
,
and
those
in
the
lest
to
the
Retiring
of
the
Waters
in
the
time
of
the
Deluge
.
we
may
call
the
●…ittou
.
Of
this
bird
,
hath
an
Epigram
call
it
and
it
is
described
with
the
wings
spread
abroad
and
as
it
were
striking
with
his
bill
at
the
South
Fish
,
in
that
part
where
he
boweth
himself
.
This
Asterisme
consisteth
of
Stars
●…nf
whi●…h
that
of
the
second
magnitude
in
his
head
is
called
the
and
it
hath
●…wo
other
tars
also
of
the
same
magnitu●…e
,
one
in
his
back
and
the
other
in
his
l●…twing
.
And
those
two
which
are
in
the
middle
of
his
neck
.
calleth
his
Collar
or
Chaine
Lastly
we
are
to
take
notice
that
the
call
the
south
Pole
for
so
testifieth
in
his
DIonysius
Afer
Mare
Se●…
Strabo
,
Pliny
,
Mela
Mare
Maggiore
Mare
dellezahacche
Cornelius
Nep●…s
Turannius
Graccula
Promontorium
Album
Pliny
▪
This
Northern
part
of
Europe
began
first
to
be
discovered
and
known
to
the
world
,
in
the
raign
,
or
rather
through
the
meanes
,
and
by
the
direction
of
For
as
The
Northern
Ocean
for
the
greatest
part
was
first
searched
by
who
sent
forth
a
Navy
,
which
passing
all
along
the
Coasts
of
Germany
,
came
so
far
as
the
Promontory
of
the
Cimbrians
,
and
thence
passing
on
through
a
vast
Sea
,
which
they
h●…d
only
heard
of
,
before
,
they
went
as
far
as
the
Coasts
of
In
which
place
meaneth
those
Sea
expeditions
,
performed
by
but
especially
that
of
as
may
appeare
by
those
words
of
where
he
saith
thus
Wee
left
not
the
Ocean
unattempted
that
way
also
,
and
it
is
a
common
fame
,
that
Pillars
are
yet
remaining
;
whether
it
be
true
indeed
,
that
ever
went
so
●…ar
,
or
else
,
that
●…hat
ever
Magnificent
thing
is
any
where
to
be
found
,
we
all
conspire
un●…nimusly
to
honour
him
therewith
.
Neither
was
there
wanting
courage
for
the
attempt
to
only
the
Ocean
would
not
suffer
it self
,
nor
to
be
sarther
inquired
into
.
After
this
no
man
att●…mpted
it
:
and
is
was
thought
a
greater
poynt
of
reverence
and
religion
,
to
believe
the
Actions
of
the
gods
,
then
to
know
〈◊〉
.
Thus
he
.
Now
before
this
time
,
all
this
tract
of
land
lying
towards
the
North
,
the
Romans
called
the
new
and
unknown
world
:
as
I
remember
I
have
seen
it
,
in
a
certain
Elegy
of
upon
the
death
of
the
same
And
the
Promontory
of
the
Cimbria●…s
,
which
speakes
of
,
is
now
called
and
is
the
most
northern
point
of
Denmarke
.
And
as
concerning
these
Pillars
of
mentioned
by
who
sometimes
saw
these
coasts
,
r●…ferreth
the
same
to
that
high
rock
or
Promontory
in
hath
it
but
not
rightly
)
which
is
at
this
day
called
bath
by
the
Natives
,
and
our
Mariners
also
.
For
in
this
place
they
have
a
superstitious
custome
,
that
as
reportes
of
the
Gad
tane
Pilla●…s
,
when
any
ships
had
arrived
there
,
as
if
they
had
attained
the
end
of
their
labours
and
travaile
,
they
forthwith
sacrificed
to
in
like
manner
in
this
place
they
have
a
custome
,
that
if
they
have
fresh
men
that
never
sailed
tbose
Northern
Seas
before
,
they
have
certain
Ceremonies
with
which
they
use
to
make
them
free
of
the
Sea
,
(
as
I
my self
once
saw
done
sailing
by
this
Promontory
)
for
they
ta●…k
and
bind
them
to
the
Mast
of
the
ship
and
then
taking
the
scoope
,
and
filling
it
with
Sea
water
,
they
make
as
it
were
a
Libation
,
powring
it
upon
their
heads
,
which
done
,
they
are
forthwith
expiated
,
and
accounted
free
of
the
place
.
But
whereas
would
have
the
word
to
be
only
corrupted
from
I
much
doubt
whether
he
will
have
any
more
of
his
opinion
But
of
this
place
,
as
also
of
all
this
Northern
tract
of
land
,
I
shall
have
a
more
convenient
opportunity
to
speak
elsewhere
.
Egyptus
Inferior
Julius
Scaliger
This
Sea
is
alwaies
rendered
by
the
Septuagint
,
and
by
St.
but
the
Hebrew
text
it self
,
unders●…ding
this
gulfe
of
the
Sea
(
which
is
called
also
by
calleth
it
which
is
as
much
as
to
say
,
because
it
bringeth
sorth
great
store
of
and
Sea
weeds
.
Which
is
observed
also
by
where
he
saith
There
are
also
bred
shrubs
in
the
Sea
,
and
in
our
Sea
,
little
trees
also
.
For
the
Red
Sea
,
and
all
the
Eastern
Ocean
is
full
of
trees
.
For
no
other
Language
hath
a
proper
word
to
expresse
that
which
the
Greeks
call
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
because
that
is
more
usually
taken
for
the
name
of
an
hearb
,
but
in
this
place
it
signifieth
a
shrub
.
Thus
You
may
also
see
That
place
which
the
Author
cit●…th
out
of
is
in
his
Exercitation
against
And
I
thinke
it
not
a
misse
to
heare
him
speakeing
in
his
owne
words
,
that
so
it
may
appeare
what
his
judgement
is
of
that
which
is
objected
by
those
Cavillers
.
His
words
are
these
.
About
the
coast
of
India
(
saith
hee
)
where
the
Rivers
disburthen
themselves
into
the
Sea
,
there
are
very
high
tides
:
So
likewise
in
the
Red
Sea
,
they
are
so
great
,
as
that
the
contemners
of
Holy
Writers
have
impiously
forged
that
Moses
,
when
he
led
the
out
of
AEgypt
,
took
the
opportunity
of
the
Waters
,
retireing
after
the
Tide
.
Which
notwithstanding
could
not
possibly
be
,
because
that
as
farr
as
which
is
situated
in
the
innermost
corner
of
the
gulf●…
,
the
Sea
covereth
the
very
shore
;
neither
,
when
it
ebbeth
,
doth
it
ever
leave
the
ground
so
bare
,
as
that
the
lower
parts
,
through
which
the
passed
,
should
be
free
from
passage
on
foot
.
Heraclides
Ponticus
Eudoxus
Cyzicenus
Strabo
,
Pliny
Cornelius
Nepos
Pytheas
,
Evemerus
Cape
of
good
hope
C.
Caesar
Nova
Zemla
Cornelius
Nepos
Q.
Matellus
Cesar
Bactrians
,
Hircania
Cinamomifera
,
Strabo
Geography
,
lib.
Dionysius
Afer
Europa
Tyria
In
Europe
these
things
are
chiefely
observable
.
The
most
famous
Monarchies
which
are
in
it
;
as
namely
the
Emperour
of
Germany
,
the
Kings
of
Spain
,
France
,
Great
Britaine
,
Denmarke
,
Swethland
,
Polonia
,
and
Moscovia
.
To
which
we
may
add
the
Pope
of
Rome
,
who
,
though
he
usurpe
not
the
title
of
a
King
,
yet
is
his
power
no
whit
inferiour
to
theirs
:
a●…
also
the
great
Turke
,
who
at
this
day
possesseth
a
great
part
of
Europe
also
.
The
principall
hills
,
which
are
the
dividing
Italy
from
Germany
and
France
;
and
also
the
Pyrenoean
Hills
,
severing
Spain
s●…om
France
.
The
noteable
Rivers
,
as
the
Da●…ow
,
the
Rheine
,
the
Elue
,
the
Wetsell
,
Bortsthenes
,
and
Tanais
,
now
called
Don.
To
which
we
may
adde
the
River
Tagus
in
Spain
,
the
Rhene
and
Guar●…nn
:
in
France
,
and
Thames
in
England
.
Lastly
,
the
principall
commodities
in
Europe
,
are
Gold
,
Silver
,
Tin
,
Lead
,
Iron
,
Oyle
,
all
kind
of
graine
,
Flax
,
Wooll
,
Salt
,
Johannes
Leo
Fretum
Gaditanum
Morocco
,
Fez.
Algier
Gualata
,
Guinea
,
Melli
,
Tombutum
,
Gagos
,
Gub●…ris
,
Agades
,
Canos
,
Casena
,
Zegz●…ga
,
Zanfar●…
,
Burnum
,
Gaoga
,
Nubia
,
&c.
Prester
John
Arias
Montanus
Benyamine
Tudelersis
D'
Angola
Melinde
,
Quiloa
,
Mozambique
Cape
Verd
S.
Thomas
Island
hath
these
things
in
it
considerable
.
It
is
greater
then
Europe
but
lesse
then
and
lesse
inhabited
,
and
civiliz●…d
then
either
.
It
is
b●…unded
with
the
Sea
on
all
sides
,
sa●…e
on●…ly
where
it
is
is
con
terminat
with
The
principali
regions
of
it
,
are
,
The
mast
famous
kingdoms
are
these
,
and
also
that
of
The
greatest
Mountains
are
and
that
other
whence
The
principall
r●…rs
of
which
is
accounted
to
bee
the
greatest
in
the
world
,
and
as
affirmeth
,
encompasseth
The
principall
Merchandise
of
is
Ivory
,
Civet
,
Gold
Cotton
Wooll
,
Jewels
,
and
certain
kinds
of
spices
,
as
also
Salt
,
Lions
,
Camels
,
Muscovites
,
Tartarians
Sumatra
,
Zeilam
.
Java
,
Major
That
it
ought
to
be
written
as
our
Author
in
this
place
,
and
commonly
all
other
writers
use
to
doe
,
appeareth
manifestly
out
of
who
alwayes
calleth
them
The
eighth
Table
also
of
Geography
,
placeth
the
(
which
our
Author
calleth
the
region
of
betw●…xt
th●…
mountaines
and
the
region
of
the
a
part
of
it
beyond
the
same
which
are
hills
in
the
Country
of
the
and
looking
towards
the
South
East
.
So
that
I
cannot
but
wonder
that
a
Jesuite
,
in
his
expedition
should
take
so
much
pains
to
prove
,
that
the
Kingdom
of
and
of
the
is
all
one
.
But
it
were
easi●…
,
by
other
,
and
those
more
proper
arguments
and
testimonies
,
(
were
this
place
convenient
)
to
prove
the
contrary
to
this
his
assertion
.
Now
as
concerning
these
things
occurre
n●…it
worth
our
observation
.
That
it
is
twofold
,
Asia
or
the
lesser
is
bounded
on
the
East
by
the
Sea
;
on
the
South
by
the
river
on
the
West
by
the
on
the
North
by
the
The
principall
countries
it
contained
anciently
,
were
these
:
To
the
greater
th●…se
Regions
appertained
In
both
of
them
there
are
setled
at
this
day
these
Empires
;
namely
,
the
The
chiefe
hills
of
note
in
it
,
are
The
principall
Rivers
The
chiefest
traffick
is
,
Gold
,
Pearle
,
Jewels
,
all
kind
of
Spices
,
Muske
,
Frankincense
,
Balsame
,
Amber
,
Silks
,
Ivory
,
and
Elephants
.
Americus
Vespuccius
del
Zur
Martin
Frobisher
John
Davis
Tierra
de
Labrador
Nova
Francia
Nova
Hispania
Nova
Guinea
Europe
,
Asia
de
Coelo
Cleomedes
lib.
Strabo
,
Vitruvius
,
Pliny
Pliny
.
lib.
cap.
ult
Eratosthenes
,
Pliny
Eratosthenes
Posidonius
Ptolomy
,
lib.
Almagest
.
Proclus
▪
Canobus
in
Alexandria
consp●…euè
cerni
,
quar●…a
〈◊〉
Signi
portione
supra
Horizontem
〈◊〉
Marinus
Tyrius
Heroe
Mechanicus
Franciscus
Maurolycus
,
Abbot
Rhodes
Posidonius
Rodulphus
Brugensis
Eudoxus
Cnidius
Pliny
,
Proclus
Posidonius
.
Eratosthenes
Petrus
Nonius
De
Nauigatione
Terrestriall
Globe
Cleomedes
,
Firmicus
Maternus
Designation
.
Astronomi
lib.
Almagest
.
Ptolomy
Dialog.
Cosmograph
Aristarchus
Samius
De
magnitud
,
&
distant
.
Solis
&
Luna
.
cap.
Designation
.
Astronom
Terrestriall
Globe
Herodotus
Xenophon
Herodotus
,
Xenophon
Schoenus
:
P.
Nonius
Jacobus
Christmannus
For
the
finding
out
of
the
circumference
or
circuit
of
the
are
first
to
be
laid
down
for
a
ground
〈◊〉
That
the
greatest
circle
in
the
Earth
,
as
well
as
in
the
Heavens
,
is
to
be
divided
into
parts
,
or
degrees
That
one
of
these
degrees
doth
contain
furlongs
or
Romane
pases
,
and
English
miles
furlong
,
and
a
third
part
make
an
English
Mile
.
These
things
being
presupposed
,
we
must
multiply
degrees
by
miles
,
which
done
,
the
product
will
be
English
miles
.
Or
if
you
multiply
degrees
,
by
furlongs
;
the
whole
will
be
furlongs
,
which
is
the
measure
of
the
circumference
of
the
Earth
.
So
likewise
if
be
multiplyed
by
the
whole
will
be
Germane
miles
:
and
if
the
number
of
the
degrees
be
multiplyed
by
there
well
arise
French
miles
.
All
which
may
be
thus
expressed
.
In
like
manner
the
Circumferance
of
the
Earth
mayas
easily
bee
found
out
by
any
of
the
fixed
Starrs
,
as
the
or
the
like
.
For
if
we
take
any
two
places
which
are
situated
under
the
same
Meridian
,
and
the
distances
in
a
right
line
exactly
known
,
so
that
in
both
places
the
Meridian
Altitude
of
the
same
Star
be
certainly
known
also
:
the
difference
of
it's
Altitude
will
be
the
number
of
degrees
of
distance
betwixt
the
same
places
,
Wherefore
seeing
it
is
certainly
known
,
as
we
have
already
said
,
how
many
miles
answer
to
a
degree
,
it
is
very
easie
then
to
gather
how
many
miles
the
circumference
of
the
whole
Earth
is
also
As
for
example
:
suppose
to
be
under
the
same
Meridian
,
and
the
Elevation
of
the
Pole
at
to
be
degrees
,
and
at
m.
Now
if
you
substract
the
lesser
number
,
which
is
from
the
greater
m.
the
difference
wil
be
m.
which
being
resolved
into
minutes
,
it
will
be
found
to
be
the
distance
of
miles
betwixt
Therefore
we
must
now
say
,
that
as
m.
is
to
miles
:
so
is
degrees
to
English
miles
For
the
better
understanding
of
those
things
which
shall
bee
spoken
hereafter
,
there
are
two
things
especially
to
be
promised
:
the
first
whereof
is
,
concerning
the
position
of
the
and
the
other
Climates
.
Now
touching
the
position
of
the
you
are
,
first
of
all
,
to
take
care
that
it
bee
pla●…
perpendicularly
to
the
true
Horizon
:
That
the
distinction
of
the
winds
answere
directly
to
the
winds
of
the
reall
Horizon
,
that
so
the
East
on
your
materiall
may
look
directly
toward
the
true
East
of
the
World
.
For
which
purpose
especially
there
is
usually
placed
a
Nauticall
Compasse
in
the
bottome
of
the
frame
.
When
you
have
thus
placed
your
so
that
it
may
be
turned
about
any
way
at
pleasure
,
yet
so
that
the
base
or
foot
bee
not
moved
out
of
its
place
,
the
next
thing
that
is
to
bee
enquired
after
,
is
the
Latitude
of
the
place
Wherein
you
live
:
which
according
as
it
is
greater
,
or
lesser
,
you
must
elevate
the
Pole
of
your
above
the
Horizon
proportionally
.
As
for
example
,
if
the
Latitude
be
grad.
or
lesse
Northward
,
then
must
you
elevate
the
Arctick
Pole
just
so
many
degrees
above
the
Horizon
.
And
so
likewise
if
the
latitude
be
Southern
,
you
must
do●…
the
like
by
the
Antartick
or
South
Pole
.
But
under
the
AEquator
,
where
there
is
no
latitude
at
all
,
both
the
Poles
must
bee
placed
in
the
very
Horizon
,
at
opposite
points
.
A
Climate
is
a
space
of
the
habitable
parts
of
the
Earth
,
comprehended
betwixt
two
circles
Parallel
to
the
AEquator
,
in
which
space
there
is
halfe
an
hours
difference
in
the
longest
day
.
Now
those
that
inhabit
under
the
AEquator
have
a
perpetuall
AEquinoxe
,
for
the
day
with
them
is
alwaies
twelve
hours
longer
,
and
the
night
as
much
.
But
as
their
situation
is
removed
from
the
AEquinoctiall
nearer
to
either
Pole
,
the
further
they
are
from
the
AEquinoctiall
,
the
greater
is
the
the
inequality
of
the
Artificiall
day
and
night
:
out
of
which
variation
of
Artificiall
daies
,
the
diversity
of
Climates
also
is
takon
and
distiuguished
.
For
wheresoever
this
difference
amounteth
to
halfe
an
houre
,
there
presently
beginnes
another
Climate
.
Now
the
ancient
Geographers
constitutede
in
every
Clime
,
three
Parallels
,
〈◊〉
which
the
two
outwardmost
,
namely
the
first
and
the
third
,
do
comprehend
and
terminate
every
Climate
:
and
the
second
divideth
it
in
the
midst
.
So
that
the
proportion
betwixt
the
Clime
and
the
Parallels
was
Duple
;
for
the
Climes
,
as
wee
have
said
,
were
distant
from
each
other
halfe
an
houres
space
in
the
length
of
the
day
,
but
the
Parallols
were
distinguished
by
quarters
of
an
houre
.
Now
as
concerning
the
number
of
Climates
,
The
Ancients
,
at
first
,
reckoned
but
seven
,
but
in
his
Tables
of
Ascensions
,
in
the
acknowledgeth
nine
:
all
of
which
derived
their
names
from
some
eminent
place
,
either
hill
or
river
,
situate
in
the
midst
of
the
said
Climate
.
The
first
Clime
to
ward
the
Arctick
Pole
,
beginning
from
the
AEquator
,
they
called
because
the
midst
of
this
Clime
runneth
through
which
is
an
Island
in
encompassed
about
with
the
river
where
the
longest
day
is
thirteen
hours
:
in
the
beginning
therefore
of
this
Clime
it
must
be
hours
long
.
On
the
opposite
part
of
the
AEquator
the
first
Southern
Climate
may
in●…
manner
be
called
,
But
these
other
Climes
were
not
constituted
neither
by
nor
any
of
the
ancient
Geographers
.
Yet
by
the
like
reason
that
part
of
the
world
also
may
as
well
be
deseribed
into
Climate
,
reserving
the
same
names
that
the
Northern
Climes
are
known
by
,
and
onely
adding
to
them
the
preposition
〈◊〉
which
signifies
as
much
as
,
Opposite
,
or
over
against
.
And
the●…
the
Scheme
,
of
them
all
will
be
thus
,
Yet
some
there
are
that
do
not
approve
of
this
distinction
of
Climates
,
among
whom
is
in
his
And
the
reasons
they
alledg
are
these
.
Because
of
their
great
in
equality
,
in
so
much
that
the
latitude
of
the
first
is
above
English
miles
,
whereas
the
last
of
all
is
scarce
a
mile
.
Because
that
the
increase
of
hours
is
but
a
weake
ground
to
build
upon
,
and
of
no
great
use
:
seeing
it
is
as
easie
to
enquire
out
the
length
of
the
day
,
as
the
number
of
the
Climate
.
And
therefore
hee
thinkes
,
it
were
farr
better
,
that
every
Hemisphaere
were
equally
distinguished
by
tenn
degrees
into
nine
Climates
.
So
that
the
first
Climate
should
begin
at
the
AEquinoctiall
,
and
end
where
the
Elevation
of
the
Pole
is
tenn
gr.
which
might
be
called
the
Climate
.
The
second
should
reach
to
the
gr.
and
should
bee
named
the
Clime
:
because
that
part
of
is
situated
therein
.
The
third
should
reach
to
the
gr.
and
be
called
the
The
fourth
the
ending
at
the
gr.
The
fifth
the
to
the
gr.
The
extending
to
the
gr.
The
seventh
the
Climate
,
reaching
to
the
gr.
The
eighth
,
the
Climate
,
ending
at
the
gr.
And
the
Ninth
and
last
,
the
Climate
,
reaching
to
the
Pole
it selfe
.
So
likewise
the
same
Method
might
bee
observed
on
the
othes
side
of
the
and
then
by
this
meanes
each
Hemisphaere
should
have
nine
Climates
:
whereof
seven
would
be
convenient
for
habitation
,
and
the
Parallels
might
passe
through
every
fifth
degree
.
And
the
situation
of
any
place
might
be
known
by
the
number
of
degrees
of
the
Poles
elevation
.
So
because
it
hath
above
gr.
of
latitude
,
is
in
the
fourth
in
the
fifth
in
the
third
the
chiefe
City
in
in
the
second
in
the
first
;
and
so
of
the
rest
.
Fortunate
Islands
Canary
Islands
Fortunate
Islands
Canary
Islands
Cabo
Verde
Canary
Islands
Jacobus
Christmannus
Johannes
Wernerus
If
you
would
know
how
to
find
out
the
longitude
of
any
place
by
the
Eclipse
of
the
Moon
,
you
must
first
goe
to
some
as
the
〈◊〉
Tables
,
or
of
any
other
learned
Mathematicians
calculation
;
and
see
,
what
hour
such
an
Eclipse
of
the
Moon
shall
happen
at
that
place
,
for
which
the
said
Tables
or
were
made
.
Then
afterward
you
must
observe
the
same
Eclipse
in
that
place
,
whose
longitude
you
desire
to
know
,
Now
if
the
time
of
the
Eclipse
agree
with
that
other
,
for
which
the
Tables
were
made
,
then
you
may
conclude
that
both
places
have
the
same
latitude
,
and
are
situate
under
the
same
Meridian
.
But
is
the
number
of
the
hours
be
more
,
then
the
place
you
are
in
,
is
suuate
more
Eastward
,
you
must
therefore
substract
the
less
number
out
of
the
greater
,
and
the
remainder
must
be
converted
into
degrees
and
minutes
,
multiplying
the
hours
by
fifteen
and
deviding
the
minutes
of
hours
(
if
there
be
any
)
by
foure
;
for
so
will
the
number
of
degrees
arise
:
and
if
there
remain
any
minutes
after
the
division
,
they
must
bee
multiplyed
again
by
fifteen
,
and
so
will
the
number
of
the
minutes
of
degrees
arise
,
by
which
these
places
are
distant
from
each
other
:
which
distance
is
called
the
difference
of
longitude
.
This
difference
must
bee
added
to
the
Longitude
of
that
place
for
which
the
Tables
were
calculated
,
if
the
other
place
be
more
Eastward
:
otherwise
if
it
bee
more
Westward
,
it
is
to
bee
substracted
from
the
longitude
of
the
other
.
An
example
herof
is
thus
proposed
by
in
his
I
find
(
saith
hee
)
out
of
the
Prutenick
Tables
,
by
exact
calculation
,
that
there
will
be
an
Eclipse
of
the
Moon
in
the
yeare
upon
the
eleventh
day
of
at
foure
of
the
Clock
and
sixteen
minutes
,
in
the
morning
,
and
that
at
a
City
in
whose
longitude
or
distance
from
the
m.
For
this
Longitude
where
these
Tables
calculated
.
Now
I
set
my self
to
observe
this
same
Eclipse
at
and
find
it
to
happen
at
three
of
the
Clock
and
twelve
minutes
,
on
the
same
day
of
Now
because
the
number
of
hours
here
is
lesse
,
it
appeares
that
is
more
Westward
then
Therefore
I
take
away
a
lesse
number
from
the
greater
,
that
is
.
m.
from
m.
and
the
remainder
is
minutes
:
which
sheweth
the
difference
of
longitude
in
hours
,
which
makes
up
sixteen
degrees
.
Therefore
I
again
substract
these
degrees
of
difference
from
the
longitude
of
as
being
more
Eastward
then
and
so
I
find
the
Latitude
of
from
the
Island
,
to
be
Seeing
that
the
Latitude
of
every
place
is
alwayes
equall
to
the
elevation
of
the
Pole
:
It
will
not
be
amisse
to
shew
,
how
the
elevation
of
the
Pole
,
or
the
Latitude
of
any
region
may
be
found
out
,
by
the
observing
of
the
same
fixed
Star
in
the
Heavens
,
which
is
so
neare
the
Pole
,
a●…
that
it
never
sets
in
that
region
:
which
to
doe
you
must
work
thus
.
You
must
observe
both
the
least
and
also
the
greatest
altitude
of
the
sad
Star
;
both
which
must
necessarily
happen
in
the
Meridian
:
the
least
whereof
will
be
beneath
the
Pole
,
and
the
greatest
above
it
.
Which
done
,
you
must
adde
the
least
altitude
of
it
to
the
greatest
;
and
so
the
halfe
of
the
degrees
thus
numbered
together
,
will
bee
the
latitude
of
the
Pole
,
and
latitude
of
that
plaee
.
An
example
whereof
may
be
this
.
The
first
Star
of
the
three
in
the
taile
of
the
great
Beare
is
in
his
least
altitude
observed
at
to
be
about
gr.
and
the
greatest
altitude
of
the
same
,
when
it
is
above
the
Pole
,
is
found
to
be
neare
upon
degrees
.
Both
which
numbers
being
added
together
,
do
make
up
halfe
of
which
Summ
,
namely
is
the
true
elevation
ond
Latitude
of
The
〈◊〉
of
places
●…ring
only
in
latitude
may
bee
found
after
this
manner
First
you
must
substract
the
lesser
Latitude
from
the
greater
,
resolving
a
degree
in
minutes
,
if
the
substraction
cannot
be
done
otherwise
conveniently
.
Then
multiply
the
degrees
by
and
divide
the
minutes
by
and
the
summ
produced
will
be
the
distance
of
those
two
places
in
common
miles
,
one
whereof
containeth
foure
of
our
miles
.
As
for
example
have
both
the
same
longitude
.
but
differ
in
Latitude
,
which
at
m.
and
at
m.
Therefore
substracting
the
lesser
from
the
greater
,
the
remainder
will
bee
m.
which
being
reduced
into
miles
,
will
amount
to
and
a
quarter
or
a
mile
.
which
is
the
distance
of
these
two
places
assigned
.
Now
if
the
place
proposed
bee
in
diverse
Hemispheres
,
then
the
degrees
and
minutes
of
Latitude
must
first
be
added
together
,
and
so
the
whole
resolved
into
miles
,
as
formerly
hath
been
said
.
As
for
example
:
The
are
almost
situate
under
the
same
meridian
,
but
in
diverse
Hemisphaeres
.
Now
the
elevation
of
the
Pole
Articke
at
gr.
or
thereabout
:
and
at
the
the
Antarctick
Pole
is
elovated
aboue
gr.
the
whole
summ
therefore
is
degrees
.
that
is
to
say
The
distance
of
places
differing
onely
in
longitude
,
is
found
thus
.
First
substract
the
lesse
number
from
the
greater
:
then
look
in
the
Table
here
under
written
,
how
many
miles
answere
to
a
degree
〈◊〉
every
Parallel
,
seeking
for
the
degree
of
Latitude
in
the
first
columne
descending
,
and
the
number
of
miles
over
against
it
.
Then
lastly
let
the
difference
of
longitude
be
multiplyed
into
miles
and
minutes
:
and
you
have
your
desire
.
As
for
example
are
in
the
same
latitude
of
fortie
one
gr.
where
eleven
miles
,
and
nineteen
minutes
answer
to
a
degree
of
that
Parallel
:
but
these
places
differ
in
longitude
,
which
at
m
but
at
m.
Naw
the
difference
betwixt
them
is
which
is
as
much
as
miles
,
and
fifty
scruples
:
the
just
distance
betwixt
these
two
places
.
The
Longitude
or
Latitude
,
of
any
place
or
City
being
known
,
either
by
observation
,
as
hath
already
been
shewed
,
or
else
out
of
some
Geographicall
Table
,
the
situation
os
the
same
in
the
Globe
may
also
be
found
out
by
this
same
meanes
.
You
must
first
reckon
the
Longitude
of
your
place
,
among
the
circles
of
Longitude
which
are
described
upon
the
Globe
beginning
at
that
which
is
drawn
through
the
Fortunate
Islands
:
and
observe
the
circle
where
you
end
your
reckoning
.
Then
if
the
Latitude
of
your
place
be
Northern
:
you
must
reckon
that
also
among
the
Parallels
toward
the
Arctick
Pole
,
begnining
from
the
AEquator
:
but
if
it
have
Southern
Latitude
you
must
then
proceed
in
like
manner
,
but
reckon
toward
the
Antarctique
▪
And
the
intersection
,
or
point
where
these
two
circles
cut
each
other
,
sheweth
the
situation
of
your
place
.
But
if
these
circles
of
Long●…ude
be
expressed
in
your
Globe
,
then
must
you
place
that
degree
of
the
AEquinoctiall
,
that
answereth
to
the
Longitude
of
your
place
,
under
the
Meridian
,
and
so
reckon
the
Latitude
of
your
place
among
the
degrees
of
the
Meridian
,
toward
either
Pole
:
and
you
have
the
situation
of
the
place
you
look
after
.
Gemma
Frisius
You
also
find
out
the
Suns
greatest
Declination
,
by
his
greatest
and
least
Altitude
both
in
Summer
and
Winter
,
by
substracting
the
least
out
of
the
greatest
.
For
then
halfe
that
which
remaineth
,
will
be
the
declination
you
seek
for
So
found
the
Meridian
Altitude
of
the
Sun
,
at
the
Summer
Solstice
to
be
and
the
least
Altitude
of
it
,
on
the
Winter
Solstice
,
to
be
when
therefore
;
he
had
deducted
the
least
number
,
out
of
be
found
the
remainder
to
be
the
halfe
of
which
was
the
Suns
greatest
declination
,
namely
which
is
the
number
of
degrees
now
commonly
received
:
notwithstanding
it
hath
been
since
observed
by
some
in
our
time
to
be
somewhat
lesse
.
Now
to
know
the
Longitude
of
the
Sunne
for
any
time
,
that
is
to
say
,
in
what
degree
of
the
Zodiaque
hee
is
,
you
must
do
thus
.
Seeke
in
the
limbe
of
the
Horizon
for
the
day
of
the
Moneth
,
for
which
you
would
know
the
Longitude
of
the
Sun
:
which
found
,
you
shall
see
,
over
against
it
,
among
the
Signs
of
the
Zodiaque
,
described
also
upon
the
Horizon
,
the
degree
of
the
Signe
that
exactly
answereth
to
it
,
and
which
is
the
place
of
the
Sunne
for
that
day
and
Moneth
.
But
if
it
bee
Leape
yeare
,
you
must
remember
after
the
to
adde
one
day
more
still
as
you
go
,
as
if
you
should
look
for
the
place
of
the
Sunne
on
the
March
,
you
must
take
that
degree
which
is
set
for
the
of
March
:
which
is
the
of
V.
The
Meridian
altitude
of
the
Sunne
,
being
found
by
the
help
of
of
the
Meridian
circle
,
it
will
be
very
easie
to
find
out
the
latitude
of
the
place
or
elevation
of
the
Pole
,
in
any
region
whatsoever
.
For
seeing
the
Zenith
or
Vertex
of
every
place
is
distant
aquarter
of
a
circle
that
is
degrees
from
the
Horizon
:
if
then
,
the
Sun
being
in
either
of
the
AEquinoctiall
points
,
the
Meridian
altitude
be
substracted
from
degrees
;
the
remainder
wil
be
the
distance
betwixt
the
Zenith
of
the
place
and
the
AEquinoctiall
circle
:
which
will
be
the
latitude
of
the
same
place
.
And
the
reason
also
of
this
deduction
is
manifest
,
because
that
the
AEquinoctiall
Altitude
of
the
Sun
,
is
nothing
else
,
but
the
Elevation
of
the
AEquator
,
the
complement
whereof
is
always
equali
to
the
elevation
of
the
Pole
.
But
this
will
appear
more
plaine
by
an
example
,
which
shall
be
thus
.
The
AEquinoctiall
altitude
of
the
Sunne
at
degrees
:
which
being
substracted
from
gr.
the
remainder
,
which
is
gr.
is
the
elevation
of
the
Pole
,
and
the
latitude
of
So
likewise
here
at
in
the
Meridian
altitude
of
the
Sunne
,
when
he
is
in
the
AEquinoctiall
,
is
found
to
bee
degrees
and
an
half
:
which
being
deducted
out
of
gr.
which
is
the
Quadrant
of
a
circle
,
there
w●…ll
remain
gr.
which
is
the
latitude
of
and
the
elevation
of
the
Pole
.
The
same
also
may
be
done
,
by
observing
any
one
of
the
fixed
Sarres
,
which
is
is
so
neare
the
Pole
,
as
that
it
never
sets
in
that
Country
,
whose
latitude
you
seek
.
For
you
must
observe
both
the
greatest
and
least
altitude
of
the
same
Starre
;
both
which
will
happen
in
the
Meridian
:
the
least
of
them
beneath
the
Pole
,
and
the
greatest
above
it
.
Which
done
,
you
must
adde
the
least
altitude
to
the
greatest
,
and
so
dividing
the
whole
into
two
parts
,
the
half
will
be
the
altitude
of
the
Pole
.
As
hath
been
shewed
before
.
This
Ascension
and
descension
is
also
called
the
Astro
nomicall
rising
and
setting
of
the
Stars
:
and
that
in
respect
of
the
Arches
and
parts
of
the
Ecl
ptick
,
or
Stars
,
either
above
or
beneath
the
Horizon
.
Now
an
Arch
of
the
Ecliptick
or
Zodiacke
is
tobe
understood
two
manner
of
ways
namely
Continued
,
or
Discrete
.
A
continued
Arch
,
is
when
it
is
reckoned
in
the
AEquator
in
a
continued
Series
from
the
beginning
of
and
so
forward
into
the
consequent
signes
.
A
Discrete
Arch
is
so
called
because
it
is
not
reckoned
from
the
first
degree
of
but
from
any
other
point
in
the
AEquator
:
as
if
you
should
say
,
an
Arch
from
the
gr.
of
to
the
gr.
of
Beside
,
this
Right
Ascension
is
called
also
the
greater
Ascension
,
because
that
in
it
,
a
greater
Arch
of
the
AEquator
riseth
above
the
Horizon
,
then
of
the
Zodiack
:
&
it
is
called
Right
,
because
that
in
this
,
the
Angle
which
is
made
by
the
Horizon
and
Eclipticke
,
is
nearer
to
a
Right
Angle
,
then
that
that
is
made
by
any
other
part
of
the
Eclipticke
with
the
same
.
And
that
is
said
to
bee
a
greater
Arch
or
portion
of
the
AEquator
,
which
is
more
than
degrees
in
the
Ascension
or
Descension
:
and
that
is
called
a
lesser
Arch
,
which
falls
short
of
thirtie
,
degrees
in
rising
or
setting
.
In
a
Right
Sphaere
foure
signs
onely
ascend
Rightly
,
which
are
all
the
rest
ascend
Obliquely
In
an
Oblique
Sphaere
six
signes
rise
Rightly
and
the
other
six
Obliquely
.
The
right
are
these
,
and
all
the
rest
Obliquely
Oblique
ascension
,
is
when
a
lesse
Arch
or
portion
of
the
AEquator
riseth
,
then
of
the
Zodiaque
:
or
else
,
that
Starre
may
be
said
to
rise
Obliquely
,
with
whom
a
lesse
portion
of
the
AEquator
ascendeth
above
the
Horizon
.
And
so
the
Oblique
descention
or
setting
of
a
Starre
is
,
where
a
lesse
portion
of
the
AEquator
descendeth
with
it
.
As
for
example
.
At
with
the
Arch
of
which
containeth
gr.
in
the
Zodiaque
,
there
riseth
an
arch
of
the
AEquinoctiall
of
gr
So
that
this
sign
is
said
there
to
rise
rightly
:
Because
that
a
greater
Arch
of
the
AEquator
ascendeth
with
it
,
then
of
the
Zodiaque
,
But
then
,
at
the
same
place
,
with
the
Arch
of
there
arise
only
gr.
of
the
AEquator
.
Whence
it
followeth
that
riseth
Obliquely
at
In
our
position
of
Sphaere
also
here
at
which
is
Oblique
,
like
as
that
at
there
ariseth
an
Arch
of
the
AEquinoctial
concoutaining
about
gr.
but
with
the
Arch
of
there
ariseth
not
above
degrees
.
Therefore
in
our
Sphaere
ascendeth
or
riseth
rightly
,
but
THe
Rules
of
Astronomicall
rising
in
a
right
Sphaere
are
these
.
The
whole
Quadrants
or
quarters
of
the
Zodiaque
and
AEquinoctiall
rise
and
set
in
an
equall
space
of
time
.
But
the
the
parts
of
the
Quadrants
rise
and
set
unequally
.
Those
signes
that
are
equally
distant
from
any
of
those
points
,
have
also
equall
ascensions
:
as
The
Ascension
of
a
sign
is
alwayes
equall
to
the
Descension
of
the
same
.
Four
signs
only
rise
rightly
,
namely
and
all
the
rest
Obliquely
IN
an
Oblique
Sphaere
,
the
two
halfes
that
begin
at
the
two
AEquinoctiall
points
,
do
rise
together
.
The
parts
of
these
halfes
do
rise
unequally
.
Those
signs
that
rise
rightly
,
descend
Obliquely
,
and
so
contrarily
.
The
Ascension
of
any
sign
is
equall
to
the
Descention
of
the
same
.
The
Ascensionall
Arches
of
the
Northern
signs
are
lesse
in
a
right
sphoere
,
but
in
the
Southerne
signes
they
are
greater
.
The
Ascension
of
Opposite
signes
in
an
Oblique
Sphaere
,
taken
together
,
are
equall
to
the
Ascension
of
the
same
in
a
right
Sphaere
.
Those
signes
that
are
equidistant
from
either
of
the
AEquinoctiall
points
,
have
equall
Ascensions
,
because
they
decline
equally
from
the
AEquator
.
And
here
you
are
to
understand
,
that
the
Amplitude
of
the
Sunnes
rising
and
setting
,
is
an
Arch
of
the
Horizon
intercepted
betwixt
the
AEquator
,
and
the
place
of
the
rising
and
setting
of
the
Sun
.
And
it
is
either
Northerne
or
Southerne
.
The
Northern
Amplitude
,
is
when
hee
sets
and
riseth
on
this
side
of
the
AEquator
,
toward
the
North
Pole
:
and
the
Southern
when
he
sets
or
riseth
on
the
contrary
side
.
Now
when
the
Sun
is
in
the
AEquator
,
he
hath
no
amplitude
at
all
:
but
when
he
is
in
the
Solsticall
points
,
he
hath
then
the
greatest
amplitude
of
all
:
of
which
that
in
the
Tropique
of
Cancer
is
called
the
AEstivall
,
or
summer
solsticiall
amplitude
;
and
the
other
the
Brumall
or
Winter
solsticiall
amplitude
.
And
here
it
is
to
be
noted
that
in
all
places
the
Ortive
amplitude
of
any
Starre
is
equall
to
the
Occidentall
amplitude
of
the
same
.
And
likewise
,
that
two
stars
being
equally
distant
from
the
AEquator
the
one
Northward
,
and
the
other
Southward
,
or
both
of
them
Northward
or
Southward
,
have
equal
amplitude
of
rising
and
setting
.
Ortus
Matutinus
,
sive
Cosmicus
Concerning
the
rising
and
setting
of
the
Starrs
,
which
is
considered
in
respect
of
the
Horizon
and
AEquator
,
hath
been
spoken
already
in
the
seventh
where
we
also
shewed
,
that
that
kind
of
rising
and
setting
of
the
Starres
was
called
astronomicall
.
But
in
this
place
the
rising
of
the
Starres
is
considered
in
relation
onely
to
the
Horizon
and
Sunnes
aspect
,
but
not
of
the
AEquator
;
and
therefore
it
is
also
commonly
called
,
the
Poëtioall
rising
and
setting
of
the
Stars
.
cap
ult
Almag
The
use
and
benefit
of
this
discourse
concerning
these
kinds
of
rising
and
setting
of
the
Starres
is
principally
seen
,
in
reading
of
the
ancient
Authors
and
Poëts
,
especially
those
that
have
written
of
Husbandry
,
and
the
severall
seasons
of
the
yeare
.
For
so
makes
mention
of
the
Cosmicall
rising
of
the
Starres
in
these
verses
.
T.
May.
In
which
place
hee
meaneth
to
intimate
the
moneth
of
when
as
the
Snnne
is
in
the
sign
and
riseth
with
it
.
And
we
have
an
example
also
of
the
Cosmicall
setting
in
the
same
place
,
where
he
saith
,
Exercebi●…
humum
solisque
instabis
aristis
An
●…ibi
Eoae
Atlant●…des
abscondantur
Deb●…ta
quam●…ulcis
cōmi●…tas
s●…ina
,
quamque
T.
May.
Where
hee
would
have
them
to
expect
their
sowing
time
,
till
that
the
that
is
,
the
er
seven
Starres
be
hid
in
the
East
,
that
is
,
in
the
Morning
by
the
approach
of
the
Sunne
,
which
is
also
called
At
which
time
also
the
bright
Starre
in
the
Northern
Crown
sets
in
the
Evening
with
the
Sunne
,
or
Heliacally
.
and
so
the
Poet
,
by
a
twofold
kind
of
setting
of
the
Starrs
,
describes
the
An
example
of
the
Achronycall
rising
you
have
in
where
he
decribeth
the
tediousness
of
his
ex●le
,
from
the
Autumnall
or
Vespertine
rising
of
the
in
words
Quatuor
Autumnos
Plë●as
orta
facit
And
he
also
mentioneth
the
Achronicall
setting
,
where
speaking
of
the
third
of
he
doth
it
by
this
Periphrasis
,
An
example
of
the
Heliacall
rising
in
you
have
in
the
same
Author
,
in
these
words
.
And
for
the
Heliacall
setting
,
you
had
an
instance
above
,
out
of
In
which
place
the
speaketh
of
sowing
millet
and
beans
in
the
spring
time
.
To
these
wee
may
also
adde
these
severall
kinds
of
Poeticall
rising
and
setting
of
Starres
exprest
.
Evening
Twilight
P.
Nonius
Our
Northern
regions
have
their
or
Twilight
,
of
above
an
houre
long
.
But
those
Countries
,
where
the
are
very
farre
beneath
their
Horizon
,
have
in
a
manner
no
no
Twilight
or
breake
of
day
.
And
therefore
those
that
inhabite
neare
the
AEquator
,
have
not
the
beginning
nor
later
part
of
the
night
enlightned
at
all
,
neither
is
there
any
appearance
of
light
,
before
the
Sunne
bee
risen
.
Whereas
,
on
the
contrary
side
,
those
that
have
the
very
near
their
Horizon
,
must
necessarily
have
Twilight
almost
all
the
night
long
in
Summer
.
And
therefore
when
the
came
into
and
perceived
that
,
at
the
Summer
Sostice
,
their
nights
were
light
almost
all
the
night
long
:
they
did
not
ac
ount
this
Twilight
to
bee
night
,
but
said
,
that
the
were
contented
with
a
very
short
night
.
Now
this
as
it
is
defined
by
is
nothing
else
but
a
kind
of
Antiperistasis
,
or
Circumstipation
(
as
we
may
call
it
)
of
the
light
:
which
can
be
none
at
all
,
in
those
places
,
where
the
and
Horizon
,
are
farre
distant
.
For
this
in
that
place
accurately
observeth
,
is
onely
found
under
those
signes
which
are
neare
the
Solsticiall
point
,
as
and
that
in
those
Countries
too
,
where
the
night
is
somewhat
larger
,
then
it
is
under
the
Pole
of
the
Ecliptick
:
as
for
example
.
(
to
use
own
words
)
those
that
have
not
the
for
their
Articke
circle
,
nor
where
it
toucheth
the
North
point
of
the
Horizou
;
with
them
the
night
is
so
long
darke
,
as
while
the
commeth
to
strike
upon
the
North
point
of
the
Horizon
.
As
wee
know
it
hapneth
an
where
our
Countrie
men
that
were
Souldiers
there
,
could
see
to
play
at
dice
all
night
long
without
any
Candle
,
about
the
time
that
the
dayes
were
at
the
longest
.
Now
the
is
distant
from
the
Horzizon
at
m.
or
thereabout
.
And
therefore
so
much
is
the
distance
betwixt
the
Sun
and
their
Horizon
at
midnight
in
the
Summer
Solstice
:
so
that
necessarily
the
rest
of
the
night
must
bee
Twilight
,
and
of
minutes
,
which
is
the
length
of
their
night
,
not
above
m.
which
is
not
much
above
halfe
an
hour
,
are
quite
dark
:
and
all
the
rest
of
the
night
is
light
.
Whence
you
may
perceive
the
reason
of
the
long
continuance
of
the
day
in
those
regions
,
that
have
the
neare
bordering
on
their
Horizon
.
And
therefore
the
being
not
well
acquainted
with
this
Antiperistasis
of
the
light
,
thought
that
in
those
parts
they
had
had
scarce
any
night
at
all
.
And
hence
it
necessarily
followes
,
that
by
how
much
the
is
more
remote
from
the
Horizon
,
by
so
much
are
the
nights
lesse
enlightned
:
and
those
that
inhabite
neare
the
AEquinoctiall
are
so
farre
from
having
their
day
extended
farther
,
either
before
the
Sun
rises
,
or
after
it
sets
,
as
that
with
them
there
is
no
appearance
of
light
at
all
,
before
the
Sun
is
up
.
And
there
is
scarcely
any
Twilight
or
dawning
of
the
Day
at
all
in
those
regions
that
lye
within
tenne
,
degrees
of
the
AEquinoctiall
:
for
which
there
can
b●…
no
other
reason
given
,
but
onely
the
distance
betwixt
the
and
their
Horizon
.
And
if
they
have
no
Twilight
in
the
Summer
,
how
much
lesse
will
there
be
any
when
the
Sun
is
in
the
other
So
that
we
have
no
reason
to
give
any
credit
to
who
when
he
had
occasion
to
write
of
this
argument
,
gave
this
to
be
the
reason
of
it
,
because
there
are
no
mountaines
there
to
hinder
,
but
that
the
Sun
may
be
seen
at
the
instant
of
his
rising
.
But
this
is
a
ridiculous
reason
,
and
not
worthy
a
consutation
.
Thus
Artificiall
day
Artificiall
Night
Artificiall
day
Artificial
day
Artificiall
day
Artificiall
day
September
:
Artificial
day
The
unequall
hours
do
answer
to
the
which
,
as
you
have
heard
before
,
)
is
defined
to
be
the
space
of
time
that
the
Sun
remains
in
the
uppper
Hemisphoere
:
to
which
is
opposed
the
comprehending
all
that
time
,
while
the
sun
is
hid
from
us
.
Which
space
of
time
,
seeing
that
it
is
always
divided
into
equall
parts
,
which
are
therefore
called
equall
houres
,
because
they
are
alwayes
of
equall
length
,
fifteen
degrees
of
the
AEquator
rising
&
setting
every
hour
.
For
the
whole
AEquator
being
divided
into
parts
,
there
are
contained
in
the
revolution
of
it
parts
of
time
,
which
is
the
measure
of
an
hour
so
that
an
equall
hour
is
the
part
of
the
while
AEquinoctiall
circle
.
Artificiall
day
The
manner
how
to
find
the
longitude
and
latitude
of
Starres
,
may
bee
shewed
by
this
example
.
First
,
let
us
propose
the
head
of
which
is
found
in
the
Tables
to
bee
in
the
twentie
one
gr.
and
it
hath
in
Northerne
latitude
twentie
three
degrees
.
Now
therefore
in
the
superficies
of
the
wee
must
looke
for
the
signe
and
reckon
gr.
from
the
beginning
of
the
same
on
the
Eclipticke
:
And
the
circle
that
shall
bee
drawn
from
the
Pole
of
the
Ecliptick
,
through
this
degree
,
shall
be
called
the
the
circle
of
longitude
of
the
head
of
After
this
,
reckon
the
latitude
of
the
Starre
also
in
the
same
circle
among
the
Parallels
of
latitude
,
beginning
from
the
Eclipticke
,
and
so
forward
toward
the
Articke
Pole
,
(
because
the
latitude
of
it
is
Northerne
.
)
untill
you
have
accounted
gr.
which
is
the
number
of
the
degrees
of
latitude
,
and
sheweth
the
place
of
that
Star
.
Now
because
that
all
the
circles
of
Longitude
,
and
latitudes
neither
are
,
nor
indeed
can
conveniently
be
expressed
on
the
therefore
the
Quadrant
of
altitude
is
to
serve
in
stead
of
the
same
,
for
the
finding
out
of
the
longitudes
and
situations
of
the
Starres
that
are
set
in
the
and
that
after
this
manner
.
Let
us
take
our
former
example
of
's
head
:
the
latitude
of
which
being
Northerne
,
I
apply
the
end
of
the
Quadrant
to
the
North
Pole
of
the
Zodiack
:
(
otherwise
,
had
it
been
Southern
,
it
must
have
been
fitted
to
the
Southern
Pole
:
)
which
do●…e
,
I
seeke
in
the
Eclipticks
for
the
21
gr.
of
which
is
the
logitude
of
the
Starre
;
and
having
found
it
,
I
lay
the
other
end
of
my
Quadrant
over
it
.
For
by
this
means
the
Quadrant
shall
supply
the
office
of
the
circle
of
Longitude
of
head
.
〈◊〉
therefore
if
I
reckon
23
degrees
on
the
said
Quadrant
beginning
from
the
Eclipticke
,
I
shall
have
the
true
situation
of
this
Starre
in
the
In
like
manner
,
may
we
find
,
by
a
that
hath
the
Starres
described
on
it
,
the
longitude
and
latitude
of
any
Starre
in
the
Heavens
.
For
if
we
fit
the
Quadrant
to
the
Northern
Pole
of
the
(
if
the
Starre
have
Northerne
latitude
)
and
then
let
it
passe
through
the
center
of
any
Starre
:
the
degree
of
the
Ecliptick
that
the
other
end
of
it
shall
point
out
,
will
be
the
longitude
of
the
said
Starre
:
and
the
degrees
that
are
contained
betwixt
the
ECliptick
and
the
Starre
,
will
shew
you
the
latitude
of
the
same
.
A
for
example
if
the
Quadrant
being
first
applied
to
the
Northern
Pole
of
the
bee
afterward
laid
along
over
the
the
bright
Star
in
the
the
other
end
of
it
will
fall
on
the
6.
gr.
m.
which
is
the
longitude
of
this
Starre
.
And
then
if
you
reckon
the
number
of
degrees
betwixt
the
Eclipticke
and
the
same
Starre
,
you
shall
find
them
to
bee
44½
.
which
is
the
Northern
latitude
of
the
same
.
The
Declination
of
Starres
,
as
also
their
Right
Ascension
,
may
be
known
by
the
in
this
manner
.
The
Star
proposed
must
be
applied
to
the
Meridian
,
and
forthwith
the
same
Meridian
will
discover
,
among
the
degrees
of
the
AEquator
,
the
Right
Ascension
of
the
same
:
and
it
will
also
give
you
the
Declination
,
if
you
reckon
upon
it
the
number
of
degrees
that
are
comprehended
betwixt
the
AEquinoctiall
and
the
Star
proposed
.
And
for
an
example
of
this
,
let
us
propose
the
Great
Dog
,
whose
right
Ascension
and
Declination
wee
desire
to
know
.
First
,
therefore
we
set
the
Starre
it selfe
directly
under
the
Meridian
,
and
find
the
Meridian
to
cut
the
AEquinoctiall
at
97.
gr.
15.
min.
And
this
is
the
right
Ascension
of
this
Star
.
And
then
reckoning
the
number
of
the
degrees
comprehended
betwixt
it
and
the
AEquinoctiall
Southward
,
we
find
them
to
be
16
degrees
,
which
we
conclude
to
bee
the
Southern
latitude
of
the
Starr
.
The
same
also
may
be
demonstrated
by
the
Sun
,
For
when
the
Sunne
is
in
the
3.
gr.
of
he
is
carried
under
the
Meridian
,
which
crosseth
the
AEquinoctiall
about
the
63.
gr.
reckoning
from
the
first
degree
of
in
the
AEquator
.
And
this
is
the
Ascension
of
the
Sun
when
he
is
in
the
〈◊〉
.
degree
of
Now
the
number
of
the
P.
De
Medina
P.
Nonius
C.
Frio
Cape
of
good
hope
Portugalls
,
Rio
de
las
Agulias
.
At
the
end
of
this
Chapter
,
I
think
it
not
amisse
to
set
down
,
that
which
sometime
upon
occasion
offered
,
wrote
unto
concerning
the
declination
of
the
Magneticall
Needle
from
the
true
Meridian
.
This
Epistle
of
his
is
extant
among
those
Epistles
that
were
set
forth
at
with
some
other
of
his
workes
,
Aad
because
that
there
is
something
in
the
same
that
concerns
the
controversie
of
the
Praecession
of
the
AEquinoctiall
points
;
I
will
set
down
very
near
the
whole
Epistle
:
and
thus
it
is
.
Your
Letters
I
have
receceived
,
and
with
very
great
satisfaction
and
delight
:
wherein
I
perceived
two
things
chiefely
to
bee
insisted
upon
:
which
were
,
the
Declination
of
the
Magneticall
Needle
;
and
the
Precession
of
the
AEquinoctiall
points
.
In
my
former
Letters
I
made
mention
indeed
of
the
same
,
but
with
an
intention
rather
to
discover
the
opinion
of
others
,
then
to
proclaim
mine
own
.
For
I
onely
made
a
bare
proposall
of
the
matter
,
and
no
dogmaticall
Position
:
that
so
,
i●…
the
said
declination
bee
to
bee
examined
by
the
Meridians
,
add
the
Meridians
,
according
to
my
Hypothesis
,
be
moveable
;
that
then
our
Astronomers
and
Navigators
should
see
,
whether
or
no
,
there
might
not
some
cause
and
reason
of
this
so
manifest
disagreement
bee
discovered
,
out
of
this
Essay
of
mine
.
For
I
would
not
have
proposed
it
onely
,
had
I
been
certainly
assured
of
it
:
but
would
rather
have
endeavoured
to
make
it
appear
by
demonstration
.
Whether
therefore
,
that
be
the
cause
of
it
,
which
I
desire
should
be
searched
for
out
of
my
Hypothesis
;
or
whether
it
be
some
other
it
shall
be
all
one
to
me
.
But
the
investigation
of
the
Meridians
is
not
sufficient
for
this
matter
.
For
wee
must
first
dispute
concerning
the
nature
of
the
Magnet
,
whether
or
no
it
be
the
property
of
it
,
always
to
respect
the
North
point
:
and
if
so
,
yet
seeing
that
it
declines
from
the
tearm
proposed
,
so
many
degrees
,
we
are
next
to
enquire
,
whence
this
Uariation
proceeds
:
which
certainly
can
be
assigned
to
no
other
thing
,
then
to
the
Meridians
.
But
that
wee
may
not
urge
this
question
any
farther
:
we
must
consult
with
those
Authors
that
have
written
of
the
Magnet
;
and
especially
with
a
Philosopher
and
Practitioner
of
Physick
in
who
about
three
yeares
since
put
forth
three
large
bookes
of
the
same
subject
:
wherein
hee
hath
discovered
to
me
his
own
learning
rather
,
then
the
nature
of
the
Magnet
.
For
now
I
am
more
in
doubt
,
then
before
.
The
other
part
of
your
Letter
is
,
concerning
the
Praecession
of
the
AEquinoctiall
points
.
It
was
observed
first
of
all
by
out
of
the
observations
of
the
fixed
Starres
of
that
the
AEquinoctiall
points
were
gone
gone
forward
into
the
precedent
parts
;
because
that
hee
had
found
that
the
four
points
(
AEquinoctiall
and
Solsticiall
)
were
farther
off
from
the
Starres
assigned
for
the
same
,
then
they
were
in
the
time
of
those
Astronomers
.
Which
when
hee
saw
,
bee
doubted
not
forthwith
to
affirme
,
that
the
AEquinostiall
points
were
immoveable
,
and
that
the
Sphaere
of
the
fixed
Starrs
was
gone
backe
into
the
sacceeding
parts
.
And
he
did
not
perswad●…
himselfe
onely
to
this
,
but
even
also
;
and
all
that
came
after
him
,
so
great
is
the
power
of
Prejudicate
Authority
.
And
he
also
rectified
the
and
made
the
taile
of
the
little
to
be
distant
from
the
Pole
twelve
twenty
four
min.
choosing
rather
to
believe
it
to
be
so
,
then
to
consult
with
the
Starrs
to
see
whether
it
were
so
indeed
,
or
no.
Which
thing
I
cannot
sufficiently
wonder
at
in
him
;
seeing
,
that
not
only
in
his
time
,
but
also
two
hunared
and
eighteen
yeares
before
him
,
the
taile
of
the
lesser
Bear
was
no
farther
from
the
Pole
of
the
world
,
then
it
is
at
this
day
:
as
observed
,
Which
I
have
most
plainly
demonstrated
in
my
book
of
the
also
,
who
wrote
one
hundred
twenty
eight
years
after
affirmed
the
same
of
the
same
Starre
:
and
so
did
those
that
wrote
in
his
time
.
If
therefore
two
hundred
and
eighteen
years
before
time
,
that
Starre
was
where
it
is
now
;
how
then
can
that
position
of
stand
,
who
placed
it
of
the
Pole
of
the
world
?
For
if
the
Sphaere
of
the
fixed
Starres
laid
more
backward
into
the
succeeding
parts
,
(
as
hee
would
have
it
)
and
that
in
his
time
the
Taile
of
the
Cynosure
was
distant
from
the
Pole
:
it
necessarily
follows
,
that
in
time
it
must
have
been
farther
distant
from
the
Pole
,
by
For
this
is
the
proportion
of
degrees
required
for
that
motion
.
But
it
was
then
no
farther
distant
,
then
it
is
at
this
day
:
and
therefore
hath
abused
both
himselfe
,
and
all
that
have
come
after
him
.
And
indeed
I
my selfe
have
made
a
collection
out
of
him
,
of
all
the
risings
and
settings
of
the
Starres
;
which
no
man
shall
ever
be
able
to
understand
,
except
he
first
make
such
a
Globe
,
wherein
the
taile
of
the
Cynosure
shall
be
distant
from
the
Pole
.
which
thing
when
I
imparted
to
that
great
Astronomer
he
was
amused
,
and
wondred
very
much
at
the
novelty
and
strangeness
of
the
thing
:
and
indeed
not
without
cause
.
For
I
did
not
speak
a
word
to
him
of
the
construction
of
and
the
distance
of
the
Cynosure
from
the
Pole
of
it
.
And
therefore
we
plainly
see
,
that
for
as
much
as
this
Star
keeps
the
same
distance
from
the
Pole
at
this
day
,
that
it
did
years
since
,
there
is
no
motion
at
all
of
the
eighth
Sphaere
into
the
succeding
parts
,
but
of
the
AEquinoctiall
points
into
the
precedent
.
For
of
the
motion
there
is
no
doubt
at
all
to
be
made
,
for
at
this
time
the
AEquinoxe
falleth
before
the
first
Star
in
which
notwithstanding
in
his
time
happened
at
the
very
Star
.
But
now
whether
the
Star
hath
left
the
Sun
behind
it
,
or
the
Sun
the
Star
,
is
the
principall
matter
in
question
.
For
it
must
be
,
that
one
of
them
must
stand
still
,
and
the
other
move
:
but
wee
have
already
shewed
that
the
Starrs
are
immoveable
:
and
therefore
the
Sun
and
AEquinoctiall
points
are
movable
.
And
indeed
they
have
manifestly
gone
forward
since
(
that
great
Scholar
,
and
second
of
our
age
)
perceived
,
when
he
spake
these
words
.
You
think
(
saith
he
)
that
the
eighth
Sphaere
moveth
into
the
consequent
parts
:
but
consider
whether
the
AEquinoctiall
points
do
not
rather
move
forward
.
Whence
it
appears
,
that
this
never
suffioiently
commended
man
,
concluded
,
that
there
was
a
praecession
of
the
AEquinoctiall
points
,
and
not
a
motion
of
the
eighth
Sphaere
into
the
subs●…quent
paerts
.
For
one
of
these
being
granted
,
the
other
must
necessarily
bee
taken
away
:
for
if
the
eighth
Sphaere
doth
not
move
backward
,
the
AEquinoctiall
points
must
necessarily
move
forward
.
And
therefore
herein
conjectured
aright
.
But
hee
omitted
the
chiefest
matter
of
all
,
either
because
perhaps
hee
perceived
it
not
,
or
else
despaired
of
ever
being
able
to
demonstrate
it
.
For
seeing
that
the
AEquinoctiall
points
are
Moveable
,
it
must
needs
follow
,
that
a
greater
Circle
described
by
the
same
must
bee
Moveable
also
,
by
the
twenty
And
if
the
Circle
bee
Moveable
,
the
Pole
must
also
be
Moveable
.
And
therefore
the
Pole
of
the
AEquinoctiall
is
not
the
same
with
the
Pole
of
the
world
:
for
this
is
Immoveable
,
but
the
other
Moveable
:
for
so
consequently
all
the
greater
Circles
passing
through
these
Poles
,
which
are
the
Meridians
,
are
also
Moveable
.
So
that
Sunne-Dialls
,
and
all
Sciotericall
instruments
,
that
are
placed
upon
a
Meridian
Line
,
after
some
certain
tearm
of
years
,
must
necessarily
be
defective
:
because
the
line
it selfe
is
removed
from
its
former
situation
.
Of
which
variablenesse
wee
have
obse
ved
notable
arguments
in
monuments
of
Antiquity
.
These
things
,
it
did
concern
either
to
have
seene
,
or
demonstrated
,
who
was
the
first
man
that
ever
rejected
that
fabulous
and
ridiculousmotionof
the
eighth
Sphaere
,
and
withall
proposed
this
opinion
of
the
Praecession
of
the
AEquinoctiall
points
:
who
,
had
hee
but
seen
seen
those
things
,
which
we
have
observed
historically
out
of
the
writings
of
the
Ancient
Astronomers
,
so
great
was
the
ingenuity
of
the
man
,
that
he
would
have
instantly
consented
,
and
demonstrated
the
matter
Mathematically
;
which
certainly
is
no
hard
matter
to
do
.
For
,
is
there
any
man
so
void
of
all
reason
and
judgement
,
as
having
granted
the
AEquinoctiall
points
to
bee
Moveable
,
to
deny
that
a
great
Circle
described
by
the
same
,
must
necessarily
be
moveable
also
:
and
if
so
,
that
the
Poles
are
also
Moveable
:
and
again
this
〈◊〉
granted
,
that
the
Meridians
are
so
too
?
He
that
shall
deny
this
,
I
cannot
see
,
what
it
hath
profited
him
to
have
studied
the
Mathematicks
.
But
you
will
object
,
that
the
Meridians
are
not
changed
,
because
they
pass
through
the
Poles
of
the
world
,
which
are
Immutable
.
But
then
you
have
forgotten
our
Hypothesis
,
which
is
,
that
the
Poles
of
the
AEquinoctiall
are
not
the
same
with
the
Poles
of
the
world
.
For
these
are
immutable
,
but
those
other
Mutable
.
And
therefore
wee
see
the
necessity
of
this
Argument
;
and
withal
,
that
these
things
being
so
,
we
are
yet
very
farre
to
seek
in
many
things
necessary
for
the
situation
and
construction
of
the
Sphaere
.
For
by
this
reckoning
it
followeth
necessarily
,
that
the
AEquinoctiall
Circle
should
not
bee
described
directly
Parallel
to
the
Pole
of
the
world
:
and
many
other
things
of
this
nature
,
which
might
hence
bee
concluded
,
I
might
willingly
omit
,
because
I
speak
to
a
Mathematician
,
who
might
better
teach
in
these
things
.
Wherefore
I
think
I
may
boldly
say
,
that
none
can
be
so
impudent
as
to
deny
these
things
which
are
so
manifest
,
as
that
we
can
prove
them
not
only
Historically
,
but
also
Apodictically
,
by
certain
demonstrations
.
And
it
behoves
you
to
see
and
examine
more
narrowly
whatsoever
hath
been
written
by
Mathematicians
concerning
this
matter
.
For
there
is
now
no
place
left
of
deny
all
,
but
rather
to
see
,
how
these
things
may
be
better
demonstrated
,
and
this
done
,
the
construction
and
position
of
the
Sphaere
corrected
.
But
I
do
not
speak
this
to
the
common
sort
of
Astrologers
,
who
never
have
read
any
thing
but
the
Theories
of
the
Planets
,
and
never
so
much
as
saw
any
of
the
ancient
Writers
:
unto
whom
,
although
they
should
perhaps
have
recourse
,
they
could
not
understand
.
Now
as
concerning
the
motion
of
it
is
long
since
exploded
:
and
for
his
motion
of
which
is
also
a
very
vain
conceit
,
and
I
shall
speak
more
of
it
here
,
and
shew
whence
this
so
idle
a
dream
should
possesse
so
worthy
a
man
:
for
it
differeth
not
much
from
that
imposture
of
And
as
the
truth
hath
at
length
got
place
,
and
removed
that
fabulous
motion
of
so
we
doubt
not
but
necessity
will
at
the
last
send
after
it
this
motion
of
the
eighth
Sphaere
also
.
This
therefore
is
the
summe
of
our
answer
:
that
we
desire
,
that
the
skillfull
Artists
would
consider
,
whether
the
knowledge
of
the
variation
of
the
Magneticall
Needle
may
be
illustrated
by
those
things
which
we
have
delivered
concerning
the
Mutability
of
the
Meridians
:
That
there
is
no
motion
of
the
eighth
Sphaere
into
the
consequent
parts
:
That
we
are
the
first
that
have
demonstrated
the
same
:
And
that
from
thence
must
necessarily
follow
the
praecession
of
of
the
AEquinoctiall
points
.
And
this
being
granted
,
that
then
the
AEquinoctiall
points
,
AEquinoctia
Circles
,
and
their
Poles
,
and
Meridians
,
passing
through
them
are
also
movable
:
and
their
Poles
also
different
from
the
Poles
of
the
world
.
And
that
the
situation
of
Sun
Dialls
doth
vary
after
s●…me
tearm
of
years
:
and
that
we
are
the
first
that
observed
the
History
of
this
not
able
piece
of
Antiquity
;
which
also
may
be
demonstrated
out
of
the
Mathematicks
.
This
is
my
opinion
,
which
I
will
ever
defend
.
But
do
you
consider
better
of
it
:
and
in
the
mean
time
Farewell
.
And
this
is
Epistle
,
in
which
whereas
he
speaketh
of
three
Books
of
the
Magnet
,
written
by
it
seems
to
be
a
slip
of
his
memory
:
for
the
same
Author
wrote
not
three
,
but
sixe
Books
which
were
Printed
at
the
fourth
and
sifth
books
whereof
do
especially
handle
the
doctrine
of
the
variation
of
the
Compass
.
And
whereas
he
addeth
,
that
himselfe
had
plainly
demonstrated
in
a
certain
book
of
his
,
that
the
Tail
of
the
Cynosure
had
the
same
situation
anciently
,
that
it
bath
at
this
day
;
he
meaneth
that
book
which
beareth
title
,
and
was
printed
at
Paris
Which
Book
I
understand
since
,
that
and
professor
of
the
Mathematicks
in
hath
undertaken
to
confute
:
as
appears
by
the
Catalogue
of
Books
in
the
year
where
there
is
mention
made
of
the
same
confutation
printed
at
and
at
in
quarto
.
In
which
book
the
Author
takes
upon
him
to
impugne
certain
new
Tenets
,
concerning
the
Polar
Star
,
and
the
mutation
of
the
AEquinoctiall
points
,
and
immobility
of
the
fixed
Starrs
:
with
divers
Astronomicall
matters
,
which
the
title
promiseth
:
notwithstanding
it
hath
not
yet
been
my
good
hap
,
though
I
have
made
very
diligent
enquiry
,
to
meet
with
any
of
these
books
.
Petrus
Nonius
Petrus
Nonius
de
Navigand●…
ratione
Gemma
Frisius
P.
Appians
Jul
,
Scaliger
Ludovicus
Vertomannus
Ferdinand
Magellane
Pet.
Nonius
Michael
Coignet
Gemma
Frisius
Cap.
Appian
Cosmography
Michael
Coignet
Gemma
Frisius
Appians
Cosmography
Verbum
hoc
obi●…er
annotandum
,
&c.
Wernerus
,
Peucerus
De
Dimensione
Terrae
C.
Ortegall
C.
Dalguer
Expectata
seges
vanis
deludet
avenis
Serra
Liona
Serra
Liona
Serra
Liona
C.
Cantin
C.
Cantin
C.
Verde
C.
Saint
Augustine
C.
Verde
C.
Saint
Augustine
C.
Verde
C.
Saint
Augustine
C.
D'alguer
C.
D'alguer
C.
Blanco
Cape
of
good
Hope
Tho.
Wykes
Lond.
Capel
.
Domest