The
Second
Book
.
Shewing
the
Practical
Use
of
the
GLOBES
.
Applying
them
to
the
Solution
of
Astronomical
and
Geographical
Problems
.
PRAEFACE
.
Some
Advertisements
in
Choosing
and
Using
the
GLOBES
.
1.
SEE
the
Papers
be
well
and
neatly
pasted
on
the
Globes
:
which
you
may
know
,
if
the
Lines
and
Circles
discribed
thereon
meet
exactly
,
and
continue
all
the
way
even
and
whole
:
the
lines
not
swerving
out
or
in
,
and
the
Circles
not
breaking
into
several
Arches
;
nor
the
Papers
either
come
short
,
or
lap
over
one
the
other
.
2.
See
that
the
Culler
be
transparent
,
and
ly
not
too
thick
on
the
Globe
;
lest
it
hide
the
superficial
Descriptions
.
3.
See
the
Globe
hang
evenly
between
the
Meridian
and
Horizon
,
not
inclining
more
to
one
side
then
the
other
.
4.
See
the
Globe
swim
as
close
to
the
Meridian
and
Horizon
as
conveniently
it
may
;
lest
you
be
too
much
puzzeld
to
find
against
what
point
of
the
Globe
any
degree
of
the
Horizon
or
Meridian
is
.
5.
See
the
Equinoctal
line
be
one
with
the
Horizon
,
when
the
Globe
is
set
in
a
Parallel
Sphear
.
6.
See
the
Equinoctal
line
cut
the
East
and
West
point
of
the
Horizon
,
when
the
Globe
is
set
to
an
Oblique
Sphear
.
7.
See
the
Degrees
marked
with
90.
and
00
,
hang
exactly
over
the
Equinoctial
line
of
the
Globe
.
8.
See
that
exactly
half
the
Meridian
be
above
the
Horizon
,
and
half
under
the
Horizon
:
which
you
may
know
if
you
bring
any
of
the
Decimal
Divisions
to
the
North
Side
of
the
Horizon
,
and
find
their
Complement
to
90.
int
h
South
.
9.
See
that
when
the
Quadrant
of
Altitude
is
placed
at
the
Zenith
,
the
Beginning
of
the
Graduations
reach
just
to
the
superficies
of
the
Horizon
.
10.
See
that
while
the
Index
of
the
Hour
Circle
(
by
the
motion
of
the
Globe
)
passes
from
one
hour
to
the
other
,
15.
degrees
of
the
Equator
pass
through
the
Meridian
.
11.
If
you
have
a
Circle
of
Position
,
see
the
Graduations
agree
with
those
of
the
Horizon
.
12.
See
that
your
wooden
Horizons
be
made
substantial
and
strong
;
for
(
besides
the
Inconveniences
that
thin
wood
is
subject
unto
,
in
respect
of
warping
and
shrinking
)
I
have
had
few
Globes
come
to
mending
that
have
not
had
either
broken
Horizons
,
or
some
other
notorious
fault
,
occasioned
through
the
sleightness
of
the
Horizons
.
In
the
Using
the
Globes
.
KEep
the
East
side
of
the
Horizon
alwaies
towards
you
,
unless
your
Proposition
requires
the
turning
of
it
:
which
East
side
you
may
know
by
the
Word
East
,
placed
on
the
outmost
verge
thereof
.
For
then
have
you
the
graduated
side
of
the
Meridian
alwaies
towards
you
;
the
Quadrant
of
altitude
before
you
,
and
the
Globe
divided
exactly
into
two
equal
parts
.
So
oft
as
I
name
to
,
at
,
of
,
or
under
the
Meridian
,
or
Horizon
,
I
mean
the
East
side
of
the
Meridian
,
and
Superficies
of
the
Horizon
:
because
the
East
side
of
the
Meridian
passes
through
the
North
and
South
points
,
both
of
the
Globe
and
Horizon
;
and
agrees
just
with
the
middle
of
the
Axis
:
And
the
Superficies
of
the
Horizon
divideth
the
Globe
exactly
into
two
equal
parts
.
It
you
happen
to
use
the
Globes
on
the
South
side
the
Equator
,
you
must
draw
the
wyers
out
of
either
Pole
,
and
change
them
to
the
contrary
Poles
;
putting
the
longest
wyer
into
the
South
Pole
.
And
because
on
the
other
side
the
Equator
the
South
Pole
is
elevated
,
therefore
you
must
elevate
the
South
Pole
of
the
Globe
above
the
Horizon
;
according
to
the
South
Latitude
of
your
Place
;
as
shall
be
shewed
hereafter
.
In
the
working
some
Problems
it
will
be
required
that
you
turn
the
Globe
to
look
on
the
West
side
thereof
:
which
turning
will
be
apt
to
jog
the
Ball
,
so
as
the
degree
that
was
at
the
Horizon
or
Meridian
,
will
be
moved
away
,
and
thereby
the
Position
of
the
Globe
altered
.
To
avoid
which
inconvenince
you
may
make
use
of
a
Quill
,
thrusting
the
Feather
end
between
the
Ball
and
the
Brazen
Meridian
,
and
so
wedge
it
up
,
without
wronging
the
Globe
at
all
,
till
your
Proposition
be
answered
.
PROBLEME
I.
To
find
the
Longitude
and
Latitude
of
Places
,
on
the
Terrestrial
Globe
.
SEek
the
Place
on
the
Terrestrial
Globe
,
whose
Longitude
and
Latitude
you
would
know
,
and
bring
that
Place
to
the
Brazen
Meridian
;
and
see
how
many
degrees
of
the
Equator
is
cut
by
the
Meridian
,
from
the
first
general
Meridian
,
(
which
on
my
Globes
pass
through
Gratiosa
,
one
of
the
Isles
of
the
Azores
,
)
for
that
number
of
degrees
is
the
Longitude
of
the
Place
.
Example
.
I
desire
to
know
the
Longitude
of
London
,
and
close
to
the
name
London
I
find
a
smal
mark
0
thus
,
(
which
smal
mark
is
in
some
Globes
and
Maps
adorned
with
the
Picture
of
a
Steeple
,
&c.
)
therefore
I
do
not
bring
the
word
London
to
the
Meridian
,
but
that
smal
mark
;
for
that
alwaies
represents
the
the
Town
or
Citty
sought
for
:
And
keeping
the
Globe
steddy
in
this
Position
,
I
examine
how
many
degrees
of
the
Equator
are
contained
between
the
Brazen
Meridian
,
and
the
first
general
Meridian
;
which
I
find
to
be
24.
deg.
00.
min.
Therefore
I
say
the
Longitude
of
London
is
24.
degrees
00.
min.
For
the
Latitude
.
See
on
the
Brazen
Meridian
how
many
degrees
are
contained
between
the
Equator
and
the
mark
for
London
;
which
in
this
Example
is
51½
:
therefore
I
say
London
hath
51½
degrees
North
Latitude
.
PROBLEME
II.
The
Longitude
and
Latitude
being
know
,
to
Rectifie
the
Globe
fit
for
use
.
1.
WHen
you
rectifie
the
Globe
to
any
particular
Latitude
you
must
move
the
Brazen
Meridian
through
the
notches
of
the
Horizon
till
the
same
number
of
degrees
accounted
on
the
Meridian
from
the
Pole
(
about
which
the
Hour-Circle
is
)
towards
the
North
point
in
the
Horizon
(
if
in
North
Latitude
,
and
toward
the
South
if
in
South
Latitude
)
come
just
to
the
edge
of
the
Horizon
.
Example
.
By
the
former
Proposition
I
found
the
Latitude
of
London
to
be
51½
degrees
North
Latitude
:
therefore
I
count
51½
degrees
from
the
Pole
downwards
towards
my
right
hand
,
and
turn
the
Meridian
through
the
notches
of
the
Horizon
till
those
51½
degrees
comes
exactly
to
the
uppermost
edge
of
the
North
point
in
the
Horizon
;
and
then
is
the
Meridian
rectified
to
the
Latitude
of
London
.
2.
Next
rectifie
the
Quadrant
of
altitude
,
after
this
manner
,
Screw
the
edge
of
the
Nut
that
is
even
with
the
graduated
edge
of
the
thin
Plate
,
to
51½
degrees
of
the
Brazen
Meridian
,
accounted
from
the
Equinoctial
on
the
Southern
side
the
Horizon
,
which
is
just
the
Zenith
of
London
:
and
then
is
your
Quadrant
Rectified
.
3.
Bring
the
degree
of
the
Ecliptick
the
Sun
is
in
that
day
,
to
the
Meridian
:
which
you
shall
learn
to
know
by
the
next
Probleme
,
and
then
turn
the
Index
of
the
Hour
Circle
to
the
hour
12.
on
the
South
side
the
Hour
Circle
,
and
then
is
your
Hour
Circle
also
rectified
fit
to
use
,
for
that
Day
.
4.
Lastly
If
you
will
rectifie
the
Globe
to
correspond
in
all
respects
with
the
Position
and
Scituation
of
the
Sphear
,
you
must
set
the
four
Quarters
of
the
Horizon
.
viz.
East
,
West
,
North
,
and
South
,
agreeable
with
the
four
quarters
of
the
World
;
which
you
may
do
by
the
Needle
in
the
bottom
of
the
Horizon
;
for
you
must
turn
the
Globe
so
long
till
the
Needle
point
just
to
the
Flower
de
luce
.
Next
you
must
set
the
Plain
of
the
wooden
Horizon
parallel
to
the
Horizon
of
the
World
;
which
you
may
try
by
setting
a
common
Level
on
the
four
Quaters
of
the
Horizon
.
And
then
positing
the
degree
of
the
Ecliptick
the
Sun
is
in
,
to
the
Height
above
,
or
depth
below
the
Horizon
,
the
Sun
hath
in
Heaven
,
(
as
by
the
11th
Probleme
)
your
Globe
is
made
Correspondent
in
all
points
with
the
frame
of
the
Sphear
,
for
that
particular
Time
,
and
Latitude
.
PROBLEME
III.
To
find
the
Place
of
the
Sun
in
the
Ecliptick
,
the
Day
of
the
Moneth
being
first
known
.
SEek
the
Day
of
the
Moneth
in
the
Circle
of
Moneths
upon
the
Horizon
,
and
right
against
it
in
the
Circle
of
Signes
is
the
degree
of
the
Ecliptick
the
Sun
is
in
.
Example
.
Imagine
the
Day
to
be
given
is
May
10.
therefore
I
seek
on
the
Horizon
in
the
Circle
of
Moneths
,
for
May
,
and
find
the
Moneths
divided
into
so
many
parts
as
there
is
Daies
in
the
Moneth
;
which
parts
are
marked
with
Arithmetical
figures
,
from
the
beginning
of
the
Moneth
to
the
end
,
and
denote
the
number
of
the
Day
of
the
Moneth
that
each
Division
represents
:
therefore
among
the
Divisions
I
seek
for
10
,
and
directly
against
it
in
the
Circle
of
Signes
,
I
find
♉
29.
degrees
.
Therefore
I
say
May
10.
the
Suns
Place
is
in
29.
degrees
of
♉
.
But
note
,
that
if
it
be
Leap
Year
,
instead
of
the
10.
of
May
you
must
take
the
11.
of
May
:
because
February
having
in
a
Leap
Year
29.
Daies
,
the
29.
of
February
must
be
reckoned
for
the
first
of
March
,
and
the
first
of
March
for
the
second
of
March
;
the
second
of
March
for
the
third
of
March
;
and
so
throughout
the
year
.
The
Leap
Year
is
caused
by
the
six
od
hours
more
then
365.
daies
that
are
assigned
to
every
common
Year
:
so
that
in
a
Revolution
of
4.
Years
,
one
Day
is
gained
,
which
is
added
to
February
;
and
therefore
February
hath
every
fourth
or
Leap
Year
29.
Daies
.
PROBLEME
IIII.
To
find
the
Day
of
the
Moneth
,
the
Place
of
the
Sun
being
given
.
AS
in
the
last
Probleme
it
was
your
task
to
find
on
the
Horizon
the
Day
of
the
Moneth
first
,
so
now
you
must
first
seek
the
Signe
and
degree
the
Sun
is
in
,
and
against
it
in
the
Circle
of
Moneths
you
shall
see
the
Day
of
the
Moneth
:
As
against
♉
29.
you
have
May
10.
PROBLEME
V.
The
Place
of
the
Sun
given
,
to
find
its
Declination
.
HAving
by
the
third
Probleme
found
the
Suns
Place
on
the
Plain
of
the
Horizon
,
you
must
seek
the
same
degree
in
the
Ecliptick
,
on
the
Globe
;
then
bring
that
degree
to
the
Brazen
Meridian
;
and
the
number
of
degrees
intercepted
between
the
Equinoctial
and
the
degree
just-over
the
degree
of
the
Ecliptick
the
Sun
is
in
,
is
the
Declination
of
the
Sun
for
that
Day
:
and
bears
its
Denomination
of
North
or
South
,
according
to
its
Position
either
on
the
North
or
South
side
the
Equinoctial
.
Example
.
By
the
third
Probleme
aforesaid
,
of
May
10.
I
find
♉
29.
the
Suns
Place
;
Therefore
I
seek
in
the
Ecliptick
Line
on
the
Globe
for
♉
29.
and
bring
it
to
the
East
side
of
the
Brazen
Meridian
,
which
is
the
graduated
side
;
and
over
♉
29.
I
find
on
the
Brazen
Meridian
20.
deg.
5.
min.
(
numbred
from
the
Equinoctial
:
)
and
because
♉
is
on
the
North
side
the
Equinoctial
,
therefore
I
say
,
The
Sun
hath
May
10.
North
Declination
20.
degrees
5.
min.
PROBLEME
VI.
The
Place
of
the
Sun
given
,
to
find
its
Meridian
Altitude
.
THe
Globe
rectified
,
Bring
the
degree
of
the
Sun
to
the
Meridian
,
(
or
which
is
all
one
,
the
degree
of
the
Ecliptick
the
Sun
is
in
;
)
and
the
number
of
degrees
contained
between
the
Horizon
and
the
Suns
Place
in
the
Meridian
,
is
the
number
of
degrees
that
the
Sun
is
Elevated
above
the
Horizon
at
Noon
,
or
(
which
is
all
one
)
the
Meridian
Altitude
of
the
Sun
.
Example
.
To
know
what
Meridian
Altitude
the
Sun
hath
here
at
London
,
May
10.
I
bring
the
Suns
Place
(
found
by
the
third
Probleme
)
to
the
Meridian
,
and
count
on
the
Meridian
the
number
of
degrees
contained
between
the
Horizon
and
the
degree
just
over
the
Suns
Place
;
which
in
this
Example
I
find
to
be
58½
▪
Therefore
I
say
the
Suns
Meridian
Altitude
May
10.
is
here
at
London
58½
degrees
.
PROBL.
VII
.
The
Suns
Place
given
,
to
find
the
Hour
of
Sun
Rising
,
and
the
length
of
the
Night
and
Day
.
THe
Globe
and
Hour
Index
rectified
,
Seek
the
degree
the
Sun
is
in
on
the
Globe
,
and
bring
that
degree
to
the
Eastern
Side
of
the
Horizon
;
and
the
Index
of
the
Hour
Circle
will
point
at
the
Hour
of
Sun
Rising
.
Example
.
To
know
the
Hour
of
Sun
Rising
here
at
London
,
May
10.
The
Suns
Place
(
as
before
)
is
♉
29.
Therefore
the
Globe
being
rectified
(
as
before
)
I
seek
♉
29.
degrees
on
the
Globe
,
and
bring
that
degree
to
the
East
Side
of
the
Horizon
;
and
looking
on
the
Index
of
the
Hour
Circle
,
I
find
it
point
at
4.
a
clock
and
⅙
part
of
an
hour
more
towards
5
;
therefore
I
say
May
10.
the
Sun
rises
here
at
London
at
⅙
(
which
is
12.
minutes
)
after
4
a
clock
in
the
Morning
.
If
you
double
4
hours
12.
minutes
,
it
gives
you
the
length
of
the
Night
,
8
hours
24.
minutes
.
And
if
you
substract
the
length
of
the
Night
8.
hours
24.
minutes
,
from
24.
hours
,
the
length
of
Day
and
Night
;
it
leaves
the
length
of
the
Day
15.
hours
36.
minutes
.
PROB.
VIII
.
To
find
the
Hour
of
Sun
Set.
TUrn
the
Place
of
the
Sun
to
the
West
side
of
the
Horizon
,
and
the
Index
of
the
Hour
Circle
shews
on
the
Hour-Circle
the
hour
of
Sun
set
;
which
on
the
10th
of
May
aforesaid
,
is
〈◊〉
parts
of
an
hour
after
〈◊〉
7.
a
clock
at
Night
,
Viz.
the
Sun
Sets
at
48.
minutes
past
7.
a
clock
.
PROB.
IX
.
To
find
how
long
it
is
Twilight
in
the
Morning
,
and
Evening
.
TWilight
is
that
promiscuous
and
doubtfull
light
which
appears
before
the
Rising
of
the
Sun
in
the
Morning
,
and
continues
after
the
setting
of
the
Sun
in
the
Evening
:
It
is
made
by
the
extension
of
the
Suns
beams
into
the
Vapours
of
the
Air
,
when
the
Sun
is
less
then
18.
deg.
below
the
Horizon
:
for
the
Sun
ere
it
Rises
,
and
after
it
Sets
,
shoots
forth
its
Beams
through
the
Air
,
and
so
illuminates
the
Vapours
of
the
Air
;
which
illumination
does
by
degrees
enlighten
the
Horizon
,
and
spreads
through
the
Zenith
,
even
into
the
West
,
ere
the
Sun
Rises
;
and
also
continues
above
the
Horizon
,
afte●
the
Sun
sets
.
Now
though
it
be
Twilight
when
the
Sun
is
18.
degrees
below
the
Horizon
;
yet
the
duration
of
Twilight
(
is
alterable
both
in
respect
of
Time
)
and
Place
:
for
at
such
Time
at
the
Sun
is
farthest
distant
from
any
Place
,
the
Twilight
shall
be
greater
,
then
when
it
is
neerest
.
And
in
respect
of
Place
,
All
Places
that
have
great
Latitude
from
the
Equator
,
have
longer
Twilight
than
those
that
are
neerer
to
the
Equator
:
for
as
Authors
say
,
under
the
Equator
there
is
no
Twilight
;
when
again
in
many
Climes
both
Northward
and
Southward
,
the
Nights
are
indeed
no
Nights
but
only
(
as
it
were
)
a
little
over-spread
with
a
cloudy
Shade
;
and
is
either
increased
or
diminished
according
to
the
●autation
of
Meo●erological
Causes
.
Therefore
to
know
the
beginning
of
Twilight
in
the
Morning
here
at
London
,
May
10
;
you
must
(
having
the
Globe
rectified
)
turn
the
degree
of
the
Ecliptick
which
is
opposite
to
the
Place
of
the
Sun
till
it
be
elevated
18.
degrees
in
the
Quadrant
of
Altitude
above
the
Horizon
in
the
West
;
So
shall
the
Index
of
the
Hour-Circle
point
at
the
Hour
that
Twilight
begins
:
Then
subtract
the
Hour
and
Minute
that
Twilight
begins
from
the
Hour
and
Minute
of
Sun
Rising
,
if
in
the
Morning
,
or
substract
the
Hour
of
Sun
sett
from
the
Hour
of
Twilight
,
if
at
Night
;
and
the
remainder
is
the
length
of
Twilight
.
Example
.
The
Globe
Quadrant
and
Hour-Index
being
rectified
,
as
before
;
and
the
Suns
place
given
,
♉
29.
I
seek
the
opposite
degree
on
the
Globe
,
after
this
manner
▪
I
bring
♉
29.
to
the
Meridian
,
and
observe
what
degree
of
the
Ecliptik
the
opposite
part
of
the
Meridian
cuts
;
and
because
I
find
it
cuts
♏
29.
therefore
I
say
♏
29.
is
opposite
to
♉
29.
Having
found
the
opposite
degree
,
I
bring
it
into
the
West
,
and
also
the
Quadrant
of
Altitude
,
and
joyn
♏
29.
to
18.
degrees
(
accounted
upwards
on
the
Quadrant
)
so
shall
♉
29.
be
depressed
18.
degrees
in
the
East
Side
the
Horizon
:
Then
looking
what
Hour
the
Hour-Index
points
at
in
the
Hour-Circle
,
I
find
it
to
be
,
1.
Hor.
8.
Min.
which
shews
that
Twilight
begins
at
8.
Minutes
past
1.
a
clock
in
the
Morning
.
And
if
you
substract
1.
Hour
8.
Minutes
,
from
4.
Hours
11.
Minutes
,
the
time
of
Sun
Rising
,
found
by
the
7th
.
Probleme
,
it
leaves
3.
Hours
3.
Minutes
for
the
length
of
Twilight
:
And
if
you
double
1.
Hour
8.
Minutes
,
the
beginning
of
Twilight
,
it
makes
2.
Hours
16.
Minutes
for
the
intermission
of
Time
between
Twilight
in
the
Evening
,
and
Twilight
in
the
Morning
.
So
that
May
10.
absolute
Night
is
but
2.
Hours
16.
Minutes
long
,
here
at
London
.
The
reason
why
you
bring
the
degree
opposite
to
the
Suns
Place
to
the
West
,
is
,
because
the
Quadrant
containing
but
90.
degrees
will
reach
no
lower
then
the
Horizon
;
but
this
Probleme
requires
it
to
reach
18.
degrees
beneath
it
:
therefore
by
this
help
,
you
have
the
Proposition
Answered
,
as
well
as
if
the
Quadrant
did
actually
reach
18.
degrees
below
the
Horizon
.
This
shift
you
may
have
occasion
to
make
in
some
other
Problemes
.
If
you
would
know
when
Twilight
ends
after
Sun
set
;
you
shall
find
it
by
bringing
the
degree
of
the
Ecliptick
opposite
to
the
Place
of
the
Sun
to
18.
degrees
of
the
Quadrant
of
Altitude
,
on
the
East
side
the
Horizon
;
for
then
shall
the
Index
of
the
Hour-Circle
point
at
10.
Hours
52.
Minutes
:
which
shews
that
it
continues
Twilight
till
52.
Minutes
past
10.
a
clock
at
Night
,
May
10.
here
at
London
.
PROB.
X.
The
Suns
Place
given
,
to
find
its
Amplitude
;
And
also
to
know
upon
what
point
of
the
Compass
it
Riseth
.
THe
Globe
&c.
rectified
:
Bring
the
Suns
Place
to
the
East
Side
the
Horizon
;
and
the
number
of
degrees
intercepted
between
the
East
point
of
the
Horizon
and
the
Suns
Place
,
is
the
number
of
degrees
of
Amplitude
that
the
Sun
hath
at
its
Rising
;
and
bears
its
denomination
either
of
North
or
South
,
according
to
its
inclination
to
either
point
in
the
Horizon
.
Or
,
if
you
would
know
upon
what
point
of
the
Compass
the
Sun
Rises
,
Look
but
in
the
Circle
of
Winds
;
and
against
the
Place
of
the
Sun
you
have
the
name
of
the
point
of
the
Compass
upon
which
the
Sun
Riseth
.
Examples
of
both
.
May
10.
the
Suns
Place
is
♉
29.
There●●re
●
the
Globe
being
rectified
;
I
bring
♉
29.
to
the
East
side
the
Horizon
,
and
find
it
touch
against
33
,
degrees
20.
Minutes
from
the
East
point
towards
the
North
:
Therefore
I
say
the
Sun
hath
North
Amplitude
33
,
degrees
20.
Minutes
.
And
to
know
upon
what
point
of
the
Compass
the
Sun
rises
;
I
keep
the
Globe
to
its
Position
,
and
look
in
the
Circle
of
Winds
,
in
the
outmost
verge
of
the
Horizon
,
and
find
the
Suns
Place
against
the
Wind
named
North
East
and
by
East
;
Therefore
I
say
May
10.
here
at
London
the
Sun
riseth
upon
the
North
East
and
by
East
point
of
the
Compass
.
PROBL.
XI
.
The
Hour
of
the
Day
given
,
to
find
the
Heigth
of
the
Sun
.
THe
Globe
&c.
Rectified
.
Turn
about
the
Globe
till
the
Index
of
the
Hour-Circle
point
(
in
the
Hour-Circle
)
to
the
Hour
of
the
Day
:
Then
bring
the
Quadrant
of
Altitude
to
the
Suns
Place
in
the
Ecliptick
,
and
the
degree
on
the
Quadrant
which
touches
the
Suns
Place
,
shall
be
the
number
of
degrees
of
the
Suns
Altitude
.
Example
.
May
10.
here
at
London
;
At
53.
Minutes
past
8.
a
clock
in
the
Morning
,
I
would
know
the
Heigth
of
the
Sun
above
the
Horizon
.
Therefore
I
turn
about
the
Globe
till
the
Index
of
the
Hour-Circle
come
to
53
:
Minutes
past
8.
a
clock
(
which
is
almost
9.
)
in
the
Hour-Circle
:
And
keeping
the
Globe
to
this
Position
,
I
bring
the
Quadrant
of
Altitude
to
the
Suns
place
,
viz.
〈◊〉
29.
(
found
by
the
third
Probleme
)
and
because
the
Suns
Place
touches
upon
40.
degrees
of
the
Quadrant
,
therefore
I
say
May
10.
53.
Minutes
past
8.
a
clock
in
the
Morning
,
here
at
London
,
The
Sun
is
just
40.
degrees
above
the
Horizon
;
or
which
is
all
one
,
hath
40.
degrees
of
Altitude
.
PROB.
XII
.
The
Altitude
〈◊〉
Sun
,
and
Day
of
the
Moneth
given
,
to
find
the
Hour
of
the
Day
.
AN
Hour
is
the
24th
.
part
of
a
Day
and
a
Night
,
or
the
space
of
time
that
15.
degrees
of
the
Equator
takes
up
in
An
Hour
defined
.
passing
through
the
Meridian
;
for
the
whole
Equator
which
contains
360.
degrees
,
passes
through
the
Meridian
in
24.
Hours
,
therefore
15.
degrees
which
is
the
24th
.
part
of
360
,
pass
through
in
one
Hour
.
These
Hours
are
Vulgarly
divided
into
halfs
,
quarters
,
and
half
quarters
;
but
Mathematically
into
Minutes
,
Seconds
.
Thirds
,
Fourths
,
&c.
A
Minute
is
the
60th
.
part
of
an
Hour
,
so
that
60
,
minutes
make
an
Hour
,
30
,
half
an
Hour
,
15.
a
quarter
of
an
Hour
:
A
Second
is
the
60th
Minutes
,
Seconds
,
and
Thirds
,
&c.
defined
.
part
of
a
Minute
:
a
third
is
the
60th
part
of
a
Second
:
a
Fourth
is
the
60th
part
of
a
Third
:
and
so
you
may
run
on
to
Fifths
,
Sixths
,
Sevenths
,
&c.
if
you
please
.
12.
of
these
Hours
make
a
Day
,
and
12.
more
make
a
Night
:
so
that
Day
and
Night
contain
24.
hours
as
aforesaid
▪
which
are
Volgarly
numbred
from
Noon
with
1
,
2
,
3
,
to
12
,
at
Night
▪
and
then
begin
again
with
1
,
2
,
3
,
till
12
at
Noon
:
But
by
Astronomers
they
are
Numbred
from
Noon
with
1
,
2
,
3
,
&c.
to
12.
at
Night
;
and
so
forward
to
13
,
14
,
15
,
till
24
;
which
is
just
full
Noon
the
next
Day
.
Yet
in
this
Treatise
I
shall
mention
the
Hours
as
they
are
Vulgarly
co●●ted
,
viz.
from
〈◊〉
.
after
noon
,
to
12.
at
Night
,
and
call
the
Hours
after
Midnight
by
1
,
2
,
3
,
4
,
&c.
in
the
Morning
,
to
12.
at
Noon
again
,
the
next
Day
.
But
to
the
operation
.
The
Globe
,
&c.
Rectified
,
Bring
the
Place
of
the
Son
to
the
Number
of
degrees
of
Altitude
accounted
upon
the
Quadrant
of
Altitude
,
and
the
Hour-Index
shall
point
at
the
Hour
in
the
Hour-Circle
:
yet
herein
respect
must
be
had
to
the
Fore
or
After
noons
Elevation
;
as
shall
be
shewed
in
the
next
Probleme
.
Example
.
May
10.
The
Sun
is
elevated
40.
degrees
above
the
Horizon
,
here
at
London
:
Therefore
having
found
the
Place
of
the
Sun
,
by
the
third
Probleme
,
to
be
●29
.
I
move
the
Globe
and
Quadrant
till
I
can
joyn
the
29.
degree
of
〈◊〉
to
the
40.
deg
,
upon
the
Quadrant
of
Altitude
;
and
then
looking
on
the
Hour-Circle
,
I
find
the
Index
point
at
53.
Minutes
past
8.
a
clock
,
for
the
Fore
noon
Elevation
;
and
at
3.
hours
7.
Minutes
for
the
After
noons
Elevation
.
Therefore
if
it
be
Fore-noon
,
I
say
,
It
is
53.
Minutes
past
8.
a
clock
in
the
Morning
.
But
if
it
be
After
noon
I
say
,
It
is
7.
Minutes
past
3.
a
clock
in
the
After
noon
.
PROB.
XIII
.
How
to
know
whether
it
be
Before
or
After
Noon
.
HAving
made
one
Observation
,
you
must
make
a
Second
a
little
while
after
the
First
;
and
if
the
Sun
increase
in
Altitude
,
it
is
Before
Noon
:
but
if
it
decrease
in
Altitude
,
it
is
After
Noon
.
Example
.
The
Sun
was
at
8.
hor.
53.
Min.
elevated
40.
degr.
above
the
Horizon
:
A
little
while
after
(
suppose
for
examples
sake
aquarter
of
an
hour
,
)
viz.
at
9.
hor.
8.
Min.
I
observe
again
the
heigth
of
the
Sun
,
and
find
it
42.
degrees
high
;
so
that
the
Altitude
is
increased
2.
degrees
;
Therefore
I
say
,
It
is
Fore-Noon
:
But
if
the
Sun
had
decreased
in
Altitude
,
I
should
have
said
it
had
been
After-Noon
.
How
to
take
Altitudes
by
the
Quadrant
,
Astrolabe
,
and
Cross-staff
.
There
are
divers
Instruments
whereby
Altitudes
may
be
taken
:
but
the
most
in
use
are
the
Quadrant
,
Astrolabe
,
and
Cross-staff
.
A
Quadrant
is
an
Instrument
comprehended
between
two
Straight
lines
making
a
Right
Angle
,
and
an
Arch
discribed
upon
the
Right
Angle
,
as
on
the
Center
,
containing
90.
degrees
,
which
is
a
quarter
of
a
Circle
:
and
therefore
the
Instrument
is
called
a
Quadrant
.
See
this
Figure
.
A
prepresents
the
Center
;
upon
which
is
fastned
a
Plumb-line
,
A
B
the
one
side
,
A
C
the
other
side
,
upon
which
the
Sights
are
placed
:
B
C
the
Arch
or
Quadrant
,
which
is
divided
into
90.
equal
parts
,
and
numbred
from
B
to
C.
D
one
Sight
,
E
the
other
Sight
:
F
the
Plumbet
fastned
to
the
Plumb-line
.
When
by
this
Instrument
you
would
observe
the
heigth
of
the
Sun
,
you
must
turn
the
Center
A
to
the
Sun
,
and
let
the
beams
thereof
dart
in
at
the
hole
in
the
first
Sight
D
,
through
the
hole
in
the
second
Sight
E
;
so
shall
the
Plumb-line
ly
upon
the
degree
in
the
Limb
,
of
the
Suns
Elevation
:
As
if
the
plumb-line
ly
upon
the
20th
degree
,
then
shall
the
Altitude
be
20.
degrees
;
if
on
25.
the
Altitude
shall
be
25.
degrees
:
and
so
for
any
number
of
Degrees
the
thred
or
Plumb-line
lies
on
,
the
same
number
of
Degrees
is
the
Altitude
of
the
Sun
.
But
if
it
be
a
Star
whose
Altitude
you
would
observe
;
you
must
hold
up
the
Quadrant
,
and
joyn
the
Limb
to
your
Cheek
bone
,
and
turn
the
Center
towards
the
Star
:
then
winking
with
one
Ey
,
look
through
the
holes
of
the
Sights
with
the
other
Ey
,
till
you
can
see
the
Star
through
those
holes
;
so
shall
the
Plumb-line
(
as
before
in
the
Sun
)
hang
upon
the
degree
in
the
Limb
of
the
Stars
Elevation
.
Another
sort
of
Quadrants
is
made
with
a
moveable
Index
,
as
is
represented
in
this
Figure
.
A
is
the
Center
,
A
Band
A
C
the
two
sides
,
B
C
the
Limb
,
D
E
two
Sights
fixed
upon
a
moveable
Index
or
Label
;
F
G
two
other
Sights
,
for
observing
the
Horizon
.
When
by
this
Quadrant
you
would
observe
an
Altitude
,
the
side
B
A
must
be
parallel
to
the
Horizon
,
and
the
Index
must
be
moved
till
the
Object
(
be
it
either
the
Sun
Moon
or
any
Star
)
be
seen
through
the
holes
or
slitts
of
the
Sights
placed
on
the
Index
;
for
then
the
Arch
D
B
shall
be
the
Elevation
required
.
You
may
know
when
the
side
B
A
is
parallel
to
the
Horizon
,
by
observing
the
parting
of
Heaven
from
the
Earth
through
the
Sights
on
the
Side
B
A.
To
take
Altitudes
by
the
Astrolabe
.
The
Astrolabe
is
a
round
Instrument
,
flat
on
either
side
,
upon
one
of
the
flats
or
Plains
is
discribed
a
Circle
as
B
C
D
E
,
divided
into
360
,
equal
parts
or
degrees
,
numbred
from
the
line
of
Level
B
A
C
,
with
10
,
20
,
30
,
&c.
to
90.
in
the
Perpendicular
D
C.
Upon
the
perpendicular
is
fastned
a
Ring
as
F
,
so
as
the
Instrument
hanging
by
it
,
the
line
of
Level
may
hang
parallel
to
the
Horizon
.
Upon
the
Center
is
a
moveable
Label
or
Ruler
,
as
G
H
,
whereupon
is
placed
two
Sights
as
I
K.
If
you
desire
further
instructions
for
making
this
Instrument
,
you
may
peruse
Mr
Wright
in
his
Division
of
the
whole
Art
of
Navigation
,
annexed
to
his
Correction
of
Errors
:
where
he
also
shews
the
use
of
it
at
large
;
which
in
brief
is
as
follows
.
You
must
hold
the
Astrolabe
by
the
Ring
in
your
left
hand
,
and
turning
your
right
side
to
the
Sun
,
lift
up
the
Label
with
your
right
hand
,
till
the
beams
of
the
Sun
entring
by
the
hole
of
the
uppermost
Vane
or
Sight
,
doth
also
pierce
through
the
hole
in
the
nethermost
Vane
of
Sight
;
and
the
deg.
and
part
of
deg.
that
the
Label
lies
on
is
the
height
of
the
Sun
above
the
Horizon
.
But
if
it
be
a
Star
you
would
observe
;
you
must
use
the
Astrolabe
as
you
were
directed
to
use
the
Quadrant
,
holding
it
up
to
your
Cheek
bone
,
and
looking
through
the
Sights
,
&c.
To
take
Altitudes
by
the
Cross-staff
.
This
Instrument
consists
of
a
Staf
about
a
yard
long
,
and
three
quarters
of
an
inch
square
:
Upon
it
is
fitted
a
Vane
,
(
or
sometimes
two
,
or
three
,
)
so
as
it
may
slide
pretty
stiff
upon
the
Staff
,
and
stand
at
any
of
the
Divisions
it
is
set
to
.
The
making
is
taught
by
Mr
Wright
,
aforesaid
:
But
the
use
is
as
follows
.
You
must
put
that
end
of
the
Cross-staff
which
is
next
90.
degrees
to
your
Cheek
bone
,
upon
the
outter
corner
of
your
Ey
,
and
holding
it
there
steddy
,
you
must
move
the
Vane
till
you
see
the
Horizon
joyned
with
the
lower
end
thereof
,
and
the
Sun
or
Star
with
the
higher
end
;
then
the
degree
and
part
of
degree
which
the
Vane
cutteth
upon
the
Staff
,
is
the
height
of
the
Sun
or
Star
.
Some
of
these
waies
for
taking
Altitudes
have
been
formerly
taught
by
others
,
that
have
treated
upon
the
Use
of
Globes
:
and
therefore
because
some
would
be
apt
to
think
this
Treatise
uncompleat
if
I
did
not
shew
these
waies
also
,
I
have
thought
fit
to
insert
them
:
Yet
the
same
things
may
be
performed
by
the
Globe
alone
,
without
troubling
your self
with
multiplicity
of
Instruments
;
if
your
Globe
be
made
with
a
hollow
Axis
;
for
then
if
the
Globe
stand
Horizontal
,
you
shall
by
Observing
the
Object
through
the
Axis
have
the
degree
of
Elevation
,
noted
by
the
superficies
of
the
Horizon
.
PROB.
XIV
.
To
observe
with
the
Globe
the
Altitude
of
the
Sun
.
PLace
the
Globe
so
that
the
upper
plain
of
the
Horizon
may
stand
parallel
to
the
Plain
of
the
Horizon
of
your
Place
;
as
was
taught
by
the
Second
Probleme
;
then
turn
the
North
Pole
towards
the
Sun
,
and
place
it
higher
or
lower
,
by
moving
the
Meridian
through
the
notches
of
the
Horizon
,
till
the
beams
of
the
Sun
pierce
quite
through
the
Axis
of
the
Globe
:
So
shall
the
arch
of
the
Meridian
comprehended
between
the
Pole
and
the
Horizon
,
be
the
number
of
Degrees
that
the
Sun
is
elevated
above
the
Horizon
.
Example
.
March
20.
just
at
noon
,
here
at
London
,
I
would
observe
the
Meridian
Altitude
of
the
Sun
.
Therefore
placing
the
Horizon
Horizontal
,
as
by
the
Second
Probleme
:
I
turn
the
North
Pole
towards
the
Sun
,
and
move
it
with
the
Meridian
upwards
or
downwards
,
either
to
this
side
or
that
,
till
I
can
fit
it
to
such
a
Position
that
the
Sun
Beams
may
dart
quite
through
the
Axis
of
the
Globe
;
which
when
it
does
,
I
look
on
the
Meridian
and
find
42.
degrees
25.
min.
comprehended
between
the
Pole
and
the
superficies
of
the
Horizon
;
Therefore
I
say
the
Meridian
Altitude
of
the
Sun
March
20.
here
at
London
,
is
42.
degrees
25.
min.
PROB.
XV.
To
find
the
Elevation
of
the
Pole
,
by
the
Meridian
Altitude
of
the
Sun
,
and
Day
of
the
Moneth
given
.
THe
Day
of
the
Moneth
is
March
20.
By
the
4th
Prob.
you
may
find
the
place
of
the
Sun
to
be
♈
10.
Therefore
bring
the
Place
of
the
Sun
to
the
Meridian
,
and
elevate
it
above
the
Horizon
the
same
number
of
degrees
it
hath
in
Heaven
;
so
shall
the
arch
of
the
Meridian
comprehended
between
the
Pole
and
the
Horizon
,
be
the
elevation
of
the
Pole
,
in
your
Place
.
Otherwise
.
The
Day
of
the
Moneth
given
is
March
20.
so
that
by
the
fourth
Prob.
you
have
the
Suns
Place
♈
10
;
and
by
the
fifth
,
the
Declination
of
the
Sun
3.
55.
North
:
therefore
the
Declination
being
North
,
and
you
on
the
North
side
the
Equator
;
you
must
substract
3.
55.
from
the
Meridian
Altitude
42.
25.
and
there
remains
38
,
30.
for
the
heighth
of
the
Equinoctial
above
the
Horizon
;
but
if
your
Declination
had
been
South
,
you
must
have
added
3
55.
to
the
Meridian
Altitude
,
and
the
Sum
would
have
been
the
Elevation
of
the
Equinoctial
.
Having
the
Elevation
of
the
Equinoctial
,
you
may
easily
have
the
Elevation
of
the
Pole
;
for
the
one
is
alwaies
the
Complement
of
the
other
to
90.
Thus
the
Height
of
the
Equinoctial
38.
30.
subtracted
from
90.
leaves
51.
30.
for
the
Elevation
of
the
Pole
,
here
at
London
.
And
thus
it
follows
,
that
the
Latitude
of
any
Place
from
the
Equinoctial
,
is
alwaies
equal
to
the
Elevation
of
the
Pole
:
for
between
the
Zenith
and
the
Equinoctial
is
contained
the
Complement
of
the
Heighth
of
the
Equinoctial
above
the
Horizon
to
90.
PROB.
XVI
.
To
take
the
Altitude
of
any
Star
above
the
Horizon
;
by
the
Globe
.
THe
Horizon
of
the
Globe
set
parallel
to
the
Horizon
of
the
World
,
as
before
:
Turn
the
North
Pole
towards
the
Star
,
and
when
you
can
see
the
Star
through
the
Axis
,
the
Northern
notch
of
the
Horizon
will
cut
the
degree
of
Elevation
on
the
Meridian
.
Example
.
April
19.
at
11.
a
clock
at
Night
,
I
would
observe
the
Altitude
of
Spica
Virgo
:
Therefore
I
set
the
Horizon
parallel
to
the
Horizon
of
the
World
,
as
by
the
Second
Probleme
,
and
turn
the
Northern
Pole
till
it
point
towards
the
Star
:
Then
looking
in
at
the
South
Pole
of
the
Globe
through
the
Axis
,
I
shall
see
the
Star
,
and
have
on
the
Meridian
the
Question
resolved
.
But
if
it
point
not
exactly
,
then
I
move
the
North
Pole
upwards
or
downwards
,
either
to
the
right
hand
,
or
to
the
left
,
according
as
I
may
find
occasion
,
till
I
can
see
the
Star
through
the
Axis
:
and
then
the
edge
of
the
notch
in
the
Horizon
cuts
28.
degrees
57.
min.
on
the
Brazen
Meridian
.
Therefore
I
say
April
19.
at
11.
a
clock
at
Night
,
here
at
London
,
the
Altitude
of
Spica
〈◊〉
is
30.
degrees
above
the
Horizon
.
PROB.
XVII
.
By
the
Meridian
Altitude
of
any
Star
given
,
to
find
the
Height
of
the
Pole
.
JOyn
the
Star
to
the
Meridian
,
and
place
it
to
the
Altitude
observed
;
so
shall
the
number
of
degrees
intercepted
between
the
Pole
and
the
Horizon
,
be
the
Elevation
of
the
Pole
.
Example
.
Spica
Virgo
is
observed
to
have
28.
degrees
57.
min
Meridian
Altitude
;
therefore
I
bring
Spica
Virgo
to
the
Meridian
,
and
raise
it
or
depress
it
higher
or
lower
as
I
find
occasion
,
till
it
is
just
28.
degrees
57.
min.
above
the
Horizon
:
Then
I
count
the
number
of
degrees
between
the
Pole
and
the
Horizon
,
and
find
them
51½
.
Therefore
I
say
the
Elevation
of
the
Pole
is
here
at
London
51½
.
Yet
note
,
If
the
Star
whose
Altitude
you
observe
have
fewer
number
of
degrees
of
Declination
from
the
Pole
,
then
the
Elevation
of
the
Pole
,
you
may
be
apt
to
mistake
in
its
coming
to
the
Meridian
;
for
those
Stars
never
set
;
and
therefore
are
twice
Visible
in
the
Meridian
in
24.
hours
,
once
above
the
Pole
,
and
once
under
the
Pole
.
If
your
Star
have
greater
Altitude
then
the
North
Star
,
it
is
above
the
Pole
;
but
if
it
have
less
,
it
is
below
the
Pole
:
so
that
if
you
know
but
whether
it
be
above
or
below
,
it
is
enough
;
for
so
you
may
accordingly
raise
it
to
the
Altitude
on
the
Meridian
it
hath
in
Heaven
,
and
joyn
it
to
the
Meridian
either
above
or
beneath
the
Pole
,
as
the
Star
is
placed
in
Heaven
:
and
then
the
arch
of
the
Meridian
comprehended
between
the
Pole
and
the
Horizon
,
is
the
Elevation
of
the
Pole
,
as
aforesaid
.
Otherwise
.
Having
the
Meridian
Altitude
of
the
Star
,
you
must
find
its
Declination
by
the
27.
Probleme
:
and
if
the
Declination
be
South
,
and
you
on
the
North
side
the
Equator
,
you
must
ad
the
Declination
to
the
Meridian
Altitude
,
and
the
sum
of
both
makes
the
Altitude
of
the
Equinoctial
:
But
if
the
Declination
be
North
,
and
you
on
the
North
side
the
Equator
,
you
must
substract
the
Declination
from
the
Meridian
Altitude
,
(
as
was
taught
by
the
15.
Prob.
in
the
Example
of
the
Sun
)
and
the
remainder
is
the
Altitude
of
the
Equinoctial
Then
(
as
was
taught
by
the
15
Probleme
aforesaid
)
substract
the
Altitude
of
the
Equinoctial
from
90
,
the
Remainder
is
the
Elevation
of
the
Pole
in
your
Place
.
Example
.
By
the
last
Probleme
the
Meridian
Altitude
of
Spica
Virgo
was
28
degrees
57
min
,
and
the
Declination
of
Spica
by
the
27th
Probleme
is
found
9.
degrees
33.
min.
South
:
therefore
because
the
Declination
is
South
,
I
ad
9.
degrees
33.
min.
to
the
Meridian
Altitude
,
which
makes
38.
deg.
30.
min.
for
the
Elevation
of
the
Equinoctial
:
which
38.
deg.
30.
min.
substracted
from
90.
leaves
51.
degrees
30.
min.
for
the
Elevation
of
the
Pole
here
at
London
.
PROB.
XVIII
.
Another
way
to
find
the
Height
of
the
Pole
by
the
Globe
;
if
the
Place
of
the
Sun
be
given
:
and
also
to
find
the
Hour
of
the
Day
,
and
Azimuth
,
and
Almicantar
of
the
Sun
.
THis
must
be
performed
by
help
of
a
Spherick
Gnomon
,
(
as
Blaew
calls
it
,
)
which
is
a
small
Pin
or
Needle
fixed
perpendicularly
into
a
smal
Basis
with
an
hollow
concave
bottom
,
that
it
may
stand
upon
the
convexity
of
the
Globe
.
Therefore
the
Horizon
of
the
Globe
being
set
parallel
to
the
Horizon
of
the
World
,
(
as
by
the
Second
Probleme
)
the
Spherick
Gnomon
must
be
set
exactly
upon
the
Place
of
the
Sun
;
and
then
turning
the
Globe
about
(
upon
its
Axis
)
either
from
East
to
West
,
or
contrarily
from
West
,
to
East
;
or
else
by
the
Meridian
,
through
the
notches
of
the
Horizon
,
till
the
Spherick
Gnomon
cast
no
shadow
on
any
side
thereof
;
you
have
on
the
Meridian
in
the
North
point
of
the
Horizon
the
number
of
degrees
that
the
Pole
is
elevated
above
the
Horizon
.
Example
.
Imagine
the
four
Quarters
of
the
Horizon
of
the
Globe
correspond
with
the
four
Quarters
of
the
Horizon
of
the
World
;
and
the
Plain
of
the
Horizon
of
the
Globe
is
parallel
to
the
Plain
of
the
Horizon
of
the
World
:
The
Suns
Place
is
♉
29¼
,
which
I
find
on
the
Globe
,
and
place
the
Spherick
Gnomon
thereon
;
Then
at
a
guess
I
move
the
Globe
both
on
its
Axis
,
and
by
the
Meridian
,
(
as
neer
as
I
can
)
so
as
the
Spherick
Gnomon
may
cast
no
shadow
;
yet
if
it
do
,
and
the
shadow
fall
towards
the
North
Pole
;
then
I
elevate
the
North
Pole
more
,
till
the
shadow
fals
just
in
the
middle
of
it self
:
but
if
the
shadow
fall
downwards
,
towards
the
South
Pole
,
then
I
depress
the
North
Pole
:
If
the
shadow
fall
on
the
East
side
,
I
turn
the
Globe
on
its
Axis
more
to
the
West
;
and
if
the
shadow
fall
to
the
West
,
I
turn
the
Globe
more
into
the
East
:
and
the
degree
of
the
Meridian
which
the
North
point
of
the
Horizon
touches
,
is
the
degree
of
the
Poles
Elevation
:
which
in
this
Example
is
51½
.
the
Latitude
of
the
City
of
London
.
By
this
Operation
you
have
also
given
the
Hour
of
the
Day
in
the
Hour-Circle
,
if
you
keep
the
Globe
unmoved
:
and
the
Azimuth
,
and
Almicantar
,
if
you
apply
but
the
Quadrant
of
Altitude
to
the
Place
of
the
Sun
,
as
by
the
22
,
and
23.
Problemes
.
PROB.
XIX
.
To
observe
by
the
Globe
the
Distance
of
two
Stars
.
YOu
must
pitch
upon
two
Stars
in
the
Meridian
;
and
observe
the
Altitude
of
one
of
them
first
,
and
afterwards
the
Altitude
of
the
other
:
Then
substract
the
lesser
Altitude
from
the
greater
,
and
the
remainder
shall
be
the
distance
required
.
Example
.
March
7.
at
11.
a
clock
at
Night
here
at
London
,
I
see
in
the
Meridian
the
two
Stars
in
the
foremost
Wheels
of
the
Waggon
,
in
the
Constellation
of
the
Great
Bear
,
called
by
Sea-men
the
Pointers
,
(
because
they
alwaies
point
towards
the
Pole-Star
.
)
Therefore
to
observe
the
distance
between
these
two
Stars
,
I
first
observe
(
as
by
the
last
Probleme
)
the
Altitude
of
the
most
Northern
to
be
77.
degree
59.
minutes
,
and
set
down
that
number
of
Degrees
and
minutes
with
a
Pen
and
Ink
on
a
Paper
,
or
with
a
peece
of
Chalk
or
a
Pencil
on
a
Board
:
and
afterwards
I
observe
the
Altitude
of
the
other
Star
which
is
under
it
,
as
I
did
the
first
,
to
be
83.
deg.
21.
min.
and
set
that
number
of
degrees
and
minutes
also
down
,
under
the
other
number
of
degrees
and
minutes
:
Then
by
substracting
the
lesser
from
the
greater
,
I
find
the
remainder
to
be
5.
degrees
22.
min.
which
is
the
distance
of
the
two
Stars
in
the
Great
Bear
,
called
the
Pointers
.
PROB.
XX.
How
you
may
learn
to
give
a
guess
at
the
number
of
degrees
that
any
two
Stars
are
distant
from
one
another
;
or
the
number
of
degrees
of
Altitude
the
Sun
or
any
Star
is
elevated
above
the
Horizon
:
only
by
looking
up
to
Heaven
,
without
any
Instrument
.
BEtween
the
Zenith
and
the
Horizon
is
comprehended
an
Arch
of
a
Circle
containing
90.
degrees
;
so
that
if
you
see
any
Star
in
or
neer
the
Zenith
,
you
may
know
that
Star
is
90.
or
neer
90.
degrees
high
;
and
by
so
much
as
you
may
conceive
it
wants
of
the
Zenith
,
so
much
you
may
guess
it
wants
of
90.
degrees
above
the
Horizon
.
By
this
Rule
you
may
guess
at
an
Arch
of
Heaven
containing
90.
degrees
,
or
at
an
Arch
of
Heaven
containing
45.
degrees
;
if
by
your
imagination
you
divide
the
whole
Arch
into
two
equal
parts
,
for
then
shall
each
of
them
contain
45.
degrees
;
And
if
by
your
imagination
you
divide
the
Arch
of
90.
into
3.
equal
parts
,
each
division
shall
contain
an
Arch
of
30.
degrees
,
&c.
But
this
way
is
a
little
too
rude
for
guessing
at
Stars
elevated
but
few
degrees
,
or
for
Stars
distant
but
few
degrees
from
one
another
.
Therefore
that
you
may
learn
to
guess
more
precisely
at
Distances
in
Heaven
,
you
may
either
with
a
Quadrant
,
Astrolabe
,
or
the
Globe
;
find
the
exact
distance
of
any
two
known
Stars
that
are
but
few
degrees
asunder
,
and
by
a
little
revolving
the
distance
of
those
Stars
in
your
fancy
,
you
may
at
length
so
imprint
their
distance
in
your
memory
,
that
you
may
readily
guess
the
distance
of
other
Stars
by
the
distance
of
them
.
Example
.
You
may
find
either
by
the
Globe
,
Quadrant
,
or
As●rotabe
,
(
for
they
all
agree
)
3.
degrees
comprehended
between
the
first
Star
in
Orions
Girdle
,
and
the
last
;
therefore
by
a
little
〈◊〉
nating
upon
that
distance
,
you
may
imprint
it
in
your
fancy
for
3.
degrees
,
and
so
make
it
applicable
to
other
Stars
,
either
of
the
same
distance
,
or
more
,
or
less
:
And
the
Pointers
(
by
the
last
Probleme
)
are
distant
from
one
another
5.
degrees
and
almost
an
half
:
These
are
alwaies
above
our
Horizon
,
and
therefore
may
alwaies
stand
as
a
Scale
for
five
and
an
half
degrees
;
So
that
by
these
for
5½
degrees
,
and
those
in
Orions
Girdle
for
3.
degrees
,
and
others
observed
,
either
of
greater
or
lesser
distance
,
you
may
according
to
your
own
Judgement
shape
a
guess
,
if
not
exactly
,
yet
pretty
neer
the
matter
of
Truth
,
when
you
come
to
other
Stars
.
Thus
you
may
exercise
your
fancy
upon
Stars
found
to
be
10.
or
15.
degrees
asunder
,
or
more
,
or
less
;
and
with
a
few
experiments
of
this
nature
enure
your
Judgement
to
guess
distances
,
and
enable
your
memory
to
retain
your
Judgement
.
This
way
of
guessing
will
be
exact
enough
for
finding
the
Hour
of
the
Night
by
the
Stars
,
for
most
common
Uses
;
or
the
Hour
of
the
Day
,
by
guessing
at
the
Altitude
of
the
Sun
;
if
after
you
have
guessed
at
the
Altitude
,
you
shall
work
as
was
taught
by
Prob.
12.
for
the
Hour
of
the
Day
:
and
as
shall
be
taught
in
the
next
Probleme
,
for
the
Hour
of
the
Night
.
PROB.
XXI
.
The
Day
of
the
Moneth
,
and
Altitude
of
any
Star
given
,
to
find
the
Hour
of
the
Night
.
THe
Globe
,
Quadrant
,
and
Hour
Index
rectified
:
Bring
the
Star
on
the
Globe
to
the
same
number
of
Degrees
on
the
Quadrant
of
Altitude
that
it
hath
in
Heaven
:
So
shall
the
Index
of
the
Hour-Circle
point
in
the
Hour-Circle
at
the
Hour
of
the
Night
.
Example
.
March
10.
the
Altitude
of
Arcturus
is
35.
degrees
above
the
Horizon
,
here
at
London
:
Therefore
having
the
Globe
,
Quadrant
and
Hour
Index
rectified
,
I
bring
Arcturus
on
the
Globe
to
35.
degrees
on
the
Quadrant
of
Altitude
:
And
then
looking
in
the
Hour-Circle
,
I
find
the
Index
point
at
10.
a
clock
;
which
is
the
Hour
of
the
Night
.
PROB.
XXII
.
The
Place
of
the
Sun
,
and
Hour
of
the
Day
given
,
to
find
its
Azimuth
in
any
Latitude
assigned
.
THe
Globe
,
&c.
rectified
to
your
Latitude
:
Turn
the
Globe
till
the
Index
of
the
Hour-Circle
come
to
the
given
hour
;
and
bring
the
Quadrant
of
Altitude
to
the
Place
of
the
Sun
:
so
shall
the
number
of
degrees
contained
between
the
East
point
of
the
Horizon
and
the
degree
cut
by
the
Quadrant
of
Altitude
on
the
Horizon
,
be
the
number
of
degrees
of
the
Suns
Azimuth
,
at
that
time
.
Example
.
May
10.
at
53.
minutes
past
8.
a
clock
in
the
Morning
,
I
would
know
the
Azimuth
of
the
Sun
:
Therefore
(
the
Globe
being
first
rectified
)
I
turn
about
the
Globe
till
the
Index
of
the
Hour-Circle
point
to
53.
minutes
past
8.
a
clock
,
or
which
is
all
one
,
within
half
a
quarter
of
an
hour
of
9
;
then
I
move
the
Quadrant
of
Altitude
to
the
degree
the
Sun
is
in
that
Day
,
and
there
let
it
remain
till
I
see
how
many
degrees
is
contained
between
the
North
point
and
the
Quadrant
;
which
in
this
Example
is
108.
deg.
25.
min.
And
because
this
distance
from
the
North
,
exceeds
90.
degrees
;
therefore
I
substract
90.
degrees
from
the
whole
,
and
the
remains
is
18.
degrees
25.
min.
for
the
Azimuthal
distance
of
the
Sun
from
the
East
point
towards
the
South
.
But
if
it
had
wanted
of
90.
degrees
from
the
North
point
,
then
should
the
Complement
of
90.
have
been
the
Azimuthal
distance
of
the
Sun
from
the
East
point
.
PROB.
XXIII
.
The
Place
of
the
Sun
,
and
hour
of
the
Day
given
,
to
find
the
Almicantar
of
the
Sun
.
THe
Almicantars
of
the
Sun
is
upon
the
matter
the
same
thing
with
the
Altitude
of
the
Sun
:
only
with
this
distinction
.
The
Almicantars
are
Circles
parallel
to
the
Horizon
,
discribed
by
the
degree
of
the
Quadrant
of
Altitude
upon
the
Zenith
as
its
Center
,
by
turning
the
Quadrant
round
about
the
Globe
till
it
comes
again
to
its
first
Place
:
But
the
Altitude
is
an
Arch
of
the
Vertical
Circle
,
comprehended
between
the
Horizon
and
any
point
of
the
Globe
assigned
.
Their
agreement
consists
in
this
;
When
the
Sun
or
any
Star
ha●●
any
known
Almicantar
,
they
are
said
to
have
the
same
number
of
degrees
of
Altitude
;
As
if
the
Sun
be
in
the
20th
Almicantar
;
he
hath
20
degrees
of
Altitude
;
if
in
the
30th
Almicantar
,
he
hath
30.
degrees
of
Altitude
,
&c.
Now
because
the
Operation
is
the
same
for
finding
the
Altitude
and
Almicantar
,
I
shall
refer
you
to
the
11th
Probleme
;
which
shews
you
how
to
find
the
Altitude
or
Heighth
;
and
by
consequence
the
Almicantar
.
PROB.
XXIV
.
The
Place
of
the
Sun
given
,
to
find
what
Hour
it
comes
to
the
East
,
or
West
,
and
what
Almicantar
it
then
shall
have
.
THe
Globe
,
Quadrant
,
and
Hour
Index
rectified
,
Bring
the
Quadrant
of
Altitude
to
the
East
point
in
the
Horizon
,
if
you
would
know
what
hour
it
comes
to
the
East
;
or
to
the
West
point
,
if
you
would
know
what
hour
it
comes
to
the
West
:
Then
turn
about
the
Globe
till
the
place
of
the
Sun
come
to
the
Quadrant
of
Altitude
;
and
the
Index
of
the
Hour
Circle
shall
point
at
the
hour
of
the
Day
:
which
on
the
Day
aforesaid
will
be
7.
hor.
7
min.
in
the
Morning
,
that
the
Sun
commeth
to
the
East
,
and
4
hor.
53.
min.
after
noon
,
that
the
Sun
commeth
to
the
West
.
And
if
you
then
count
the
number
of
degrees
from
the
Horizon
upwards
on
the
Quadrant
of
Altitude
,
it
will
shew
you
the
Almicantar
of
the
Sun
for
that
time
;
which
will
both
Morning
and
Evening
be
15
,
deg.
30.
min.
as
was
taught
you
by
the
last
Probleme
.
PROB.
XXV
.
To
know
at
any
time
what
a
clock
it
is
in
any
other
Part
of
the
Earth
.
THe
difference
of
Time
is
reckoned
by
the
access
and
progress
of
the
Sun
:
for
the
Sun
gradually
circumvolving
the
Earth
in
24.
hours
,
doth
by
reason
of
the
Earths
rotundity
enlighten
but
half
〈…〉
at
one
and
the
same
moment
of
Time
;
as
shall
be
shewed
hereafter
:
so
that
hereby
it
comes
to
pass
,
that
when
with
us
here
in
England
it
is
6.
a
clock
in
the
Morning
,
with
those
that
have
90.
degrees
of
Longitude
to
the
Westward
of
us
,
it
is
yet
Midnight
:
with
those
that
have
180.
degrees
of
Longitude
from
us
,
it
is
Evening
;
And
with
those
that
have
90.
degrees
of
Longitude
to
the
Eastwards
,
it
is
Noon
.
So
that
those
to
the
Eastward
have
their
Day
begin
sooner
then
ours
:
But
to
the
Westward
their
Day
begins
after
ours
.
Therefore
that
you
may
know
what
Hour
it
is
in
any
Place
of
the
Earth
,
of
what
distance
soever
it
be
,
you
must
first
Bring
the
Place
of
your
own
Habitation
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
on
the
Hour
Circle
;
Then
bring
the
other
Place
to
the
Meridian
,
and
the
Arch
of
the
Hour
Circle
comprehended
between
the
hour
12.
and
the
Index
,
is
the
difference
in
Time
between
the
two
Places
.
Example
.
London
in
England
,
and
Surat
in
the
East
Indies
:
First
I
bring
London
to
the
Meridian
,
and
turn
the
Index
of
the
Hour-Circle
to
12
;
then
I
turn
the
Globe
Westward
,
because
London
●s
Westward
of
Surat
,
till
Surat
come
to
the
Meridian
;
and
see
at
what
Hour
the
Index
of
the
Hour
Circle
points
,
which
in
this
Example
is
5.
hor.
54.
minutes
:
And
because
Surat
lies
to
the
Eastward
of
us
so
many
degrees
,
therefore
as
was
said
before
,
their
Day
begins
so
much
before
ours
:
So
that
when
here
at
London
it
is
6.
a
clock
in
the
Morning
,
at
Surat
it
will
be
11.
a
clock
54.
minutes
;
when
with
us
it
is
12.
a
clock
,
with
them
it
will
be
5
a
clock
54.
minutes
afternoon
.
If
you
would
know
the
difference
of
Time
between
London
and
Jamaica
;
Working
as
before
,
you
may
find
5.
hor.
15.
min.
But
Jamaica
is
to
the
West
of
London
;
therefore
their
Day
begins
5.
hor.
15.
min.
after
ours
:
so
that
when
with
us
it
is
Noon
,
with
them
it
will
be
but
three
quarters
of
an
hour
past
6.
a
clock
in
the
Morning
:
and
when
with
them
it
is
Noon
,
with
us
it
will
be
one
quarter
past
5.
a
clock
after
Noon
,
&c.
Or
you
may
yet
otherwise
know
the
difference
of
Time
,
if
you
divide
the
number
of
Degrees
of
the
Equinoctial
that
pass
through
the
Meridian
while
the
Globe
is
moved
from
the
first
Place
to
the
second
,
by
15.
so
shall
the
product
give
you
the
difference
of
hours
and
minutes
between
the
two
Places
:
as
you
will
find
if
you
try
either
of
these
Examples
,
or
any
other
.
PROB.
XXVI
.
To
find
the
Right
Ascension
of
the
Sun
,
or
Stars
.
THe
Right
Ascension
of
any
point
on
the
Globe
is
found
by
bringing
the
point
proposed
to
the
Meridian
,
and
counting
the
number
of
degrees
comprehended
between
the
Vernal
Colure
,
and
the
Meridian
.
Example
,
for
the
Sun
.
June
1.
I
would
know
the
Right
Ascension
of
the
Sun
:
His
Place
found
,
as
by
the
third
Probleme
,
is
♊
20.
Therefore
I
bring
♊
20.
to
the
Meridian
;
and
then
the
Meridian
cuts
the
Equinoctial
in
79.
degrees
15.
minutes
,
accounted
from
the
Vernal
point
♈
:
Therefore
I
say
the
Right
Ascension
of
the
Sun
June
1.
is
79.
deg.
15.
Minutes
.
Example
,
for
a
Star
.
I
take
Capella
,
alias
Hircus
,
the
Goat
on
Auriga's
sholder
,
and
bring
it
to
the
Meridian
;
and
find
the
Meridian
cut
the
Equinoctial
(
counting
as
before
from
the
Vernel
point
♈
)
in
73.
degrees
58.
minutes
:
Therefore
I
say
,
the
Right
Ascension
of
Hircus
is
73.
degrees
58.
min.
Do
the
like
for
any
other
point
of
the
Globe
proposed
.
PROB.
XXVII
.
To
find
the
Declination
of
the
Sun
,
or
Stars
.
THe
Declination
of
any
point
on
the
Globe
is
found
by
bringing
the
point
proposed
to
the
Meridian
,
and
counting
the
number
of
degrees
comprehended
on
the
Meridian
between
the
Equinoctial
and
the
point
proposed
:
and
bears
its
Denomination
of
North
or
South
,
according
as
it
is
scituate
on
the
North
or
South
side
the
Equinoctial
.
Example
,
for
the
Sun
.
June
1.
I
would
know
the
Declination
of
the
Sun
.
His
Place
found
,
as
before
,
i●
♊
20.
Therefore
I
bring
♊
20.
to
the
Meridian
;
and
find
23.
degrees
8.
min.
comprehended
on
the
Meridian
between
the
Equinoctial
and
♊
20.
and
because
♊
is
on
the
North
side
the
Equinoctial
;
Therefore
I
say
,
June
1.
The
Sun
hath
North
Declination
23.
degrees
8.
minutes
.
Example
,
for
a
Star
.
I
take
Hircus
aforesaid
,
and
bring
it
to
the
Meridian
,
and
find
45.
degrees
40.
minutes
comprehended
on
the
Meridian
between
the
Equinoctial
and
the
Star
Hircus
.
And
because
Hircus
is
on
the
North
side
the
Equinoctial
;
Therefore
I
say
,
Hircus
hath
North
Declination
45.
degrees
40.
min.
Do
the
like
for
any
other
point
on
the
Globe
proposed
.
But
Note
,
The
Right
Ascension
and
Declination
of
the
Sun
alters
dayly
;
for
in
twelve
Moneths
he
runs
through
every
degree
of
Right
Ascension
,
and
in
three
Moneths
to
his
greatest
Declination
:
But
the
Right
Ascension
and
Declination
of
the
Stars
is
scarce
perceiveable
for
some
Years
:
Yet
have
they
also
an
alteration
of
Right
Ascension
and
Declination
:
For
,
those
Stars
that
have
but
few
degrees
of
Right
Ascension
,
will
in
process
of
Time
have
many
;
and
those
Stars
between
the
Tropick
that
have
North
Declination
,
will
in
length
of
Time
have
South
Declination
;
and
the
contrary
(
as
shall
be
more
fully
shewed
hereafter
:
)
For
,
the
Stars
moving
upon
the
Poles
of
the
Ecliptick
go
forwards
in
Longitude
one
whole
Degree
in
70½
Years
(
as
hath
been
shewed
before
,
Book
1.
Chap.
3.
Sect.
3.
)
and
so
alter
both
their
Right
Ascension
,
and
Declination
;
as
may
be
seen
by
this
following
Table
of
Right
Ascensions
and
Declinations
of
100.
of
the
most
eminent
fixed
Stars
,
Calculated
by
Tycho
Brahe
,
for
the
Years
1600.
and
1670.
which
I
have
inserted
;
partly
,
because
by
it
you
may
see
the
differences
of
their
Right
Ascensions
and
Declinations
in
70½
Years
;
and
partly
to
Accomodate
those
that
may
have
occasion
to
know
their
Right
Ascensions
and
Declinations
neerer
than
the
Globe
can
shew
them
.
A
Table
of
the
Right
Ascensions
and
Declinations
of
100.
Select
fixed
Stars
;
Calculated
by
Tycho
Brahe
,
for
the
Years
1600
,
and
1670.
As
also
their
Difference
of
Right
Ascensions
and
Declinations
,
in
70.
Years
.
|
1600
|
|
Differentia
.
|
1900
|
Names
of
the
Stars
.
|
R.
Asc.
|
Declin
.
|
|
R.
As.
|
Decl.
|
R.
Asc.
|
Declin
.
|
Scedir
,
in
Casssopeae
.
|
4
36
|
54
21
|
N
|
1
22
|
34
S
|
5
58
|
54
55
|
The
Pole
Star
.
|
5
47
|
87
9½
|
N
|
3
59
|
34
S
|
9
46
|
87
43½
|
Southern
in
the
whales
tail
.
|
5
51
|
20
12
|
S
|
1
17
|
34
N
|
7
8
|
19
38
|
Cassiopeae's
Belly
.
|
8
21
|
58
33
|
N
|
1
27
|
34
S
|
9
48
|
59
7
|
Girdle
Andromeda
.
|
11
50
|
33
32
|
N
|
1
23
|
33
S
|
13
13
|
34
5
|
Knee
of
Cassiopeae
.
|
15
3
|
58
7
|
N
|
1
35
|
33
S
|
16
38
|
58
40
|
1.
in
♈
horn
.
|
22
56
|
17
19
|
N
|
1
23
|
31
S
|
24
19
|
17
50
|
Whales
belly
.
|
22
59
|
12
16
|
S
|
1
15
|
31
N
|
24
14
|
11
45
|
2.
in
♈
horn
.
|
23
10
|
18
50
|
N
|
1
22
|
31
S
|
24
32
|
19
31
|
South
foot
of
Andromeda
.
|
24
55
|
40
23
|
N
|
1
29
|
30
S
|
26
24
|
40
53
|
In
the
Knot
in
the
line
♓
.
|
25
22
|
0
50
|
N
|
1
18
|
30
S
|
26
40
|
1
20
|
*
Star
in
♈
head
.
|
26
23
|
21
33
|
N
|
1
25
|
30
S
|
27
38
|
22
3
|
*
In
the
wtales
jaw
.
|
40
25
|
2
29
|
N
|
1
15
|
25
S
|
41
40
|
2
54
|
Caput
Medusae
|
40
38
|
39
22
|
N
|
1
37
|
25
S
|
42
15
|
39
47
|
*
In
Persons
side
.
|
44
2
|
48
22
|
N
|
1
28
|
21
S
|
45
30
|
48
43
|
*
In
the
Pletades
.
|
50
57
|
22
49
|
N
|
1
29
|
21
S
|
52
26
|
23
10
|
In
the
Nostrils
of
♉
.
|
59
16
|
14
37
|
N
|
1
25
|
17
S
|
60
41
|
14
54
|
North
Ey
of
♉
.
|
61
21
|
18
14
|
N
|
1
24
|
17
S
|
62
45
|
18
31
|
Aldebaran
.
|
63
16
|
15
38
|
N
|
1
26½
|
15
S
|
64
43
|
15
53
|
Hircus
,
Capella
.
|
71
49
|
45
30
|
N
|
1
49
|
10
S
|
73
38
|
45
40
|
*
Orions
foot
,
Rigel
.
|
73
51
|
8
43
|
S
|
1
15
|
9½
S
|
75
7
|
8
33½
|
North
Horn
♉
.
|
75
16
|
28
12
|
N
|
1
37
|
8
S
|
76
53
|
28
20
|
Orions
left
sholder
.
|
75
58
|
5
55
|
N
|
1
19
|
3
S
|
77
17
|
6
3
|
Belly
of
the
Hare
|
77
48
|
71
6
|
S
|
1
5
|
7
N
|
78
53
|
20
59
|
1.
In
Orions
Girdle
|
77
58
|
〈◊〉
39
|
S
|
1
17
|
7
N
|
79
15
|
0
32
|
Uppermost
in
Orions
face
|
78
21
|
9
36
|
N
|
1
22
|
7
S
|
79
41
|
0
43
|
South
Horn
♉
.
|
78
26
|
20
51
|
N
|
1
31
|
7
S
|
79
57
|
20
58
|
2.
In
Orions
Girdle
.
|
79
1
|
1
30
|
S
|
1
17
|
6
N
|
80
18
|
1
24
|
Last
in
Orions
Girdle
.
|
80
10
|
2
12
|
S
|
1
16
|
5
N
|
81
26
|
2
7
|
Auriga's
right
Sholder
.
|
82
40
|
44
50
|
N
|
1
55
|
4
S
|
84
35
|
44
54
|
Orions
right
Sholder
.
|
83
26
|
7
16
|
N
|
1
22
|
4
S
|
84
48
|
7
20
|
*
Foot
♊
.
|
93
38
|
16
40
|
N
|
1
28
|
2
N
|
95
6
|
16
38
|
Great
Dog
Sirius
.
|
96
53
|
16
11
|
S
|
1
7
|
4
S
|
98
0
|
16
15
|
Head
of
Castor
,
the
first
Twin
.
|
107
9
|
32
41
|
N
|
1
44
|
11
N
|
108
53
|
32
30
|
The
little
Dog
,
Procyon
.
|
109
37
|
6
12
|
N
|
1
20
|
12
N
|
110
57
|
6
0
|
Head
Pollux
,
second
Twin
.
|
110
13
|
28
55
|
N
|
1
34
|
12
N
|
111
47
|
28
43
|
*
In
the
Stern
of
the
|
117
39
|
23
11
|
S
|
1
4
|
15
S
|
118
43
|
23
26
|
Praesepe
♋
|
124
20
|
21
2
|
N
|
1
28
|
19
N
|
125
48
|
20
43
|
Northern
Asse
♋
Ship
.
|
124
58
|
22
51
|
N
|
1
30
|
20
N
|
126
28
|
22
31
|
Southern
Asse
♋
|
125
27
|
19
35
|
N
|
1
27
|
20
N
|
126
54
|
19
15
|
The
Heart
of
Hydra
.
|
137
1
|
6
57
|
S
|
1
15
|
25
S
|
138
16
|
7
22
|
South
of
3.
in
neck
♌
|
146
22
|
18
42
|
N
|
1
28
|
28
N
|
147
50
|
18
14
|
Lions
Heart
,
Basiliscus
.
|
146
45½
|
13
53½
|
N
|
1
53½
|
28½
N
|
148
8
|
13
25
|
North
of
3.
in
neck
♌
|
148
33
|
25
23
|
N
|
1
23
|
29
N
|
150
1
|
24
54
|
Middle
of
3.
in
neck
♌
|
140
〈◊〉
|
21
50
|
N
|
1
50
|
29
N
|
150
51
|
21
21
|
First
lowest
in
〈◊〉
Vrsa
Ma●
.
|
159
12
|
58
31
|
N
|
1
37
|
32
N
|
160
49
|
57
59
|
First
upper
in
□
Dubbe
|
159
37
|
63
54
|
N
|
1
41
|
32
N
|
161
18
|
63
22
|
*
back
♌
.
|
163
10
|
22
43
|
N
|
1
27
|
34
N
|
164
37
|
22
9
|
Lions
tail
.
|
172
9
|
16
49
|
N
|
1
19
|
34
N
|
173
28
|
16
15
|
following
lowest
in
□
Ursa
Major
.
|
173
3
|
55
57
|
N
|
1
23
|
34
N
|
174
26
|
55
23
|
Uppermost
following
in
□
.
|
178
50
|
59
15
|
N
|
1
20
|
34
N
|
180
10
|
58
41
|
Girdle
〈◊〉
.
|
188
53
|
5
37
|
N
|
1
18
|
34
N
|
190
11
|
5
3
|
Rump
Ursa
Major
,
Aliot
.
|
189
1
|
58
10
|
N
|
1
19
|
33
N
|
190
10
|
57
37
|
Vindemiatrix
,
♍
.
|
190
36
|
13
8
|
N
|
1
17
|
33
N
|
191
53
|
12
35
|
Spica
♍
.
|
196
4
|
9
1
|
S
|
1
19½
|
32½
S
|
197
23½
|
9
33½
|
Middle
tail
Ursa
Major
.
|
196
54
|
57
3
|
N
|
1
3
|
32
N
|
197
57
|
56
31
|
End
Tail
Urs.
Major
.
|
202
54
|
51
22
|
N
|
1
2
|
31
N
|
203
56
|
50
51
|
Arcturus
.
|
209
23½
|
21
18½
|
N
|
1
11
|
29½
N
|
210
34½
|
20
49
|
Left
Sholder
of
Bootes
.
|
214
2
|
40
3
|
N
|
1
2
|
27
N
|
215
4
|
39
36
|
South
Scale
♎
.
|
217
14½
|
14
18
|
S
|
1
23
|
27
S
|
218
37½
|
14
45
|
North
Scale
♎
.
|
223
54½
|
7
50
|
S
|
1
21½
|
24
S
|
225
16
|
8
14
|
*
Northern
Crown
.
|
229
26
|
28
6
|
N
|
1
5
|
21
N
|
230
31
|
27
45
|
*
Serpents
neck
.
|
231
12
|
7
46
|
N
|
1
15
|
21
N
|
232
27
|
7
25
|
Northern
of
3.
*
in
front
♍
.
|
235
34
|
18
38
|
S
|
1
28
|
19
S
|
237
2
|
18
57
|
Lest
hand
Ophiucus
.
|
238
25
|
2
37
|
S
|
●1
23
|
18
S
|
239
48
|
2
55
|
Heart
〈◊〉
.
Antares
,
|
241
18
|
25
26
|
S
|
1
32
|
16
S
|
242
50
|
25
42
|
Right
Shold
▪
Hercules
.
|
243
15
|
22
27
|
N
|
1
5
|
15
N
|
244
20
|
22
12
|
Left
knee
of
Ophiucus
.
|
243
49
|
9
39
|
S
|
1
23
|
15
S
|
245
12
|
9
54
|
Right
knee
of
Ophiucus
.
|
251
50
|
15
7
|
S
|
●0
50
|
10
S
|
252
40
|
15
17
|
Head
of
Hercules
.
|
254
6
|
14
55
|
N
|
1
8
|
8
N
|
255
14
|
14
47
|
Left
Sholder
of
Hercules
.
|
254
40
|
25
22
|
N
|
0
52
|
8
N
|
255
32
|
25
14
|
Head
of
Ophiucus
.
|
259
5
|
12
56
|
N
|
1
11
|
7
N
|
260
16
|
12
49
|
Right
Sholder
of
Ophiucus
.
|
260
56
|
4
49
|
N
|
1
13
|
5
N
|
262
9
|
4
44
|
*
head
of
the
Dragon
.
|
266
52
|
51
37
|
N
|
0
35
|
2
N
|
267
27
|
51
35
|
*
Lyrae
.
|
275
52
|
38
28
|
N
|
●0
50
|
4
S
|
276
42
|
38
32
|
Most
Eastern
in
Head
♐
.
|
281
32
|
21
35
|
S
|
1
31
|
8
N
|
283
3
|
21
27
|
Vultures
tail
.
|
281
47
|
13
20
|
N
|
1
13
|
8
S
|
283
0
|
13
28
|
In
the
Swans
Beak
.
|
288
40
|
27
10
|
N
|
1
1
|
11
S
|
289
41
|
27
21
|
*
in
Vulture
.
|
292
49
|
7
54
|
N
|
1
17
|
13
S
|
294
6
|
8
7
|
In
the
Swans
North
wing
.
|
293
10
|
44
12
|
N
|
0
48
|
14
N
|
293
58
|
44
26
|
Upper
horn
♑
.
|
289
57
|
13
40
|
S
|
1
25
|
16
N
|
300
22
|
13
24
|
Lower
horn
♑
.
|
299
39
|
15
57
|
S
|
1
27
|
17
N
|
301
6
|
15
40
|
In
the
Swans
breast
.
|
302
1½
|
39
1
|
N
|
0
53½
|
18
S
|
302
55
|
39
19
|
Left
hand
of
♒
.
|
306
32
|
10
53
|
S
|
1
16
|
19
N
|
307
48
|
10
34
|
Swans
Tail
.
|
306
57
|
43
53½
|
N
|
0
51½
|
20½S
|
307
49
|
44
14
|
In
the
Swans
South
wing
|
307
31
|
32
30
|
N
|
1
0
|
21
S
|
308
31
|
32
51
|
Left
Sholder
♒
.
|
317
37
|
7
15
|
S
|
1
21
|
26
N
|
318
58
|
6
49
|
1.
In
tail
♑
.
|
319
28
|
18
21
|
S
|
1
26
|
26
N
|
320
54
|
17
55
|
In
Cepheus
Girdle
.
|
320
46
|
68
50
|
N
|
0
22
|
26
S
|
321
8
|
69
16
|
In
Pegasus
mouth
.
|
321
10
|
8
5
|
N
|
1
18
|
26
S
|
322
28
|
8
31
|
2.
in
tail
♑
.
|
321
16
|
17
51
|
S
|
1
25
|
27
N
|
322
41
|
17
24
|
Right
Sholder
of
♒
.
|
326
19
|
2
13
|
S
|
1
20
|
29
N
|
327
39
|
1
44
|
Fomahant
,
♒
.
|
338
46
|
31
39
|
S
|
1
25
|
31
N
|
340
11
|
31
8
|
Scheat
.
P●gasus
.
|
241
9
|
25
56
|
N
|
1
12
|
32
S
|
342
11
|
26
28
|
Marchab
,
Pegasus
.
|
341
15
|
13
5
|
N
|
1
15
|
32
S
|
342
30
|
13
37
|
Mouth
of
Southern
fi●h
.
|
344
9
|
1
7
|
N
|
1
17
|
33
S
|
345
26
|
1
40
|
Head
of
Andromeda
.
|
356
59
|
26
54
|
N
|
1
17
|
34
S
|
358
16
|
27
28
|
*
Cassiopeae's
chair
.
|
357
5
|
56
58
|
N
|
1
15
|
34
S
|
358
20
|
57
32
|
End
of
Pegasus
wing
.
(
tail
.
|
358
14
|
12
58
|
N
|
1
16
|
34
S
|
359
30
|
13
32
|
Northern
in
the
wh●les
|
359
49
|
11
1
|
S
|
1
18
|
34
S
|
1
7
|
10
27
|
The
Vse
of
this
Table
.
The
first
Collumne
on
the
left
hand
is
the
names
of
the
Stars
.
The
Second
Collumne
shews
the
degrees
and
minutes
of
Right
Ascension
,
for
the
Year
1600.
The
third
the
Declination
for
the
same
Year
.
The
fourth
shews
whether
the
Declination
be
North
or
South
;
N
stands
for
North
,
S
for
South
.
The
fifth
shews
the
difference
in
degrees
and
minutes
of
Right
Ascension
of
the
Stars
,
between
the
Years
1600
▪
and
1670.
The
sixth
shews
the
Difference
of
Declination
;
and
whether
it
be
North
,
or
South
.
The
seventh
shews
the
Right
Ascension
in
degrees
and
minutes
,
for
the
Year
1670.
The
eighth
shews
the
D●clination
in
degrees
and
minutes
for
the
same
Year
.
By
this
Table
you
may
perceive
the
fixed
Stars
increase
in
Right
Ascension
,
till
they
come
to
the
Vernal
Colure
;
from
whence
the
number
of
their
Right
Ascension
is
reckoned
:
and
by
the
Collumne
of
their
Difference
of
Right
Ascension
,
you
may
see
how
much
they
increase
in
70.
Years
▪
And
if
you
would
know
how
much
they
increase
for
any
other
number
of
Years
,
you
must
find
what
proportion
they
have
to
70
,
and
the
same
proportion
the
Difference
of
the
Right
Ascension
of
the
Stars
will
have
to
the
Difference
in
the
Table
.
Example
.
I
would
know
the
Difference
of
Right
Ascension
the
Pole-Star
will
have
in
35.
Years
.
I
find
in
the
fifth
Collumne
the
Difference
of
Right
Ascension
of
the
Pole
Star
to
be
3.
degrees
59.
min.
Therefore
by
the
Rule
of
Proportion
.
I
say
,
If
70.
Years
give
3.
degrees
59.
min.
35.
Years
shall
give
1.
degree
59½
▪
min:
and
so
proportionably
for
any
other
number
of
Years
.
Though
this
Rule
serves
for
finding
the
Difference
of
Right
Ascension
of
any
Star
;
Yet
it
will
not
serve
for
finding
the
Difference
of
any
Stars
Declination
.
For
the
Stars
on
the
North
side
the
Equinoctial
between
the
Hyemnal
and
Solsticial
Colures
,
and
on
the
South
side
the
Equinoctial
between
the
Solsticial
and
Hyemnal
Colures
,
increase
in
Declination
.
But
the
Stars
on
the
South
side
the
Equinoctial
between
the
Hyemnal
and
Solsticial
Colures
,
and
on
the
North
side
the
Equinoctial
between
the
Solsticial
and
Hyemnal
Colures
,
Decrease
in
Declination
:
as
you
may
yet
more
plainly
see
by
the
Globe
,
if
you
bring
66½
deg.
of
the
Meridian
to
the
North
side
of
the
Horizon
,
and
screw
the
Quadrant
of
Altitude
to
66½
degrees
in
the
Zenith
,
and
Declination
of
the
Pole
of
the
Ecliptick
;
and
bring
the
Hyemnal
Colure
to
the
Meridian
;
for
so
shall
the
Pole
of
the
Ecliptick
be
joyned
with
the
center
of
the
Quadrant
of
Altitude
,
and
the
Ecliptick
with
the
Horizon
;
and
all
the
Circles
that
the
several
degrees
on
the
Quadrant
make
in
a
Revolution
from
West
to
East
upon
the
Poles
of
the
Ecliptick
,
represent
the
great
Revolution
of
every
Star
that
each
degree
on
the
Quadrant
cuts
.
And
thus
demonstratively
will
be
represented
the
progress
of
the
fixed
Stars
through
every
degree
of
Longitude
,
and
by
consequence
the
alteration
of
their
Right
Ascension
,
and
Declination
.
For
,
Imagining
that
degree
of
the
Quadra●t
of
Altitude
to
be
the
Star
,
which
just
reaches
the
Star
;
you
may
by
turning
about
the
Quadrant
,
see
how
Obliquely
the
Star
(
or
the
degree
representing
the
Star
)
either
moves
about
,
or
cuts
the
Equinectial
,
and
all
Circles
parallel
to
the
Equinoctial
;
and
thereby
observe
it
sometimes
to
incline
in
motion
to
,
and
other
times
to
decline
in
motion
from
the
Equinoctial
.
But
how
long
time
it
will
be
●re
the
Star
inclines
to
,
or
declines
from
the
Equinoctial
,
you
may
know
by
finding
the
distance
of
Longitude
in
degrees
it
hath
from
either
the
Solsticial
or
Hy●mnal
Colure
;
and
with
respecting
the
foregoing
Rules
in
its
Position
,
you
may
by
the
Table
in
Book
1
,
Chap.
3.
Sect.
3.
satifie
your self
.
Example
.
The
most
Northerly
Star
in
the
Girdle
of
Orion
doth
yet
decrease
in
Declination
.
But
I
would
know
how
long
it
shall
decrease
;
Therefore
by
the
32.
Probleme
,
I
find
the
Longitude
of
that
Star
to
be
for
the
Year
1670.
77.
deg.
51.
min.
which
subducted
out
of
90
,
(
the
distance
of
the
Solsticial
Colure
from
the
Equinoctial
,
)
leaves
12.
9
,
for
the
distance
of
that
Star
from
the
Solsticial
Colure
.
Therefore
by
the
Table
aforesaid
,
I
find
what
number
of
Years
answers
to
the
motion
of
12.
deg.
9.
min.
And
because
I
cannot
find
exactly
the
same
number
of
degrees
and
minutes
in
the
Table
,
I
take
the
number
neerest
to
it
;
which
is
14.
degrees
10.
minutes
,
and
that
is
the
motion
of
the
Ecliptick
in
1000.
Years
.
But
because
this
14.
degrees
10.
minutes
is
2.
degrees
1.
minute
too
much
,
I
seek
2.
degrees
,
1.
min.
in
the
Table
,
and
the
number
of
Years
against
it
I
would
subduct
from
the
number
of
Years
against
14
,
deg
,
10.
min.
and
the
remainder
would
be
the
number
of
Years
required
:
But
2.
deg.
1.
min.
I
cannot
find
neither
,
therefore
I
must
take
the
number
of
degrees
and
minutes
neerest
to
it
,
which
is
2.
deg.
50.
min.
and
that
yeelds
200.
Years
;
which
subducted
out
of
1000.
leaves
800.
Years
.
But
because
this
is
also
too
much
by
the
motion
of
49.
min.
Therefore
I
seek
for
49.
min.
in
the
Table
,
and
subduct
the
number
of
Years
against
it
from
800
,
and
the
remainder
would
be
the
number
of
Years
required
.
But
49.
min.
is
not
in
the
Table
neither
,
Therefore
I
take
the
neerest
to
it
,
which
is
51.
min.
and
that
yeelds
60.
Years
;
which
subducted
out
of
800.
leaves
740.
But
this
is
likewise
too
much
by
the
motion
of
two
min.
Therefore
I
seek
2.
min.
in
the
Table
,
but
cannot
find
it
neerer
then
2½
,
and
against
it
I
find
3.
Years
,
which
3.
Years
I
subduct
out
of
740
,
and
the
Remainder
is
737.
the
number
in
Years
required
.
You
may
if
you
please
for
exactness
,
subduct
for
the
½
min.
8.
Moneths
;
so
have
you
736
,
Years
4.
Moneths
,
for
the
Time
that
the
most
Northerly
Star
in
the
Girdle
of
Orion
will
decrease
in
Declination
after
the
Year
1670.
which
will
be
till
An.
Dom.
●406
.
after
which
time
it
will
increase
in
Declination
for
12706.
Years
together
,
till
it
come
to
have
47.
degrees
8.
min.
of
Declination
:
at
which
time
it
will
be
in
or
very
neer
the
place
of
the
most
Southerly
Star
of
the
Southern
Crown
;
and
that
Star
in
its
place
.
And
thus
the
Pole
Star
is
now
found
to
increase
in
Declination
,
and
will
yet
this
421
Years
:
after
which
time
it
will
decrease
in
Declination
for
12706
Years
together
,
till
it
come
to
be
within
42.
degrees
42.
minutes
of
the
Equinoctial
,
in
the
void
space
now
between
Draco
and
Lyra
;
at
which
time
Lyra
will
be
almost
as
neer
the
Pole
,
as
the
Pole
Star
now
is
;
and
then
the
most
proper
to
be
the
Northern
Pole
Star
:
And
the
last
Star
in
the
Stalk
of
the
Doves
mouth
will
be
then
very
neer
the
Southern
Pole
,
and
therefore
most
fit
to
be
the
Southern
Pole-Star
.
PROB.
XXVIII
.
The
Place
of
the
Sun
or
any
Star
given
,
to
find
the
Right
Descension
,
and
the
Oblique
Ascension
,
and
the
Oblique
Descension
.
BRing
the
Place
of
the
Sun
or
the
Star
to
the
Meridian
under
the
Horizon
,
and
the
degree
of
the
Equator
that
comes
to
the
Meridian
with
it
is
the
Degree
of
Right
Descension
.
For
the
Oblique
Ascension
.
Bring
the
Place
of
the
Sun
or
the
Star
to
the
East
side
the
Horizon
,
and
the
degree
of
the
Equator
cut
by
the
Horizon
,
is
the
Degree
of
Oblique
Ascension
of
the
Sun
or
Star
.
For
the
Oblique
Descension
.
Bring
the
Place
of
the
Sun
or
Star
to
the
West
side
the
Horizon
,
and
the
degree
of
the
Equinoctial
cut
by
the
Horizon
is
the
Degree
of
Oblique
Descension
.
They
need
no
Examples
.
PROB.
XXIX
.
Any
Place
on
the
Terrestrial
Globe
being
given
,
to
find
its
Antipodes
.
BRing
the
given
Place
to
the
Meridian
,
so
may
you
(
as
by
the
first
Probleme
)
see
its
Longitude
and
Latitude
;
then
turn
about
the
Globe
till
180.
degrees
of
the
Equator
pass
through
the
Meridian
;
and
keeping
the
Globe
to
this
Position
,
number
on
the
Meridian
180.
degrees
from
the
Latitude
of
the
given
Place
:
and
the
point
just
under
that
degree
is
the
Antipodes
.
Example
.
I
would
find
the
Antipodes
of
Cuida
Real
,
an
Inland
Town
of
the
West
Indies
,
which
lies
upon
the
River
Parana
,
an
Arm
of
Rio
de
la
Plata
:
Therefore
I
bring
Cuida
Real
to
the
Meridian
,
and
find
(
as
by
the
first
Probleme
)
its
Latitude
23.
50
:
South
;
and
its
Longitude
333.
degrees
:
Then
I
turn
about
the
Globe
till
180.
degrees
of
the
Equator
pass
through
the
Meridian
;
and
keeping
the
Globe
to
that
position
,
I
number
so
many
degrees
North
Latitude
as
Parana
hath
South
,
viz.
23
,
50
,
and
just
under
that
degree
I
find
Lamoo
,
a
Town
lying
upon
the
Coast
of
China
,
in
the
Province
of
Quancij
:
Therefore
I
say
Lamoo
is
just
the
Antipodes
of
Cuida
Real
.
Another
way
.
Bring
the
given
Place
to
the
North
or
South
point
of
the
Horizon
,
and
the
point
of
the
Globe
denoted
by
the
opposite
point
of
the
Horizon
,
is
the
Antipodes
of
the
given
Place
.
PROB.
XXX
.
To
find
the
Perecij
of
any
given
Place
,
by
the
Terrestrial
Globe
.
BRing
your
Place
to
that
side
the
Meridian
which
is
in
the
South
notch
of
the
Horizon
,
and
follow
the
Parallel
of
that
Place
on
the
Globe
till
you
come
to
that
side
the
Meridian
which
is
in
the
Northern
notch
of
the
Horizon
;
and
that
is
the
Perecij
of
your
Place
.
PROB.
XXXI
.
To
find
the
Antecij
of
any
given
Place
,
upon
the
Terrestrial
Globe
.
BRing
your
Place
to
the
Meridian
,
and
find
its
Latitude
by
the
first
Probleme
;
If
it
have
North
Latitude
,
count
the
same
number
of
degrees
on
the
Meridian
from
the
Equator
Southwards
;
But
if
it
have
South
Latitude
,
count
the
same
number
of
degrees
from
the
Equator
Northwards
:
and
the
point
of
the
Globe
directly
under
that
number
of
degrees
is
the
Antecij
of
your
Place
.
PROB.
XXXII
.
To
find
the
Longitude
and
Latitude
of
the
Stars
,
by
the
Coelestial
Globe
.
THe
Quadrant
of
Altitude
will
reach
but
90.
degrees
,
as
was
said
Prob.
9.
Therefore
if
the
Star
you
enquire
after
be
on
the
North
side
the
Ecliptick
,
you
must
elevate
the
North
Pole
66½
degrees
above
the
North
side
the
Horizon
:
If
on
the
South
side
the
Ecliptick
,
you
must
elevate
the
South
Nole
66½
degrees
above
the
South
side
the
Horizon
:
Then
bring
the
Solsticial
Colure
to
the
Meridian
on
the
North
side
the
Horizon
,
and
screw
the
Quadrant
of
altitude
to
the
Zenith
,
which
will
be
in
23½
degrees
from
the
Pole
of
the
World
:
So
shall
the
Ecliptick
ly
in
the
Horizon
,
and
the
Pole
of
the
Ecliptick
also
ly
under
the
Center
of
the
Quadrant
of
Altitude
(
as
was
shewed
Prob.
27.
)
Now
to
find
the
Longitude
of
any
Star
,
do
thus
Turn
the
Quadrant
of
Altitude
about
till
the
graduated
edge
of
it
ly
on
the
Star
;
and
the
degree
in
the
Ecliptick
that
the
Quadrant
touches
is
the
Longitude
of
that
Star
.
Example
,
for
a
Star
on
the
North
side
the
Ecliptick
.
I
would
know
the
Longitude
of
Marchab
,
a
bright
Star
in
the
wing
of
Pegasus
:
I
find
it
on
the
North
side
the
Ecliptick
,
Therefore
I
elevate
the
North
Pole
,
and
placing
♋
on
the
North
side
the
Meridian
,
I
screw
the
Quadrant
of
Altitude
to
the
Zenith
,
as
aforesaid
:
Then
laying
the
edge
of
the
Quadrant
of
Altitude
upon
that
Star
,
I
find
that
the
end
of
it
reaches
in
the
Ecliptick
to
♓
18.
56.
Therefore
I
say
,
the
Longitude
of
Marchab
is
♓
.
18.
56.
For
the
Latitude
of
a
Star
.
The
Degree
of
the
Quadrant
of
Altitude
that
touches
the
Star
is
the
Latitude
of
the
Star
.
Example
.
The
Globe
and
Quadrant
posited
as
before
,
I
find
19.
deg.
26.
min.
(
accounted
upwards
on
the
Quadrant
)
to
touch
Marchab
aforesaid
:
Therefore
I
say
,
the
Latitude
of
Marchab
is
19.
deg.
26.
min.
And
thus
by
elevating
the
South
Pole
and
placing
the
Globe
and
Quadrant
of
Altitude
as
aforesaid
,
I
shall
find
Canicula
have
15.
degrees
57.
min.
South
Latitude
,
and
21.
degr.
18.
min
in
♋
,
Longitude
.
PROB.
XXXIII
.
To
find
the
Distance
between
any
two
Places
,
on
the
Terrestrial
Globe
.
THis
may
be
performed
either
with
the
Quadrant
of
Altitude
,
or
with
a
pair
of
Compasses
:
with
the
Quadrant
of
Altitude
,
〈◊〉
:
Lay
the
lower
end
thereof
to
one
Place
,
and
see
what
degree
reaches
the
other
Place
,
for
that
is
the
number
of
degrees
between
the
two
Places
.
If
you
multiply
that
number
of
Degrees
by
60
the
Product
shall
be
the
number
of
English
Miles
between
the
two
Places
.
Example
.
I
would
know
the
distance
between
London
and
the
most
Easterly
point
of
Jama●ca
;
I
lay
the
lower
end
of
the
Quadrant
of
Altitude
to
Jamaica
,
and
extending
the
other
end
towards
London
,
I
find
68½
.
deg.
comprehended
between
them
:
Therefore
I
say
68½
is
the
number
of
degrees
comprehended
between
London
and
Jamaica
.
If
you
would
find
the
Distance
between
them
with
your
Compasses
,
you
must
pitch
one
foot
of
your
Compasses
in
the
East
point
of
Jamaica
,
and
open
your
Compasses
till
the
other
foot
reach
London
;
and
keeping
your
Compasses
at
that
Distance
apply
the
feet
to
the
Equinoctial
line
,
and
you
wil
find
68½
degree
comprehended
between
them
:
as
before
.
If
you
multiply
68½
.
by
60
,
is
it
gives
4110.
English
miles
.
If
you
multiply
it
by
20
,
it
gives
1370.
English
Leagues
.
If
you
multiply
it
by
17½
,
it
gives
1199.
Spanish
Leagues
.
If
you
multiply
it
by
15
,
it
gives
1054
Dutch
Leagues
.
PROB.
XXXIV
.
To
find
by
the
Terrestrial
Globe
upon
what
point
of
the
Compass
any
two
Places
are
scituate
one
from
another
.
FInd
the
two
Places
on
the
Terrestrial
Globe
,
and
see
what
●umb
passes
through
them
;
for
that
is
the
point
of
the
Compass
they
bear
upon
.
Example
.
Bristol
and
Bermudas
are
the
Places
:
I
examine
what
Rhumb
passes
through
them
both
:
and
because
I
find
no
Rhumb
to
pass
immediately
through
them
both
,
Therefore
I
take
that
Rhumb
which
runs
most
Parallel
to
both
the
Places
;
which
in
this
Example
is
the
tenth
Rhumb
counted
from
the
North
towards
the
left
hand
;
and
is
called
as
you
may
see
by
this
following
Figure
West
South
West
;
Therefore
I
say
Bermudos
lies
scituate
from
Bristol
West
South
West
;
and
by
contraries
Bristol
lies
cituate
from
Bermudas
East
North
East
.
PROB.
XXXV
.
To
find
by
the
Coelestial
Globe
the
Cosmical
Rising
and
Setting
of
the
Stars
.
WHen
any
Star
Rises
with
the
Sun
,
it
is
said
to
Rise
Cosmically
.
And
when
any
Star
Sets
when
the
Sun
Rises
,
it
is
sa●d
to
Set
Cosmically
.
To
find
these
,
Rectifie
the
Globe
to
the
Latitude
of
your
Place
,
and
bring
the
Place
of
the
Sun
to
the
East
side
the
Horizon
;
and
the
Stars
then
cut
by
the
Eastern
Semi-Circle
of
the
Horizon
,
Rise
Cosmically
;
and
those
Stars
cut
by
the
Western
Semi-Circle
of
the
Horizon
,
Set
Cosmically
.
Example
.
Novemb.
9.
I
would
know
what
Stars
Rise
and
Set
Cosmically
▪
here
at
London
.
The
Suns
Place
found
,
as
by
the
third
Probleme
is
〈◊〉
27.
Therefore
I
bring
〈◊〉
27.
to
the
East
side
the
Horizon
,
and
in
the
Eastern
Semi-Circle
I
find
Rising
with
the
Sun
the
right
Wing
of
Cygnus
,
the
Star
in
the
end
of
Aquila's
tail
,
Serpentarius
and
Centaurus
:
Therefore
these
Constellations
are
said
to
the
Cosmically
.
In
the
Western
Semi-Circle
of
the
Horizon
I
find
Setting
Andromeda
,
the
Triangle
,
Taurus
,
Orion
,
(
anis
Major
,
and
Argo
Navis
;
Therefore
I
say
,
these
Constellations
Set
Cosmically
.
PROB.
XXXVI
.
To
find
by
the
Coelestial
Globe
the
Acronical
Rising
and
Setting
of
the
Stars
.
THe
Stars
that
Rise
when
the
Sun
Sets
,
are
said
to
Rise
Acronically
.
And
,
The
Stars
that
Set
with
the
Sun
,
are
said
to
Set
Acronically
.
To
find
these
,
Rectifie
the
Globe
to
the
Latitude
of
your
Place
,
and
bring
the
Place
of
the
Sun
to
the
West
side
the
Horizon
;
and
the
Stars
then
cut
by
the
Eastern
Semi-Circle
of
the
Horizon
,
Rise
Acronically
:
And
those
Stars
cut
by
the
Western
Semi-Circle
of
the
Horizon
,
Set
Acronically
.
Example
.
November
9.
I
would
know
what
Stars
Rise
and
Set
Acronically
here
at
London
.
The
Suns
Place
as
before
,
is
〈◊〉
27.
Therefore
I
bring
〈◊〉
27.
to
the
West
side
the
Horizon
;
and
in
the
Eastern
Semi-Circle
I
find
Rising
the
Southern
Fi●h
,
Fomahant
,
Ce●us
,
Taurus
,
Auriga
,
and
the
Feather
in
Castor's
Cap.
Therefore
these
Constellations
are
said
to
Rise
Acronically
.
In
the
Western
Semi-Circle
of
the
Horizon
I
find
Setting
the
Lyons
tail
,
Virgo
,
Scorpio
,
and
Sagittarius
,
Therefore
I
say
,
these
Constellations
Set
Acronically
.
PROB.
XXXVII
.
To
find
by
the
Coelestial
Globe
the
Heliacal
Rising
,
and
Setting
of
the
Stars
.
WHen
a
Star
formerly
in
the
Suns
Beams
gets
out
of
the
Suns
Beams
it
is
said
to
Rise
Heliacally
.
And.
When
a
Star
formerly
out
of
the
Suns
Beams
,
gets
into
the
Suns
Beams
,
it
is
said
to
set
Heliacally
.
A
Star
is
said
to
be
in
the
Suns
Beams
,
when
it
is
made
inconspicuous
by
reason
of
its
neerness
to
the
Suns
Light
.
The
Bigger
Stars
are
discernable
more
neer
the
Suns
Light
,
then
the
Lesser
are
:
For
,
Stars
of
the
first
Magnitude
may
(
according
to
the
received
Rules
of
ancient
Authors
)
be
seen
when
the
Sun
is
but
12.
degrees
below
the
Horizon
but
Stars
of
Second
Magnitude
cannot
be
seen
unless
the
Sun
be
13.
degrees
below
the
Horizon
:
Stars
of
the
third
Magnitude
require
the
Sun
to
be
14.
degrees
below
the
Horizon
ere
they
can
be
seen
;
of
the
fourth
Magni●ude
15.
degrees
.
of
the
fifth
Magnitude
16.
degrees
of
the
sixth
Magnitude
17
degrees
;
the
Nebulous
ones
18.
degrees
.
Yet
this
Rule
is
not
so
certain
but
that
either
clear
or
cloudy
weather
may
alter
it
.
Read
more
of
this
subject
in
Mr
Palmer
on
the
Plamsphear
.
Book
4.
Chap.
20
Now
to
find
the
Time
that
any
Star
shall
Rise
Heliacally
.
Do
thus
Rectifie
the
Globe
and
Quadrant
of
Altitude
to
your
Latitude
.
Then
bring
the
given
Star
to
the
East
side
the
Horizon
,
and
turn
the
Quadrant
of
Altitude
into
the
West
side
,
and
see
what
degree
of
the
Ecliptick
is
elevated
so
many
degrees
above
the
Horizon
as
the
Magnitude
of
the
Star
you
enquire
after
requires
,
according
to
the
foregoing
Rules
;
for
the
opposite
degree
of
the
Ecliptick
is
the
degree
the
Sun
shall
be
in
when
that
Star
Rises
Heliacally
.
Having
the
degree
of
the
Ecliptick
the
Sun
is
in
,
you
may
find
the
Day
of
the
Moneth
,
by
the
4th
Probleme
.
Example
.
I
would
know
when
Cor
Leonis
shall
Rise
Heliacally
here
at
London
:
Therefore
I
Rectifie
the
Globe
and
Quadrant
of
Altitude
for
London
,
and
bring
Cor
Leonis
to
the
East
side
the
Horizon
,
and
turn
the
Quadrant
of
Altitude
into
the
West
;
and
because
Cor
Leonis
is
a
Star
of
the
first
Magnitude
,
therefore
I
see
what
degree
of
the
Ecliptick
is
elevated
in
the
West
side
the
Horizon
12.
degrees
on
the
Quadrant
of
Altitude
,
and
find
♓
9.
deg.
Now
the
degree
of
the
Ecliptick
opposite
to
♓
9.
is
〈◊〉
9.
Therefore
I
say
,
when
the
Sun
comes
to
〈◊〉
9.
degrees
(
which
by
the
4th
Probleme
I
find
is
August
.
23.
)
Cor
Leonis
shall
Rise
Heliacally
.
For
the
Heliacal
Setting
.
The
Globe
,
&c.
Rectified
,
as
before
:
Bring
the
Star
to
the
West
side
the
Horizon
,
Then
see
what
degree
of
the
Ecliptick
is
elevated
on
the
Quadrant
of
Altitude
so
many
degrees
as
the
Stars
Magnitude
requires
;
for
when
the
Sun
comes
to
the
opposite
degree
of
the
Ecliptick
that
Star
shall
set
Heliacally
.
Example
.
I
would
know
when
Bilanx
a
Star
in
the
Beam
of
the
Scales
,
will
Set
Heliacally
here
at
London
.
The
Globe
and
Quadrant
Rectified
,
I
bring
Bilanx
to
the
West
side
the
Horizon
,
and
turn
the
Quadrant
of
Altitude
into
the
East
;
Then
I
examine
what
degree
of
the
Ecliptick
is
elevated
13.
degrees
of
the
Quadrant
of
Altitude
(
because
Bilanx
is
a
Star
of
the
second
Magnitude
)
and
find
♉
4½
.
opposite
to
♉
4½
.
is
〈◊〉
4½
.
Therefore
I
say
,
When
the
Sun
comes
to
〈◊〉
4½
.
(
which
by
Probleme
4.
will
be
October
18
)
Bilanx
shall
set
Heliacally
.
PROB.
XXXVIII
.
To
find
the
Diurnal
and
Nocturnal
Arch
of
the
Sun
,
or
Stars
,
in
any
given
Latitude
.
THe
Semi-Diurnal
Arch
is
the
number
of
degrees
of
the
Equator
that
passes
through
the
Meridian
whiles
the
Sun
or
any
Star
is
ascending
above
the
East
side
the
Horizon
to
the
Meridian
.
To
know
the
number
of
degrees
it
contains
,
Rectifie
the
Globe
to
the
given
Latitude
,
and
bring
the
Place
of
the
Sun
or
Star
to
the
East
side
the
Horizon
,
and
note
what
number
of
degrees
of
the
Equinoctial
is
then
cut
by
the
Meridian
:
Then
remove
the
Place
of
the
Sun
or
Star
to
the
Meridian
,
and
see
again
what
number
of
degrees
of
the
Equinoctial
is
then
cut
by
the
Meridian
,
and
substract
the
former
from
the
latter
,
and
the
remainder
shall
be
the
number
of
degrees
of
the
Sun
or
Stars
Semi-Diurnal
Arch.
But
Note
,
If
the
Equinoctial
point
♈
pass
through
the
Meridian
while
the
Sun
or
Star
is
turned
from
the
East
side
the
Horizon
to
the
Meridian
,
then
you
must
substract
the
number
of
degrees
of
the
Equinoctial
cut
by
the
Meridian
when
the
Sun
or
Star
is
at
the
East
side
the
Horizon
from
360.
degrees
,
and
to
the
remainder
ad
the
number
of
degrees
of
the
Equinoctial
that
comes
to
the
Meridian
with
the
Place
of
the
Sun
or
Star
,
and
the
Sum
of
them
both
is
the
number
of
degrees
of
the
Sun
or
Stars
Semi-diurnal
Arch
;
which
being
doubled
is
the
number
of
degrees
of
the
whole
Diurnal
Arch
:
and
which
being
substracted
from
360
,
given
the
Nocturnal
Arch.
Example
,
of
the
Sun
.
Having
Rectified
the
Globe
,
I
would
May
10.
know
the
Diurnal
Arch
of
the
Sun
:
His
Place
found
by
Prob.
3.
is
8
29.
Therefore
I
bring
♉
29.
to
the
Fast
side
the
Horizon
,
and
find
then
at
the
Meridian
299.
degrees
30.
min.
of
the
Equinoctial
;
then
I
turn
the
Place
of
the
Sun
to
the
Meridian
,
and
find
56.
deg.
30.
min.
of
the
Equinoctial
come
to
the
Meridian
with
it
.
Here
the
Equinoctial
point
♈
passes
through
the
Meridian
while
the
Sun
moves
between
the
Horizon
and
the
Meridian
;
Therefore
as
aforesaid
,
I
substract
the
first
number
of
degrees
and
minutes
viz.
299.
deg.
30.
min.
from
360.
degrees
,
and
there
remains
60
▪
degr.
30.
min.
for
the
number
of
degrees
and
minutes
contained
between
the
degree
of
the
Equinoctial
at
the
Meridian
and
the
Equinoctial
point
♈
;
and
to
this
60.
deg.
30.
min.
I
ad
the
second
number
of
degrees
and
minutes
,
viz.
56.
deg.
30.
min.
the
number
of
degrees
and
minutes
between
the
point
♈
and
the
deg.
of
the
Equinoctial
at
the
Meridian
,
and
they
make
together
117.
degrees
,
for
the
Suns
Semi
diurnal
Arch
;
By
doubling
of
which
,
you
have
234.
degrees
,
for
the
Suns
Diurnal
Arch
;
And
by
substracting
234.
(
the
Diurnal
Arch
)
from
360.
you
have
126.
degrees
,
for
the
Suns
Nocturnal
Arch.
Example
,
for
a
Star
.
I
take
Sirius
,
a
bright
Star
in
the
Great
Dogs
mouth
.
The
Globe
rectified
,
as
before
;
I
bring
Sirius
to
the
East
side
the
Horizon
,
and
find
then
29.
degrees
30
minutes
of
the
Equinoctial
at
the
Meridian
,
then
I
turn
Sirius
to
the
Meridian
and
find
97.
degrees
38
minutes
of
the
Equinoctial
come
to
the
Meridian
with
it
:
Therefore
I
substract
the
first
number
viz.
29.
degrees
30.
minutes
,
from
the
second
,
97.
38
,
and
the
remains
is
68.
degrees
8
minutes
,
for
the
Semi-diurnal
Arch
of
Sir●us
.
His
Nocturnal
Arch
you
may
find
as
before
.
PROB.
XXXIX
.
To
find
the
Azimuth
and
Almicantar
of
any
Star
.
THis
Probleme
is
like
the
22
,
and
23.
Problemes
,
which
shew
the
finding
the
Azimuth
and
Almicantar
of
the
Sun
;
only
,
whereas
there
you
were
directed
to
bring
the
degree
of
the
Sun
to
the
Quadrant
of
Altitude
,
you
must
now
bring
the
Star
proposed
to
the
Quadrant
of
Altitude
;
and
by
the
Directions
in
those
Problemes
the
resolution
will
be
found
.
PROB.
XL.
To
find
the
Hour
of
the
Night
,
by
observing
two
known
Stars
in
one
Azimuth
,
or
Almicantar
.
REctifie
the
Globe
Quadrant
and
Hour
Index
.
Then
find
the
two
known
Stars
on
the
Globe
;
and
if
the
two
Stars
be
in
one
Azimuth
,
turn
about
the
Globe
and
Quadrant
of
Altitude
till
you
can
fit
the
two
Stars
to
ly
under
the
graduated
edge
of
the
Quadrant
of
Altitude
:
so
shall
the
Index
of
the
Hour-Circle
p●int
at
th●
Hour
of
the
Night
.
If
the
two
Stars
be
in
one
Almicantar
,
Turn
the
Globe
forward
or
backward
till
the
two
Stars
come
to
such
a
Position
that
by
moving
the
Quadrant
of
Altitude
,
the
same
degree
on
it
will
ly
on
both
the
Stars
;
so
shall
the
Index
of
the
Hour-Circle
point
at
the
Hour
of
the
Night
.
PROB.
XLI
.
The
Hour
given
that
any
Star
in
Heaven
comes
to
the
Meridian
,
to
know
thereby
the
Place
of
the
Sun
,
and
by
consequence
the
Day
of
the
Moneth
,
though
it
were
lost
.
BRing
the
Star
proposed
to
the
Meridian
,
and
turn
the
Index
of
the
Hour-Circle
to
the
Hour
given
,
Then
turn
about
the
Globe
till
the
Index
point
at
the
Hour
of
12
,
for
Noon
;
and
the
Place
of
the
Sun
in
the
Ecliptick
shall
be
cut
by
the
Meridian
.
Example
.
March
7.
at
11
,
aclock
at
Night
the
Pointers
come
to
the
Meridian
of
London
.
Therefore
I
place
the
Pointers
on
the
Caelestial
Globe
under
the
Meridian
,
and
turn
the
Index
of
the
Hour-Circle
to
11.
past
Noon
,
afterwards
I
turn
back
the
Globe
till
the
Index
point
to
12.
at
Noon
;
Then
looking
in
the
Ecliptick
,
I
find
the
Meridian
cuts
it
in
♓
26.
45.
minutes
;
Therefore
I
say
,
when
the
Pointers
come
to
the
Meridian
at
11.
a
clock
at
Night
,
the
Place
of
the
Sun
is
♓
26.
45.
Having
thus
the
Place
of
the
Sun
,
I
may
find
the
Day
of
the
Moneth
by
the
fourth
Probleme
;
and
so
either
know
the
Day
that
the
Pointers
come
to
the
Meridian
at
11.
a
clock
at
Night
,
or
at
any
other
Hour
given
.
The
Day
of
the
Moneth
might
also
be
found
by
the
Declination
and
the
Quarter
of
the
Ecliptick
the
Sun
is
in
,
given
:
For
the
Meridian
will
cut
the
degree
of
the
Suns
Place
in
the
Ecliptick
in
the
Parallel
of
Declination
:
So
that
having
respect
to
the
Quarter
of
the
Ecliptick
,
you
'le
find
the
Suns
Place
;
and
having
the
Suns
Place
,
you
may
as
aforesaid
find
the
Day
of
the
Moneth
.
PROB.
XLII
.
The
Day
of
the
Moneth
given
,
to
find
in
the
Circle
of
Letters
on
the
Plain
of
the
Horizon
,
the
Day
of
the
Week
.
THe
seven
Daies
of
the
Week
were
by
the
Idolatry
of
the
ancient
Roman
Heathenish
Times
Dedicated
to
the
Honour
of
seven
of
their
Gods
,
which
we
call
Planets
.
The
first
is
the
most
eminent
,
and
therefore
doubtless
by
them
set
in
the
first
Place
,
called
Dia
Solis
,
or
the
Suns
Day
:
The
second
Dia
Luna
,
the
Moons
Day
:
The
third
Dia
Martis
,
the
Day
of
Mars
:
by
us
called
Tuesday
:
The
fourth
Dia
Mercurius
,
Mercuries
Day
:
by
us
called
Wednesday
;
from
Woden
,
an
Idol
the
Saxons
Worshipt
,
to
whose
Honour
they
Dedicated
that
Day
,
and
is
by
all
those
Germain
Nations
still
called
Wodensdagh
:
The
fifth
Dia
Jovis
,
Jupiter
or
Joves
Day
:
which
doubtless
the
Saxons
(
from
whom
probably
we
receive
it
)
called
Donder-dagh
,
because
Jupiter
is
the
God
of
Thunder
;
and
we
either
by
corruption
or
for
shortness
,
or
both
,
call
it
Thursday
:
The
sixth
Dia
Veneris
,
the
Day
of
Venus
:
but
the
Saxons
transferring
her
Honour
to
another
of
their
Goddesses
named
Fria
,
called
it
Fridagh
:
and
we
from
them
call
it
Fryday
:
The
seventh
is
Dia
Saturnis
,
Saturus
Day
.
The
same
Day
of
the
Moneth
in
other
Years
happens
not
on
the
same
Day
of
the
Week
,
therefore
the
Dominical
Letter
for
one
Year
is
not
the
same
it
is
the
next
:
Now
because
you
cannot
come
to
the
knowledge
of
the
Day
of
the
Week
unless
you
first
know
the
Sundaies
Letter
,
therefore
have
I
in
Prob.
5●
inserted
a
Table
of
Mr
Palmers
,
by
which
you
may
find
the
Dominical
or
Sundaies
Letter
for
ever
;
and
having
the
Dominical
Letter
you
may
in
the
Circle
of
Letters
on
the
Horizon
find
it
neer
the
day
of
that
Moneth
,
and
count
that
for
Sunday
,
the
next
under
it
for
Monday
,
the
next
under
that
for
Tuesday
,
and
so
in
order
,
till
you
come
to
the
Day
of
the
Moneth
.
Example
.
I
would
know
what
Day
of
the
Week
June
1.
Anno
1658.
Old
Style
,
falls
on
;
I
find
by
the
Table
aforesaid
the
Dominical
Letter
is
C
,
then
I
look
in
the
Calender
of
Old
Style
for
June
1.
and
against
it
I
find
Letter
E
,
which
because
it
is
the
second
Letter
in
order
from
C
,
therefore
it
is
the
second
Day
in
order
from
Sunday
,
which
is
Tuesday
.
PROB.
XLIII
.
The
Azimuth
of
any
Star
given
,
to
find
its
Hour
in
any
given
Latitude
.
THe
Hour
of
a
Star
is
the
number
of
Hours
that
a
Star
is
distant
from
the
Meridian
.
To
find
which
,
Rectifie
the
Globe
and
Quadrant
of
Altitude
,
and
bring
the
Star
proposed
to
the
Meridian
,
and
the
Index
of
the
Hour-Circle
to
12.
Then
place
the
lower
end
of
the
Quadrant
of
Altitude
to
the
given
Azimuth
in
the
Horizon
,
and
turn
the
Globe
till
the
Star
come
to
the
graduated
edge
of
the
Quadrant
of
Altitude
;
so
shall
the
Index
of
the
Hour-Circle
point
at
the
Hour
of
the
Star
.
Only
this
caution
you
must
take
;
If
the
Star
were
turned
from
the
Meridian
towards
the
Eastern
side
of
the
Horizon
,
you
must
substract
the
number
of
Hours
the
Index
points
at
from
12.
and
the
remainder
shall
be
the
Hour
of
the
Star
.
But
if
the
Star
were
turned
from
the
Meridian
towards
the
West
side
the
Horizon
,
the
Hour
the
Index
points
at
is
(
without
more
adoe
)
the
Hour
of
the
Star
.
PROB.
XLIV
.
How
you
may
learn
to
know
all
the
Stars
in
Heaven
,
by
the
Coelestial
Globe
.
REctifie
the
Globe
,
Quadrant
,
Hour-Index
and
Horizon
,
as
by
Prob.
2.
Then
turn
about
the
Globe
till
the
Index
of
the
Hour-Circle
point
at
the
Hour
of
the
Night
on
the
Hour-Circle
.
Then
if
every
Star
on
the
Globe
had
a
hole
in
the
midst
,
and
your
Ey
were
placed
in
the
Center
of
the
Globe
;
you
might
by
keeping
your
Ey
in
the
Center
and
looking
through
any
Star
on
the
Globe
see
its
Ma●ch
in
Heaven
:
that
is
,
the
same
Star
in
Heaven
which
that
Star
on
the
Globe
represents
:
for
from
the
Center
of
the
Globe
there
proceeds
a
straight
line
through
the
Star
on
the
Globe
,
even
to
the
same
Star
in
Heaven
.
Therefore
those
Stars
that
are
in
the
Zenith
in
Heaven
,
will
then
be
in
the
Zenith
on
the
Globe
;
those
that
are
in
the
East
in
Heaven
,
will
be
in
the
East
on
the
Globe
;
those
in
the
West
in
Heaven
,
in
the
West
on
the
Globe
;
and
those
Stars
that
are
in
any
Altitude
in
Heaven
,
will
at
the
same
time
have
the
same
Altitude
on
the
Globe
;
So
that
if
you
see
any
Star
in
Heaven
whose
Name
you
desire
to
know
,
you
need
but
observe
its
Azimuth
and
Altitude
,
and
in
the
same
Azimuth
and
Altitude
on
the
Globe
,
you
may
find
the
same
Star
:
and
if
it
be
an
eminent
Star
,
you
will
find
its
Name
adjoyned
to
it
.
Example
.
December
10.
at
half
an
hour
past
9.
a
clock
at
Night
,
here
at
London
,
I
see
two
bright
Stars
at
a
pretty
distance
one
from
another
in
the
South
;
I
desire
to
know
the
Names
of
them
;
Therefore
having
the
Globe
rectified
to
the
Latitude
of
London
,
and
the
Quadrant
of
Altitude
screwed
to
the
Zenith
,
the
Hour-Index
also
Rectified
,
and
the
Horizon
posited
Horizontally
,
as
by
Prob.
2.
I
observe
the
Altitude
of
those
Stars
in
Heaven
,
(
either
with
a
Quadrant
,
Astrolabe
,
Cross-staff
,
or
the
Globe
it self
,
as
hath
been
shewed
Prob.
13
,
16.
)
to
be
,
the
one
78.
degrees
,
the
other
42
,
degrees
above
the
Horizon
.
Therefore
having
their
Altitudes
,
I
count
the
same
number
of
degrees
as
for
the
first
78.
upon
the
Quadrant
of
Altitude
upwards
,
and
turn
it
into
the
South
,
under
the
Meridian
,
and
see
what
Star
is
under
78.
degrees
,
for
that
is
the
same
Star
on
the
Globe
which
I
saw
in
Heaven
.
Now
at
the
first
examination
of
the
Globe
you
may
see
that
that
Star
is
placed
in
the
Ey
of
that
After
time
which
is
called
Caput
Medusa
,
and
indeed
,
that
being
the
only
Star
of
Note
in
that
Constellation
,
bears
the
Name
of
the
whole
Constellation
.
The
other
Stars
about
it
you
may
easily
know
by
their
Scituation
.
As
,
Seeing
two
little
Stars
to
the
Westwards
of
that
Star
in
Heaven
,
you
may
see
on
the
Globe
that
the
hithermost
is
in
the
other
Ey
of
Caput
Medusa
,
and
the
furthermost
in
the
Hair
or
Snakes
of
the
same
Asterisme
.
Looking
a
little
to
the
Southwards
of
those
Stars
in
Heaven
,
you
may
see
two
other
smal
Stars
a
little
below
those
in
the
Eyes
;
Therefore
to
know
those
also
,
you
may
look
on
the
Globe
,
and
see
that
there
is
one
on
the
Nose
,
and
another
Starre
in
the
Cheek
of
Caput
Medusa
In
like
manner
for
the
second
Star
in
the
Meridian
,
which
is
42
degrees
above
the
Horizon
:
If
you
move
the
Quadrant
of
Altitude
(
as
before
)
to
the
South
or
Meridian
,
and
count
42
degrees
upon
the
Quadrant
of
Altitude
,
you
will
find
a
Star
of
the
second
Magnitude
in
the
Mouth
of
the
Whale
:
Therefore
you
may
say
,
that
Star
in
Heaven
is
in
the
Mouth
of
the
Whale
:
and
because
close
to
it
on
the
Globe
is
written
Menkar
,
Therefore
you
may
know
the
name
of
that
Star
in
Heaven
is
Menkar
.
In
the
South
East
and
by
South
56
degrees
above
the
Horizon
,
I
●ee
a
very
bright
Star
in
Heaven
;
therefore
I
bring
the
Quadrant
of
Altitude
to
the
South
East
and
by
South
point
in
the
Horizon
,
and
find
under
56
degrees
of
the
Quadrant
of
Altitude
a
great
Star
,
to
which
is
prefixed
the
name
Occulus
Taurus
;
Therefore
I
say
,
the
name
of
that
Star
in
Heaven
is
Occulus
Taurus
.
In
the
South
East
in
Heaven
you
may
see
three
bright
Stars
ly
directly
in
a
straight
line
from
one
another
,
the
middlemost
whereof
is
25.
degrees
or
thereabouts
above
the
Horizon
,
therefore
bring
the
Quadrant
of
Altitude
to
the
South
East
point
of
the
Horizon
,
and
about
25
degrees
above
the
Horizon
you
will
see
the
same
great
Stars
on
the
Globe
,
in
the
Girdle
of
Orion
:
Therefore
those
Stars
are
called
Orions
Girdle
.
At
the
same
time
South
East
and
by
East
you
have
about
10
degrees
above
the
Horizon
the
brightest
Star
in
Heaven
,
called
Sirius
,
in
the
Mouth
of
the
Great
Dog
;
Canicula
a
bright
Star
in
the
Little
Dog
East
and
by
South
,
about
25
degrees
above
the
Horizon
:
Cor
Leonis
just
Rising
East
North
East
:
you
have
also
at
the
same
time
on
the
East
side
the
Horizon
,
the
Twins
,
Auriga
,
the
Great
Bear
;
and
divers
other
Stars
,
eminent
both
for
their
splendor
and
Magnitude
.
In
the
West
side
the
Horizon
you
have
South
West
and
by
West
about
4
degrees
above
the
Horizon
a
bright
Star
in
the
Right
Leg
of
Aquarius
:
and
all
along
to
the
Southwards
in
Cetus
the
Whale
,
you
have
other
eminent
bright
Stars
:
More
upwards
towards
the
Zenith
you
have
a
bright
Star
in
the
Line
of
the
two
Fishes
:
Higher
yet
,
you
have
the
first
Star
in
♈
,
an
eminent
Star
,
because
the
first
in
all
Catalogues
that
we
have
cognizance
of
;
and
therefore
probably
in
the
Equinoctial
Colure
when
the
Stars
were
first
reduced
into
Constellations
:
yet
more
neer
the
Zenith
you
have
a
bright
Star
in
the
Left
Leg
of
Andromeda
:
From
thence
towards
the
North
,
you
find
other
very
eminent
bright
Stars
in
Cassiopea
,
Cepheus
,
Ursa
Minor
,
in
the
Tail
whereof
is
the
Pole
Star
:
and
Draco
:
Hecules
:
where
you
turn
back
,
to
Lyra
,
Cygnus
,
Pegasus
,
the
Dolphin
,
&c.
all
which
,
or
any
other
,
you
may
easily
know
by
their
Altitude
above
the
Horizon
,
and
the
point
of
the
Compass
they
bear
upon
.
Thus
knowing
some
of
the
most
eminent
Fixed
Stars
,
you
may
by
the
Figure
of
the
rest
come
to
the
knowledge
of
them
also
.
For
Example
,
Looking
towards
the
North
North
East
in
Heaven
,
you
may
see
seven
bright
Stars
constituted
in
this
Figure
;
Therefore
looking
towards
the
same
Quarter
on
the
Globe
,
you
may
(
without
taking
their
Altitude
)
see
the
same
Stars
lying
in
the
same
Figure
in
the
hinder
parts
of
the
Great
Bear
;
from
whence
you
may
conclude
,
that
those
Stars
in
Heaven
are
scituate
in
the
hinder
parts
of
the
Asterisme
called
Ursa
Major
.
Yet
nevertheless
you
may
see
some
Stars
of
Note
in
Heaven
,
which
you
shall
not
find
on
the
Globe
,
and
those
in
or
neer
about
the
Ecliptick
:
They
are
called
Planets
,
and
cannot
be
placed
on
the
Globe
,
unless
it
be
for
a
particular
Time
,
with
Black
Lead
,
or
some
such
thing
that
may
be
rubbed
out
again
:
Because
they
having
a
continual
motion
alwaies
alter
their
Places
.
Of
those
there
are
five
in
number
,
besides
the
Sun
and
Moon
,
which
are
also
Planets
,
though
they
shew
not
like
Stars
.
These
five
are
called
Saturn
,
Jupiter
,
Mars
,
Venus
,
Mercury
;
yet
Mecury
is
very
rarely
seen
:
because
he
never
Rising
above
an
Hour
before
the
Sun
,
or
Setting
above
a
Hour
after
,
for
the
most
part
hath
his
light
so
overspread
with
the
dazelling
Beams
of
the
glittering
Sun
,
that
sometimes
when
he
is
seen
he
seems
rather
to
be
a
More
in
the
Suns
Beams
,
then
a
Body
endowed
with
so
much
brightness
as
Stars
and
Planets
seem
to
be
.
Now
there
are
divers
waies
(
by
some
of
which
you
may
at
all
times
)
know
those
Planets
from
the
Fixed
Stars
:
as
first
,
Their
not
twinkling
,
for
therein
they
differ
from
fixed
Stars
;
because
they
most
commonly
do
twinkle
,
but
Planets
never
;
unless
it
be
♂
Mars
;
and
yet
he
twinkles
but
very
seldom
neither
.
Secondly
,
They
appear
of
a
considerable
Magnitude
,
as
♃
sometimes
appears
greater
ly
far
then
a
Star
of
the
first
Magnitude
;
and
☿
many
times
bigger
then
he
.
They
are
both
glittering
Stars
,
of
a
bright
Silver
collure
;
but
♀
most
radient
,
especially
when
she
is
in
her
Perigeon
.
♂
appears
like
a
Star
of
the
second
Magnitude
;
and
is
of
a
Copperish
colloure
.
♄
shewes
like
a
Star
of
the
third
Magnitude
,
and
is
of
a
Leaden
Collour
;
and
he
(
of
all
the
others
,
)
is
most
difficult
to
be
known
from
a
fixed
Star
;
partly
because
of
his
minority
,
and
partly
because
of
the
slowness
of
his
motion
.
☿
is
very
seldom
seen
(
as
aforesaid
)
unless
it
be
in
a
Morning
when
he
Rises
before
the
Sun
,
or
in
an
Evening
when
he
Sets
after
the
Sun
:
He
is
of
a
Pale
Whitish
Collour
,
like
Quick
silver
,
and
appears
like
a
Star
of
the
third
Magnitude
.
He
may
be
known
by
the
Company
he
keeps
,
for
he
is
never
above
29.
degrees
distant
from
the
Sun
.
Thirdly
,
The
Planets
may
be
known
from
fixed
Stars
by
their
Azimuths
and
Altitudes
observed
:
(
as
hath
been
taught
before
)
for
if
when
you
have
taken
the
Azimuth
and
Altitude
of
the
Star
in
Heaven
you
doubt
to
be
a
Planet
,
and
you
find
not
on
the
Globe
in
the
same
Azimuth
and
Altitude
a
Star
appearing
to
be
of
the
same
Magnitude
that
that
in
Heaven
appears
to
be
,
you
may
conclude
that
that
in
Heaven
is
a
Planet
.
Yet
notwithstanding
it
may
happen
that
a
Planet
may
be
in
the
same
degree
of
Longitude
and
Latitude
in
the
Zodiack
that
some
eminent
fixed
Star
is
in
;
as
in
the
degree
and
minute
of
Longitude
and
Latitude
that
Cor
Leonis
,
or
the
Bulls
Ey
,
or
Scorpions
heart
is
in
,
and
so
may
eclipse
that
Star
,
by
being
placed
between
us
and
it
:
But
that
happens
very
seldom
and
rarely
;
but
if
you
doubt
it
▪
you
may
apply
your self
to
some
other
of
the
precedent
and
subsequent
Rules
here
set
down
for
knowing
Planets
from
fixed
Stars
.
The
fourth
way
is
by
shifting
their
Places
;
for
the
Planets
having
a
continual
motion
,
do
continually
alter
their
Places
:
as
♂
moves
about
half
a
degree
in
a
day
:
♀
a
whole
degree
;
but
♃
and
♄
move
very
slowly
;
♃
not
moving
above
5.
minutes
,
and
♄
seldom
above
2.
minutes
.
Yet
by
their
motions
alone
the
Planets
may
be
known
to
be
Planets
,
if
you
will
precisely
observe
their
distance
from
any
known
fixed
Star
in
or
near
the
Ecliptick
as
on
this
Night
,
and
the
next
Night
after
observe
whether
they
retain
the
same
distance
they
had
the
Night
before
;
which
if
they
do
,
then
are
they
fixed
Stars
;
but
if
they
do
not
then
are
they
Planets
:
yet
this
Ca●●on
is
to
be
given
you
in
this
Rule
also
,
That
the
Planets
sometimes
are
said
to
be
Stationary
,
as
not
altering
1.
minute
in
Place
,
forwards
,
or
backwards
in
6.
or
7.
daies
together
.
Therefore
,
if
you
find
cause
to
doubt
whether
your
Star
be
a
Planet
,
or
a
fixed
Star
,
you
may
for
the
help
of
your
understanding
confer
with
some
of
the
former
Rules
,
unless
you
are
willing
to
wait
8
or
9
daies
longer
,
and
so
by
observation
of
its
motion
resolve
your self
,
Or
,
Fifthly
,
you
may
apply
your self
to
an
Ephemeris
for
that
Year
,
and
see
if
on
that
day
you
find
any
Planet
in
the
degree
and
minute
of
the
Zodiack
you
see
the
Star
you
question
in
Heaven
;
and
if
there
be
no
Planet
in
that
degree
of
the
Zodiack
,
you
may
conclude
it
is
no
Planet
,
but
a
fixed
Star
.
PROB.
XLV
.
How
to
hang
the
Terrestrial
Globe
in
such
a
position
that
by
the
Suns
shining
upon
it
you
may
with
great
delight
at
once
behold
the
demonstration
of
many
Principles
in
Astronomy
,
and
Geography
.
TAke
the
Terrestrial
Ball
out
of
the
Horizon
,
and
fasten
a
thred
on
the
Brazen
Meridian
to
the
degree
of
the
Latitude
of
your
Place
;
by
this
thred
hang
the
Globe
in
a
place
where
the
Suns
Beams
may
have
a
free
access
to
it
;
Then
direct
the
Poles
of
the
Globe
to
their
proper
Poles
in
Heaven
,
the
North
Pole
to
the
North
,
and
the
South
Pole
to
the
South
;
and
with
a
thred
fastned
to
either
Pole
,
brace
the
Globe
,
so
,
that
it
do
not
turn
from
his
position
:
then
bring
your
Habitation
to
the
Meridian
;
so
shall
your
Terrestrial
Globe
be
Rectified
to
correspond
in
all
respects
with
the
Earth
it self
;
even
as
in
Prob.
44.
the
Celestial
Globe
doth
;
the
Poles
of
the
Globe
,
to
the
Poles
of
the
World
;
the
Meridian
of
the
Globe
,
to
the
Meridian
of
the
World
;
and
the
several
Regions
on
the
Globe
made
Correspondent
to
the
same
Regions
on
the
Earth
:
So
that
with
great
delight
you
may
behold
,
1.
How
the
counterfeit
Earth
(
like
the
true
one
)
will
have
one
Hemisphear
Sun
shine
light
,
and
the
other
shadowed
,
and
as
it
were
dark
.
By
the
shining
Hemisphear
you
may
see
that
it
is
Day
in
all
Places
that
are
scituate
under
it
;
for
on
them
the
Sun
doth
shine
;
and
that
it
is
Night
at
the
same
time
in
those
Places
that
are
situate
in
the
shadowed
Hemisphear
;
for
on
them
the
Sun
doth
not
shine
;
and
therefore
they
remain
in
darkness
.
2.
If
in
the
middle
of
the
enlightned
Hemisphear
you
set
a
Spherick
Gnomon
Perpendicularly
,
it
will
project
no
shadow
,
but
shews
that
the
Sun
is
just
in
the
Zenith
of
that
Place
;
that
is
,
directly
over
the
heads
of
the
Inhabitants
of
that
Place
:
and
the
point
that
the
Spherick
Gnomon
stands
on
,
being
removed
to
the
Meridian
,
shews
the
Declination
of
the
Sun
on
the
Meridian
for
that
Day
.
3.
If
you
draw
a
Meridian
line
from
one
Pole
to
the
other
,
in
all
Places
under
that
line
,
it
is
Noon
:
in
those
Places
scituate
to
the
West
,
it
is
Morning
;
for
with
them
the
Sun
is
East
:
and
in
those
Places
scituate
to
the
East
,
it
is
Evening
;
for
with
them
the
Sun
is
West
.
4
:
Note
the
degree
of
the
Equator
where
the
enlightned
Hemisphear
is
parted
from
the
shadowed
;
for
the
number
of
degrees
of
the
Equator
intercepted
between
that
degree
and
the
Meridian
of
any
Place
,
converted
into
Hours
(
by
accounting
for
every
15.
degrees
1.
Hour
)
shews
,
if
the
Sun
be
Eastwards
of
that
Place
,
how
long
it
will
be
ere
the
Sun
Rises
,
Sets
,
or
comes
to
the
Meridian
of
that
Place
:
or
if
the
Sun
be
Westward
of
that
Place
,
how
long
it
is
since
the
Sun
Rose
,
or
Set
,
or
was
at
the
Meridian
of
that
Place
.
5.
The
Inhabitants
of
all
Places
between
the
enlightned
and
shadowed
Hemisphear
,
behold
the
Sun
in
the
Horizon
:
Those
Westwards
of
the
Meridian
Semi-Circle
drawn
through
the
middle
of
the
enlightned
Hemisphear
behold
the
Sun
Rising
:
Those
in
the
East
,
see
it
Setting
.
6.
So
many
degrees
as
the
Sun
reaches
beyond
either
the
North
or
South
Pole
,
so
many
degrees
is
the
Declination
of
the
Sun
,
either
Northwards
or
Southwards
:
and
in
all
those
Places
comprehended
in
a
Circle
described
at
the
termination
of
the
Sun-shine
,
about
that
Pole
,
it
is
alwaies
Day
,
till
the
Sun
decrease
in
Declination
:
for
the
Sun
goes
not
below
their
Horizon
:
as
you
may
see
by
turning
the
Globe
about
upon
its
Axis
:
and
a
the
opposite
Pole
at
the
same
distance
,
the
Sun-shine
not
reaching
thither
,
it
will
be
alwaies
Night
,
till
the
Sun
decrease
in
Declination
:
because
the
Sun
Rises
not
above
their
Horizon
.
7.
If
you
let
the
Globe
hang
steddy
,
you
may
see
on
the
East
side
of
the
Globe
,
in
what
Places
it
grows
Night
;
and
on
the
West
side
the
Globe
how
by
little
and
little
the
Sun
encroaches
upon
it
;
and
therefore
there
makes
it
Day
.
8.
If
you
make
of
Paper
or
Parchment
a
narrow
Girdle
,
to
begirt
the
Globe
just
in
the
Equinoctial
,
and
divide
it
into
24.
equal
parts
,
to
represent
the
24.
hours
of
Day
and
Night
,
and
mark
it
in
order
with
I
,
II
,
III
,
&c.
to
XII
.
and
then
begin
again
with
I
,
II
,
III
,
&c.
to
the
other
XII
.
you
may
by
placing
one
of
the
XII
s.
upon
the
Equinoctial
under
the
Meridian
of
your
Place
,
have
a
continual
Sun-Dyal
of
it
,
and
the
hour
of
the
Day
given
on
it
,
at
once
in
two
places
;
one
by
the
parting
the
enlightned
Hemisphear
from
the
shadowed
on
the
Eastern
side
,
the
other
by
the
parting
the
enlightned
Hemisphear
from
the
shadowed
on
the
Western
side
the
Globe
.
Much
more
might
be
said
on
this
Probleme
:
But
the
Ingenuous
Artist
may
of
himself
find
out
diversities
of
Speculations
:
therefore
I
forbear
.
PROB.
XLVI
.
To
know
by
the
Terrestrial
Globe
in
the
Zenith
of
what
Place
of
the
Earth
the
Sun
is
.
THis
may
be
performed
by
the
former
Probleme
in
the
Day
time
,
if
the
Sun
shines
:
but
not
else
.
But
to
find
it
at
all
times
,
do
thus
.
Bring
the
Place
of
your
Habitation
to
the
Meridian
,
and
the
Index
of
the
Hour-Circle
to
12
;
Then
turn
the
Globe
Eastwards
,
if
Afternoon
,
or
Westwards
,
if
Before
Noon
,
till
the
Index
of
the
Hour-Circle
pass
by
so
many
Hours
from
12.
as
your
Time
given
is
,
either
before
or
After-Noon
:
so
shall
the
Sun
be
in
the
Zenith
of
that
Place
where
the
Meridian
intersects
the
Parallel
of
the
Suns
Declination
for
that
Day
.
Example
.
May
10
at
¾
of
an
hour
past
4.
a
clock
After
Noon
▪
I
would
know
in
what
Place
of
the
Earth
the
Sun
is
in
the
Zenith
.
My
Habitation
is
London
.
Therefore
I
bring
London
to
the
Meridian
,
and
the
Index
of
the
Hour-Circle
to
12.
and
because
it
is
After
Noon
:
I
turn
the
Globe
Eastwards
,
till
the
Index
passes
through
4
hours
and
3
quarters
,
or
(
which
is
all
one
)
till
70
degrees
15
minutes
of
the
Equator
pass
through
the
Meridian
.
Then
I
find
by
Prob.
5.
the
Suns
Declination
is
20.
degrees
5.
minutes
which
I
find
upon
the
Meridian
,
and
in
that
Place
just
under
that
degree
and
minute
on
the
Globe
,
the
Sun
is
in
the
Zenith
:
which
in
this
Example
is
in
the
North
East
Cape
of
Hispaniola
.
Having
thus
found
in
what
Place
of
the
Earth
the
Sun
is
in
the
Zenith
.
Bring
that
Place
to
the
Meridian
,
and
Elevate
its
respective
Pole
according
to
its
respective
Elevation
;
so
shall
all
Places
cut
by
the
Horizon
have
the
Sun
in
their
Horizon
:
Those
to
the
Eastwards
shall
have
the
Sun
Setting
;
those
to
the
Westward
shall
have
it
Rising
in
their
Horizon
:
those
at
the
Intersection
of
the
Meridian
and
Horizon
under
the
Elevated
Pole
,
have
the
Sun
in
their
Horizon
at
lowest
,
but
Rising
;
those
at
the
Intersection
of
the
Meridian
and
Horizon
under
the
Depressed
Pole
,
have
the
Sun
in
their
Horizon
at
highest
,
but
Setting
.
Thus
in
those
Countries
that
are
above
the
Horizon
it
is
Day-light
,
and
in
those
but
18
degrees
below
the
Horizon
,
it
is
Twilight
:
But
in
those
Countries
further
below
the
Horizon
it
is
at
that
time
dark
Night
:
And
those
Countries
within
the
Parallel
of
the
same
number
of
degrees
from
the
Elevated
Pole
that
the
Suns
Declination
is
from
the
Equinoctial
,
have
the
Sun
alwaies
above
the
Horizon
,
till
the
Sun
have
less
Respective
Declination
then
the
Elevated
Pole
;
and
those
within
the
same
Parallel
of
the
Depressed
Pole
have
the
Sun
alwayes
below
their
Horizon
,
till
the
Sun
inclines
more
towards
the
Depressed
Pole
;
As
you
may
see
by
turning
about
the
Globe
;
for
in
this
position
,
that
portion
of
the
Globe
intercepted
between
the
Elevated
Pole
,
and
the
Parallel
Circle
of
20.
degrees
5.
minutes
from
the
Pole
doth
not
descend
below
the
Horizon
:
neither
doth
that
portion
of
the
Globe
intercepted
between
the
Depressed
Pole
and
the
Parallel
Circle
within
20.
degrees
5.
minutes
of
that
Pole
,
ascend
above
the
Horizon
.
PROB.
XLVII
.
To
find
in
what
different
Places
of
the
Earth
the
Sun
hath
the
same
Altitude
,
at
the
same
time
.
FInd
by
the
former
Probleme
in
what
Place
of
the
Earth
the
Sun
is
in
the
Zenith
,
and
bring
that
Place
on
the
Globe
to
the
Zenith
,
and
on
the
Meridian
[
there
]
screw
the
Quadrant
of
Altitude
,
and
turn
it
about
the
Horizon
,
describing
degrees
of
Almicantars
thereby
,
as
by
Prob.
23.
and
all
those
Countries
in
any
Almicantar
on
the
Globe
shall
have
the
Sun
Elevated
the
same
number
of
degrees
above
their
Horizon
.
Thus
those
Countries
in
the
tenth
Almicantar
shall
have
the
Sun
Elevated
10.
degrees
above
their
Horizon
;
those
in
the
20th
Almicantar
shall
have
the
Sun
Elevated
20
degrees
above
their
Horizon
;
those
in
the
30th
,
30.
degrees
&c.
So
that
you
may
see
,
when
the
Sun
is
in
the
Zenith
of
any
Place
,
All
the
Countries
or
Cities
in
any
Almicantar
have
the
Sun
in
one
heighth
at
the
same
time
above
their
Horizon
.
But
to
find
in
what
different
Places
the
Sun
hath
the
same
heighth
at
the
same
time
,
as
well
Before
or
After
Noon
,
as
at
Full
Noon
;
and
that
in
Countries
that
have
greater
Latitude
then
the
Suns
greatest
Declination
,
(
and
therefore
cannot
have
the
Sun
in
their
Zenith
,
)
requires
another
Operation
.
Therefore
,
Elevate
its
respective
Pole
according
to
your
respective
Latitude
;
and
let
the
Degree
of
the
Brazen
Meridian
which
is
in
the
Zenith
represent
your
Habitation
,
and
the
degree
of
the
Ecliptick
the
Sun
is
in
represent
the
Sun
:
Then
bring
the
Sun
to
the
Meridian
,
and
the
Index
of
the
Hour-Circle
to
12
,
and
turn
the
Globe
Eastwards
,
if
Before
Noon
,
or
Westwards
,
if
After
Noon
,
till
the
Index
point
to
the
Hour
of
the
Day
:
Then
place
the
lower
end
of
the
Quadrant
of
Altitude
to
the
East
point
of
the
Horizon
,
and
move
the
upper
end
(
by
sliding
the
Nut
over
the
Meridian
)
till
the
edge
of
the
Quadrant
touch
the
place
of
the
Sun
:
Then
see
at
what
degree
of
the
Meridian
the
upper
end
of
the
Quadrant
of
Altitude
touches
the
Meridian
and
substract
that
number
of
Degrees
from
the
Latitude
of
your
Place
,
and
count
the
number
of
remaining
degrees
on
the
Meridian
,
on
the
contrary
side
the
degree
of
the
Meridian
where
the
upper
end
of
the
Quadrant
of
Altitude
touches
the
Meridian
,
and
where
that
number
of
degrees
ends
on
the
Meridian
,
in
that
Latitude
and
your
Habitations
Longitude
,
hath
the
Sun
the
same
heighth
at
the
same
time
.
Example
.
May
10.
at
53.
minutes
past
8.
a
clock
in
the
Morning
I
would
know
in
what
Place
the
Sun
shall
have
the
same
Altitude
it
shall
have
at
London
,
London's
Latitude
found
by
Prob.
1.
is
51½
degrees
Northwards
:
And
because
the
Elevation
of
the
Pole
is
equal
to
the
Latitude
of
the
Place
(
as
was
shewed
Prob.
15.
)
Therefore
I
Elevate
the
North
Pole
51½
degrees
,
so
shall
51½
degrees
on
the
Meridian
be
in
the
Zenith
:
This
51½
degrees
on
the
Meridian
represents
London
.
The
Suns
Place
found
by
Prob.
3.
is
♉
29.
Therefore
I
bring
♉
29
to
the
Meridian
,
and
the
Hour
Index
to
12.
on
the
Hour
Circle
:
Then
I
turn
the
Globe
Eastwards
(
because
it
is
before
Noon
)
till
the
Index
point
at
8.
hours
53
minutes
on
the
Hour-Circle
,
and
place
the
lower
end
of
the
Quadrant
of
Altitude
to
the
East
point
in
the
Horizon
,
and
slide
the
upper
end
either
North
or
Southwards
on
the
Meridian
till
the
graduated
edge
cut
the
degree
of
the
Ecliptick
the
Sun
is
in
:
Then
I
examine
on
the
Meridian
what
degree
the
upper
end
of
the
Quadrant
of
Altitude
touches
;
which
in
this
example
,
I
find
is
38½
degrees
.
Therefore
I
substract
38½
from
51½
Londons
Latitude
,
and
there
remains
13.
Then
counting
on
the
Meridian
13.
degrees
backwards
,
from
the
Place
where
the
Quadrant
of
Altitude
touched
the
Meridian
,
I
come
to
25½
on
the
Meridian
,
Northwards
.
Therefore
I
say
,
In
the
North
Latitude
of
25½
degrees
,
and
in
the
Longitude
of
London
(
which
is
in
Africa
,
in
the
Kingdom
of
Numidia
)
the
Sun
May
10.
at
53.
minutes
past
8.
a
clock
in
the
Morning
hath
the
same
Altitude
above
the
Horizon
it
hath
here
at
London
.
The
Quadrant
of
Altitude
thus
applyed
to
the
East
point
of
the
Horizon
makes
right
angles
with
all
points
on
the
Meridian
,
even
as
all
the
Meridians
proceeding
from
the
Pole
,
do
with
the
Equator
:
therefore
the
Quadrant
being
applyed
both
to
the
East
point
,
and
the
Suns
Place
,
projects
a
line
to
intersect
the
Meridian
Perpendicularly
in
equal
degrees
;
from
which
intersection
the
Sun
hath
at
the
same
time
equal
Heighth
,
be
the
degrees
few
or
many
;
for
those
5.
degrees
to
the
Northwards
of
this
intersection
,
have
the
Sun
in
the
same
heighth
that
they
5
degrees
to
the
Southwards
have
it
:
and
those
10
,
20
,
30.
degrees
,
more
,
or
less
,
to
the
Northwards
,
have
the
Sun
in
the
same
heighth
that
they
have
that
are
10
,
20.
30.
degrees
more
or
less
to
the
Southwards
:
So
that
this
Prob.
may
be
performed
another
way
more
easily
,
with
your
Compasses
,
Thus
:
Having
first
rectified
the
Globe
,
and
Hour
Index
,
Turn
about
the
Globe
till
the
Hour
Index
point
to
the
Hour
of
the
Day
;
Then
pitch
one
foot
of
your
Compasses
in
the
Suns
Place
,
and
extend
the
other
to
the
degree
of
Latitude
on
the
Meridian
,
which
in
this
example
is
51½
degrees
North
;
then
keeping
the
first
foot
of
your
Compasses
on
the
degree
of
the
Sun
,
turn
about
the
other
foot
to
the
Meridian
,
and
it
will
fall
upon
25½
.
as
before
.
Blaew
commenting
upon
this
Probleme
,
takes
notice
how
grosly
they
ere
that
think
they
can
find
the
heighth
of
the
Pole
at
any
Hour
of
the
Day
,
by
the
Suns
height
:
because
they
do
not
consider
that
it
is
impossible
to
find
the
Hour
of
the
Day
,
unless
they
first
know
the
height
of
the
Pole
.
PROB.
XLVIII
.
To
find
the
length
of
the
Longest
and
Shortest
Artificial
Day
or
Night
.
THe
Artificial
Day
is
that
space
of
Time
which
the
Sun
is
above
the
Horizon
of
any
Place
:
and
the
Artificial
Night
is
that
space
of
Time
which
the
Sun
is
under
the
Horizon
of
any
Place
.
They
are
measured
in
the
Hour
Circle
,
by
Hours
and
Minutes
.
There
is
a
constant
unequallity
of
proportion
in
the
Length
of
these
Daies
and
Nights
;
which
is
caused
both
by
the
alteration
of
the
Suns
Declination
,
and
the
difference
of
the
Poles
Elevation
.
Those
that
inhabite
on
the
North
side
the
Equator
have
their
longest
Day
when
the
Sun
enters
♋
;
and
those
that
inhabite
on
the
South
side
the
Equator
,
have
their
longest
Day
when
the
Sun
enters
♑
.
But
to
know
how
long
the
longest
Day
is
in
any
North
or
South
Elevation
,
Raise
the
North
or
South
Pole
according
to
the
Elevation
of
the
Place
,
and
bring
♋
for
North
Elevation
,
or
♑
for
South
Elevation
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
Then
turn
the
Globe
about
till
♋
for
North
Elevation
,
or
♑
for
South
Elevation
,
come
to
the
West
side
the
Horizon
and
the
number
of
Hours
and
minutes
pointed
at
on
the
Hour
Circle
,
doubled
,
is
the
number
of
Hours
and
minutes
of
the
Longest
Day
.
The
length
of
the
Night
to
that
Day
is
found
by
substracting
the
length
of
the
day
from
24.
for
the
remainder
is
the
length
of
the
Night
.
The
shortest
Day
in
that
Latitude
is
the
length
of
the
shortest
Night
,
found
as
before
.
And
the
longest
Night
is
of
the
same
length
with
the
longest
Day
.
Example
.
I
would
know
the
length
of
the
longest
Day
at
London
.
Therefore
I
Elevate
the
North
Pole
51½
degrees
,
and
bring
♋
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
Then
I
turn
♋
to
the
Western
side
the
Horizon
,
and
find
the
Index
point
at
8.
hours
18.
minutes
,
which
being
doubled
makes
16.
hours
36.
minutes
,
for
the
length
of
the
longest
Day
here
at
London
.
PROB.
XLIX
.
To
find
how
much
the
Pole
is
Raised
,
or
Depressed
,
where
the
longest
Day
is
an
Hour
longer
or
shorter
then
it
is
in
your
Habitation
.
REctifie
the
Globe
to
the
Latitude
of
your
Place
;
and
make
a
prick
at
that
point
of
the
Tropick
which
is
at
the
Meridian
;
I
mean
at
the
Tropick
of
♋
,
if
your
Habitation
be
on
the
North
side
the
Equator
;
or
♑
,
if
your
Habitation
be
on
the
South
side
the
Equator
:
And
if
you
would
know
where
the
longest
Day
is
just
an
hour
longer
then
it
is
at
your
Habitation
,
turn
the
Globe
to
the
Westward
till
7½
degrees
of
the
Equato●
pass
through
the
Meridian
,
and
make
there
another
prick
on
the
Tropick
:
Then
turn
about
the
Globe
till
the
first
prick
come
to
the
Horizon
;
and
move
the
Meridian
through
the
notches
of
the
Horizon
till
the
second
prick
on
the
Tropick
come
to
the
Horizon
;
so
shall
the
arch
of
the
Meridian
contained
between
the
Elevation
of
your
Place
,
and
the
Degree
of
the
Meridian
at
the
Horizon
,
be
the
number
of
Degrees
that
the
Pole
is
Elevated
higher
then
it
is
in
your
Latitude
.
Example
.
I
would
know
in
what
Latitude
the
longest
Day
is
an
Hour
longer
then
it
is
at
London
.
Therefore
I
Rectifie
the
Globe
to
51½
deg.
and
where
the
Meridian
cuts
the
Tropick
of
♋
I
make
a
prick
;
then
I
note
what
degree
of
the
Equator
is
at
the
Meridian
,
and
from
that
degree
on
the
Equator
count
7½
degrees
to
the
Eastwards
,
and
bring
those
7½
degrees
to
the
Meridian
also
;
and
again
where
the
Meridian
cuts
the
Tropick
of
♋
I
make
another
prick
,
so
shall
7½
degrees
of
the
Tropick
be
contained
between
those
〈◊〉
pricks
.
Then
I
turn
the
Globe
about
,
till
the
first
prick
comes
to
the
Horizon
,
and
(
with
a
Quill
thrust
between
the
Meridian
and
the
Ball
)
I
fasten
the
Globe
in
this
position
:
Afterwards
I
move
the
Meridian
through
the
〈◊〉
of
the
Horizon
,
till
the
second
prick
rises
up
to
the
Horizon
,
and
then
I
find
56½
degrees
of
the
Meridian
cut
by
the
Superficies
of
the
Horizon
:
Therefore
I
say
,
In
the
Latitude
of
56½
degrees
,
the
longest
Day
is
an
Hour
longer
then
it
is
here
at
London
.
But
if
you
would
know
in
what
Latitude
the
Dayes
are
an
Hour
shorter
,
you
must
make
your
second
prick
7½
degrees
to
the
Westwards
of
the
first
,
and
after
you
have
brought
the
first
prick
to
the
Horizon
,
you
must
depress
the
Pole
till
the
second
prick
descends
to
the
Horizon
:
so
shall
the
degree
of
the
Meridian
at
the
Horizon
,
shew
in
what
Elevation
of
the
Pole
the
Daies
shall
be
an
Hour
shorter
.
By
this
Probleme
may
be
found
the
Alteration
of
Climates
:
for
(
as
was
said
in
the
Definition
of
Climates
,
Book
1.
fol.
28.
)
Climates
alter
according
to
the
half-hourly
increasing
of
the
Longest
Day
:
therefore
the
Latitude
of
56½
degrees
having
its
Daies
increased
an
whole
Hour
)
is
distant
from
the
Latitude
of
London
by
the
space
of
two
Climates
.
PROB.
L.
The
Suns
Place
given
,
to
find
what
alteration
of
Declination
be
must
have
to
make
the
Day
an
Hour
longer
,
or
shorter
:
And
in
what
number
of
Da●es
it
will
be
.
REctifie
the
Globe
to
the
Latitude
of
the
Place
,
and
b●ing
the
Suns
place
to
the
East
side
the
Horizon
,
and
note
against
what
degree
of
the
Horizon
it
is
:
then
bring
one
of
the
Colures
to
intersect
the
Horizon
in
that
degree
of
the
Horizon
,
and
at
the
point
of
Intersection
make
a
prick
in
the
Colure
;
and
observe
what
degree
of
the
Equator
is
then
at
the
Meridian
:
Then
turn
the
Globe
Westward
,
if
the
Daies
shorten
;
but
Eastwards
,
if
they
lengthen
,
till
7½
degrees
of
the
Equator
pass
through
the
Meridian
,
and
where
the
Horizon
intersects
the
same
Colure
,
make
another
prick
in
the
Colure
:
Afterwards
bring
the
Colure
to
the
Meridian
,
and
count
the
number
of
degrees
between
the
two
pricks
,
for
so
many
degrees
must
the
Suns
Declination
alter
to
lengthen
or
shorten
the
Day
an
Hour
.
Example
.
The
Suns
Place
is
♉
10.
I
would
know
how
much
he
must
alter
his
Declination
before
the
Day
is
an
Hour
longer
here
at
London
.
Therefore
I
rectifie
the
Globe
to
the
Latitude
of
London
,
and
bring
♉
10.
to
the
East
side
the
Horizon
,
and
find
it
against
24½
degrees
from
the
East
point
:
therefore
I
bring
one
of
the
Colures
to
this
24½
degrees
,
and
close
by
the
edge
of
the
Horizon
I
make
a
prick
with
black
lead
,
in
the
Colure
:
then
keeping
the
Globe
in
this
position
,
I
look
what
degree
of
the
Equator
is
then
at
the
Meridian
,
and
find
250¼
,
and
because
the
Daies
lengthen
,
I
turn
the
Globe
Eastwards
,
till
7½
degrees
from
the
foresaid
250¼
pass
through
the
Meridian
:
then
keeping
the
Globe
in
this
position
I
make
another
prick
in
the
Colure
,
and
bringing
this
Colure
to
the
Meridian
,
I
find
a
little
more
then
5
degrees
of
the
Meridian
contained
between
the
two
pricks
:
therefore
I
say
,
when
the
Sun
is
in
♉
10.
degrees
,
he
must
alter
his
Declination
a
little
more
then
5
degrees
,
to
make
the
Day
an
Hour
longer
.
Now
to
know
in
what
number
of
Daies
he
shall
alter
this
Declination
,
you
must
find
the
Declination
of
the
two
pricks
on
the
Colure
as
you
found
the
Suns
Declination
by
Prob.
5.
and
the
Arch
of
the
Ecliptick
that
passes
through
the
Meridian
while
the
Globe
is
turned
from
the
first
pricks
Declination
to
the
second
pricks
Declination
,
is
the
number
of
Ecliptical
degrees
that
the
Sun
is
to
pass
while
he
alters
this
Declination
:
and
the
degree
of
the
Ecliptick
then
at
the
Meridian
is
(
with
respect
had
to
the
Quarter
of
the
Year
)
the
place
the
Sun
shall
have
when
its
Declination
shall
be
altered
so
much
as
to
make
the
Day
an
Hour
longer
Thushaving
the
Suns
first
place
given
,
and
its
second
place
found
▪
you
may
by
finding
those
two
places
on
the
Plain
of
the
Horizon
,
also
find
the
number
of
Daies
comprehended
between
them
,
as
you
are
taught
by
the
fourth
Probleme
.
This
Probleme
thus
wrought
for
different
Times
of
the
Year
,
will
shew
the
falacy
of
that
Vulgar
Rule
which
makes
the
Day
to
be
lengthned
or
shortned
an
Hour
in
every
Fifteen
Daies
:
when
as
the
lengthning
or
shortning
of
Daies
keeps
no
such
equality
of
proportion
:
for
when
the
Sun
is
neer
the
Equinoctial
points
the
Daies
lengthen
or
shorten
very
fast
:
but
when
he
is
neer
the
Tropical
points
,
very
slowly
.
PROB.
LI.
Of
the
Difference
of
Civil
and
Natural
Daies
,
commonly
called
the
Equation
of
Civil
Daies
.
And
how
it
may
be
found
by
the
Globe
.
THe
Civil
Day
is
that
space
of
Time
containing
just
24.
Hours
,
reckoned
from
12
a
clock
on
one
Day
to
12
a
clock
the
next
Day
;
in
which
space
of
Time
the
Equinoctial
makes
upon
the
Poles
of
the
World
a
Diurnal
Revolution
.
The
Natural
Day
is
that
space
of
Time
wherein
the
Sun
moveth
from
the
Meridian
of
any
Place
to
the
same
Meridian
again
.
These
Daies
are
at
one
time
of
the
Year
longer
then
at
another
;
and
at
all
Times
longer
then
the
Civil
Daies
.
There
is
but
smal
discrepancy
between
them
,
yet
some
there
is
,
made
by
a
two-fold
Cause
.
For
first
,
The
Suns
Apparent
motion
is
different
from
his
true
motion
;
He
being
much
slower
in
his
Apogeum
then
he
is
in
his
Perigeum
:
For
when
the
Sun
is
in
his
Apogeum
he
scarce
moves
58
minutes
from
West
to
East
in
a
Civil
Day
,
but
when
he
is
in
his
Perigeum
he
moves
above
61
minutes
in
a
Civil
Day
:
and
therefore
increases
his
Right
Ascension
more
in
equal
Time
.
The
second
Cause
is
the
difference
of
Right
Ascensions
answerable
to
equal
parts
of
the
Ecliptick
:
for
about
♋
and
♑
the
differences
of
Right
Ascensions
are
far
greater
then
about
♈
and
♎
:
for
about
♈
and
♎
the
Right
Ascension
of
10.
degrees
is
but
9.
degrees
11.
minutes
;
but
about
♋
and
♑
the
Right
Ascension
of
10
degrees
will
be
found
to
be
10.
degrees
53.
minutes
,
as
by
the
Globe
will
appear
.
But
because
of
the
smalness
of
the
Globes
graduation
▪
you
cannot
actually
distinguish
to
parts
neer
enough
for
the
solution
of
this
Probleme
,
if
you
should
enquire
the
difference
in
length
of
two
single
Daies
;
it
will
be
requisite
to
take
some
number
of
Daies
together
;
Suppose
20.
Therefore
find
by
Prob.
3.
the
Places
of
the
Sun
for
the
beginning
and
ending
of
those
Daies
you
would
compare
;
and
find
the
Right
Ascensions
answerable
to
each
place
in
the
Ecliptick
;
and
also
the
differences
of
Right
Ascensions
answerable
to
the
Suns
motion
in
each
number
of
Daies
:
Then
compare
the
differences
of
Right
Ascensions
together
;
and
by
substracting
the
lesser
from
the
greater
,
you
will
have
the
number
of
degrees
and
minutes
of
the
Equator
that
have
passed
through
the
Meridian
more
in
one
number
of
Daies
then
in
the
other
number
of
Daies
:
which
degrees
of
the
Equator
converted
into
Time
,
is
the
number
of
minutes
that
the
one
number
of
Daies
is
longer
then
the
other
number
of
Daies
.
Example
.
I
would
know
what
difference
of
Time
there
is
in
the
length
of
the
first
20.
Daies
of
December
,
and
the
first
20
,
Daies
of
March
.
I
find
by
Prob.
3.
the
Suns
place
December
1
,
is
〈◊〉
19.
45.
at
the
end
of
20
Daies
.
viz.
on
the
21
Day
his
place
is
〈◊〉
10.
11.
The
Suns
place
March
1.
is
♓
21.
16.
at
the
20.
Daies
end
,
viz.
March
21
,
his
place
is
♈
11.
3.
I
find
by
Prob.
26.
the
Right
Ascension
answerable
to
|
♐
19.
45
|
is
|
258.
10.
|
♑
10.
11
|
280.
25.
|
♓
21.
16
|
352.
00.
|
♈
11.
3
|
9.
40.
|
and
the
difference
of
Right
Ascensions
contained
between
the
first
Day
in
each
Moneth
,
and
the
21
of
the
same
Moneth
,
by
substracting
the
lesser
from
the
greater
is
for
258.
10.
|
And
for
|
352.
00.
|
280.
25.
|
9.
40.
|
22.
15
|
17.
40.
|
But
note
,
because
the
Vernal
Colure
,
where
the
degrees
of
Right
Ascension
begin
and
end
their
account
,
is
intercepted
is
the
Arch
of
the
Suns
motion
from
the
first
to
the
21.
of
March
,
therefore
instead
of
substracting
the
lesser
number
of
degrees
of
Right
Ascension
from
the
greater
,
viz.
9.
40
from
35.
2.
I
do
for
finding
the
difference
of
the
Right
Ascensional
arch
of
the
Suns
motion
in
those
20
Daies
,
sustract
the
foresaid
352
degrees
from
360
,
and
the
remains
is
8.
which
is
the
difference
of
Right
Ascension
from
♓
21
,
16.
to
the
Equinoctial
Colure
:
to
which
8
adding
9
degrees
40
minutes
,
the
Right
Ascension
from
the
Equinoctial
Colure
.
to
♈
11.
3.
it
makes
17
degrees
40.
minutes
for
the
difference
of
Right
Ascensions
between
♓
21
,
16.
and
♈
11.
3
Then
I
find
the
difference
of
this
Difference
of
Right
Ascension
,
by
substracting
the
less
from
the
greater
,
viz.
17.
40.
from
22.
15.
and
the
remains
is
4.
degrees
35.
minutes
,
for
the
number
of
degrees
and
minutes
of
the
Equator
that
pass
through
the
Meridian
in
the
first
20
Daies
in
the
Moneth
of
December
more
then
in
the
first
20
Daies
of
the
Moneth
of
March
:
which
4.
degrees
35.
minutes
converted
into
Time
,
gives
19.
minutes
,
that
is
,
a
quarter
of
an
Hour
and
4
minutes
that
the
first
20
Daies
of
December
aforesaid
,
are
longer
then
the
first
20
Daies
of
March.
PROB.
LII
.
How
to
find
the
Hour
of
the
Night
,
when
the
Moon
shines
on
a
Sun
Dyal
,
by
help
of
the
Globe
.
REctifie
the
Globe
,
and
find
by
Prob.
54.
or
an
Ephemeris
,
the
Moons
place
at
Noon
:
Bring
it
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
and
turn
about
the
Globe
till
the
Index
of
the
Hour
Circle
points
to
the
same
Hour
the
shade
of
the
Moon
falls
on
,
on
the
Sun
Dyal
.
Then
by
Prob.
3.
find
the
Suns
place
at
Noon
,
and
see
how
many
degrees
of
Right
Ascension
are
contained
between
the
Suns
place
and
the
degree
of
the
Equator
at
the
Meridian
,
when
the
Index
of
the
Hour
Circle
is
brought
to
the
Hour
the
Moon
shines
on
in
the
Sun
Dyal
;
for
those
number
of
degrees
converted
into
Time
,
shall
be
the
Time
from
Noon
,
or
the
Hour
of
the
Night
.
Only
note
,
Respect
must
be
had
to
the
motion
of
the
Moon
from
West
to
East
,
for
so
swift
is
her
mean
motion
,
that
it
is
accounted
to
be
above
12.
degrees
in
24.
Hours
;
that
is
6
degrees
in
12
Hours
,
3
degrees
in
6
Hours
,
&c.
and
this
also
converted
into
Time
,
as
aforesaid
,
you
must
add
proportionably
to
the
Time
found
from
Noon
;
and
the
sum
shall
give
you
the
true
Hour
of
the
Night
.
Example
.
Here
at
London
,
I
desired
to
know
the
Hour
of
the
Night
January
6.
this
present
Year
1658.
The
Moons
place
found
by
an
Ephemeris
,
or
for
want
of
an
Ephemeris
,
by
Prob.
54.
is
in
♊
21.
degree
22
,
minutes
;
Therefore
I
rectified
the
Globe
to
Londons
Latitude
,
and
brought
♊
21.
22.
minutes
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
then
by
Prob.
3.
I
found
the
Suns
place
in
♑
26.
degrees
46.
minutes
,
and
by
Prob.
26.
I
found
his
Right
Ascension
to
be
300
degrees
;
Then
I
turned
about
the
Globe
,
till
the
Index
of
the
Hour
Circle
pointed
at
10
Hours
,
and
at
the
degree
of
the
Equator
at
the
Meridian
I
made
a
prick
;
then
I
counted
the
number
of
degrees
of
the
Equater
contained
between
the
foresaid
300
deg.
and
this
prick
and
found
them
111¼
degrees
which
converted
into
Time
,
by
allowing
15
degrees
for
an
Hour
,
gives
7
hours
,
25
minutes
,
Time
from
Noon
:
which
if
the
Moons
motion
were
not
to
be
considered
,
should
be
the
immediate
Hour
of
the
Night
:
But
by
the
Rule
aforesaid
,
the
Moons
motion
from
West
to
East
,
in
7
hours
25
minutes
is
3
degrees
42
minutes
,
and
this
3
degrees
42
minutes
being
converted
into
Time
,
is
14
minutes
more
,
which
being
added
to
7
hours
25
minutes
:
make
7
hours
39
minutes
,
for
the
true
Hour
of
the
Night
.
PROB.
LIII
.
To
find
the
Dominical
Letter
,
the
Prime
,
Epact
,
Easter
Day
,
and
the
rest
of
the
Moveable
Feasts
,
for
ever
.
THough
these
Problemes
cannot
be
performed
by
the
Globe
,
because
of
the
several
changes
,
and
irregular
accounts
that
their
Rules
are
framed
upon
,
yet
because
they
are
of
frequent
and
Vulgar
use
,
and
for
that
the
solution
of
many
other
Questions
will
have
dependency
on
the
knowledge
these
;
Therefore
I
have
thought
fit
here
to
inserte
this
Table
of
Mr
Palmers
,
by
which
you
may
find
them
All.
I
shall
not
insist
upon
the
Reasons
of
the
several
changes
of
Letters
,
and
Numbers
,
Himself
having
already
very
learnedly
handled
that
subject
,
in
his
Book
of
the
Catholick
Planisphear
,
Book
1.
Chapter
11.
(
to
which
I
refer
you
)
Neither
shall
I
need
to
give
you
any
other
Instructions
for
finding
what
is
here
proposed
,
then
what
himself
hath
given
in
his
fourth
Book
,
Chapter
66
,
and
part
of
67.
Therefore
take
it
as
he
there
delivers
it
.
An
Example
,
shall
serve
here
instead
of
a
Rule
.
For
the
Year
1657.
I
would
know
all
these
:
wherefore
I
seek
the
Year
1657.
in
the
Table
of
the
Suns
Cycle
,
and
over
against
it
,
I
find
14.
for
the
Year
of
the
Cycle
of
the
Sun
,
and
D
for
the
Dominical
Letter
.
And
note
here
,
that
every
Leap-year
hath
2
Dominical
Letters
(
as
1660
,
hath
A
G
)
and
the
first
(
viz.
A
)
serveth
that
Year
till
February
25
,
and
the
second
(
G
)
for
the
rest
of
the
Year
.
And
note
that
these
Letters
go
alwayes
backwards
when
you
count
forwards
(
as
B
A
,
then
G
F
,
&c.
not
F
G
,
and
,
then
A
B
)
as
you
may
see
by
the
Table
.
To
find
the
Age
of
the
Moon
.
Remember
first
that
the
Epact
begins
with
March
,
which
must
be
here
accounted
the
first
Moneth
:
Then
if
you
add
to
the
Epact
the
number
of
the
Moneth
current
,
and
the
number
of
the
day
of
the
Moneth
current
,
the
sum
or
the
excess
above
30
,
is
the
Moons
age
.
Example
.
January
20.
1656.
According
to
the
accompt
of
the
Church
of
England
,
(
who
begin
the
Year
with
March
25.
which
was
the
Equinoctial
day
about
Christ
time
)
the
Epact
is
14.
January
is
the
11th
Moneth
,
and
the
20th
day
is
proposed
;
now
add
14.
11.
and
20.
together
,
they
make
45.
out
of
which
I
take
30.
and
there
remains
15
,
the
Moons
age
.
PROB.
LIV.
The
Age
of
the
Moon
given
,
to
find
her
place
in
the
Ecliptick
according
to
her
mean
motion
.
THis
Probleme
may
be
performed
exact
enough
for
Common
uses
by
the
Globe
,
but
in
regard
it
only
shews
the
Moons
place
in
the
Ecliptick
according
to
her
meat
motion
,
it
will
often
fail
you
some
few
degrees
of
her
true
Place
.
The
work
is
thus
,
First
set
figures
to
every
twelth
degree
of
the
Equinoctial
,
accounted
from
the
Equinoctial
Colure
,
marking
them
with
1
,
2
,
3
,
4.
&c.
to
30
which
will
end
where
you
began
viz.
at
the
Equinoctial
Colure
again
:
so
shall
the
Equinoctial
be
divided
into
30
equal
parts
,
representing
the
30
Dayes
of
the
Moons
Age
These
figures
(
to
distinguish
them
from
the
degrees
of
the
Equator
)
were
best
be
writ
with
Red
Ink.
When
you
would
enquire
the
Moons
Place
,
Elevate
the
North
Pole
90
degrees
,
that
is
,
in
the
Zenith
,
so
shall
the
Equator
ly
in
the
Horizon
:
Then
bring
the
Equinoctial
Colure
against
the
Day
of
the
Moneth
in
the
Horizon
,
so
shall
the
Moons
Age
written
in
Red
figures
,
stand
against
the
Signe
and
degree
in
the
Horizon
that
the
Moon
is
in
at
that
Time
.
Example
.
September
28.
1658.
I
would
know
the
Moons
place
in
the
Ecliptick
,
she
being
then
12
Daies
old
.
Therefore
I
Elevate
the
North
Pole
90
degrees
above
the
Horizon
,
and
turn
the
Globe
about
till
the
Equinoctial
Colure
come
to
September
28.
in
the
Circle
of
Daies
on
the
Horizon
;
then
looking
against
what
Signe
and
degree
of
the
Ecliptick
Circle
in
the
Horizon
the
12th
division
in
Red
figures
stands
,
I
find
♓
9.
which
is
the
Signe
and
degree
the
Moon
is
in
,
according
to
her
mean
Motion
.
This
Probleme
may
be
applyed
to
many
Uses
:
for
,
having
the
Moons
Place
you
may
find
the
Time
of
her
Rising
,
Southing
,
Setting
,
and
Shining
&c.
by
working
with
her
,
as
you
were
taught
to
work
with
the
Sun
,
in
several
fore-going
Problemes
,
proper
to
each
purpose
.
PROB.
LV.
Having
the
Longitude
and
Latitude
,
or
Right
Ascension
and
Declination
of
any
Planet
,
or
Comet
,
to
place
it
on
the
Globe
,
to
correspond
with
its
place
in
Heaven
.
PLanets
and
Comets
cannot
be
placed
on
the
Globe
so
as
their
places
will
long
retain
correspondence
with
their
places
in
Heaven
;
Because
as
was
said
Chap.
44.
they
have
a
continual
motion
from
West
to
East
upon
the
Poles
of
the
Ecliptick
:
yet
never-the-less
you
may
by
having
their
Longitude
and
Latitude
,
or
Right
Ascension
and
Declination
,
for
any
set
Time
,
place
a
Mark
for
them
on
the
Globe
,
either
with
Ink
if
your
Globe
be
Varnisht
,
for
then
you
may
with
a
wet
finger
wipe
it
off
again
;
or
with
Black-lead
,
if
it
be
not
Varnisht
,
and
then
you
may
rub
it
out
again
with
a
little
White
Bread
:
which
Mark
for
that
Time
,
will
as
effectually
serve
you
to
work
by
,
as
any
of
the
Fixed
Stars
placed
on
the
Globe
will
do
.
Therefore
if
the
Longitude
and
Latitude
of
any
Planet
,
or
Comet
,
be
given
;
Do
thus
,
Elevate
the
North
Pole
,
if
the
Latitude
given
be
North
;
but
if
the
Latitude
given
be
South
,
Elevate
the
South
Pole
66
½
degrees
;
and
place
the
Pole
of
the
Ecliptick
in
the
Zenith
,
and
over
it
screw
the
Quadrant
of
Altitude
:
so
shall
the
Ecliptickly
in
the
Horizon
;
and
the
Quadrant
of
Altitude
being
turned
about
the
Horizon
shall
pass
through
all
the
Degrees
of
Longitude
:
Then
find
the
point
of
given
Longitude
in
the
Ecliptick
,
and
bring
it
to
the
Quadrant
of
Altitude
,
and
hold
it
there
:
Then
count
upwards
on
the
Quadrant
of
Altitude
the
number
of
degrees
and
minutes
of
given
Latitude
,
and
at
the
point
where
the
number
ends
,
close
to
the
Quadrant
of
Altitude
,
make
a
smal
Prick
,
and
that
Prick
shall
represent
the
Planet
or
Comet
you
were
to
place
on
the
Globe
.
If
it
be
the
Right
Ascension
and
Declination
of
a
Planet
or
Comet
that
is
given
;
you
must
find
the
degree
and
minute
of
Right
Ascension
on
the
Equinoctial
,
and
bring
it
to
the
Meridian
,
and
keep
the
Globe
there
steddy
;
then
find
the
degree
and
minute
of
Declination
on
the
Meridian
,
and
under
that
degree
and
minute
on
the
Globe
make
a
Prick
,
and
that
Prick
shall
represent
the
Planet
,
or
Comet
,
as
aforesaid
,
If
it
be
♄
or
♃
that
this
Prick
is
to
represent
,
it
may
stand
on
the
Globe
sometimes
a
Week
or
a
Fortnight
,
without
much
difference
from
the
Planets
place
in
Heaven
.
But
if
the
Prick
were
to
represent
the
other
Planets
,
you
must
(
in
regard
of
their
swift
motion
)
alter
it
very
often
,
especially
for
the
Moon
;
for
so
swift
is
her
motion
,
that
in
every
two
Hours
she
alters
about
a
degree
in
Longitude
.
Having
thus
placed
this
Mark
on
the
Globe
,
you
may
find
out
the
Time
of
its
several
Positions
,
and
Aspects
,
if
you
work
by
it
as
you
are
directed
to
work
by
the
Sun
,
in
the
several
respective
Problemes
throughout
this
Book
.
The
End
of
the
Second
Book
.
The
Fifth
BOOK
,
Shewing
the
Practical
Use
of
the
GLOBES
:
Applying
them
t●
the
Solution
of
Gnomonical
Problems
PRAEFACE
DYals
are
of
two
sorts
,
Pendent
,
and
Fixed
.
Pende●
are
such
as
are
hung
by
the
hand
,
and
turned
towards
the
Sun
;
that
by
its
Beams
darting
throug●
smal
Pin-holes
made
for
that
purpose
,
the
hour
of
the
Da●
may
be
found
.
These
are
of
two
sorts
,
Vniversal
,
and
P●●ticular
.
Vniversal
Dyals
are
those
commonly
called
Equi●oc●●●
or
Ring-Dyals
:
They
are
used
by
Sea-men
and
Tr●vellers
,
that
often
shift
Latitudes
.
Particular
are
such
as
are
made
and
only
serve
for
Particular
Latitudes
.
Of
these
sorts
are
the
several
Dya●●
discribed
on
Quadrants
,
Cilinders
,
&c.
Fixed
Dya●s
shall
be
the
matter
of
this
discourse
;
and
they
are
such
as
are
made
upon
fixed
Planes
,
and
shew
the
Hour
of
the
Day
by
a
Stile
or
Gnomon
made
Parallel
to
the
Axi●
of
the
World
.
Of
the
several
Kinds
of
Dyal
Plains
:
and
how
you
may
know
them
.
A
Plain
in
Dyalling
is
that
flat
whereon
a
Dyal
is
discribed
.
There
is
some
disagreement
among
Older
and
Later
Authors
in
the
naming
of
Plains
:
for
some
name
them
according
to
the
Great
Circle
in
Heaven
they
ly
in
:
and
others
according
to
the
scituation
of
the
Poles
of
the
Plains
.
Thus
they
which
name
them
according
to
the
Great
Circle
in
Heaven
their
Plains
ly
in
,
call
that
an
Horizontal
Plain
,
which
others
call
a
Vertical
Plain
;
those
Vertical
,
which
others
will
call
Horizontal
;
and
those
Polar
,
which
others
call
Equinoctial
.
However
they
be
called
it
matters
not
,
so
you
can
but
distinguish
their
kinds
,
which
with
a
little
consideration
you
may
easily
learn
to
do
:
For
remembring
but
upon
what
grounds
either
the
Order
or
Later
Authors
gave
the
Plains
their
Names
,
upon
the
same
grounds
you
may
also
learn
to
know
them
.
I
confess
both
waies
admit
of
some
just
exception
against
for
in
the
Older
Rule
a
Plain
about
the
Pole
,
is
called
an
Equinoctial
Plain
;
when
as
to
a
sudden
apprehension
it
would
sound
more
significant
to
call
it
a
Polar
Plain
,
as
Later
Authors
do
:
Again
,
Later
Authors
call
an
Horizontall
Plain
a
Vertical
Plain
;
when
as
it
sounds
more
significant
to
call
it
an
Horizontal
Plain
,
as
Older
Authors
do
because
it
lie
flat
upon
the
Horizon
:
But
I
shall
give
you
the
names
according
to
both
Rules
,
and
leave
you
to
your
liberty
to
accept
of
which
you
please
.
First
therefore
,
you
have
an
Equinoctial
Plain
otherwise
called
a
Polar
Plain
.
This
Plain
hath
two
Faces
,
upper
,
and
under
:
These
two
Faces
ly
in
the
Plain
of
the
Equinoctial
:
the
upper
Face
beholding
the
Elevated
Pole
,
the
under
Face
the
depressed
Pole
.
2.
An
Horizontal
Plain
,
otherwise
called
a
Vertical
Plain
:
it
lies
in
the
Plain
of
the
Horizon
,
directly
beholding
the
Zenith
.
Erect
Plains
,
otherwise
called
Horizontal
Plains
are
the
sides
of
Walls
,
and
these
are
of
seven
sorts
,
viz
1.
Erect
Direct
Vertical
,
North
or
South
,
2.
Erect
Direct
,
East
or
West
.
3.
Erect
Vertical
Declining
.
4.
Erect
Inclining
Direct
.
5.
Erect
Inclining
Declining
.
6.
Erect
Reclining
Direct
.
7.
Erect
Reclining
Declining
.
3.
Erect
Vertical
,
North
or
South
Direct
,
otherwise
called
Direct
North
or
South
Horizontals
,
behold
the
North
or
South
Directly
,
and
ly
in
the
East
or
West
Azimuth
.
4.
Erect
Direct
East
or
West
,
otherwise
called
Direct
East
or
West
Equinoctials
,
behold
the
East
or
West
Directly
,
and
lies
in
the
Plain
of
the
Meridian
,
having
its
Poles
in
the
Equinoctial
.
5.
Erect
Vertical
Declining
Plains
,
otherwise
called
Declining
Horizontals
,
do
not
behold
the
North
or
South
Directly
,
but
swerves
from
them
so
much
as
the
Azimuth
Parallel
to
their
Plains
swerves
or
Declines
from
them
.
6.
Erect
Inclining
Direct
Plains
,
have
the
upper
side
of
their
Plains
Inclining
or
coming
towards
you
,
and
their
Plains
do
exactly
behold
either
the
East
,
West
,
North
,
or
South
.
7.
Erect
Reclining
Direct
Plains
,
have
the
upper
side
of
their
Plains
Reclining
or
falling
from
you
,
and
their
Plains
exactly
beholding
either
the
East
,
West
,
North
,
or
South
.
8.
E●●ct
Reclining
Declining
,
or
Erect
Inclining
Declining
Plains
are
those
Plains
which
are
either
Inclining
or
Reclining
,
but
〈◊〉
behold
the
East
,
West
,
North
or
South
,
Directly
but
〈◊〉
or
Decline
more
or
less
from
them
.
9.
Polar
Plains
are
Parallel
to
the
Axis
of
the
World
,
and
to
the
M●ridians
that
cuts
the
East
and
West
,
or
North
and
South
,
points
of
the
Horizon
.
All
these
kinds
of
Plains
have
two
Faces
;
the
one
beholding
the
North
Pole
with
the
same
respect
that
the
other
beholds
the
South
Pole
;
except
the
Equinoctial
Plain
,
which
,
because
neither
Pole
is
Elevated
,
hath
but
one
Face
:
yet
that
one
contains
as
many
Hour
lines
as
two
other
Faces
.
These
two
Faces
or
Plains
will
receive
just
24.
hour
lines
,
fo●
the
24
Hour-lines
of
Day
and
Night
:
for
so
much
as
the
one
side
or
Face
wanteth
or
exceedeth
12.
the
other
side
shall
either
exceed
or
want
of
12.
Every
Dyal
Plain
is
Parallel
to
the
Horizon
of
some
Country
or
other
in
the
World
:
therefore
a
Dyal
made
for
any
Horizon
in
the
World
may
be
set
to
such
a
Position
that
it
will
shew
you
the
Hour
of
the
Day
in
your
own
Habitation
:
At
least
for
so
long
as
the
Sun
continues
upon
that
Plan●
.
All
Plains
may
be
aptly
demonstrated
by
the
Globe
,
by
setting
it
correspondent
to
all
the
Circles
in
Heaven
,
as
by
Prob.
2.
of
the
second
B
ok
:
for
if
you
imagine
the
Globe
in
that
Position
were
prest
flat
into
the
Plain
of
any
Circle
,
that
Flat
shall
represent
a
Dyal
plain
,
which
shall
be
called
after
the
name
of
that
Circle
it
is
prest
into
.
Thus
if
the
Quadrant
of
Altitude
be
applyed
to
any
degree
of
Azimuth
,
and
you
imagine
the
Globe
were
prest
flat
to
the
edge
of
the
Quadrant
of
Altitude
,
so
much
as
that
Azimuth
Declines
from
the
East
,
West
,
North
,
or
South
,
in
the
Horizon
,
so
much
shall
that
flat
on
the
Globe
be
said
to
Decline
either
from
the
East
,
West
,
North
,
or
South
.
Or
if
you
imagine
the
Globe
were
prest
flat
down
even
with
the
Plain
of
the
Horizon
,
that
flat
shall
represent
an
Horizontal
Plain
;
because
as
was
said
before
,
the
Plain
lies
in
that
Circle
cal'd
the
Horizon
.
The
Style
or
Gnomon
is
that
straight
wyre
that
casts
the
shadow
upon
the
Hour
of
the
Day
:
it
is
alwaies
placed
Parallel
to
the
Axis
of
the
World
.
There
are
several
waies
to
find
the
scituation
of
all
Plains
;
but
the
readiest
and
speediest
is
by
a
Clinatory
.
The
Clinatory
is
made
of
a
square
board
,
as
A
B
C
D
,
of
a
good
thickness
,
and
the
larger
the
better
;
between
two
of
the
sides
is
discribed
on
the
Center
A
a
Quadrant
as
E
F
divided
into
90
equal
parts
or
degrees
,
which
are
figured
with
10
,
20
,
30
,
to
90
;
and
then
back
again
with
the
Complements
of
the
same
numbers
to
90
:
between
the
Limb
and
the
two
Semidiameters
is
made
a
Round
Box
,
into
which
a
Magnetical
Needle
is
fitted
;
and
a
Card
of
the
Sea
Compass
,
divided
into
4
Nineties
,
beginning
their
numbers
at
the
East
,
West
,
North
,
and
South
points
of
the
Compass
,
from
which
points
the
opposite
sides
of
the
Clinatory
receives
their
Names
of
East
,
West
,
North
,
or
South
.
Upon
the
Center
A
whereon
the
Quadrant
was
discribed
is
fastned
a
Plumb-line
,
having
a
Plumbet
of
Lead
or
Brass
fastned
to
the
end
of
it
,
which
Plumb-line
is
of
such
length
that
the
Plumbet
may
fall
just
into
the
Grove
G
H
below
the
Quadrant
,
which
is
for
that
purpose
made
of
such
a
depth
that
the
Plumbet
may
ride
freely
within
it
,
without
stopping
at
the
sides
of
it
.
See
the
Figure
annexed
.
But
admit
there
be
Variation
,
Having
by
Prob.
19.
of
the
third
Book
found
the
number
of
degrees
of
this
Variation
towards
the
East
,
or
West
,
count
the
same
number
of
degrees
from
the
North
point
in
the
Card
either
to
the
Eastwards
or
Westwards
,
and
note
the
degree
in
the
Card
terminating
at
that
number
,
for
that
degree
shall
be
the
North
point
;
and
its
opposite
degree
the
South
point
:
90.
degrees
from
it
either
way
shall
be
the
East
and
West
points
.
Therefore
,
whereas
before
you
were
directed
to
turn
the
Clinatory
till
the
North
point
of
the
Needle
point
to
the
Flower-de-luce
on
the
●aid
you
m●st
now
turn
(
or
move
)
the
Clinatory
till
the
North
point
of
the
Needle
●arg
just
over
the
degree
of
Variation
thus
sound
;
and
then
a
line
drawn
as
aforesaid
,
by
the
side
of
the
Clinatory
Paral●el
to
the
Needle
shall
be
a
North
and
South
line
or
(
to
speak
more
properly
▪
a
Meridional
line
.
You
may
fi●d
a
M●ridian
li●e
several
other
waies
;
as
first
;
If
the
Sun
shine
just
at
Noon
,
hold
up
a
Plumb-line
so
as
the
shadow
of
it
may
fall
upon
your
Plain
;
and
that
shadow
shall
be
a
Meridian
li●e
.
Secondly
,
on
the
backside
the
Clinatory
discribe
a
Circle
,
and
draw
a
line
through
the
Center
to
both
sides
the
Circumference
;
cross
this
line
with
an
other
line
at
R●ght
Angles
in
the
Center
,
so
shall
the
Circle
be
divided
into
four
equal
parts
.
These
four
parts
you
must
ma●k
with
East
,
West
,
North
,
South
and
divide
each
of
them
into
90.
degrees
.
In
the
Center
of
this
Plain
erect
a
straight
wyer
prependicularly
:
when
you
would
find
a
Meridian
line
examine
by
the
tenth
Prob.
of
the
second
Book
the
Amplitude
of
the
Suns
Rising
or
Setting
from
the
East
or
West
points
,
and
waiting
the
just
Rising
or
Setting
that
Day
,
turn
the
Instrument
about
till
the
shadow
of
the
wyer
falls
upon
the
same
degree
from
the
East
or
West
the
Amplitude
is
of
,
for
then
the
North
and
South
line
in
the
Instrument
will
be
the
same
with
the
North
and
South
line
in
Heaven
.
Thirdly
by
the
Suns
Azimuth
:
Find
the
Azimuth
of
the
Sun
by
Prob.
22.
of
the
second
Book
:
and
at
the
same
instant
turn
the
Instrument
till
the
shadow
of
the
wyer
fall
upon
the
degree
on
the
Instrument
opposite
to
the
degree
of
the
Suns
Azimuth
▪
so
shall
the
Meridional
line
of
the
Instrument
agree
with
the
Meridional
line
in
Heaven
.
You
may
the
same
way
work
by
the
Azimuth
of
any
Star
.
Only
,
whereas
the
shadow
of
the
wyer
should
fall
upon
the
opposite
degree
aforesaid
:
Now
you
must
place
a
Sight
or
Perpendicular
upon
that
opposite
degree
,
and
turn
the
Instrument
about
till
the
wyer
at
the
Center
,
the
Sight
in
the
opposite
degree
of
the
Stars
Azimuth
,
and
the
Star
in
Heaven
,
come
into
one
straight
line
,
so
shall
the
Meridian
line
of
the
Instrument
agree
with
the
Meridional
line
in
Heaven
.
Fourthly
It
may
be
found
by
any
Star
observed
in
the
Meridian
,
if
two
Perpendiculars
be
erected
in
the
Meridian
line
of
your
Instrument
;
for
then
by
turning
the
Instrument
till
the
two
Perpendiculars
and
the
Star
come
into
a
straight
line
,
the
Meridian
line
of
your
Instrument
will
be
the
same
with
the
Meridian
line
in
Heaven
.
See
more
waies
in
Mr.
Palmer
on
the
Planisphear
Book
4.
Chap.
9
:
If
your
Plain
either
Recline
or
Incline
,
apply
one
of
the
sides
of
your
Clinatory
Parallel
to
one
of
the
Semi-diameters
of
the
Quadrant
to
the
Plain
,
in
such
sort
that
the
Plumb-line
hanging
at
liberty
may
fall
upon
the
Circumference
of
the
Quadrant
,
for
then
the
number
of
degrees
of
the
Quadrant
comprehended
between
the
side
of
the
Quadrant
Parallel
to
the
Plain
,
and
the
Plumb-line
shall
be
the
number
of
degrees
of
Reclination
,
if
th●
Center
of
the
Quadrant
points
upwards
,
or
Inclination
if
th●
Center
points
downwards
.
If
your
Reclining
or
Inclining
Plain
Decline
,
draw
upon
it
a
line
Parallel
to
the
Horizon
,
which
you
may
do
by
applying
the
back-side
of
the
Clinatory
,
and
raising
or
depressing
the
Center
of
the
Quadrant
till
the
Plumb-line
hang
just
upon
one
of
the
Semi-diameters
,
for
then
you
may
by
the
upper
side
of
the
Clinatory
draw
an
Horizontal
line
if
the
Plain
Incline
,
or
by
the
under
side
if
it
Recline
.
If
it
neither
Incline
or
Recline
,
you
may
draw●
an
Horizontal
line
both
by
the
upper
and
under
sides
of
the
Clinatory
.
Having
drawn
the
Horizontal
line
,
apply
the
North
〈◊〉
●
of
the
Clinatory
to
it
,
and
if
the
North
end
of
the
Needle
〈◊〉
directly
towards
the
Plain
,
it
is
then
a
South
Plain
.
If
the
〈◊〉
point
of
the
Needle
points
directly
from
the
Plain
,
it
is
a
Nor●●
plain
:
but
if
it
points
towards
the
East
,
it
is
an
East
Plain
:
if
towards
the
West
a
West
Plain
.
If
it
do
not
point
directly
〈◊〉
East
,
West
,
North
,
or
South
,
then
so
many
degrees
as
the
〈◊〉
declines
from
any
of
these
four
points
to
any
of
the
other
of
〈◊〉
four
points
,
so
many
degrees
is
the
Declination
of
the
Plain
,
〈◊〉
respect
(
as
aforesaid
)
had
to
the
Variation
of
the
Compass
.
Or
if
you
find
the
Azimuth
of
the
Sun
by
its
Altitude
observed
just
when
its
beams
are
coming
on
or
going
off
you●
Plain
,
that
Azimuth
shall
be
the
Azimuth
of
your
Plain
.
Or
you
may
erect
a
wyer
Perpendicularly
on
your
Plain
,
and
wait
till
the
shadow
of
that
wyer
comes
to
be
Perpendicular
with
the
Horizon
,
which
you
may
examine
by
applying
a
Plumb-line
to
it
,
for
then
the
shadow
of
the
Plumb-line
and
the
shadow
of
the
Perpendicular
will
be
in
one
:
then
taking
the
Altitude
of
the
Sun
you
may
by
Prob.
22.
of
the
second
Book
find
its
Azimuth
,
and
thereby
know
in
what
Azimuth
the
Plain
of
your
Dyal
lies
:
for
the
Azimuth
your
Plain
lies
in
is
distant
from
the
Azimuth
of
the
Sun
just
90.
degrees
.
PROB.
I.
How
by
one
position
of
the
Globe
to
find
the
distances
of
the
Hour-lines
on
all
manner
of
Plains
.
YOu
may
have
Meridian
lines
drawn
from
Pole
to
Pole
through
every
15.
degrees
of
the
Equinoctial
,
to
represent
the
Horary
motion
of
the
Sun
both
Day
and
Night
;
and
when
the
Pole
of
the
Globe
is
Elevated
to
the
height
of
the
Pole
in
any
Place
and
one
of
these
Meridian
lines
be
brought
to
the
Brazen
Meridian
,
all
the
rest
of
the
Meridian
lines
shall
cut
any
Circle
which
you
intend
shall
represent
the
Plain
of
a
Dyal
in
the
number
of
degrees
on
the
same
Circle
that
each
respective
Hour-line
is
distant
from
the
Noon-line
point
in
the
same
Circle
.
Thus
if
you
should
enquire
the
distance
of
the
Hour-lines
upon
an
Horizontal
Plain
in
Londons
Latitude
;
The
Pole
of
the
Globe
as
aforesaid
)
must
be
Elevated
51½
degrees
,
and
one
of
the
Meridian
lines
(
you
may
chuse
the
Vernal
Colure
)
be
brought
to
the
Brazen
Meridian
,
which
being
done
,
you
are
only
to
examine
in
the
Horizon
(
Because
it
is
an
Horizontal
Plain
)
at
what
distance
from
the
Meridian
(
which
in
Horizontals
is
the
Noon-line
)
the
several
Meridians
drawn
on
the
Globe
intersect
the
Horizon
,
for
that
distance
in
degrees
shall
be
the
distance
on
a
Circle
divided
into
360.
degrees
that
each
respective
Hour-line
must
have
from
the
Meridian
or
a
Noon
line
chosen
in
the
same
Circle
;
and
lines
drawn
from
the
Center
of
that
Circle
through
those
degrees
shall
be
the
Hour
lines
of
an
Horizontal
Plain
.
If
your
Plain
be
not
Direct
but
declines
East
or
West
▪
〈◊〉
must
number
the
Declination
Eastwards
or
Westwards
re●pectively
in
the
degrees
of
the
Horizon
and
(
the
Quadrant
〈◊〉
Altitude
screwed
to
the
Zenith
,
(
as
aforesaid
)
bring
the
lower
end
of
the
Quadrant
of
Altitude
to
the
said
degrees
of
Declination
,
and
the
number
of
degrees
cut
by
the
Meridians
in
the
Quadrant
of
Altitude
numbred
downwards
,
is
the
number
of
degrees
that
the
Hour-lines
are
distant
from
the
Noon
line
in
a
Circle
of
360
,
degrees
:
And
lines
drawn
from
the
Center
of
that
Circle
through
those
degrees
be
the
Hour
lines
of
half
the
Day
.
And
if
you
turn
about
the
Quadrant
of
Altitude
upon
the
Zenith
point
till
the
lower
end
of
it
come
to
the
degree
of
the
Horizon
opposite
to
the
degree
of
Declination
found
before
,
the
Meridian
lines
on
the
Globe
(
as
before
)
shall
cut
the
Quadrant
of
Altitude
in
the
number
of
degrees
(
counted
downward
)
that
each
Hour-line
is
distant
from
the
other
side
the
Noon-line
:
And
lines
drawn
from
the
Center
of
that
Circle
through
those
degrees
shall
be
the
Hour-lines
of
the
other
half
of
the
Day
,
If
your
Plane
Decline
,
and
also
Recline
or
Incline
,
you
must
use
the
Gnomonical
Semi-Circle
,
discribed
in
Prob.
12
▪
which
must
be
Elevated
on
the
Quadrant
of
Altitude
when
it
is
set
to
the
Declination
(
as
by
the
former
Rule
)
according
to
the
complement
of
Reclination
,
or
Inclination
:
But
if
your
Plane
be
Direct
,
and
Recline
,
or
Incline
,
it
must
be
set
to
the
Meridian
,
and
the
Meridians
on
the
Globe
shall
cut
that
Semi
Circle
in
the
number
of
degrees
counted
from
the
Quadrant
of
Altitude
if
the
Plane
Declines
,
or
from
the
Brasen
Meridian
,
if
it
be
Direct
,
that
the
several
Hour
lines
are
distant
from
a
line
Perpendicular
to
an
Horizontal
line
,
in
a
Circle
divided
into
360
degrees
;
And
lines
drawn
from
the
Center
through
those
degrees
shall
be
the
Hour-lines
of
such
Reclining
or
Inclining
Planes
.
The
moving
this
thred
from
wyer
to
wyer
represents
the
motion
of
the
Sun
,
which
as
it
passes
over
all
the
Meridians
causes
the
shadow
of
that
Meridional
Semi
Circle
which
it
is
directly
over
▪
and
the
Axis
,
and
the
Meridional
Semi-Circle
directly
opposite
to
the
upper
Meridional
Semi-Circle
to
fall
all
into
one
straight
line
:
And
upon
what
point
in
the
East
and
West
line
(
mentioned
before
)
that
shadow-line
shall
fall
is
marked
●ut
by
the
application
of
the
thred
as
aforesaid
:
and
is
an
Hour-line
on
any
of
the
foresaid
Planes
.
If
you
understand
this
Probleme
rightly
,
you
do
already
know
how
to
draw
the
Hour
lines
upon
all
manner
of
Planes
,
and
need
no
further
Instructions
;
yet
partly
fearing
a
raw
Student
should
not
clearly
understand
these
Rules
,
and
partly
doubting
)
because
other
Authors
have
been
more
Copious
upon
this
Subject
)
that
I
should
be
censured
to
be
too
sparing
of
my
pains
,
if
I
should
lightly
touch
so
eminent
a
Doctrine
as
Dyalling
is
:
Therefore
I
shall
more
distinctly
handle
Dyalling
by
the
Globe
,
according
to
the
way
or
Method
that
other
Authors
have
used
,
and
that
after
so
plain
a
manner
as
possibly
my
Genius
can
devise
.
PROB.
II.
To
make
an
Equinoctial
Dyal
.
DIscribe
a
Circle
,
on
a
square
board
or
Plane
as
B
C
E
D
,
and
through
A
the
Center
thereof
draw
a
straight
line
Parallel
to
one
of
the
sides
,
as
B
E
;
Cross
that
straight
line
with
another
straight
line
as
C
D
at
Right
Angles
,
so
shall
the
Circle
be
divided
into
4
equal
parts
:
Divide
each
of
these
four
equal
parts
into
90.
degrees
;
as
in
the
Figure
.
This
Circle
shall
represent
the
Horizon
.
Erect
a
wyer
exactly
perpendicular
to
the
Center
of
the
Plane
;
and
that
wyer
shall
be
the
Gnomon
or
Style
of
the
Dyal
.
Then
Elevate
one
of
the
Poles
of
your
Globe
into
the
Zenith
,
and
bring
the
Equinoctial
Colure
to
the
Meridian
.
And
because
in
every
hours
Time
15
degrees
of
the
Equator
passes
through
the
Meridian
in
Heaven
,
therefore
turn
the
Globe
till
15
degrees
of
the
Equator
pass
through
the
Meridian
of
your
Globe
;
so
shall
the
Colure
pass
by
15
degrees
of
the
Horizon
also
.
Therefore
from
the
Center
of
your
Plane
draw
straight
lines
through
15
▪
degrees
from
one
of
the
Semidiameters
both
waies
:
and
those
straight
lines
shall
be
two
Hour-lines
:
Then
turn
the
Globe
till
15
degrees
more
of
the
Equator
pass
through
the
Meridian
,
and
you
will
find
as
before
,
the
Colure
pass
by
15
degrees
more
of
the
Horizon
:
therefore
on
your
Plane
number
15.
degrees
further
beyond
both
the
former
lines
,
and
from
the
Center
draw
straight
lines
through
both
those
15.
degrees
,
and
they
shall
be
two
Hour
lines
more
.
Fór
all
the
other
Hour
lines
turn
the
Globe
till
15.
degrees
of
the
Equator
at
a
time
pass
through
the
Meridian
,
as
before
,
and
you
will
find
that
for
every
15.
degrees
of
the
Equator
that
passes
through
the
Meridian
,
the
Colure
will
pass
through
15.
degrees
of
the
Horizon
:
therefore
those
Hour
lines
must
be
drawn
from
the
Center
according
to
the
succession
of
every
15
degrees
on
your
Plane
,
Having
drawn
the
Hour
lines
,
you
may
set
figures
to
them
,
beginning
to
number
your
Hour
lines
from
one
of
the
Diameters
,
marking
it
with
XII
,
and
the
next
Hour
line
to
the
left
hand
with
I
,
and
the
next
II
,
the
next
III
,
&c.
to
XII
.
and
begin
again
with
I
,
II
,
III
,
&c.
till
you
come
to
the
other
XII
,
where
you
began
:
and
then
your
Dyal
is
finished
.
See
the
Figure
.
This
is
an
Universal
Dyal
,
and
serves
in
all
Latitudes
:
therefore
when
you
place
it
you
must
set
one
of
the
XIIs
downwards
,
and
the
Axis
Parallel
to
the
Axis
of
the
World
.
But
note
,
Both
faces
of
this
Dyal
ought
to
be
divided
,
and
the
Gnomon
must
appear
on
both
sides
like
the
stick
in
a
Whirligig
,
which
childeren
use
;
or
else
you
must
turn
it
upside
down
,
so
oft
as
the
Sun
passes
the
Equinoctial
.
PROB.
III.
To
make
an
Horizontal
Dyal
.
DIscribe
a
Circle
on
your
Plane
,
as
C
B
D
E
,
and
through
the
Center
A
of
that
Circle
draw
a
Meridian
line
,
as
B
E
;
cross
that
line
at
Right
angles
with
another
line
,
as
C
D
;
so
shall
your
Circle
be
divided
into
four
equal
parts
:
Divide
each
of
these
four
parts
into
90.
degrees
;
so
shall
the
whole
be
divided
into
360.
These
360
degrees
represent
the
360
degrees
of
the
Horizon
,
which
a
Meridian
line
drawn
through
the
place
of
the
Sun
runs
through
in
every
24.
Hours
:
The
motion
of
which
Meridian
line
through
the
degrees
of
the
Horizon
is
Regular
in
a
Parallel
Sphear
;
for
in
equal
Time
it
moves
an
equal
Space
throughout
the
whole
Circle
,
viz.
it
will
pass
through
15.
degrees
of
the
Horizon
in
one
Hours
Time
,
(
or
which
is
all
one
)
whiles
15.
degrees
of
the
Equator
passes
through
the
Meridian
;
as
was
shewed
in
the
last
Probleme
:
But
in
an
Oblique
Sphear
its
motion
through
the
Horizon
is
Irregular
,
and
that
more
or
less
according
to
the
more
or
less
Obliquity
of
the
Sphear
:
For
far
Northwards
or
Southwards
you
may
see
this
Meridian
line
pass
through
40
,
50
,
yea
60.
degrees
of
the
Horizon
in
one
Hours
time
,
viz
,
whiles
15.
degrees
of
the
Equator
passes
through
the
Meridian
:
but
in
an
other
Hours
time
you
will
scarce
have
4
or
5
degrees
pass
through
the
Horizon
whiles
15
degrees
of
the
Equator
passes
through
the
Meridian
.
But
that
you
may
know
the
motion
of
the
Sun
(
represented
by
this
Meridian
line
)
through
the
Horizon
in
all
Latitudes
;
Elevate
the
Pole
to
the
Elevation
of
your
Place
,
and
chuse
instead
of
a
Meridian
line
drawn
through
the
Place
of
the
Sun
the
Vernal
Colure
to
be
your
Meridian
line
;
both
because
it
is
most
visible
;
and
because
from
thence
the
degrees
of
the
Equator
are
begun
to
be
numbred
,
so
that
what
so
ever
decimal
degree
of
the
Equator
you
light
on
at
the
Meridian
,
or
else
where
,
you
will
find
its
number
from
that
Colure
already
set
down
to
your
hand
,
without
either
adding
to
,
or
substracting
from
it
.
Bring
this
Colure
therefore
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
in
the
Hour
Circle
.
Then
turn
the
Globe
Westwards
,
and
so
oft
as
15
degrees
of
the
Equator
passes
through
the
Meridian
,
so
oft
you
must
examine
what
degrees
of
the
Horizon
the
Vernal
Colure
cuts
;
and
those
degrees
and
minutes
so
cut
by
the
Vernal
Colure
must
be
found
in
the
Circle
C
B
D
E
,
beginning
your
account
or
reckoning
at
B
towards
D
,
and
markt
with
Pricks
:
through
which
Pricks
you
must
draw
lines
from
the
Center
A
,
and
those
lines
shall
be
the
Hour
lines
after
noon
.
Then
bring
the
Colure
to
the
Meridian
again
to
find
the
Fore-noon
Hour-lines
,
and
turn
the
Globe
Eastwards
,
and
so
oft
as
15
degrees
of
the
Equator
passes
through
the
Meridian
,
so
oft
you
must
examine
what
degrees
of
the
Horizon
the
Vernal
Colure
cuts
;
and
those
degrees
and
minutes
so
cut
by
the
Vernal
Colure
must
be
found
in
the
Circle
C
B
D
E
,
begining
your
reckoning
from
B
towards
C
,
and
markt
with
Pricks
:
through
which
Pricks
you
must
draw
lines
from
the
Center
A
,
and
those
lines
shall
be
the
Fore-noon
Hour-lines
.
These
Hour-lines
must
be
markt
from
the
Meridian
line
,
viz.
the
line
A
B
,
which
is
the
12
a
clock
line
towards
D
,
with
I
,
II
,
III
&c.
till
you
have
numbred
to
the
Hour
of
Sun
set
(
found
by
Prob.
7.
of
the
second
Book
)
the
longest
Day
,
and
from
the
Meridian
line
towards
C
with
XI
,
X.
IX
,
&c.
till
you
have
numbred
to
Sun
Rising
the
longest
Day
.
The
Stile
must
be
placed
in
the
Center
and
Elevated
so
many
degrees
above
the
Plane
,
as
the
Pole
is
elevated
above
the
Horizon
of
the
Place
,
Example
of
the
whole
.
I
would
make
an
Horizontal
Dyal
for
Londons
Latitude
:
Therefore
I
E
evate
the
North
Pole
51½
degrees
above
the
Horizon
,
and
bring
the
Vernal
Colure
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12
on
the
Hour
Circle
;
And
turning
the
Globe
Westwards
till
the
Index
points
to
|
1
|
a
clock
or
till
15
deg
of
the
Equator
pass
through
the
Meridian
;
I
find
the
Colure
cut
the
Hori
in
|
11.
4
|
from
the
Meridian
.
|
2
|
24.
15
|
3
|
38.
4
|
4
|
53.
●6
|
5
|
71.
6
|
6
|
90.
|
These
are
the
distances
of
the
Hour
lines
from
Noon
till
6
at
Night
:
and
to
these
distances
on
the
Plane
(
counting
from
B
towards
D
,
)
I
make
pricks
;
and
from
the
Center
I
draw
lines
through
these
Pricks
;
and
these
lines
are
the
Hour
lines
from
12
to
6
Afternoon
.
But
the
Sun
in
the
longest
Day
shines
till
past
8
at
Night
,
as
you
may
find
by
Prob.
48.
of
the
second
Book
,
therefore
here
wants
the
two
Evening
Hour
lines
;
which
though
they
may
be
found
after
the
same
way
I
found
the
former
,
(
viz.
by
continuing
the
turning
of
the
Globe
Westwards
)
yet
that
I
may
the
sooner
reduce
my
work
to
the
Plane
I
Count
the
number
of
degrees
between
the
6
a
clock
line
and
the
5
a
clock
line
in
the
Circle
on
the
Plane
;
for
the
same
number
of
degrees
counted
from
D
towards
E
is
the
distance
of
the
7
a
clock
Hour
line
from
the
6
a
clock
Hour
line
;
and
the
number
of
degrees
contained
between
the
6
a
clock
Hour
line
and
the
4
a
clock
Hour
line
is
the
distance
of
the
8
a
clock
Hour
line
from
the
6
a
clock
Hour-line
.
Or
I
need
not
draw
the
7
and
8
a
clock
Hour
lines
,
till
I
have
drawn
the
forenoon
Hour
lines
:
for
then
by
laying
the
edge
of
a
Ruler
(
that
will
reach
through
the
opposite
side
of
the
Plane
)
to
the
Morning
7
and
8
a
clock
Hour
lines
,
I
may
by
the
side
of
that
Ruler
draw
lines
from
the
Center
through
the
opposite
side
of
the
Plane
,
and
those
lines
shall
be
the
7
and
8
a
clock
Hour
lines
Afternoon
.
Having
thus
all
the
Afternoon
Hour
lines
,
I
bring
the
Vernal
Colure
to
the
Meridian
again
;
so
shall
the
Index
again
point
to
12.
Therefore
,
as
before
I
turned
the
Globe
Westwards
,
so
now
turning
it
Eastwards
,
till
the
Index
points
to
|
11
|
a
clock
,
or
till
15
deg.
of
the
Equator
pass
through
the
Meridian
,
I
find
the
Colure
cut
the
Hori
.
in
|
11.
40
|
from
the
Meridian
.
|
10
|
24.
15
|
9
|
38.
4
|
8
|
53.
36
|
7
|
71.
6
|
6
|
90.
|
These
are
the
distances
of
the
Hour
lines
from
Noon
to
6.
a
clock
in
the
Morning
:
and
these
distances
I
seek
in
the
Circle
of
the
Plain
(
counting
from
the
Noon
line
B
towards
C
)
and
mark
them
with
Pricks
;
through
which
pricks
(
as
before
)
I
draw
lines
from
the
Center
to
the
outside
the
Plane
:
and
those
lines
shall
be
the
Hour
lines
.
Or
having
the
distance
of
all
the
Afternoon
Hour-lines
,
I
have
also
the
distance
of
all
the
forenoon
Hour
lines
from
the
Meridian
;
as
you
may
see
by
comparing
the
two
former
Tables
.
For
the
1
a
clock
Hour
line
Afternoon
is
equidistant
from
the
Meridian
or
Noon
line
with
the
11
a
clock
Hour
line
before
Noon
,
viz.
they
are
both
11
degrees
40
minutes
distant
from
the
Noon
line
,
and
the
2
a
clock
Hour
line
Afternoon
is
from
the
Noon
line
equidistant
with
the
10
a
clock
Hour
line
Beforenoon
;
for
they
are
both
24.
degrees
15.
minutes
distant
from
the
Meridian
or
Noon
line
:
and
so
all
the
other
Morning
Hour
lines
are
distant
from
the
Noon
line
by
the
same
space
that
the
same
number
of
Afternoon
Hour
lines
(
told
from
the
Meridian
on
the
contrary
side
the
Noon
line
)
are
distant
from
the
Meridian
.
Whence
it
follows
,
that
since
(
as
aforesaid
)
the
same
number
of
Hour
lines
after
6
at
Night
,
and
before
6
in
the
Morning
have
the
same
distance
from
the
6
a
clock
line
that
the
same
number
of
Hour
lines
before
6
at
Night
and
after
6
in
the
Morning
have
from
the
6
a
clock
line
;
and
since
the
same
number
of
Hour
lines
before
Noon
are
equidistant
from
the
Meridian
or
Noon
line
by
the
same
space
of
degrees
that
the
same
number
of
Hour
lines
Afternoon
are
;
It
follows
(
I
say
)
that
having
found
the
distance
of
the
six
Hour
lines
either
before
or
after
Noon
,
you
have
also
given
the
distance
of
all
the
other
Hour
lines
.
If
you
will
have
the
half
Hour
lines
placed
on
your
Dyal
you
must
turn
the
Globe
till
the
Index
points
to
every
half
Hour
in
the
Hour
Circle
,
as
well
as
to
the
whole
,
and
examine
the
degrees
of
the
Horizon
cut
by
the
Vernal
Colure
,
as
you
did
for
the
whole
Hours
;
and
in
like
manner
transfer
them
to
your
Plane
.
Having
thus
drawn
all
the
Hour
lines
I
count
from
the
Noon
line
51½
degrees
,
the
Elevation
of
the
Pole
here
at
London
;
and
from
the
Center
A
I
draw
a
straight
line
,
as
A
F
through
these
51½
degrees
,
for
the
Gnomon
or
Style
,
and
prolong
it
to
the
farthest
extent
of
the
Plane
:
From
this
Gnomon
or
Style
I
let
fall
a
Perpendicular
upon
the
Noon
line
,
as
F
G
:
(
this
Perpendicular
is
called
the
Substile
,
and
this
Perpendicular
and
its
Base
(
which
is
the
Noon
line
)
and
Hypothenusa
(
which
is
the
Gnomon
)
shall
make
a
Triangle
,
which
being
erected
upon
the
Base
,
so
as
the
Substile
may
stand
Perpendicular
to
the
Plane
,
the
Hypothenusa
A
F
shall
be
the
Gnomon
,
and
be
Parallel
to
the
Axis
of
the
World
;
and
cast
a
shadow
upon
the
Hour
of
the
Day
.
PROB.
IIII.
To
make
an
Erect
Direct
South
Dyal
.
DRaw
on
your
Plane
an
Horizontal
line
as
C
A
D
,
as
was
shewed
in
the
Preface
:
in
the
middle
of
this
line
(
as
at
A
)
discribe
as
on
a
Center
the
Semi-Circle
C
B
D
:
from
the
Center
A
let
fall
a
Perpendicular
,
which
shall
divide
the
Semi-Circle
into
two
Quadrants
each
of
which
Quadrants
you
must
divide
into
90
degrees
,
Then
Rectifie
the
Globe
,
Quadrant
of
Altitude
,
Colure
and
Hour
Index
▪
thus
,
Elevate
the
Pole
of
the
Globe
to
the
Latitude
of
your
Place
,
and
screw
the
Quadrant
of
Altitude
to
the
Zenith
,
Then
bring
the
Vernal
Colure
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
the
Hour
of
12.
in
the
Hour
Circle
;
so
shall
your
Globe
,
Quadrant
of
Altitude
,
Colure
and
Hour
Index
be
Rectified
.
A●d
●●us
you
must
alwaies
Rectifie
them
for
the
making
of
most
sorts
of
Dyals
by
the
Globe
.
Then
to
make
an
Erect
Direct
South
Dyal
,
Bring
the
lower
end
of
the
Quadrant
of
Altitude
to
the
West
point
of
the
Horizon
;
And
turn
the
Globe
Westwards
till
the
Index
points
to
all
the
Hours
Afternoon
;
and
examine
in
what
numbers
of
degrees
from
the
Zenith
the
Colare
cuts
the
Quadrant
of
Altitude
when
the
Index
points
to
each
Hour
:
for
a
line
drawn
from
the
Center
A
through
the
same
number
of
degrees
reckoned
from
the
Perpendicular
A
B
(
which
is
the
12
a
clock
line
)
towards
D
on
the
Plane
,
shall
be
the
same
Hour
lines
the
Index
points
at
.
Thus
in
our
Latitude
,
viz.
51½
degrees
,
the
Vernal
Coloure
being
brought
to
the
Meridian
and
the
Index
to
12
;
If
you
turn
the
Globe
Westwards
,
till
the
Index
points
to
|
1
|
a
clock
,
or
till
15
deg.
of
the
Equator
pass
through
the
Meridian
,
the
Colure
will
cut
the
Quadrant
of
Altitude
in
|
9.
18
|
counted
from
the
Zenith
.
|
2
|
19.
15
|
3
|
32.
5
|
4
|
48.
0
|
5
|
67.
4
|
6
|
90.
|
And
these
are
the
distances
of
the
Afternoon
Hour
lines
;
which
you
must
transfer
to
the
East
side
of
your
Plane
,
viz
,
from
B
towards
D
;
and
draw
lines
from
the
Center
A
through
these
distances
;
and
these
lines
shall
be
your
Afternoon
Hour
lines
.
Note
(
once
for
all
)
when
the
Colure
goes
off
that
Circle
you
examine
the
Hour
distances
in
,
the
Sun
will
shine
no
longer
upon
that
Plane
;
As
in
this
example
the
Colure
goes
off
the
Quadrant
of
Altitude
at
6
a
clock
,
therefore
the
Sun
will
not
shine
longer
then
till
6
a
clock
upon
this
Plane
.
The
Hour
lines
before
Noon
have
the
same
distance
from
the
Meridian
that
the
Afternoon
Hour
lines
have
,
as
was
shewed
in
the
last
Probleme
:
Only
they
must
be
drawn
on
the
West
side
the
Noon
line
,
and
counted
from
B
towards
C.
Otherwise
.
You
may
reduce
all
Verticals
into
Horizontals
;
if
you
Elevate
the
Pole
of
the
Globe
to
the
Complement
of
the
Latitude
of
your
Place
,
and
bring
the
Vernal
Colure
to
the
Meridian
under
the
Horizon
,
and
the
Index
of
the
Hour
Circle
to
12
;
and
turn
the
Globe
Westwards
;
for
as
the
Index
passes
through
every
Hour
on
the
Hour
Circle
,
the
Colure
shews
in
the
Horizon
the
distance
of
the
several
Afternoon
Hour
lines
from
the
Meridian
,
or
12
a
clock
line
,
in
the
Circle
on
your
Plane
,
numbred
from
B
to
D
:
and
lines
drawn
from
the
Center
through
these
distances
on
your
Plane
shall
be
the
Afternoon
Hour
lines
of
your
Dyal
.
Example
.
Londons
Latitude
is
51½
degrees
,
Its
Complement
to
90.
is
38½
.
Therefore
I
Elevate
the
Pole
38½
degrees
above
the
Horizon
,
and
bring
the
Vernal
Colure
to
the
Meridian
under
the
Horizon
,
and
the
Index
of
the
Hour
Circle
to
12
on
the
Hour
Circle
.
Then
Turning
the
Globe
Westwards
,
till
the
Index
of
the
Hour
Circle
points
to
|
1
|
a
clock
,
or
till
15
deg.
of
the
Equator
pass
through
the
Meridian
,
I
find
the
Colure
cut
the
Horizon
in
|
9
18
|
from
the
Intersection
of
the
Meridian
and
the
Horizon
:
as
in
the
former
Table
.
|
2
|
19
15
|
3
|
32
5
|
4
|
48
0
|
5
|
67
0
|
6
|
90
|
And
these
are
the
distances
of
the
6
Hour
lines
from
the
Merid.
By
this
Example
you
may
see
that
it
is
easie
to
reduce
Verticals
into
Horizon●als
:
and
Horizontals
into
Verticals
:
for
this
Erect
Direct
South
Dyal
is
an
Horizontal
Dyal
to
those
People
that
Inhabite
90
degrees
from
us
,
viz.
in
the
South
Latitude
of
38½
degrees
.
Then
make
a
Triangle
,
whereof
the
Noon
line
shall
be
Base
:
from
it
count
the
Complement
of
the
Poles
Elevation
,
viz.
38½
degrees
,
and
through
them
draw
the
line
A
F
,
from
the
Center
A
which
shall
be
Hypotenusa
;
Then
●et
fall
a
Perpendicular
upon
the
Noon
line
A
B
,
so
is
your
Triangle
made
.
If
this
Triangle
be
erected
Perpendicularly
upon
the
Base
or
Noon
line
,
The
Hypotenusa
A
F
shall
stand
Parallel
to
the
Axis
of
the
World
,
and
cast
a
shadow
upon
the
Hour
of
the
Day
.
PROB.
V.
To
make
an
Erect
Direct
North
Dyal
.
IF
the
Erect
Direct
South
Dyal
were
turned
towards
the
North
;
and
the
line
C
A
D
were
turned
downwards
,
and
the
line
marked
with
7
be
now
marked
with
5
,
and
the
line
8
with
4
,
the
line
5
with
7
,
and
the
line
4
with
8
,
then
have
you
of
it
a
North
Erect
Direct
Dyal
.
All
the
other
Hour
lines
in
this
Dyal
are
useless
,
because
the
Sun
in
our
Latitude
shines
on
a
North
Face
the
longest
Day
only
before
6
in
the
Morning
,
and
after
6
at
Night
.
PROB.
VI.
To
make
an
Erect
Direct
East
Dyal
.
THese
sorts
of
Dyals
may
better
be
demonstrated
then
made
by
the
Globe
;
unless
the
Axis
of
your
Globe
were
accessible
,
as
in
the
Wyer-Globe
,
specified
in
Prob.
1.
Therefore
when
you
would
make
an
East
,
or
West
Dyal
,
or
a
Polar
Dyal
.
Provide
a
square
Board
,
as
A
B
C
D
,
draw
the
straight
line
e
f
upon
it
Parallel
to
the
sides
A
C
,
and
B
D.
and
just
in
the
middle
between
them
:
Cross
this
straight
line
at
Right
Angles
with
another
straight
line
,
as
g
h
,
quite
through
the
Board
.
Upon
this
Board
with
a
little
Pitch
or
Wax
fasten
the
Semi-Circle
of
Position
,
so
as
both
the
Poles
thereof
may
ly
in
the
line
g
h
,
and
the
middle
of
the
Semi-Circle
marked
co
may
ly
upon
the
line
e
f
,
so
shall
i
be
the
Center
of
the
Semi-circle
of
Position
:
In
this
Center
make
a
smal
hole
through
the
Board
fit
to
receive
a
Wyer
or
a
Nail
.
So
may
you
with
this
Circle
of
Position
thus
fitted
,
and
the
side
C
D
applyed
to
a
line
of
Contingence
elevated
to
the
Height
of
the
Equinoctial
,
draw
line
,
from
the
Center
through
every
15
degrees
of
the
Circle
of
Position
,
and
by
continuing
them
intersect
the
line
of
Conti●gence
in
the
points
from
whence
the
Hour
lines
of
an
East
or
West
Dyal
is
to
be
drawn
:
Example
.
But
because
in
our
Latitude
the
Sun
Rises
before
4.
in
the
Morning
,
therefore
two
Hour-lines
are
yet
wanting
,
viz.
5
,
and
4
,
which
I
may
find
either
by
applying
the
thred
first
to
15
,
and
next
to
30
degrees
from
0
towards
g
in
the
Semi-Circle
,
and
so
marking
where
it
cuts
the
Contingent
line
,
as
before
:
Or
else
by
transfering
the
distance
of
the
same
number
of
Hour
lines
from
the
6
a
clock
line
already
drawn
on
the
side
e
〈◊〉
to
the
side
e
g
,
as
in
Prob.
2.
of
this
Book
is
more
fully
shewed
.
Having
thus
marked
out
on
the
Contingent
line
the
distances
of
each
Hour
;
I
draw
a
line
Parallel
to
the
Contingent
line
,
and
draw
lines
from
every
Hour
markt
on
the
Contingent
to
cross
the
Contingent
line
at
Right
Angles
and
continue
each
line
to
the
line
Parallel
to
the
Contingent
;
and
these
lines
shall
be
the
Hour
lines
of
an
East
Plane
.
To
these
Hour-lines
I
set
Figures
as
in
the
Scheam
may
be
seen
.
The
Style
D
K
of
this
Dyal
(
as
well
as
of
others
)
must
stand
Parallel
to
the
Axis
of
the
World
:
it
must
be
also
Parallel
to
all
the
Hour
lines
,
and
stand
directly
over
the
6
a
clock
line
,
and
that
so
high
as
is
the
distance
between
the
Center
of
the
Semi-Circle
of
Position
and
the
point
where
the
6
a
clock
line
cuts
the
Contingent
line
:
Or
(
which
is
all
one
)
at
such
a
height
as
when
it
is
laid
flat
down
upon
the
Plane
it
may
just
reach
the
3
a
clock
line
,
PROB.
VII
.
To
make
an
Erect
Direct
West
Dyal
.
AN
Erect
Direct
West
Dyal
is
the
same
in
all
respects
with
an
Erect
Direct
East
Dyal
;
Only
as
the
East
shews
the
Fore-noon
Hours
,
the
West
shews
the
After-noon
Hours
.
Thus
if
you
should
draw
the
East
Dyal
on
any
transparent
Plane
,
as
on
Glass
,
Horn
,
or
an
Oyled
Paper
,
on
the
one
side
will
appear
an
East
Dyal
,
and
on
the
other
a
West
.
Only
the
Figures
as
was
said
before
(
must
be
changed
)
;
for
that
which
in
the
East
Dyal
is
11
,
in
the
West
must
be
1
:
that
which
in
the
East
Dyal
is
10
,
in
the
West
must
be
2
:
that
which
in
the
East
Dyal
is
9
in
the
West
must
be
3.
&c.
PROB.
VIII
.
To
make
a
Polar
Dyal
.
POlar
Dyals
are
Horizontal
Dyals
under
the
Equinoctial
:
They
are
of
the
same
kind
with
East
and
West
Dyals
;
Only
whereas
East
and
West
Dyals
have
but
the
Hour
lines
of
half
the
longest
Day
discribed
on
them
,
these
have
all
the
Hour
lines
of
the
whole
Day
;
and
are
marked
on
both
sides
the
Noon
line
:
as
in
the
following
Figure
.
The
Style
of
this
Dyal
must
stand
over
the
Noon
line
,
Parallel
to
the
Plane
;
for
then
it
will
also
be
Parallel
to
the
Axis
of
the
World
:
and
its
height
above
the
Plane
must
be
the
distance
between
the
Center
i
of
the
Semi-Circle
and
the
point
in
the
Contingent
line
cut
by
the
Noon-line
.
But
I
have
inserted
the
Figure
,
which
alone
is
sufficient
Instructions
.
PROB.
IX
.
To
make
Erect
South
Dyals
,
Declining
Eastwards
,
or
Westwards
.
DRaw
on
your
Plane
an
Horizontal
line
,
and
on
it
discribe
a
Semi-Circle
,
as
you
were
taught
in
Prob
4.
Then
Rectifie
the
Globe
,
Quadrant
of
Altitude
Colure
and
Hour
Index
▪
as
by
the
same
Probleme
:
and
bring
the
lower
end
of
the
Quadrant
of
Altitude
to
the
degree
of
Declination
from
the
East
or
West
point
,
according
is
your
Declination
is
Eastwards
or
Westwards
;
for
then
the
Quadrant
of
Altitude
shall
represent
a
Plane
declining
from
the
South
E●stwards
,
or
Westwards
accordingly
.
Then
tu●n
the
Globe
Eastwards
,
till
the
Index
of
the
Hour-Circle
points
to
all
the
Hours
before
Noon
,
and
examine
in
what
number
of
degrees
from
the
Zenith
the
Colure
cuts
the
Q●●drant
of
Altitude
,
when
the
Index
points
to
each
Hour
,
For
a
line
drawn
from
the
Center
A
through
the
same
number
of
degrees
reckoned
from
the
Perpendicular
A
B
,
which
is
the
12
a
clock
line
towards
Con
the
Plane
,
shall
be
the
same
Hour-lines
the
Index
points
at
.
Example
.
I
would
make
an
Erect
Dyal
declining
from
the
South
towards
the
East
27.
degrees
:
The
Globe
,
Quadrant
of
Altitude
,
Vernal
Colure
,
and
Hour
Index
Rectified
,
as
before
,
I
bring
the
lower
end
of
the
Quadrant
of
Altitude
to
27.
degrees
counted
from
the
East
point
of
the
Horizon
towards
the
North
:
Then
I
turn
the
Globe
East-wards
till
the
Index
points
to
|
11
|
a
clock
,
or
till
15.
deg.
of
the
Equator
pass
through
the
Meridian
,
and
find
the
Colure
cut
the
Quadrant
of
Altitude
in
|
9.43
|
counted
from
the
Zenith
.
|
10
|
19.0
|
9
|
25.57
|
8
|
35.10
|
7
|
45.56
|
6
|
60.15
|
5
|
79.45
|
And
these
are
the
distances
of
the
Fore-noon
Hour-lines
,
which
I
seek
in
the
West
side
of
the
Plane
,
viz.
from
B
towards
C
;
and
through
these
distances
I
draw
lines
from
the
Center
,
and
these
lines
shall
be
the
Fore-noon
Hour-lines
.
Now
herein
is
a
difference
between
Declining
Dyals
,
and
Direct
Dyals
:
For
having
found
the
distances
of
the
Hour
lines
for
one
half
of
the
Day
,
be
it
either
for
Before
Noon
or
After
Noon
in
a
Direct
Dyal
,
you
have
also
found
the
distances
for
the
other
half
Day
;
because
,
as
was
said
Prob.
3.
Equal
number
of
Hours
have
equal
distance
from
the
Noon
line
:
But
in
Declining
Dyals
it
is
not
so
:
Because
the
Sun
remaining
longer
upon
that
side
of
the
Plane
which
it
declines
to
,
then
it
doth
upon
the
contrary
side
,
there
will
be
a
greater
number
of
Hour
lines
upon
it
,
and
by
consequence
the
distance
of
the
Hour
lines
less
then
on
the
contrary
side
of
the
Plane
.
Therefore
for
finding
the
After
Noon
Hour
lines
,
I
turn
about
the
Quadrant
of
Altitude
upon
the
Zenith
point
till
the
lower
end
of
it
come
to
the
degree
of
the
Horizon
opposite
to
that
degree
of
Declination
that
the
Quadrant
of
Altitude
was
placed
at
when
I
sought
the
Fore
Noon
Hour
lines
,
viz
,
to
27.
degrees
counted
●om
the
West
towards
the
South
,
and
bring
the
Ver●al
Colure
again
to
the
Meridian
,
and
the
Index
(
as
before
)
to
12.
Then
,
turning
the
Globe
Westwards
till
the
Index
poin●s
to
|
1
|
a
clock
,
or
till
15
degr.
of
the
Equator
pass
through
the
Meridian
,
I
find
the
Colure
cut
the
Quadrant
of
Altitude
in
|
11.20
|
counted
from
the
Zenith
.
|
2
|
26.47
|
3
|
49.20
|
4
|
75.52
|
And
these
are
the
distances
of
the
After
Noon
Hour
lines
;
which
dista●●●●
I
seek
in
the
East
side
of
the
Plane
,
viz.
from
B
towards
D
(
as
before
)
and
so
drawing
lines
from
the
Center
A
through
these
distances
,
I
have
all
the
Afternoon
Hour
lines
also
drawn
on
my
Plane
.
You
may
note
,
that
this
Plane
is
capable
to
receive
no
more
Hour
lines
After
Noon
then
4.
for
when
the
Colure
goes
off
the
Quadrant
of
Altitude
,
the
Sun
goes
off
these
kind
of
Planes
.
To
these
Hour
lines
I
set
their
numbers
,
as
you
may
see
i●
the
Figure
.
Here
you
may
see
that
in
Declining
Dyals
the
Style
doth
not
stand
at
the
same
Elevation
above
the
Plane
,
that
it
doth
in
Erect
Direct
Dyals
;
neither
doth
it
stand
over
the
12
a
clock
line
;
but
swerves
from
it
towards
the
Quarter
of
Declination
.
PROB.
X.
To
make
a
North
Erect
Dyal
declining
Eastwards
,
or
Westwards
.
AS
in
Prob.
5.
an
Erect
Direct
North
Dyal
hath
the
same
Delineation
that
an
Erect
Direct
South
Dyal
hath
,
and
differs
only
in
the
placing
the
Figures
of
the
Hour
lines
:
So
a
North
Erect
Dyal
that
declines
Eastwards
,
or
Westwards
,
differs
from
a
South
Erect
Dyal
that
Declines
Eastwards
,
or
Westwards
,
the
same
number
of
degrees
,
only
in
placing
the
Hour
lines
at
the
same
distance
on
the
contrary
side
of
the
Plane
,
and
by
transposing
the
Figures
of
11
for
1
:
10
for
2
:
9
for
3.
&c.
Thus
,
if
you
draw
upon
Glass
,
Horn
,
or
an
Oyled
Paper
,
the
South
Dyal
Declining
Eastwards
,
as
in
the
foregoing
Probleme
,
and
place
it
to
its
due
scituation
,
the
back
side
of
it
shall
be
a
North
Dyal
declining
towards
the
West
so
many
degrees
as
the
foreside
Declines
towards
the
East
;
and
the
only
difference
in
it
will
be
the
Figures
of
the
Hour
lines
;
as
was
said
before
.
PROB.
XI
.
To
make
Direct
Reclining
,
or
Inclining
Dyals
.
DIrect
Reclining
or
Inclining
Dyals
are
the
same
with
Erect
Direct
Dyals
that
are
made
for
the
Latitude
of
some
other
Places
:
The
Latitude
of
which
Places
are
either
more
then
the
Latitude
of
your
own
Place
,
if
the
Plane
Recline
,
or
less
if
the
Plane
Incline
;
and
that
in
such
a
proportion
as
the
arch
of
Reclination
or
Inclination
of
your
Plane
is
.
Thus
a
Direct
South
Dyal
Reclining
10.
degrees
in
Londons
Latitude
,
viz.
51½
degrees
,
is
an
Erect
Direct
Dyal
made
for
the
Latitude
of
61½
degrees
:
And
a
Direct
South
Dyal
Inclining
10.
degrees
in
the
Latitude
51½
degrees
is
an
Erect
Direct
Dyal
in
the
Latitude
of
41½
degrees
:
and
is
to
be
made
according
to
the
Directions
in
Prob.
4.
PROB.
XII
To
make
Declining
Reclining
,
or
Declining
Inclining
Dyals
.
THe
distances
of
the
Hour
lines
either
for
a
Declining
Reclining
Plane
,
or
a
Declining
Inclining
Plane
may
most
easily
be
found
upon
the
Plane
of
the
Horizon
,
That
is
(
as
some
Authors
call
it
)
by
the
Horizontal
Dyal
,
by
changing
the
Circles
of
the
Globe
one
into
another
:
So
as
the
Plane
of
the
Horizon
may
serve
to
represent
the
Dyal
Plane
;
Yet
this
way
not
being
natural
,
because
you
must
admit
one
Circle
to
be
another
,
and
that
in
Young
Learners
might
sometimes
breed
a
little
difficulty
,
Gemma
Frisius
,
Metius
,
and
Blaew
hath
prescribed
a
thin
Brass
plate
to
be
made
equal
to
a
Semi-Circle
of
the
Equinoctial
,
and
divided
from
the
middle
point
of
it
either
way
into
90
degrees
,
which
may
not
unproperly
be
called
a
Gnomonical
Semi-Circle
.
This
Semi-Circle
must
be
bowed
close
to
the
Body
of
the
Globe
into
a
Semi-Circular
form
,
and
so
set
to
any
Reclination
,
or
Inclination
,
and
then
it
will
represent
a
Reclining
or
Inclining
Plane
:
And
by
the
motion
of
the
Colure
through
the
several
degrees
of
this
Semi-Circle
the
distances
of
the
Hour
lines
may
be
found
:
Thus
,
The
Globe
,
Quadrant
of
Altitude
,
Colure
,
and
Hour
Index
,
Rectified
;
as
by
Prob.
4.
Bring
the
lower
end
of
the
Quadrant
of
Altitude
to
the
degree
in
the
Horizon
of
the
Planes
Declination
,
if
your
Plane
be
a
South
Declining
Recliner
,
and
count
on
the
Quadrant
of
Altitude
from
the
Zenith
downwards
the
number
of
degrees
of
Reclination
,
or
Inclination
,
and
to
that
number
of
degrees
bring
the
middle
of
the
Gnomonical
Semi-Circle
,
and
let
the
ends
of
●t
cut
the
Horizon
on
either
side
in
the
degrees
of
the
Planes
Azimuth
,
so
shall
the
Gnomonical
Semi-Circle
represent
a
Reclining
Plane
.
And
so
oft
as
15.
degrees
of
the
Equator
passes
through
the
Meridian
,
so
oft
shall
you
enquire
what
degrees
of
the
Gnomonical
Semi-Circle
the
Colure
cuts
;
for
so
many
degrees
asunder
must
the
several
respective
Hour
lines
of
a
Reclining
Declining
Plane
be
in
a
Semi-Circle
divided
into
180.
degrees
.
But
if
your
Plane
be
a
South
Declining
Recliner
,
or
a
North
Declining
Incliner
;
Bring
the
Quadrant
of
Altitude
to
the
degree
of
the
Horizon
opposite
to
the
degree
of
the
Planes
Declination
,
(
because
the
upper
side
of
the
Plane
lies
beyond
the
Zenith
)
counted
from
the
South
point
in
the
South
Recliners
,
and
from
the
North
point
in
North
Incliners
.
Then
find
the
height
of
the
Style
,
and
place
of
the
Substyle
:
thus
,
Keep
your
Gnomonical
Semi-Circle
in
its
position
:
But
turn
the
Quadrant
of
Altitude
about
on
the
Zenith
point
till
the
lower
end
of
it
comes
to
the
degree
of
the
Horizon
opposite
to
the
degree
it
was
placed
at
before
,
and
turn
about
the
Globe
till
the
Colure
cut
the
Quadrant
of
Altitude
above
the
Horizon
in
the
number
of
degrees
the
Plane
Reclines
from
the
Zenith
;
so
shall
the
Colure
cut
the
Gnomonical
Semi-Circle
at
Right
Angles
;
Then
count
the
degrees
contained
between
the
middle
of
the
Gnomonical
Semi-Circle
and
the
Colure
,
for
that
number
of
degrees
is
the
distance
of
the
Substyle
from
a
Perpendicular
line
in
the
middle
of
your
Plane
,
and
must
be
placed
Westwards
of
the
said
Perpendicular
,
if
your
Plane
decline
from
the
South
East-wards
;
or
Eastwards
,
if
your
Plane
decline
from
the
South
Westwards
.
Then
observe
how
many
degrees
are
contained
between
the
Semi-Circle
and
the
Pole
;
for
that
number
of
degrees
is
the
number
of
degrees
that
the
Style
is
to
be
Elevated
above
the
Substyle
.
Example
.
Here
at
London
I
would
make
a
Dyal
upon
a
Plane
Declining
from
the
South
Eastwards
30.
degrees
,
and
Reclining
from
the
Zenith
20.
degrees
;
Londons
Latitude
is
51½
degrees
:
Therefore
,
Having
on
the
Plane
discribed
a
Semi
Circle
,
&c.
as
was
directed
Prob.
4.
I
Rectifie
the
Globe
,
Quadrant
of
Altitude
,
Colure
,
and
Hour
Index
,
as
by
the
same
Probleme
▪
and
bring
the
lower
end
of
the
Quadrant
of
Altitude
to
30.
degrees
from
the
North
point
of
the
Horizon
towards
the
West
,
because
that
is
the
degree
opposite
to
the
degree
of
the
Planes
Declination
,
viz
▪
to
30
degrees
from
the
South
Eastwards
,
And
I
bring
the
middle
of
the
Gnomonical
Semi
Circle
to
20.
degrees
of
the
Quadrant
of
Altitude
counted
from
the
Zenith
downwards
towards
the
Horizon
,
and
the
ends
of
the
Gnomonical
Semi
Circle
to
the
degrees
of
Azimuth
the
Plane
lies
in
in
the
Horizon
,
viz.
to
30.
degrees
from
the
East
point
Northwards
,
and
to
30.
degrees
from
the
West
point
Southwards
,
so
shall
11.
degrees
10.
minutes
of
the
Gnomonical
Semi
Circle
be
comprehended
between
the
Quadrant
of
Altitude
and
the
Brasen
Meridian
:
These
11.
degrees
10.
minutes
shews
that
the
12
a
clock
line
is
distant
from
the
Perpendicular
A
B
11.
degrees
10.
minutes
:
and
because
the
Plane
Declines
to
the
Eastwards
,
therefore
the
12
a
clock
line
must
stand
on
the
West
side
the
Plane
11.
degrees
10
,
minutes
.
Then
to
find
all
the
Fore
Noon
Hour
lines
,
I
turn
the
Globe
East-wards
till
the
Index
points
to
|
11
|
a
clock
,
or
till
15
,
degr.
of
the
Equator
pass
through
the
Meridian
,
and
find
the
Colure
cut
the
Gnomonical
Semi-Circle
in
|
15.
8
|
counted
from
the
middle
of
the
Gnomonical
Semi
Circle
.
|
10
|
18.
56
|
9
|
22.
37
|
8
|
26.
52
|
7
|
32.
37
|
6
|
42.
5
|
5
|
62.
43
|
And
these
are
the
distances
of
the
Fore
Noon
Hour
lines
;
to
which
distances
you
may
set
Pricks
on
the
West
side
the
Semi
Circle
of
the
Plane
,
viz.
from
B
to
C.
The
After
Noon
Hour
lines
are
found
by
bringing
the
Colure
again
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
for
then
turning
the
Globe
Westwa●s
till
the
Index
points
to
|
1
|
a
clock
,
or
till
15
degr.
of
the
Equator
pass
throug
the
Meridian
,
I
find
the
Colure
cut
the
Gnomon
,
Semi-Circle
in
|
5.
45
|
counted
from
the
middle
of
the
Gnomon
.
Semi-Circle
.
|
—
|
—
|
2
|
2.
54
|
3
|
20.
52
|
4
|
64.
36
|
Having
drawn
the
Hour-lines
,
I
remove
the
Quadrant
of
Altitude
to
the
degree
of
the
Horizon
opposite
to
the
degree
it
was
at
before
,
viz.
to
30.
degrees
from
the
South
Westwards
,
which
is
so
much
as
the
Plane
declines
Eastwards
;
But
I
let
the
Gnomonical
Semi
Circle
stand
as
it
did
:
And
turning
about
the
Globe
till
the
Colure
cut
the
Quadrant
of
Altitude
in
20.
degrees
counted
from
the
Horizon
upwards
,
viz.
the
degrees
of
Reclination
,
I
find
18.
degrees
40.
minutes
contained
between
the
middle
of
the
Gnomonical
Semi
Circle
and
the
Brasen
Meridian
,
which
is
the
distance
of
the
Substyle
from
the
Perpendicular
;
And
I
find
the
Gnomonical
Semi
Circle
cut
the
Colure
in
13.
degrees
49.
minutes
from
the
Pole
,
which
is
the
Height
that
the
Style
must
be
raised
over
the
Substyle
;
Therefore
I
prick
off
in
the
Semi
Circle
on
the
Plane
,
the
distance
of
the
Substyle
18.
degrees
40.
minutes
from
the
Perpendicular
Westwards
;
because
this
Plane
declines
Eastwards
:
And
from
the
Center
A
,
I
draw
through
that
prick
the
line
A
E
,
which
shall
be
the
Substyle
,
and
from
this
Substyle
(
either
way
)
I
count
in
the
Semi
Circle
on
the
Plane
13
▪
degrees
49.
minutes
,
and
there
make
a
Prick
:
Then
from
the
Center
A
,
I
draw
through
that
Prick
the
line
A
F
,
to
represent
the
Style
or
Gnomon
:
Then
I
let
fall
the
Perpendiculer
F
G
upon
the
Substyle
A
G
;
So
is
a
Triangle
made
;
which
if
it
be
erected
Perpendicularly
upon
the
Substyle
A
G
,
the
Style
A
F
shall
be
Parallel
to
the
Axis
of
the
World
,
and
cast
a
shadow
upon
the
Hour
of
the
Day
.
Having
made
this
Dyal
,
you
have
made
four
several
Dyals
,
whereof
this
is
one
:
And
his
opposite
,
viz.
North
Declining
Westwards
30.
degrees
Inclining
to
the
Horizon
70.
degrees
is
another
.
The
South
Declining
Westwards
30.
degrees
Reclining
from
the
Zenith
20.
degrees
is
another
:
And
his
opposite
,
viz.
North
Declining
Eastwards
30.
degrees
Inclining
to
the
Horizon
70.
degrees
is
the
other
.
PROB.
XIII
.
To
make
a
Dyal
upon
a
Declining
Inclining
Plane
.
THe
Precepts
for
making
these
Dyals
are
delivered
in
the
foregoing
Probleme
:
Therefore
we
shall
at
first
come
to
an
Example
.
I
would
make
a
Dyal
upon
a
Plane
in
Londons
Latitude
Declining
from
the
South
Westwards
25.
degrees
and
Inclining
towards
the
Horizon
by
the
space
of
an
Arch
containing
14.
degrees
.
Having
first
discribed
on
the
Plane
a
Semi
Circle
,
as
was
directed
Prob.
4.
I
rectifie
the
Globe
,
Quadrant
of
Altitude
,
Colure
,
and
Hour
Index
,
as
by
the
same
Probleme
,
and
bring
the
lower
end
of
the
Quadrant
of
Altitude
to
the
degree
of
the
Planes
Declination
,
viz.
to
25.
degrees
counted
from
the
South
Westwards
,
and
the
ends
of
the
Gnomonical
Semi
Circle
to
the
degree
of
Azimuth
the
Plane
lies
in
,
viz.
to
25.
degrees
from
the
West
Northwards
,
and
the
middle
of
the
Gnomonical
Semi
Circle
to
the
degree
of
the
Planes
Inclination
,
viz.
14.
degrees
counted
from
the
Zenith
downwards
on
the
Quadrant
of
Altitude
,
Then
counting
the
degrees
of
the
Gnomonical
Semi
Circle
contained
between
the
middle
of
the
same
and
the
Brasen
Meridian
,
I
find
5.
degrees
30.
minutes
:
These
5.
degrees
30.
minutes
shews
the
distance
of
the
12
a
clock
line
from
the
Perpendicular
;
Therefore
I
number
in
the
Semi
Circle
discribed
on
the
Plane
,
from
the
Perpendicular
Westwards
,
(
Because
the
middle
of
the
Gnomonical
Semi
Circle
lies
Westwards
on
the
Globe
)
from
the
Meridian
▪
And
for
finding
all
the
Fore-Noon
Hour-distances
I
turn
the
Globe
East-wards
till
the
Index
points
to
|
11
|
a
clock
,
or
till
15
degr.
of
the
Equa
.
pass
throug
the
Meridian
,
and
find
the
Colure
cut
the
Gnomon
,
Semi-Circle
in
|
20.
5
|
counted
from
the
middle
of
the
Gnomon
.
Semi-Circle
.
|
10
|
36.
57
|
9
|
56.
24
|
8
|
76.
31
|
And
these
are
the
distances
of
all
the
Fore
Noon
Hour
lines
;
to
which
several
distances
I
make
pricks
on
the
West
side
the
Semi
Circle
on
the
Plane
,
viz.
from
B
to
C.
The
After
Noon
Hour
lines
are
found
by
bringing
the
Colure
again
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
For
then
turning
the
Globe
Westwards
till
the
Index
points
to
|
1
|
a
clock
,
or
till
15.
degrees
of
the
Equator
pass
through
the
Meridian
,
I
find
the
Colure
cut
the
Gnomonical
Semi-Circle
in
|
6.
20
|
counted
from
the
middle
of
the
Gnomonical
Semi
Circle
.
|
2
|
18.
2
|
3
|
28.
45
|
4
|
39.
56
|
5
|
52.
30
|
6
|
67.
19
|
7
|
84.
13
|
And
these
are
the
distances
of
the
After
Noon
Hour
lines
,
which
I
also
prick
down
at
their
respective
distances
from
the
Perpendicular
Eastwards
,
viz.
from
B
towards
D
on
the
Plane
;
and
by
drawing
lines
from
the
Center
A
through
all
the
Pricks
,
I
have
all
the
Hour
lines
that
this
Plane
will
admit
of
.
Having
made
this
Dyal
you
have
also
four
Dyals
made
;
as
well
as
in
the
former
Probleme
:
For
this
is
one
▪
and
its
opposite
viz.
North
declining
Eastwards
25.
degrees
Reclining
76.
degrees
is
another
;
The
South
declining
Eastwards
25.
degrees
inclining
14
▪
degrees
is
another
;
and
its
opposite
,
viz.
North
declining
Westwards
25.
degrees
Reclining
76.
degrees
is
another
;
PROB.
XIV
.
To
find
in
what
Place
of
the
Earth
any
manner
of
Plane
that
in
your
Habitation
is
not
Horizontal
,
shall
be
Horizontal
.
IT
was
said
in
the
Preface
that
all
manner
of
Planes
however
scituate
are
Parallel
to
some
Country
or
other
on
the
Earth
:
Therefore
all
manner
of
Planes
are
indeed
Horizontal
Planes
;
and
the
distances
of
the
Hour
lines
to
be
●●scribed
on
them
may
be
found
as
the
distances
of
the
Hour
lines
of
the
Horizontal
Dyal
in
Prob.
3.
It
rests
now
to
learn
in
what
place
of
the
Earth
any
Plane
that
is
not
Horizontal
in
your
Habitation
shall
become
Horizontal
:
And
for
help
of
your
understanding
herein
,
Take
these
following
Rules
.
1.
If
your
Plane
be
Erect
Direct
North
,
or
South
,
it
shall
be
an
Horizontal
in
the
same
Longitude
at
90.
degrees
distance
on
the
Meridian
,
(
counted
from
the
Zenith
of
your
Place
,
)
through
the
Equinoctial
.
See
an
Example
of
this
in
Prob.
3.
where
I
have
reduced
an
Erect
Dyrect
Dyal
▪
to
an
Horizontal
.
Thus
an
Erect
Plane
under
the
Pole
is
an
Horizontal
under
the
Equator
;
and
an
Erect
Direct
in
80.
degrees
North
Latitude
is
in
the
same
Longitude
an
Horizontal
at
10.
degrees
South
Latitude
:
An
Erect
Direct
in
70.
degrees
North
Latitude
,
is
in
the
same
Longitude
,
an
Horizontal
at
20.
degrees
South
Latitude
:
and
so
to
any
other
degrees
of
Latitude
(
as
aforesaid
)
till
you
come
to
45.
degrees
Latitude
▪
where
an
Erect
is
an
Horizontal
,
and
an
Horizontal
an
Erect
▪
Only
as
the
Hour
lines
of
the
Horizontal
(
being
〈◊〉
downwards
)
are
numbred
from
the
right
hand
towards
the
left
,
in
the
Erect
Direct
Dyal
they
are
numbred
from
the
left
hand
towards
the
Right
.
2.
If
your
Pla●●
be
Erect
Declining
,
it
shall
be
an
Horizontal
Plane
at
that
point
on
the
Globe
which
is
against
the
degree
of
Declination
,
found
in
the
Horizon
.
But
note
,
If
your
Plane
declines
Westwards
,
the
Sun
comes
sooner
to
the
Meridian
of
it
,
then
to
the
Meridian
of
the
Place
where
it
becomes
an
Horizontal
Plane
;
and
that
by
so
many
Hours
or
minutes
as
the
degrees
of
the
difference
of
Longitude
between
the
two
Places
converted
into
Time
amounts
to
.
If
it
declines
Eastwards
,
the
Sun
comes
so
much
later
to
the
Meridian
of
it
:
And
for
this
Cause
(
though
the
making
this
Dyal
be
the
same
with
an
Horizontal
Dyal
for
another
Place
,
yet
in
Respect
of
Time
)
there
will
be
a
difference
between
them
.
Example
.
I
would
make
the
South
Dyal
Declining
East
27.
degrees
,
as
in
Prob.
9.
by
the
Plane
of
the
Horizon
:
First
I
seek
in
what
Place
of
the
Earth
it
shall
become
an
Horizontal
Plane
:
Thus
,
I
Elevate
the
Pole
of
the
Globe
51½
degrees
above
the
Horizon
,
and
bring
the
Vernal
Colure
to
the
Meridian
,
then
I
count
from
the
South
point
in
the
Horizon
Eastwards
27.
degrees
,
and
on
the
point
on
the
Globe
directly
against
those
27.
degrees
I
make
a
prick
for
the
Place
where
a
Plane
that
declines
27.
degrees
from
the
South
Eastwards
at
London
shall
be
Horizontal
;
or
which
is
all
one
,
this
Declining
Plane
at
London
shall
ly
in
the
Horizon
of
that
Prick
:
This
Prick
for
distinction
sake
we
shall
hereafter
call
the
Horizontal
Place
:
Then
by
Prob.
1.
of
the
Second
Book
,
I
examine
the
Latitude
and
Longitude
of
this
Horizontal
Place
,
and
find
Latitude
33.
40.
South
;
and
Longitude
from
the
Colure
33.
degrees
,
which
is
the
difference
of
Longitude
between
London
and
the
Horizontal
Place
:
which
being
converted
into
Time
by
allowing
for
every
15.
degrees
1.
hour
of
Time
,
gives
2
hours
12.
minutes
that
the
Sun
comes
sooner
to
the
Meridian
of
the
Horizontal
Place
,
then
to
the
Meridian
of
the
Plane
at
London
:
so
that
when
it
is
12
a
clock
there
,
it
will
be
but
9.
a
clock
48.
minutes
here
;
when
12
a
clock
here
,
it
will
be
2
a
clock
12.
minutes
There
,
&c.
Having
thus
found
in
what
Longitude
from
London
and
Latitude
this
Plane
is
Parallel
to
the
Horizon
,
I
seek
the
distances
of
the
Hour-lines
upon
the
Planes
of
the
Horizon
Thus
,
I
Elevate
the
Pole
of
the
Globe
to
the
Height
of
the
Pole
in
the
Horizontal
Place
,
viz.
33.
degrees
40
,
minutes
,
and
bring
the
Horizontal
Place
on
the
Globe
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
Then
I
examine
the
degree
of
the
Horizon
the
Colare
cuts
,
and
find
it
19¾
from
the
South
Westwards
.
This
19¾
degrees
respresents
the
Meridian
line
of
the
Horizontal
Place
:
And
also
the
Substylar
line
here
at
London
;
Therefore
this
19¾
degrees
I
count
from
the
Perpendicular
A
B
of
the
Plane
,
and
from
the
Center
A
draw
the
line
A
G
through
them
;
Because
from
this
line
on
the
Plane
all
the
Hour
lines
must
be
numbred
,
and
not
(
as
all
along
hitherto
)
from
the
Perpendicular
of
the
Plane
,
Then
turning
the
Globe
East-wards
till
the
Index
of
the
Hour
Circle
points
to
|
11
|
a
clock
,
or
till
15.
degr.
of
the
Equator
pass
through
the
Meridian
,
I
find
the
Colure
cut
the
Horizon
in
|
10.
2
|
from
the
Meridian
.
|
10
|
0.
45
|
9
|
6.
12
|
8
|
15.
25
|
7
|
26.
11
|
6
|
40.
30
|
5
|
60.
0
|
And
these
are
the
distances
of
the
Forenoon
Hour
lines
:
which
distances
I
transfer
by
pricks
to
the
Plane
.
But
as
in
Prob.
9.
I
sought
the
distances
from
the
Perpendicular
on
the
Plane
,
so
now
in
this
Case
(
as
was
said
before
)
I
seek
them
from
the
Substyle
,
and
through
these
pricks
I
draw
lines
from
the
Center
,
as
in
other
Dyals
,
and
these
lines
shall
be
the
Fore
Noon
Hour
lines
.
To
find
the
Afternoon
Hour
distances
,
I
bring
the
Horizontal
Place
on
the
Globe
again
to
the
Meridian
,
and
the
Index
of
the
Hour
Circle
to
12.
and
turning
the
Globe
Westwards
till
the
Index
points
to
|
1
|
a
clock
,
or
till
15
degr.
of
the
Equator
pass
through
the
Meridian
,
I
find
the
Colure
cut
the
Horizon
i●
|
31.
5
|
counted
from
the
Meridian
.
|
2
|
46.
32
|
3
|
68.
5
|
4
|
95.
37
|
And
these
are
the
distances
of
all
the
Afternoon
Hour
lines
;
which
I
also
transfer
to
the
Plane
,
counting
them
from
the
Substyle
,
and
draw
lines
from
the
Center
A
through
these
distances
;
and
these
lines
shall
be
all
the
Afternoon
Hour
lines
.
Then
from
the
Substyle
I
count
the
degrees
and
minutes
of
the
Latitude
of
the
Horizontal
Place
,
viz.
33.
degrees
40.
minutes
,
and
through
these
degrees
and
minutes
I
draw
the
line
A
F
from
the
Center
A
,
for
the
Style
:
Then
from
the
Style
I
let
fall
the
Perpendicular
F
G
upon
the
Substyle
,
so
is
there
a
Triangle
made
;
which
if
it
be
erected
Perpendicularly
upon
the
Substyle
A
G
,
the
Style
A
F
shall
be
Parallel
to
the
Axis
of
the
World
,
and
cast
a
shadow
upon
the
Hour
of
the
Day
.
3.
If
your
Plane
be
a
Direct
Recliner
,
Seek
in
the
Longitude
of
your
Place
the
Complement
to
90.
of
your
Planes
Reclination
▪
For
there
a
Direct
Recliner
becomes
an
Horizontal
Plane
.
4.
If
your
Plane
be
a
Declining
Recliner
:
The
Globe
and
Quadrant
of
Altitude
Rectified
,
Bring
your
Habitation
on
the
Terrestrial
Globe
to
the
Meridian
,
and
the
Quadrant
of
Altitude
to
the
Declination
,
as
by
the
second
Rule
in
this
Probleme
;
and
count
upwards
on
the
Quadrant
of
Altitude
the
Reclination
,
and
there
make
a
prick
on
the
Globe
by
the
side
of
the
Quadrant
of
Altitude
,
for
at
that
prick
on
the
Globe
the
Declining
Recliner
shall
become
an
Horizontal
Plane
.
Then
examine
the
Latitude
of
that
prick
as
by
Prob.
1.
of
the
second
Book
,
and
the
difference
of
Longitude
,
as
by
Prob.
9.
of
the
third
Book
:
And
convert
the
difference
of
Longitude
into
Time
,
by
allowing
for
every
15.
degrees
1.
hour
:
Time
,
for
every
degree
4
,
minutes
Time
,
and
so
proportionably
,
so
shall
you
know
what
Hours
and
Minutes
the
Sun
comes
sooner
or
later
to
the
Meridian
of
your
Habitation
then
to
the
Meridian
of
that
Place
where
it
becomes
an
Horizontal
Plane
:
Sooner
,
if
the
Globe
were
turned
Eastwards
;
but
Later
if
it
were
turned
Westwards
.
Having
thus
found
out
where
this
Plane
becomes
Horizontal
,
make
your
Dyal
to
this
Plane
,
as
by
the
second
Rule
in
this
Probleme
:
Find
also
the
Style
as
is
there
directed
.
5.
If
your
Plane
be
a
Declining
Incliner
,
The
Globe
and
Quadrant
of
Altitude
Rectified
,
Bring
the
Colure
to
the
Meridian
,
and
the
Quadrant
of
Altitude
to
the
degree
of
the
Horizon
opposite
to
the
degree
of
the
Planes
Declination
,
and
count
upwards
on
the
Quadrant
of
Altitude
the
degrees
of
Inclination
,
and
make
a
〈◊〉
there
;
For
in
the
〈◊〉
of
that
prick
(
found
as
by
〈◊〉
〈◊〉
,
of
the
Second
Book
)
that
Declining
In
〈◊〉
shall
become
an
Horizontal
Plane
.
Then
find
the
Latitude
and
difference
of
Longitude
of
this
〈◊〉
▪
by
the
〈◊〉
〈◊〉
and
make
a
●yal
to
that
〈◊〉
by
the
second
〈◊〉
in
this
Probleme
.
Find
also
the
Style
as
therein
is
directed
.
PROB.
XV.
To
make
a
Dyal
on
the
Ceeling
of
a
Room
,
where
the
Direct
Beams
of
the
Sun
never
come
.
FInd
some
convenient
place
in
the
Transum
of
a
Window
to
place
a
smal
round
peece
of
Looking-Glass
,
about
the
bigness
of
a
Groat
,
or
less
;
so
as
it
may
ly
exactly
Horizontal
:
The
point
in
the
middle
of
this
Glass
we
will
marke
A
,
and
for
distinctions
sake
(
with
Mr
Palmer
)
call
it
Nodus
:
Through
this
Nodus
you
must
draw
a
Meridian
line
on
the
Floor
,
Thus
:
Hang
a
Plumb
line
in
the
Window
exactly
over
Nodus
,
and
the
shadow
that
that
Plumb
line
casts
on
the
Floor
just
at
Noon
will
be
a
Meridian
line
;
Or
you
may
find
a
Meridian
line
otherwise
,
as
by
the
Preface
.
Having
drawn
the
Meridian
line
on
the
Floor
:
find
a
Meridian
line
on
the
Ceeling
,
thus
:
Ho●d
a
Plumb
line
to
the
Ceeling
,
over
that
end
of
the
Meridian
line
next
the
Window
;
If
the
Plumbet
hang
not
exactly
on
the
Meridian
line
on
the
Floor
,
remove
your
hand
on
the
Ceeling
one
way
or
other
,
as
you
see
cause
till
it
do
hang
quietly
just
over
it
:
and
at
the
point
where
the
Plumb
line
touches
the
Ceeling
make
a
mark
,
as
at
B
;
that
mark
B
shall
be
directly
over
the
Meridian
line
on
the
Floor
:
then
remove
your
Plumb
line
to
the
other
end
of
the
Meridian
line
on
the
Floor
,
and
find
a
point
on
the
Ceeling
directly
over
it
,
as
you
,
did
the
former
point
,
as
at
C
,
and
through
those
two
points
B
and
C
on
the
Ceeling
strain
and
strike
a
line
blackt
with
Smal
Cole
or
any
other
Culler
(
as
Carpenters
do
,
)
and
that
line
B
C
on
the
Ceeling
shall
be
a
Meridian
line
,
as
well
as
that
on
the
Floor
:
Then
examine
the
Altitude
of
the
Equinoctial
,
as
by
Prob.
6.
of
the
Second
Book
you
did
the
Meridian
Altitude
of
the
Sun
;
and
fasten
a
string
just
on
the
Nodus
,
and
remove
that
string
in
the
Meridian
line
on
the
Ceeling
till
it
have
the
same
Elevation
in
a
Quadrant
,
that
the
Equinoctial
hath
in
your
Habitation
;
and
through
the
point
where
the
string
touches
the
Meridian
line
in
the
Ceeling
shall
a
line
be
drawn
at
right
Angles
with
the
Meridian
,
to
represent
the
Equinoctial
line
.
Thus
in
our
Latitude
the
Elevation
of
the
Equator
being
38½
degrees
;
I
remove
the
string
fastned
to
the
Nodus
forwards
or
backwards
in
the
Meridian
line
of
the
Ceeling
,
till
the
Plumb
line
of
a
Quadrant
,
when
one
of
the
sides
are
applyed
to
the
string
,
falls
upon
38½
degrees
:
and
then
I
find
it
touch
the
Meridian
line
at
D
in
the
Ceeling
:
therefore
at
D
I
make
a
mark
and
through
this
mark
strike
the
line
D
E
(
as
before
I
did
the
Meridian
line
)
to
cut
the
Meridian
line
at
Right
Angles
:
This
line
shall
be
the
Equinoctial
line
.
Then
I
place
the
Center
of
the
Semi-Circle
of
Position
upon
Nodus
,
and
under-prop
it
so
that
the
flat
side
of
it
may
ly
Parallel
to
the
string
when
it
is
strained
between
the
Nodus
and
the
Equinoctial
,
and
also
so
as
the
string
may
ly
on
the
division
of
the
Semi-Circle
marked
o
,
when
it
is
help
up
to
the
Meridian
line
in
the
Ceeling
:
Then
removing
the
string
the
space
of
15.
degrees
in
the
Circle
of
Position
to
the
Eastwards
,
and
extending
it
to
the
Equator
on
the
Ceeling
,
where
the
string
touches
the
Equator
there
shall
be
a
point
through
which
the
1
a
clock
Hour-line
shall
be
drawn
:
and
Removing
the
string
yet
15.
degrees
further
to
the
Eastwards
in
the
Semi-Circle
of
Position
,
and
extending
it
also
to
the
Equator
,
where
it
touches
the
Equator
there
shall
be
a
point
through
which
the
2
a
clock
Hour-line
shall
be
drawn
:
Removing
the
string
yet
15.
degrees
further
to
the
Eastwards
in
the
Semi-Circle
of
Position
,
and
extending
it
to
the
Equator
,
there
shall
be
a
point
through
which
the
3
a
clock
Hour-line
shall
be
drawn
:
The
like
for
all
the
other
After-Noon
Hour
lines
;
so
oft
as
the
string
is
removed
through
15.
degrees
on
the
Semi-Circle
of
Position
,
so
oft
shall
it
point
out
the
After-Noon
distances
in
the
Meridian
line
on
the
Ceeling
.
The
scituation
of
the
Semi-Circle
of
Position
cannot
conveniently
be
shewn
in
this
Figure
,
unless
it
be
drawn
by
the
Rules
of
Perspective
;
Neither
if
it
were
would
it
suit
with
the
other
demonstrations
,
expect
they
were
drawn
by
the
same
Rules
also
;
which
to
do
would
be
hard
for
young
Learners
to
understand
:
Therefore
I
have
left
out
the
Semi-Circle
of
Position
in
this
Figure
and
refer
you
for
a
demonstration
thereof
to
the
sixth
Probleme
;
For
even
as
the
lines
drawn
through
every
15
,
degrees
of
the
Semi-Circle
there
,
denote
in
a
Contingent
line
the
distance
of
any
Hour
line
from
the
Meridian
line
,
even
so
a
line
drawn
through
every
15.
degrees
of
the
Semi-Circle
of
Position
posited
(
as
aforesaid
)
point
out
in
the
Equinoctial
line
on
the
Ceeling
the
distance
of
each
respective
Hour
line
from
the
Meridian
line
,
Having
thus
found
out
the
points
in
the
Equator
through
which
the
After-Noon
Hour-lines
are
to
be
drawn
,
I
may
find
the
Fore-Noon
Hour
distances
also
the
same
way
,
viz.
by
bringing
the
string
to
the
several
15.
degrees
on
the
West
side
the
Semi-Circle
of
Position
;
or
else
I
need
only
measure
the
distances
of
each
Hour
distance
found
in
the
Equator
from
the
Meridian
line
on
the
Ceeling
;
for
the
same
number
of
Hours
from
12
have
the
same
distance
in
the
Equinoctial
line
on
the
other
side
the
Meridian
both
Before
and
Afternoon
:
The
11
a
clock
Hour
distance
is
the
same
from
the
Meridian
line
with
the
1
a
clock
distance
on
the
other
side
the
Meridian
,
the
10
a
clock
distance
the
same
with
the
2
a
clock
distance
,
the
9
with
the
3
,
&c.
And
thus
the
distances
of
all
the
Hour
lines
are
found
out
on
the
Equator
.
Thus
upon
the
point
markt
for
each
Hour
distance
in
the
Equinoctial
line
on
the
Ceeling
,
I
discribe
the
Arches
I
,
II
,
III
,
IIII
,
as
in
the
Figure
,
and
finding
the
distance
from
the
Meridian
of
the
Hour-lines
of
an
Horizontal
Dyal
to
be
according
to
the
third
Probleme
.
Thus
The
|
1
|
a
clock
Hour-line
|
11.40
|
whose
Complement
90.
is
|
78.20
|
2
|
24.15
|
65.45
|
3
|
38.4
|
51.56
|
4
|
53.36
|
36.24
|
I
measure
in
a
Quadrant
of
the
same
Radius
with
those
arches
already
drawn
from
the
Equinoctial
line
for
the
|
1
|
a
clock
Hour
|
78.20
|
2
|
65.45
|
3
|
51.56
|
4
|
36.24
|
and
transfer
these
distances
to
the
Arches
drawn
on
the
Ceeling
:
For
then
straight
lines
drawn
through
the
mark
in
the
Arch
,
and
through
the
mark
in
the
Equator
,
and
prolonged
both
waies
to
a
convenient
length
,
shall
be
the
several
Hour-lines
(
a
foresaid
;
)
And
when
the
Sun
shines
upon
the
Glass
at
Nodus
,
its
Beams
shall
reflect
upon
the
Hour
of
the
Day
.
PROB.
XVI
.
To
make
a
Dyal
upon
a
solid
Ball
,
or
Globe
,
that
shall
shew
the
Hour
of
the
Day
without
a
Gnomon
.
THe
Equinoctial
of
this
Globe
,
or
(
which
is
all
one
)
the
middle
line
must
be
divided
into
24
equal
parts
,
and
marked
with
1
,
2
,
3
,
4
&c
to
12.
and
then
beginning
again
with
1
,
2
,
3
,
&c.
to
12.
Then
if
you
Elevate
one
of
the
Poles
so
many
degrees
above
an
Horizontal
line
as
the
Pole
of
the
World
is
Elevated
above
the
Horizon
in
your
Habitation
,
and
place
one
of
the
12s
directly
to
behold
the
North
,
and
the
other
to
behold
the
South
:
when
the
Sun
shines
on
it
the
Globe
will
be
divided
into
two
halfs
,
the
one
enlightened
with
the
Sun-shine
,
and
the
other
shadowed
:
and
where
the
enlightned
half
is
parted
from
the
shadowed
half
,
there
you
shall
find
in
the
Equinoctial
the
Hour
of
the
Day
;
and
that
on
two
places
on
the
Ball
;
because
the
Equinoctial
is
cut
in
two
opposite
points
by
the
light
of
the
Sun
.
A
Dyal
of
this
fort
was
made
by
Mr
John
L●●k
,
and
set
up
on
a
Composite
Columne
at
Leaden
Hall
Corner
in
London
,
in
the
Majoralty
of
Sr
John
Dethick
Knight
.
The
Figure
whereof
I
have
inserted
,
because
it
is
a
pretty
peece
of
Ingenuity
,
and
may
perhaps
stand
some
Lover
of
Ar●
in
stead
,
either
for
Imitation
,
or
help
of
Invention
.
PROB.
XVII
.
To
make
a
Dyal
upon
a
Glass
Globe
,
whose
Axis
shall
cast
a
shadow
upon
the
Hour
of
the
Day
.
FIrst
divide
the
Equinoctial
of
your
Globe
into
24
equal
parts
;
and
having
a
Semi-Circle
cut
out
of
some
Brass
plate
,
or
thin
Wood
to
the
same
Diameter
your
Globe
is
of
,
or
a
very
little
wider
:
Apply
this
Semi-Circle
to
the
Globe
,
so
as
the
upper
edge
of
each
end
of
the
Semi
Circle
may
touch
the
Poles
of
the
Globe
,
and
the
middle
of
the
Semi
Circle
may
at
the
same
edge
cut
through
some
division
made
in
the
Equinoctial
:
for
then
a
line
drawn
by
the
edge
of
the
Semi
Circle
thus
posited
shall
be
a
Meridian
line
;
The
same
way
you
must
draw
Meridian
lines
through
every
division
of
the
Equinoctial
,
and
set
figures
to
them
,
beginning
with
1
,
2
,
3
,
4
,
&c.
to
12
,
and
then
beginning
again
with
1
,
2
,
3
,
4
,
&c.
to
12
,
again
.
This
Globe
being
made
of
Glass
,
and
having
an
Axis
of
Wyer
passing
through
●t
from
Pole
to
Pole
,
will
be
an
Horizontal
Dyal
all
the
World
over
;
if
its
Axis
be
set
Parallel
to
the
Axis
of
the
World
in
the
same
Place
;
and
one
of
the
Meridians
marked
12
be
set
so
as
it
may
directly
behold
the
North
point
in
Heaven
,
and
the
other
the
South
point
in
Heaven
;
for
then
the
Axis
of
the
Globe
shall
cast
a
shadow
upon
the
Hour
of
the
Day
.
And
if
you
divide
the
upper
half
of
the
Glass
Globe
from
the
under
half
,
when
the
Axis
stands
Parallel
to
the
Axis
of
the
World
,
by
a
Circle
drawn
round
about
the
Globe
,
that
Circle
shall
represent
the
Horizon
;
and
the
Meridian
lines
drawn
on
the
Globe
shall
be
the
Hour
lines
,
and
have
in
the
Horizontal
Circle
the
same
distance
from
the
12
a
clock
line
that
the
same
respective
Hour
line
was
found
to
have
,
as
by
Prob.
3.
of
this
Book
.
But
because
the
shadow
of
this
Axis
will
not
be
discerned
through
the
Glass
Body
;
therefore
you
may
with
Water
and
white
Lead
ground
together
,
lay
a
Ground
on
the
Inside
of
the
under
half
of
the
Glass
to
the
Horizontal
Circle
(
as
Looking-glass
makers
do
their
Looking
Glasses
with
Tinfoil
)
for
then
the
shadow
will
appear
.
Such
a
Glass
Globe
Dyal
hath
the
Lord
Robert
Titchborn
standing
in
his
Garden
supported
by
Atlas
.
The
End
of
the
Fifth
Book
.
Here
follows
the
Ancient
STORIES
of
the
several
STARS
,
and
CONSTELLATIONS
.
Shewing
the
Poetical
Reasons
why
such
Various
Figures
are
placed
in
HEAVEN
.
Collected
from
Dr
HOOD
.
And
First
,
Of
the
Northern
Constellations
.
1.
URSA
MINOR
.
This
Constellation
hath
the
preheminence
,
because
it
is
neerest
of
all
the
rest
unto
the
North
Pole
;
And
is
called
of
the
Greeks
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
whereupon
the
Pole
is
called
the
Pole
Arctick
,
for
that
it
is
neer
unto
that
Constellation
.
It
is
also
called
Helice
minor
,
because
of
the
smal
revolution
which
it
maketh
round
about
the
Pole
:
or
rather
of
Elice
,
a
Town
in
Arcadia
,
wherein
Calysto
the
great
Bear
,
and
mother
to
the
less
,
was
bred
.
It
is
called
Cynosura
,
because
this
Constellation
,
though
it
carry
the
name
of
a
Bear
,
yet
it
hath
the
taile
of
a
Dog
:
Last
of
all
,
it
is
termed
Phoenice
,
because
that
Thales
,
who
first
gave
the
name
to
this
Constellation
,
was
,
a
Phoenician
:
And
therefore
the
Phoenicians
being
taught
how
to
use
it
in
their
Navigations
,
did
call
it
by
the
name
of
the
Country
wherein
Thales
was
born
.
It
consisteth
of
7.
stars
,
which
the
Latines
call
Septemtriones
;
because
by
their
continual
motion
,
those
seven
stars
do
as
it
were
wear
the
Heavens
.
The
Spaniards
call
them
all
Bosina
,
that
is
,
an
Horn
;
because
they
may
be
very
well
brought
into
that
form
;
whereof
that
which
is
in
the
end
of
the
tail
,
is
called
the
Pole-star
,
by
reason
of
the
neareness
thereof
unto
the
Pole
of
the
world
▪
for
it
is
distant
(
according
to
the
opinion
of
most
)
from
the
true
Pole
,
but
23.
deg.
30.
min.
The
Arabians
call
it
Alrukaba
:
And
of
the
Scythians
it
is
said
to
be
an
Iron
nail
,
and
is
worshipped
by
them
as
a
God
.
The
two
stars
that
are
in
the
sholders
of
the
Bear
,
are
called
Guards
,
of
the
Spanish
word
Guardare
,
which
is
to
behold
;
because
they
are
diligently
to
be
looked
unto
,
in
regard
of
the
singular
use
which
they
have
in
Navigation
.
The
reason
why
this
Constellation
was
brought
into
the
Heavens
,
is
diversly
set
down
,
and
first
in
this
manner
:
Saturn
having
received
of
the
Oracle
that
one
of
his
Sons
should
banish
him
out
of
his
kingdom
,
determined
with
himselfe
to
kill
all
the
men
children
that
he
should
beget
:
whereupon
he
gave
command
to
Ops
his
wife
,
being
then
great
,
that
she
should
shew
him
the
child
so
soon
as
ever
it
was
born
:
But
she
bringing
forth
Jupiter
,
and
being
greatly
delighted
with
his
hair
,
gave
the
child
unto
two
Nymphs
of
Crete
,
dwelling
in
the
mount
Dicte
;
whereof
this
was
one
,
and
was
called
Cynosura
;
the
other
was
Helice
.
Jupter
,
after
that
(
according
to
the
Oracle
)
he
had
bereft
his
Father
of
the
kingdom
,
in
recompence
of
their
paines
and
courtesie
,
translated
them
both
into
the
Heavens
,
and
made
of
them
two
Constellations
;
the
Lesser
Bear
,
and
the
Greater
Bear
.
Othersome
say
that
it
was
Arcas
,
the
son
of
Calysto
;
and
they
tell
the
tale
on
this
manner
.
Calysto
a
Nimph
of
singular
beauty
,
daughter
to
Lycaon
King
of
Arcadia
,
induced
by
the
great
desire
she
had
of
hunting
,
became
a
follower
of
the
Goddess
Diana
.
After
this
,
Jupiter
being
enamored
with
her
beauty
and
out
of
hope
,
by
reason
of
her
profession
,
to
win
her
love
in
his
own
person
,
counterfeited
the
shape
of
Diana
,
lay
with
Calysto
,
and
got
her
with
child
;
of
whom
was
born
a
son
,
which
was
called
Arcas
.
Diana
,
or
rather
Juno
,
being
very
much
offended
here-with
,
turned
Calisto
into
a
Bear
.
Arcas
her
son
at
the
Age
of
fifteen
,
hunting
in
the
woods
by
chance
lighted
upon
his
mother
in
the
shape
of
a
Bear
:
who
knowing
her
son
Arcas
,
stood
stil
,
that
he
might
come
near
unto
her
,
and
not
be
afraid
:
but
he
fearing
the
shape
of
so
cruel
a
Beast
,
bent
his
bow
of
purpose
to
have
slain
her
:
Whereupon
Jupiter
to
prevent
the
mischief
,
translated
them
both
into
Heaven
,
and
of
them
made
two
several
Constellations
:
unto
the
lesser
Bear
,
there
belongs
but
one
star
unformed
.
2.
URSA
MAIOR
,
the
Greater
Bear
,
called
also
of
the
Greeks
Arctos
,
and
Helice
,
consisteth
of
27.
stars
:
Among
the
which
,
those
seven
that
are
in
the
hinder
part
and
tail
of
the
Bear
,
are
most
observed
;
the
Latines
call
them
Pla●strum
;
and
of
our
men
they
are
called
Charles
Wayn
;
because
the
stars
do
stand
in
such
sort
,
that
the
three
which
are
in
the
tail
resemble
the
Horses
,
and
the
other
four
which
are
in
the
flank
of
the
Bear
,
stand
(
after
a
manner
)
like
the
Wheels
of
a
Waggon
,
or
Chariot
;
and
they
are
suposed
by
some
to
be
greater
then
the
Sun
.
The
reason
of
the
Translation
of
this
Constellation
into
the
Heaven
,
is
at
large
set
down
in
the
other
Constellation
,
and
therefore
needs
not
here
to
be
repeated
.
This
Constellation
was
first
invented
by
Nauplius
,
the
Father
of
Palamedes
the
Greek
:
and
in
great
use
among
the
Grecians
;
and
this
is
to
be
noted
both
in
this
and
the
former
Constellation
,
that
they
never
set
under
the
Horizon
,
in
any
part
of
Europe
:
which
though
it
fall
out
by
reason
of
their
scituation
in
the
Heavens
;
yet
the
Poets
say
,
that
it
came
to
pass
through
the
displeasure
and
hatred
of
Juno
;
who
for
that
she
was
by
Calisto
made
a
Cuckquean
,
and
they
notwithstanding
(
as
she
took
it
)
in
dispight
of
her
,
were
translated
into
Heaven
,
requested
her
brother
Neptune
,
that
he
should
never
suffer
those
Stars
to
set
within
his
Kingdom
:
To
which
request
Neptune
condiscended
;
so
that
in
all
Europe
they
never
come
neer
unto
the
Sea
,
or
touch
the
Horizon
.
If
any
one
marvel
,
that
(
seeing
she
hath
the
form
of
a
Bear
)
she
should
have
a
tail
so
long
;
Imagine
that
Jupiter
fearing
to
come
too
nigh
unto
her
teeth
,
laid
hold
on
her
tail
,
and
thereby
drew
her
up
into
heaven
;
so
that
she
of
her selfe
being
very
weighty
,
and
the
distance
from
the
Earth
to
the
Heaven
very
great
,
there
was
great
likelyhood
that
her
tail
must
stretch
.
The
unformed
stars
belonging
to
this
Constellation
are
eight
.
3
DRACO
,
the
Dragon
,
of
some
named
the
Serpent
;
of
others
the
Snake
,
by
the
Arabians
,
Aben
;
and
by
Junctinus
Florentinus
,
Vrago
;
because
he
windeth
his
tail
round
about
the
Ecliptick
Pole
;
it
containeth
31.
stars
.
This
was
the
Dragon
that
kept
the
Golden
Apples
in
the
Orchard
of
the
Hesperides
,
(
now
thought
to
be
the
Islands
of
Cape
de
Virde
)
and
for
his
diligence
and
watchfulness
,
was
afterwards
translated
into
heaven
:
Yet
others
say
that
he
came
into
Heaven
by
this
occasion
;
when
Minerva
withstood
the
Gyants
fighting
against
the
Gods
;
they
to
terrifie
her
,
threw
at
her
a
mighty
Dragon
;
but
she
catching
him
in
her
hands
,
threw
him
presently
up
into
Heaven
,
and
placed
him
there
,
as
a
memorial
of
that
her
resistance
.
Others
would
have
it
to
be
the
Serpent
Python
,
whom
Apollo
slew
,
after
the
Deluge
.
4.
CEPHUS
,
containeth
in
him
11.
stars
,
and
hath
two
unformed
.
This
was
a
King
of
the
Aethiopians
,
and
Husband
unto
Cassiopeia
,
and
father
of
Andromeda
,
whom
Perseus
married
.
He
was
taken
up
into
Heaven
,
with
his
wife
and
daughter
,
for
the
good
deeds
of
Perseus
his
son
in
law
;
that
he
and
his
whole
stock
might
be
had
in
remembrance
for
ever
.
The
Star
which
is
in
his
right
shoulder
,
is
called
by
the
Arabians
Alderahiemin
;
i.
e.
his
right
Arm.
5
BOOTES
,
the
driver
of
the
Oxen
(
for
so
I
suppose
the
name
to
signifie
,
rather
then
an
Herdsman
;
for
he
hath
not
his
name
because
he
hath
the
care
of
any
Cattle
,
but
only
because
he
is
supposed
to
drive
Charles
his
Wain
,
which
is
drawn
by
3.
Oxen
)
he
is
also
called
Arctophilax
,
the
keeper
of
the
Bear
,
as
though
the
care
of
her
were
committed
to
him
.
This
Constellation
consisteth
of
22
Stars
.
Some
will
have
Bootes
to
be
Areas
,
the
Son
of
her
who
before
was
turned
into
the
Great
Bear
;
and
they
tell
the
Tale
thus
:
Ly●aon
the
Father
of
Calisto
,
receiving
Jupiter
into
his
house
as
a
guest
,
took
Arcas
his
daughters
son
,
and
cut
him
in
pieces
;
and
among
other
Services
,
set
him
before
Jupiter
to
be
eaten
:
for
by
this
means
he
thought
to
prove
if
his
guest
were
a
God
,
as
he
pretended
to
be
.
Jupiter
perceiving
this
heinous
fact
,
overthrew
the
table
,
fired
the
house
with
lightning
,
and
turned
Lycaon
into
a
wolf
:
but
gathering
,
and
setting
together
again
the
limbs
of
the
child
,
he
commited
him
to
a
Nymph
of
Aetolia
to
be
kept
:
Arcas
afterwards
coming
to
mans
estate
,
and
hunting
in
the
woods
,
lighted
at
un-awares
upon
his
mother
,
transformed
by
Juno
into
the
shape
of
a
bear
,
whom
he
persued
into
the
Temple
of
Jupiter
Lycaeus
,
whereunto
by
the
law
of
the
Arcadians
,
it
was
death
for
any
man
to
come
.
For
as
much
therefore
as
they
must
of
likelyhood
be
both
slain
.
Calysto
by
her
son
,
and
he
by
the
Law
;
Jupiter
to
avoid
this
mischeif
,
of
meer
pitty
took
them
both
up
into
heaven
.
Unto
this
Constellation
belongeth
but
one
star
unformed
,
and
it
is
between
the
legs
of
Bootes
,
and
by
the
Grecians
it
is
called
Arcturus
,
because
of
all
the
stars
neer
the
great
Bear
named
Arctos
,
this
star
is
first
seen
neer
her
tail
in
the
evening
.
The
Poetical
invention
is
thus
.
Icarus
the
father
of
Erigone
,
having
received
of
the
God
Bacchus
a
Flagon
of
wine
,
to
declare
how
good
it
was
for
mortal
men
,
travelled
therewith
into
the
Territories
of
Athens
,
and
there
began
to
carouse
with
certain
shepheards
:
they
being
greatly
delighted
with
the
pleasantness
of
the
wine
,
being
a
new
kind
of
liquor
,
began
to
draw
so
hard
at
it
,
that
ere
they
left
off
,
they
were
past
one
and
thirty
;
and
in
the
end
,
were
fain
to
lay
their
heads
to
rest
.
But
coming
unto
themselves
again
,
and
finding
their
brains
scarce
in
good
temper
,
they
killed
Icarus
,
thinking
indeed
that
he
had
either
poysoned
them
,
or
at
the
least-wise
made
their
brains
introxicate
.
Erigone
was
ready
to
die
for
grief
,
and
so
was
Mera
,
her
little
dog
.
But
Jupiter
to
allay
their
grief
,
placed
her
father
in
Heaven
,
between
the
legs
of
Arctophilax
.
6.
CORONA
BOREA
,
the
Northern
garland
,
consisteth
of
eight
stars
;
yet
Ovid
saith
,
that
it
hath
nine
.
This
was
the
Garland
that
Venus
gave
unto
Ariadne
,
when
she
was
married
unto
Bacchus
,
in
the
Isle
Naxus
,
after
that
Theseus
had
forsaken
her
:
which
Garland
,
Bacchus
placed
in
the
Heaven
,
as
a
token
of
his
love
.
Novidius
will
have
it
to
be
the
Crown
of
the
Virgin
Mary
.
7.
ENGONASIS
:
This
Constellation
hath
the
name
,
because
it
is
expressed
under
the
shape
of
a
man
kneeling
upon
the
one
knee
,
and
is
therefore
by
the
Latines
called
Ingeniculum
.
It
containeth
29.
stars
,
and
wanteth
a
proper
name
,
because
of
the
great
diversity
of
opinions
concerning
the
same
.
For
some
will
have
it
to
be
Hercules
,
that
mighty
Conquerer
,
who
for
his
12.
labours
was
thought
worthy
to
be
placed
in
the
heaven
.
and
nigh
unto
the
Dragon
whom
he
overcame
.
Others
tell
the
tale
thus
:
That
when
the
Tyta●s
fought
against
the
Gods
,
they
for
fear
of
the
Gyants
,
ran
all
unto
the
one
side
of
the
heaven
:
whereupon
the
Heaven
was
ready
to
have
fallen
,
had
not
Hercules
together
with
Atlas
set
his
neck
unto
it
,
and
stayed
the
fall
:
and
for
this
desert
,
he
was
placed
in
the
Heaven
.
8
LYRA
,
the
Harp
,
it
containeth
10.
stars
;
whereof
thus
goeth
the
Fable
.
The
River
Nilus
swelling
above
his
banks
,
overflowed
the
Country
of
Aegypt
;
after
the
fall
whereof
there
were
left
in
the
fields
divers
kinds
of
living
things
,
and
amongst
the
rest
a
Tortois●
;
Mercury
,
after
the
flesh
thereof
was
consumed
,
the
sinews
still
remaining
,
found
the
same
,
and
striking
it
,
he
made
it
yeild
a
certain
sound
;
whereupon
he
made
an
Harp
like
unto
it
,
having
3.
strings
and
gave
it
unto
Orpheus
the
son
of
Cassiopea
.
This
Harp
was
of
such
excellent
sound
,
that
Trees
,
Stons
Fowls
,
and
wild
Beasts
are
said
to
follow
the
sound
thereof
.
After
such
time
therefore
that
Orpheus
was
slain
by
the
women
of
Thrace
,
the
Muses
by
the
good
leave
of
Jupiter
,
and
at
the
request
of
Apollo
,
placed
this
Harp
in
Heaven
.
Novidius
will
have
it
to
be
the
Harp
of
David
,
whereby
he
pacified
the
evil
spirit
of
Saul
.
This
Constellation
was
afterwards
called
Vultur
Cad●ens
,
the
falling
Grype
:
and
Falco
,
the
Falcon
;
or
Timpanum
,
he
Timbrel
.
9
OLOR
,
or
Cygnus
,
the
Swan
,
called
of
the
Caldaeans
Adigege
:
it
hath
17.
stars
:
of
this
Constellation
the
Poets
Fable
in
this
manner
.
Jupiter
being
overtaken
with
the
love
of
Laeda
,
the
wife
of
Tyndarus
King
of
Oebalia
,
and
knowing
no
honester
way
to
accomplish
his
desire
,
procured
Venus
to
turn
her selfe
into
an
Eagle
,
and
himself
he
turned
into
the
shape
of
a
Swan
:
Flying
therefore
from
the
Eagle
,
as
from
his
natural
enemy
,
that
earnestly
pursued
him
,
he
lighted
of
purpose
in
the
lap
of
Leda
,
and
,
as
it
were
,
for
his
more
safety
,
crept
into
her
bosome
.
The
woman
not
knowing
who
it
was
under
that
shape
,
but
holding
(
as
she
thought
)
the
Swan
fast
in
her
armes
,
fell
a
sleep
:
In
the
mean
while
Jupiter
enjoyed
his
pleasure
;
and
having
obtained
that
he
came
for
,
betook
him
again
unto
his
wings
;
and
in
memorial
of
his
purpose
(
attained
under
that
form
)
he
placed
the
Swan
among
the
stars
.
Ovid
calleth
this
Constellation
Milvius
,
the
Kite
,
and
telleth
the
tale
thus
.
The
Earth
being
greatly
offended
with
Jupiter
,
because
he
had
driven
Saturn
his
father
out
of
his
Kingdom
,
brought
forth
a
monstrous
Bull
,
which
in
his
hinder
parts
was
like
a
Serpent
;
and
was
afterwards
called
the
Fatal-Bull
;
because
the
Destinies
had
thus
decreed
,
that
whosoever
could
slay
him
,
and
offer
up
his
entrails
upon
an
Altar
,
should
overcome
the
eternal
Gods
.
Briarens
that
mighty
Gyant
,
and
ancient
enemy
of
the
Gods
overcame
the
Bull
,
and
was
ready
to
have
offered
up
his
entrails
according
to
the
decree
of
the
Destinies
:
But
Jupiter
fearing
the
event
,
commanded
the
Fowls
of
the
Air
to
snatch
them
away
:
which
although
to
their
power
,
they
endavoured
,
yet
there
was
none
of
them
found
so
forward
and
apt
to
that
action
as
the
Kite
,
and
for
that
cause
he
was
accordingly
rewarded
with
a
place
in
Heaven
.
Some
call
this
Constellation
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
that
is
,
the
Bird
:
others
call
it
Vultur●●
volans
,
the
Flying
Grype
:
It
is
also
called
Gallina
,
the
Hen.
Unto
this
Constellation
do
belong
two
unformed
stars
.
10.
CASSIOPEIA
,
She
consisteth
of
13.
Stars
.
This
was
the
Wife
of
Cepheus
,
and
mother
of
Andromeda
,
whom
Perseus
married
,
and
for
his
sake
was
translated
into
Heaven
,
as
some
write
.
Others
say
that
her
beauty
being
singular
,
she
waxed
so
proud
,
that
she
preferred
her self
before
the
Nereides
,
which
were
the
Nymphs
of
the
Sea
:
for
which
cause
,
unto
her
disgrace
,
and
the
example
of
all
others
that
in
pride
of
their
hearts
would
advance
themselves
above
their
betters
,
she
was
placed
in
the
Heaven
with
her
head
as
it
were
downwards
,
so
that
in
the
revolution
of
the
Heavens
,
she
seemeth
to
be
carried
head-long
.
11.
PERSEUS
,
he
hath
26.
Stars
.
This
was
the
Son
of
Jupiter
,
whom
he
in
the
likeness
of
a
Golden
shower
begat
upon
Danae
,
the
daughter
of
Acrisius
.
This
Perseus
coming
unto
mans
estate
,
and
being
furnished
with
the
Sword
,
Hat
,
and
Wings
of
his
brother
Mercury
,
and
the
Shield
of
his
sister
Minerva
,
was
sent
by
his
foster-father
Polidectes
,
to
kill
the
Monster
Medusa
,
whom
he
slew
;
and
cuting
off
her
head
,
carried
it
away
with
him
:
But
as
he
was
hastning
homeward
,
flying
in
the
Air
,
he
espied
Andromeda
the
daughter
of
Cepheus
and
Cassiopeia
,
for
the
pride
of
her
mother
,
bound
with
a
Chain
unto
a
Rock
,
by
the
Sea
side
there
to
be
devoured
by
a
Whale
:
Perseus
taking
notice
and
pitty
of
the
case
,
undertook
to
fight
with
the
Monster
,
upon
condition
that
Andromeda
might
be
his
Wife
;
to
be
short
,
he
delivered
Andromeda
,
married
her
,
and
returning
homeward
unto
the
Isle
Seriphus
▪
he
found
there
his
Grand-father
Acrisius
,
whom
by
mischance
,
and
unadvisedly
,
he
slew
with
a
quoit
:
(
or
as
Ovid
reporteth
,
with
the
terrible
sight
of
the
horrible
head
of
Medusa
,
not
knowing
that
it
was
his
Grand-father
:
but
afterwards
understanding
whom
he
had
slain
,
he
pined
away
through
extream
sorrow
:
whereupon
Jupiter
his
Father
pittying
his
grief
,
took
him
up
into
Heaven
and
there
placed
him
in
that
form
wherein
he
overcame
Medusa
,
with
the
sword
in
one
hand
,
and
the
head
of
Medusa
in
the
other
,
and
the
Wings
of
Mercury
at
his
Heels
.
This
Constellation
,
because
of
the
unluckiness
thereof
,
is
called
by
Astrologers
Cacodemon
,
(
i.
e.
)
Unlucky
,
and
Unfortunate
.
For
(
as
they
say
)
they
have
observed
it
,
that
whatsoever
is
born
under
this
Constellation
,
having
an
evil
Aspect
,
shall
be
stricken
with
sword
,
or
loose
his
Head
.
Novidius
saith
that
it
is
David
with
Goliah
his
head
in
the
one
hand
,
and
his
sword
in
the
other
.
The
unformed
Stars
belonging
unto
this
Constellation
,
are
three
.
12.
AURIGA
,
the
Waggoner
,
or
Carter
:
he
consisteth
of
14.
Stars
;
the
Arabians
call
him
Alaiot
;
the
Greeks
Heniochus
,
i.
e.
a
man
holding
a
bridle
in
his
hand
,
and
so
is
he
pictured
.
Eratostenes
affirmeth
him
to
be
Ericthonious
King
of
Athens
,
the
son
of
Vulcane
:
who
having
most
deformed
feet
,
devised
first
the
use
of
the
Wagon
or
Chariot
,
and
joyned
horses
together
to
draw
the
same
,
to
the
end
that
he
sitting
therein
,
might
the
better
conceal
his
deformities
.
For
which
invention
,
Jupiter
translated
him
into
the
Heavens
.
In
this
Constellation
there
are
two
other
particular
Constellations
to
be
noted
;
whereof
the
one
consisteth
but
of
one
Star
alone
,
which
is
in
the
left
shoulder
of
Auriga
,
and
is
called
Hircus
,
or
Capra
the
Goat
;
the
Arabians
call
it
Alhaioth
:
The
other
consisteth
of
two
little
Stars
a
little
beneath
the
other
,
standing
as
it
were
in
the
hand
of
Auriga
;
this
Constellation
is
●called
Haedi
,
the
Kids
.
The
tale
is
thus
;
Saturn
(
as
you
heard
before
)
had
received
of
the
Oracle
,
that
one
of
his
sons
should
put
him
out
of
his
Kingdom
,
whereupon
he
determined
to
devoure
them
all
:
Ops
by
stealth
conveyed
away
Jupiter
,
and
sent
him
to
Melissus
King
of
Crete
,
to
be
nourished
:
Melissus
having
two
daughters
,
Amalthaea
and
Melissa
,
committed
Jupiter
unto
their
Nursery
;
Amalthaea
had
a
Goat
that
gave
suck
unto
two
Kids
,
so
that
by
the
milk
of
this
Goat
,
she
nourished
Jupiter
very
well
.
To
requite
this
her
care
and
courtesie
,
Jupiter
(
after
he
had
put
his
Father
out
his
Kingdom
)
translated
her
Goat
and
her
two
Kids
,
into
Heaven
;
and
in
remembrance
of
the
Nurse
,
the
Goat
is
called
Capra
Amalthaea
.
Novidius
saith
,
that
when
Christ
was
born
,
and
his
birth
made
manifest
by
the
Angels
unto
the
Shepherds
,
one
of
them
brought
with
him
for
a
Present
,
a
Goat
and
two
young
Kids
;
which
in
token
of
his
good
will
,
were
placed
in
Heaven
.
13.
OPHIUCHUS
,
or
SERPENTARIUS
,
That
is
,
the
Serpent-bearer
.
This
Constellation
hath
no
proper
name
,
but
is
thus
entituled
,
because
he
holdeth
a
Serpent
in
his
hands
.
It
containeth
24.
Stars
.
Some
say
that
it
is
Hercules
,
and
report
the
tale
on
this
manner
Juno
being
a
great
enemy
to
Hercules
,
sent
two
snakes
to
kill
him
as
he
lay
sleeping
in
his
Cradle
:
but
Hercules
being
a
lusty
Child
(
for
Jupiter
had
spent
two
daies
in
begetting
him
)
without
much
ado
strangled
them
both
:
In
memorial
of
so
strange
an
event
,
Jupiter
placed
him
in
the
Heavens
,
with
a
Serpent
in
his
hands
,
14.
SERPENS
,
the
Serpent
of
Ophiuchus
,
which
consisteth
of
18.
Stars
.
Some
say
that
it
is
one
of
the
Serpents
that
should
have
slain
Hercules
in
his
Cradle
.
Novidius
saith
,
it
is
the
Viper
that
bit
Paul
by
the
hand
.
Others
deliver
the
tale
in
these
words
;
Glaucus
the
son
of
Minos
King
of
Crete
,
was
by
misfortune
drowned
in
a
Barrel
of
Honey
:
Minos
his
father
craved
the
help
of
Aesculaptus
the
Physitian
:
and
that
he
might
be
driven
per
▪
force
to
help
the
child
,
he
shut
him
up
in
a
secret
place
,
together
with
the
dead
carcass
:
whiles
Aesculapius
stood
in
a
great
maze
with
himself
what
were
best
to
be
done
,
upon
a
sudden
there
came
a
Serpent
creeping
towards
him
;
the
which
Serpent
he
slew
with
the
staff
which
he
had
in
his
hand
.
After
this
there
came
another
Serpent
in
,
bringing
in
his
mouth
a
certain
herb
,
which
he
laid
upon
the
head
of
the
dead
Serpent
,
whereby
he
restored
him
unto
life
again
.
Aesculapius
using
the
same
her●
,
wrought
the
same
effect
upon
Glaucus
.
Whereupon
(
after
that
)
Aesculapius
(
whom
some
affirm
to
be
Ophiuchus
)
was
placed
in
the
Heaven
,
and
the
Serpent
with
him
.
15.
SAGITTA
,
or
Telum
;
the
Arrow
or
Dart.
This
was
that
Arrow
wherewith
Hercules
slew
the
Eagle
or
Grype
that
fed
upon
the
Liver
of
Promotheus
,
being
tyed
with
chains
to
the
top
of
the
mount
Caucasus
;
and
in
memorial
of
that
deed
,
was
translated
into
Heaven
.
Others
will
have
it
to
be
one
of
those
Arrows
which
Hercules
at
his
death
gave
unto
Phyloctetes
,
upon
which
the
Destiny
of
Troy
did
depend
.
The
whole
Constellation
containeth
five
Stars
.
16.
AquILA
,
the
Eagle
,
which
is
called
Vultur
Volans
,
the
flying
Grype
:
It
hath
in
it
9.
Stars
.
The
Poetical
reason
of
this
Constellation
,
is
this
;
Jupiter
transforming
himself
into
the
form
of
an
Eagle
,
took
Ganimides
the
Trojan
Boy
,
whom
he
greatly
loved
,
up
into
Heaven
,
and
therefore
in
signe
thereof
(
because
by
that
means
he
performed
his
purpose
)
he
placed
the
figure
of
the
Eagle
in
the
Heaven
.
There
belong
unto
this
Constellation
6.
Stars
(
before
time
)
unformed
,
but
now
brought
into
the
Constellation
of
Antinous
.
But
whereupon
that
name
should
come
,
I
know
not
,
except
it
were
that
some
man
devised
it
there
to
curry
favour
with
the
Emperour
Adrian
,
who
loved
one
Antinous
Bithynicus
so
well
,
that
he
builded
a
Temple
in
his
honour
at
Mantinea
.
17.
DELPHINUS
,
the
Dolphin
:
It
containeth
10.
Stars
;
yet
Ovid
in
his
second
Book
de
Fastis
,
saith
that
it
hath
but
nine
.
Neither
did
the
ancient
Astronomers
attribute
unto
it
any
more
,
according
to
the
number
of
the
Muses
;
because
of
all
other
Fishes
,
the
Dolphin
is
said
to
be
delighted
with
Musick
.
The
tale
goeth
thus
concerning
this
Constellation
.
When
Neptune
the
God
of
the
Sea
greatly
desired
to
match
with
Amphitrite
,
she
being
very
modest
and
shame-faced
,
hid
her self
:
whereupon
he
sent
many
messengers
to
seek
her
out
,
among
whom
,
the
Dolphin
by
his
good
hap
,
did
first
find
her
;
and
perswaded
her
also
to
match
with
Neptune
:
For
which
his
good
and
trusty
service
,
Neptune
placed
him
in
the
Heaven
.
Others
say
,
that
when
Bacchus
had
transformed
the
Mariners
that
would
have
betrayed
him
,
into
Dolphins
,
he
placed
one
of
them
in
Heaven
,
that
it
might
be
a
lesson
for
others
to
take
heed
how
they
carried
any
one
out
of
his
way
,
contrary
both
to
his
desire
,
and
their
own
promise
.
Novidius
referreth
this
Constellation
unto
the
Fish
which
saved
Jonas
from
drowning
.
18.
EQUICULUS
,
is
the
little
Horse
,
and
it
consisteth
of
4.
Stars
.
This
Costellation
is
named
almost
of
no
Writer
,
saving
Ptolomeus
,
and
Alphonsus
,
who
followeth
Ptolomy
,
and
therefore
no
certain
tale
or
History
is
delivered
thereof
,
by
what
means
it
came
into
Heaven
.
19.
EquuS
ALATHS
,
the
Winged
Horse
,
or
Pegasus
,
it
containeth
20.
Stars
.
This
Horse
was
bred
of
the
blood
of
Medusa
,
after
that
Perseus
had
cut
off
her
head
,
and
was
afterwards
taken
and
tamed
by
Bellerophon
,
whiles
he
drank
of
the
River
Piren●
by
Corinth
,
and
was
used
by
him
in
the
conquest
of
Chimera
:
After
which
exploit
,
Bellerophon
,
being
weary
of
the
earthly
affaires
,
endevoured
to
fly
up
into
Heaven
:
But
being
amazed
in
his
flight
,
by
looking
down
to
the
earth
,
he
fell
from
his
horse
;
Pegasus
notwithstanding
continuing
his
course
,
(
as
they
feigne
)
entred
into
Heaven
,
and
there
obtained
a
place
among
the
other
Constellations
.
20.
ANDROMEDA
,
She
consisteth
of
23.
Stars
;
but
one
of
them
is
common
both
unto
her
,
and
Pegasus
,
This
was
the
daughter
of
Cepheus
and
Cassiopeia
,
and
the
Wife
of
Perseus
:
the
reason
why
Minerva
,
or
Jupiter
placed
her
in
the
Heavens
,
is
before
expressed
.
Novidius
referreth
this
Constellation
unto
Alexandria
the
Virgin
,
whom
S.
George
through
the
good
help
of
his
horse
,
delivered
from
the
Dragon
.
21.
TRIANGULUM
,
the
Triangle
,
called
also
Delt●ton
,
because
it
is
like
the
fourth
letter
of
the
Greeks
Alphabet
Δ
,
which
they
call
Delta
;
it
consisteth
of
four
stars
.
They
say
it
was
placed
in
Heaven
by
Mercury
,
that
thereby
the
head
of
the
Ram
might
be
the
better
known
.
Others
say
,
that
it
was
placed
there
in
honour
of
the
Geometricians
,
among
whom
,
the
Triangle
is
of
no
small
importance
.
Others
affirme
,
that
Ceres
in
times
past
requested
Jupiter
that
there
might
be
placed
in
Heaven
some
Figure
representing
the
form
of
Sicilie
,
an
Island
greatly
beloved
of
Ceres
,
for
the
fruitfulnesse
thereof
:
now
this
Island
being
triangular
,
(
at
her
request
)
was
represented
in
the
Heaven
under
that
form
.
Thus
much
concerning
the
Constellations
of
the
Northern
Hemisphear
.
Now
follow
the
Poeical
Stories
of
the
Constellations
of
the
Southern
Hemisphear
.
Secondly
,
Of
the
Southern
Constellations
.
1.
CETUS
,
the
Wha●●
,
it
is
also
called
the
Lion
,
or
Bear
of
the
Sea
.
This
is
that
monstrous
fish
that
should
have
devoured
Andromeda
,
but
being
overcome
by
Perseus
,
was
afterwards
translated
into
Heaven
by
Jupiter
,
as
well
for
a
token
of
Perseus
his
manhood
,
as
for
the
hugeness
of
the
fish
it self
.
This
constellation
consisteth
of
22.
Stars
.
2.
ORION
,
this
hath
38.
Stars
.
The
Poetical
reason
of
his
translation
into
the
Heaven
,
shall
be
shewn
in
the
Scorpion
,
amongst
the
Zodietical
Constellations
.
The
Ancient
Romans
called
this
Constellation
Jugala
;
because
it
is
most
pestiferous
unto
Cattel
,
and
as
it
were
the
very
cut-throat
of
them
.
There
are
bright
Stars
in
his
girdle
,
which
we
commonly
call
our
Ladies
yard
,
or
wa●d
.
Novidius
,
applying
this
sword
of
Orion
unto
Scripture
,
will
have
it
to
be
the
sword
of
Saul
,
afterwards
called
Paul
,
wherewith
he
persecuted
the
Members
of
Christ
:
which
after
his
conversion
was
placed
in
Heaven
.
In
his
left
shoulder
there
is
a
very
bright
Star
,
which
in
Latine
is
called
Bellatrix
,
the
Warriour
,
in
the
foeminine
gender
.
I
cannot
find
the
reason
except
it
be
this
;
that
Women
born
under
this
Constellation
shall
have
mighty
tongues
.
The
reason
of
the
Ox-hide
which
he
hath
in
his
hand
,
may
be
gathered
out
of
the
next
story
.
3.
FLUVIUS
,
the
River
;
it
comprehendeth
34.
Stars
.
It
is
called
by
some
Eridanus
,
or
Padus
;
and
they
say
that
it
was
placed
in
Heaven
in
remembrance
of
Phaeton
,
who
having
set
the
whole
World
on
fire
by
reason
of
misguiding
of
his
father
Phoebus
his
charriot
,
was
slain
by
Jupiter
with
a
thunder-bolt
,
and
tumbling
down
from
Heaven
,
fell
into
the
River
Eridanus
,
or
Padus
,
which
the
Italians
call
Po.
Others
say
that
it
is
Nylus
,
and
that
that
Figure
was
placed
in
the
Heaven
because
of
the
excellency
of
that
River
,
which
by
the
Divines
is
called
Gihon
;
and
is
one
of
the
Rivers
of
Paradice
.
Others
call
it
Flumen
Orionis
,
the
flood
of
Orion
;
and
say
,
that
it
was
placed
there
,
to
betoken
the
Off-spring
from
whence
Orion
came
:
for
the
tale
is
thus
reported
of
him
.
Jupiter
,
Neptune
,
and
Mercury
,
travelling
upon
the
earth
in
the
likeness
of
Men
,
were
requested
by
Hyreus
to
take
a
poor
lodging
at
his
House
for
a
Night
:
they
being
overtaken
with
the
evening
,
yeilded
unto
his
request
;
Hyreus
made
them
good
cheer
,
killing
an
Ox
for
their
better
entertainment
:
The
Gods
seeing
the
good
heart
of
the
old
man
,
willed
him
to
demand
what
he
would
in
recompence
of
his
so
friendly
cheer
.
Hyreus
and
his
Wife
being
old
,
requested
the
Gods
to
gratify
them
with
a
Son
.
They
to
fulfil
his
desire
,
called
for
the
hide
of
the
Ox
that
was
slain
,
and
having
received
it
,
they
put
it
into
the
Earth
,
and
made
water
into
it
all
three
together
,
and
covering
it
,
willed
Hyreus
within
ten
moneths
after
to
dig
it
out
of
the
Earth
again
;
which
he
did
,
and
found
therein
a
Man-child
;
whom
he
called
Ourion
,
ab
Urina
,
of
piss
;
although
afterwards
by
leaving
out
the
second
letter
,
he
was
named
Orion
.
At
such
time
therefore
as
he
was
placed
in
Heaven
,
this
flood
was
joyned
hard
to
his
heels
,
and
the
Ox
hide
wherein
the
Gods
did
piss
,
was
set
in
his
left
hand
,
in
memorial
of
his
Off-spring
.
4.
LEPUS
,
the
Hare
,
which
consisteth
of
12.
stars
.
This
Constellation
was
placed
in
Heaven
between
the
legs
of
Orion
,
to
signifie
the
great
delight
in
hunting
which
he
had
in
his
life
time
.
But
others
think
it
was
a
frivolous
thing
,
to
say
that
so
notable
a
fellow
as
Orion
would
trouble
himself
with
so
smal
and
timerous
a
beast
as
the
Hare
:
and
therefore
they
tell
the
tale
thus
.
In
times
past
there
was
not
a
Hare
left
in
the
Isle
D●r●s
:
a
certain
youth
therefore
of
that
Island
,
being
very
desirous
of
that
kind
of
beast
,
brought
with
him
from
another
Country
thereabout
,
an
Hare
great
with
young
;
which
when
she
had
brought
forth
,
they
in
time
became
so
acceptable
unto
the
other
Countrimen
,
that
every
one
almost
desired
to
have
and
keep
a
Hare
.
By
reason
whereof
,
the
number
of
them
grew
to
be
so
great
,
within
a
short
space
after
,
that
the
whole
Island
became
full
of
Hares
,
so
that
their
Masters
were
not
able
to
find
them
meat
:
whereupon
the
Hares
breaking
forth
into
the
fields
,
devoured
their
Corn.
Wherefore
the
inhabitants
being
bitten
with
hunger
,
joyned
together
with
one
consent
,
and
(
though
with
much
ado
)
destroyed
the
Hares
.
Jupiter
therefore
placed
this
Constellation
in
the
Heavens
as
well
to
express
the
exceeding
fearfulness
of
the
beast
,
as
also
to
teach
men
this
lesson
;
that
there
is
nothing
so
much
to
be
desired
in
this
life
,
but
that
at
one
time
or
an
other
it
bringeth
with
it
more
grief
then
pleasure
.
Some
say
,
that
it
was
placed
in
Heaven
at
the
request
of
Ganimedes
,
who
was
greatly
delighted
with
hunting
the
Hare
.
5.
CANIS
MAIOR
,
the
Great
Dog
,
it
consisteth
of
18.
Stars
.
It
is
called
Sirins
Canis
,
because
he
causeth
a
mighty
drought
by
reason
of
his
heat
.
This
is
the
Constellation
that
giveth
the
name
unto
the
Canicular
or
Dog-days
;
whose
beginning
and
end
is
not
alike
in
all
places
,
but
hath
a
difference
according
to
the
Country
and
Time
:
as
in
the
Time
of
Hypocrates
the
Phisitian
,
who
lived
before
the
time
of
Christ
400
,
years
,
the
Canicular
days
began
the
13.
or
14.
of
July
.
In
the
time
of
Avicenna
,
the
Spaniard
,
who
lived
in
the
year
of
our
Lord
1100.
the
Canicular
days
began
the
15
,
16
,
or
17.
of
July
.
In
our
Country
,
they
begin
about
S.
James-tide
,
but
we
use
to
account
them
from
the
6.
of
July
,
to
the
17.
of
August
;
which
is
the
time
when
the
Sun
beginneth
to
come
near
unto
,
and
to
depart
from
this
Costellation
.
Novidius
will
have
it
to
be
referred
to
Tobias
Dog
;
which
may
very
well
be
,
because
he
hath
a
tail
;
Tobias
Dog
had
one
;
as
a
certain
fellow
once
concluded
,
because
it
is
written
that
Tobias
his
Dog
fawned
upon
his
Master
,
therefore
it
is
to
be
noted
(
said
he
)
that
he
had
a
tail
.
The
Poets
say
,
that
this
is
the
Dog
whom
Jupiter
set
to
keep
Europa
,
after
that
he
had
stolen
her
away
,
and
conv●ied
her
into
Crete
,
and
for
his
good
service
was
placed
in
Heaven
.
Others
say
,
that
it
was
one
of
Orion
his
Dogs
.
There
belong
unto
this
Constellation
11.
Stars
unformed
.
6.
CANIS
MINOR
;
the
Lesser
Dog
;
this
of
the
Greeks
is
called
Procyon
,
of
the
Latines
Ante
Canis
;
it
containeth
but
two
Stars
.
Some
say
,
that
this
also
was
one
of
Orions
Dogs
,
Others
rather
affirm
it
to
be
Mera
,
the
Dog
of
Origone
,
or
rather
of
Icarius
her
father
,
of
whom
mention
is
made
in
the
Constellation
of
Bootes
,
and
Virgo
.
This
Dog
of
meer
love
to
his
Master
,
being
slain
,
as
is
aforesaid
,
threw
him self
into
the
River
Anygrus
,
but
was
afterward
translated
into
Heaven
with
Origone
.
Among
the
Poets
there
is
great
dissention
which
of
the
two
should
be
the
Dog
of
Origone
;
some
saying
one
,
and
some
the
other
,
and
therefore
they
do
many
times
take
the
one
for
the
other
.
7.
ARGO
NAVIS
,
the
Ship
Argo
,
which
comprehendeth
41.
Stars
;
this
is
the
Ship
wherein
Jason
did
fetch
the
Golden
Fleece
from
Colchis
,
which
was
afterward
placed
in
Heaven
as
a
memorial
,
not
only
because
of
the
great
Voyage
,
but
also
,
because
(
as
some
will
have
it
)
it
was
the
first
Ship
wherein
any
man
sayled
.
Their
reason
why
this
Ship
is
not
made
whole
is
,
that
thereby
men
might
be
put
in
mind
not
to
despair
,
albeit
that
their
Ship
miscarry
in
some
part
now
and
then
.
Some
avouch
it
to
be
the
Ark
of
Noe.
Novidius
saith
it
is
the
Ship
wherein
the
Apostles
were
,
when
Christ
appeared
unto
them
walking
on
the
Sea
.
In
one
of
the
Oars
of
this
Ship
,
there
is
a
great
Star
,
called
Canopus
,
or
Canobus
,
which
the
Arabians
called
Shuel
,
as
it
were
a
bone-fire
,
because
of
the
greatness
thereof
.
It
is
not
seen
in
Italy
,
nor
in
any
Country
on
this
side
of
Italy
.
Some
say
that
Canobus
the
Master
of
Menelaus
his
Ship
,
was
transformed
into
this
Star
.
8.
HYDRA
,
the
Hydre
;
that
hath
25.
Stars
,
and
two
unformed
.
9.
CRATER
,
the
Cup
,
or
standing
piece
;
that
hath
seven
Stars
.
Some
say
that
this
was
the
cup
wherein
Tagathon
,
that
is
,
the
chief
God
,
mingled
the
stuff
whereof
he
made
the
souls
of
Men.
10.
CORVUS
,
the
Crow
;
this
hath
seven
Stars
.
These
3.
Constellations
are
to
be
joyned
together
,
because
they
depend
upon
one
History
,
which
is
this
.
Upon
a
time
Apollo
made
a
solemne
feast
to
Jupiter
,
and
wanting
water
to
serve
his
turn
,
he
delivered
a
cup
to
the
Crow
(
the
bird
wherein
he
chiefly
delighted
)
and
sent
him
to
fetch
water
therein
:
The
Crow
flying
towards
the
River
,
espyed
a
Fig-tree
,
fell
in
hand
with
the
Figs
,
and
abode
there
till
they
were
ripe
:
In
the
end
,
when
he
had
fed
his
fill
of
them
,
and
had
satisfied
his
longing
,
he
bethought
himself
of
his
errand
,
and
by
reason
of
his
long
delay
,
fearing
a
check
,
he
caught
up
a
snake
in
his
bill
,
brought
it
to
Apollo
,
and
told
him
that
the
snake
would
not
let
him
fill
the
Cup
with
water
.
Apollo
seeing
the
impudency
of
the
bird
gave
him
this
gift
,
that
as
long
as
the
Figs
were
not
ripe
upon
the
Tree
,
so
long
he
should
never
drink
:
and
for
a
memorial
of
the
silly
excuse
that
he
made
,
he
placed
both
the
Crow
,
Cup
,
and
Snake
▪
in
Heaven
.
11.
CENTAURUS
,
the
Centaure
,
which
comprehendeth
37.
Stars
.
Some
say
,
that
this
is
Typhon
,
others
call
him
Chiron
,
the
Schoolmaster
of
those
three
excellent
men
,
Hercules
Achiles
,
and
Aesculapius
;
unto
Hercules
he
read
Astronomy
,
he
trained
up
Achilles
in
Musick
,
and
Aesculapius
in
Physick
:
and
for
his
upright
life
he
was
turned
into
this
Constellation
.
Yet
Virgil
calleth
Sagit●arius
by
the
name
of
Chiron
.
In
the
hinder
feet
of
this
Constellation
,
those
stars
are
set
which
are
called
the
Crosiers
,
appearing
to
the
Mariners
as
they
fail
towards
the
South
Sea
,
in
the
form
of
a
crosse
,
whereupon
they
have
their
name
.
The
four
stars
which
are
in
the
Garnish
of
the
Centaures
Spear
,
are
accounted
by
Proclus
as
a
peculiar
Constellation
,
and
are
called
by
him
Thyrsilochus
,
which
was
a
Spear
compassed
about
with
vine
leaves
:
but
they
are
called
by
Copernicus
and
Clavius
,
and
other
Astronomers
,
the
stars
of
his
Target
.
It
should
seem
that
they
were
deceived
by
the
old
translation
of
Ptolome
,
wherein
Scutum
is
put
for
Hasta
,
i.
e.
the
Target
,
for
the
Spear
,
as
it
is
well
noted
by
our
Countryman
M.
R.
Record
,
in
his
Book
intituled
The
Castle
of
knowledge
.
12
LUPUS
,
the
Wolf
,
or
the
beast
which
the
Centaùre
holdeth
in
his
hand
,
containeth
19.
stars
;
the
Poetical
reason
is
this
,
Chiron
the
Centaure
being
a
just
man
,
was
greatly
given
the
worship
of
the
Gods
:
for
which
thing
,
that
it
might
be
notified
to
all
posterity
,
they
placed
him
by
this
beast
,
which
he
seemeth
to
stick
and
thrust
through
with
his
Spear
,
(
as
it
were
)
ready
to
kill
for
sacrifice
.
13.
ARA
,
the
Alter
,
it
is
also
called
Lar
,
or
Thuribulum
,
i.
e
,
a
Chimney
with
the
fire
,
or
a
Censor
.
It
consisteth
of
seven
stars
,
and
is
affirmed
of
some
Poets
,
to
be
the
Alter
whereon
the
Centaure
was
wont
to
offer
up
his
sacrifice
.
But
others
tell
the
tale
thus
,
When
as
the
great
Gyants
called
the
Tytans
,
laboured
as
much
as
might
be
to
pull
Jupiter
out
of
Heaven
,
the
Gods
thought
it
good
to
lay
their
heads
together
,
to
advise
what
was
best
to
be
done
:
Their
conclusion
was
,
that
they
should
all
with
one
consent
joyn
hands
together
to
keep
out
such
fellows
:
and
that
this
their
league
might
be
confirmed
,
and
throughly
ratified
;
they
caused
the
Cyclops
,
(
which
were
work-men
of
Vulcan
)
to
make
them
an
Altar
:
about
this
Altar
all
the
Gods
assembled
,
and
there
sware
,
that
with
one
consent
they
would
withstand
their
enemies
;
afterwards
,
having
gotten
the
victory
,
it
pleased
them
to
place
this
Altar
in
Heaven
,
as
a
memorial
of
their
League
,
and
a
token
of
that
good
which
unity
doth
breed
.
14.
CORONA
AUSTRINA
,
the
South
Garland
,
it
hath
13.
Stars
.
Some
say
that
it
is
some
trifling
Garland
which
Sagittarius
was
wont
to
wear
,
but
he
cast
it
away
from
him
in
jest
,
and
therefore
it
was
placed
between
his
legs
:
others
call
it
the
Wheel
of
I
xion
,
whereupon
he
was
tormented
for
that
great
courtesy
he
would
have
offered
unto
Juno
,
thinking
indeed
to
have
gotten
up
her
belly
:
but
Jupiter
seeing
the
impudency
of
the
man
,
tumbled
him
out
of
Heaven
(
where
by
the
licence
of
the
Gods
he
was
somtime
admitted
as
a
guest
)
into
Hell
,
there
to
be
continually
tormented
upon
a
Wheel
.
The
Figure
of
which
Wheel
was
afterwards
placed
in
Heaven
,
to
teach
men
to
take
heed
how
they
be
so
saucie
to
make
such
courteous
proffers
unto
other
men
wives
.
The
Greeks
call
this
Constellation
by
the
name
of
Uraniscus
,
because
of
the
Figure
thereof
:
For
it
representeth
the
palate
or
roof
of
the
mouth
,
which
they
call
Uraniscus
.
15.
The
last
is
PISCIS
AUSTRINUS
,
or
Notius
,
the
South
Fish
,
which
comprehendeth
11.
Stars
besides
that
which
is
in
the
mouth
thereof
,
belonging
to
the
water
,
which
runneth
from
Aquarius
,
and
is
called
by
the
Arabians
Fomahant
.
The
reason
why
this
Fish
was
placed
in
the
Heaven
,
is
uncertain
:
yet
some
affirm
,
that
the
daughter
of
Venus
going
into
a
water
to
wash
her self
,
was
suddenly
transformed
into
a
fish
;
the
which
fish
was
afterwards
translated
into
Heaven
.
The
unformed
Stars
belonging
unto
this
Constellation
are
six
.
Thus
much
concerning
the
Constellations
of
the
Northern
and
Southern
Hemisphears
;
now
follow
the
Poetical
Stories
of
the
Zodiatical
Constellations
.
Thirdly
,
Of
the
Zodietical
Constellations
:
1.
ARIES
,
the
Ram
,
it
is
called
by
the
Greeks
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
,
it
containeth
in
it
13.
Stars
,
which
were
brought
unto
this
Constellation
by
Thyestes
,
the
son
of
Pelops
,
and
brother
of
Atreus
.
This
is
the
Ram
upon
which
Phrixus
,
and
Helle
his
sister
,
the
children
of
Athamas
did
sit
,
when
they
fled
from
their
step-mother
Ino
,
over
the
Sea
of
Hellespont
:
which
Ram
was
afterward
for
his
good
service
,
translated
into
Heaven
by
Jupiter
.
Others
say
,
that
it
was
that
Ram
which
brought
Bacchus
unto
the
spring
of
water
,
when
through
drought
he
was
likely
to
have
perished
in
the
desert
of
Lybia
.
Novidius
will
have
this
to
be
the
R●m
which
Abraham
offered
up
in
stead
of
his
son
Isaac
.
The
Star
tha●
is
first
in
the
head
of
the
Ram
,
is
that
from
whence
our
●ater
Astronomers
do
account
the
Longitude
of
all
the
rest
,
and
it
is
distant
from
the
head
of
Aries
,
in
the
tenth
Sphear
,
27.
degrees
53.
minutes
.
The
unformed
Stars
belonging
unto
this
Constellation
,
are
five
.
2.
TAURUS
,
the
Bull
,
which
consisteth
of
23.
stars
.
This
was
translated
into
Heaven
in
memorial
of
the
rape
committed
by
Jupiter
on
Europa
the
daughter
of
Agenor
,
King
of
Sidon
;
whom
Jupiter
in
the
likeness
of
a
white
Bull
stole
away
,
and
transported
into
Candia
.
Others
say
,
That
it
was
〈◊〉
the
daughter
of
Inacus
:
whom
Jupiter
loved
,
and
turned
into
the
form
of
a
Cow
,
to
the
intent
that
Juno
comming
at
unawares
,
should
not
perceive
what
a
part
he
had
playd
:
Jupiter
afterward
in
memorial
of
that
craftie
conveyance
,
placed
that
Figure
in
Heaven
;
The
reason
why
the
Poets
name
not
certainely
whether
it
be
a
Cow
or
a
Bull
,
is
because
it
wanteth
the
hinder
parts
;
yet
of
the
most
of
them
it
is
called
a
Bull.
In
the
Neck
of
the
Bull
there
are
certain
stars
standing
together
in
a
cluster
,
which
are
commonly
called
the
seven
Stars
;
although
there
can
hardly
he
discerned
any
more
then
six
.
These
are
reported
to
be
the
seven
daughters
of
Atlas
,
called
Atlan●iades
,
whereof
six
had
company
with
the
immortal
Gods
,
but
the
seventh
(
whose
name
was
Merope
)
being
married
unto
Sysiphus
a
mortal
man
,
did
herefore
withdraw
and
hide
her self
,
as
being
ashamed
that
she
was
not
so
fortunate
in
matching
her self
as
her
sisters
were
.
Some
say
,
that
that
star
which
is
wanting
is
Electra
,
the
eldest
daughter
of
Atlas
,
and
that
therefore
it
is
so
dim
,
because
she
could
not
abide
to
behold
the
destruction
of
Troy
;
but
at
that
time
and
ever
since
,
she
hid
her
face
.
The
reason
why
they
were
taken
up
into
Heaven
,
was
,
their
great
pittie
towards
their
father
,
whose
mishap
they
bewayled
with
continual
tears
.
Others
say
,
that
whereas
they
had
vowed
perpetual
virginity
,
and
were
in
danger
to
lose
it
,
by
reason
of
Orion
,
who
greatly
assayled
them
,
being
overtaken
,
with
their
love
;
they
requested
Jupiter
to
stand
their
friend
;
who
translated
them
into
stars
,
and
placed
them
in
that
part
of
Heaven
.
The
Poets
call
them
Pleiades
,
because
when
they
rise
with
the
Sun
,
the
Mariners
may
commit
themselves
to
the
Sea
.
Others
will
have
them
to
be
so
termed
a
pluendo
;
because
they
procure
rain
.
Others
give
them
this
name
,
of
the
Greek
word
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
,
because
they
be
many
in
number
.
They
be
also
called
Vergiliae
,
because
they
rise
with
the
Sun
in
the
Spring
time
:
likewise
Athoraiae
,
because
they
stand
so
thick
together
.
Our
men●call
them
by
the
name
of
the
seven
Stars
,
or
Brood
Hen.
The
Astronomers
note
this
as
a
special
thing
concerning
these
stars
,
that
when
the
Moon
and
these
stars
do
meet
together
,
the
eyes
are
not
to
be
medled
withall
,
or
cured
if
they
be
sore
:
their
reason
is
,
because
they
be
of
the
nature
of
Mars
and
the
Moon
.
Moreover
,
there
be
five
stars
in
the
face
of
the
Bull
,
representing
the
form
of
the
Roman
letter
V
,
whereof
one
(
which
is
the
greatest
)
is
called
the
Bull
's
Ey
.
They
be
called
Hyades
,
and
were
also
the
daughters
of
Atlas
,
who
so
long
bewayled
the
death
of
Hyas
their
brother
,
slain
by
a
Lion
,
that
they
died
for
sorrow
,
and
were
afterwards
placed
in
Heaven
for
a
memorial
of
that
great
love
they
bare
to
their
brother
.
The
ancient
Romans
call
the
Bul
's
Ey
,
Parilicium
,
or
Palelicium
;
of
Pales
their
goddesse
;
whose
feast
they
celebrated
after
the
conjunction
of
this
star
and
the
Sun
.
The
unformed
stars
belonging
unto
this
Constellation
,
are
eleven
.
3.
GEMINI
,
the
Twins
;
it
consisteth
of
18.
stars
.
The
Poets
say
they
are
Castor
and
Pollux
,
the
sons
of
Leda
,
brethren
most
loving
,
whom
therefore
Jupiter
translated
into
Heaven
.
Some
say
that
the
one
of
them
is
Appollo
,
and
the
other
Hercules
:
but
the
most
affirm
the
former
.
The
unformed
stars
of
this
Constellation
are
seven
,
whereof
one
is
called
Tropus
,
because
it
is
placed
next
before
the
foot
of
Castor
.
4.
CANCER
,
the
Crab
,
it
hath
9.
Stars
.
This
is
that
Crab
which
bit
Hercules
by
the
heele
as
he
fought
with
the
Serpent
Hydra
i●
the
Fen
Lerna
,
and
for
his
forward
service
,
was
placed
in
Heaven
by
Juno
,
the
utter
enemy
of
Hercules
.
In
this
Constellation
,
there
are
Stars
much
spoken
of
by
the
Poets
;
although
they
be
but
small
;
whereof
one
is
called
the
Crib
,
other
two
are
the
two
Asses
,
whereof
one
was
the
Asse
of
Bacchus
,
the
other
of
Vulcan
,
whereon
they
rode
to
battel
,
when
as
the
Gyants
made
war
with
the
Gods
;
with
whose
braying
and
strange
noise
,
the
Gyants
were
so
scared
upon
the
sudden
,
that
they
forsook
the
field
,
and
fled
.
The
Gods
getting
the
victory
,
in
tryumphing
manner
translated
both
the
Asses
,
and
their
manger
into
Heaven
.
The
unformed
stars
of
this
Constellation
are
four
.
It
is
called
animal
re●rogradum
,
for
when
the
Sun
cometh
into
his
Signe
,
he
maketh
Retrogradation
.
5.
LEO
,
the
Lyon
;
it
hath
27.
Stars
,
this
is
that
Lyon
which
Hercules
overcame
in
the
wood
of
Nemaea
and
was
placed
in
Heaven
in
remembrance
of
so
notable
a
deed
.
Novidius
saith
,
this
was
one
of
the
Lyons
which
were
in
the
den
into
which
Daniel
was
cast
,
and
was
therefore
placed
in
Heaven
,
because
of
all
other
he
was
most
friendly
unto
Daniel
.
In
the
breast
of
this
Constellation
is
that
notable
great
Star
,
the
light
whereof
is
such
,
as
that
therefore
it
is
called
by
Astronomers
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
or
Regulus
i.
e.
the
Victroy
,
or
little
King
among
the
rest
.
The
unformed
Stars
belonging
to
the
Lyon
are
eight
;
whereof
three
make
the
Constellation
which
is
now
called
Coma
Berenices
,
that
is
,
the
hair
of
Berenice
.
This
Constellation
was
first
found
out
and
invented
,
by
Canon
the
Mathematician
,
but
described
by
Calimachus
the
Poet.
The
occasion
of
the
Story
was
this
,
P●olomeus
Evergetes
having
married
his
sister
Berenice
,
was
shortly
after
enforced
to
depart
from
her
,
by
reason
of
the
wars
he
had
begun
in
Asia
:
whereupon
Berenice
made
this
vow
,
that
if
he
returned
home
again
in
safety
,
she
would
offer
up
her
hair
in
Venus
Temple
.
P●olome
returned
safe
;
and
Berenice
,
according
to
her
vow
,
cut
off
her
hair
and
hung
it
up
.
After
certain
daies
,
the
hair
was
not
to
be
found
;
whereupon
Ptolome
the
King
was
greatly
displeased
:
but
Canon
,
to
please
the
humor
of
the
King
,
and
to
curry
favour
with
him
,
perswaded
him
that
Venus
had
conveyed
the
hair
into
Heaven
.
Canon
attributeth
seven
Stars
unto
it
,
but
Ptolome
allotteth
it
but
three
,
because
the
other
be
insensible
,
6.
VIRGO
,
the
Virgin
,
it
hath
26.
Stars
.
This
is
affirmed
to
be
Justice
,
which
among
all
the
Gods
somtime
living
upon
the
Earth
,
did
last
of
all
forsake
the
same
,
because
of
the
wickedness
that
began
to
multiply
therein
,
and
chose
this
place
for
her
seat
in
Heaven
.
Others
say
,
that
it
was
Astraea
,
the
daughter
of
Astraeus
,
one
of
the
Gyants
that
were
called
Titans
,
who
fighting
against
the
Gods
,
Aftraea
took
their
parts
against
her
own
Father
,
and
was
therefore
after
her
death
commended
unto
the
Heavens
,
and
made
one
of
the
12.
Signes
.
Others
say
,
that
it
was
Erigone
,
the
daughter
of
Icarius
,
who
for
that
her
father
was
slain
by
certain
drunken
men
,
for
very
grief
thereof
did
hang
her self
:
but
Jupiter
taking
pitty
of
the
Virgin
for
her
natural
affection
,
translated
her
into
Heaven
.
In
her
right
wing
there
is
one
Star
of
special
note
,
which
by
the
Astronomers
is
called
Vindemeator
(
i.
e.
)
the
gatherer
of
Graps
.
This
was
Ampelos
the
son
of
a
Satyr
and
a
Nymph
,
and
greatly
beloved
of
Bacchus
,
unto
whom
in
token
of
his
love
,
Bacchus
gave
a
singular
fair
Vine
,
planted
at
the
foot
of
an
Elme
,
(
as
the
manner
was
in
old
time
.
)
But
Ampelos
in
Harvest
gathering
Graps
,
and
taking
little
heed
to
his
footing
,
fell
down
out
of
the
Vine
,
and
brake
his
neck
.
Bacchus
in
memorial
of
his
former
affection
,
translated
him
into
Heaven
,
and
made
him
one
of
the
principal
Stars
in
this
Constellation
.
There
is
another
great
Star
in
the
hand
of
the
Virgin
,
called
of
the
Latines
Spica
,
of
the
Greeks
Stachus
,
of
the
Arabians
Azimech
(
i.
e.
)
the
Ear
of
Corn
:
whereby
they
signify
,
that
when
the
Sun
cometh
to
this
Signe
,
the
Corn
waxeth
ripe
.
Albumazar
the
Arabian
,
and
Novidius
,
take
this
Constellation
for
the
Virgin
Mary
.
The
unformed
Stars
in
this
Constellation
,
are
six
.
7.
LIBRA
,
the
Ballance
,
it
containeth
8
Stars
.
Cicero
calleth
it
Jugum
the
Yoak
,
and
here
it
is
to
be
noted
,
that
the
Ancient
Astronomers
that
first
set
down
the
number
of
the
Constellations
contained
in
the
Zodiack
,
did
account
but
eleven
therein
,
so
that
the
Signe
which
now
is
called
Libra
,
was
heretofore
called
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
,
that
is
to
say
,
the
Claws
of
the
Scorpion
,
which
possesseth
the
space
of
two
whole
Signes
.
But
the
latter
Astronomers
,
being
desirous
to
have
12.
Signes
in
the
Zodiack
,
called
those
eight
whereof
the
Claws
of
the
Scorpion
do
consist
,
by
the
name
of
Libra
;
not
that
there
was
any
Poetical
Fiction
to
induce
them
thereto
,
but
only
moved
by
this
reason
,
because
the
Sun
joyning
with
this
Constellation
,
the
Day
and
the
Night
are
of
an
equal
length
,
and
are
(
as
it
were
)
equally
poyzed
in
a
pair
of
Ballance
.
Yet
(
as
I
remember
)
some
will
have
this
to
be
the
Ballance
wherein
Justice
,
called
also
Astraea
,
weighed
the
deeds
of
mortal
men
,
and
therein
presented
them
unto
Jupiter
.
It
hath
9.
unformed
Stars
appertaining
unto
it
.
8.
SCORPIO
,
the
Scorpion
;
called
of
the
Arabians
,
Alatrab
;
of
Cicero
,
Nepa
.
It
consisteth
of
21
,
Stars
.
The
Fiction
is
thus
.
Orion
the
son
of
Hyreus
greatly
beloved
of
Diana
,
was
wont
to
make
his
boast
,
that
he
was
able
to
overcome
what
beast
soever
was
bred
upon
the
Earth
:
The
Earth
being
moved
with
this
speech
brought
forth
the
Scorpion
,
whereby
Orion
was
stung
to
death
.
Jupiter
thereupon
(
at
the
request
of
the
Earth
,
)
translated
both
the
Scorpion
,
and
Orion
into
Heaven
;
to
make
it
a
lesson
for
ever
for
mortal
men
,
not
to
trust
too
much
unto
their
own
strength
▪
and
to
the
end
he
might
signify
the
great
enmity
between
them
,
he
placed
them
so
in
the
Heaven
,
that
whensoever
the
one
ariseth
,
the
other
setteth
;
and
they
are
never
both
of
them
seen
together
above
the
Horizon
at
once
:
Gulielmus
Postellus
will
have
it
to
be
the
Serpent
which
beguiled
Eve
in
Paradise
.
The
unformed
Stars
about
this
Scorpion
are
three
.
9.
SAGITTARIUS
,
the
Archer
.
It
hath
thirty
one
Stars
.
Touching
this
Signe
,
there
are
among
the
Poets
many
and
sundry
opinions
.
Some
say
that
it
is
Crocus
,
the
son
of
Puphen●
,
that
was
nurse
unto
the
Muses
.
This
Crocus
was
so
forward
in
learning
of
the
liberal
sciences
,
and
in
the
practise
of
feats
of
activity
,
that
the
Muses
entreated
Jupiter
that
he
might
have
a
place
in
Heaven
.
To
whose
request
Jupiter
inclining
,
made
him
one
of
the
12.
Signes
:
And
to
the
end
that
he
might
express
the
excellent
qualities
of
the
Man
,
he
made
his
hinder
parts
like
unto
a
Horse
,
thereby
to
signify
his
singular
knowledge
in
Horse-manship
:
and
by
his
Bow
and
Arrow
,
he
declared
the
sharpness
of
his
Wit.
Whereupon
the
Astrologers
have
this
conceit
,
that
he
that
is
born
under
Sagittarius
,
shall
attain
to
the
knowledge
of
many
Arts
,
and
be
of
prompt
wit
,
and
great
courage
.
Virgil
affirmeth
this
to
be
Chiron
the
Centaur
,
who
for
his
singular
learning
and
Justice
,
was
made
the
Master
of
Achilles
.
At
which
time
Hercules
coming
to
visit
him
(
for
he
had
heard
both
of
the
worthiness
of
the
School-master
,
and
of
the
great
hopes
of
the
Scholler
)
brought
with
him
his
quiver
of
Arrows
dipped
in
the
blood
of
the
Serpent
Hydra
;
but
Chiron
being
desirous
to
see
his
shafts
,
and
not
taking
heed
of
them
,
being
in
his
hand
,
let
one
of
them
fall
upon
his
foot
,
and
being
greatly
tormented
,
not
only
by
the
anguish
of
the
poyson
working
in
the
wound
,
but
much
more
because
he
knew
himself
to
be
immortal
,
and
his
wound
not
to
be
recovered
by
medicine
,
he
was
enforced
to
make
request
unto
the
Gods
,
that
he
might
be
taken
out
of
the
World
,
who
pittying
his
case
,
took
him
up
into
Heaven
,
and
made
him
one
of
the
12.
Signes
.
10.
CAPRICORNUS
,
the
Goat
,
it
consisteth
of
28.
Stars
.
The
Poets
say
,
that
this
was
Pan
,
the
God
of
the
Shepherds
,
of
whom
they
faign
in
this
manner
:
The
Gods
having
war
with
the
Gyants
,
gathered
themselves
together
into
Aegypt
,
Typhon
the
Gyant
pursued
them
thither
,
whereby
the
Gods
were
brought
into
a
quandary
,
that
well
was
he
that
by
changing
his
shape
might
shift
for
himself
,
Jupiter
turned
himself
into
a
Ram
:
Apollo
became
a
Crow
:
Bacchus
,
a
Goat
:
Diana
lurked
under
the
form
of
a
Cat
:
Juno
transformed
her self
into
a
Cow
:
Venus
into
a
Fish
:
Pan
leaping
into
the
River
Nilus
,
turned
the
upper
part
of
his
body
into
a
Goat
,
and
the
lower
part
into
a
Fish
.
Jupiter
wondring
at
his
strange
device
,
would
needs
have
that
Image
and
Picture
translated
into
Heaven
,
and
made
one
of
the
12.
Signes
.
In
that
the
hinder
part
of
this
Signe
is
like
a
Fish
,
it
betokeneth
that
the
latter
part
of
the
moneth
wherein
the
Sun
possesseth
this
Signe
,
inclineth
unto
Rain
,
11.
AQUARIUS
,
the
Waterman
.
It
hath
42.
Stars
,
whereof
some
make
the
Figure
of
the
Man
:
other
some
the
Waterpot
;
and
some
,
the
stream
of
water
that
runneth
out
of
the
pot
.
This
is
feigned
to
be
Ganimedes
the
Trojan
,
the
son
of
Oros
,
and
Callirhoe
whom
Jupiter
did
greatly
love
for
his
excellent
favour
and
beauty
,
and
by
the
service
of
his
Eagle
carried
him
up
into
Heaven
,
where
he
made
him
his
Cup
bearer
,
and
called
him
Aquarius
.
Others
notwithstanding
thinke
it
to
be
Deucallon
the
son
of
Prometheus
whom
the
Gods
translated
into
Heaven
,
in
remembrance
of
that
mighty
deluge
which
happned
in
his
time
,
whereby
mankind
was
almost
utterly
taken
away
from
the
face
of
the
earth
.
The
unformed
stars
belonging
unto
this
Signe
are
three
.
12.
PISCES
,
the
Fishes
:
these
,
together
with
the
line
that
knitteth
them
together
,
contain
24.
Stars
.
The
Poets
say
that
Venus
and
Cupid
her
son
coming
upon
a
certain
time
unto
the
River
Euphrates
,
and
sitting
upon
the
bank
thereof
,
upon
a
sudden
espied
Typhon
the
Gyant
,
that
mighty
and
fearfull
enemy
of
the
Gods
coming
towards
them
;
Upon
whose
sight
,
they
being
stricken
with
exceeding
fear
,
lept
into
the
River
,
where
they
were
received
by
two
Fishes
,
and
by
them
saved
from
drowning
.
Venus
for
this
good
turn
,
translated
them
into
Heaven
.
Gulielmus
Postellus
would
have
them
to
be
the
two
Fishes
wherewith
Christ
fed
the
5000.
men
.
The
unformed
stars
of
this
Constellation
,
are
four
.
Thus
have
I
breifly
run
over
the
Poetical
reasons
of
the
Constellations
:
It
remains
now
that
I
speak
of
the
Milky
way
.
VIA
LACTEA
,
or
Circulus
Lacteus
;
by
the
Latines
so
called
;
and
by
the
Greekes
Galaxia
;
and
by
the
English
the
Milkey
way
.
It
is
a
broad
white
Circle
that
is
seen
in
the
Heaven
,
in
the
North
Hemisphere
,
it
beginneth
at
Cancer
,
on
each
side
the
head
thereof
,
and
passeth
by
Auriga
,
by
Perseus
,
and
Cassiopeia
,
the
Swan
;
and
the
head
of
Capricorn
the
tayl
of
Scorpio
,
add
the
feet
of
Centaur
,
Argo
the
Ship
,
and
so
unto
the
head
of
Cancer
.
Some
in
a
sporting
manner
do
call
it
Wa●ling
street
;
but
why
they
call
it
so
,
I
cannot
tell
;
except
it
be
in
regard
of
the
narrownesse
that
it
seemeth
to
have
;
or
else
in
respect
of
that
great
high
way
that
lieth
between
Dover
and
S.
Albons
,
which
is
called
by
our
men
,
Watling
street
.
Ovid
saith
,
that
it
is
the
great
Causey
,
and
the
high
way
that
leadeth
unto
the
Pallace
of
Jupiter
;
but
he
alledgeth
not
the
cause
of
the
whiteness
:
belike
he
would
have
us
imagine
that
it
is
made
of
white
Marble
.
Others
therefore
alledge
these
causes
:
Jupiter
having
begotten
Mercury
of
Mai●●
the
daughter
of
Atlas
,
brought
the
child
when
he
was
born
,
to
the
breast
of
Juno
lying
a
sleepe
:
But
Juno
awaking
threw
the
child
out
of
her
lap
,
and
let
the
milke
run
out
of
her
breast
in
such
aboundance
that
(
spreading
it self
about
the
Heaven
)
it
made
that
Circle
which
we
see
.
Others
say
,
that
it
was
not
Mercury
,
but
Hercules
;
and
that
Juno
did
not
let
the
milke
run
out
of
her
breast
;
but
that
Hercules
suckt
them
so
earnestly
,
that
his
mouth
run
over
,
and
so
this
Circle
was
made
.
Others
say
;
that
Saturn
being
desirous
to
devour
his
children
,
his
wife
Ops
presented
him
with
a
stone
wrapped
in
a
clout
,
instead
of
his
child
:
This
stone
stuck
so
fast
in
Saturn
his
throat
as
he
would
have
swallowed
it
,
that
without
doubt
he
had
there-withall
been
choaked
,
had
he
not
been
relived
by
his
wife
,
who
by
pressing
the
milke
out
of
her
breasts
saved
his
life
:
the
milke
that
missed
his
mouth
(
whereof
you
must
suppose
some
sufficient
quantity
)
fell
on
the
Heavens
,
and
running
along
made
this
Circle
.
Dr
HOOD
Commenting
upon
Constellations
,
saith
;
The
Stars
are
brought
into
Constellations
,
for
Instruction
sake
,
things
cannot
be
taught
without
names
:
to
give
a
name
to
every
Star
had
been
troublesome
to
the
Master
and
for
the
Scholler
;
for
the
Master
to
devise
,
and
for
the
Scholler
;
to
remember
:
and
therefore
the
Astronomers
have
reduced
many
Stars
into
one
Constellation
,
that
thereby
they
may
tell
the
better
where
to
seek
them
;
and
being
sought
,
how
to
express
them
.
Now
the
Astonomers
did
bring
them
into
these
Figures
,
and
not
into
other
,
being
moved
thereto
by
these
three
reasons
:
first
these
Figures
express
some
properties
of
the
Stars
that
are
in
them
;
as
those
of
the
Ram
to
to
be
hot
and
dry
;
Andromeda
chained
betokeneth
imprisonment
,
the
head
of
Medusa
cut
off
signifieth
the
loss
of
that
part
:
Orion
with
his
terrible
and
threatning
gesture
,
importeth
tempest
and
terrible
effects
:
The
Serpent
,
the
Scorpion
,
and
the
Dragon
,
signify
poyson
:
The
Bull
insinuateth
a
melancholy
passion
:
The
Bear
inferreth
cruelty
,
&c.
Secondly
,
the
Stars
,
(
if
not
precisely
,
yet
after
a
sort
)
do
represent
such
a
Figure
,
and
therefore
that
Figure
was
assigned
them
:
as
for
example
,
the
Crown
,
both
North
and
South
:
the
Scorpion
,
and
the
Triangle
,
represent
the
Figures
which
they
have
.
The
third
cause
was
the
continuance
of
the
memory
of
some
notable
men
,
who
either
in
regard
of
their
singular
pains
taken
in
Astronomy
,
or
in
regard
of
some
other
notable
deed
,
had
well
deserved
of
Man-kind
.
The
first
author
of
every
particular
Constellation
is
uncertain
;
yet
are
they
of
great
antiquity
;
we
receive
them
from
Ptolomie
,
and
he
followed
the
Platonick●
;
so
that
their
antiquity
is
gre●a
▪
Moreover
we
may
perce●ve
them
to
be
ancient
by
the
Scriptures
,
and
by
the
Poets
.
In
the
38.
Chapter
of
Job
there
is
mention
made
of
the
Pleiades
,
Orion
,
and
Aucturus
,
and
Mazzaroth
,
which
some
interpret
the
12.
Signes
:
Job
lived
in
the
time
of
Abraham
,
as
Syderocrates
maketh
mention
in
his
Book
de
Commensurandis
locorum
distantiis
.
Now
besides
all
this
,
touching
the
reason
of
the
invention
o●
these
Constellations
,
the
Poets
in
setting
forth
those
Stories
,
〈◊〉
this
purpose
,
to
make
men
fall
in
love
with
Astronomy
:
When
Demosthenes
could
not
get
the
people
of
Athens
to
hear
him
in
a
matter
of
great
moment
,
and
profitable
for
the
Common-wealth
,
he
began
to
tell
them
a
tale
of
a
fellow
that
sold
an
Ass
;
by
the
which
tale
he
so
brought
on
the
Athenians
,
that
they
were
both
willing
to
hear
his
whole
Oration
,
and
to
put
in
practice
that
whereunto
he
exhorted
them
.
The
like
intent
had
the
Poets
in
these
Stories
:
They
saw
that
Astronomy
being
for
commodity
singular
in
the
life
of
man
,
was
almost
of
all
men
utterly
neglected
:
Hereupon
they
began
to
set
forth
that
Art
under
these
Fictions
;
that
thereby
such
as
could
not
be
perswaded
by
commodity
,
might
by
the
Pleasure
be
induced
to
take
a
view
of
these
matters
,
and
thereby
at
length
fall
in
love
them
.
For
commonly
note
this
,
that
he
that
is
ready
to
read
the
Stories
,
cannot
content
himselfe
therewith
,
but
desireth
also
to
know
the
Constellation
,
or
at
leastwise
some
principal
Star
therein
.
FINIS
.
A
Discourse
OF
THE
Antiquity
,
Progress
,
AND
Augmentation
OF
ASTRONOMIE
.
FIRST
it
seems
not
to
be
doubted
,
but
Articl
.
I.
that
there
was
some
kind
of
observation
of
Bodies
Coelestial
,
as
soon
as
Observation
Celestial
,
from
the
beginning
of
the
world
▪
though
rude
and
in-artificial
.
there
were
Men
:
considering
that
the
spectacle
which
the
Heavens
constantly
present
,
is
both
so
glorious
,
and
so
usefull
,
that
men
could
not
have
eyes
to
see
,
and
not
fix
them
attentively
and
considerately
thereupon
.
For
,
among
other
Apparences
,
when
they
saw
the
Sun
dayly
to
change
the
places
of
its
rising
and
setting
;
at
certain
times
of
the
Year
:
to
approach
neerer
to
the
Earth
in
its
Diurnal
arch
,
and
at
others
again
to
mount
up
to
a
height
much
more
sublime
and
remote
from
it
:
and
that
his
coming
neerer
to
the
Earth
made
Winter
,
and
his
remove
higher
made
Summer
:
we
say
,
when
they
beheld
these
things
;
doubtless
,
they
could
not
but
seriously
remark
and
consider
this
vicissitude
,
according
to
which
they
might
expect
the
Season
would
be
more
hard
,
or
mild
,
to
them
in
this
lower
Region
of
the
World
.
Again
,
so
admirably
various
did
the
Moon
appear
,
in
her
several
shapes
and
dresses
of
light
,
that
she
could
not
but
invite
mens
eyes
,
and
engage
them
to
frequent
Speculations
:
specially
when
she
assumed
those
various
faces
or
apparences
,
at
set
and
certain
Times
;
in
respect
whereof
it
came
to
pass
,
that
every
Nation
measured
their
times
and
Seasons
,
by
those
her
constant
and
periodical
circuits
;
and
this
,
because
those
periods
succeded
much
more
frequently
,
than
the
Erections
and
Depressions
of
the
Sun
.
To
these
,
we
may
add
that
beautifull
shew
of
the
Nightly
Stars
,
undergoing
likewise
their
Variations
,
according
the
variety
of
Seasons
;
and
more
particularly
that
bright
star
of
Lucifer
,
rising
sometimes
later
,
sometimes
earlier
,
and
sometimes
not
at
all
before
the
Sun
,
and
the
like
.
But
,
what
we
shall
principally
note
,
is
only
this
;
that
though
Mankind
was
long
,
before
they
came
to
make
inquiries
into
the
Causes
of
these
Coelestial
changes
and
variations
,
restrained
to
set
periods
:
yet
they
observed
them
from
the
very
first
Age
,
and
not
only
admired
,
but
also
accommodated
what
they
observed
,
to
the
uses
of
their
Lives
and
their
Successors
.
Here
it
might
not
be
fruitless
,
to
remember
,
that
PROMETHEUS
,
who
was
imagined
to
have
framed
the
first
Man
,
was
also
imagined
to
have
given
him
an
erected
Figure
,
and
sublime
Countenance
;
to
the
end
he
might
the
more
advantageously
advance
his
eyes
to
the
Heavens
,
and
contemplate
the
glory
and
motions
of
the
Coelestial
Lights
.
But
,
because
this
is
too
General
,
and
rude
a
way
of
observation
;
and
it
is
our
business
to
look
back
into
those
times
wherein
men
first
made
such
Observations
of
Sydereral
bodies
,
as
gave
hem
the
hint
and
occasion
of
reducing
them
to
Method
,
and
founding
the
principles
of
the
Art
,
or
science
of
Astronomy
,
thereupon
:
we
must
have
recourse
to
the
monuments
in
Sacred
Writ
,
for
the
understanding
of
that
obscure
matter
.
And
indeed
,
the
light
we
expect
from
Sacred
Leaves
,
would
Articl
.
II.
Sacred
records
examined
,
and
Moses
found
to
b
the
First
Astronomer
there
spoken
of
.
soon
be
clear
enough
to
discuss
all
the
darkness
,
wherein
the
Original
of
Astronomy
seems
involved
;
could
we
but
from
them
deduce
the
least
evidence
for
that
which
the
learned
Antiquarie
among
the
Jewes
,
Josephus
affirms
of
the
Sons
of
Seth
;
viz.
that
they
invented
the
science
of
the
Heavens
,
before
the
Flood
,
and
engraved
the
same
on
two
Pillars
,
the
one
of
Brick
,
the
other
lib.
1.
Ant.
c.
3.
of
Stone
,
that
so
it
might
be
preserved
in
the
one
,
in
case
the
fury
of
the
Deiuge
to
come
,
should
demolish
and
deface
the
other
:
or
if
there
remained
to
us
any
the
most
slender
testimony
of
the
Reason
he
there
gives
,
of
the
so
great
Longevity
of
men
in
those
cap.
4.
dayes
;
namely
,
that
the
duration
of
their
lives
was
sufficiently
long
,
to
perfect
the
knowledge
of
Astronomy
,
which
requires
full
600
Years
,
at
the
least
,
to
the
observation
of
all
the
Varieties
of
Coelestial
motions
:
Whereupon
He
notes
,
that
the
Great
Year
(
as
they
call
it
)
doth
consist
of
six
hundred
common
Years
;
the
vulgar
opinion
being
,
that
the
Celestial
Motions
do
continually
vary
,
Donec
consumpto
,
Magnus
qui
dicitur
,
Anno
,
Epigram
.
de
etat
,
Anim.
Rursus
in
〈◊〉
antiquum
redeant
vaga
sidera
cursum
,
Qualia
praeteriti
steterant
ab
origine
mundi
.
Again
,
the
business
might
be
deduced
from
not
long
after
the
Flood
,
if
in
Scripture
we
could
find
but
the
least
word
from
whence
might
be
argued
the
truth
of
what
the
same
Author
writes
;
namely
that
the
Egyptians
were
taught
Astronomy
,
by
Abraham
.
Probable
enough
it
is
,
we
confess
,
that
Berosus
and
others
,
quoted
aswell
by
Josephus
,
as
Eusebius
,
had
read
some
such
thing
in
some
Books
of
the
old
Rabbins
:
but
that
the
same
should
be
fetched
from
Holy
Writ
,
is
most
improbable
,
therein
being
no
mention
at
all
of
any
such
thing
.
Besides
,
there
are
pious
and
learned
Doctors
,
and
among
them
Salianus
,
who
will
not
allow
it
to
be
so
much
as
probable
,
that
Abraham
should
instruct
the
Egyptians
in
Astronomy
:
because
of
the
very
smal
time
of
his
stay
among
them
in
Egypt
.
It
is
written
indeed
,
that
Abraham
came
from
Ur
of
the
Chaldeans
:
but
not
that
he
received
Gen.
11.
Astronomy
from
the
Chaldeans
,
or
that
he
delivered
it
from
them
to
the
Egyptians
.
And
therefore
they
conclude
,
that
what
Josephus
said
of
Abrahams
reading
Astronomy
in
Egypt
,
may
with
more
probability
be
imputed
to
his
Great-grand
child
,
Joseph
.
Concerning
Him
,
therefore
,
we
read
(
in
truth
)
that
he
was
singularly
favourable
to
the
Priests
in
Egypt
,
at
such
time
,
as
all
the
rest
of
the
people
mortgaged
their
lands
to
the
King
,
for
bread
,
during
that
wofull
and
long
Famine
.
For
,
He
excepted
the
Lands
belonging
to
the
Priesthood
,
and
(
as
the
Text
saith
)
assigned
them
certain
portions
out
of
the
publick
Granaries
;
Gen.
47.
so
that
from
hence
may
be
proved
(
what
Aristotel
tells
us
,
from
other
Authority
)
that
amongst
the
Egyptians
,
the
most
ancient
Nation
,
the
Priests
were
exempted
from
labour
,
and
left
to
1.
Polit.
cap.
and
1
Metaph.
cap.
1.
the
easy
imploiment
of
their
minds
:
and
that
this
gave
them
occasion
to
invent
and
constitute
the
Mathematiques
:
and
yet
for
all
this
,
it
is
not
written
,
either
that
Joseph
taught
those
Egyptian
Priests
the
Mathematiques
,
or
that
they
taught
them
to
him
.
And
,
perhaps
that
Favour
He
shewed
the
Priests
,
was
an
argument
not
only
of
the
Respect
and
Veneration
,
born
them
by
the
King
and
all
his
people
;
but
also
of
his
particular
Gratitude
toward
them
;
in
that
He
,
who
had
been
bred
up
only
to
Sheppardry
and
Country
imployments
,
and
was
wholy
ignorant
of
all
Arts
and
Sciences
,
at
his
first
comming
among
them
being
afterwards
advanced
to
the
height
of
a
Courtier
,
and
lustre
of
a
Favorite
,
had
bin
instructed
by
them
in
something
more
noble
and
sublime
.
And
truely
,
the
Divine
Moses
,
not
long
after
admitted
into
the
same
Court
,
is
not
delivered
so
much
to
have
erudited
any
others
,
as
to
have
been
himself
learned
in
all
the
Wisdom
of
the
Egyptians
.
Nevertheless
,
considering
that
this
Wisedom
of
the
Egyptians
,
Act.
●7
doubtless
contained
the
Mathematiques
;
and
that
Astronomy
was
ever
esteemed
the
best
and
noblest
part
of
them
:
this
Erud●tion
of
Moses
seems
to
be
the
most
Ancient
monument
of
the
Science
of
the
Stars
,
that
can
be
found
in
Holy
Writ
.
Astronomy
,
you
see
,
is
of
great
Antiquity
,
even
upon
the
Records
of
Divinity
;
and
might
be
proved
of
much
greater
,
could
we
but
evince
(
what
some
alleage
)
that
the
History
of
Job
was
penn'd
by
Moses
,
as
living
a
good
while
after
him
.
Because
Job
there
mentions
Arcturus
,
Orion
,
and
the
Hyades
,
or
watery
Constellation
:
and
therefore
it
must
be
,
that
before
Cap.
9.
that
time
the
Stars
had
been
ranged
and
dispossed
into
certain
Asterisms
according
to
some
certain
method
or
artificial
Theory
then
in
use
.
But
,
be
the
time
of
his
life
never
so
uncertain
,
yet
we
may
certainly
observe
from
the
History
thereof
;
that
it
seems
Job
,
being
an
Alien
to
the
Hebrews
,
derived
his
knowledge
of
God
from
that
which
in
Scripture
is
called
,
Coelorum
Exercitus
,
the
Host
of
Heaven
.
Forasmuch
,
as
the
Invisible
things
of
God
are
not
so
well
learned
from
any
visible
things
of
Nature
,
or
the
effects
of
his
Wisedom
and
Power
,
as
from
the
Coelestial
Orders
and
therefore
Synesius
justly
calling
Astronomy
[
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
]
a
truly-venerable
Science
;
he
saith
,
that
it
advanceth
de
done
ad
Poeon
.
the
mind
to
somthing
of
greater
both
Antiquity
and
Nobility
,
viz.
ineffable
Theology
.
That
we
may
be
breef
,
and
only
touch
upon
that
sentence
in
the
Book
of
Wisedom
that
God
gave
to
Solomon
,
among
other
of
Natural
Science
,
to
understand
the
cap.
7.
Course
of
the
Year
and
the
Dispositions
of
the
Stars
:
if
any
thing
in
Sacred
Writ
doth
expressly
prove
the
Antiquity
of
Observations
Astronomical
,
and
the
founding
or
erecting
any
setled
Art
thereupon
;
it
must
be
that
,
of
which
the
Holy
Prophets
complaind
Esa.
47.
in
their
dayes
;
viz.
that
there
were
Chaldaeans
,
who
at
Babylon
,
did
contemplate
the
Stars
,
and
compute
the
Months
,
that
from
them
they
might
foretell
things
to
come
.
For
,
from
hence
we
understand
,
that
the
observation
of
the
Motions
of
Heavenly
bodies
was
a
certain
profest
Art
;
and
of
great
Antiquity
,
among
the
Chaldeans
.
In
the
Second
place
,
we
are
to
revolve
the
Records
of
Ethnick
Articl
,
3.
Ethnick
monuments
likewise
revolved
;
and
first
those
of
Fabulous
times
:
according
to
which
Coelus
is
found
the
most
ancient
Astronomer
:
lib.
3.
Authors
,
to
see
if
among
them
we
can
find
the
time
of
the
Nativity
of
Astronomy
.
Look
we
therefore
back
,
first
,
into
the
remains
of
that
part
of
Time
,
which
is
called
Obscure
,
or
Fabulous
;
because
possibly
enough
something
of
truth
,
concerning
our
enquiry
,
may
be
found
wrapt
up
in
the
darksome
shrouds
of
Fables
.
And
begin
we
at
the
most
ancient
of
Heathen
Gods
,
Coelus
,
in
Greek
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
who
,
as
Diodorus
Siculus
delivers
,
was
so
named
,
because
of
his
high
devotion
to
,
and
delight
in
the
observation
of
the
Stars
.
This
eminent
person
being
the
Father
of
many
Sons
as
Ailas
,
Saturnus
,
the
Titanes
,
and
among
those
especially
Hyperion
and
Japetus
;
it
is
lawfull
for
us
to
conjecture
,
that
led
by
his
example
,
his
whole
family
were
addicted
to
the
same
Study
,
For
seeing
,
that
Coelus
lived
in
Mauritania
,
not
and
after
him
his
Senns
.
1.
Atlas
,
who
taught
Astromy
to
his
Son
.
far
from
the
Ocean
;
and
thence
extended
his
Kingdom
not
only
over
all
Africa
,
but
also
into
a
considerable
part
of
Europe
:
it
is
well
known
that
his
Son
Atlas
,
who
succeded
him
in
the
same
Dominions
,
is
allowed
to
have
given
his
name
to
the
highest
Mountain
of
that
Country
;
only
because
he
had
made
his
observations
of
the
motions
of
the
Heavens
and
Stars
,
from
the
top
thereof
.
For
,
the
Ancients
in
those
dayes
,
as
the
vulgar
now
in
ours
,
imagined
the
arch
of
the
Heavens
to
be
so
little
distant
from
the
tops
of
great
Mountains
;
as
that
by
how
much
the
higher
any
man
ascended
on
those
hills
,
by
so
much
the
more
clearly
and
distinctly
might
he
behold
Coelestial
objects
.
To
this
,
Diodorus
,
Plinie
,
and
others
add
;
that
Atlas
lib.
3.
lib.
2.
cap.
8.
was
feigned
to
support
Heaven
on
his
Shoulders
,
only
because
He
had
framed
a
Sphear
,
wherein
the
whole
Heavenly
machine
was
strongly
represented
:
and
Clemens
Alexandrinus
observes
,
Astrom
.
1.
that
Hercules
,
being
both
Vates
and
Physicus
,
a
Prophet
and
Philosopher
,
was
reported
to
come
and
relieve
Atlas
(
his
great
Uncle
)
by
taking
the
vast
Burden
of
Heaven
upon
his
own
Shoulders
;
because
He
succeded
him
in
that
difficult
task
the
Study
,
or
science
of
Coelestial
bodies
.
Of
Hesperus
,
the
Sonne
Hisperus
.
of
Atlas
,
it
is
recorded
,
that
while
he
was
busy
in
speculating
the
Stars
,
on
the
top
of
the
same
mountain
,
he
was
snatched
away
by
the
violence
of
some
disease
,
and
could
never
be
found
:
and
that
thereupon
,
the
common
people
,
in
respect
of
his
piety
and
justice
,
gave
his
name
to
the
most
beautifull
and
resplendent
Star
,
which
is
also
called
Vesperugo
,
being
Venus
,
while
she
is
in
the
West
.
As
for
his
Sisters
,
called
both
Atlantiades
,
and
And
Daughters
,
the
Atlantides
and
Pleiades
,
from
one
of
whom
came
Mercury
.
1.
Astron.
Pleiades
;
these
likewise
gave
their
name
to
that
glomeration
of
Stars
,
which
are
visible
in
the
back
of
Taurus
:
and
of
one
of
them
,
named
Maia
,
was
born
the
Famous
Mercurius
,
said
to
have
brought
the
Science
of
the
Stars
first
into
Egypt
.
Whence
Marcilius
,
writing
of
the
Astronomy
of
the
Egyptians
,
Saies
of
Mercury
Tu
Princeps
,
Authorque
,
sacri
,
Cyllenie
,
tanti
.
&c.
Though
we
well
know
,
that
the
Ethiopians
,
allowing
the
Egyptians
to
be
no
other
,
but
one
of
their
Colonies
,
sent
abroad
to
find
room
to
subsist
in
,
contend
;
that
they
recieved
Astronomy
from
them
:
as
first
Diodorus
,
and
after
Lucian
have
observed
.
lib.
3.
lib.
de
Astrol.
5.
Tusculan
.
Here
it
is
well
worthy
our
commemoration
,
what
Cicero
saith
,
as
of
Atlas
and
Promotheus
,
so
also
Cepheus
,
a
King
of
the
Ethiopians
:
viz.
Neither
had
Atlas
been
beleived
to
have
sustain'd
Heaven
,
nor
Prometheus
to
have
been
chain'd
on
Caucasus
:
nor
Cepheus
with
his
Wife
,
Son-in
Law
,
and
Daughter
,
to
have
been
Stellified
:
had
not
their
Divine
cognition
of
Coelestial
bodies
first
occasioned
the
perpetuation
of
their
Names
in
the
disguise
of
Fables
.
To
return
to
Saturn
,
another
Sonne
of
Coelus
;
He
,
leaving
2.
Saturn
,
who
delivered
the
same
to
his
Son
.
Africa
,
and
reigning
only
in
Italy
,
Sicily
and
Crete
;
may
be
thought
to
have
prosecuted
his
Fathers
studies
,
no
less
than
the
former
:
and
we
have
this
argument
for
it
,
that
the
Slowest
of
all
the
Planets
bears
his
name
,
to
this
very
Day
;
probably
,
bacause
he
was
the
first
,
who
understood
the
motion
and
course
of
that
Planet
,
which
was
by
the
Greeks
called
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
from
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
Time
,
forasmuch
as
of
all
the
Coelestial
Circuits
none
was
found
so
diuturn
.
And
of
his
Sons
,
since
Pluto
addicted
himself
intierly
to
Husbandry
,
Neptune
to
Navigation
;
we
may
conceive
,
that
Jupiter
,
applying
his
mind
to
nobler
cares
,
succeded
his
Father
in
the
Study
of
the
Heavens
:
as
also
that
he
chose
Jupiter
.
Olympus
,
accounted
the
highest
mountain
,
to
make
his
observations
upon
:
so
that
in
process
of
time
,
he
came
therefore
to
be
called
Olympius
;
and
the
name
of
that
mountain
to
be
transferred
upon
Heaven
it self
;
whose
orders
and
laws
He
well
understanding
,
was
thereupon
said
to
have
the
Dominion
of
Heaven
.
Certain
it
is
,
that
the
Grecians
ascribed
the
Original
of
this
noblest
Science
,
partly
to
the
Gods
themselves
,
and
partly
to
ancient
Hero's
:
which
Achilles
Tatius
seasonably
alluding
Isagog
.
ad
Phoen.
unto
,
introduceth
old
Aeschylus
attributing
to
God
,
that
He
shewed
the
risings
and
settings
of
the
Stars
,
and
distinguish't
Winter
,
Summer
,
and
the
other
Seasons
;
and
Ovid
Fathers
the
same
wholly
upon
Jupiter
.
Perque
Hiemes
,
Aestusque
,
&
in
aequales
Autumnos
,
1.
Metamorph.
Et
breve
Ver
,
spatijs
exegit
quatuor
Annum
.
Besides
,
it
is
in
the
Fiction
,
that
Jupiter
took
his
Father
,
Saturn
,
bound
him
,
and
precipitated
him
into
Hell
.
Now
this
seems
to
intimate
,
that
Jupiter
having
imposed
his
own
name
upon
one
of
the
most
eminent
and
illustrious
of
the
Planets
,
gave
that
of
his
Father
to
another
of
them
,
that
was
more
remote
,
situate
in
the
deepest
part
of
the
Aetherial
spaces
,
and
of
the
slowest
progress
:
though
all
this
while
we
are
not
ignorant
,
that
those
names
were
fixed
upon
those
Planets
a
long
time
after
:
since
more
anciently
the
Planet
Jupiter
was
called
Phaeton
,
and
that
of
Saturn
,
Phoenon
.
For
,
we
may
collect
very
neer
as
much
from
Lucian
,
who
by
Tartarus
understands
the
immense
Altitude
,
or
Profunditie
of
the
Aetherial
Region
:
&
so
denies
that
Saturn
was
either
exil'd
by
Jupiter
into
Hell
,
or
cast
into
bonds
;
as
common
heads
were
perswaded
to
beleeve
.
As
for
Hyperion
;
Diodorus
hath
a
tradition
,
that
he
being
3.
Hyperion
.
of
the
progeny
of
old
Coelus
,
demonstrated
the
courses
of
the
Sun
and
Moon
:
and
therefore
called
the
Sun
,
Helios
,
after
the
name
of
his
Sonne
;
and
the
Moon
,
Selene
,
after
that
of
his
Daughter
.
Last
of
all
comes
Japetus
,
who
also
was
the
Sonne
of
Coelus
,
4.
Japetus
:
from
whom
came
Prometheus
,
who
followed
the
same
study
.
in
Eccles.
7.
but
performed
nothing
worthy
commendation
in
the
advance
of
his
Fathers
Speculations
:
but
Promotheus
,
whom
he
begat
,
was
therefore
imagined
to
have
been
chained
on
the
hill
Caueasus
,
and
to
have
his
heart
perpetually
torn
by
a
hungry
Eagle
or
Vultur
;
Because
(
as
Servius
expounds
the
riddle
)
with
restless
care
,
and
solicitude
of
mind
,
he
constantly
excruciated
himself
with
observing
the
Stars
,
and
studying
their
Ascensions
and
Declinations
.
We
shall
not
insist
upon
what
follows
in
the
same
Author
,
namely
that
this
Prometheus
was
the
first
,
who
introduced
Astrology
to
the
Assyrians
(
not
far
from
Caucasus
:
)
it
being
more
usefull
for
us
now
to
observe
,
that
He
was
imagined
to
have
stolen
Fire
from
Heaven
,
for
the
inanimation
of
Man
,
for
no
other
reason
,
but
because
he
infused
this
Heavenfetch't
Knowledge
into
the
breasts
of
men
,
and
inflamed
their
souls
with
the
desire
and
love
thereof
.
For
,
as
to
the
remainder
;
for
as
much
as
Belus
was
the
same
with
Jupiter
,
among
the
Assyrians
,
as
Diodorus
testifies
:
it
is
He
rather
,
who
was
accounted
both
the
most
sacred
of
their
Dieties
,
and
the
Inventor
lib.
2.
lib.
37
,
o.
10.
of
this
Sideral
Science
;
as
Pliny
affirms
.
It
is
not
needfull
for
us
here
to
examine
many
other
of
the
ancient
Traditions
,
accounted
likewise
among
the
Fabulous
;
as
,
in
so
did
Phaeton
,
particular
,
the
Fable
of
Phaeton
,
which
hath
this
Mythology
,
that
in
his
life
time
he
had
made
a
considerable
progress
toward
the
discovery
of
the
Suns
Annual
course
;
but
dying
immaturely
,
he
left
the
Theory
thereof
imperfect
.
That
other
of
Bellerophon
,
whom
Interpreters
maintain
to
have
been
carried
up
to
Heaven
,
not
by
a
flying
horse
,
but
a
studious
and
contemplative
mind
,
eager
in
the
the
quest
of
Syderal
mysteries
.
That
of
Doedalas
,
who
indeed
,
by
Doedalus
,
Icarus
,
th●
same
towring
speculations
,
as
by
the
artifice
of
wings
mounted
up
to
the
Northern
part
of
Heaven
;
while
his
less
ingenious
Sonne
,
Icarus
,
falling
short
in
his
attempt
of
imitating
his
Fathers
sublime
flight
(
as
not
so
well
understanding
the
demonstrations
of
the
reasons
of
his
Theory
)
flaggd
very
low
in
his
Studies
:
and
fell
from
the
true
and
apodicticall
cognition
of
Coelestial
motions
and
vicissitudes
:
with
many
other
the
like
,
recounted
by
Lucian
;
as
that
of
Endymion
,
the
favourite
of
the
Moon
;
of
Tiresias
,
the
Prophet
,
&c.
Yet
one
thing
there
is
,
de
Astrol.
in
Isagog
.
mentioned
as
well
by
Lucian
,
as
Tatius
;
which
we
cannot
well
pass
by
;
which
falling
under
the
account
of
Heroicall
times
,
seems
to
come
somwhat
neer
to
that
which
is
called
Historicall
.
And
that
is
the
notable
Centention
that
arose
betwixt
Atreus
Atreus
and
Thyestes
.
and
Thyestes
about
supreme
dominion
.
For
when
by
the
publike
Consent
and
Vote
of
the
Argives
,
the
Kingdom
was
to
be
his
of
the
two
,
who
should
give
the
most
eminent
testimony
of
Science
:
it
came
to
Atreus
share
to
be
King
:
because
,
though
Thyestes
showed
them
the
signe
Aries
,
in
Heaven
(
for
which
he
was
honourd
with
a
golden
Ram
)
yet
had
Aireus
declared
a
thing
more
excellent
:
while
discoursing
about
the
variety
of
the
Suns
rising
,
he
made
it
appear
,
that
the
Sun
and
the
World
(
i.
e.
the
Starry
Orb
)
were
not
carryed
the
same
,
but
quite
contrary
wayes
;
and
consequently
,
that
that
part
of
the
Heavens
which
was
the
West
or
Occident
of
the
Starry
Orb
,
was
the
very
rising
,
or
Orient
of
the
Solary
.
Hence
that
verse
of
Euripides
,
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
Qui
Astrorum
enim
contrariam
ostendi
viam
.
To
the
same
times
likewise
are
we
to
refer
the
Institution
of
Hercules
and
Iphitus
.
the
Olympick
Games
,
by
Hercules
;
which
after
a
long
interruption
were
renewed
by
Iphitus
.
For
,
inasmuch
as
those
sports
cap.
18.
were
instituted
for
no
other
end
(
as
may
be
assured
from
Censorius
)
but
that
their
celebration
might
put
men
in
mind
of
that
Intercalation
of
a
month
and
half
,
that
was
to
be
made
constantly
every
fourth
Year
,
in
respect
of
those
four
times
eleven
,
or
44.
Dayes
,
by
which
the
mo●ion
of
the
Moon
anticipated
that
of
the
Sun
;
and
the
four
times
six
hours
,
or
one
whole
Day
,
by
which
the
circuit
of
the
Sun
exceded
365
Dayes
:
manifest
it
is
,
that
Hercules
could
not
understand
this
,
without
having
first
exactly
observed
the
Motions
of
Sun
and
Moon
.
Hither
also
belongs
that
which
is
reported
of
Orpheus
,
who
must
Orpheus
.
needs
have
attentively
observed
the
seven
Planets
,
if
it
be
true
,
as
Lucian
averrs
,
that
he
represented
their
Harmony
by
his
Seven-stringed
de
Ast●ol
Harp
:
which
the
Grecians
thereupon
designed
in
Heaven
,
by
some
Stars
,
that
to
this
Day
retain
the
name
of
Lyra.
So
likewise
doth
what
Sophocles
saith
of
Palamedes
,
Palamedes
.
who
pointed
out
the
several
Asterisms
,
and
particularly
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
Vrsum
volutam
,
gel●dum
&
occasum
Canis
.
And
lastly
,
what
Homer
recounts
,
that
in
those
times
were
well
known
(
besides
Bootes
and
the
Bear
,
or
Wain
)
Homer
.
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
.
Odyss.
E.
Pleiades
,
atque
Hyades
,
roburque
ipsum
Orionis
.
We
have
now
struggled
through
the
Darkness
of
Fabulous
Times
,
and
are
advanced
as
far
as
to
discerne
the
twilight
of
Articl.
4.
Historicall
.
An
here
,
the
first
thing
we
clearly
perceive
,
is
that
Secondly
,
those
Historical
times
;
according
to
which
the
antiquity
of
Astron.
Observations
belongs
either
to
the
Egyptians
,
or
Babylonians
.
the
whole
controversy
about
the
Antiquity
of
Astronomical
Observations
,
lies
betwixt
the
Egyptians
and
the
Assirians
,
or
Babylonians
.
For
,
as
to
the
Grecians
,
though
some
have
thought
they
might
put
in
also
for
a
claim
to
the
honour
of
being
the
Anthors
of
this
admirable
Science
;
yet
by
the
Verdict
even
of
Plato
himself
,
they
are
to
lay
by
the
presence
of
Competition
,
For
,
sayth
He
,
the
first
who
made
Syderal
inspections
,
was
a
Barbarian
;
a
more
ancient
Nation
than
ours
bred
those
men
,
in
Epinom
.
who
first
devoted
their
minds
to
that
Study
,
in
respect
of
the
Summer-like
serenity
and
perspicuity
of
the
Air
,
such
as
Egypt
enjoyes
,
and
Syria
,
where
all
the
Stars
are
,
clearly
visible
and
no
Clouds
or
Mists
to
obscure
the
beautifull
face
of
Heaven
.
And
certainly
,
if
we
except
what
we
newly
mentioned
,
the
Institution
of
the
Olympick
Games
by
Hercules
,
and
the
restauration
of
them
after
some
Intermission
,
by
Iphytus
,
which
hapned
about
800.
Years
before
Christ
;
and
some
places
in
the
writings
of
Homer
,
and
more
especially
of
Hesiod
,
who
lived
neer
upon
the
same
time
,
or
not
long
before
;
we
shall
find
that
the
Grecians
can
produce
no
Monuments
of
their
Observations
of
the
Heavens
,
more
ancient
than
those
of
Thales
,
who
flourisht
,
full
600.
Years
before
Christ
;
and
who
yet
borrowed
his
knowledge
of
Aetherial
Matters
from
Egypt
.
It
being
manifest
therefore
,
that
the
Aegyptians
,
or
their
Priests
,
are
the
only
men
,
that
ought
to
be
admitted
to
a
Dispute
with
the
Assirians
or
Babylonians
,
or
their
Philosophers
,
concerning
the
Antiquity
of
Observations
;
and
that
their
several
Pleas
seem
equally
reasonable
.
Truly
,
it
is
no
easy
matter
to
determine
the
difference
,
so
as
to
place
the
Lawrell
on
their
heads
to
whom
it
doth
of
right
belong
.
For
,
albeit
Josephus
assignes
the
Honour
to
the
Chaldaeans
,
and
1.
Antiq.
8.
others
again
stand
firmely
for
the
Egyptians
:
yet
Plato
,
Diodorus
,
in
Epinom
.
2.
lib.
de
Astrolog
.
Isagog
.
Lucian
,
Achilles
Tatius
,
and
others
alleadge
such
quotations
for
each
party
,
as
seem
to
have
no
other
,
but
the
authority
of
the
parties
themselves
.
Nor
ought
that
to
seem
strange
;
since
both
sides
equally
alleadge
the
convenience
of
their
vast
Companies
,
and
the
serenity
of
the
sky
;
since
they
both
boast
themselves
the
Original
Nation
and
allow
their
Competitors
to
be
only
Colonies
;
since
both
glory
in
fabulous
beginnings
,
which
we
cannot
trace
or
discusse
;
and
both
recur
to
egregious
falshoods
about
the
time
when
their
Ancestors
first
made
Coelestiall
Scrutenies
.
For
,
the
Chaldaeans
(
as
we
find
on
the
Register
of
Diodorus
)
affirm
,
that
their
Nation
applied
themselves
to
loc.
citat
.
these
Studies
,
from
times
of
incredible
Antiquity
viz.
of
four
hundred
and
three
thousand
Years
:
And
the
Egyptians
(
as
Cicero
de
Divi●at
.
observes
)
talk
of
Observations
of
four
hundred
thousand
and
seventy
Years
standing
.
Unless
you
shall
please
to
consigne
the
Victory
to
the
Egyptians
,
because
they
put
a
value
only
themselves
by
Auction
.
As
if
it
were
not
enough
for
them
to
boast
those
four
hundred
nine
thousand
Years
(
mentioned
by
Laertius
)
in
which
from
the
time
of
V●lcan
,
the
Sonne
of
Nilus
,
to
that
of
Alexander
of
Macedon
,
there
hapned
of
Eclipses
of
the
Sun
in
praefat.
three
hundred
seventy
three
,
and
of
the
Moon
eight
hundred
thirty
two
.
These
considerations
premised
,
we
cannot
indeed
deny
,
but
the
Egyptians
had
some
Observations
,
some
ages
before
Thales
and
other
Grecians
travelled
among
them
:
but
,
when
we
would
enquire
more
precisely
into
the
time
,
when
those
Observations
first
begun
;
we
find
our selves
at
a
loss
,
and
brought
back
again
into
the
cimmerian
obsurity
of
Fabulous
Times
.
Now
forasmusch
as
,
though
Pliny
writes
,
that
Epigenes
found
lib.
9.
c.
56.
no
Observations
among
the
Babylonians
of
above
seven
hundred
and
twenty
Years
antiquity
,
and
those
engraven
on
artificial
Tyles
or
Slates
;
and
the
most
ancient
Eclipses
deduced
from
them
,
were
transmitted
to
Ptolomy
,
about
the
same
Number
of
Years
before
in
Almagest
.
lib.
4.
cap
6.
Christ
:
and
that
by
the
great
Hipparchus
.
And
to
the
same
Time
belongs
what
Berosus
and
Critodemus
say
,
that
in
their
Dayes
,
there
were
extant
no
Observations
of
more
than
four
hundred
and
thirty
Years
as
may
be
found
also
in
Pliny
:
forasmuch
,
we
say
,
as
we
have
brought
some
considerable
Monuments
of
Observations
much
elder
than
that
time
;
yet
shall
not
concede
beyond
what
the
Chaldeans
themselves
profest
,
when
they
testified
to
Callisthenes
(
who
went
to
them
upon
no
other
errand
,
by
the
perswasion
of
Aristotel
,
as
Simplicius
relates
)
that
they
had
in
lib.
2.
de
Coe
lo
,
and
comment
.
46.
nothing
of
that
kind
among
them
beyond
a
thousand
nine
hundred
and
Three
Years
past
:
which
Years
seem
to
commense
at
Ninus
,
the
Sonne
of
Belus
,
and
first
King
of
the
Assyrians
.
It
is
clear
,
that
the
Antiquity
of
Observations
ariseth
to
(
but
not
above
)
one
thousand
and
ninety
Years
before
Alexander
the
Great
.
But
,
alas
!
after
all
this
great
adoe
,
What
did
the
Observations
Articl
.
5.
Yet
neither
of
of
them
observed
any
thing
considerable
;
at
to
the
designation
of
Times
:
but
corrupted
what
they
had
observed
,
to
the
introduction
of
Astrology
Judicial
.
themselves
amount
to
?
Why
truely
,
for
ought
we
can
gather
from
all
that
is
extant
concerning
them
,
those
of
the
Aegyptians
amounted
to
nothing
at
all
:
and
those
of
the
Chaldeans
to
very
little
.
For
the
Egyptians
,
we
confess
,
are
said
to
have
observed
the
rising
of
the
Dog-Star
,
and
some
other
,
no
very
difficult
apparences
:
but
we
have
no
remains
delivered
down
to
us
,
of
that
or
any
other
particular
they
observed
,
with
the
exact
designation
of
the
Time
,
as
they
ought
.
And
from
the
Chaldaeans
we
have
as
little
,
besides
those
Eclipses
mentioned
in
Ptolomy
.
But
,
when
I
speak
of
the
Egyptians
,
I
except
Ptolomy
himself
and
some
others
,
who
lived
and
studied
at
Alexandria
,
about
there
hundred
Years
before
the
Nativity
of
our
Saviour
;
or
after
Alexander
:
as
Timocharis
,
Eratosthenes
,
Hipparchus
:
for
all
these
were
either
Grecians
,
or
to
be
accounted
among
Grecians
,
in
respect
of
the
language
they
used
and
wrote
in
,
rather
than
among
the
ancient
Egyptians
,
by
whose
Inventions
even
Ptolomy
himself
(
one
of
their
own
Country
men
,
without
dispute
)
was
very
little
,
or
nothing
at
all
assisted
in
his
Study
of
Astronomy
.
But
,
what
concerns
aswell
the
Egyptians
,
as
Chaldeans
;
their
Observations
are
to
be
distinguisht
(
according
to
the
division
vulgarly
received
into
(
1.
)
Astronomical
,
and
(2)
Astrological
:
the
former
relating
to
the
Motions
,
Magnitudes
,
Distances
,
and
proportion
of
the
Stars
;
the
Latter
to
the
Effects
of
them
,
which
they
conjectured
were
dependent
on
the
Vertues
and
Influences
of
Heavenly
Bodies
,
aswell
in
the
affections
of
the
Air
,
as
in
the
actions
and
affairs
of
Mankind
.
For
,
both
Nations
being
wonderfully
prone
to
Supersttition
,
and
surprised
with
excess
of
Admiration
at
the
Eclipses
of
the
Sun
and
Moon
,
when
they
first
beheld
them
;
and
observing
ever
now
and
then
some
Stars
that
moved
in
Courses
contrary
to
the
West
,
they
began
presently
to
think
,
that
those
apparences
hapned
not
without
natural
Causes
;
and
that
it
remained
only
on
Mans
part
,
to
Study
how
those
events
might
come
to
be
fore-known
,
which
those
apparences
did
portend
.
Hereupon
,
having
attributed
the
most
powerfull
Vertue
to
the
five
wandering
Stars
(
as
Diodorus
loc.
citat
.
testifieth
particularly
of
the
Chaldaeans
)
as
understanding
them
to
be
the
Proclaimers
of
the
will
and
purposes
of
the
Gods
;
because
they
sometimes
arose
,
and
sometimes
set
in
various
places
of
the
Heavens
;
because
they
varied
their
magnitude
and
colour
:
therefore
they
conceived
,
that
they
ought
to
adress
their
Studies
and
Disquisitions
principally
to
these
varieties
.
And
,
because
they
imagined
,
that
the
higher
the
place
was
,
from
whence
they
should
observe
these
Wandering
Stars
,
the
more
clearly
and
distinctly
might
they
be
discerned
;
they
builded
Structures
of
vast
altitude
;
and
particularly
that
immense
Tower
at
Babylon
,
described
by
Herodotus
,
from
the
highest
area
whereof
(
where
lib.
1.
stood
also
the
Temple
of
Belus
)
they
might
exactly
behold
and
observe
the
rising
and
setting
of
the
Stars
,
and
other
Syderal
occurrences
They
took
notice
likewise
,
that
those
five
Planets
did
keep
almost
the
same
Course
,
as
the
Sun
and
Moon
;
and
thereupon
they
pointed
out
the
Zodiack
,
imagining
that
there
must
be
some
eminent
vertue
in
that
part
of
the
Heavens
,
because
all
the
Planets
kept
constantly
to
it
.
And
this
Zodiack
they
divided
into
12.
parts
,
or
Signes
;
because
the
Moon
run
it
over
12.
times
,
and
the
Sun
only
once
,
in
one
Year
:
and
according
to
the
number
of
the
Dayes
,
during
which
the
Sun
was
in
passing
through
one
Signe
,
they
distinguished
each
Signe
again
into
30.
parts
,
which
we
call
Degrees
.
I
shall
not
recount
to
you
,
how
they
would
have
Twelve
Principal
Dieties
belonging
to
these
12.
Signes
,
whereof
each
had
his
particular
regiment
over
his
proper
Signe
and
Moneth
dependent
thereupon
:
nor
how
they
substituted
thirty
of
the
fixt
Stars
,
to
assist
the
Planets
,
and
called
them
Concelling
Gods
:
nor
how
they
placed
12.
Stars
always
visible
in
the
North
,
for
government
of
the
Living
;
and
as
many
more
in
the
South
,
alwaies
visible
,
for
the
government
of
the
Dead
,
there
gathered
together
;
with
many
other
the
like
dreams
and
ridiculous
absurdities
.
But
the
thing
I
think
most
worthy
your
notice
,
is
,
by
what
rude
kind
of
artifice
they
distinguished
the
Zodiack
into
12.
Signes
;
as
we
find
it
described
,
concerning
the
Chaldaeans
,
by
Sextus
Empiricus
,
ad
Astrolog
.
1.
in
Somn.
21.
and
concerning
the
Egyptians
,
by
Macrobius
.
The
manner
this
.
They
took
a
vessell
with
a
small
hole
in
the
bottom
,
and
filling
it
with
Water
,
suffered
the
same
to
distill
Drop
by
Drop
into
another
Vessell
,
placed
beneath
to
receive
it
;
and
this
from
the
moment
of
the
rising
of
some
one
Star
or
other
,
observed
in
one
Night
,
untill
the
Moment
of
its
rising
again
the
next
Night
following
.
The
Water
fallen
down
into
the
Receiver
,
they
divided
into
●2
.
equal
parts
,
and
having
two
other
smaller
vessells
in
readiness
each
of
them
fit
to
contain
one
twelfth
part
of
the
Water
,
they
again
poured
all
the
Water
into
the
upper
Vessel
,
and
strictly
marking
the
rising
of
some
one
Star
in
the
Zodiack
,
they
at
the
same
Moment
gave
the
Water
leave
to
distill
into
one
of
the
smaller
Vessells
,
and
so
soon
as
that
was
filled
,
observing
likewise
another
rising
Star
,
they
put
under
another
small
Vessell
;
and
so
alternately
shifting
the
small
vessels
,
they
noted
,
if
not
in
one
Night
,
yet
in
many
,
the
twelve
Stars
,
by
which
they
might
discriminate
the
whole
Zodiack
into
twelve
equal
parts
.
Now
with
what
Art
and
exactness
these
Ancients
measured
out
the
Heavens
,
may
be
conjectured
from
this
one
example
.
I
might
adferr
another
foppery
of
the
Chaldaeans
,
from
the
same
Empiricus
,
who
relates
;
that
taking
it
for
granted
,
that
the
future
fortunes
of
Men
did
depend
on
their
particular
Horoscope
,
or
Signe
rising
at
their
Birth
,
when
they
had
a
mind
to
divine
in
this
Kind
;
Two
of
their
wise
men
agreed
together
in
the
calculation
of
the
Nativity
of
the
Person
proposed
:
the
one
stood
by
the
Mother
in
Travell
,
the
other
on
some
high
place
neer
at
hand
;
and
as
he
that
was
below
gave
the
Signe
,
that
the
Infant
was
then
newly
come
into
the
World
,
the
other
above
took
care
to
observe
the
Signe
,
that
was
just
then
newly
risen
.
ibid.
cap.
20.
But
,
it
will
be
of
more
use
for
us
to
hear
what
Macrobius
tells
of
the
Egyptians
.
They
,
when
they
would
know
the
Diameter
of
the
Sun
,
had
in
readiness
a
Vessell
of
Stone
,
hollowed
to
the
form
of
an
Hemisphere
,
exactly
made
,
with
a
style
or
Gnomen
erected
in
the
middle
,
and
twelve
Horary
Lines
drawn
within
.
And
on
the
very
Day
of
the
Equinox
,
observing
the
Moment
,
when
the
upper
Limbus
of
the
Sun
first
shewed
it self
above
the
Horizon
;
they
marked
that
place
on
the
brim
of
the
Vessel
,
on
which
the
Gnomen
cast
its
shadow
.
Then
again
marking
that
place
on
which
the
shadow
ended
,
when
the
lower
Limbus
of
the
Suns
body
appeared
just
above
the
edge
of
the
Horizon
;
they
measured
the
space
or
distance
betwixt
the
two
marks
of
the
Shadowes
,
and
found
it
to
be
the
ninth
part
of
an
hour
,
or
the
hundred
and
eight
part
of
the
Hemisphere
,
and
consequently
the
two
hundred
and
sixteenth
part
of
the
whole
Circuit
:
and
from
thence
they
deduced
,
that
the
Diameter
of
the
Sun
was
the
two
hundredth
and
sixteenth
part
of
its
whole
Orb
;
(
which
,
in
truth
,
is
the
700th
neer
upon
)
or
did
contain
one
Degree
and
an
hundred
Minutes
;
which
yet
is
no
more
than
halfe
a
degree
,
or
31.
Minutes
,
at
most
.
To
this
we
might
super-ad
,
that
it
was
the
practice
of
elder
times
,
to
commensurate
the
Diameter
of
the
Sun
by
an
Hydrologie
,
or
Vessel
of
Water
;
collecting
the
same
from
part
of
the
Water
flowing
down
the
whole
Day
,
which
had
dropped
until
the
Sun
was
wholly
risen
;
as
is
insinuated
by
Plutarch
,
and
deduced
from
Capella
:
but
Cleomedes
hath
at
large
declared
,
that
this
way
of
measuring
by
Water
falling
slowly
and
equally
from
Vessel
to
Vessel
,
was
an
Invention
of
the
Egyptians
.
Now
the
reason
,
why
we
touch
upon
these
particulars
,
was
only
to
satisfy
,
that
(
as
we
said
afore
)
no
great
matter
in
Astronomy
was
ever
observed
either
by
the
Egyptians
,
or
by
the
Babylonians
.
And
,
if
you
desire
any
further
Argument
thereof
;
Pray
take
this
.
They
were
very
far
from
suspecting
that
the
Fixt
Stars
had
any
motion
proper
to
themselves
;
or
that
they
had
any
Eccentricity
(
excepting
only
that
the
Egyptians
thought
Venus
and
Mercury
to
move
round
about
the
Sun
,
as
their
center
;
as
is
affirmed
by
Macrobius
,
and
some
others
)
or
that
the
Sun
had
any
Apogaeum
at
all
,
with
many
other
Particulars
fully
as
considerable
.
Which
doubtless
must
be
the
reason
,
why
they
invented
no
Hypotheses
,
by
which
they
might
regulate
themselves
,
in
making
their
Caluclations
of
the
various
motions
of
the
heavenly
bodies
.
And
Peter
Ramus
not
long
since
complaind
,
that
we
have
not
our
Astronomy
free
from
the
trouble
of
Hypotheses
;
such
as
the
Interpreters
of
Aristotel
themselves
,
and
Proclus
on
Timaeus
have
recorded
the
Egyptians
and
Babylonians
to
have
had
amongst
them
:
while
,
incroth
,
he
complaind
,
that
we
had
not
our
Astronomy
as
rude
wild
and
imperfect
,
as
theirs
was
.
For
,
however
some
Hypotheses
are
more
simple
(
and
so
more
easy
)
than
other-some
:
yet
it
is
absolutely
impossible
,
that
Astronomy
should
consist
without
some
or
other
.
Hereupon
,
they
could
observe
,
indeed
,
that
the
Planets
were
one
while
Direct
in
their
Progress
,
another
while
Retrogarde
,
and
then
again
Stationary
;
that
they
in
their
wanderings
sometimes
inclined
towards
the
North
,
and
sometimes
deflected
again
toward
the
South
:
but
all
that
while
,
they
could
neither
comprehended
the
reasons
of
those
various
apparences
,
nor
calculate
them
by
numbers
.
The
most
they
could
doe
,
was
darkly
to
represent
those
motions
,
by
certain
Hieroglyphicks
,
as
in
particular
by
the
windings
and
flexures
of
Serpents
;
and
the
motion
of
the
Sun
,
by
only
a
Beetle
rowling
his
pill
of
dung
backward
:
as
we
may
read
in
Clemens
Alexandrinus
:
and
then
came
Eudoxus
,
who
having
learned
that
variety
of
motions
among
them
,
was
the
first
who
invented
Hypotheses
of
various
Orbs
,
for
the
Solution
of
the
Phenomena
.
Again
,
they
were
very
far
from
attaining
the
determinate
places
of
the
Fixt
Stars
,
according
to
Longitude
and
Latitude
;
or
according
to
their
Right
Ascension
,
and
Declination
:
so
that
neither
could
they
define
the
true
places
of
the
Planets
,
by
Comparation
to
the
Fixt
Stars
,
nor
(
consequently
)
designe
any
Observations
with
due
exactness
.
And
truely
,
this
was
the
Cause
why
Hipparchus
met
with
no
Observations
,
either
of
the
Egyptians
or
Babylonians
,
by
which
he
could
receive
the
least
help
or
advantage
,
toward
his
composing
either
Hypotheses
,
or
Tables
,
to
represent
the
motions
of
the
Five
errant
Stars
:
and
Ptolomy
was
the
first
,
who
partly
by
the
benefit
of
Observations
left
him
by
Hipparchus
,
and
partly
by
those
he
made
himself
,
became
able
to
attempt
such
a
Work
;
as
stands
recorded
in
his
Almagest
.
There
were
only
the
Eclypses
,
which
both
these
Nations
had
set
down
:
as
observed
in
their
Commentaries
:
and
those
only
so
,
as
that
from
Past
,
they
might
be
able
to
conjecture
somthing
of
what
were
to
Come
.
Not
from
the
motions
of
Sun
and
Mon
,
exactly
calculated
by
the
help
of
Tables
;
but
having
learnd
from
common
experience
,
that
every
ninetneenth
Year
,
Eclypses
did
return
again
upon
the
same
Day
,
for
the
most
part
:
thereupon
they
endeavoured
to
praedict
what
Eclipses
would
happen
,
and
the
time
when
;
and
this
after
they
had
perceived
not
any
Anomaly
in
the
Sun
,
but
some
certain
Inequality
in
the
Moon
,
which
reducing
to
a
medium
,
they
concluded
that
the
Moon
did
every
Day
run
throug●
thirteen
Degrees
,
and
a
little
more
than
one
sixth
part
of
a
degree
;
as
Geminus
delivers
of
the
Chaldaeans
.
But
in
their
predictions
of
Lunar
Eclipses
,
they
were
somwhat
more
confident
;
aswell
because
these
Eclipses
usually
uturn
,
for
the
three
Ages
next
succeding
,
within
the
compass
of
the
same
Dayes
;
as
because
it
is
very
rare
,
in
respect
of
the
greatness
of
the
Earths
shadow
,
but
the
Moon
,
either
in
the
whole
,
or
some
part
of
her
,
more
or
less
,
falls
into
it
:
but
,
because
(
as
to
Solary
Eclypses
)
the
Moon
is
both
so
small
,
and
hath
so
large
a
Parrallax
,
as
that
she
doth
not
for
the
most
part
intercept
the
light
of
the
Sun
from
the
Earth
;
therefore
was
it
(
as
Diodorus
witnesseth
specially
of
the
Babylonians
)
that
they
durst
not
determine
Eclypses
of
the
Sun
to
come
,
to
any
certaine
time
;
but
if
they
predicted
any
,
with
limitation
of
time
,
they
alwayes
(
to
save
their
credit
,
in
case
of
failing
)
annexed
this
Condition
,
If
the
Gods
be
not
prevailed
upon
,
by
Sacrifices
and
Praiers
,
to
avert
them
.
Truth
is
,
these
Astronomers
were
also
Priests
,
and
it
was
their
interest
to
cast
in
this
Proviso
.
For
,
being
ambitious
to
be
reputed
interpreters
of
the
Will
of
the
Gods
to
the
People
,
and
so
both
knowing
in
things
to
come
,
and
skillfull
in
such
Ceremonies
,
wherewith
their
respective
Deities
were
most
attoned
and
delighted
:
unwilling
to
be
thought
able
to
predict
nothing
,
and
as
unwilling
again
to
be
found
erring
in
their
chief
predictions
,
they
wrapt
up
all
in
Misteries
,
and
amused
the
vulgar
with
superstitious
opinions
and
rites
.
The
Egyptians
,
in
a
great
part
of
their
sacred
Worship
,
had
recourse
to
the
Astrological
Books
of
their
Mercurius
(
one
of
the
Order
of
the
Fixt
Stars
;
a
second
,
of
the
Conjunction
of
Sun
and
Moon
;
a
third
and
fourth
,
of
their
rising
.
)
which
with
what
ceremonious
Pomp
they
used
to
carry
about
with
them
,
in
a
kind
of
solemne
Procession
,
you
may
find
amply
described
by
Clem.
Alexandrinus
.
Nor
is
it
lib.
6.
stromat
.
strange
that
those
Priests
accounted
so
sacred
and
knowing
,
should
also
be
estemed
for
Prophets
.
Further
,
you
meet
with
no
mention
of
the
Five
Errant
Stars
,
all
this
while
;
and
the
reason
seems
to
be
,
because
they
attributed
an
energie
of
them
only
as
they
were
referrable
to
the
Inerrant
or
Fixt
,
and
particularly
,
as
they
possest
this
or
that
part
of
some
Signe
in
the
Zodiack
,
and
together
with
it
had
their
rising
,
or
setting
.
For
,
so
much
did
they
ascribe
to
the
Zodiack
,
as
that
the
Babylonians
,
and
(
in
imitation
of
them
,
the
Persians
and
Indians
)
thought
,
that
each
decimal
of
degrees
,
or
thirds
of
the
Signes
,
(
and
the
Egyptians
came
as
low
as
to
each
single
degree
)
could
not
be
varied
in
the
rising
,
but
some
eminent
variation
most
happen
,
especially
in
him
,
who
should
be
borne
at
that
time
.
And
hereupon
was
it
,
that
the
Egptians
made
that
great
Circle
of
Gold
(
described
in
Diodorus
)
of
a
cubit
in
thickness
,
and
three
hundred
sixty
five
cubits
in
circumference
(
plundred
at
last
by
Cambyses
)
that
upon
each
cubits
space
might
be
inscribed
each
Day
of
the
Year
,
365.
Dayes
in
the
whole
round
,
and
also
what
Stars
did
rise
,
what
set
upon
each
Day
,
nay
the
very
hour
of
their
respective
rising
and
setting
,
and
what
they
did
signifie
:
and
whereas
others
used
to
assigne
the
form
of
some
Animal
or
other
,
to
each
ten
degrees
;
they
assigned
one
to
each
single
degree
,
and
so
made
their
harsolations
or
conjectural
predictions
accordingly
.
For
Example
;
to
the
first
degree
of
Aries
they
assigned
the
figure
of
a
Man
,
holding
a
Sicle
or
hook
in
his
right
hand
,
and
a
Sling
in
his
left
;
to
the
second
,
a
Man
with
a
Dogs-head
,
his
right
hand
stretcht
forth
,
and
a
staff
in
his
left
;
and
so
of
the
rest
;
then
annexing
the
signification
to
each
,
they
determined
,
that
he
,
who
should
have
the
first
degree
of
Aries
for
his
Horoscope
,
should
be
some
part
of
his
life
a
Husbandman
,
and
the
rest
of
it
a
Soldier
;
that
he
,
who
should
be
born
under
the
second
,
should
be
contentious
,
quarrelsom
,
and
envious
;
and
so
of
the
rest
,
all
which
Scaliger
hath
fully
deduced
from
Aben
Ezra
.
In
a
Word
;
what
ever
knowledge
either
the
Egyptians
or
Chaldeans
had
of
the
Stars
;
certain
it
is
,
they
referred
it
wholly
to
Astronomantie
,
or
Divination
by
Stars
:
and
therefore
among
them
there
flourisht
,
no
true
and
genuine
Astronomy
,
but
a
spurious
and
false
,
one
i.
e.
Astrology
Divinatory
,
or
the
fraudulent
Art
of
Fortune-telling
by
the
Heavens
.
Berosus
(
whom
we
formerly
mentioned
)
coming
into
Grece
,
a
little
after
the
death
of
Alexander
,
is
discovered
to
have
brought
with
him
nothing
sollid
touching
Astronomy
,
but
only
Judicial
Astrology●
;
lib.
9.
cap.
7.
lib.
9.
cap.
37.
for
which
,
as
a
thing
new
,
and
strange
to
the
people
,
he
was
highly
esteemed
,
as
Vitruvius
and
Pliny
remark
.
And
Eudoxus
,
who
had
returned
out
of
Egypt
before
that
,
well
knew
what
sort
of
Astrology
this
was
(
the
principal
Contrivers
and
Founders
of
which
are
said
to
have
been
Petosires
,
Necepsus
,
Esculapius
)
2.
de
divinat
.
but
he
highly
contenmed
it
as
Cicero
remembers
,
and
brought
home
no
other
fruit
of
his
tedious
Travells
,
beside
a
list
of
some
Eclipses
,
and
the
varieties
of
the
motions
of
the
wandering
Stars
,
by
which
he
first
essaied
to
compose
accommodate
Hypotheses
,
as
we
have
formerly
hinted
.
Nay
,
Plato
himself
,
who
was
Companion
to
Eudoxus
,
for
thirteen
Years
together
,
in
Egypt
:
profest
:
in
Epinom
.
that
he
could
attain
nothing
sollid
and
satisfactory
touching
those
Stars
,
and
therefore
placed
all
his
hope
only
in
the
sagacity
and
industry
of
the
Grecians
,
such
as
he
knew
Eudoxus
to
be
.
For
,
having
first
recounted
what
ever
he
knew
concerning
them
;
he
saith
,
It
is
to
beleeved
that
the
Grecians
make
more
perfect
whatsoever
they
receive
from
Barbarians
;
and
therefore
is
it
fit
,
we
allow
the
same
,
touching
the
argument
of
which
we
have
discoursed
.
Truth
is
,
it
is
difficult
to
find
out
the
way
,
how
all
these
Apparences
,
so
involved
in
obscurity
may
be
explicated
:
nevertheless
there
is
great
hope
that
things
of
that
sort
will
be
better
and
more
advantageously
handled
,
than
they
were
delivered
to
us
by
Barbarians
.
From
the
Egyptians
and
Chaldeans
,
therefore
(
as
Astronomy
Articl
.
6.
And
after
them
to
the
Grecians
among
whom
the
most
ancient
mention
of
Astron.
is
in
Hesiod
.
her self
,
while
young
and
rude
)
we
come
to
the
Graecians
:
and
the
most
antique
record
of
Syderal
Observations
to
be
found
among
them
,
seems
to
be
that
of
Hesiod
;
who
in
his
Book
of
Weeks
and
Dayes
teacheth
Husbandmen
the
most
opportune
times
of
reaping
,
sowing
,
and
other
labours
of
Agriculture
,
from
the
rising
and
setting
of
the
Pleiades
,
and
Hyades
,
and
Arcturus
,
the
Dog-star
,
and
Orion
:
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
.
Donec
Pleiades
,
quae
&
Atlantiades
,
exoviuntur
,
&c.
And
I
cannot
tell
,
whether
it
were
that
book
,
or
some
other
,
that
Pliny
meant
,
when
speaking
of
Hesiod
,
he
sayes
,
Hujus
quoque
,
nomine
extat
Astrologia
,
there
is
extant
an
Astrology
of
his
.
However
,
we
are
here
to
remark
two
things
,
in
order
to
our
more
exact
disquisition
;
the
First
is
,
that
the
Ancient
Greeks
principally
attended
to
these
risings
and
settings
,
aswell
that
they
might
distinguish
the
several
Seasons
of
the
Year
,
as
that
they
might
fore-know
Rain
,
Winds
and
other
dispositions
of
the
Air
,
usually
attending
those
Seasons
.
And
hereupon
,
Thales
,
Anaximander
,
Democritus
,
Euctemon
,
Meton
,
Eudoxus
,
and
Ex
Gem
Ptol.
&
aliis
.
many
others
,
composed
certain
Parapegmata
,
Tables
,
(
as
Ephemerides
,
or
Diaries
)
in
which
they
inscribed
each
Day
of
the
Year
,
with
the
particular
Stars
rising
or
setting
on
each
Day
,
and
what
mutations
of
the
Air
each
one
did
portend
.
Such
a
Darapegme
as
these
,
was
composed
likewise
by
Julius
Caesar
himself
,
for
the
Horizon
of
Kome
;
in
allusion
where
to
he
might
justly
own
,
what
Lucan
said
for
him
,
lib.
10.
Nec
meus
Eudoxi
fastis
superabitur
Annus
.
And
,
him
doubtless
,
did
Ovid
translate
into
his
Fasti
;
promising
lib.
1.
in
the
beginning
,
that
he
would
sing
of
the
Stars
and
Signes
,
that
rose
and
again
descended
under
the
Earth
.
But
,
to
keep
close
to
the
Grecians
;
among
them
,
he
was
held
a
great
Astrologer
,
who
had
discovered
and
observed
only
these
risings
and
settings
here
spoken
of
;
and
so
of
whom
that
might
be
spoken
,
which
Catullus
said
of
Conon
,
Omnia
qui
magni
dispexit
lumina
Mundi
,
Stellorumque
ortus
comperit
,
atque
obitus
.
For
,
before
the
Advent
of
Berosus
,
this
was
the
only
[
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
]
Praesignification
or
Divination
by
the
Stars
,
the
Grecians
had
among
them
:
unless
what
Hesiod
hints
,
in
his
in
●●ebns
.
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
,
Primùm
prima
dies
,
&
quarta
&
septima
sacra
,
&c.
where
he
points
out
,
what
Dayes
of
the
Moon
were
accounted
Lucky
,
and
what
Unlucky
.
The
Second
observable
is
;
that
among
the
Grecians
,
and
indeed
among
divers
other
Nations
,
beyond
all
Memorials
of
either
Traditions
or
books
,
the
Stars
were
reduced
to
certain
Images
,
or
Constellations
,
and
denominated
accordingly
(
as
their
names
yet
shews
)
as
it
pleased
the
fancies
of
Husbandmen
,
Shepheards
,
Matiners
and
the
like
,
who
used
to
be
vigillant
and
gizing
upon
the
Heavens
in
clear
Nights
.
Though
there
have
been
some
Constellations
added
of
latter
times
,
as
that
of
the
lesser
Wain
,
by
Thales
,
which
Lacrtius
and
Tatius
recite
out
of
Eb.
1.
de
vit.
〈◊〉
de
Com.
〈◊〉
Callimachus
,
who
also
took
the
same
elswhere
,
and
that
of
Berenices
Hair
,
removed
into
Heaven
by
Conon
,
as
Catullus
relates
.
Cleostratus
likewise
(
as
we
have
it
from
Hyginus
)
found
lib.
2.
A
〈◊〉
.
lib.
2.
cap
8.
out
the
Kidds
:
though
,
(
which
Pliny
moreover
attributes
to
him
,
)
his
invention
of
the
Signes
in
the
Zodiack
,
is
so
to
be
understood
,
as
that
he
taught
men
through
what
Signes
the
Sun
and
other
Planets
passed
.
But
(
that
we
may
couch
also
upon
this
)
at
first
,
the
Grecians
had
only
Eleven
Signes
in
their
Zodiack
;
and
it
was
long
after
ere
they
came
to
add
the
twelfth
,
in
imitation
of
the
Egyptians
,
who
(
as
may
be
collected
from
Servins
,
in
1.
Geog.
l.
8.
Marcianus
,
and
others
)
instead
of
the
Clawes
of
the
Scorpion
,
placed
Libra
,
the
place
destined
to
Augustus
,
by
Virgil
,
—
Ipse
tibi
jam
brachia
contrahit
ardens
Scorpius
.
—
1.
Georg.
They
added
the
Twelfth
,
we
say
,
to
the
end
,
that
as
the
whole
Compass
of
the
Zodiack
was
divided
into
Dodecatemoria
(
as
they
call
them
)
twelve
equal
parts
,
so
it
might
consist
also
of
twelve
Signes
.
Albeit
,
being
(
as
it
were
)
necessitated
to
make
use
of
such
Signes
,
as
had
been
brought
up
,
rather
by
chance
,
than
Art
;
those
12.
Signes
were
not
exactly
proportionate
to
the
12.
Divisions
of
the
Zodiack
,
but
took
up
more
space
some
,
than
others
as
in
particular
,
Leo
possest
more
room
than
Cancer
;
Taurus
than
Gemini
.
I
say
,
than
Gemini
,
which
though
composed
of
Castor
and
Pollux
;
in
so
little
space
as
is
allowed
them
,
it
is
impossible
the
one
should
rise
,
when
the
other
Sets
,
and
both
in
the
East
:
but
this
Empiricus
interprets
of
the
two
1.
adven
.
Physic.
Hemisphears
.
I
omit
to
insist
upon
this
,
that
all
Nations
had
not
the
same
Constellations
:
as
among
the
Egyptians
was
no
Bear
,
no
Cepheus
,
no
Dragon
;
but
other
formes
or
representations
,
as
Tatius
reports
;
and
shall
add
only
,
that
Eudoxus
seems
to
have
been
the
first
,
who
partly
out
of
the
Egyptian
Figures
,
partly
out
of
the
Grecian
,
furnished
the
whole
Zodiack
with
Images
resembling
the
Asterismes
,
(
as
men
had
fancied
,
at
least
)
and
caused
them
to
be
drawn
on
a
Globe
,
or
solid
Sphear
.
For
,
Aratus
(
upon
whose
Poem
,
intitul'd
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
,
Apparences
,
there
have
been
so
many
Commentaries
set
forth
,
as
that
no
fewer
than
forty
have
been
extant
in
Greek
;
besides
those
of
Cicero
,
Germanicus
,
Avienus
,
and
other
Latin
Interpreters
.
)
did
no
more
,
but
only
express
in
verse
,
what
Eudoxus
had
said
before
in
prose
,
of
this
argument
;
as
Hipparchus
Bythinus
demonstrates
.
I
know
not
,
whether
it
would
be
seasonable
for
me
,
lib.
1.
in
Arat.
●han●
.
here
to
advertise
,
that
it
is
no
wonder
Aratus
erred
so
grosly
in
many
particulars
;
considering
that
(
as
is
written
in
his
life
)
he
Living
with
Antigonus
Gonata
,
in
the
quality
of
his
Physician
,
and
Nicander
in
the
quality
of
his
Astrologer
;
and
both
were
good
at
Poetry
:
Antigonus
commanded
the
Physician
to
give
him
a
tryall
of
his
Poesie
,
upon
an
Argument
in
Astrology
;
and
the
Astrologer
to
give
another
of
his
,
upon
somthing
in
Physick
:
delivering
to
the
one
,
the
Book
of
Eudoxus
;
and
to
the
other
,
all
that
was
extant
of
Treacles
,
Antidotes
,
or
Counterpoisons
.
So
each
wrote
of
what
he
did
not
well
understand
.
One
thing
I
shall
not
,
forget
;
and
that
is
,
that
the
Phenomena
of
Euclid
,
who
lived
neer
about
the
same
time
,
and
taught
at
Alexandria
(
as
in
the
Memorials
of
Pappus
)
were
quite
of
another
kind
;
lib.
7.
being
indeed
no
other
,
but
certain
Principles
of
Astronomy
,
concerning
the
figure
of
the
World
,
and
the
Circles
of
the
Sphear
,
and
chiefly
,
that
of
the
Zodiack
.
But
,
to
return
back
to
the
more
primitive
Greeks
;
I
remember
and
next
of
Thales
Milesius
.
I
said
,
that
Thales
Melesius
was
accounted
the
First
,
who
after
old
Hesiod
and
Homers
Dayes
,
enquired
into
the
Order
of
the
Stars
.
And
,
certainly
He
was
the
Man
,
who
among
the
Grecians
may
challenge
the
Palme
;
as
to
Antiquity
;
for
,
Apuleius
calls
him
,
ut
antiquissimus
,
sic
peritissimus
Astrorum
Contemplator
,
and
Eudemus
in
Laertius
attesteth
,
that
this
was
lib.
1.
the
Opinion
of
most
,
adding
moreover
,
that
Xenophanes
and
Herodotus
highly
admired
him
,
for
that
he
had
first
predicted
the
Eclypses
and
Conversions
of
the
Sun
;
and
that
Heraclitus
and
Democritus
witnesseth
as
much
.
And
whereas
Apuleius
further
subjoyns
,
that
he
found
out
the
motions
and
oblique
tracts
of
the
Syderal
Lights
:
Pliny
ascribes
that
to
Auaximander
,
a
Disciple
of
Thales
Milesius
,
(
whence
he
was
said
Rerum
fores
aperuisse
,
to
have
opened
the
Doors
of
Celestial
matters
)
and
Diodorus
to
one
Oenopides
Chius
:
which
Thales
could
not
yet
be
ignorant
of
the
Obliquity
of
the
Zodiack
,
when
he
had
written
of
the
Solstices
,
and
Equinoxes
,
and
had
conversed
a
long
time
with
the
Egyptians
in
their
own
Country
,
as
Laertius
remembers
.
Further
,
it
is
delivered
to
us
,
that
among
others
,
he
predicted
that
notable
Eclipse
of
the
Sun
,
which
hapned
in
the
time
of
the
warre
betwixt
the
Meads
and
Lydians
;
which
he
could
not
doe
by
any
other
reason
,
but
only
because
,
coming
newly
out
of
Egypt
,
he
had
learned
,
that
Eclipses
generally
return
upon
the
same
Day
after
the
space
of
nineteen
Years
;
and
having
taken
notice
of
one
,
that
fell
out
19.
Years
before
,
he
concluded
that
there
would
be
one
at
such
a
time
.
Nor
is
there
reason
why
any
should
think
,
that
otherwise
his
whole
life
might
be
sufficient
to
observe
all
the
motions
of
the
Sun
and
Moon
,
as
from
thence
to
be
able
to
invent
all
things
necessary
for
the
calculation
of
the
times
of
their
Several
Eclipses
.
Moreover
,
it
in
vit.
Dionys.
doth
not
appear
,
how
by
any
other
way
,
but
that
Helicon
Cyzicenus
came
afterward
to
fore-tell
that
Eclipse
of
the
Sun
(
mentioned
in
Plutarch
)
for
which
he
was
so
much
admired
by
Dyonisius
,
and
rewarded
with
a
Talent
of
Gold
.
Nor
likewise
,
how
Sulpitius
Gallus
could
fore-tell
that
other
of
the
Moon
.
which
as
most
opportunely
predicted
to
the
Roman
Army
,
then
ready
to
joyne
battell
with
the
Persian
,
is
so
higly
celebrated
,
not
only
by
Plutarch
and
Pliny
,
but
also
by
Valerius
,
Quintilian
,
and
other
Historians
:
for
other
Rule
for
the
calculation
of
future
Eclipses
,
there
was
none
before
Hipparchus
,
who
invented
Hypotheses
and
Tables
fit
for
that
purpose
.
Besides
,
what
Laertius
imputed
to
Anaximander
,
Plinius
as
confidently
imputes
to
one
Anaximenes
,
an
Auditor
of
his
:
(
namely
that
he
should
be
the
Inventor
of
that
Gnomon
,
by
which
the
Conversions
of
the
Sun
,
or
the
Solstices
and
Equinoxes
,
were
indicated
,
and
that
he
set
up
such
a
one
at
Lacedemon
.
)
Neer
upon
the
same
then
of
Pythagoras
,
and
his
Disciples
.
time
was
it
,
that
Pythagoras
is
said
to
have
first
discoursed
(
though
Phavorinus
,
in
Laertius
,
confers
that
honour
upon
Parmenides
,
)
that
Lucifer
and
Vesper
was
one
and
the
same
Star
of
Venus
,
Now
,
whether
may
we
conceive
,
that
he
borrowed
this
of
the
Egyptians
,
from
whom
being
taught
,
that
not
only
Venus
,
but
Mercury
also
,
were
carried
round
about
the
Sun
,
as
their
Center
,
so
that
one
and
the
same
might
be
both
Morning
and
Evening
Star
:
possibly
,
from
thence
he
might
take
the
hint
of
his
Conjecture
,
that
the
Sun
was
the
Center
of
not
only
those
two
,
but
of
the
other
Planets
also
,
and
consequently
of
the
whole
World
:
and
moreover
that
the
Earth
it self
,
as
one
of
the
Planets
,
moved
about
the
Sun
?
For
truely
,
this
was
an
eminent
and
constant
Tenent
in
his
School
;
as
may
be
understood
not
only
from
Aristotle
in
the
general
,
but
also
from
Laertius
in
particular
of
2.
de
coelo
.
13.
de
Arenar
,
num.
Philolaus
,
and
from
Archimed
of
Aristarchus
,
both
Pythagorus
his
Disciples
:
that
we
may
not
rehearse
all
those
many
passages
in
Plutarch
,
concerning
this
memorable
particular
;
nor
name
those
,
who
held
,
that
the
Earth
was
not
so
much
moved
about
the
Philolaus
,
Aristarehus
,
Timaeus
.
Sun
as
dayly
turned
rouud
upon
an
Axis
of
its
own
;
as
Timaeus
,
a
Pythagorian
also
,
who
is
therefore
by
Synesius
esteemed
,
after
de
don
.
ad
paeon.
in
Timaeun
.
Plato
,
the
most
excellent
Astronomer
.
Furthermore
,
in
the
next
Age
after
Thales
,
or
neere
upon
,
comes
Cleostratus
(
the
same
who
was
beleeved
to
have
deprehended
.
After
these
succeeded
Cleostratus
.
the
Signes
of
the
Zodiack
)
and
he
,
seriously
remarking
that
the
Intercalation
,
which
as
we
said
,
was
wont
to
be
made
every
fourth
Year
,
celebrated
with
the
Olympick
Games
,
did
indeed
restore
the
motion
of
the
Sun
to
the
same
Day
again
;
but
did
not
restore
the
motion
of
the
Moon
till
the
eight
Year
,
or
two
Olympiades
,
in
which
the
intercalatory
Dayes
amounted
to
ninety
Dayes
,
or
three
months
:
He
,
we
say
,
thereupon
interduced
,
instead
of
the
Tetacteris
,
or
space
of
four
Years
,
the
Octaeteris
,
or
space
of
eight
Years
,
which
compleatly
past
,
the
New-Moons
,
and
Full-Moons
would
returne
again
on
the
same
Dayes
.
But
,
when
in
short
time
men
had
perceived
,
that
this
Institution
failed
them
,
in
exactness
of
computation
;
and
that
sundry
wayes
had
bin
attempted
to
cure
this
uncertainty
:
at
length
riseth
up
Meton
,
somwhat
more
ancient
than
Eudoxus
;
and
he
demonstrateth
from
Meron
.
&c.
the
New-Moons
,
and
Full-Moons
Eclyptical
,
that
they
did
not
return
upon
the
same
Dayes
,
till
after
full
nineteen
Years
:
and
thereupon
he
became
the
Author
of
the
Enneadecaeteris
,
or
Period
,
or
Cycle
of
19.
Years
.
In
respect
of
which
discovery
,
together
with
the
Heliotrope
,
or
Sun
Diall
he
made
at
Athens
,
and
some
other
the
like
Inventions
,
he
was
in
eminent
esteem
among
the
Athenians
.
But
as
concerning
that
Period
;
Callippos
,
familarly
acquainted
with
Aristotle
,
discovering
it
to
be
too
long
,
by
the
fourth
part
of
a
Day
;
inferred
,
that
from
four
Periods
one
whole
Day
ought
to
be
detracted
:
and
so
erected
a
new
Period
,
or
Cycle
of
Sixty
six
Years
,
or
four
times
nine
,
at
the
end
of
which
one
Day
was
to
be
cut
off
;
and
this
was
called
the
Callippik
Period
,
and
remained
in
use
for
a
long
time
together
.
After
him
succeeded
Hipparchus
,
who
detecting
this
Period
,
to
be
yet
too
long
;
demonstrateth
that
after
four
Callippik
Periods
,
or
three
hundred
and
four
Years
,
there
would
remain
one
whole
Day
too
much
.
And
in
truth
,
the
experience
of
many
succeding
Ages
declared
,
that
to
this
detraction
of
Hipparchus
,
nine
or
ten
Years
over
and
above
were
to
be
expected
.
However
,
it
is
worthy
our
notice
,
that
the
Period
of
Meton
,
together
with
the
Conection
of
it
,
applied
by
Callippus
,
was
of
long
use
in
the
Church
under
the
name
of
the
Golden-Number
:
though
wanting
the
Application
of
Hipparchus
his
Correction
:
also
,
a
mistake
of
about
four
Dayes
,
relating
to
the
New
and
Full
Moons
,
crept
into
the
account
,
even
from
the
time
of
the
Nicene
Councel
;
which
was
one
of
the
two
main
causes
of
the
Reformation
of
the
Kalender
in
the
eighty
second
Year
of
the
last
Age.
And
now
we
have
an
opportunity
to
speak
more
expresly
of
Articl
.
7.
Eudoxus
,
who
first
discovered
the
necessitie
of
manifold
Spheares
.
Eudoxus
,
so
frequently
mentioned
.
This
man
,
well
understanding
,
after
his
return
out
of
Egypt
,
that
not
only
the
Sun
and
Moon
,
but
also
the
five
Errant
Stars
,
did
keep
their
courses
round
in
the
Zodiack
;
and
so
,
as
that
aswell
the
Sun
and
Moon
,
as
those
wandering
Stars
did
sometimes
vary
their
latitude
,
or
deviate
from
the
Ecliptick
Line
in
the
midle
of
the
Zodiack
;
(
for
,
he
thought
that
the
Sun
was
also
extravagant
,
as
well
as
the
rest
;
and
again
,
that
the
other
Planets
did
not
only
go
forward
,
but
were
also
some
times
upon
their
retreat
backward
;
and
somtimes
made
a
hault
or
stood
still
:
we
say
,
pondering
all
these
various
motions
in
his
mind
,
and
casting
about
what
might
be
the
reasons
thereof
in
nature
;
he
at
last
imagined
to
himself
,
that
besides
the
Aplanes
or
Sphear
of
Fixt
Stars
,
which
being
supreme
,
carried
all
the
rest
toward
the
West
,
there
ought
also
to
be
allowed
three
other
Sphears
,
as
well
to
the
Sun
,
as
to
the
Moon
,
and
four
to
each
one
of
the
other
Errant
Stars
;
of
which
one
,
and
that
the
highest
,
should
follow
the
Impression
of
the
Fixt
Stars
,
or
rather
of
the
Primum
Mobile
;
the
next
to
that
should
move
counter
to
the
First
,
or
toward
the
East
;
the
third
make
the
deviation
from
the
Ecliptick
,
or
midle
of
the
Zodiack
;
and
the
fourth
,
or
lowest
,
cause
in
the
Stars
their
Direction
,
Station
and
Retrogradation
,
and
that
by
a
certain
Vibration
,
or
Waving
to
and
agen
.
So
that
he
supposed
in
all
,
twenty
seven
Sphears
,
and
all
those
Concentricall
,
that
the
Superior
might
carry
on
the
Inferior
,
and
these
might
be
turned
round
within
those
.
Afterwards
,
Callippus
adjoyned
two
Sphears
to
the
Sun
,
two
to
the
Moon
,
and
one
a
peece
to
Mars
,
Venus
,
and
Mercury
:
and
so
made
thirty
three
.
And
Aristotle
,
to
all
the
Sphears
,
which
did
not
follow
the
motion
of
the
Aplanes
,
or
Primum
Mobile
(
excepting
only
the
Lunar
Sphears
)
added
as
many
more
,
which
he
called
the
Revolvent
ones
,
to
the
end
he
might
conform
them
to
the
motion
of
the
Inerrant
Sphear
,
or
Primum
Mobile
:
and
so
in
the
whole
he
constituted
Fifty
six
Sphears
;
for
as
much
,
at
least
,
as
we
can
collect
from
his
own
context
.
Now
all
these
,
and
even
Plato
himself
likewise
,
thought
that
the
Moon
was
the
lowest
of
all
the
Planets
;
next
to
her
,
the
Sun
;
and
above
the
Sun
the
five
wandering
Stars
:
Nor
indeed
doth
it
appear
,
that
Archimedes
himself
Living
a
whole
Age
or
two
after
them
,
represented
the
Planets
in
any
other
,
than
this
very
order
,
in
that
so
famous
Sphear
of
his
In
which
though
Claudian
tells
us
,
that
no
more
was
represented
,
but
only
the
motions
of
the
Sun
and
Moon
;
Percurrit
proprium
mentitus
Signifer
annum
,
in
Epigram
.
Et
simulata
novo
Cynthia
mense
redit
:
Yet
Cicero
adds
other
motions
,
when
speaking
of
Archimedes
,
he
saith
;
when
he
collected
together
the
motions
of
the
2.
de
divinat
.
Moon
,
Sun
,
and
five
wandering
Stars
;
he
did
the
same
as
that
God
,
who
in
Platoes
Timaeus
framed
the
World
,
that
one
and
the
same
Conversion
might
regulate
sundry
motions
,
most
different
each
from
other
in
slowness
and
swiftness
.
But
,
Hipparchus
afterwards
finding
,
that
aswell
the
Sun
,
as
the
Moon
and
the
other
five
Stars
did
come
somtimes
neerer
to
the
Earth
,
and
sometimes
again
mounted
up
farther
from
it
;
and
plainly
perceiving
that
that
particular
apparence
could
not
possibly
be
explicated
by
those
Sphears
,
that
were
all
Concentrical
to
the
Earth
:
therefore
,
wholly
rejecting
them
,
he
resolved
,
that
the
motions
of
the
Planets
were
to
be
accounted
Eccentrick
;
and
though
he
could
not
himself
determine
each
particular
,
he
yet
demonstrated
the
way
,
in
which
Ptolomy
afterwards
insisting
,
accomplisht
the
Invention
.
But
,
before
wee
advance
further
,
we
are
to
commemorate
two
or
three
Persons
of
note
,
by
whose
Observations
both
Hipparchus
and
Ptolomy
profited
very
much
.
One
was
Timocharis
,
who
,
about
three
hundred
Years
before
Christ
,
among
other
things
relating
to
the
Fixt
Stars
,
observed
that
that
Star
which
is
called
Spica
Virginis
,
doth
antecede
the
point
of
the
Atumnal
Equinox
,
by
eight
degrees
.
And
with
him
are
we
to
joyn
Arist●ll●s
,
whose
Observations
of
something
about
the
Fixt
Star
;
Ptolomy
made
great
use
of
,
in
order
to
his
demonstrating
that
the
Fixt
Stars
never
change
their
latitude
.
Afterwards
(
scarce
in
Age
)
succeded
Eratosthenes
,
who
being
Library-keeper
to
Ptolomy
Evergeta
the
fomer
,
perswaded
him
to
set
up
the
Armillae
in
the
Porticus
of
Alexandria
;
which
Hipparchus
and
Ptolomy
Prolom
.
lib.
1.
cap.
11.
afterwards
made
use
of
;
and
himself
,
among
other
things
observed
,
that
the
Obliquity
of
the
Zodiack
was
of
twenty
three
degrees
,
and
fifty
one
minutes
;
which
account
Hipparchus
and
Ptolomy
constantly
adhered
to
.
Now
that
we
may
at
length
remember
the
great
Hipparchus
,
Articl
.
8.
Hipparchus
,
who
first
observed
the
places
of
the
Fixt
Stars
,
according
to
Long.
and
Latitude
.
who
florish't
neer
upon
an
hundred
and
forty
Years
before
Christ
:
truely
,
we
find
it
no
easy
task
to
recount
,
how
highly
Astronomy
was
beholding
to
him
.
For
,
in
the
first
place
,
examining
that
foresaid
Observation
of
Timocharis
,
with
some
others
;
albeit
he
could
not
conceive
them
to
be
in
all
points
exact
,
yet
because
himself
had
found
that
Spica
Virginis
did
not
antecede
the
Equinoctial
point
by
more
than
six
degrees
,
and
the
other
Stars
in
the
like
Proportion
:
he
thence
understood
,
that
the
Fixt
Stars
also
were
moved
Eastward
according
to
the
Zodiack
;
and
thereupon
wrote
a
Book
of
the
Transgression
of
the
Solstices
&
Equinoxes
.
And
,
being
that
in
his
time
,
as
not
long
agoe
in
Tycho
Brahes
,
there
appeared
a
certain
New
Star
,
he
therefore
came
to
doubt
(
to
speak
the
language
of
Pliny
lib.
2.
cap.
26.
concerning
him
)
whether
the
like
happened
often
,
or
not
;
and
whether
those
Stars
,
that
were
thought
to
be
fixt
,
had
also
some
certain
motion
peculiar
to
themselves
.
Wherefore
(
as
the
same
Pliny
goes
on
)
he
attempted
a
task
of
difficulty
sufficient
even
for
the
Gods
themselves
,
namely
to
number
the
Stars
for
Posterity
,
and
reduce
the
heavenly
Lights
to
a
rule
,
so
that
by
the
help
of
Instruments
invented
,
the
particular
place
of
each
one
,
together
with
its
magnitude
,
might
be
exactly
designed
:
and
whereby
men
might
discern
,
not
only
whether
they
disappeared
,
or
newly
appeared
,
but
also
whether
they
removed
their
Stations
;
as
likewise
,
whether
their
magnitude
encreased
,
or
diminished
;
Leaving
Heaven
for
and
Inheritance
for
the
Witts
of
succeding
Ages
,
if
any
were
found
acute
and
industrious
enough
to
comprehended
the
mysterious
orders
thereof
.
And
this
was
the
first
time
when
the
places
of
the
Fixt
Stars
were
observed
and
markt
out
according
to
Longitude
and
Latitude
:
and
that
Catalogue
of
the
Fixt
Stars
,
which
he
composed
,
is
the
very
same
,
which
Ptolomy
afterward
inserted
into
his
Almagest
.
In
the
lib.
7.
cap.
next
place
,
he
denoted
was
positions
sundry
Stars
had
in
respect
each
of
other
;
whether
they
were
posited
in
a
right
Line
;
or
in
a
triangular
form
;
or
in
quadrate
or
square
,
&c.
as
is
manifest
even
from
Ptolomy
himself
.
Further
,
though
the
motions
of
ibid
cap.
1.
Sun
and
Moon
were
already
in
some
measure
known
;
he
yet
made
that
knowledge
much
more
exact
.
For
,
He
did
not
only
much
correct
the
Callippick
Period
,
formerly
spoken
of
,
but
also
,
He
also
corrected
the
Callippick
Period
,
and
predicted
future
Eclipses
,
for
600.
Years
together
.
having
collected
a
long
Series
of
Eclipses
(
namely
,
from
the
time
of
those
Babylonish
ones
,
in
the
Dayes
of
Mardocempades
,
down
to
those
observed
by
himself
,
for
full
six
hundred
Years
together
.
)
and
remarking
,
that
neither
the
like
Eclipses
did
return
on
the
same
Dayes
,
after
the
space
of
every
nineteen
Years
,
nor
that
after
some
recurses
of
ten
Novennales
,
or
ten
times
nine
Years
,
any
such
Eclipses
happened
at
the
times
supposed
;
and
that
the
cause
thereof
consisted
both
in
the
various
Latitude
of
the
Moon
,
and
the
anticipation
of
her
Nodi
,
or
Knotts
,
and
her
Eccentricicy
,
by
reason
whereof
her
motions
to
her
Apogeium
were
found
to
be
sometimes
slower
,
and
those
to
her
Perigeium
more
speedy
:
therefore
,
we
say
,
He
comprehended
and
gave
Reasons
for
all
these
difficulties
,
and
composed
certain
Hypotheses
,
and
according
to
them
,
certain
Tables
,
by
which
he
could
safely
and
exactly
calculate
and
predict
what
Eclipses
were
to
follow
,
how
great
they
were
,
and
when
.
And
this
was
it
,
which
Pliny
remembred
,
when
having
spoken
of
Thales
,
and
Sulpitius
Gallus
,
he
comes
to
mention
Hipparchus
.
After
these
(
saith
He
)
Hipparchus
foretold
the
courses
of
both
Luminaries
,
for
six
hundred
Years
to
come
;
comprehending
the
months
,
Dayes
and
hours
of
Nations
,
and
the
Scituations
of
Places
,
and
turns
of
People
:
his
age
testifying
,
that
he
did
all
these
great
things
,
only
as
he
was
partaker
of
Natures
Councels
.
For
,
it
must
be
,
that
Hipparchus
,
besides
the
precise
times
,
when
such
or
such
Eclipses
were
to
be
visible
to
the
Horizon
of
Rhodes
,
or
Alexandri●
,
pointed
forth
also
some
Countries
,
and
principal
Citties
,
together
with
the
Designation
of
the
Months
in
use
among
them
;
as
also
the
very
Days
and
hours
when
each
Eclipse
would
happen
;
and
other
praedictions
succeding
to
Rome
,
in
the
Dayes
of
Pliny
.
Again
,
it
is
well
worthy
our
recital
,
that
Hipparchus
labouring
with
long
desire
both
to
constitute
Hypotheses
,
and
reduce
into
Tables
the
motions
of
the
other
Planets
,
or
five
wandering
Stars
;
and
yet
not
being
able
to
furnish
himself
either
from
the
Egyptians
,
or
from
his
Country
men
the
Grecians
,
with
any
competent
Observations
respective
to
those
Planets
,
(
for
while
the
places
of
the
Fixt
Stars
remained
unknown
,
it
was
impossible
any
such
could
be
made
)
and
again
those
he
had
himself
made
,
were
of
a
much
shorter
time
,
than
was
requisite
for
the
establishing
any
thing
certain
and
permanent
in
that
sort
:
He
therefore
only
digested
such
Observations
as
he
had
recorded
by
him
,
into
the
best
order
and
method
he
could
devise
;
and
so
left
them
for
their
use
and
improvement
,
who
should
come
after
him
,
in
case
any
were
found
capable
of
understanding
and
advancing
them
.
And
at
length
,
by
good
fortune
,
it
so
fell
out
,
that
those
his
Observations
came
into
the
hands
of
Ptolomy
;
who
comparing
them
with
his
own
,
and
finding
them
judicious
and
exact
,
thereupon
first
began
to
erect
both
Hypotheses
,
and
Tables
of
Motions
fit
for
those
Planets
:
yet
not
without
much
timerousness
and
diffidence
;
because
his
Observations
being
but
few
,
nor
of
sufficient
time
,
he
durst
not
promise
himself
any
certainty
of
his
Tables
for
any
considerable
space
,
or
number
of
Years
.
But
,
for
more
assurance
let
us
hear
his
own
ingenious
Confession
in
that
point
.
The
Time
(
saith
He
)
from
whence
Almagest
.
lib.
9
cap
2.
we
have
the
Observations
of
the
Planets
set
down
,
is
so
vastly
short
,
in
comparison
of
the
greatness
of
Coelestial
vicissitudes
,
as
that
it
renders
all
predictions
,
that
are
for
any
great
number
of
Years
to
come
,
infirm
and
uncertain
.
And
therefore
I
judge
that
Hipparchus
(
that
zealous
lover
of
truth
)
considering
this
difficulty
,
and
withall
receiving
not
so
many
true
Obsertions
from
the
Ancients
,
as
he
bequeath'd
to
us
,
undertook
indeed
the
business
of
the
Sun
and
Moon
,
and
demonstrated
that
it
might
be
performed
,
by
equal
and
circular
motions
:
yet
,
as
for
that
of
the
Planets
,
those
Commentaries
of
his
,
which
have
come
into
our
hands
,
clearly
shews
,
that
he
attempted
it
not
:
but
collecting
all
his
own
Observations
concerning
them
together
,
into
one
order
and
method
,
for
their
more
commodious
use
,
resigned
them
to
the
industry
of
after
times
;
having
first
demonstrated
,
that
they
were
not
congruous
to
those
Hypotheses
,
which
the
Mathematicians
of
those
Dayes
made
use
of
.
And
,
for
Others
;
sure
I
am
,
that
either
they
demonstrated
nothing
at
all
,
or
else
only
attempted
the
business
,
and
left
it
unfinisht
.
But
,
Hipparchus
being
eminently
knowing
in
all
kinds
of
learning
,
conceived
,
that
he
ought
not
(
as
others
had
done
before
him
)
to
attempt
,
what
he
should
not
be
able
to
accomplish
.
So
that
we
see
,
Ptolomy
was
the
first
,
who
from
true
Observations
,
reduced
the
Motions
of
the
Planets
into
Hypotheses
and
Tables
correspondent
.
But
before
we
speak
more
particularly
of
him
,
who
lived
Articl.
9.
about
an
hundred
and
thirty
Years
after
Christ
;
forasmuch
as
in
the
space
of
time
betwixt
Hipparchus
and
Ptolomy
,
these
studies
Betwixt
Hipparchus
and
Ptolemy
,
came
Sosigenes
,
of
Alexandria
,
by
whose
help
Jul.
Caesar
endeavored
the
reformation
of
the
Calendar
.
so
florisht
at
Alexandria
,
as
that
Julius
Caesar
returning
thence
,
brought
along
with
him
that
Sosigenes
,
by
whose
assistance
he
endeavoured
the
restitution
of
the
Calendar
,
and
so
may
be
thought
to
have
propagated
the
Study
of
Astronomy
among
the
Romans
:
let
us
reflect
a
little
upon
that
time
,
and
see
what
care
they
then
had
of
Celestial
matters
.
In
the
first
place
,
we
are
to
lay
aside
the
Commemoration
of
Sulpitius
Gallus
(
of
whom
more
then
once
afore
,
as
one
that
falls
not
under
this
account
,
concerning
whom
we
may
not
yet
forget
,
what
Cato
is
induced
by
Cicero
,
saying
.
While
we
saw
that
Gallus
dye
,
that
familiar
friend
of
thy
Father
,
O
Scipio
,
who
was
restless
in
measuring
Heaven
and
Earth
;
I
say
,
while
we
saw
him
dying
even
in
that
Study
.
How
often
did
Day
oppress
him
,
when
he
had
set
himself
to
observe
and
describe
somthing
in
the
Night
?
and
how
often
did
Night
oppress
him
,
when
he
had
begun
his
Speculations
in
the
Morn
?
How
was
he
delighted
,
when
he
had
a
long
time
before
predicted
to
us
Eclipses
of
the
Sun
and
Moon
?
&c.
For
he
was
a
man
clearly
singular
,
and
in
an
Age
when
so
great
ignorance
and
neglect
of
good
Arts
tyrannized
over
mens
minds
,
being
himself
studious
and
inquisitive
,
could
not
but
have
borrowed
his
skill
either
from
Egypt
or
Greece
,
where
having
obtained
a
Series
of
Eclipses
,
and
the
way
of
deducing
them
through
the
circuit
of
of
nineteen
Years
(
as
we
said
afore
)
he
became
able
to
calculate
them
,
so
as
Cicero
relates
For
,
as
to
the
rest
;
how
great
doe
you
think
was
the
ignorance
and
neglect
,
nay
even
contempt
of
studies
of
this
nature
among
the
Romans
?
Why
,
truely
so
great
,
as
that
Virgil
could
not
dissemble
it
,
in
the
Poesy
attributed
to
Anchisa
,
according
to
which
the
Romans
should
indeed
come
to
rule
the
World
;
but
yet
should
yeeld
to
others
,
in
learning
to
know
the
Stars
,
and
describe
the
Heavens
.
—
Caelique
meatus
Describent
radio
,
&
surgentia
sidera
dicent
.
6.
A●nl
.
And
Cato
himself
is
cited
by
Agellius
to
have
left
in
writing
that
it
was
not
lawfull
to
write
what
is
in
a
Table
kept
by
the
High
Preist
,
how
often
scarcity
of
Provision
would
happen
,
how
lib.
2.
c
28.
often
the
light
of
the
Sun
,
or
Moon
should
be
darkned
:
so
far
,
saith
Gellius
,
did
Cato
contemne
the
Science
of
Astronomy
,
and
thought
it
useless
either
to
know
,
or
fore-tell
the
Eclipses
of
Sun
and
Moon
.
Furthermore
,
though
from
times
as
high
as
Numa
,
the
Romans
made
several
Intercalations
;
yet
they
took
all
their
art
of
that
Sort
,
from
the
Greeks
:
and
Pliny
remarks
,
that
in
France
,
Spain
and
Africa
,
there
was
no
one
man
,
who
could
so
much
as
tell
the
Rising
of
the
Stars
.
Nevertheless
we
are
not
to
1.
Meteor
7.
Pythias
Massiliensis
,
a
Gaul
.
and
contemporary
to
Alex.
of
Maced
.
forget
,
that
among
the
Gauls
was
one
Pythias
,
the
Philosopher
(
as
Cleomedes
calls
him
)
of
Masilia
,
who
about
the
time
of
Alexander
of
Macedon
,
found
the
proportion
of
the
Gnomon
to
the
Solsticial
shadow
,
to
be
the
same
at
Massilta
,
as
Strabo
tells
us
Hipparchus
had
observed
it
at
Byzantium
;
who
first
attempted
the
Northern
Ocean
,
and
discovered
the
utmost
Thule
,
in
which
Cleomedes
cohaerently
proves
the
Summer
Tropick
to
be
the
same
with
the
Polar
,
or
greatest
of
allwayes
apparent
ones
:
and
who
(
as
from
his
Book
,
de
Oceano
,
may
be
inferred
)
was
excedingly
curious
to
find
out
what
was
the
Position
of
Heaven
,
respective
to
the
variety
of
Countries
and
Climates
.
But
,
not
so
lib.
7.
cap.
60.
soon
to
digress
from
the
Romans
;
Pliny
delivers
,
that
in
those
first
times
of
Romes
being
a
Common-wealth
,
the
Invention
of
Dialls
was
very
raw
and
imperfect
:
for
that
they
had
only
the
risings
and
settings
named
,
out
of
twelve
Tables
.
That
after
some
Years
,
they
added
the
Meridian
,
and
by
the
indication
of
a
certaine
columne
,
the
last
hour
:
nor
that
neither
,
but
only
in
clear
weather
,
even
as
long
as
till
the
first
Punick
warre
.
Afterward
they
advanced
so
far
,
as
to
make
one
,
or
two
Sun
Dialls
;
but
not
with
lines
exactly
correspondent
to
the
hours
,
untill
about
an
Age
after
,
when
Q.
Marcus
Philippus
ordered
the
busi
Quintus
Marcius
Philippus
,
&c.
ness
more
diligently
and
succesfully
.
And
,
because
the
hours
of
the
Day
remained
yet
uncertain
in
dark
and
cloudy
weather
,
Nasica
Scipio
began
to
divide
the
Hours
of
Day
and
Night
equally
Nasica
Scipio
,
Romans
.
by
Water
distilling
from
Vessel
to
Vessel
,
and
called
it
The
Diall
within
Doores
,
in
the
Year
Urbis
conditae
DXCV.
And
till
then
,
saith
Pliny
,
Populi
Romani
indiscreta
lux
fuit
.
And
thus
much
of
Hipparchus
,
and
some
Astronomers
betwixt
him
and
the
Prince
of
them
all
,
Ptolomy
.
And
of
him
,
so
great
is
his
name
,
all
we
need
to
say
,
is
only
,
Articl.
10.
that
He
was
the
very
Founder
of
the
Art
,
or
Science
of
Astronomy
.
Prolemy
,
the
true
Founder
of
Astronomy
in
one
intire
structure
.
For
,
though
Hipparchus
had
indeed
,
as
it
were
hewn
out
the
Stones
and
Beams
fit
for
so
noble
a
Structure
,
and
prepared
good
part
of
the
Materials
;
yet
was
it
Ptolomy
alone
who
put
them
into
Order
and
Form
,
and
by
adding
many
admirable
Inventions
of
his
own
,
by
infinite
labour
and
cost
,
erected
that
so
famous
Building
,
worthily
called
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
,
the
great
Co-ordination
,
Construction
,
or
Composition
;
which
consisting
of
no
less
than
thirteen
Books
,
contains
all
the
Doctrine
,
that
could
then
be
advanced
,
concerning
the
Sun
,
Moon
,
and
aswell
the
Fixt
,
as
wandering
Stars
.
And
,
albeit
one
Day
teacheth
another
,
and
that
(
as
Himself
had
truely
foretold
)
there
came
others
after
him
,
who
saw
good
cause
for
the
Castigation
and
Correction
of
many
things
delivered
in
that
Work
:
yet
,
in
the
general
,
the
Art
he
had
instituted
,
remained
firm
and
constant
,
and
was
afterwards
imbraced
,
not
only
by
the
Alexandrians
,
but
also
by
all
the
Arabians
,
Latins
and
others
,
who
devoted
themselves
to
the
service
of
Urania
,
ever
since
.
For
,
that
the
Study
of
her
Celestial
mysteries
continued
in
great
esteem
and
Veneration
,
at
Alexandria
,
for
some
Ages
after
his
desease
,
may
be
undeniably
attested
,
not
only
from
hence
,
that
(
among
others
)
both
Theon
,
and
Who
next
resigned
it
to
Theon
and
Pappus
,
both
Alexandrians
.
Pappus
,
named
Alexandrians
,
were
eminent
therein
;
of
which
the
one
put
forth
eminent
Commentaries
upon
Ptolomies
Works
,
and
the
other
,
among
sundry
excellent
peeces
,
of
which
his
sixth
Book
of
Mathematicall
Collections
is
one
,
observed
,
that
about
four
hundred
Years
from
Christ
,
the
Obliquity
of
the
Ecliptick
was
not
so
great
,
as
Erathosthenes
,
Hipparchus
and
Ptolomy
had
conceived
:
but
neer
upon
the
same
we
discover
it
to
be
in
our
Dayes
:
we
say
,
that
this
is
not
the
only
Monument
that
is
extant
of
the
flourishing
of
Astronomy
at
Alexandria
,
long
after
Prolomy
had
given
it
so
great
a
Reputation
there
;
but
there
remains
another
as
fresh
and
lively
,
which
is
the
memorialls
of
those
Patriarchs
of
the
Alexandrine
Church
,
to
whose
judgement
the
determination
of
that
great
dispute
about
the
true
time
of
Easter
,
was
thought
fit
to
be
wholly
referred
,
aswell
by
the
Nicene
Councel
,
as
by
divers
learned
Bishops
afterward
,
and
by
Holy
Leo
himself
,
then
Pope
.
Now
,
among
these
Patriarchs
were
Theophilus
,
Cyrillus
and
Proterius
,
whose
advice
and
directions
were
thought
necessary
,
in
regard
that
the
Controversies
raised
about
the
Celebration
of
Easter
,
about
the
time
of
the
Veneral
Equinox
,
about
the
Full-Moon
next
following
,
and
about
constituting
certain
constant
Rules
respective
to
them
;
could
not
be
better
composed
,
than
by
the
definitive
sentence
of
these
Prelates
,
who
Living
at
Alexandria
,
where
Astronomy
was
in
such
Height
,
had
the
advantage
of
others
,
in
point
of
knowing
those
things
which
were
requisite
to
the
finding
out
of
the
truth
.
But
,
of
the
Arabians
,
who
in
the
Study
of
Astronomy
succeded
the
Alexandrians
,
and
translated
into
their
own
language
,
the
Great
Composition
of
Ptolomy
,
which
they
called
Almagestum
;
the
First
,
and
most
worthy
to
be
remembred
,
was
Albategnius
otherwise
and
long
after
.
to
Albategnius
,
then
to
called
Mahometes
Aractensis
,
born
of
a
Family
of
the
Dynastae
of
Syria
;
He
about
800
,
Years
after
Christ
,
made
divers
Celestial
Observations
,
partly
at
Aracta
,
and
partly
at
Antioch
:
and
found
,
both
that
the
Apogeium
of
the
Sun
,
since
the
Dayes
of
Ptolomy
,
was
advanced
to
the
following
Signes
;
and
that
the
Stars
did
regress
toward
the
East
,
one
degree
,
not
in
the
space
of
a
hundred
Years
,
as
Ptolomy
also
had
designed
;
but
of
somwhat
less
than
seventy
;
as
also
,
that
the
Obliquity
of
the
Ecliptick
,
according
to
Pappus
his
Theory
,
was
less
(
viz.
above
23.
degr.
35.
minutes
)
with
many
other
particulars
concerning
aswell
the
Fixt
Stars
,
as
the
Planets
:
whereupon
he
both
corrected
Ptolomy
in
many
things
,
and
composed
new
Tables
,
and
wrote
a
Book
intituled
,
De
Scientia
Stellarum
.
After
him
,
within
2
or
3
Ages
following
,
succeeded
Alphraganus
,
Arzachel
,
Alphraganus
and
other
Arabians
.
Almeon
,
and
other
Arbians
;
among
whom
,
(
as
being
already
tainted
with
that
superstition
which
had
corrupted
the
simplicity
of
Astronomy
,
with
Astrological
Fooleries
)
some
certain
Jewes
,
as
ambitiously
affecting
the
glory
of
Divination
as
the
others
,
intermixed
themselves
.
After
them
,
for
a
long
time
,
the
Worship
of
Urania
lay
neglected
,
Articl
.
11.
Alphonsus
,
K.
of
Castile
;
who
made
and
named
the
Alphonsine
Tables
.
nor
did
Astronomy
receive
any
the
least
(
considerable
)
advantage
by
Observators
;
till
neer
about
four
hundred
Years
since
,
Alphonsus
King
of
Castile
and
Lion
,
being
himself
also
toucht
with
the
curiosity
of
Astrological
predictions
,
and
discovering
that
the
Tables
aswell
of
Ptolomy
,
as
Albategnius
were
not
exactly
agreeable
with
the
Celestial
motions
;
set
himself
to
the
composing
of
new
ones
;
and
to
that
purpose
convocated
as
many
Arabians
and
Jewes
,
as
were
eminent
in
those
Dayes
for
Astronomy
;
imploying
them
about
Observations
necessary
to
so
great
a
Work
,
and
comparing
with
them
those
of
their
Predecessors
,
that
so
they
might
be
the
more
exact
in
the
performance
of
their
task
proposed
.
And
very
memorable
it
is
,
that
(
as
hath
been
credibly
reported
)
He
spent
four
hundred
thousand
peeces
of
Gold
on
that
undertaking
:
a
munificence
truely
worthy
the
Heroick
mind
of
so
great
a
Prince
,
and
which
well
deserves
to
be
had
in
perpetual
commemoration
by
all
lovers
of
Learning
:
but
somwhat
unhappily
imployed
,
in
respect
the
Persons
set
a
Work
were
not
so
strict
in
studiously
and
constantly
observing
,
as
scrupulosly
computing
,
directing
their
calculations
not
so
much
to
what
themselves
and
others
had
really
observed
,
as
to
certain
traditional
,
mysteries
,
or
Caballistical
dreams
:
that
we
may
pass
by
their
heedlesness
,
which
Regiomontanus
detecting
,
perceived
,
that
they
had
mistaken
the
true
places
of
the
Fixt
Stars
,
by
very
neer
two
whole
degrees
;
as
accounting
the
numbers
of
Ptolomy
,
as
if
they
had
bin
constituted
by
him
from
the
beginning
of
the
Years
of
Christ
.
Which
considered
,
we
have
the
less
reason
to
wonder
,
if
the
Tables
composed
by
them
,
called
from
the
Kings
name
,
the
Alphonsine
,
and
sometimes
from
the
place
,
where
they
were
made
the
Toletane
Tables
(
whence
also
He
,
who
was
President
of
that
assembly
of
Astronomers
,
is
said
to
have
been
one
Isaac
Chanter
of
the
Toletun
Synagogue
)
have
been
found
,
ever
since
the
time
of
K.
Alphonsus
,
to
disagree
with
the
Heavens
,
and
to
require
the
review
and
castigation
of
some
new
and
more
faithfull
hands
.
Thence
forward
Astronomy
lay
neglected
,
and
after
whom
,
the
Science
lay
neglected
.
till
,
Georg.
Peurbaechius
and
Ioh.
Regiomontanus
arose
,
and
again
caltivated
the
same
.
almost
buried
in
oblivion
,
(
only
Thebitius
an
Arabian
,
and
Prophalius
a
Jew
,
observed
in
the
mean
time
some
small
matters
,
about
the
motion
of
the
Fixt
Stars
,
and
the
obliquity
of
the
Ecliptick
,
)
untill
about
two
hundred
Years
since
,
Georgius
Peurhacchius
,
and
Joh.
Regiomontanus
,
his
disciple
,
seemed
to
revive
it
.
For
,
these
worthy
men
delivered
it
cut
of
the
double
cloud
of
ignorance
and
vanity
,
which
the
Arabians
and
Jewes
had
raised
,
to
the
Observation
of
its
lustre
;
and
kindled
the
Light
thereof
afresh
in
Germany
:
reducing
Ptolomy
,
providing
Instruments
,
and
making
not
a
few
faithfull
Observations
:
though
they
were
not
so
happy
,
as
to
bring
their
designe
to
that
perfection
they
hoped
and
had
proposed
to
themselves
;
both
of
them
dying
in
the
middle
and
flower
of
their
Age.
Animated
by
their
example
,
Nicholaus
Copernicus
(
a
Borussian
born
,
and
Canon
of
the
Cathedral
Church
of
Warmes
,
scituate
neer
Articl
.
12.
Then
followed
the
m●st
accute
Nich.
Coper
.
Fruemburgh
,
in
the
same
Country
)
about
the
beginning
of
the
last
Age
,
seriously
addressed
himself
to
the
Illustration
of
Astronomy
;
nicus
,
who
revived
the
doctrine
of
Pythagoras
,
concerning
the
Earths
motion
.
and
reviving
the
long
neglected
Systeme
of
the
World
excogitated
by
Pythagoras
,
he
made
many
good
Observations
,
in
order
to
the
composing
of
new
Tables
But
,
forasmuch
as
he
could
not
determine
any
thing
concerning
the
Fixt
Stars
,
besides
their
Promotion
Eastward
,
which
they
appeared
to
have
made
since
Ptolomy's
time
;
he
therefore
composed
some
Canons
of
their
motions
,
and
those
as
exact
as
possibly
he
could
:
yet
both
those
,
and
the
Prutenick
Tables
that
were
built
upon
them
,
were
incorrespondent
to
the
motions
of
the
Heavens
,
though
less
incorrespondent
than
the
Alphonsine
.
Nevertheless
,
the
man
is
to
be
highly
commended
,
both
for
his
sublime
perspicuity
,
and
modesty
,
in
that
foreseeing
his
Canons
would
need
correction
,
he
was
wont
frequently
to
exhort
and
encourage
that
ingenious
young
man
,
Georgius
Joachimus
Rheticus
,
deeply
enamoured
of
the
beauties
of
Astronomy
,
to
apply
himself
principally
to
the
Restitution
of
the
Fixt
Stars
,
and
cheifly
of
those
,
which
were
in
the
Zodiack
,
or
neer
it
,
and
with
which
the
Planets
might
be
most
conveniently
compared
:
because
,
without
their
restitution
,
it
was
impossible
either
to
attain
to
the
true
places
of
the
Planets
,
or
to
atcheive
any
thing
of
Moment
or
certainty
,
toward
the
advance
of
Astronomy
.
And
then
at
last
enters
that
Noble
Dane
,
Tycho
Brahe
,
upon
Articl
.
13.
And
last
of
All
,
the
noble
Tycho
Brahe
,
who
out-did
all
the
rest
in
discoveries
and
inventions
.
the
Theatre
of
Astronomy
.
Who
,
as
by
in
the
impulse
of
his
Genius
,
being
addicted
to
beholding
and
noting
the
Stars
,
even
almost
as
soon
as
he
saw
the
light
of
them
;
was
so
much
the
more
spurred
on
by
that
advice
of
Copernicus
,
published
in
the
Works
of
George
Joachim
newly
mention'd
,
by
how
much
the
more
clearly
he
discerned
the
impossibility
of
determining
the
true
and
proper
place
of
that
famous
New
Star
,
(
appearing
in
the
Constellation
of
Cassiopeia
,
from
the
beginning
of
November
,
in
the
Year
M.
D.
LXXII
.
for
above
sixteen
months
together
)
without
the
restitution
of
the
Fixt
Stars
to
theirs
.
For
,
He
plainly
perceived
,
that
most
,
if
not
all
the
Errors
,
which
had
bin
found
in
Astronomy
even
from
its
first
foundation
or
original
,
took
their
rise
chiefly
from
hence
,
that
the
Fixt
Stars
really
were
not
in
those
places
,
in
which
they
were
supposed
to
be
,
by
Observators
;
But
some
of
them
were
much
neerer
,
and
others
again
as
much
farther
off
;
and
this
,
whether
because
Hipparchus
in
the
beginning
had
not
with
due
exactness
consigned
all
the
Fixt
Stars
to
peculiar
places
,
which
indeed
he
had
designed
by
the
Sextant's
of
degrees
(
and
truely
it
is
very
difficult
at
once
to
invent
any
thing
of
Moment
,
and
perfect
the
invention
)
or
whether
because
the
Transcribers
of
Ptolomy
,
out
of
carelesness
,
or
ignorance
,
had
corrupted
the
Original
Text
in
many
places
;
or
whether
the
additions
afterward
made
,
in
respect
of
the
Stars
progress
to
the
following
Signes
,
had
occasioned
any
mistake
and
imperfection
in
that
Theory
;
or
whether
by
any
other
unhappy
cause
whatever
.
Now
,
in
Order
to
this
great
Work
,
of
rectifying
those
fundamental
Errors
,
it
pleased
Fate
,
that
about
the
very
same
time
,
that
truely
generous
and
never
enough
commendable
Prince
William
Landgrave
of
Hassia
,
had
zealously
devoted
his
mind
and
industry
to
the
same
care
,
of
restoring
the
Fixt
Stars
to
their
true
mansions
:
but
yet
the
honour
he
aimed
at
,
was
decreed
only
for
the
incomparable
Tycho
;
who
in
an
Heriocal
bravery
of
Soul
,
had
now
resolved
with
himself
to
enterpise
no
less
than
the
Instauration
of
the
whole
Science
of
Astronomy
from
its
very
fundamentals
;
and
so
to
spare
neither
labour
,
nor
cost
(
especially
while
he
was
so
happy
,
as
to
have
good
part
of
his
expences
defraied
by
the
liberal
contributions
of
that
eminent
Mecenas
,
Frederick
the
II.
King
of
Denmark
,
who
thereby
recorded
his
name
in
immortal
Characters
on
the
leaves
of
Fame
)
that
should
be
necessary
to
the
making
all
Sorts
of
Observations
requisite
.
As
soon
therefore
as
he
had
furnished
himself
with
that
Astronomical
Colledge
,
or
Tower
for
Observations
,
built
by
him
in
the
Island
of
Huenna
,
to
that
purpose
assigned
him
by
the
King
,
and
furnished
that
Heavenly
Cittadel
by
him
called
Uraniburg
,
with
store
of
exquisite
and
magnificent
Instruments
Mathematical
,
he
begun
(
having
provided
himself
of
sundry
learned
and
competent
Coadjutors
)
exactly
to
observe
the
Altitude
of
the
Pole
,
in
that
place
,
by
the
Circum-polary
Stars
.
By
which
understanding
likewise
the
Altitude
of
the
Equator
,
he
pointed
out
the
Equinoctial
points
,
by
the
passing
of
the
Sun
through
them
:
and
attending
besides
to
the
middle
parts
of
Taurus
and
Leo
,
he
found
out
the
Apogeium
of
the
Sun
,
and
the
Eccentricity
of
it
,
and
deduced
its
Course
from
the
point
of
the
Vernal
Equinox
.
Moreover
,
from
Venus
,
in
the
Day
time
compared
with
the
Sun
,
and
in
the
Night
with
the
Fixt
Stars
;
he
endeavoured
to
search
out
the
right
Ascensions
,
and
Declinations
of
the
Fixt
Stars
:
which
the
Ancients
had
performed
,
but
fallaciously
,
by
using
the
Moon
,
not
Venus
,
to
that
purpose
.
And
his
success
was
as
exquisite
as
his
care
in
this
,
that
he
constituted
that
bright
Star
which
is
in
the
top
of
Aries
,
and
ranged
the
chief
of
those
in
order
along
the
Zodiack
:
and
then
advancing
to
enquire
or
rather
find
out
the
distances
of
the
rest
aswell
from
them
,
as
each
from
other
,
he
defined
both
the
right
Ascensions
and
Declinations
of
all
;
prescribed
their
several
Longitudes
and
Latitudes
,
and
added
to
the
Catalogue
of
the
Ancients
about
200.
other
Stars
,
wholly
by
them
omitted
.
Because
the
Ancients
,
Living
in
an
Horizon
much
more
Southern
,
had
observed
and
set
down
neer
upon
200.
Stars
,
that
are
invisible
in
the
Danish
Horizon
,
which
is
highly
Northern
:
and
Tycho
again
collected
about
200.
more
than
they
could
discern
;
and
as
being
somwhat
small
,
he
intermixed
them
among
others
of
greater
magnitude
.
Further
,
having
in
the
mean
space
,
alwaies
observed
the
passings
of
all
the
Planets
through
the
Meridian
,
and
their
several
distances
from
the
cheif
Fixt
Stars
neerest
to
them
:
he
laid
such
sollid
foundations
,
as
by
them
might
be
exactly
known
not
only
the
true
places
of
each
,
but
also
their
several
Motions
.
So
that
he
came
very
neer
the
heighth
of
his
noble
hopes
of
building
the
whole
Theory
of
Astronomy
a
new
from
the
very
ground
,
and
of
erecting
compleat
and
everlasting
Tables
for
Calculation
thereupon
:
but
,
alas
!
prevented
by
an
immature
death
,
He
could
not
accomplish
his
designe
.
It
was
very
much
,
however
,
that
He
went
so
far
,
as
●o
have
recorded
and
bequeathed
to
Posterity
such
excellent
Observations
,
by
which
Kepler
was
soon
after
enabled
to
compose
an
intire
Theory
,
and
make
the
Tables
called
the
Rudolphine
;
and
by
which
,
and
others
afterward
contriveable
,
whatever
can
be
desired
in
these
Tables
,
may
be
fully
supplied
and
perfected
.
And
this
among
the
rest
deserves
singular
commendations
,
that
He
left
us
the
Fixt
Stars
re-installed
in
their
true
mansions
:
wherein
He
alone
,
in
few
Years
practice
,
performed
and
finished
that
prodigiously
great
Work
,
which
no
man
,
from
the
Dayes
of
Hipparchus
,
had
either
attempted
,
or
in
any
measure
advanced
.
I
pass
by
many
other
admirable
discoveries
of
his
;
as
that
he
was
the
first
,
who
demonstrated
all
Comets
to
be
carried
freely
through
the
Etherial
Spaces
;
that
Refractions
ought
to
be
carefully
considered
and
allowed
for
,
and
how
;
that
he
perceived
that
the
Latitude
of
the
Moon
ought
to
be
augmented
by
more
than
a
Quadrant
,
or
fourth
part
,
than
had
been
conceived
;
that
He
almost
demonstrately
convinced
the
Latitudes
of
the
Fixt
Stars
to
be
varied
;
that
he
excogitated
an
Hypothesis
,
which
all
those
,
who
cannot
allow
of
the
Ptolomaicall
,
or
fear
to
allow
the
Copernican
,
may
well
adhere
to
and
defend
;
with
many
other
things
,
as
difficult
in
their
Invention
,
as
excellent
in
their
use
.
And
observe
only
how
vastly
he
transcended
all
that
went
before
him
,
in
point
of
exactness
and
certainty
.
As
for
Instruments
Mathematicall
,
it
is
well
known
,
He
made
such
,
as
for
the
condition
of
their
matter
,
for
the
Vastness
of
their
magnitude
,
for
the
variety
of
forms
,
for
the
care
of
their
elaboration
,
for
the
preciseness
of
their
divisions
,
and
for
the
facility
in
using
;
as
the
World
had
never
the
like
before
.
Again
,
so
prodigious
was
his
and
his
Coadjutors
subtility
,
diligence
,
industry
;
that
whereas
the
Observations
of
Hipparchus
,
Ptolomy
,
and
all
others
before
him
,
had
bin
marked
out
only
by
the
Sixth
or
at
most
by
the
twelfth
parth
of
degrees
;
he
designed
all
his
by
the
sixtieth
parts
of
degrees
,
called
Minutes
,
or
Scruples
,
and
very
often
also
by
subdivisions
of
Minutes
.
So
that
we
may
well
demand
what
comparison
can
be
made
betwixt
that
gross
way
found
out
by
Erastothenes
,
and
approved
and
followed
afterward
by
Hipparchus
and
Ptolomy
,
for
the
Observation
of
the
Obliquity
of
the
Zodiack
;
and
that
most
fine
and
exact
one
invented
by
Tycho
?
His
being
,
by
a
division
of
the
Meridian
into
83
,
parts
,
and
the
Interval
of
the
Tropicks
deprehended
to
take
up
11.
of
them
,
it
appeared
that
the
distance
of
one
Tropick
from
the
Equator
,
amounted
to
5.
of
thoseparts
and
an
half
,
or
,
by
a
reduction
of
them
again
to
degrees
,
of
23.
degr.
51.
Min.
and
⅓
:
and
theirs
,
being
by
an
hollowed
Hemispear
of
Stone
,
with
a
Gnomon
erected
in
the
middle
,
as
we
have
formerly
described
it
;
and
to
what
degree
of
subtility
and
exactness
this
way
of
commensuration
could
arrive
,
the
meanest
Novice
in
Astronomy
may
soon
judge
.
That
Quadram
likewise
of
Ptolomy
,
so
much
admired
by
ancient
Authors
;
Pray
,
How
vastly
short
did
it
come
of
the
perfection
of
the
least
that
Tycho
used
?
And
the
same
may
be
said
of
his
Rules
;
for
,
that
those
Armillae
,
set
up
by
Pt●lo●y
in
the
entrance
of
Alexandria
had
any
thing
in
them
comparable
to
those
erected
by
Tycho
,
in
his
Uraniburg
,
cannot
in
the
lest
measure
be
argued
from
the
other
Instruments
then
in
use
.
It
is
not
necessary
,
we
should
here
again
review
those
machinaments
,
or
engines
,
which
the
old
Egyptians
and
Babylonians
made
use
of
,
either
in
discerning
the
Signes
of
the
Zodiack
,
or
taking
the
Diameter
of
the
Sun
:
or
those
,
which
Aristarchus
and
Archimedes
used
,
for
commensurating
the
same
Diamater
.
Only
we
cannot
but
wonder
,
by
the
by
,
how
Aristarchus
,
having
aimed
so
neer
the
white
of
truth
,
in
the
matter
of
the
Suns
Diameter
,
and
determining
it
to
be
the
720th
.
part
of
the
Circle
,
or
half
a
degree
;
as
is
delivered
de
Acenar
.
num.
by
Archimed
:
should
yet
err
so
widely
in
his
Book
of
Magnitudes
and
Distances
,
as
to
make
the
Diameter
of
the
Moon
(
which
in
truth
;
is
very
neer
as
great
as
that
of
the
Sun
)
to
be
the
180th
.
part
of
the
Circle
,
or
2.
degr.
when
he
called
it
the
Fifteenth
part
of
a
Signe
;
which
mistake
of
his
was
long
since
taken
notice
of
by
Pappus
.
Nor
is
there
any
necessity
,
why
we
should
survey
those
Instruments
,
that
Albateginus
,
Peurbacchius
,
Regiomontanus
,
Copernicus
,
and
other
more
moderne
Astronomers
used
:
considering
,
that
besides
the
Rules
made
by
Regiomontanus
(
which
Bernardus
Waltherus
,
his
disciple
,
preserved
,
and
had
recourse
to
,
in
his
Observations
of
the
Suns
Altitude
)
they
came
so
short
of
the
least
of
Tychoes
,
in
point
of
exact
reasoning
,
and
amplitude
,
that
they
deserve
rather
to
be
perpetually
forgotten
,
than
remembred
to
competition
.
However
it
is
seriously
to
be
wished
,
that
the
Observations
made
by
those
incomparable
Instruments
of
His
,
may
ly
no
longer
concealed
from
the
World
(
for
by
singular
Providence
,
they
have
been
hitherto
preserved
,
as
Gassendus
attesteth
,
ïn
the
Life
of
Tycho
)
but
soon
be
brought
to
Light
.
And
this
aswell
for
sundry
weighty
Considerations
there
alleadged
by
Gassendus
;
as
for
this
,
that
not
all
the
Stars
,
of
which
Tyeho
hath
given
a
copious
Catalogue
,
in
his
Progymnasmata
,
may
be
found
reduced
to
congruous
Calculation
(
in
as
much
as
they
doe
not
exactly
correspond
with
the
Heavens
)
and
that
various
Catalogues
have
been
pretended
from
the
same
,
which
are
very
much
different
each
from
other
:
for
all
the
difficulties
hereupon
depending
may
soon
be
removed
,
and
all
mistakes
rectified
,
by
having
recourse
to
the
Fountain
,
or
Original
observations
,
which
!
will
clearly
declare
,
what
hath
bin
already
corruptly
deduced
,
and
what
may
be
at
length
carefully
and
demonstratively
deduced
from
them
.
And
,
in
the
mean
while
,
if
Hipparchus
his
memory
be
so
highly
and
(
indeed
)
justly
precious
among
learned
men
,
for
his
great
merrits
in
excogitating
and
framing
Instruments
,
whereby
to
take
the
dimensions
,
distances
,
motions
&c.
of
Heavenly
bodies
:
certainly
,
that
of
our
Tycho
ought
to
be
as
highly
esteemed
by
us
and
all
Posterity
;
since
he
alone
,
for
so
many
Ages
together
was
found
,
that
durst
not
only
imitate
him
in
those
sublime
inventions
;
but
so
imitate
,
as
very
much
to
exceed
him
.
For
my
part
,
truely
;
since
Hipparchus
may
rightfully
be
called
Atlas
the
Second
:
I
shall
doe
but
justice
to
name
Tycho
,
Hercules
the
Second
,
who
releived
his
Predecessor
,
long
languishing
and
ready
to
faint
under
so
prodigious
a
burden
;
which
doubtless
was
the
Reason
,
why
Kepler
called
him
,
the
Modern
Hipparchus
.
And
thus
have
we
in
a
short
Relation
,
rehearsed
to
you
,
what
we
could
gather
together
,
concerning
the
Original
,
Progress
,
and
Advance
of
Astronomy
,
from
the
highest
of
times
,
of
which
there
remain
any
Authentick
memorials
,
down
to
the
decease
of
Tycho
Brahe
,
the
Noble
and
the
Great
.
As
for
what
Additions
this
excellent
Science
hath
received
,
by
the
industry
of
Astronomers
in
this
present
Age
,
by
the
help
of
the
Telescope
,
whose
Invention
may
seem
to
have
been
unhappily
deferred
too
long
,
as
being
deferred
till
some
Years
after
Tychoes
death
:
they
may
be
easily
summed
up
.
For
,
all
that
our
Dayes
can
justly
challenge
the
honour
of
discovering
,
is
(
1.
)
the
spotts
in
the
Sun
:
(
2.
)
the
inequality
of
the
superficies
of
the
Moon
:
(
3.
)
Venus
shifting
her
apparences
,
as
doth
the
Moon
:
(
4.
)
Mercury
and
Jupiter
,
in
some
Proportion
,
doing
the
like
:
(
5.
)
Jupiter
with
a
kind
of
bound
about
him
,
and
guarded
with
four
lesser
Stars
,
as
Attendants
:
(
6.
)
Saturn
triple-bodied
:
(
7.
)
the
Gallaxy
fully
beset
with
small
Stars
:
and
(
8.
)
divers
pale
assemblies
of
very
small
Stars
,
seeming
to
be
only
little
white
clouds
in
the
Welkin
;
with
some
other
particulars
lately
remarked
.
Now
,
if
you
please
to
add
this
to
the
former
summary
:
you
have
the
whole
(
though
brief
)
Story
of
Astronomy
,
from
its
very
infancy
to
that
augmented
state
it
now
hath
attained
to
:
I
wish
I
might
have
said
,
to
its
Full
growth
and
Perfection
.
But
,
alas
!
that
is
reserved
for
Posterity
.