Of
the
vse
of
the
SPHAERE
and
GLOBE
.
Pars
,
1.
The
Description
of
the
Sphaere
and
Globe
,
diuided
into
three
principall
parts
..
Whereof
this
first
intreateth
specially
of
the
Circles
of
the
vppermost
moueable
Sphaere
and
of
their
peculiar
vses
.
CHAP.
I.
The
definition
and
diuision
of
the
Sphaere
.
THis
Sphaere
,
is
nothing
else
but
a
representation
of
the
Coelestiall
orbes
and
circles
,
that
haue
beene
imagined
for
the
easier
vnderstanding
,
expressing
,
and
counting
of
the
motions
and
appa●ences
,
eyther
common
to
the
whole
Heauens
,
or
proper
to
the
Sunne
and
Moone
.
The
circles
of
this
Sphaere
are
eyther
inmoueable
,
as
the
two
greatest
and
vtmost
circles
,
the
Horizon
and
Meridian
,
(
whereto
is
adioyned
the
little
houre
circle
that
is
fixed
to
the
Meridian
)
or
else
moueable
▪
as
all
the
rest
contayned
within
these
.
CHAP.
II.
The
Description
of
the
Horizon
.
THe
greatest
and
vtmost
circle
of
the
Sphaere
that
lyeth
leuell
on
all
sides
from
the
ground
,
is
called
the
Horizon
,
which
is
deuided
into
7.
limbs
,
or
borders
.
The
first
and
vtmost
of
them
conteyneth
the
32.
points
of
the
Compasse
,
or
the
windes
(
as
they
are
at
this
day
deuided
and
vsed
by
Sea-men
)
with
their
Latine
names
adjoyned
vnto
them
.
The
second
limbe
conteyneth
the
names
and
diuisions
of
the
12.
Windes
as
they
were
wont
to
bee
deuided
in
old
time
.
The
third
is
deuided
into
the
moneths
and
dayes
of
the
new
Kalender
,
first
established
by
Pope
GREGORIE
the
XIII
.
and
now
vsed
in
many
places
beyond
the
Seas
.
In
the
fourth
limbe
are
set
downe
the
moneths
and
dayes
of
the
ordinarie
Kalender
vsed
in
England
.
Next
within
this
,
are
placed
the
12.
Signes
and
degrees
of
the
Zodiacke
,
that
so
the
place
of
the
Sunne
might
bee
presently
knowne
for
any
day
of
the
yeare
giuen
,
or
contrariwise
,
that
the
day
of
the
Moneth
might
be
readily
found
by
the
place
of
the
Sunne
.
After
this
,
followeth
the
sixt
limbe
conteyning
the
32.
Windes
or
points
of
the
Compasse
,
with
letters
representing
the
names
now
in
vse
amongst
English
Marriners
.
The
seuenth
and
last
limbe
next
the
innermost
edge
of
the
Horizon
,
is
deuided
into
360.
degrees
with
figures
set
to
euery
tenth
degree
,
beginning
from
the
points
of
East
and
West
,
and
ending
at
North
and
South
;
that
so
the
number
of
any
degree
of
the
Horizon
might
bee
the
easilier
knowne
:
Which
Circle
appeareth
most
plainely
to
them
that
are
in
a
plaine
Champion
Countrie
,
or
vpon
the
Sea
close
by
the
water
in
a
cleare
calme
day
.
CHAP.
III.
The
vses
of
the
Horizon
.
1.
IT
deuideth
the
vpper
and
visible
part
of
the
Heauens
from
the
nether
halfe
that
is
hidden
out
of
our
sight
.
2.
It
sheweth
partly
the
difference
of
a
right
and
oblique
Sphaere
,
for
when
this
circle
and
the
Equinoctiall
,
crosse
each
other
at
the
right
Angles
,
it
is
said
to
be
a
right
Sphaere
,
otherwise
when
they
make
oblique
Angles
one
with
another
,
it
is
called
an
oblique
Sphaere
.
3.
In
an
oblique
Sphaere
this
circle
seuereth
those
Starres
which
neuer
rise
nor
set
,
but
are
alwayes
eyther
aboue
or
beneath
the
Horizon
,
from
such
Starres
as
rise
and
set
in
euery
24.
houres
.
For
all
the
Northerly
starres
that
are
no
further
distant
from
the
North
pole
,
then
the
North
pole
is
from
the
Horizon
,
doe
neuer
set
,
but
are
alwayes
aboue
the
Horizon
:
And
contrariwise
,
those
Starres
that
bee
about
the
South
pole
,
no
further
distant
from
it
then
it
is
from
the
Horizon
,
doe
neuer
rise
,
but
are
alwayes
hidden
out
of
sight
vnder
the
Horizon
.
4.
In
respect
of
this
circle
,
the
Sunne
,
Moone
and
Starres
,
or
any
other
part
or
point
of
the
Heauens
,
are
sayd
to
rise
or
set
:
For
when
they
come
vp
from
vnder
the
Horizon
,
they
are
sayd
to
rise
;
otherwise
when
they
goe
from
aboue
the
Horizon
downe
vnderneath
the
same
,
they
are
sayd
to
set
.
5.
And
hereof
it
commeth
that
the
ascendent
,
and
descendent
are
found
by
this
Circle
:
for
that
part
of
the
Ecliptick
that
is
at
the
East
part
of
the
Horizon
arising
,
is
the
Ascendent
;
and
the
point
opposite
to
this
at
the
West
part
of
the
Horizon
,
may
be
called
the
Descendent
.
6.
This
Circle
partly
sheweth
the
difference
of
ascention
of
any
part
or
point
of
the
Heauens
.
7.
In
this
Circle
we
reckon
how
farre
the
Sunne
,
the
Moone
,
or
any
Starre
,
or
point
of
Heauen
,
ariseth
from
the
point
of
due
East
.
8.
The
Horizon
determineth
the
time
of
the
artificiall
day
and
night
:
for
we
call
the
time
w●●rein
the
Sunne
abideth
aboue
the
Horizon
,
an
artificiall
day
:
And
the
time
that
he
continueth
vnder
the
Horizon
,
is
the
artificiall
night
.
9.
This
Circle
sheweth
the
reason
of
the
equality
of
artificiall
dayes
and
nights
,
in
a
right
Sphaere
:
and
of
the
inequality
of
them
in
an
oblique
Sphaere
.
For
in
a
right
Sphaere
,
the
Horizon
deuideth
all
the
paralels
of
the
Sunne
or
Circles
of
the
naturall
dayes
,
into
equall
parts
:
But
in
an
oblique
Sphaere
,
it
deuideth
them
into
vnequall
parts
.
10.
By
meanes
of
this
Circle
,
wee
know
what
Starres
,
and
what
Eclipses
,
Coniunctions
,
or
other
aspects
of
the
Planets
may
bee
seene
in
our
Hemisphere
at
any
time
.
11.
From
the
Horizon
is
measured
the
twilight
:
For
in
the
morning
the
Sunne
being
vnder
the
Horizon
about
18.
degrees
of
the
verticall
,
Circle
,
the
twilight
beginneth
:
And
when
the
Sunne
is
so
much
vnder
the
Horizon
at
Euening
,
the
twilight
endeth
.
12.
This
Circle
is
of
especiall
vse
in
Geography
,
for
from
it
wee
begin
to
account
the
eleuation
of
the
Pole
,
and
of
the
Equinoctiall
circle
,
whereby
the
Latitude
of
any
place
is
knowne
.
13.
In
Astrologie
for
erecting
a
figure
,
this
Circle
sheweth
the
beginning
of
the
first
and
seauenth
Houses
.
CHAP.
IIII.
The
description
of
the
Meridian
.
NExt
the
Horizon
,
succeeds
the
Meridian
standing
vpright
on
edge
,
and
crossing
the
Horizon
at
right
angles
in
the
points
of
North
and
South
.
This
circle
is
diuided
on
both
sides
at
the
inner
edge
into
360
▪
Degrees
,
with
figures
set
to
euery
tenth
degree
,
beginning
at
the
Equinoctiall
,
and
ending
at
the
Poles
with
90.
and
beginning
also
at
the
Poles
,
and
ending
at
the
Equinoctiall
with
90.
The
numbers
beginning
at
the
Pole
,
serue
to
set
the
Sphaere
readily
to
any
eleuation
desired
.
The
other
numbers
beginning
at
the
Equinoctiall
,
shew
presently
the
declination
of
any
degree
of
the
Zodiacke
,
or
of
any
point
assigned
in
the
Sphaere
,
one
quarter
of
the
Meridian
on
eyther
side
thereof
from
the
Equinoctiall
to
both
Poles
,
sheweth
the
Climates
,
and
the
quantities
of
the
longest
dayes
.
CHAP.
V.
The
vses
of
the
Meridian
.
1.
IT
deuideth
the
World
into
two
halfes
or
Hemisphaeres
:
that
is
,
the
East
and
the
West
hemisphaeres
.
The
Easterly
hemisphaere
is
all
that
part
of
the
world
which
is
on
the
East-side
of
the
Meridian
,
and
the
other
halfe
may
bee
called
the
West
hemisphaere
.
2.
It
sheweth
the
North
and
South
parts
of
the
world
,
for
the
two
intersections
of
the
Meridian
with
the
Horizon
,
shew
the
very
points
of
North
and
South
.
The
South
point
is
that
which
is
directly
vnder
the
Sunne
at
noone
:
And
the
point
right
ouer
against
this
,
is
called
the
North-point
.
3.
It
deuideth
the
arches
of
the
Equinoctiall
,
and
of
all
his
Paralels
,
into
two
equall
parts
both
aboue
and
beneath
the
Horizon
.
4.
And
therefore
it
deuideth
the
artificiall
Day
and
Night
into
two
equall
parts
.
5.
And
consequently
,
it
sheweth
midday
and
midnight
.
6.
In
an
oblique
Sphaere
it
serueth
in
stead
of
a
right
Horizon
(
that
is
)
an
Horizon
that
maketh
right
angles
with
the
Equinoctiall
.
7.
Therefore
the
Astronomers
begin
their
account
of
times
(
which
are
measured
by
the
equall
motion
of
the
Equinoctiall
)
from
the
Meridian
:
the
principall
of
which
times
,
is
the
naturall
day
which
is
vsually
begun
from
midday
,
or
midnight
.
8.
This
Circle
sheweth
the
highest
and
lowest
heights
of
the
Sunne
and
Starres
,
which
is
most
manifest
in
those
Starres
that
are
alwayes
aboue
the
Horizon
.
These
heights
are
called
the
Meridian
altitudes
of
the
Sun
or
Starres
,
which
heights
are
chiefely
obserued
by
Astronomers
and
Nauigators
with
great
diligence
.
9.
In
this
Circle
,
wee
obserue
the
distance
of
the
Tropickes
,
and
the
greatest
obliquitie
of
the
Zodiacke
.
10.
In
this
Circle
,
wee
obserue
and
count
the
Latitudes
of
places
,
the
height
of
the
Pole
,
and
of
the
Equinoctiall
.
For
the
height
of
the
Pole
or
Equinoctiall
,
is
nothing
else
but
the
arch
of
the
Meridian
contained
betweene
the
Pole
or
Equinoctiall
and
the
Horizon
.
The
height
of
the
Pole
is
alwayes
equall
to
the
Latitude
of
the
place
.
The
height
of
the
Equinoctiall
is
equall
to
the
Complement
of
the
Latitude
and
therefore
it
being
substracted
out
of
90.
〈◊〉
shall
remaine
the
height
of
the
Pole
.
11.
The
Meridian
sheweth
the
longit●●●
of
places
in
Geographie
.
12.
In
the
Meridian
,
are
measured
the
bredth
of
the
Zones
and
Climates
.
13.
This
circle
in
Astrologie
,
sheweth
the
highest
and
lowest
parts
of
Heauen
,
which
are
the
beginnings
of
two
principall
Houses
:
that
is
,
the
fourth
and
the
tenth
houses
.
CHAP.
VI.
The
description
of
the
Houre-circle
,
and
Poles
.
THe
little
Circle
fastned
to
the
Meridia●
is
called
the
Houre-circle
,
which
is
deuided
into
24.
equall
parts
,
signifying
and
representi●●
vnto
vs
so
many
equall
houres
,
whereof
both
the
〈◊〉
houres
are
fixed
iust
vpon
the
Meridian
,
becaus●●●hen
the
Sunne
commeth
to
the
Meridian
,
it
is
iust
twelue
a
clocke
:
the
vpper
XII
.
serueth
for
the
Day
;
and
the
other
XII
.
beneath
serueth
for
the
Night
.
The
Index
,
or
the
Painter
in
forme
of
an
Arrow
,
fastned
vpon
the
Pinne
that
commeth
through
the
midst
and
Center
of
this
circle
,
is
made
to
shew
and
point
out
the
said
houres
as
need
shall
requite
,
in
the
vse
of
the
Sphaere
.
The
vse
of
this
houre
Circle
shall
be
shewed
hereafter
,
when
we
shall
speake
of
the
common
vse
of
many
circles
of
the
Sphaere
together
.
And
these
two
Circles
(
that
is
,
the
Meridian
and
Horizon
)
are
called
immoueable
,
because
they
keepe
themselues
alwayes
,
and
in
all
places
ouer
the
same
parts
of
the
Earth
;
where
as
all
the
rest
(
conteyned
within
these
two
)
moue
round
about
altogether
with
one
motion
in
the
space
of
foure
and
twenty
houres
.
This
motion
(
being
common
to
the
whole
Heauens
)
is
made
about
two
Points
or
Poles
,
represented
in
this
Sphaere
,
by
the
two
Wyre
pinnes
about
which
the
Sphaere
is
turned
;
whereof
the
one
that
commeth
through
the
middest
of
the
little
Circle
fastned
to
the
Meridian
(
which
wee
call
the
houre
Circle
)
representeth
vnto
vs
the
Pole
Articke
or
the
North
Pole
:
the
other
because
it
is
opposite
to
this
,
is
called
the
Antartick
pole
,
that
is
the
right
opposit
,
to
,
or
right
ouer
against
the
North
pole
,
which
is
also
the
South
pole
.
CHAP.
VII
.
Of
the
Equinoctiall
Circle
.
THat
Circle
which
compasseth
about
the
midst
of
the
Sphaere
,
It
is
deuided
at
the
vtmost
edge
,
or
both
sides
thereof
into
360.
Degrees
,
with
figures
〈◊〉
to
euery
tenth
degree
,
beginning
at
the
beginning
of
Aries
,
and
proceeding
Eastwards
,
till
you
become
about
to
the
same
point
againe
.
This
Circle
hath
many
vses
.
1.
It
is
the
measure
of
the
first
〈◊〉
.
For
this
onely
amongst
all
the
Circle
of
the
Sphaere
is
moued
equally
both
in
a
right
and
〈…〉
Sphaere
,
because
●
alone
being
perpendicular
to
the
〈…〉
world
,
about
which
the
Sphaere
is
equally
turned
,
is
deuided
into
two
haltes
by
euery
Horizon
in
the
same
points
.
2.
It
is
the
measure
of
time
;
because
it
measureth
the
quantitie
of
the
artificiall
and
naturall
dayes
,
of
which
Moneths
and
Yeares
are
made
:
It
measureth
also
the
quantitie
of
Houres
and
of
other
times
which
the
Sunne
maketh
going
vnder
the
Zodiacke
.
And
therefore
the
degrees
of
the
Equinoctiall
are
called
tempora
(
that
is
)
times
.
3.
It
sheweth
the
two
Equinoctiall
points
in
the
Eclipticke
,
cutting
the
Ecliptick
in
two
places
,
which
are
the
beginnings
of
Aries
and
Libra
:
and
the
Sun
when
hee
commeth
to
those
two
points
,
is
equally
distant
from
both
Poles
of
the
World
,
and
maketh
equalitie
of
dayes
and
nights
in
all
places
;
which
hapneth
in
our
time
about
the
10.
or
11.
day
of
March
,
and
the
13.
or
14.
of
September
.
4.
The
irregularitie
of
the
Zodiacke
,
and
of
all
the
Signes
and
degrees
thereof
,
is
measured
by
this
Circle
.
For
seeing
the
most
part
of
the
apparences
of
the
first
motion
are
referred
to
the
Zodiacke
,
which
is
not
turned
about
his
owne
Poles
,
but
about
the
Poles
of
the
Sphaere
,
and
therefore
must
needs
bee
vnequally
turned
about
;
it
was
needfull
that
this
inequalitie
should
be
ruled
and
measured
by
some
other
equall
motion
.
5.
It
deuideth
the
Sphaere
into
two
halfes
(
which
they
call
Hemisphaeres
)
that
is
,
into
the
North
halfe
or
hemisphaere
,
wherein
is
the
North
pole
,
and
into
the
South
hemisphaere
,
wherein
is
the
South
pole
.
6.
So
it
deuideth
the
Zodiacke
into
the
North
halfe
,
and
the
South
halfe
;
or
into
the
North
signes
,
and
the
South
signes
.
7.
From
this
Circle
are
numbred
the
declinations
of
the
Starres
,
and
of
the
degrees
and
parts
of
the
Eclipticke
,
and
of
any
other
point
of
Heauen
.
8.
And
in
this
Circle
are
counted
the
right
ascentions
of
the
same
Degrees
and
Starres
,
&c.
For
the
right
ascention
of
any
starre
or
point
of
the
Heauens
,
is
nothing
else
but
the
Arch
of
the
Equinoctiall
circle
contained
betweene
the
beginning
of
Aries
and
the
Meridian
,
the
same
Starre
or
point
being
first
brought
vnder
the
Meridian
.
9.
In
the
Equinoctiall
is
counted
the
ascentionall
difference
and
the
oblique
Ascention
and
Descention
of
any
point
of
Heauen
.
And
from
the
same
Circle
is
reckoned
the
distance
of
the
Sunne
rising
from
the
true
East
point
.
For
the
oblique
ascention
or
descention
is
nothing
else
but
the
arch
of
the
Equinoctiall
,
contained
betweene
the
beginning
of
Aries
,
and
that
point
of
the
Equinoctiall
Eastwards
,
which
ariseth
or
setteth
together
with
the
Starre
or
point
that
is
giuen
,
in
an
oblique
Sphaere
.
And
the
difference
ascentionall
or
descentionall
is
nought
else
but
the
arch
of
the
Equator
,
whereby
the
right
and
oblique
ascention
or
descention
of
a
Starre
,
or
any
other
point
in
Heauen
doe
differ
each
from
other
.
The
distance
of
the
sunnes
rising
from
the
true
East
point
(
which
in
Latine
is
called
Amplitudo
ortiua
,
)
is
the
arch
of
the
Horizon
contayned
betweene
the
Equinoctiall
and
the
paralell
of
the
Sunne
,
or
his
Center
when
he
riseth
.
10.
In
Geographie
wee
count
the
Longitudes
of
places
in
this
Circle
;
and
from
it
we
reckon
the
Latitudes
,
in
the
Globe
of
the
earth
,
and
in
Maps
,
and
sea
Charts
.
For
the
longitude
of
a
place
is
nothing
else
but
the
arch
of
the
Equinoctiall
circle
contayned
betweene
two
Meridians
,
whereof
one
goeth
by
the
canary
Ilands
,
and
the
other
by
the
place
that
is
giuen
,
And
the
latitude
of
a
place
is
the
arch
of
a
Meridian
contayned
betweene
the
Equinoctiall
,
and
the
Zenith
of
the
place
that
was
giuen
.
11.
In
Dialling
this
Circle
is
of
especiall
vse
.
For
by
meanes
of
it
the
spaces
of
the
houres
are
deuided
in
all
kindes
of
Dials
,
horizontall
,
erect
,
direct
,
declining
,
inclining
,
reclining
,
&c.
12.
In
Astrologie
the
twelue
Houses
are
set
out
by
the
equall
diuisions
of
this
Circle
into
twelue
parts
,
according
to
the
way
deuised
by
Regiomontanus
,
which
way
is
commonly
called
rationall
or
reasonable
.
And
this
Circle
gouerneth
the
directions
,
whereby
things
to
come
are
artificially
fore-told
.
CHAP.
VIII
.
The
description
of
the
Zodiacke
.
THe
great
broad
Circle
that
compasseth
about
the
Sphaere
obliquely
,
comming
nearer
the
Pole
of
the
Sphaere
in
one
place
then
in
another
,
is
called
the
Zodiacke
.
Round
about
through
the
middest
of
this
Circle
,
is
drawne
the
Circumference
commonly
called
the
Eclipticke
line
,
deuiding
the
whole
Sphaere
,
and
the
whole
bredth
of
the
Zodiacke
throughout
,
into
two
equall
parts
.
In
this
Sphaere
there
are
represented
vnto
vs
two
Eclipticke
lines
.
The
one
may
be
called
the
middle
,
or
fixed
Eclipticke
,
which
keepeth
alwayes
the
same
distance
or
obliquitie
from
the
Equinoctiall
.
The
other
may
bee
called
the
true
or
moueable
Eclipticke
,
because
it
maketh
not
alwayes
the
same
angles
of
intersection
with
the
Equator
,
but
sometimes
greater
,
sometimes
lesse
.
For
the
greatest
obliquitie
of
the
Zodiacke
,
which
not
long
before
Ptolomees
time
was
obserued
to
bee
23.
Degrees
and
52.
Minutes
;
in
Copernicus
his
time
,
was
hardly
found
to
exceed
23.
degrees
28.
minutes
,
according
to
his
obseruation
,
and
therefore
hee
thought
that
the
difference
betweene
the
greatest
and
least
obliquitie
of
the
Zodiacke
,
was
24.
Minutes
:
and
the
middle
or
meane
obliquitie
betweene
both
these
,
to
bee
23.
Degrees
40.
Minutes
.
The
manner
of
the
variation
of
this
obliquitie
may
in
some
sort
bee
shewed
by
this
Sphaere
,
if
we
suppose
the
fixed
Eclipticke
drawne
round
about
through
the
middest
of
the
Zodiack
to
be
23.
degrees
40.
min.
distant
from
the
Equinoctial
at
the
beginning
of
Cancer
and
Capricorne
:
and
the
moueable
Eclipticke
(
fastned
as
it
were
vpon
two
Poles
at
the
beginning
of
Aries
and
Libra
,
and
so
hauing
alwayes
the
same
points
of
intersection
with
the
middle
Eclipticke
and
Equinoctiall
)
to
bee
moued
vp
and
downe
aboue
and
beneath
the
middle
Eclipticke
,
by
the
space
of
12.
Minutes
at
the
beginning
of
Cancer
and
Capricorne
:
and
this
motion
to
finish
his
reuolution
once
in
3432.
Iulian
yeares
.
The
bredth
of
the
Zodiacke
is
bounded
by
the
greatest
latitudes
of
the
Planets
,
especially
of
Venus
and
Mars
,
which
sometimes
hath
almost
7.
degrees
of
latitude
.
The
Zodiacke
is
diuided
by
the
Equinoctiall
into
two
semicircles
.
The
one
aboue
the
Equinoctiall
is
called
the
Northerly
semicircle
:
the
other
halfe
beneath
the
Equinoctiall
,
is
the
Southerne
semicircle
of
the
Zodiacke
.
So
long
as
the
Sunne
moueth
vnder
the
first
of
these
semicircles
,
the
dayes
are
longer
then
the
nights
,
otherwise
they
are
shorter
.
Each
of
these
semicircles
is
againe
deuided
into
two
parts
,
and
so
the
whole
Zodiack
into
foure
quarters
:
the
first
from
Aries
to
Cancer
,
may
be
called
the
vernall
or
Spring-quarter
,
which
in
this
Sphaere
is
also
shewed
by
the
word
Ver
(
signifying
the
Spring
:
)
The
next
from
Cancer
to
Libra
,
the
Summer
quarter
,
wherein
is
written
the
word
Ae●tas
signifying
the
Summer
.
The
3.
from
Libra
to
Capricorne
,
is
the
Haruest
quarter
,
wherein
you
shall
finde
in
this
Sphaere
the
word
Autumnus
which
signifieth
Autumne
or
Haruest
.
The
fourth
and
the
last
,
from
the
beginning
of
Capricorne
to
Aries
,
is
called
the
winter
Quarter
,
which
in
this
Sphaere
is
shewed
by
this
word
Hiems
,
which
signifieth
the
Winter
.
And
these
foure
quarters
of
the
Zodiacke
are
thus
called
by
the
names
of
the
Quarters
of
the
yeare
,
because
the
Sunne
mouing
vnder
those
quarters
of
the
Zodiacke
,
maketh
those
foure
Quarters
of
the
yeare
.
Euery
one
of
these
quarters
of
the
Zodiacke
is
againe
deuided
into
three
parts
,
and
so
the
whole
compasse
of
the
Zodiacke
into
12.
which
are
called
the
12.
Signes
,
whereof
euery
one
contayneth
30.
Degrees
in
length
from
West
to
East
,
and
is
in
bredth
equall
to
the
bredth
of
the
Zodiacke
.
These
Signes
,
and
the
Zodiacke
it selfe
haue
their
beginning
from
that
common
meeting
,
or
crossing
of
the
Eclipticke
,
and
the
Equinoctiall
,
where
the
Eclipticke
beginneth
to
arise
aboue
the
Equinoctiall
towards
the
North
pole
:
and
they
are
called
by
these
names
;
Aries
,
Taurus
,
Gemini
,
Cancer
,
Leo
,
Virgo
,
Libra
,
Scorpio
,
Sagitarie
,
Capricorne
,
Aquarie
,
Pisces
.
That
is
to
say
,
The
Ramme
,
the
Bull
,
the
Twinnes
,
the
Crab
,
the
Lyon
,
the
Virgin
,
the
Ballance
,
the
Scorpion
,
the
Shooter
,
the
Goat
,
the
Water-pourer
,
the
Fishes
.
And
they
are
signified
by
these
Characters
,
♈
♉
,
♊
,
♋
,
♌
,
♍
,
♎
,
♏
,
♐
,
♑
,
♒
,
♓
.
This
deuision
of
the
Zodiacke
into
12.
Signes
and
of
euery
signe
into
30.
Degrees
,
nature
it selfe
seemeth
to
haue
shewed
by
the
motions
of
the
Sun
and
Moone
.
For
in
what
time
the
Sunne
moueth
once
about
the
whole
compasse
of
the
Zodiacke
,
the
Moone
maketh
twelue
reuolutions
through
the
same
.
Therefore
as
the
time
of
a
yeare
is
deuided
into
12.
Moones
,
so
the
Zodiacke
is
deuided
into
12.
Signes
:
And
as
euery
Moneth
contayneth
30.
dayes
,
so
euery
signe
is
deuided
into
30.
parts
,
which
they
call
Degrees
,
which
signifieth
as
much
as
steps
,
because
the
Sunne
steppeth
,
or
goeth
forwards
almost
so
much
as
a
degree
in
euery
day
,
from
the
West
Eastwards
vnder
the
Zodiacke
.
The
Zodiacke
is
otherwise
also
deuided
into
two
semicircles
,
the
one
(
from
Capricorne
to
Cancer
)
ascending
,
because
that
so
long
as
the
Sunne
or
any
of
the
Planets
are
in
that
semicircle
,
they
still
ascend
and
rise
higher
and
higher
aboue
the
Horizon
.
The
other
semicircle
of
the
Zodiacke
,
from
Cancer
to
Capricorne
,
is
called
descending
,
because
the
Sunne
or
Planets
being
in
that
semicircle
,
come
downe
euery
day
lower
then
other
.
The
12.
Signes
are
by
the
Astrologians
diuersly
deuided
,
first
into
chiefe
,
meane
,
and
common
signes
.
The
chiefe
signes
(
which
are
also
called
Cardinall
,
that
is
the
principall
signes
)
are
Aries
,
Cancer
,
Libra
,
and
Capricorne
,
because
they
come
next
after
the
principall
points
of
the
Zodiacke
,
that
is
,
the
two
Equinoctiall
points
at
the
beginnings
of
Aries
,
and
Libra
;
and
the
two
solstitiall
points
of
Cancer
and
Capricorne
.
The
meane
signes
(
which
are
also
called
fixed
)
are
Taurus
,
Leo
,
Scorpio
,
and
Aquarius
.
They
are
called
meane
,
because
they
are
placed
betweene
the
chiefe
or
principall
,
and
the
common
signes
.
They
are
called
fixed
signes
,
because
that
when
the
Sunne
is
in
those
signes
,
wee
finde
a
more
perfect
temperature
of
the
Ayre
,
then
when
he
is
in
the
other
signes
.
The
common
signes
(
which
are
also
called
double
bodyed
)
are
Gemini
,
Virgo
,
Sagitarie
,
and
Pisces
.
They
are
called
common
,
because
they
take
part
of
the
nature
of
the
fixed
signes
going
before
them
,
and
of
the
Cardinall
signes
following
after
them
.
They
are
called
double
bodied
,
by
reason
of
their
Images
,
as
they
are
imagined
in
the
eight
Sphaere
,
which
are
compounded
of
two
bodies
:
For
there
be
two
Twinnes
;
and
the
Virgin
holdeth
an
eare
of
corne
in
her
hand
;
Sagitarie
is
made
of
a
Man
and
an
Horse
;
and
there
are
two
Fishes
.
The
placing
,
and
nature
of
these
signes
brought
in
this
diuision
.
The
Astrologians
also
deuide
the
12.
Signes
into
foure
trigons
of
triplicities
,
so
called
because
they
are
distant
the
third
part
of
a
Circle
,
one
from
another
.
The
first
triplicitie
contayneth
Aries
,
Leo
,
and
Sagitarius
;
and
is
called
the
fiery
trigon
,
or
triplicitie
:
The
second
triplicitie
contayneth
Taurus
,
Virgo
,
and
Capricorne
;
and
is
called
the
earthly
trigon.
The
third
triplicitie
contayneth
Gemini
,
Libra
,
and
Aquarius
;
and
is
called
the
ayrie
trigon.
The
fourth
triplicitie
contayning
Cancer
,
Scorpio
,
and
Pisces
;
is
called
the
watrie
trigon.
Nature
it selfe
is
the
cause
of
this
diuision
of
the
Signes
also
.
For
into
these
Trigons
of
the
signes
,
shee
hath
distributed
the
Coniunctions
of
the
three
superiour
Planets
:
especially
the
coniunctions
of
Saturne
and
Iupiter
,
which
the
Astrologians
call
great
coniunctions
.
For
examples
sake
,
if
there
bee
a
great
coniunction
in
Aries
,
the
same
shall
be
twenty
yeares
after
in
Sagitarie
,
and
other
twenty
yeares
after
in
Leo
;
and
after
as
many
more
yeares
,
it
returneth
againe
into
Aries
.
The
reuolution
of
one
Trigon
contayneth
almost
200.
yeares
,
after
which
time
the
same
great
conjunctions
remoue
into
the
next
trigon.
CHAP.
IX
.
The
vse
of
the
Zodiack
.
1.
THe
Zodiack
is
the
measure
of
the
second
motions
,
as
the
Equinoctiall
is
the
measure
of
the
first
motion
.
2.
For
in
this
Circle
wee
reckon
the
longitudes
,
and
from
it
we
count
the
latitudes
of
all
the
Starres
.
For
the
longitude
of
a
Starre
is
nothing
else
but
the
arch
of
the
Ecliptck
conteyned
betweene
the
beginning
of
Aries
,
and
the
circle
of
the
Starres
latitude
.
And
the
latitude
is
the
Arch
of
a
great
circle
,
drawne
by
the
poles
of
the
Ecliptick
,
conteyned
betweene
the
Starre
and
the
Ecliptick
.
3.
According
to
this
circle
,
the
whole
Heauen
,
yea
,
the
whole
world
is
deuided
into
twelue
Signes
.
Whereof
it
commeth
that
because
of
this
Circle
,
aswell
the
fixed
,
as
the
wandring
Starres
which
we
call
Planets
,
yea
,
and
those
Starres
also
that
appeare
of
a
sudden
,
as
blazing
Starres
or
Comets
,
and
other
Meteors
,
are
said
to
be
in
this
or
that
signe
;
and
that
three
manner
of
wayes
.
First
,
to
be
in
a
signe
,
is
to
be
vnder
some
one
of
the
12.
parts
of
the
Ecliptick
.
Thus
the
Starres
which
are
vnder
the
Ecliptick
,
but
especially
the
Sunne
which
runneth
alwayes
vnder
it
,
are
said
to
be
in
the
Signes
.
Secondly
,
because
the
Zodiack
hath
latitude
,
those
Starres
are
said
to
be
in
a
signe
,
which
although
they
be
beside
the
Ecliptick
,
yet
are
vnder
the
Zodiack
,
and
so
any
of
the
other
Planets
,
which
for
the
most
part
wander
beside
the
Ecliptick
,
may
be
said
to
bee
in
some
signe
.
Thirdly
,
if
we
vnderstand
six
great
Circles
to
bee
drawne
by
the
beginnings
of
the
twelue
signes
,
and
by
the
poles
of
the
Eclipticke
;
by
these
circles
the
whole
heauen
(
or
rather
the
whole
world
)
is
deuided
into
twelue
parts
,
which
with
a
generall
name
are
called
signes
:
Thus
all
the
Starres
aswell
fixed
as
Planets
and
Comets
,
which
are
without
the
Zodiacke
in
any
of
these
parts
,
may
be
said
to
be
in
some
signe
.
4.
In
this
circle
are
noted
the
degrees
of
the
signes
,
with
which
the
Starres
doe
rise
and
set
,
as
well
in
a
right
as
in
an
oblique
Sphaere
.
For
because
this
circle
is
the
chiefest
,
all
Caelestiall
apparances
(
or
at
least
the
most
part
of
them
)
are
referred
vnto
it
,
and
not
vnto
the
Equinoctiall
.
But
the
Equinoctiall
measureth
the
times
of
their
risings
and
settings
.
5.
The
obliquitie
of
the
Ecliptick
is
the
cause
of
the
inequalitie
,
aswell
of
naturall
dayes
in
both
Sphaeres
,
as
of
artificiall
dayes
in
an
oblique
Sphaere
.
For
seeing
it
is
moued
vnequally
,
because
it
is
moued
vpon
other
Poles
then
his
owne
,
the
Sunne
which
is
the
author
,
and
maker
of
times
mouing
vnder
it
,
must
needs
make
vnequall
dayes
.
6.
The
chiefe
times
are
defined
by
this
circle
,
as
the
time
of
a
yeare
,
by
the
motion
of
the
Sunne
;
the
time
of
a
moneth
by
the
motion
of
the
Moone
,
through
the
whole
compasse
of
this
circle
.
Also
the
foure
quarters
of
the
yeare
,
Spring
,
Summer
,
Autumne
,
and
Winter
,
whereto
may
be
added
Plato
his
great
yeare
,
which
is
the
time
wherein
the
fixed
Starres
make
one
reuolution
about
the
axtree
and
poles
of
the
Zodiack
,
if
God
would
haue
the
world
to
last
so
long
.
7.
The
Eclipticke
line
sheweth
the
places
,
and
times
of
the
Eclipses
:
For
the
Sunne
and
Moone
,
are
Eclipsed
onely
vnder
it
,
or
neere
vnto
it
.
8.
As
the
description
of
the
Tropicks
dependeth
on
the
obliquitie
of
the
Eclipticke
,
so
the
polar
Circles
are
described
by
the
Poles
thereof
.
9.
Hereof
it
commeth
,
that
by
reason
of
the
same
obliquitie
,
the
Zones
and
Climats
are
set
forth
and
bounded
.
10.
This
Circle
is
of
especiall
vse
in
Astrologie
,
for
it
distinguisheth
the
points
of
the
12.
Houses
,
and
in
it
the
Aspects
and
configurations
of
the
Planets
are
obserued
.
The
chiefest
judgement
aswell
in
casting
Figures
as
in
reuolutions
and
directions
is
taken
from
this
circle
.
CHAP.
X.
The
description
of
the
two
Colures
.
THe
two
circles
crossing
each
other
at
right
Angles
in
the
poles
of
the
Sphaere
,
are
called
the
Colures
:
whereof
the
one
that
passeth
by
the
common
meeting
of
the
Eclipticke
and
Equinoctiall
,
is
called
Colurus
aequinoctiorum
,
that
is
the
Equinoctiall
Colure
,
or
the
colure
of
equall
dayes
and
nights
.
The
other
passing
by
the
poles
of
the
Eclipticke
,
and
the
Solstitiall
points
,
is
called
Colurus
solstitiorum
,
the
Solstitiall
colure
,
or
colure
of
the
Sunne-standings
.
Vses
common
to
both
Colures
.
-
1.
By
meanes
of
these
two
Colures
,
all
the
mouable
circles
of
the
materiall
Sphaere
are
framed
together
,
that
so
they
might
be
turned
about
,
like
as
the
whole
Heauens
are
moued
.
-
2.
The
Poles
are
fastened
in
the
common
meeting
of
these
two
Circles
:
and
the
Poles
are
also
shewed
by
the
same
common
meetings
.
-
3.
They
shew
the
foure
principall
points
of
the
Eclipticke
;
that
is
,
the
two
Equinoctiall
,
and
the
two
Solstitiall
points
.
-
4.
These
circles
shew
those
points
of
the
Eclipticke
,
wherein
the
Sunne
is
either
equally
distant
from
both
poles
of
the
Sphaere
,
or
commeth
neerest
to
either
of
them
:
In
which
points
the
Sunne
maketh
the
dayes
longest
or
shortest
,
or
of
a
meane
length
betweene
both
these
in
an
oblique
Sphaere
.
-
5.
They
deuide
the
Ecliptick
into
foure
quarters
,
in
which
the
Sunne
maketh
foure
quarters
of
the
yeare
,
the
Spring
,
the
Summer
,
Autumne
,
and
Winter
.
-
6.
They
deuide
the
Ecliptick
and
Equinoctiall
into
such
foure
quarters
,
as
in
a
right
Sphaere
doe
rise
together
in
equall
time
.
CHAP.
XI
.
Vses
of
the
Equinoctiall
Colure
.
1.
THe
section
of
this
Circle
with
the
Ecliptick
;
sheweth
the
Equinoctiall
points
,
wherein
the
Equinoctiall
and
the
Eclipticke
doe
deuide
and
crosse
each
other
.
In
which
points
the
Sunne
maketh
equality
of
dayes
and
nights
throughout
the
whole
world
:
whereof
this
circle
is
also
called
Colurus
Aequinoctiorum
;
that
is
,
the
colure
of
equall
dayes
and
nights
,
or
the
Equinoctiall
colure
.
2.
It
deuideth
the
Eclipticke
into
the
North
and
South
halfes
.
3.
It
deuideth
the
Signes
wherein
the
Sunne
maketh
the
dayes
longer
then
the
nights
,
from
those
signes
wherein
the
dayes
are
made
shorter
then
the
nights
.
4.
It
sheweth
which
halfes
of
the
Eclipticke
and
Equator
,
doe
arise
together
in
equall
time
in
an
oblique
Sphaere
.
5.
It
sheweth
the
two
high
Sunne-standings
in
a
right
Sphaere
,
in
the
time
of
which
Sunne-standings
,
the
Sunne
passeth
by
the
Zenith
.
CHAP.
XII
.
Vses
of
the
Solstitiall
Colure
.
1.
THe
common
meetings
of
this
circle
with
the
Ecliptick
,
shew
the
Solstitiall
or
Tropicall
points
;
in
which
points
the
Sunne
seemeth
to
stand
,
and
then
returneth
backe
againe
:
for
which
cause
this
circle
is
called
the
Colure
of
the
Sun-standings
.
These
points
are
called
tropicall
(
which
is
as
much
to
say
as
turne-points
,
or
points
of
returne
)
because
that
when
the
Sunne
going
alwayes
vnder
the
Eclipticke
commeth
to
these
points
,
which
are
furthest
distant
from
the
Equinoctiall
circle
,
it
returneth
againe
towards
the
same
circle
.
But
they
were
called
Solstitiall
or
Sun-ding
points
,
because
that
whilest
the
Sunne
is
about
those
points
,
the
difference
of
the
Sunnes
returning
is
(
for
certaine
dayes
)
insensible
.
Hereof
the
Sunne
is
said
to
make
his
station
,
or
to
stand
,
when
he
commeth
to
either
of
those
points
.
They
that
dwell
without
the
Tropickes
,
haue
two
sunne-standings
,
that
is
the
Summer
sun-standing
,
or
high
sun-standing
(
when
the
Sunne
in
Summer
time
is
at
the
highest
,
and
next
vnto
our
Zenith
being
in
the
beginning
of
Cancer
)
and
the
winterly
,
or
low
sun-standing
,
when
the
Sunne
in
Winter
time
is
lowest
in
the
Meridian
,
and
furthest
from
our
Zenith
.
But
they
that
dwell
within
the
Tropicks
(
by
a
certaine
similitude
taken
from
our
sun-standings
,
wherein
the
Sunne
is
either
highest
or
lowest
)
are
said
to
haue
foure
sun-standings
;
that
is
two
high
sun-standings
,
when
the
Sunne
passeth
by
their
Zenith
(
the
highest
point
in
the
Heauens
)
which
hapneth
twice
euery
yeare
in
two
places
,
equally
distant
from
the
beginnings
of
Cancer
and
Capricorne
:
and
two
low
sun-standings
,
when
the
Sunne
is
in
the
beginning
of
Cancer
and
Capricorne
.
2.
In
this
Circle
by
the
arch
conteyned
betweene
the
Equator
and
Eclipticke
,
we
measure
the
greatest
declination
of
the
Sunne
,
or
obliquity
of
the
Eclipticke
,
which
in
Ptolomees
time
was
23.
degrees
51.
minutes
,
and
one
third
part
of
a
minute
.
But
euer
since
that
time
it
hath
beene
found
by
obseruation
to
decrease
;
so
as
in
this
our
age
,
it
is
no
more
then
23.
degrees
and
one
halfe
,
or
little
more
:
Notwithstanding
Copernicus
thought
that
the
greatest
obliquity
was
23.
degrees
28.
minutes
.
3.
It
sheweth
the
places
of
the
Eclipticke
,
in
which
the
Sunne
(
comming
neerest
to
our
Zenith
)
maketh
the
artificiall
day
longest
;
or
going
furthest
from
the
same
point
,
maketh
the
same
shortest
.
4.
It
deuideth
the
Zodiacke
into
two
halfes
,
the
one
ascending
,
and
the
other
descending
.
5.
Hereby
also
the
signes
are
distinguished
,
which
doe
rise
rightly
,
and
which
rise
obliquely
in
an
oblique
Sphaere
.
For
the
descending
halfe
riseth
rightly
,
and
the
ascending
halfe
riseth
obliquely
.
6.
So
the
points
of
the
Eclipticke
are
shewed
by
this
Circle
,
wherein
the
greatest
difference
of
right
and
oblique
ascensions
happeneth
.
It
distinguisheth
those
signes
in
which
when
the
Sunne
moueth
,
the
artificiall
dayes
are
increased
,
and
the
nights
decrease
;
from
those
signes
wherein
the
dayes
are
diminished
,
and
the
nights
increase
.
7.
In
this
circle
are
the
bredths
of
the
Zones
bounded
;
for
the
obliquity
of
the
Eclipticke
doubled
,
sheweth
the
bredth
of
the
torrid
or
burnt
Zone
:
the
distance
of
the
poles
of
the
Ecliptick
,
and
of
the
Poles
of
the
Equator
,
shew
the
bredth
of
the
cold
or
frozen
Zones
;
and
the
other
two
Arches
remaining
,
shew
the
bredths
of
the
temperate
Zones
.
CHAP.
XIII
The
Description
of
the
two
Tropickes
.
THe
two
smaller
Circles
Equidistant
in
all
places
from
the
Equinoctiall
,
and
comming
vnder
these
Solstitiall
points
of
the
Eclipticke
on
both
sides
,
are
called
the
Tropicks
,
that
is
circles
of
returne
.
And
they
are
so
called
,
because
that
when
the
Sun
commeth
to
them
,
it
beginneth
to
returne
backe
againe
towards
the
Equinoctiall
circle
.
Or
else
they
may
be
so
called
,
because
they
are
described
by
the
turning
about
of
the
Tropicall
points
of
Cancer
and
Capricorne
.
They
are
also
called
solstitiall
Circles
;
that
is
Circles
of
the
sun-standings
;
because
that
by
reason
of
the
insensible
alteration
of
the
declination
of
the
Ecliptick
,
for
some
space
both
before
,
and
after
the
Tropicall
points
,
the
Sunne
(
in
respect
of
his
Meridian
altitudes
,
or
in
respect
of
the
motion
he
hath
towards
the
North
or
South
,
by
reason
of
the
obliquity
of
the
Eclipticke
)
seemeth
to
stand
(
as
it
were
)
for
certaine
dayes
in
those
places
.
There
be
two
Tropicks
,
the
Tropick
of
Cancer
,
and
the
tropicke
of
Capricorne
.
The
tropick
of
Cancer
,
toucheth
the
Ecliptick
in
the
beginning
of
Cancer
,
which
is
the
most
northerly
point
of
the
Ecliptick
:
or
it
is
the
Tropick
described
in
the
first
mouable
Sphaere
,
by
the
Summer
solstitiall
point
.
This
circle
is
called
the
Tropick
of
Cancer
,
because
it
toucheth
the
Ecliptick
in
the
beginning
of
Cancer
.
It
is
also
called
the
Summer
Tropick
,
and
the
Tropick
of
the
Summer
sun-standing
,
because
that
when
the
Sunne
commeth
to
it
,
the
Summer
beginneth
.
It
is
called
the
North
tropick
,
because
it
is
in
the
North
part
of
the
world
:
and
the
Circle
of
the
high
sunne-standing
,
because
the
Sunne
comming
to
it
,
is
highest
in
the
Meridian
,
and
next
vnto
our
Zenith
which
dwell
in
the
North
part
of
the
world
,
without
the
Tropicks
.
The
Tropick
of
Capricorne
is
the
Tropick
which
toucheth
the
Ecliptick
in
the
first
point
of
Capricorne
.
It
is
called
the
Tropick
of
Capricorne
,
because
it
toucheth
the
Ecliptick
in
the
beginning
of
Capricorne
.
It
is
called
the
winter
Tropicke
and
Tropick
of
the
Winter
sun-standing
,
because
the
Sunne
commeth
to
it
in
Winter
.
It
is
also
called
the
circle
of
the
lowest
Sunne-standing
,
because
that
when
the
Sunne
commeth
to
this
Tropicke
,
it
is
furthest
distant
from
our
Zenith
,
and
hath
his
lowest
height
in
the
Meridian
.
CHAP.
XIIII
.
Vses
of
the
Tropickes
.
1.
THe
Tropicks
shew
the
Tropicall
,
or
Solstitiall
points
of
the
Eclipticke
:
that
is
,
the
points
wherein
the
Sunne
seemeth
to
stand
,
and
beginneth
to
returne
backe
againe
.
2.
They
bound
out
the
greatest
declinations
of
the
Sunne
,
which
in
our
times
is
about
23.
degrees
and
an
halfe
.
3.
Therefore
they
doe
also
bound
out
the
obliquity
of
the
Ecliptick
,
for
they
are
the
bounds
of
the
Sunnes
way
,
beyond
which
the
Sunne
goeth
not
at
any
time
.
4.
The
Sunne
comming
to
either
of
these
circles
,
is
either
neerest
,
or
furthest
distant
from
our
verticall
point
.
5.
In
an
oblique
Sphaere
,
they
measure
out
the
shortest
,
and
longest
artificiall
day
and
night
.
6.
The
Tropicks
(
aswell
in
Heauen
as
in
Earth
,
conteyne
betwixt
them
the
Torrid
Zone
,
and
separate
it
from
the
temperate
.
CHAP.
XV.
The
Polar
Circles
.
THe
two
smallest
circles
that
are
next
about
the
poles
of
the
Sphaere
,
are
called
the
polar
circles
.
They
are
drawne
by
the
poles
of
the
Eclipticke
,
and
are
euery
where
Equidistant
from
the
Equinoctiall
,
and
from
the
poles
of
the
Sphaere
.
They
are
called
polar
Circles
,
either
because
they
are
neere
the
poles
of
the
Sphaere
,
or
else
because
they
are
described
by
the
motion
of
the
poles
of
the
Eclipticke
.
And
therefore
there
be
two
polar
Circles
,
that
is
,
so
many
as
there
are
poles
of
the
Ecliptick
:
the
Polar
circle
Artick
,
and
the
Polar
Antartick
.
The
Articke
polar
circle
,
is
that
which
passeth
by
the
North
pole
of
the
Ecliptick
,
or
which
is
described
by
the
North
pole
of
the
Ecliptick
being
carried
about
with
the
motion
of
the
first
moueable
Sphaere
.
The
Antartick
polar
circle
,
is
that
which
goeth
by
the
South
pole
of
the
Eclipticke
,
being
described
with
the
first
motion
by
the
Antartick
pole
of
the
Ecliptick
.
The
distance
of
these
polar
Circles
from
the
poles
of
the
Sphaere
,
is
equall
to
the
distance
of
the
tropicks
from
the
Equinoctiall
,
which
in
our
time
is
about
23.
degr.
and
an
halfe
:
for
so
much
as
is
the
obliquity
of
the
Zodiack
(
whereto
the
distance
of
the
Tropicks
from
the
Equinoctiall
is
alwayes
equall
)
so
much
are
the
poles
of
the
Ecliptick
distant
from
the
Poles
of
the
world
.
CHAP.
XVI
.
Vses
of
the
Polar
Circles
.
1.
THe
Polar
Circles
shew
the
poles
of
the
Zodiack
,
and
shew
their
distance
from
the
poles
of
the
Equinoctiall
.
2.
The
temperate
Zones
are
bounded
by
these
polar
circles
;
for
the
Articke
circle
boundeth
the
North
side
of
the
North
temperate
Zone
;
and
the
Antartick
circle
boundeth
out
the
South
side
of
the
South
temperate
Zone
.
3.
The
Polar
circles
separate
the
temperate
Zones
,
from
the
cold
Zones
which
they
compasse
round
about
,
and
inclose
within
them
.
Therefore
the
foure
lesser
circles
,
that
is
the
two
Polar
circles
,
and
the
Tropicks
,
deuide
Heauen
and
Earth
,
into
fiue
Zones
.
CHAP.
XVII
.
Of
the
Zones
.
A
Zone
is
a
space
of
Heauen
,
or
Earth
,
conteyned
betweene
two
of
the
smaller
Circles
;
or
inclosed
within
the
compasse
of
either
Polar
circle
.
They
are
called
Zones
(
that
is
as
much
to
say
as
girdles
)
because
they
compasse
about
Heauen
or
Earth
like
a
girdle
.
The
Zones
are
deuided
by
auncient
Writers
into
two
kindes
;
that
is
into
temperate
,
and
vntemperate
Zones
.
A
temperate
Zone
is
the
space
of
Heauen
or
earth
,
conteyned
betweene
either
of
the
Tropicks
,
and
the
next
Polar
circle
.
There
be
two
temperate
Zones
;
the
one
North
,
the
other
South
.
The
North
temperate
Zone
is
conteyned
betweene
the
Tropicke
of
Cancer
,
and
the
Artick
polar
circle
.
The
South
temperate
Zone
is
that
which
is
conteyned
betweene
the
Tropicke
of
Capricorne
,
and
the
Antartick
polar
circle
.
They
are
called
temperate
Zones
,
because
they
haue
a
better
temperature
of
the
ayre
for
the
most
part
,
and
more
meer
for
habitation
,
then
the
vntemperate
Zones
.
The
bredth
of
eyther
temperate
Zone
is
alwayes
equall
to
the
complement
of
the
distance
of
the
Tropicks
,
and
therefore
in
this
age
is
about
43.
degrees
,
that
is
2580.
English
miles
.
There
be
two
kinde
of
vntemperate
Zones
,
the
one
exceeding
in
heat
,
the
other
in
cold
,
for
the
most
part
.
The
hot
vntemperate
Zone
,
(
called
also
the
Torrid
;
that
is
,
the
burnt
or
broyled
zone
)
is
that
space
of
Heauen
or
Earth
,
which
is
conteyned
betweene
the
tropicks
.
It
is
called
the
burnt
Zone
,
because
that
by
reason
of
the
Sunnes
continuall
going
ouer
that
zone
;
and
casting
his
beames
directly
downe
thereupon
,
it
is
scorched
with
ouer-much
heat
,
and
is
not
so
meet
to
be
inhabited
as
the
temperate
zones
.
The
bredth
of
this
Zone
is
alwayes
equall
to
the
obliquitie
of
the
Zodiack
,
or
greatest
declination
of
the
Sunne
,
doubled
;
which
in
our
time
is
about
47.
degrees
,
that
is
2820.
English
miles
.
The
cold
or
frozen
zones
,
are
the
spaces
of
Heauen
or
earth
,
conteyned
within
the
Polar
circles
.
There
be
two
cold
zones
,
the
one
North
,
conteyned
within
the
compasse
of
the
Articke
circle
:
the
other
South
,
conteyned
within
the
compasse
of
the
Antartick
Polar
circle
.
These
zones
exceed
in
cold
,
because
they
want
the
sight
of
the
sunne
for
a
great
part
of
the
yeare
,
and
when
the
Sunne
appeareth
vnto
them
,
his
beames
fall
so
obliquely
vpon
them
,
that
they
can
(
in
all
likelyhood
)
receiue
but
small
heat
thereby
for
the
most
part
.
The
bredth
of
these
Zones
is
measured
from
the
Poles
of
the
world
to
the
Polar
circles
,
and
therefore
must
alwayes
bee
so
much
as
the
Polar
circles
are
distant
from
the
Poles
:
that
is
,
in
our
age
about
23.
Degrees
and
a
halfe
,
which
make
1410.
English
miles
.
CHAP.
XVIII
.
The
difference
of
Shadowes
that
the
Sunne
maketh
in
these
Zones
.
THey
that
dwell
in
the
torride
Zone
,
doe
cast
their
shadowes
which
the
Sunne
maketh
at
noone
(
which
we
may
therefore
call
their
noone
shadowes
)
both
towards
the
North
,
and
towards
the
South
:
towards
the
North
,
when
the
sunne
is
betwixt
their
zenith
and
the
south
point
of
the
Horizon
;
and
towards
the
South
,
where
the
sunne
is
betweene
their
Zenith
and
the
North.
For
seeing
the
zenith
of
them
that
dwell
in
that
Zone
is
betweene
the
Tropicks
,
the
sunne
must
needs
bee
sometimes
Northwards
from
their
zenith
,
and
so
make
a
south
shadow
:
and
sometime
Southwards
,
and
then
make
a
north
shadow
.
For
which
cause
they
that
inhabite
this
Zone
are
called
Amphiscij
;
that
is
,
such
as
cast
their
noone
shadowes
on
both
sides
.
But
they
that
dwell
in
the
temperate
Zones
,
are
called
Heteroscij
;
that
is
,
such
as
cast
their
shadowes
at
noone
,
one
way
onely
.
For
they
that
dwell
in
the
North
temperate
Zone
,
haue
the
Sunne
alwayes
at
noone
from
their
Zenith
Southwards
,
and
therefore
must
needs
alwayes
cast
their
noone
shadowes
Northwards
.
Whereas
contrariwise
they
that
inhabit
the
South
temperate
Zone
,
hauing
the
Sunne
at
noone
alwayes
Northwards
from
their
Zenith
,
must
needs
haue
their
shadowes
at
noone
,
alwayes
towards
the
South
.
And
they
that
are
in
the
cold
Zones
,
are
called
Periscij
;
that
is
,
such
as
cast
their
shadowes
round
about
them
.
For
seeing
the
Sunne
continueth
euery
yeare
for
certaine
dayes
together
,
alwayes
aboue
their
Horizon
,
and
therefore
moueth
round
about
them
without
setting
:
it
must
needs
bee
,
that
their
shadowes
also
are
carried
round
about
them
,
falling
towards
all
parts
of
the
world
in
the
space
of
24.
houres
.
*
⁎
*
THE
SECOND
PART
.
Of
the
vses
of
the
vppermost
SPHAERE
,
and
of
the
Circles
thereof
joyntly
.
PROP.
I.
To
rectifie
the
Sphaere
to
the
Latitude
.
&c.
FIrst
finde
by
obseruation
,
or
otherwise
the
height
of
the
Pole
,
or
Latitude
of
that
place
for
which
you
would
rectifie
the
Sphaere
.
Then
(
by
turning
about
the
Meridian
of
the
Sphaere
;
lift
vp
or
put
downe
the
North
Pole
of
the
Sphaere
(
about
which
the
houre
circle
is
fastened
)
till
the
arch
of
the
Meridian
from
the
North
part
of
the
Horizon
vpwards
vnto
the
Pole
,
be
iust
so
many
degrees
as
the
eleuation
of
the
Pole
or
latitude
of
the
place
was
found
to
be
:
for
so
haue
you
the
Sphaere
duly
rectified
.
As
for
example
,
the
Latitude
of
the
Citie
of
London
is
51.
degrees
and
32.
minutes
,
therefore
if
you
lift
vp
the
North
Pole
of
the
Sphaere
,
aboue
the
North
part
of
the
Horizon
,
so
many
degrees
and
minutes
you
shall
haue
your
Sphaere
rectified
for
that
place
.
PROP.
II.
To
know
the
place
of
the
Sunne
;
&c.
LOoke
the
day
of
the
moneth
(
for
which
you
desire
to
know
the
place
of
the
Sunne
)
in
the
Horizon
,
and
see
what
signe
and
degree
of
the
Zodiacke
vpon
the
Horizon
answereth
thereto
;
for
there
haue
you
the
place
of
the
Sunne
.
Take
for
example
the
25.
of
December
:
looke
this
day
therefore
in
the
Horizon
,
and
you
shall
finde
answerable
thereto
13.
degrees
,
and
about
40.
minutes
of
Capricorne
,
which
is
the
place
of
the
Sunne
at
that
time
.
PROP.
III.
To
know
the
declination
of
the
Sunne
,
&c.
BRing
the
point
whose
declination
you
desire
to
know
,
vnto
the
Meridian
of
the
Sphaere
,
and
look
what
number
of
degrees
and
minutes
of
the
Meridian
is
conteyned
betweene
that
point
,
and
the
Equinoctiall
,
for
so
much
is
the
declination
.
As
if
you
would
know
the
declination
of
the
10.
degree
of
Taurus
,
bring
that
degree
to
the
Meridian
,
and
you
shall
finde
the
arch
of
the
Meridian
between
that
degree
and
the
Equinoctiall
,
to
be
14.
degrees
and
about
51.
minutes
.
PROP.
IIII.
To
know
the
right
ascention
of
the
Sunne
,
&c.
BRing
that
point
(
as
before
)
to
the
Meridian
,
and
see
then
how
many
degrees
and
minutes
of
the
Equinoctiall
are
conteyned
betweene
the
beginning
of
Aries
and
the
Meridian
:
for
that
is
the
right
ascension
of
that
point
.
So
you
shall
finde
the
right
ascension
of
the
10.
degr.
of
Taurus
to
be
37.
degr.
35.
min.
for
if
you
bring
that
degree
of
Taurus
to
the
Meridian
,
you
shall
finde
so
many
degrees
and
min.
between
the
beginning
of
Aries
,
and
the
Meridian
.
PROP.
V.
To
know
the
oblique
ascension
of
the
Sunne
,
&c.
SEt
the
Sphaere
to
the
eleuation
of
the
place
for
which
you
desire
to
know
the
oblique
ascension
;
then
bring
the
Sunne
,
Starre
,
or
point
whose
oblique
ascention
you
would
know
,
vnto
the
East
semicircle
of
the
Horizon
,
and
looke
how
many
degrees
and
minutes
of
the
Equinoctiall
circle
,
are
conteyned
between
the
East
point
of
the
Horizon
,
and
the
beginning
of
Aries
;
for
so
much
is
the
oblique
ascension
desired
:
As
for
example
,
if
you
see
the
Sphaere
to
the
Latitude
of
London
51.
degr.
32.
min.
and
then
bring
the
10.
degree
of
Taurus
to
the
East
part
of
the
Horizon
,
you
shall
finde
about
19.
degrees
and
an
halfe
of
the
Equinoctiall
,
at
the
same
East
part
of
the
Horizon
;
which
is
the
oblique
ascension
of
that
degree
of
Taurus
,
for
the
Latitude
of
the
Citie
of
London
.
PROP.
VI.
To
finde
the
difference
of
Ascension
.
COmpare
the
right
and
oblique
ascensions
of
the
Sunne
,
(
or
of
any
point
of
the
Zodiacke
)
together
,
and
subtract
the
lesse
from
the
greater
,
for
the
remainder
shall
bee
the
difference
of
ascension
.
As
for
example
,
the
right
ascension
of
the
10.
degree
of
Taurus
,
being
found
by
the
4.
Propo.
to
be
37.
degrees
,
35.
min.
and
the
oblique
ascention
of
the
same
degree
at
London
,
by
the
5.
Prop.
19.
degree
30.
min.
by
subtraction
of
the
lesse
out
of
the
greater
,
the
difference
shall
be
found
to
be
18.
degr.
and
5.
minutes
,
which
is
the
difference
of
ascension
sought
for
.
PROP.
VII
.
To
finde
at
what
time
the
Sunne
riseth
or
setteth
.
REduce
the
difference
of
Ascention
into
houres
and
minutes
(
taking
for
euery
15
degrees
1.
houre
,
and
for
euery
one
degree
that
remayneth
4.
minutes
,
and
for
euery
minute
of
a
degree
4
seconds
)
for
these
houres
,
minutes
and
seconds
,
being
added
to
6.
houres
,
if
the
Sunne
bee
in
any
of
the
South
signes
;
or
subtracted
,
if
hee
be
in
the
North
signes
,
sheweth
the
time
of
the
Sun-rising
.
And
contrariwise
,
the
same
houres
and
minutes
subtracted
from
sixe
houres
when
the
Sunne
is
in
the
South
signes
,
or
added
when
he
is
in
the
North
signes
,
sheweth
the
the
time
of
the
Sunne-setting
.
As
for
example
,
the
Sunne
being
in
the
10.
degree
of
Taurus
which
happeneth
about
the
20.
or
21.
day
of
Aprill
)
I
would
know
at
what
houre
and
minute
the
Sunne
riseth
,
and
setteth
at
London
:
Hauing
therefore
found
by
the
former
Proposition
the
difference
of
ascention
to
be
18.
degr.
and
5.
minutes
I
take
for
15.
degrees
thereof
one
houre
,
and
for
the
three
degr.
remaining
,
12.
minutes
of
an
houre
,
and
for
the
5.
minutes
,
20.
seconds
of
an
houre
.
Which
houre
,
minutes
and
seconds
being
subtracted
out
of
6.
houres
,
because
the
Sunne
is
in
a
North
signe
,
there
remaineth
the
time
of
the
Sunnes
rising
at
4.
a
clocke
47.
minutes
,
40.
seconds
.
And
adding
the
same
houre
,
min.
and
seconds
to
6.
houres
,
you
haue
the
time
of
the
Sun-setting
that
day
at
7.
a
clocke
,
12.
min.
and
20.
seconds
.
PROP.
VIII
.
To
finde
the
length
of
the
artificiall
day
or
night
.
THe
artificiall
day
,
is
the
time
conteyned
between
the
Sun-rising
and
the
Sun-setting
:
and
the
artificiall
night
is
the
time
betweene
Sunne-setting
and
Sun-rising
.
The
length
of
both
these
is
found
after
this
manner
:
hauing
found
the
difference
of
ascension
,
and
reduced
it
into
houres
and
minutes
(
as
in
the
former
Proposition
)
double
th●se
houres
and
minutes
,
and
adde
them
to
12.
houres
if
the
Sunne
be
in
the
North
signes
,
or
subtract
them
from
12.
houres
if
the
Sunne
be
in
the
South
signes
,
for
so
shall
you
haue
the
length
of
the
day
:
But
(
contrariwise
)
subtract
the
same
houres
and
minutes
(
being
doubled
)
from
12.
houres
,
the
Sunne
being
in
the
North
signes
;
and
adde
them
to
12.
houres
when
he
is
in
the
South-signes
;
so
haue
you
the
length
of
the
night
.
Or
else
,
double
the
time
of
the
Sun-setting
,
so
haue
you
the
length
of
the
day
.
And
double
the
time
of
the
Sun-rising
,
so
haue
you
the
length
of
the
right
.
As
the
time
of
the
Sun-rising
being
found
by
the
former
Proposition
to
be
4
houres
48.
minutes
after
mignight
at
London
,
the
Sunne
being
in
the
10.
degr.
of
Taurus
,
by
doubling
the
time
of
the
Sun-rising
,
the
length
of
the
night
shall
be
found
to
be
9.
houres
and
36.
minutes
.
And
doubling
the
time
of
the
sun-setting
that
is
7.
houres
,
and
12.
minutes
,
you
haue
the
length
of
the
day
,
14.
houres
;
and
24.
minutes
.
PROP.
IX
.
To
know
the
time
of
the
Sun
rising
and
Sun
setting
.
THe
place
of
the
Sunne
being
found
by
the
2.
Proposition
,
bring
the
same
to
the
Meridian
,
and
withall
set
the
point
of
the
Index
of
the
houre
circle
,
to
the
12.
houre
in
the
same
circle
:
Then
bring
the
place
of
the
Sunne
to
the
Horizon
Eastwards
;
and
the
point
of
the
houre
Index
shall
shew
you
in
the
houre
circle
,
the
time
of
the
Sun-rising
.
But
if
you
bring
the
place
of
the
Sunne
to
the
Horizon
Westwards
,
the
point
of
the
Index
will
shew
in
the
houre
circle
the
time
of
the
Sun-setting
.
As
for
example
,
the
Sunne
being
in
the
10.
degree
of
Taurus
,
bring
the
same
degree
to
the
Meridian
,
and
bring
the
point
of
the
houre
Index
also
to
the
Meridian
:
then
(
the
Sphaere
being
set
to
the
Latitude
of
London
)
bring
the
same
10.
degree
of
Taurus
to
the
East
part
of
the
Horizon
,
for
then
the
houre
Index
will
shew
you
in
the
houre
circle
,
that
the
Sunne
riseth
at
4.
of
the
clocke
and
48.
minutes
.
And
bringing
the
same
degree
to
the
West
semicircle
of
the
Horizon
,
the
same
Index
will
shew
the
time
of
the
Sun-setting
to
be
7.
houres
and
12.
min.
after
noone
.
PROP.
X.
To
finde
the
length
of
the
artificiall
day
or
night
.
BRing
the
place
of
the
Sun
(
being
found
as
before
to
the
East
semicircle
of
the
Horizon
:
set
the
houre
Index
12.
a
clocke
in
the
Houre
circle
:
turne
about
the
Sphaere
from
the
East
Westwards
,
till
the
place
of
the
sunne
come
to
the
Horizon
,
and
marke
how
many
houres
the
Index
hath
runne
ouer
vpon
the
Houre
circle
in
the
meane
time
,
for
so
much
is
the
length
of
the
day
.
And
to
finde
the
length
of
the
night
:
Bring
the
place
of
the
sunne
to
the
West
semicircle
of
the
Horizon
,
and
set
the
Index
to
12.
a
clocke
as
before
;
Then
turning
forwards
the
Sphaere
from
East
Westward
till
the
place
of
the
sunne
come
to
the
East
semicircle
of
the
Horizon
;
see
how
many
houres
the
Index
passeth
ouer
in
the
Houre-circle
,
for
so
many
houres
long
is
the
night
.
As
for
example
;
supposing
the
Sunne
to
be
as
before
in
the
10.
degree
of
Taurus
,
bring
the
same
degree
to
the
East
part
of
the
Horizon
,
and
the
point
of
the
Index
to
the
Meridian
:
then
turning
about
the
Sphaere
,
till
the
same
degree
come
to
the
West
part
of
the
Horizon
;
you
shall
finde
that
in
the
meane
time
,
the
point
of
the
Index
shal
passe
ouer
14.
houres
and
24.
minutes
,
which
is
the
length
of
the
day
.
Likewise
,
if
you
bring
the
same
10.
degr.
of
Taurus
to
the
West
part
of
the
Horizon
,
and
the
Index
to
the
Meridian
,
and
turne
about
the
Sphaere
,
till
that
degree
come
to
the
East
semicircle
of
the
Horizon
,
the
number
of
houres
that
the
Index
runneth
ouer
in
the
meane
time
vpon
the
Houre
circle
,
shall
be
found
to
bee
9.
Degrees
,
and
36.
Minutes
.
PROP.
XI
.
To
know
the
Meridian
altitude
,
or
the
height
of
the
Sunne
at
noone
,
for
any
time
and
place
.
SEt
the
Sphaere
to
the
latitude
of
the
place
where
you
d●sire
to
know
the
Sunnes
height
at
noone
:
bring
the
place
of
the
Sunne
(
being
found
as
before
by
the
2.
Prop.
)
to
the
Meridian
,
then
see
how
many
degrees
of
the
Meridian
,
are
contayned
betweene
the
Horizon
,
and
the
place
of
the
sunne
,
for
so
much
is
the
height
of
the
Sunne
at
noone
.
In
like
sort
it
may
be
knowne
how
much
the
Sunne
is
vnder
the
Horizon
at
midnight
,
after
this
manner
:
Bring
the
place
of
the
sunne
in
the
Zodiacke
to
the
Meridian
vnder
the
Horizon
,
and
see
how
many
degrees
of
the
Meridian
,
are
contayned
betweene
the
vpper-side
of
the
Horizon
,
and
the
place
of
the
Sunne
downewards
:
and
so
shall
you
haue
that
you
sought
for
.
Or
else
if
you
cannot
well
come
to
the
Meridian
vnder
the
Horizon
:
bring
that
point
of
the
Eclipticke
which
is
opposite
to
the
place
of
the
sunne
,
vnto
the
Meridian
aboue
the
Horizon
;
for
the
arch
of
the
Meridian
,
or
the
number
of
degrees
and
minutes
of
the
Meridian
,
betweene
that
point
and
the
Horizon
sheweth
how
much
the
sunne
is
vnder
the
Horizon
at
midnight
.
After
this
manner
▪
the
Sunne
being
in
the
10.
degr.
of
Taurus
,
you
shall
find
that
his
Meridian
altitude
at
London
is
53.
degrees
,
and
about
one
halfe
.
As
also
that
hee
is
vnder
the
Horizon
at
midnight
about
23.
degrees
and
a
halfe
at
London
.
PROP.
XII
.
To
know
how
high
the
Sunne
is
aboue
the
Horizon
at
any
time
of
the
day
.
BRing
the
place
of
the
Sun
(
found
by
the
2.
Prop.
)
to
the
Meridian
:
set
the
houre
Index
to
12.
a
clock
vpon
the
houre
circle
:
turne
the
Sphaere
about
till
the
Index
come
to
the
houre
at
which
you
desire
to
know
the
height
of
the
Sunne
aboue
the
Horizon
;
take
the
distance
of
the
place
of
the
Sunne
from
the
Horizon
with
a
large
payre
of
Compasses
:
then
set
both
feet
of
the
Compasses
in
the
Ecliptick
,
and
looke
how
many
degrees
are
conteyned
betweene
them
,
for
so
much
is
the
height
of
the
Sunne
.
Thus
may
you
finde
by
the
Sphaere
,
that
when
the
Sunne
is
in
the
tenth
degree
of
Taurus
,
his
height
at
10.
of
the
clocke
in
the
fore-noone
(
the
Sphaere
being
duly
rectified
by
the
first
Proposition
)
shall
be
about
45.
degrees
and
an
halfe
at
London
.
PROP.
XIII
.
To
finde
the
houre
of
the
day
by
the
height
of
the
Sunne
;
&c.
SEt
the
pole
Artick
of
the
Sphaere
to
his
eleuation
for
that
place
where
you
desire
to
know
the
houre
of
the
day
:
bring
the
place
of
the
Sunne
in
the
Zodiack
to
the
Meridian
,
and
the
houre
Index
to
12.
a
clocke
of
the
houre
circle
:
take
so
many
degrees
of
the
Ecliptick
betweene
the
feet
of
your
Compasses
,
as
the
height
of
the
Sunne
amounteth
vnto
.
Then
set
one
foot
of
your
Compasses
in
the
place
of
the
Sunne
,
and
turne
the
Sphaere
about
,
Eastwards
,
if
it
be
in
the
fore-noone
,
or
West-wards
,
if
in
the
after-noone
,
till
you
can
but
onely
touch
the
Horizon
with
the
other
foot
of
your
Compasses
;
for
then
the
Index
pointeth
out
the
houre
of
the
day
in
the
Houre
circle
.
As
suppose
you
obserue
the
height
of
the
Sun
being
in
the
10.
degr.
of
Taurus
,
and
find
him
to
bee
30.
degrees
high
in
the
fore-noone
:
you
shall
find
(
following
the
directions
prescribed
in
this
Proposition
)
that
it
shall
then
be
about
8.
of
the
clocke
in
the
morning
.
PROP.
XIIII
.
To
finde
the
Amplitude
or
bredth
of
the
Sunnes
rising
,
or
setting
,
&c.
THe
pole
of
the
Sphaere
being
set
to
his
eleuation
,
and
the
place
of
the
Sunne
to
the
East
semicircle
of
the
Horizon
:
see
how
many
degrees
of
the
Horizon
,
are
contayned
betweene
the
place
of
the
Sunne
,
and
the
true
East
point
,
for
so
you
shall
haue
the
bredth
of
the
sunnes
rising
.
Thus
the
sunne
being
in
the
10.
degree
of
Taurus
,
you
shall
find
by
the
Sphaere
,
that
(
for
the
latitude
of
London
)
hee
riseth
about
23.
degr.
and
a
halfe
Northwards
,
from
the
true
East
point
,
and
that
hee
setteth
as
many
degrees
towards
the
North
,
from
the
true
West
point
.
PROP.
XV.
To
finde
the
place
of
the
Sunne
,
&c.
THe
quarter
of
the
yeare
being
knowne
,
bring
the
quarter
of
the
Eclipticke
that
is
answerable
thereto
,
vnder
the
Meridian
;
and
turne
the
Sphaere
to
or
fro
,
till
there
bee
so
many
degrees
and
minutes
of
the
Meridian
,
conteyned
betweene
the
Ecliptick
and
the
Equator
,
as
the
declination
commeth
to
:
then
looke
what
degree
of
the
Ecliptick
is
vnder
the
Meridian
,
for
that
is
the
place
of
the
Sunne
.
As
suppose
the
declination
of
the
Sun
in
some
day
of
the
Spring-time
of
the
yeare
be
found
to
bee
14.
degr.
51.
min.
(
turning
therefore
the
Sphaere
to
and
fro
,
till
some
part
of
the
spring
quarter
of
the
Ecliptick
,
come
right
vnder
that
degree
and
minute
of
declination
in
the
Meridian
)
you
may
finde
that
the
Sunne
is
then
in
the
tenth
degree
of
Taurus
.
PROP.
XVI
.
To
finde
what
day
of
the
moneth
it
is
,
&c.
THe
place
of
the
Sunne
being
found
by
his
declination
(
as
is
already
shewed
)
seeke
the
place
of
the
Sunne
in
the
Horizon
of
the
Sphaere
,
and
looke
what
day
is
answerable
thereto
,
for
that
is
the
day
of
the
moneth
which
was
sought
for
.
As
the
place
of
the
Sunne
being
found
by
his
declination
(
as
is
shewed
in
the
former
Proposition
)
to
be
in
the
10.
degree
of
Taurus
,
the
day
of
the
moneth
shall
thus
be
found
to
be
the
21.
of
Aprill
.
PROP.
XVII
.
The
day
of
the
moneth
being
knowne
,
to
finde
at
what
time
the
day
breaketh
.
FInde
the
place
of
the
Sunne
(
by
the
2.
Prop.
)
and
bring
it
to
the
Meridian
,
then
bring
the
houre
Index
,
to
12.
a
clocke
vpon
the
houre
circle
.
Finde
out
also
the
point
of
the
Eclipticke
that
is
right
ouer
against
the
place
of
the
Sunne
:
then
take
betweene
the
feet
of
your
Compasses
17.
degrees
of
the
Eclipticke
,
and
setting
one
foot
of
the
Compasses
in
the
point
opposite
to
the
place
of
the
Sunne
,
turne
the
Sphaere
Westwards
,
till
you
can
but
onely
touch
the
Horizon
with
the
other
foot
,
for
then
the
Index
sheweth
in
the
houre
circle
at
what
time
the
day
breaketh
.
So
the
21.
of
Aprill
,
the
Sun
being
in
the
10
degr.
of
Taurus
,
you
shall
finde
that
the
day
breaketh
about
halfe
an
houre
past
2.
of
the
clocke
in
the
morning
.
PROP.
XVIII
.
To
finde
how
long
the
twylight
continueth
.
FInde
out
by
the
former
Prop.
at
what
time
the
day
breaketh
,
and
learne
also
at
what
time
the
Sunne
riseth
by
the
7.
or
9.
Prop.
Then
subtract
the
lesser
from
the
greater
,
and
there
shall
remayne
the
length
of
the
twylight
.
Or
else
thus
:
hauing
brought
the
point
that
is
opposite
to
the
place
of
the
Sunne
to
be
17.
degrees
aboue
the
Horizon
West-wards
,
in
such
sort
as
is
shewed
in
the
former
Proposition
;
and
keeping
the
Sphaere
in
that
position
,
bring
about
the
point
of
the
houre
Index
vnto
12.
a
clocke
vpon
the
houre
circle
;
then
tune
the
Sphaere
Westwards
vntill
the
degree
or
point
of
the
Eclipticke
that
is
opposite
to
the
place
of
the
sunne
come
to
the
Horizon
:
and
see
how
many
houres
the
point
of
the
Index
hath
runne
ouer
in
the
meane
time
vpon
the
houre
circle
:
for
so
many
houres
continueth
the
twylight
.
By
eyther
of
these
wayes
,
the
Sunne
being
in
the
10.
degr.
of
Taurus
,
you
shall
finde
that
the
twylight
(
that
is
the
time
from
the
breake
of
the
day
till
Sun-rise
)
is
about
2.
houres
and
20.
minutes
.
PROP.
XIX
.
To
finde
how
much
the
declination
of
the
Sunne
must
alter
at
any
time
of
the
yeare
,
to
make
the
day
an
houre
longer
or
shorter
.
BRing
the
place
of
the
Sunne
(
found
by
the
second
Prop.
)
to
the
East
semicircle
of
the
Horizon
,
and
marke
what
degree
or
point
of
the
Horizon
it
falleth
vpon
;
bring
one
of
the
Colures
to
the
same
degree
or
point
,
and
there
make
a
pricke
in
that
colure
;
and
holding
the
Sphaere
immoueable
,
)
marke
withall
what
degree
of
the
Equinoctiall
,
or
of
eyther
of
the
Tropickes
is
then
at
the
Horizon
:
Then
turne
the
Sphaere
7.
degrees
and
an
halfe
forwards
,
towards
the
West
,
if
the
dayes
shorten
:
but
contrariwise
if
the
dayes
lengthen
;
and
holding
the
sphaere
there
immoueable
,
make
another
prick
in
the
colure
at
the
Horizon
:
for
the
distance
of
these
two
prickes
in
the
colure
taken
with
the
Compasses
and
brought
to
the
Ecliptick
,
or
Equinoctiall
,
sheweth
how
much
the
Sunnes
declination
must
alter
to
make
the
day
an
houre
longer
,
if
the
dayes
increase
;
or
shorter
,
if
they
decrease
.
After
this
manner
you
shall
finde
that
the
sunne
being
in
the
10.
degree
of
Taurus
,
his
declination
must
increase
about
5.
degrees
,
(
or
little
more
)
to
make
the
day
an
houre
longer
;
but
when
the
sunne
is
in
the
20.
degree
of
Pisces
,
his
declination
,
or
rather
his
Meridian
altitude
,
must
increase
about
6.
degrees
to
make
the
day
an
houre
longer
:
and
when
hee
is
in
the
beginning
of
Capricorne
,
his
declination
decreaseth
scarce
5.
degrees
to
make
the
day
an
houre
longer
.
PROP.
XX.
To
find
how
many
dayes
it
is
ere
the
day
lengthen
or
shorten
an
houre
.
BRing
the
foresaid
prickes
(
made
in
the
Colure
by
the
former
Proposition
)
vnto
the
Meridian
,
and
there
make
two
markes
iustly
answerable
vnto
those
prickes
in
the
Colure
:
turne
about
the
Sphaere
till
the
Eclipticke
line
come
iust
vnder
one
of
those
markes
,
and
there
make
a
pricke
in
the
Eclipticke
:
then
againe
turne
the
Sphaere
till
the
Ecliptick
come
iust
vnder
the
other
marke
made
in
the
Meridian
,
and
there
make
another
pricke
in
the
Eclipticke
:
(
But
here
it
is
to
bee
noted
,
that
whereas
the
Eclipticke
may
be
brought
vnder
that
marke
whether
way
soeuer
you
turne
the
Sphaere
,
it
must
(
I
say
be
noted
that
the
Sphaere
must
be
turned
that
way
which
may
soonest
bring
the
Eclipticke
vnder
that
marke
.
(
Lastly
,
finde
out
amongst
the
signes
and
degrees
described
vpon
the
Horizon
,
the
like
arch
to
this
,
that
is
contayned
betweene
these
prickes
in
the
Eclipticke
:
For
the
number
of
dayes
answerable
to
this
arch
in
the
Horizon
,
is
the
time
wherein
the
day
groweth
an
houre
longer
or
shorter
.
Thus
shall
you
finde
,
that
when
the
Sunne
is
in
the
beginning
of
Aries
,
it
will
bee
about
18.
dayes
after
,
ere
the
day
be
one
houre
longer
.
But
when
the
Sun
is
in
the
beginning
of
Capricorne
,
you
shall
finde
that
it
will
be
almost
twice
so
much
,
that
is
neare
34.
dayes
before
the
day
will
be
an
houre
longer
.
Hereby
therefore
the
error
of
them
manifestly
appeareth
,
which
thinke
that
in
euery
15.
dayes
,
the
day
is
lengthened
or
shortened
an
houre
,
whereas
indeed
the
lengthning
or
shortning
of
the
dayes
,
keepeth
no
such
rule
.
For
when
the
Sunne
is
about
the
Equinoctiall
points
,
the
dayes
lenghthen
or
shorten
very
fast
:
but
when
he
is
neere
the
Tropicall
points
,
they
grow
longer
or
shorter
very
slowly
.
PROP.
XXI
.
To
make
an
Horizontall
Diall
.
SEt
the
Sphaere
to
the
eleuation
of
the
place
for
which
you
would
make
the
Diall
turne
about
the
Sphaere
,
till
the
solstitiall
Colure
be
15.
degrees
(
measured
in
the
Equinoctiall
)
from
the
Meridian
;
and
where
the
Colure
crosseth
the
Horizon
,
there
make
a
prick
;
then
turne
the
Colure
yet
15.
degr.
further
,
that
is
30.
degrees
from
the
Meridian
;
and
where
the
Colure
crosseth
the
Horizon
,
there
make
an
other
prick
:
againe
turne
the
Colure
forwards
yet
15.
deg.
more
,
(
that
is
45.
degrees
from
the
Meridian
)
and
at
the
common
meeting
of
the
Colure
and
Horizon
,
make
the
third
prick
in
the
Horizon
;
and
so
proceed
with
the
rest
,
till
you
haue
made
so
many
pricks
on
that
side
of
the
Horizon
as
there
are
houres
in
halfe
the
longest
day
.
Then
looke
how
many
degrees
the
first
,
second
,
third
,
fourth
pricks
,
&c.
are
from
the
Meridian
,
for
so
many
degrees
must
the
houre
lines
of
11.
a
clocke
,
and
one
a
clocke
;
of
10.
and
2
,
of
9.
and
3.
of
8.
and
4.
&c.
be
from
the
12.
a
clock
line
in
the
Horizontall
Dyall
.
After
this
manner
in
an
Horizontall
Diall
made
for
the
Latitude
of
London
,
(
which
is
51.
degr.
and
32.
minutes
(
you
shall
finde
the
distances
of
all
the
rest
of
the
Houre-lines
from
the
12.
a
clocke
line
as
followeth
:
Betwixt
twelue
and
11.
and
twelue
and
1.
are
conceyned
12.
degrees
almost
:
Betweene
12.
and
10.
and
12.
and
2.
there
are
conteyned
14.
degr.
and
an
halfe
:
Betweene
12.
and
9.
and
12.
and
3.
38.
degr.
Betweene
12.
and
8.
and
12.
and
4.
53.
degr.
Betweene
12.
and
7.
and
12.
and
5.
70.
degrees
and
an
halfe
.
Betweene
12.
and
6.
both
before
and
after
noone
,
90.
degr.
The
other
houre
spaces
before
6.
in
the
morning
;
and
after
6.
in
the
euening
,
are
equall
to
the
Houre
spaces
after
sixe
in
the
morning
,
and
before
6.
in
the
afternoone
.
PROP.
XXII
.
How
to
make
a
direct
mural
Diall
.
SEt
the
Pole
artick
of
the
Sphaere
so
much
vnder
the
Horizon
as
is
the
complement
of
the
Poles
eleuation
:
the
Horizon
therefore
being
thus
set
as
it
were
to
the
Zenith
of
the
Sphaere
,
and
so
representing
the
verticall
Circle
of
East
and
West
(
that
is
the
plaine
super
fices
of
a
direct
mural
Diall
)
you
shall
finde
the
distances
of
all
the
houre-lines
,
(
both
before
and
after
noone
)
from
the
12.
a
clock
line
,
in
such
sort
as
you
did
before
for
the
Horizontall
Dial.
So
you
shall
finde
the
distances
of
the
houre-lines
in
an
erect
direct
murall
Dial
made
for
the
Latitude
of
London
to
bee
as
followeth
:
Betweene
the
twelue
a
clock
line
and
the
lines
of
11.
and
1.
9
,
degr.
and
about
one
third
part
of
a
degree
:
Betweene
12.
and
10.
and
12.
and
2.
19.
degrees
and
one
quarter
;
Betweene
12.
and
9.
and
12.
and
3.
32.
degr.
or
little
more
:
betweene
12.
and
8.
and
12.
and
4.
48.
degrees
:
betweene
12.
and
7.
and
12.
and
5.
67.
degr.
or
little
more
:
betweene
12.
and
6.
both
before
and
afternoone
90.
degrees
.
PROP.
XXIII
.
How
to
make
any
direct
inclining
,
or
direct
reclining
Dial.
REckon
from
the
Equinoctiall
vpwards
in
the
Meridian
,
so
many
degrees
as
the
height
of
the
Pole
commeth
to
at
that
place
where
you
would
make
your
Diall
;
for
there
is
the
verticall
point
or
Zenith
of
that
place
:
from
this
Zenith
reckon
Southwards
in
the
Meridian
,
the
inclination
of
south
Dials
,
and
the
reclination
of
North
Dialls
;
but
contrarywise
,
reckon
from
the
Zenith
Northwards
the
inclination
of
North
Dialls
,
and
the
reclination
of
South
Dialls
.
Then
bring
that
degree
of
the
Meridian
,
where
this
reckoning
endeth
to
the
Horizon
,
for
so
the
Horizon
representeth
vnto
you
the
plaine
or
the
flat
superficies
of
the
Diall
which
you
would
make
.
Therefore
you
shall
finde
how
〈…〉
euery
one
of
the
houre
lines
should
be
dist●●●
from
the
12.
a
clock
line
,
in
such
sort
as
you
did
before
in
making
the
Horizontall
Diall
.
Thus
in
a
South
direct
Diall
inclining
30.
degr.
or
in
a
North
direct
reclining
30.
degrees
made
for
the
Latitude
or
eleuation
of
the
Pole
at
London
,
you
may
finde
the
distances
of
the
eleuen
a
clock
line
,
and
of
the
one
a
clock
line
,
from
the
12.
a
clock
line
,
to
be
about
14.
degrees
.
But
the
houre
lines
of
10.
in
the
forenoone
,
and
of
2.
in
the
afternoon
,
are
distant
from
the
12.
a
clock
line
28.
degr.
&
one
halfe
;
From
12.
to
9.
and
to
3.
you
shall
find
43.
deg.
From
12.
to
8.
in
the
forenoone
,
and
4.
in
the
afternoone
,
you
shall
haue
58.
deg.
&
an
halfe
:
also
from
12.
to
7.
&
to
5.
shall
be
about
74.
deg.
And
from
12.
to
6.
in
the
morning
,
&
6.
afternoone
90.
degrees
.
Likewise
in
a
South
direct
reclining
,
or
North
direct
inclining
20.
deg.
for
the
eleuation
of
London
;
the
spaces
between
12.
&
11.
&
12.
&
1.
shall
be
about
5.
deg.
or
little
lesse
:
Between
12
,
&
10.
&
12
,
&
●
.
about
10.
deg.
&
●
.
third
parts
.
From
12
,
to
9.
in
the
forenoone
,
&
3.
in
the
afternoon
,
18.
almost
▪
From
12.
to
8.
&
4.
●g
.
deg.
or
little
more
.
From
the
1●
.
a
clock
line
;
to
the
line
of
7.
a
clock
in
the
forenoone
,
&
5.
in
the
afternoone
,
50.
deg.
or
thereabouts
.
From
12.
to
6.
both
before
and
afternooe
▪
90.
deg.
as
in
the
former
kindes
of
D●
.
In
all
which
it
is
to
be
noted
,
that
there
is
alwaies
〈◊〉
distance
betweene
the
houre
lines
of
5
,
&
●
.
&
4
,
&
6.
that
there
is
betweene
7
,
&
6.
and
8
,
&
6.
in
the
forenoone
,
and
betweene
5
,
&
●
.
&
4
,
&
●
.
and
7
,
&
6.
&
8
,
&
6.
in
the
afternoone
.
So
as
the
distances
of
all
the
houre
lines
from
the
12.
a
clock
line
being
found
from
6.
in
the
morning
,
till
6.
at
night
,
the
distances
of
the
other
Houre-lines
before
6.
in
the
morning
,
and
after
6.
at
night
shall
easily
be
had
.
PROP.
XXIIII
.
To
know
at
what
time
the
Moone
,
or
any
other
of
the
Planets
or
fixed
Stars
,
that
are
within
the
bredth
of
the
Zodiack
;
rise
or
set
,
or
come
to
the
Meridian
,
&c.
FInde
the
place
of
the
Moone
,
or
any
other
of
the
Planets
,
both
in
longitude
and
Latitude
,
by
the
Epheme●ides
:
and
finde
the
place
(
that
is
,
the
Longitude
and
Latitude
)
of
any
of
the
fixed
Star●es
in
the
Zodiack
by
some
table
of
the
fixed
Starres
,
or
otherwise
;
and
marke
the
same
place
of
the
Moone
;
Planet
or
Starre
,
in
the
Zodiack
of
the
Sphaere
:
and
hauing
set
the
Sphaere
to
the
Latitude
of
the
place
,
bring
the
place
of
the
Sunne
(
found
by
the
2.
Proposition
)
to
the
Meridian
,
and
the
Houre-index
to
12.
a
clock
vpon
the
houre-circle●
,
then
turne
the
Sphaere
till
the
place
of
the
Moone
,
Planet
or
Starre
marked
in
the
Zodiack
,
come
to
the
East
semi-circle
of
the
Horizon
;
for
then
the
Index
sheweth
the
time
when
the
Moone
,
or
that
Planet
or
fixed
Starre
riseth
.
Al●●
the
number
of
degree
in
the
Horizon
,
contayned
betweene
the
point
of
the
Moones
,
Planets
,
or
Starres
rising
,
and
the
point
of
true
East
,
sheweth
the
bredth
,
●●denesse
,
or
amplitude
of
rising
;
And
you
may
at
the
same
instant
,
〈◊〉
,
what
degree
of
the
Ecliptick
riseth
with
any
of
them
,
and
what
the
oblique
ascension
of
any
of
them
is
:
For
if
you
tell
hour
many
degrees
of
the
Equinoctiall
are
〈…〉
betweene
the
beginning
of
Aries
in
the
Horizon
,
proceeding
Eastwards
,
or
according
to
the
order
of
the
signes
:
you
shall
haue
the
oblique
ascension
of
the
Moone
,
Planet
or
Starre
,
that
〈…〉
for
.
But
bring
the
same
place
of
the
Moone
,
Planet
,
or
Starre
to
the
Meridian
,
and
the
Index
sheweth
in
the
houre
circle
at
what
time
they
come
to
the
Meridian
:
where
you
may
also
see
,
first
what
degree
of
the
Zodiath
middeth
Heauen
(
that
is
,
〈◊〉
to
the
Meridian
)
with
any
of
them
;
secondly
,
you
may
see
how
much
the
declination
of
any
of
them
is
;
for
count
how
many
degrees
of
the
Meridian
are
contayned
betweene
the
Equinoctiall
and
the
place
of
the
Moone
,
Planet
,
or
fixed
Starre
,
and
so
much
is
the
declination
.
Thirdly
,
you
may
there
see
what
the
right
ascension
of
any
of
them
is
:
for
the
place
of
any
of
them
being
brought
to
the
Meridian
and
there
〈◊〉
,
r●ckon
Eastwards
how
many
degrees
of
the
Equinoctiall
are
contayned
betweene
the
beginning
of
Aries
and
the
Meridian
,
so
haue
you
the
right
ascension
.
Lastly
,
bring
the
place
of
the
Moone
,
Planet
or
Star
,
to
the
West
semi-circle
of
the
Horizon
;
for
then
the
Index
sheweth
the
time
of
their
setting
;
and
the
number
of
the
degrees
of
the
Horizon
betweene
the
point
where
any
of
them
setteth
,
and
the
Equinoctiall
,
or
true
West
point
(
where
the
Equinoctiall
,
and
Horizon
crosse
each
other
)
is
the
amplitude
or
bredth
of
the
setting
of
any
of
them
,
shewing
how
much
they
set
from
the
true
West
point
.
You
may
there
also
see
what
degree
;
either
of
the
Ecliptick
,
or
of
the
Equinoctiall
,
setteth
with
any
of
the●
and
consequently
you
may
know
the
oblique
descension
of
any
of
them
,
by
reckoning
how
many
degr.
of
the
Equinoctiall
there
are
from
the
beginning
of
Aries
Eastwards
,
till
you
come
about
to
the
West
part
of
the
Horizon
.
Take
for
example
the
great
Starre
called
the
Bulls
eye
,
whose
place
in
longitude
is
about
the
4.
degr.
of
Taurus
,
and
his
latitude
about
5.
degrees
and
an
halfe
Southwards
.
Following
therefore
the
directions
prescribed
in
this
Proposition
,
you
shall
finde
that
vpon
the
first
day
of
Aprill
this
present
yeare
,
1600.
the
same
Starre
riseth
here
at
London
about
halfe
an
houre
past
7.
of
the
clock
in
the
morning
,
and
setteth
about
a
quarter
of
an
houre
past
10.
at
night
,
and
commeth
to
the
Meridian
about
3.
a
clock
afternoone
:
Also
you
shall
finde
that
it
riseth
with
the
15.
degree
of
Gemini
,
and
setteth
with
the
last
degr.
of
Taurus
,
and
commeth
to
the
Meridian
,
or
middeth
Heauen
,
with
the
5.
deg.
of
Gemini
:
Thirdly
you
shall
finde
his
declination
to
be
about
15.
deg.
and
2.
third
parts
,
his
right
ascension
63.
degr.
and
a
quarter
,
his
oblique
asce●sion
43.
degr.
and
his
oblique
descension
about
84.
deg.
and
an
halfe
:
and
lastly
his
amplitude
of
bredth
of
rising
or
letting
about
25.
degr.
and
an
halfe
from
the
true
East
and
West
points
towards
the
North.
PROP.
XXV
.
To
know
how
long
the
Moone
,
or
any
of
the
Planets
of
fixed
Stars
doe
shine
or
continue
aboue
the
Horizon
.
THe
Sphaere
bring
set
up
the
latitude
of
the
place
,
and
the
place
of
the
Moone
,
Planet
,
or
fixed
Starre
,
being
found
and
marked
in
the
Zodiack
,
both
in
Longitude
and
Latitude
,
(
as
in
the
〈◊〉
Prop.
)
bring
the
place
of
the
Moone
,
Planet
,
or
Star
,
〈◊〉
East
semi-circle
of
the
Horizon
,
and
the
Index
of
houres
to
12.
a
clock
:
Then
〈◊〉
about
the
Sphaere
West-wards
,
till
the
same
place
of
the
Moone
,
or
〈◊〉
the
same
Planet
,
or
Starre
,
come
to
the
West
semi-circle
of
the
Horizon
,
and
marke
〈◊〉
how
many
houres
the
Index
runneth
ouer
in
the
meane
time
vpon
the
houre
circle
,
for
so
many
houres
continueth
the
Moone
,
Planet
,
or
Starre
aboue
the
Horizon
.
Thus
shall
you
finde
that
the
foresaid
〈…〉
The
Bulls
eye
〈…〉
the
Horizon
at
London
,
about
14.
〈…〉
and
3.
quarters
.
PROP.
XXVI
.
To
finde
which
of
the
Planets
or
fixed
Starres
are
aboue
or
vnder
the
Horizon
at
any
time
,
&c.
THe
place
of
the
Plantes
or
fixed
Starres
being
marked
in
the
Zodiack
of
the
Sphaere
,
as
in
the
former
propositions
,
and
the
place
of
the
Sunne
brought
to
the
Meridian
,
and
then
the
Index
to
12.
〈…〉
Sphaere
〈◊〉
the
Index
〈◊〉
to
that
houre
vpon
the
houre
〈◊〉
at
which
you
desire
to
know
what
Planets
are
aboue
or
vnder
the
Horizon
;
and
then
hold
still
the
Sphaere
,
and
marke
what
Planets
or
Starres
are
aboue
or
vnder
the
Horizon
in
the
Sphaere
for
the
same
Planets
or
Starres
are
aboue
or
vnder
the
Horizon
in
the
Heauens
.
As
for
example
:
the
1.
of
Aprill
1600
at
9.
of
the
clocke
at
night
,
you
may
by
the
Proposition
finde
;
that
the
most
part
of
the
fixed
Starres
,
that
are
in
the
constestation
of
Taurus
,
Gemini
,
Cancer
,
Leo
,
Virgo
,
and
Libra
,
together
with
the
three
superiour
Planets
,
〈◊〉
,
●upiter
,
&
Mars
,
are
at
〈…〉
to
be
seene
aboue
the
Horizon
,
and
that
the
rest
of
the
Planets
and
fixed
Stars
,
that
are
within
the
compasse
of
the
Zodiack
,
are
vnder
the
Horizon
,
and
cannot
then
be
seene
.
PROP.
XXVII
.
To
finde
in
what
time
any
Signe
or
part
of
the
Ecliptick
riseth
or
setteth
.
BRing
the
beginning
of
the
Signe
,
or
part
of
the
Ecliptick
to
the
East
semi-circle
of
the
Horizon
,
if
you
would
know
in
how
long
time
it
riseth
,
or
to
the
West
part
of
the
Horizon
,
if
you
would
know
in
what
time
it
setteth
;
then
set
the
Index
to
12.
a
clock
,
and
turne
forwards
the
Sphaere
,
till
the
whole
signe
or
part
of
the
zodiack
be
risen
,
or
set
:
For
then
the
Index
sheweth
vpon
the
houre
circle
in
how
long
time
,
that
signe
or
part
of
the
Zodiack
riseth
or
setteth
.
Thus
you
may
finde
(
for
example
)
that
the
whole
signe
of
Aries
here
at
London
riseth
in
one
houre
or
somewhat
lesse
,
and
setteth
in
two
houres
and
three
quarters
,
or
something
more
:
And
that
the
whole
quarter
of
the
Zodiack
,
from
the
beginning
of
Aries
to
the
beginning
of
Cancer
,
riseth
in
lesse
then
foure
houres
,
but
setteth
in
more
then
8.
houres
.
PROP.
XXVIII
.
To
finde
the
houre
of
the
night
by
any
of
the
Planets
or
fixed
Starres
in
the
Zodiack
,
&c.
THe
place
(
that
is
to
say
,
the
longitude
&
latitude
)
of
any
Planet
,
or
fixed
Starre
in
the
Zodiacke
,
that
is
aboue
the
Horizon
,
being
first
found
,
and
marked
in
the
Zodiack
of
the
Sphaere
;
bring
the
place
of
the
Sunne
(
found
by
the
2.
Proposition
)
to
the
Meridian
,
and
the
Index
to
12.
a
clocke
vpon
the
houre
circle
:
Then
hauing
found
the
height
of
the
Starre
,
or
Planet
by
obseruation
,
and
the
Sphaere
also
being
set
to
the
Latitude
of
the
place
of
obseruation
,
take
betweene
the
feet
of
your
Compasses
,
so
many
degrees
of
the
Ecliptick
,
or
Equinoctiall
,
as
the
height
of
the
Planet
,
or
Starre
obserued
,
commeth
to
;
and
setting
one
foote
of
your
Compasses
in
the
place
of
the
Planet
,
or
fixed
Starre
that
you
obserued
in
th
Zodiack
,
turne
the
Sphaere
forwards
or
backwards
,
till
you
can
but
onely
touch
the
Horizon
with
the
other
foot
:
for
then
the
Index
in
the
houre
circle
,
shall
shew
you
the
houre
of
the
night
.
Suppose
(
for
example
)
I
should
obserue
the
height
of
the
foresaid
Bulles
eye
,
and
should
finde
the
same
to
be
29.
degrees
the
first
day
of
March
at
euening
:
finding
therefore
the
place
of
that
Starre
in
the
Zodiack
of
the
Sphaere
,
and
bringing
it
(
with
helpe
of
the
Compasses
)
to
the
height
obserued
(
hauing
first
set
the
place
the
Sunne
and
houre-Index
both
together
to
the
Meridian
)
the
Index
of
the
houres
will
shew
,
that
when
that
Starre
hath
that
height
of
29.
degrees
,
it
is
about
9.
of
the
clock
at
night
.
PROP.
XXIX
.
To
know
at
any
time
of
the
yeare
,
what
Stars
in
the
Zodiack
,
arise
or
set
,
Cosmically
,
Achronically
,
or
Heliacally
.
SVch
Stars
as
rise
together
with
the
Sunne
,
are
said
to
rise
cosmically
:
and
such
Stars
as
set
when
the
Sunne
riseth
,
are
said
to
set
cosmically
;
But
those
Stars
which
set
together
with
the
Sun
,
set
achronycally
;
and
those
Stars
that
rise
when
the
Sunne
setteth
,
are
said
to
rise
achronically
.
Lastly
,
those
Starres
that
rise
a
little
before
the
Sunne
,
rise
heliacally
;
and
those
that
set
a
little
after
the
Sunne
,
set
heliacally
.
All
which
may
thus
bee
found
:
Bring
the
place
of
the
sunne
to
the
East
semicircle
of
the
Horizon
:
for
the
Stars
that
are
then
a
little
aboue
the
Horizon
rise
heliacally
;
but
those
that
are
in
the
Horizon
in
the
East
,
rise
cosmically
;
and
they
that
are
in
the
West
semicircle
of
the
Horizon
set
cosmically
:
But
bring
the
place
of
the
Sunne
to
the
West
semicircle
of
the
Horizon
,
for
those
Starres
as
are
at
the
West
part
of
the
Horizon
at
the
same
time
,
set
achronycally
;
but
those
that
are
then
in
the
East
semicircle
of
the
Horizon
,
rise
achronycally
:
and
they
which
are
a
little
aboue
the
West
semicircle
of
the
Horizon
set
heliacally
.
Thus
you
may
know
that
vpon
the
26.
or
27.
day
of
May
(
it
our
latitude
of
London
)
the
Bulles
eye
riseth
cosmically
,
and
the
Starres
in
Serpentarius
his
right
foot
,
set
cosmically
,
you
may
see
also
that
the
same
day
the
Starre
in
the
Bulls
South
horne
setteth
achronycally
:
and
the
Northermost
starre
in
Serpentarius
his
right
foot
,
riseth
achronycally
:
and
lastly
,
you
may
finde
that
about
the
same
time
the
Ple●ades
and
the
Starre
in
the
Bulls
North
home
,
rise
heliacally
,
and
that
the
same
Starre
also
,
and
the
former
Twinnes
feet
set
heliacally
.
PROP.
XXX
.
To
finde
the
foure
principall
or
Cardinall
points
of
Heauen
(
as
the
Astrologians
call
them
)
at
any
time
.
THese
foure
Cardinall
points
are
nothing
else
but
foure
points
of
the
Ecliptick
,
whereof
one
is
at
the
East
part
of
the
Horizon
,
ascending
,
and
is
therefore
called
the
Ascendent
:
another
is
at
the
vpper
part
of
the
Meridian
aboue
the
Horizon
,
and
is
called
the
midst
of
Heauen
,
and
the
hart
of
Heauen
:
the
third
is
at
the
West
part
of
the
Horizon
descending
,
and
may
be
therfore
called
the
descendent
:
the
fourth
point
is
that
which
is
at
the
nether
part
of
the
Meridian
vnder
the
Horizon
.
Which
foure
points
are
the
beginnings
of
the
first
,
tenth
,
seuenth
,
and
fourth
Houses
.
Therefore
to
finde
these
points
at
any
time
by
the
Sphaere
,
bring
the
place
of
the
Sunne
(
being
found
for
that
time
by
the
2.
Proposition
)
to
the
Meridian
,
and
the
Index
to
12.
a
clocke
:
then
turne
the
Sphaere
till
the
Index
come
to
that
houre
at
which
you
desire
to
know
those
foure
points
,
and
there
hold
the
Sphaere
that
it
moue
not
:
and
looke
withall
,
what
points
of
the
Ecliptick
are
at
the
East
and
West
semicircle
of
the
Horizon
;
and
at
the
vpper
and
nether
parts
of
the
Meridian
:
for
those
bee
the
foure
principall
or
Cardinall
points
you
sought
for
.
Take
for
example
the
time
of
the
Sunnes
entrance
into
Aries
this
present
yeare
1600.
which
was
vpon
the
tenth
day
of
March
about
eight
of
the
clocke
in
the
morning
,
or
little
after
with
vs
here
at
London
,
Hauing
therefore
brought
the
beginning
of
Aries
together
with
the
houre
Index
to
the
Meridian
,
and
then
turned
back
the
whole
Sphaere
till
the
Index
come
to
8.
of
the
clocke
vpon
the
houre
circle
:
you
shall
finde
the
ascendent
at
that
time
,
to
be
the
27.
degree
of
Taurus
;
the
middest
or
hart
of
Heauen
,
the
27.
of
Capricorne
▪
the
descendent
,
the
27.
deg.
of
Scorpio
;
and
the
lowest
part
of
Heauen
the
27.
degree
of
Cancer
.
PROP.
XXXI
.
To
finde
out
the
bredth
of
any
climate
,
&c.
LIft
vp
,
or
put
downe
the
pole
of
the
Sphaere
,
till
you
finde
that
there
are
7.
deg.
and
an
halfe
of
the
Tropick
of
Cancer
,
more
or
lesse
aboue
the
Horizon
,
then
there
were
before
;
and
marke
with
all
how
much
the
pole
of
the
Sphaere
is
raised
,
or
let
fall
in
the
meane
time
,
more
then
it
was
before
;
for
so
much
is
the
bredth
of
that
climate
.
As
far
example
:
hauing
set
the
Sphaere
to
our
Latitude
of
London
of
51.
deg.
and
an
halfe
,
with
the
point
of
your
Compasses
,
holding
and
guiding
some
point
of
the
Tropick
of
Cancer
right
vnder
the
Horizon
;
then
lifting
vp
the
Pole
till
you
finde
7.
degrees
and
an
halfe
more
aboue
the
Horizon
then
were
before
,
you
shall
finde
the
Pole
eleuated
about
2.
degr.
and
an
halfe
more
then
it
was
before
.
Likewise
,
if
you
put
downe
the
Pole
till
there
be
7.
degrees
and
an
halfe
of
the
Tropicke
of
Cancer
,
fewer
aboue
the
Horizon
then
was
before
;
you
shall
finde
the
eleuation
of
the
Pole
to
be
about
3.
degrees
lesse
then
before
.
PROP.
XXXII
.
The
reason
of
the
inequalitie
of
naturall
dayes
,
&c.
THe
reason
hereof
is
shewed
partly
by
the
inequality
of
the
differences
of
right
ascentions
answerable
to
equall
arcks
of
the
Zodiack
;
and
partly
by
the
vnequall
apparent
motion
of
the
Sunne
.
For
the
first
:
the
differences
of
right
ascentions
answerable
to
the
parts
of
the
Ecliptick
,
about
the
Tropicall
points
of
Cancer
and
Capricorne
,
are
much
greater
then
about
the
Equinoctiall
points
of
Aries
and
Libra
.
In
so
much
that
whereas
the
difference
of
right
ascension
answerable
to
one
signe
,
or
30.
degrees
taken
about
those
Tropicall
points
,
is
more
then
32.
degrees
and
an
halfe
:
about
the
Equinoctiall
points
it
is
little
more
then
27.
degrees
and
an
halfe
;
as
it
may
appeare
by
the
Sphaere
.
So
as
you
may
hereby
gather
,
that
the
difference
of
ascention
answerable
to
one
degree
,
which
about
the
beginning
of
Capricorne
is
one
degree
,
and
about
6.
minutes
;
about
the
beginning
of
Aries
,
or
Libra
,
is
onely
55
minutes
.
Secondly
,
the
apparent
motion
of
the
Sun
is
much
swifter
about
his
Parig●●●
,
in
the
signe
of
Capricorne
,
then
about
his
Apogaeum
in
Cancer
,
or
in
other
parts
of
the
Zodiacke
:
so
that
whereas
the
Sunne
being
in
Capricorne
moueth
61.
minutes
and
something
more
in
a
day
:
in
Aries
or
Libra
he
moueth
but
59.
min.
or
very
little
more
in
the
same
time
.
Therefore
seeing
the
naturall
day
is
nothing
else
,
but
the
time
wherein
the
Sunne
moueth
from
the
Meridian
about
,
till
it
returne
again
to
the
same
part
of
the
Meridian
;
it
must
needs
bee
that
alwayes
in
one
naturall
day
,
there
is
made
one
whole
reuolution
of
the
Equinoctiall
circle
,
and
so
much
more
as
is
the
difference
of
right
ascention
answerable
to
the
apparent
motion
of
the
Sun
in
the
meane
time
:
which
differences
of
ascention
because
they
be
vnequall
,
for
the
two
causes
before
alledged
;
the
naturall
dayes
must
needs
also
bee
vnequall
,
the
motion
of
the
Equinoctiall
circle
about
his
owne
center
being
(
as
it
hath
beene
alwayes
supposed
to
be
)
equall
,
that
is
mouing
alwayes
an
equall
space
in
equall
time
.
Which
by
this
example
may
most
plainly
appeare
:
The
Sunne
being
in
Capricorne
moueth
61.
minutes
in
a
naturall
day
:
difference
of
ascention
agreeable
thereto
is
67.
minutes
,
or
something
more
.
Therefore
at
that
time
,
in
the
space
of
one
naturall
day
,
the
Equinoctial
circle
must
make
one
full
reuolution
,
and
67.
minutes
more
.
But
when
the
Sun
is
in
Aries
,
mouing
onely
59.
minutes
in
a
day
,
and
the
difference
of
right
ascention
answerable
thereto
,
scarce
54.
minutes
more
then
one
reuolution
of
the
Equinoctiall
circle
;
there
shall
passe
onely
54.
minutes
more
in
a
naturall
day
;
so
as
here
the
Equinoctiall
circle
moueth
not
about
so
much
in
one
day
as
before
by
13.
minutes
.
Seeing
then
that
15.
degr.
or
little
more
of
the
Equinoctiall
circle
doe
passe
the
Meridian
in
euery
houre
,
and
consequently
one
degree
of
the
Equinoctiall
passeth
the
Meridian
in
4.
minutes
of
an
houre
,
and
one
minute
of
a
degree
in
4.
seconds
of
an
houre
;
therefore
13.
minutes
of
the
Equinoctiall
shall
passe
the
Meridian
in
52.
seconds
:
that
is
,
almost
in
one
minute
of
an
houre
:
Whereby
it
manifestly
appeareth
that
the
naturall
day
,
that
is
to
say
,
the
space
of
24.
houres
,
which
is
the
time
wherein
the
Sunne
moueth
from
the
Noone-stead
to
the
same
noone-stead
againe
,
is
in
our
age
greater
almost
by
one
minute
of
an
houre
,
when
the
sunne
is
in
Capricorne
,
then
when
hee
is
in
Aries
or
Libra
▪
PROP.
XXXIII
.
To
finde
by
the
Sphaere
how
much
the
naturall
dayes
are
longer
at
one
time
of
the
yeare
then
at
another
.
FOr
this
purpose
it
will
be
best
to
take
a
good
number
of
dayes
together
;
as
for
example
,
take
the
whole
moneth
of
December
,
and
the
whole
moneth
of
March
:
both
which
moneths
consist
of
the
same
number
of
31.
naturall
dayes
:
find
the
place
of
the
Sunne
for
the
beginning
and
ending
of
both
moneths
,
which
you
may
finde
by
the
second
Proposition
to
be
for
the
beginning
of
March
this
present
yeare
1600.
about
20.
degrees
and
13.
minutes
of
Pisces
;
and
for
the
ending
about
20.
degr.
48.
minutes
of
Aries
:
Also
for
the
beginning
of
December
the
same
yeare
18.
degr.
46.
minutes
of
S●gitarie
;
and
for
the
ending
,
20.
degrees
24.
minutes
of
Capricorne
:
Then
seeke
out
the
right
ascensions
of
the
same
places
of
the
Sunne
for
the
beginnings
and
endings
of
both
those
moneths
by
the
fourth
Proposition
,
and
the
differences
of
ascension
answerable
to
the
motion
of
the
Sunne
in
each
moneth
,
by
the
sixt
Proposition
;
which
you
may
finde
by
the
Sphaere
to
be
about
33.
degrees
,
24
▪
minutes
for
December
,
and
28.
degrees
,
39.
minutes
for
March.
Lastly
,
finde
out
the
difference
of
these
differences
of
ascension
by
substracting
the
lesser
out
of
the
greater
;
which
in
this
example
is
4.
degrees
45.
minutes
;
which
resolued
into
minutes
of
an
houre
,
by
taking
for
euery
degree
4.
minutes
of
an
houre
,
and
for
euery
15.
minutes
of
a
degree
,
one
minute
of
an
houre
shall
amount
to
19.
minutes
of
an
houre
,
that
is
a
quarter
of
an
houre
and
4.
minutes
.
And
so
much
is
the
moneth
of
December
longer
then
the
moneth
of
March
;
Notwithstanding
both
of
them
consist
of
the
same
number
of
31.
naturall
dayes
.
The
third
Part.
Of
the
Orbes
whereof
the
SPHAERES
of
the
Sunne
and
Moone
haue
beene
imagined
to
bee
made
,
and
of
their
Motions
and
Vses
.
CHAP.
I.
Of
the
Orbes
whereof
the
Sphare
of
the
Sunne
is
made
.
WIthin
the
Sphaere
or
Orbe
contayning
all
the
Circles
that
wee
haue
hitherto
spoken
of
,
and
representing
vnto
vs
the
Primum
mobile
;
that
is
,
the
first
and
highest
moueable
Heauen
,
that
hath
been
imagined
by
the
Astronomers
,
to
shew
the
reason
of
that
daily
motion
,
which
appeareth
to
bee
in
all
the
Heauens
,
and
of
all
the
apparences
that
follow
thereupon
,
are
included
the
Sphaeres
and
Orbes
of
the
Sunne
and
Moone
.
The
sphaere
of
the
Sunne
contayneth
three
Orbes
:
The
vppermost
of
them
(
which
in
this
Sphaere
is
signified
by
the
yellow
Circle
that
commeth
next
within
the
compasse
of
the
Zodiacke
)
is
called
Deferens
apogaeum
Solis
;
that
is
,
the
Orbe
which
carrieth
about
that
point
,
wherein
the
sunne
is
furthest
distant
from
the
earth
.
Next
within
this
Orbe
is
placed
the
Eccentrick
carying
about
the
body
of
the
Sunne
;
which
in
this
Sphaere
is
represented
by
the
greene
coloured
circle
that
commeth
next
vnder
the
Deferens
apogaeum
.
Againe
,
within
this
Eccentrick
is
included
the
third
Orbe
of
the
Sphaere
of
the
Sunne
called
Deferens
Perigaeum
solis
;
that
is
,
the
Orbe
carying
about
that
point
wherein
the
Sun
is
nearest
to
the
Earth
.
This
is
the
nethermost
of
the
three
Orbes
of
the
sunne
,
and
in
this
Sphaere
is
represented
vnto
you
by
the
yellow
coloured
circle
next
vnder
the
sunnes
Eccentricke
.
CHAP.
II.
Of
the
vppermost
and
nethermost
Orbes
of
the
Sphaere
of
the
Sunne
,
more
particularly
.
IN
the
vppermost
and
nethermost
of
these
three
Orbes
,
there
be
4.
points
especially
to
bee
considered
:
That
is
,
the
points
where
they
bee
narrowest
and
where
they
be
broadest
,
and
where
they
are
of
a
meane
bredth
betwixt
the
narrowest
and
broadest
.
For
at
the
narrowest
part
of
the
vppermost
Orbe
,
where
you
may
see
written
Aux
solis
,
and
the
broadest
part
of
the
nethermost
Orbe
,
is
the
place
of
the
sunnes
Apogaeum
;
so
that
whensoeuer
the
Sun
commeth
there
,
he
is
furthest
distant
from
the
earth
.
As
you
may
easily
try
,
if
(
with
a
payre
of
Compasses
,
or
otherwise
)
you
take
the
distance
betwixt
the
Earth
and
the
Sunne
,
being
brought
about
to
that
place
,
and
compare
the
same
with
the
distances
that
the
Sun
hath
from
the
Earth
in
other
places
.
This
point
is
called
Aux
Solis
,
and
Longitude
longior
,
that
is
,
the
point
of
the
sunnes
furthest
distance
from
the
earth
.
But
vnder
the
broadest
part
of
the
vppermost
and
vttermost
Orbe
,
where
you
see
printed
PERIGAEVM
,
and
right
aboue
the
narrowest
part
of
the
nethermost
Orbe
,
is
the
place
where
the
Sun
commeth
nearest
to
the
Earth
,
as
you
may
easily
find
(
with
your
Compasses
,
or
otherwise
)
in
like
sort
as
before
was
shewed
.
The
point
where
the
Sun
commeth
nearest
to
the
earth
,
is
called
oppositum
A●gis
,
and
longitudo
propior
,
that
is
,
the
point
opposite
to
the
Apogaeum
,
and
the
nearest
distance
.
And
at
those
parts
of
this
Orbe
,
which
are
in
the
midst
betweene
the
former
;
the
Sunne
hath
a
meane
distance
from
the
earth
:
a
meane
(
I
say
)
betweene
the
least
,
and
greatest
distance
.
The
very
point
wherein
this
meane
or
middle
distance
hapneth
,
is
shewed
by
the
points
that
are
iust
in
the
middest
betweene
the
short
lines
AB
,
and
IK
,
which
are
drawne
ouerthwart
on
eyther
side
of
this
Orbe
.
These
points
are
called
longitudines
media
;
that
is
,
the
meane
distances
of
the
Sunne
,
because
the
sunne
comming
to
these
points
,
hath
a
meane
distance
betweene
the
least
and
the
greatest
.
About
these
points
also
,
the
true
motion
of
the
sun
,
is
as
it
were
in
a
meane
between
the
slowest
,
which
hapneth
the
sunne
being
about
the
Apogaeum
,
and
the
swiftest
,
which
hapneth
about
his
Perigaeum
.
Moreouer
the
lines
A
,
and
K
,
shew
the
places
wherin
there
is
the
greatest
Prosthaphaerisis
,
or
Equation
of
the
sunne
:
that
is
,
the
greatest
difference
betweene
the
true
,
and
middle
,
or
meane
place
of
the
sunne
.
Lastly
,
the
distance
betweene
the
lines
I
,
and
K
,
or
A
,
and
B
,
shew
how
much
the
eccentricitie
of
the
sunnes
eccentricke
is
,
that
is
,
how
farre
the
Center
of
the
eccentricke
is
distant
from
the
Center
of
Earth
.
CHAP.
III.
To
finde
how
much
the
Sunne
is
nearer
or
further
from
the
earth
,
at
one
time
then
at
another
.
BY
meanes
of
this
Circle
,
you
may
easily
find
with
your
Compasses
,
how
much
the
Sunne
is
nearer
to
,
or
further
from
the
earth
at
one
time
,
then
at
another
:
for
hauing
set
one
foot
of
the
Compasses
vpon
the
vtmost
edge
of
the
Deferens
Apogaeum
,
vnder
the
place
of
the
Sunne
in
the
Zodiacke
,
found
by
the
second
Prop.
stretch
out
the
other
foot
,
to
the
innermost
edge
of
the
same
Orbe
;
for
then
,
if
you
set
one
foot
of
your
Compasses
,
vpon
the
vtmost
edge
of
this
Orbe
,
at
the
Apogaeum
,
the
other
foot
turned
inwards
towards
the
center
of
the
Sphaere
,
will
shew
you
how
much
the
Sunne
is
nearer
to
the
Earth
at
that
time
,
then
when
he
is
in
his
Apogaeum
:
for
so
much
as
that
foot
reacheth
within
the
inner
edge
of
the
Orbe
,
so
much
is
the
sunne
nearer
.
Likewise
if
you
set
one
foot
of
your
Compasses
,
vpon
the
vttermost
edge
of
this
Orbe
,
at
the
Perigaeum
,
and
turne
the
other
foot
towards
the
center
of
the
Sphaere
,
so
much
as
this
foot
of
the
Compasse
,
is
from
the
inner
edge
of
the
Deferens
Paerigaeum
,
so
much
is
the
Sun
further
distant
from
the
earth
at
that
time
,
then
when
he
is
in
his
Paerigaeum
.
CHAP.
IIII.
Of
the
situation
and
motion
of
the
uppermost
,
and
nethermost
Orbes
of
the
Sunne
.
THe
vppermost
,
and
nethermost
of
these
three
Orbes
,
called
Deferens
Apogaeum
,
&
Perigaeum
solis
,
doe
alwayes
answer
each
to
other
,
in
such
sort
that
the
broadest
part
of
the
one
,
is
alwayes
against
the
narrowest
part
of
the
other
:
And
therefore
both
of
them
are
moued
thgether
,
with
one
motion
about
the
Axtree
and
poles
of
the
Ecliptick
,
making
one
reuolution
vnder
the
Zodiack
,
in
the
space
of
17000.
yeares
almost
.
For
in
Ptolemee
his
time
(
that
is
about
the
yeare
of
our
Lord
134.
)
the
place
of
the
Sunnes
Apogaeum
,
was
about
the
middest
of
the
6.
deg.
of
Gemini
;
as
it
may
appeare
by
the
4.
Chapter
of
the
3.
booke
of
his
Almagest
.
But
in
our
time
we
finde
that
it
cannot
exceed
the
7.
degr.
of
Cancer
,
although
after
the
account
of
Copernicus
,
and
of
the
Prutenicke
tables
,
it
should
be
in
the
9.
degr.
of
Cancer
.
So
as
,
if
the
rest
of
the
motion
of
the
Sunnes
Apogaeum
,
that
is
to
come
hereafter
,
be
proportionable
to
that
is
past
,
the
whole
reuolution
thereof
shal
be
finished
in
1699.
yeares
vnder
the
Zodiack
.
For
in
1463.
yeares
betwixt
Ptolemee
his
time
and
ours
,
it
hath
moued
about
31.
degn
therefore
it
shall
moue
300.
degrees
,
(
that
is
,
the
compasse
of
the
whole
circle
)
in
16990.
yeares
.
Which
number
of
yeares
being
deuided
by
360.
it
shall
appeare
that
the
Apogaeum
of
the
Sunne
moueth
one
degr.
in
little
more
then
47.
yeares
whereby
the
yearely
motion
thereof
may
be
sound
to
be
little
more
then
one
minute
and
a
quarter
.
CHAP.
V.
How
to
find
the
place
of
the
Suns
Aux
or
Apogaeum
,
&c.
THerefore
the
place
of
the
Sunnes
Apogaeum
,
being
found
for
the
yeare
1600.
to
be
about
7.
degr.
in
Cancer
,
the
place
thereof
for
any
other
yeare
before
or
after
,
may
easely
be
found
in
our
age
,
onely
by
subtracting
,
or
adding
for
euery
4
,
yeares
5
,
min.
and
for
euery
single
yeare
1.
minute
and
a
quarter
,
Although
indeed
we
need
not
stand
so
precisely
neyther
vpon
quarters
of
minutes
,
neither
yet
vpon
whole
minutes
,
in
the
place
of
the
sunnes
Apogaeum
,
which
cannot
be
by
any
Art
so
exactly
found
,
but
that
the
diligentest
man
that
is
,
may
erre
many
minutes
therein
.
Take
for
example
the
yeare
of
our
Lord
1558.
(
in
which
our
gracious
Q.
Elizabeth
began
her
happie
reigne
,
which
is
now
42.
yeares
since
)
taking
therefore
for
euery
4.
yeares
5.
minutes
,
that
is
,
for
40.
yeares
50.
minutes
,
and
for
the
two
yeares
remaining
2.
minutes
and
one
halfe
;
that
is
in
all
52.
minutes
and
an
halfe
,
and
subtracting
the
same
out
of
7
,
deg
of
Cancer
,
there
shall
remaine
the
place
of
the
sunnes
Apogaeum
at
the
beginning
of
her
Maiesties
reigne
,
in
6.
degr.
and
about
8.
min.
of
Cancer
.
The
vses
of
these
two
Orbes
are
these
.
1.
First
to
make
the
sphaere
of
the
Sunne
concentricall
;
for
these
Orbes
be
framed
together
,
that
the
narrowest
part
of
the
one
,
answereth
alwayes
to
the
broadest
part
of
the
other
:
it
commeth
to
passe
by
this
meanes
,
that
both
the
out-side
,
and
the
in-side
of
the
Sphaere
of
the
sunne
,
haue
alwayes
the
same
center
,
that
the
world
it selfe
hath
.
2.
The
second
vse
is
to
shew
the
reason
,
and
manner
of
the
motion
of
the
Sunnes
Apogaeum
and
Perigaeum
.
CHAP.
VI.
Of
the
eccentrick
of
the
Sunne
,
&c.
THe
Orbe
conteined
betweene
the
two
former
,
and
carying
about
the
body
of
the
Sunne
it selfe
,
is
called
the
eccentricke
of
the
Sunne
;
because
it
hath
another
center
,
then
the
center
of
the
world
.
The
especiall
reason
,
that
moued
the
skilfull
in
this
coelestiall
science
,
to
make
this
Orbe
(
wherein
the
body
of
the
sunne
is
carryed
)
eccentricall
,
was
because
they
found
the
apparent
motion
of
the
sunne
vnder
the
ecliptick
line
to
be
vnequall
,
that
is
,
swifter
in
the
Southerly
Signes
:
and
slower
in
the
Northerly
.
For
Hipparehus
,
and
Ptolemee
found
in
their
times
,
that
the
sunne
continued
in
the
Northerne
semicircle
of
the
ecliptick
,
from
Aries
to
Libra
,
187.
dayes
:
and
in
the
other
halfe
of
the
Zodiack
,
that
is
Southward
from
Libra
to
Aries
,
178.
dayes
and
a
quarter
onely
.
But
in
our
time
by
diligent
obseruation
it
is
sound
,
that
the
time
of
the
sunnes
continuance
in
the
first
of
those
semicircles
from
Aries
to
Libra
,
is
186.
dayes
14.
houres
and
an
halfe
:
and
consequently
in
the
other
semicircle
,
from
Libra
to
Aries
,
178.
dayes
15.
houres
and
an
halfe
.
Taking
it
therefore
for
a
ground
,
according
to
the
doctrine
of
Aristotle
,
that
the
motion
of
the
coelestiall
bodies
is
circular
and
equal
;
it
must
needs
follow
,
that
a
greater
part
of
the
circle
described
by
the
proper
motion
of
the
sunne
must
be
conteined
vnder
the
Northerly
semicircle
of
the
ecliptick
,
then
vnder
the
Southerly
:
and
consequently
that
the
circle
or
Orbe
that
caryeth
about
the
body
of
the
Sunne
vnder
the
ecliptick
,
hath
another
center
then
the
center
of
the
Ecliptick
.
2.
Another
reason
to
proue
,
that
the
Sunne
is
caryed
in
an
eccentricall
Circle
,
is
the
vnequall
apparent
,
bignes
of
the
Sunnes
diameter
,
the
Sunne
being
of
the
same
height
aboue
the
Horizon
and
the
ayre
alike
affected
,
and
alike
cleare
;
so
as
if
there
were
any
refraction
by
reason
of
the
thicknes
of
the
ayre
,
it
must
needs
be
the
same
in
both
places
.
For
in
Sommer
,
when
the
Sun
is
at
,
or
neare
his
Apogaeum
,
his
apparent
diameter
hath
beene
found
by
exquisit
obseruation
to
be
13.
minutes
48
seconds
.
But
in
winter
being
about
his
Perigaeum
33.
min.
54.
seconds
,
as
it
may
appeare
in
Copernicus
his
reuolutions
4.
booke
21.
Chapter
.
Therefore
seeing
euery
visible
obiect
appeareth
greater
when
it
is
neare
,
and
lesse
when
it
is
further
remoued
from
vs
,
it
is
manifest
that
the
Sun
appearing
greater
in
winter
,
then
in
sommer
,
must
needes
be
nearer
to
the
earth
in
winter
,
then
in
sommer
.
The
reason
of
which
apparance
is
most
easely
shewed
,
by
supposing
the
Sunne
to
be
moued
,
in
an
eccentricall
Orbe
.
3.
A
third
reason
may
bee
the
vnequall
greatnesse
and
continuance
of
the
eclipses
of
the
Moone
,
euen
at
those
times
when
she
hath
had
the
same
latitude
,
or
distance
from
the
Ecliptick
,
and
the
same
distance
from
the
Center
of
the
earth
:
which
argueth
that
the
conicall
sharp
pointed
shadow
of
the
earth
,
in
the
place
where
the
Moone
in
time
of
the
Eclipse
passeth
through
that
shadow
,
at
the
same
distance
from
the
earth
,
is
sometimes
greater
,
and
sometimes
lesser
:
wherof
there
can
no
cause
be
shewed
more
reasonable
then
this
,
that
the
Sun
is
sometimes
further
distant
from
the
earth
,
and
the
maketh
the
shadow
greater
and
sometimes
nearer
,
and
so
maketh
it
lesser
.
Whereby
it
is
also
manifestly
proued
,
that
the
Sun
is
moued
about
another
center
then
the
center
of
the
earth
,
and
therefore
that
the
circle
or
Orbe
,
wherein
the
Sunne
is
moued
,
is
an
Eccentricke
.
CHAP.
VII
.
Of
the
vses
of
the
Sunnes
eccentricall
Orbe
.
THerefore
the
vses
of
the
Sunnes
eccentricke
may
bee
these
:
1.
First
to
shew
the
reason
of
the
apparent
inequalitie
,
which
seemeth
to
bee
in
the
motion
of
the
Sunne
:
for
although
the
Sunne
mo●e
equally
in
his
owne
O●be
,
and
about
his
owne
center
;
yet
to
them
that
are
at
the
center
of
the
world
,
or
vpon
the
earth
,
he
shall
seeme
to
moue
vnequally
;
that
is
,
swiftly
when
he
is
in
that
part
of
his
eccentricke
which
is
nearest
vnto
the
earth
;
and
slowly
when
he
is
farthest
from
the
earth
.
And
therefore
in
sommer
,
when
the
Sunne
is
about
his
Apogaeum
,
and
in
his
greatest
distance
from
the
earth
,
he
seemeth
to
moue
little
aboue
57.
min.
in
one
day
.
But
in
winter
,
being
about
his
Perigaeum
and
nearest
vnto
the
earth
,
he
seemeth
to
moue
more
then
16.
minutes
:
whereas
notwithstanding
he
moueth
equally
in
his
Eccentricke
,
euery
day
about
nine
and
fifty
minutes
and
8.
seconds
;
and
so
finisheth
his
reuolution
in
365.
dayes
,
and
six
houres
almost
.
2.
The
second
vse
of
the
Sunnes
Eccentricke
,
may
be
to
shew
the
reason
why
the
Sun
appeareth
greater
at
one
time
then
at
another
;
for
the
Sun
being
in
those
parts
of
the
eccentrick
that
are
nearest
vnto
vs
,
seemeth
greatest
,
and
when
he
is
in
those
parts
of
his
eccentrick
that
are
furthest
from
vs
,
he
appeareth
to
be
least
.
3.
And
lastly
the
inequality
of
the
Sunnes
distance
from
the
earth
,
caused
by
his
eccentrick
,
is
one
especiall
cause
of
the
inequalitie
of
the
Eclipses
,
both
of
the
Sunne
and
Moone
.
CHAP.
VIII
.
The
definitions
of
certaine
Astronomicall
wordes
of
art
,
for
the
better
vnderstanding
of
the
Theorick
of
the
Sunne
.
1.
WHat
the
Aux
or
Apogaeum
of
the
Sunne
is
it
hath
beene
partly
shewed
already
:
that
●●mely
it
is
that
part
,
or
rather
point
of
the
Orbe
carying
the
Sunnes
Apogaeum
,
wherein
the
said
Orbe
is
thinnest
,
or
narrowest
:
Or
it
is
that
point
of
the
eccentrick
which
is
furthest
distant
from
the
earth
,
and
is
alwayes
shewed
by
a
right
line
vnderstood
to
be
drawn
from
the
center
of
the
world
,
by
the
center
of
the
eccentrick
,
vnto
the
Orbe
carying
the
Sunnes
Apogaeum
.
Which
line
is
therefore
called
the
line
of
the
Sun
his
Aux
or
the
line
of
the
Sunnes
Apogaeum
.
2.
The
motion
of
the
Aux
,
or
of
the
Apogaeum
of
the
Sunne
(
which
is
also
called
the
Sunnes
Aux
in
the
second
signification
)
is
nothing
els
but
the
arch
of
the
Ecliptick
,
conteyned
betweene
the
beginning
of
Aries
,
and
the
line
of
the
Sunnes
Apogaeum
,
drawne
forth
to
the
Zodiack
;
where
this
line
also
sheweth
the
place
of
the
Sunnes
Apogaeum
.
3.
The
middle
or
meane
place
of
the
Sunne
in
the
Zodiack
,
is
shewed
by
a
line
drawne
from
the
center
of
the
world
vnto
the
Zodiack
,
equidistant
from
the
center
of
the
Eccentricke
,
and
of
the
Sunne
.
4.
This
line
is
therefore
called
the
line
of
the
meane
or
middle
place
of
the
Sun
.
5.
The
middle
or
meane
motion
of
the
Sunne
is
the
arch
of
the
ecliptick
betweene
the
beginning
of
Aries
,
and
the
middle
place
of
the
Sun
.
6.
The
true
place
of
the
Sunne
is
shewed
by
a
streight
line
drawne
from
the
center
of
the
earth
by
the
center
of
the
Sun
vnto
the
Zodiack
,
which
line
is
therefore
called
the
line
of
the
true
place
of
the
Sun
.
7.
The
true
motion
of
the
Sun
is
the
arch
of
the
eclipticke
from
the
beginning
of
Aries
,
vnto
the
true
place
of
the
Sun
.
8.
The
argument
of
the
Sun
(
at
the
〈◊〉
●erme
it
)
or
the
motion
of
the
Sunnes
Anomalie
(
as
Copernicus
calleth
it
)
is
the
arch
of
the
ecliptick
conteyned
betweene
the
place
of
the
Sunnes
Apogaeum
and
the
middle
place
of
the
Sunne
according
to
the
order
and
succession
of
the
Signes
.
This
arch
is
called
the
argument
,
or
motion
of
the
sunnes
Anomalie
or
irregularitie
,
because
that
by
it
is
alwayes
found
how
much
the
suns
true
motion
which
(
is
vnequall
and
irregular
)
differeth
from
his
middle
motion
;
which
difference
they
call
the
Suns
equation
,
or
prosthapheresis
.
9.
The
equation
,
or
prosthapheresis
of
the
Sun
is
nothing
els
but
the
arch
of
the
ecliptick
conteyned
betweene
the
true
,
and
middle
places
of
the
sunne
.
This
arch
is
called
the
sunnes
equation
,
because
it
maketh
the
suns
middle
motion
equal
to
his
true
motion
,
being
added
to
it
or
subtracted
from
it
,
as
occasion
requireth
:
for
which
cause
it
is
more
significantly
and
fitly
called
Prosthaphaeresis
,
that
is
as
much
to
say
,
as
that
which
is
to
be
added
to
or
subtracted
from
the
middle
motion
,
that
so
we
might
haue
the
true
motion
.
For
so
long
as
the
Sunne
is
in
the
semicircle
of
his
eccentrick
,
discending
from
his
Apogaeum
to
his
●●●gaeum
,
so
long
this
Prosthapheresis
is
to
be
subtracted
from
the
middle
motion
:
but
the
Sunne
being
in
the
other
halfe
of
his
eccentrick
ascending
,
the
Prosthapheresis
or
equation
of
the
Sun
must
be
added
to
the
middle
motion
,
that
〈…〉
motion
and
place
of
the
Sunne
may
be
found
,
Because
that
in
the
first
semicircle
of
the
eccentricke
descending
,
the
middle
place
of
the
Sunne
goeth
before
the
〈◊〉
,
and
the
middle
motion
is
〈…〉
greater
〈…〉
the
Sun
,
and
therefore
the
difference
of
these
〈◊〉
motions
,
(
that
is
to
say
,
the
〈◊〉
or
Prosthaphaeresis
)
must
be
subtracted
,
to
findeth
〈…〉
for
the
true
place
of
the
Sunne
goeth
alwaies
〈…〉
motion
and
place
of
the
same
,
CHAP.
IX
.
Of
the
vppermost
Orbe
of
the
Sphaere
of
the
Moone
carying
the
Dragons
head
and
tayle
.
NExt
within
the
Orbes
of
the
Sun
in
this
Sphaere
are
conteyned
the
Orbes
of
the
Sphaere
of
the
Moone
:
which
〈…〉
in
number
.
The
vppermost
of
them
(
which
in
this
Sphaere
is
next
vnder
the
Orbe
that
caryeth
the
Suns
Perigaeum
and
is
coloured
with
red
)
is
called
the
Caryer
of
the
Dragons
head
and
tayle
,
or
〈…〉
which
is
as
much
to
say
as
the
Caryer
of
the
knots
,
that
is
of
the
two
intersections
,
or
pointes
wherein
the
rest
of
the
Orbes
of
the
Moone
,
doe
crosse
ouer-thwart
this
Orbe
.
This
Orbe
is
deuided
into
foure
nineties
of
degree
,
for
the
easier
reckoning
of
the
motion
and
place
of
the
Dragons
head
or
tayle
in
this
Sphaere
.
And
it
is
moued
about
in
18.
Iulian
yeares
224.
dayes
3.
houres
and
5.
minutes
almost
,
from
the
East
Westwards
,
vnder
the
ecliptick
.
By
reason
of
this
motion
it
commeth
to
passe
,
that
the
Eclipses
,
or
rather
the
places
wherein
the
eclipses
of
the
Sunne
or
Moone
doe
happen
in
the
Heauens
,
are
remoued
continually
more
backwards
in
the
Zodiack
,
contrary
to
the
order
and
succession
of
the
Signes
.
As
for
example
;
the
eclipse
of
the
Moone
hapning
this
present
yeare
1600.
the
20.
of
Ianuarie
neare
vnto
the
Dragons
tayle
about
the
9.
degree
and
40.
min.
of
Leo
;
the
next
eclipse
that
shall
happen
neare
the
same
intersection
of
the
Dragons
taile
,
in
the
yeare
1601.
the
29.
of
Nouember
,
shall
be
in
17.
degrees
and
an
halfe
of
Gemini
;
And
that
eclipse
which
shall
be
the
next
yeare
after
neare
the
same
intersection
the
19.
of
Nouember
in
the
morning
,
shall
be
about
the
6.
degree
and
40.
minutes
of
Gemini
,
&c.
All
this
remouing
of
the
Eclipses
backwards
commeth
to
passe
,
by
reason
of
the
motion
of
this
Orbe
carying
the
Dragons
head
and
tayle
,
contrary
to
the
course
and
order
of
the
Signes
.
This
Orbe
continueth
alwaies
right
vnder
,
The
rest
of
the
Orbes
of
the
Moone
,
Tig●●
Brahe
his
obseruation
)
5.
degr.
and
a
quarter
almost
sometimes
,
and
sometimes
lesse
then
5.
degr.
That
point
or
intersection
of
these
Orbes
with
the
former
,
from
which
they
begin
to
arise
about
the
playne
of
the
ecliptick
towards
the
North
,
proceeding
East-wards
,
is
called
the
Dragons
head
;
and
is
signified
by
this
character
☊
:
and
the
other
point
or
intersection
diametrally
opposite
vnto
this
,
is
called
the
Dragons
tayle
,
which
is
also
signified
by
the
former
character
turned
vp
side
downe
after
this
manner
,
☋
.
The
two
points
of
these
Orbes
that
are
furthest
distant
from
the
plaine
of
the
〈◊〉
,
are
called
the
bounds
or
limites
of
the
Moones
latitude
,
and
they
are
90.
deg.
from
the
Dragons
head
and
tayle
,
and
5.
deg.
and
a
quarter
almost
from
the
playne
of
the
Ecliptick
,
according
to
the
obliquity
,
or
greatest
declination
of
the
playnes
of
these
Orbes
,
from
the
playne
of
the
ecliptick
:
Of
these
two
points
,
that
which
is
in
the
north
side
of
the
ecliptick
,
is
called
the
North
limit
,
or
bound
of
the
Moones
latitude
;
and
contrariwise
,
the
other
point
opposit
to
this
on
the
south
side
of
the
Ecliptick
,
is
called
the
South
limite
of
the
Moones
latitude
.
And
when
the
Moone
commeth
to
eyther
of
these
two
points
,
she
hath
her
greatest
latitude
.
CHAP.
X.
Of
the
Orbes
carying
the
Moones
Apogaeum
and
Perigaeum
.
NExt
within
the
Orbe
carying
the
Dragons
head
and
tayle
,
is
contayned
the
Orbe
called
Deferens
Apogaeum
lunae
which
is
the
point
wherein
the
Moone
is
furthest
distant
from
the
earth
.
And
vnder
this
Orbe
is
placed
the
Moones
Eccentrick
,
which
is
also
called
Deferens
Epiculum
Lunae
;
that
is
the
Orbe
carying
the
Moones
Epicycle
.
Againe
within
this
eccentrick
of
the
Moone
,
is
conteyned
the
least
and
lowest
Orbe
,
of
all
that
are
in
this
Sphaere
,
Which
they
call
Diferens
Perigaeum
Lunae
;
that
is
,
the
Orbe
carying
the
Moones
Perigaeum
,
which
is
the
point
wherein
the
Moone
commeth
nearest
to
the
earth
.
The
vppermost
and
nethermost
of
these
three
Orbes
,
that
is
to
say
,
the
Orbes
carying
the
Moones
Apogaeum
and
Perigaeum
(
both
which
Orbes
in
this
Sphaere
are
coloured
with
blew
)
are
alwaies
placed
in
such
sort
,
that
the
nar●●west
part
of
the
one
,
is
continually
answerable
to
the
broadest
part
of
the
other
;
whereby
it
commeth
to
passe
,
that
the
Sphaere
of
the
Moone
is
made
concentricall
,
that
is
to
say
,
to
haue
the
same
center
with
the
world
:
which
also
is
one
especiall
vse
,
why
these
Orbes
were
deuided
.
Another
vse
of
these
Orbes
,
is
to
shew
the
reason
of
the
motion
of
the
Moones
Apogaeum
and
Perigaeum
:
Therefore
both
these
Orbes
are
moued
togither
with
one
motion
equally
,
about
the
center
of
the
world
,
in
the
same
time
from
the
East
Westwards
,
in
the
space
of
32.
dayes
3.
houres
and
5.
minutes
almost
:
So
mouing
in
one
day
11.
deg.
12.
min.
and
1.
third
part
almost
.
The
axtree
,
about
which
these
Orbes
are
moued
equally
,
passeth
through
the
center
of
the
world
and
of
the
ecliptick
:
but
the
poles
of
these
Orbes
differ
from
the
poles
of
the
Ecliptick
and
of
the
Orbe
carying
the
Dragons
head
and
tayle
,
by
the
space
of
5.
degr.
and
a
quarter
,
or
thereabouts
,
which
poles
are
caryed
about
the
poles
of
the
Orbe
carying
the
Dragons
head
and
tayle
,
with
the
motion
of
the
same
Orbe
,
in
the
space
of
19.
yeares
almost
.
Whereby
it
commeth
to
passe
,
that
the
poles
of
the
Orbe
carying
the
Apogaeum
and
Perigaeum
of
the
Moone
,
describe
certaine
litle
circles
about
the
poles
of
the
Orbe
that
carieth
the
Dragons
head
and
taile
,
euen
as
the
Arctick
,
and
Antarctick
circle
in
the
ordinary
Sphaere
,
are
described
by
the
motion
of
the
poles
of
the
Ecliptick
,
caryed
about
dayly
with
the
motion
of
the
first
and
highest
moueable
Sphaere
,
in
the
space
of
24.
houres
almost
.
CHAP.
XI
.
Of
the
eccentricke
of
the
Moone
.
THe
Eccentrick
of
the
Moone
contained
betweene
the
two
former
Orbes
and
coloured
with
a
sad
yealow
colour
in
this
Sphaere
,
is
moued
equally
about
the
center
of
the
same
Orbes
,
from
the
West
towards
the
East
,
finishing
his
motion
vnder
the
Zodiack
,
in
the
space
of
27.
dayes
,
and
8.
houres
almost
:
and
with
this
motion
,
it
caryeth
about
the
Moones
Epicycle
equally
,
vnder
the
Zodiack
.
Therefore
the
motion
of
this
Orbe
,
about
his
owne
center
,
must
needs
be
vnequall
,
that
is
to
say
,
swifter
in
those
parts
that
are
about
the
Apogaeum
,
and
slower
in
the
lower
parts
about
the
Perigaeum
:
Because
that
greater
arches
of
the
Eccentrick
,
doe
answer
to
equall
arches
of
the
Zodiack
about
the
Apogaeum
,
then
about
the
Perigaeum
of
the
Eccentrick
.
The
axtree
about
which
this
Orbe
is
moued
,
is
alwaies
in
all
places
equidistant
from
the
axtree
of
the
Orbe
carying
the
Apogaeum
of
the
Moone
:
and
the
poles
of
the
axtree
of
the
Moones
eccentrick
,
are
fastned
in
the
Orbe
carying
the
Moones
Apogaeum
,
equidistantly
from
the
poles
of
the
same
Orbe
:
therefore
these
poles
together
with
the
whole
axtree
of
the
eccentrick
,
are
caryed
and
equally
moued
about
the
poles
and
axtree
of
the
Orbe
carying
the
Apogaeum
from
the
East
,
towards
the
West
.
With
this
motion
therefore
,
the
poles
and
center
of
the
eccentrick
,
describe
certaine
litle
circles
of
equall
bignes
,
about
the
poles
,
and
center
of
the
Orbe
carying
the
Apogaeum
,
from
the
East
West-wards
.
And
therefore
also
the
Apogaeum
of
the
eccentrick
,
is
moued
about
equally
,
vnder
the
ecliptick
,
contrary
to
the
order
of
Signes
from
the
East
West-wards
.
Whereby
it
commeth
to
passe
,
that
both
the
Apogaeum
and
center
of
the
eccentricke
,
are
somtimes
vnder
the
Ecliptick
,
that
is
,
when
they
are
vnder
the
Dragons
head
or
taile
:
but
for
the
most
part
they
are
beside
the
plaine
of
the
ecliptick
,
either
towards
the
North
,
or
else
towards
the
South
.
Hereby
also
it
appeareth
,
that
the
plaine
of
the
Ecliptick
doth
not
alwayes
deuide
the
plaine
of
the
eccentricke
into
epqall
parts
or
halfes
;
but
then
onely
,
when
the
Center
and
Apogaeum
of
the
Eccentrick
,
is
right
vnder
the
Dragons
head
or
tayle
;
for
then
onely
the
plaine
of
the
Ecliptick
deuideth
the
plaine
of
the
Eccentrick
,
by
the
center
therof
;
and
consequently
deuideth
it
precisely
into
two
halfes
.
Otherwise
,
if
the
Apogaeum
of
the
eccentrick
,
be
not
vnder
the
Dragons
head
or
tayle
,
looke
on
which
side
of
the
plaine
of
the
ecliptick
the
Apogaeum
is
,
for
on
the
same
side
of
the
ecliptick
is
the
greater
part
of
the
eccentrick
.
CHAP.
XII
.
In
what
proportion
the
Moones
eccentrick
,
and
Orbe
,
carying
her
Apogaeum
are
moued
.
NOw
the
Eccentrick
of
the
Moone
,
and
the
Orbe
carying
her
Apogaeum
,
are
moued
in
such
sort
,
that
the
middle
place
of
the
Sunne
,
is
alwayes
right
in
the
midst
betweene
the
center
of
the
Epicycle
caried
in
the
eccentrick
,
and
the
Apogaeum
of
the
Eccentrick
;
except
it
be
when
the
center
of
the
epicycle
is
in
coniunction
,
or
opposition
to
the
middle
place
of
of
the
Sunne
.
For
in
euery
middle
coniunction
and
opposition
of
the
Sunne
and
Moone
,
the
center
of
the
Epicycle
,
and
the
Apogaeum
of
the
eccentrick
are
vnited
together
;
But
in
the
coniunction
they
are
both
conioyned
with
the
middle
place
of
the
Sun
;
and
in
the
opposition
they
are
both
together
opposite
to
the
same
.
Whereof
it
followeth
,
that
in
the
first
and
last
quarters
of
the
Moone
,
the
center
of
her
epicycle
is
diametrally
opposite
to
the
Apogaeum
of
her
eccentrick
.
Hereof
it
commeth
to
passe
,
that
although
the
Moone
haue
the
same
position
in
her
epicycle
at
the
time
of
the
new
and
full
Moone
,
and
of
the
first
and
last
quarters
;
yet
the
equation
,
or
prosthaphaeresis
of
the
Moones
Argument
(
as
they
call
it
)
that
is
the
difference
betweene
the
true
,
and
middle
places
of
the
Moone
,
is
alwayes
greater
in
the
first
and
last
quarter
,
then
in
the
full
and
new
Moone
.
Hereby
likewise
it
appeareth
that
in
the
time
contayned
betweene
new
Moone
and
new
Moone
(
which
they
call
Mensem
synodicum
,
that
is
the
moneth
coniunctional
,
or
the
time
from
coniunction
to
coniunction
)
the
center
of
the
epicycle
maketh
two
complete
reuolutions
,
vnder
the
Orbe
carying
the
Apogaeum
of
the
Moones
eccentrick
.
And
therefore
in
euery
moneth
,
the
center
of
the
epicycle
commeth
twise
to
the
Apogaeum
and
twise
to
the
Perigaeum
of
the
eccentrick
;
and
so
the
monthly
motion
of
the
center
of
the
epicycle
,
describeth
an
oual
figure
:
the
ends
whereof
are
alwayes
towards
the
place
of
the
full
and
new
Moone
,
and
the
●ides
towards
the
places
of
the
first
and
last
quarter
.
By
this
that
hath
beene
spoken
,
it
is
also
manifest
,
that
if
the
middle
motion
of
the
Sunne
,
be
subtracted
out
of
the
middle
motion
of
the
Moone
,
there
remaineth
the
middle
motion
of
the
Moones
longitude
from
the
sunne
,
and
that
if
this
longitude
againe
be
doubled
,
you
shall
haue
the
motion
of
the
center
of
the
Moones
Epicycle
from
the
Apogaeum
of
her
eccentrick
,
which
motion
they
call
the
center
of
the
Moone
,
CHAP.
XIII
.
Of
the
Epicycle
of
the
Moone
,
and
how
it
is
moued
.
THe
little
Orbe
placed
in
the
Eccentrick
,
is
called
the
Epicycle
of
the
Moone
;
in
the
circumference
whereof
is
also
placed
the
body
of
the
Moone
,
represented
by
the
round
Beade
,
set
into
the
Moones
Epicycle
in
this
Sphaere
.
The
plaine
superficies
of
this
epicycle
agreeth
euen
with
the
plaine
of
the
eccentrick
:
and
the
axtree
about
which
it
is
moued
,
is
perpendicular
to
the
plaine
of
the
eccentrick
.
This
Epicycle
is
moued
equally
from
his
middle
Apogaeum
,
about
his
owne
center
and
axtree
from
the
East
Westwards
,
contrary
to
the
motion
of
the
eccentrick
,
carying
forwards
the
body
of
the
Moone
with
this
motion
13.
degrees
and
almost
4.
min.
euery
day
,
and
finishing
his
reuolution
in
27.
dayes
13.
houres
and
19.
minutes
almost
.
The
middle
Apogaeum
of
the
Epicycle
is
shewed
by
a
right
line
,
imagined
to
be
drawne
,
from
that
point
of
the
little
circle
(
described
by
the
motion
of
the
center
of
the
Moones
eccentrick
)
which
is
opposite
to
the
center
of
the
Eccentrick
,
by
the
center
of
the
Epicycle
vnto
the
vpper
part
of
the
Epicycle
.
But
the
true
Apogaeum
of
the
Epicycle
,
is
shewed
by
a
right
line
,
vnderstood
to
be
drawne
from
the
Center
of
the
earth
by
the
center
of
the
Epicycle
,
vnto
the
vpper
part
of
the
circumference
thereof
.
By
the
motion
of
this
Epicycle
it
may
easily
be
conceiued
why
the
Moone
seemeth
to
moue
sometimes
swifter
and
somteimes
slower
:
But
when
the
Moone
commeth
in
the
nether
part
of
the
Epicycle
,
the
Eccentrick
caryeth
the
Epicycle
and
the
Epicycle
caryeth
the
body
of
the
Moone
both
one
way
:
that
is
,
from
the
West
East-wards
,
and
therefore
at
that
time
the
Moone
seemeth
to
moue
more
swiftly
.
According
as
you
may
see
in
Ephemerides
,
the
d●●●ne
motion
of
the
Moone
to
be
sometimes
little
more
then
11.
degrees
and
sometimes
againe
little
lesse
then
15.
degrees
.
The
true
motion
of
the
Moone
seemeth
then
to
be
swifter
,
when
the
Moone
is
in
the
Perigaeum
of
her
Epicycle
,
and
the
Epicycle
in
the
Perigaeum
of
the
Eccentrick
;
because
then
she
is
not
onely
caryed
forwards
the
same
way
both
by
her
Epicycle
and
Eccentrick
,
but
she
is
also
at
that
time
nearest
vnto
vs
for
which
cause
her
motion
shall
seeme
swifter
,
then
when
the
Epicycle
is
in
other
parts
of
the
Eccentrick
.
〈…〉
CHAP.
XIIII
.
The
definitions
of
certayne
Astronomicall
wordes
of
Art
,
for
the
better
vnderstanding
of
the
Theoricke
of
the
Moone
.
1.
THe
line
of
the
Moones
middle
motion
,
is
a
line
vnderstood
to
be
drawne
from
the
center
of
the
earth
,
by
the
center
of
the
Moones
Epicycle
,
vnto
the
Zodiack
.
2.
This
line
sheweth
the
middle
place
of
the
Moon
in
the
Zodiack
.
3.
And
the
middle
motion
of
the
Moone
,
is
the
arch
of
the
Zodiack
,
from
the
beginning
of
Aries
,
vnto
the
same
line
.
4.
So
likewise
the
line
of
the
true
motion
,
or
of
the
true
place
of
the
Moone
,
is
drawne
from
the
center
of
the
world
,
by
the
center
of
the
Moone
,
to
the
Zodiack
.
5.
This
line
therefore
sheweth
the
true
place
of
the
Moone
in
the
Zodiack
.
6.
And
the
true
motion
of
the
Moone
,
is
the
arch
of
the
Zodiack
,
from
the
beginning
of
Aries
,
vnto
the
true
place
of
the
Moone
.
7.
The
middle
longitude
of
the
Moone
from
the
Sunne
,
is
the
arch
of
the
Zodiack
,
from
the
middle
place
of
the
Sunne
Eastwards
vnto
the
middle
place
of
the
Moone
.
8.
And
this
arch
doubled
,
is
called
the
doubled
longitude
of
the
Moone
from
the
Sunne
,
or
the
center
of
the
Moone
(
as
the
Alphonsines
call
it
)
which
is
nothing
else
but
the
arch
of
the
Zodiack
,
betweene
the
place
of
the
Apogaeum
of
the
Eccentrick
and
the
middle
place
of
the
Moone
.
It
is
called
the
doubled
longitude
of
the
Moone
from
the
Sunne
,
because
it
is
alwayes
twice
so
much
,
as
is
the
middle
longitude
of
the
Moone
from
the
Sunne
.
9.
And
it
is
called
the
center
of
the
Moone
,
because
it
sheweth
the
distance
of
the
center
of
the
Moones
Epicycle
from
the
Apogaeum
.
10.
The
equation
,
or
Prosthaphaeresis
of
the
center
,
is
the
arch
of
the
Epicycle
,
betweene
the
middle
and
true
Apogaeum
of
the
Epicycle
.
This
equation
or
Prosthaphaeresis
is
nothing
at
all
,
when
the
center
of
the
Epicycle
is
in
the
Apogaeum
,
or
Perigaeum
of
the
Eccentrick
.
But
the
Epicycle
being
in
any
other
part
of
the
Eccentricke
there
is
alwaies
some
equation
of
the
center
;
yea
in
some
parts
thereof
,
where
it
groweth
greatest
,
it
is
13.
degr.
9.
minutes
:
and
so
long
as
the
center
of
the
Epicycle
,
is
in
the
halfe
of
the
Eccentrick
descending
from
the
Apogaeum
to
the
Perigaeum
,
that
equation
is
to
be
added
to
the
motion
of
the
Epicycle
;
but
in
the
other
halle
of
the
Eccentricke
ascending
;
,
it
must
be
subtracted
;
that
so
the
true
Argument
〈…〉
the
Epicycle
may
be
had
.
11.
The
Argument
,
or
Anamalie
of
the
Moone
is
nothing
els
,
but
the
motion
of
the
Moones
Epicycle
.
12.
The
true
or
middle
argument
,
〈…〉
is
the
arch
of
the
Epicycle
from
the
true
or
middle
Apogaeum
of
the
Epicycle
,
vnto
the
center
of
the
body
of
the
Moone
,
reckoned
that
way
,
which
the
epicycle
moueth
.
13.
The
equation
of
the
argument
,
or
Prosthaphaeresis
of
the
epicycle
,
is
the
arch
of
the
Zodiack
,
〈…〉
the
middle
,
and
〈◊〉
place
of
the
Moone
.
This
equation
is
〈◊〉
,
when
the
Moone
is
in
the
true
Apogaeum
,
or
Perigaeum
of
her
epicycle
.
But
it
is
greatest
,
when
the
center
of
the
Moone
commeth
〈…〉
of
the
world
,
and
touching
the
epicycle
,
when
it
is
in
the
Perigaeum
of
the
eccentrick
.
And
the
Moone
being
in
the
first
,
that
is
in
the
〈…〉
of
the
Epicycle
,
〈…〉
from
the
true
Apogaeum
thereof
,
the
middle
place
of
the
Moone
goe
〈◊〉
before
the
true
place
,
and
the
equation
of
the
argument
must
therefore
be
subtracted
:
but
when
the
Moone
is
〈…〉
semicircle
of
the
epicycle
,
〈…〉
before
the
middle
place
,
and
to
that
equation
must
be
added
to
the
Moones
〈◊〉
middle
motion
,
that
the
true
motion
and
place
of
the
〈…〉
may
be
found
.
CHAP.
XV.
The
reason
of
the
variety
of
the
Moones
equation
,
&c.
THis
equation
becommeth
lesser
or
greater
,
according
as
the
epicycle
〈…〉
or
nearer
to
the
center
of
the
world
.
The
least
equations
are
,
when
the
epicycle
is
in
the
Apogaeum
of
the
eccentrick
,
and
contrarywise
,
the
greatest
must
happen
,
the
epicycle
being
in
the
Perigaeum
of
the
eccentrick
.
The
difference
between
these
greatest
,
and
least
Equations
,
Ptolemee
and
Copernicus
call
the
excesse
:
but
〈◊〉
,
and
the
Alphonsines
call
it
the
diuersitie
of
the
Diameter
;
because
that
difference
of
the
equations
ariseth
by
reason
of
the
diuerse
apparent
hignesse
of
the
diameter
of
the
Epicycle
,
according
as
it
is
nearer
to
vs
,
or
further
from
vs
.
Therefore
in
the
Astronomicall
tables
,
they
vse
to
set
downe
those
equations
onely
,
which
happen
when
the
Epicycle
is
in
the
Apogaeum
of
the
eccentrick
,
which
are
the
least
equations
,
whereto
they
also
adioyne
the
excesse
,
or
diuersity
of
diameter
,
shewing
how
much
those
equations
,
which
happen
when
the
Epicycle
is
in
the
Perigaeum
of
the
Eccentrick
,
exceed
those
which
happen
,
the
epicycle
being
in
the
Apogaeum
of
the
eccentrick
.
Moreouer
,
there
are
annexed
certaine
min.
which
they
call
Scrupula
,
or
minuta
proportion●alia
:
that
is
,
proportionall
minutes
:
whereby
is
found
,
how
much
of
the
sayd
excesse
,
is
to
be
added
to
the
foresayd
equations
,
when
the
epicycle
is
in
any
other
part
of
the
eccentrick
,
then
in
the
Apogaeum
:
that
so
the
true
equation
of
the
argument
,
for
the
same
part
of
the
eccentrick
might
at
any
time
be
found
.
For
then
onely
is
that
whole
excesse
to
be
added
,
when
the
epicycle
is
in
the
Perigaeum
of
the
eccentrick
.
But
if
the
epicycle
be
in
any
other
part
of
the
eccentrick
;
then
looke
what
proportion
60.
hath
to
the
whole
excesse
,
the
same
proportion
haue
the
proportionall
minutes
,
answerable
to
that
part
of
the
eccentrick
,
wherein
the
epicycle
is
,
vnto
the
part
proportional
of
the
excesse
,
which
(
part
proportionall
)
being
added
to
the
equation
before
found
,
shall
giue
you
the
true
equation
.
CHAP.
XVI
.
The
reason
〈◊〉
Moones
proportionall
minutes
,
&c.
THe
reason
of
those
proportionall
minutes
,
may
in
some
sort
be
shewed
,
by
those
concentricall
arches
of
circles
,
which
you
see
drawne
vppon
the
Moones
eccentricall
Orbe
,
in
this
Sphaere
:
but
indeed
all
those
arches
must
bee
vnderstood
,
to
haue
alwayes
the
same
center
with
the
world
,
and
not
to
be
moued
about
togither
with
the
Eccentrick
.
The
vppermost
of
them
is
to
be
drawne
by
the
center
of
the
Epicycle
being
in
the
Apogaeum
of
the
Eccentrick
,
and
the
nethermost
is
drawne
by
the
same
center
when
it
is
in
the
Perigaeum
of
the
Eccentrick
:
so
as
the
distance
of
these
two
arches
,
or
Peripheryes
,
is
iust
twise
so
much
as
the
eccentricitie
;
that
is
the
distance
of
the
center
of
the
Eccentrick
,
from
the
center
of
the
world
,
shewed
by
the
distance
of
the
short
lines
NO
,
or
FF
,
vppon
the
Orbe
carying
the
Apogaeum
;
or
of
PQ
,
or
GH
,
vpon
the
caryer
of
the
Perigaeum
of
the
Moone
.
The
whole
distance
,
between
these
two
peripheries
,
from
the
vttermost
to
the
innermost
,
is
vnderstood
to
be
deuided
into
60.
equall
parts
,
imagining
euery
one
of
these
to
contayne
10.
as
may
appeare
by
the
figures
set
to
euery
one
of
them
,
from
the
vppermost
to
the
nethermost
,
in
this
order
:
10.
20.
30.
40.
50.
60.
Now
the
intersections
of
these
Peripheries
with
the
Eccentrick
(
that
is
)
with
the
vppermost
of
the
two
deuided
Peripheries
,
which
are
drawne
round
about
through
the
midst
of
the
Moones
eccentricall
Orbe
)
do
shew
what
proportionable
min.
answer
to
any
part
of
the
eccentrick
,
These
proportionall
min.
therefore
may
be
defined
to
be
nothing
else
,
Otherwise
also
,
these
proportionall
min.
may
be
defined
,
to
be
sixtieth
parts
of
the
excesse
,
wherewith
the
line
drawne
from
the
center
of
the
earth
,
to
the
Apogaeum
of
the
Moones
Eccentrick
,
exceedeth
the
line
drawne
from
the
same
center
to
the
Perigaeum
of
the
Eccentrick
:
For
these
sixtieth
parts
also
may
not
vnfitly
be
called
proportionall
min.
because
that
alwaies
looke
how
many
of
these
parts
there
are
left
without
the
circumference
of
the
Eccentrick
,
or
beyond
the
center
of
the
Epicycle
;
so
many
of
the
former
sixtieth
parts
of
the
diuersity
of
diameter
,
or
of
the
excesse
of
the
Prostaphaerses
of
the
Epicycle
,
must
be
added
to
the
Equation
of
the
argument
,
that
the
true
equation
of
the
argument
may
bee
had
,
for
that
position
,
or
scituation
of
the
Epicycle
,
in
the
Eccentrick
.
CHAP.
XVII
.
The
reason
of
the
Eclipses
of
the
Sunne
and
Moone
,
&c.
NOw
by
this
Sphere
,
it
may
easily
be
conceiued
,
why
there
is
not
an
Eclipse
,
in
euery
coniunction
or
opposition
of
the
Sunne
and
Moone
.
For
seeing
that
the
Moone
hath
for
the
most
part
a
greater
apparent
latitude
,
then
the
visible
or
apparent
conioyned
semediameters
of
the
Sunne
and
Moone
in
the
coniunction
:
and
because
the
true
latitude
of
the
Moone
,
is
also
for
the
most
part
greater
then
the
apparent
semediameters
of
the
Moone
and
shadow
of
the
earth
(
at
that
place
where
the
Moone
should
passe
through
that
shadow
)
in
the
oppossition
,
to
make
an
Eclipse
:
it
commeth
to
passe
,
that
in
most
coniunctions
and
oppositions
of
the
Sunne
and
Moone
,
there
is
no
Eclipse
.
And
the
reason
hereof
is
this
,
because
that
the
Moone
commeth
vnder
the
way
of
the
Sunne
(
which
wee
call
the
Ecliptick
line
)
onely
twise
in
a
moneth
,
and
those
2.
points
(
wherin
the
wayes
of
the
Sunne
and
Moone
crosse
each
other
)
onely
twise
in
a
synodicall
moneth
,
which
two
points
wee
called
the
Dragons
head
and
taile
;
whereof
wee
haue
also
spoken
before
,
)
Wherfore
,
seeing
the
Sunne
(
going
but
once
only
through
the
compasse
of
the
Ecliptick
in
a
yeare
)
can
come
but
once
in
a
yeare
to
eyther
of
those
points
;
the
Moone
for
the
most
part
,
when
she
commeth
to
bee
in
opposition
,
or
coniunction
with
the
Sun
,
must
needs
be
so
farre
wide
from
the
Ecliptick
line
,
or
way
of
the
Sunne
,
either
towards
the
North
or
South
:
that
she
can
neither
come
betwixt
vs
and
the
Sun
in
the
coniunction
,
nor
yet
within
the
compasse
of
the
shadow
of
the
earth
in
the
opposition
.
But
when
the
Sunne
commeth
neare
eyther
of
those
points
(
which
hapneth
once
in
six
moneths
(
there
must
needs
for
the
most
part
be
some
Eclipse
,
eyther
of
the
Sunne
or
Moone
,
or
both
.
CHAP.
XVIII
.
Of
the
diuersity
of
the
bounds
or
spaces
,
within
which
an
Eclipse
may
happen
:
and
the
reason
of
that
diuersity
.
THe
bounds
or
distances
from
the
Dragons
head
or
taile
,
within
which
there
may
happen
an
Eclipse
of
the
Moone
,
are
sometimes
greater
and
sometimes
lesse
,
by
reason
of
the
diuers
distances
of
the
Sunne
,
or
Moone
,
or
both
of
them
,
from
the
earth
.
For
seeing
the
body
of
the
Sunne
is
greater
then
the
globe
of
the
whole
earth
(
as
it
is
manifestly
demonstrated
by
Ptolemee
and
Copernicus
)
it
must
needs
be
,
that
the
greater
distance
the
Sun
hath
from
the
earth
,
the
greater
shadow
must
the
earth
haue
;
and
the
nearer
the
Sunne
is
to
the
earth
,
the
lesse
shadow
shall
the
earth
haue
,
at
the
place
of
the
Moons
passage
through
the
shadow
,
at
equall
distances
from
the
earth
.
Contrariwise
,
the
further
that
the
Moone
is
from
the
earth
,
the
lesse
shall
the
shadow
of
the
earth
be
,
and
the
nearer
the
Moone
is
to
the
earth
,
the
greater
shall
the
shadow
be
,
at
the
place
where
the
Moone
is
to
passe
through
the
shadow
.
The
greatest
distance
therefore
from
the
Dragons
head
or
taile
,
wherein
there
can
at
any
time
happen
any
Eclipse
of
the
Moone
,
is
about
13.
degrees
.
And
the
least
distance
at
which
it
is
possible
for
the
Moone
to
auoid
an
Eclipse
,
is
about
10.
degr.
and
one
third
part
of
a
degree
;
which
hapneth
when
the
Moone
is
in
the
Apogaeum
of
her
Epicycle
,
in
her
greatest
distance
from
the
earth
,
and
the
Sunne
in
his
Perigaeum
,
in
the
time
of
his
greatest
eccentricity
,
for
then
the
Sunne
commeth
nearest
to
the
earth
and
maketh
the
least
shadow
:
as
contrarywise
at
the
same
time
of
his
greatest
eccentricity
,
beeing
in
his
Apogaeum
,
he
hath
his
greatest
distance
from
the
earth
,
and
so
maketh
the
earth
cast
forth
her
greatest
shadow
.
At
which
time
,
if
the
Moone
also
chance
to
be
in
the
Perigaeum
of
her
Epicycle
,
and
so
in
her
nearest
distance
from
the
earth
,
she
may
be
something
Eclipsed
,
although
she
be
full
13.
degrees
or
something
more
from
the
Dragons
head
or
taile
.
CHAP.
XIX
.
How
to
find
the
place
of
the
Dragons
head
and
taile
for
any
time
.
NOw
the
place
,
and
time
of
the
full
Moone
,
being
easily
knowne
by
some
Almanack
,
or
Prognostication
;
it
shall
not
be
hard
,
to
giue
a
reasonable
neare
estimate
,
and
to
foretell
both
the
time
,
and
quantity
of
the
Eclipse
of
the
Moone
,
the
place
of
the
Dragons
head
and
taile
,
being
first
knowne
after
this
manner
.
The
place
of
the
Dragans
head
,
being
first
giuen
for
any
time
,
for
euery
yeare
before
the
same
time
,
adde
to
the
same
place
:
and
for
euery
yeare
after
the
same
time
subtract
19.
degrees
and
one
third
part
of
a
degree
and
for
euery
moneth
a
degree
and
an
halfe
and
a
tenth
part
of
a
degree
and
for
euery
day
3.
minutes
and
the
remainder
shall
shew
you
the
place
of
the
Dragons
head
after
the
same
time
:
or
the
summe
before
that
time
without
any
great
errour
.
As
for
example
,
The
30.
of
Iune
this
present
yeare
1600.
suppose
you
would
know
the
place
of
the
Dragons
head
:
The
place
therefore
of
the
Dragons
head
being
first
giuen
,
for
the
beginning
of
the
same
yeare
,
in
0.
degree
45.
minutes
,
of
Aquarius
:
and
six
moneths
onely
of
that
yeare
being
passed
,
I
take
for
those
six
moneths
6.
degrees
and
6.
halfe
degrees
that
is
9.
degrees
and
sixteenth
parts
of
a
degree
that
is
36.
min.
the
summe
of
all
which
is
9.
degrees
and
36.
minutes
.
Which
being
subtracted
out
of
0.
degree
,
45.
minutes
of
Aquarius
,
there
remaine
21.
degrees
9.
min.
of
Capricorne
,
for
the
place
of
the
Dragons
head
at
that
time
.
CHAP.
XX.
A
table
for
finding
the
place
of
the
Dragons
head
and
taile
more
exactly
and
the
declaration
thereof
.
BVt
if
you
would
haue
the
place
of
the
Dragons
head
more
exactly
,
you
may
find
the
same
most
easily
,
by
meanes
of
the
table
following
,
for
any
time
within
the
space
of
these
20.
yeares
,
yet
to
come
.
This
table
conteyneth
three
principall
parts
or
columnes
,
the
first
part
sheweth
you
in
what
signe
,
degr.
and
min.
the
Dragons
head
is
,
at
the
beginning
of
any
yeare
;
from
this
present
yeare
1600.
till
the
yere
1620.
The
second
part
sheweth
how
much
the
Dragons
head
moueth
,
in
any
number
of
moneths
of
the
yeare
:
the
third
part
giueth
you
the
motion
of
the
Dragons
head
,
in
any
number
of
dayes
of
the
moneth
.
|
The
place
of
the
Dragons
head
.
|
|
|
Yeare
|
Sign
.
|
Deg.
|
Mt.
|
Moneths
Complete
.
|
De.
Mi.
|
Da.
|
De.
Mi.
|
|
1600
|
Aquarius
|
0
|
45
|
Ianuary
|
1
38
|
1
|
0
3
|
|
1601
|
Capricorn
|
11
|
21
|
February
|
3
8
|
2
|
0
6
|
|
1602
|
Sagittar
.
|
22
|
2
|
March
|
4
46
|
3
|
0
10
|
|
1603
|
Sagittar
.
|
2
|
42
|
Aprill
|
6
22
|
4
|
0
13
|
|
1604
|
Scorpio
|
13
|
22
|
May
|
8
0
|
5
|
0
16
|
|
1605
|
Libra
|
23
|
59
|
Iune
|
9
36
|
6
|
0
19
|
|
1606
|
Libra
|
4
|
39
|
Iuly
|
11
14
|
7
|
0
22
|
|
1607
|
Virgo
|
15
|
19
|
August
|
12
53
|
8
|
0
25
|
|
1608
|
Leo
|
25
|
59
|
Septemb.
|
14
28
|
9
|
0
29
|
|
1609
|
Leo
|
6
|
35
|
October
|
16
7
|
10
|
0
32
|
|
1610
|
Cancer
|
17
|
15
|
Nouemb.
|
17
42
|
11
|
0
35
|
|
1611
|
Gemini
|
27
|
55
|
Decemb.
|
19
21
|
12
|
0
38
|
|
1612
|
Gemini
|
8
|
35
|
|
|
13
|
0
41
|
|
1613
|
Taurus
|
19
|
12
|
|
|
14
|
0
44
|
|
1614
|
Aries
|
29
|
52
|
|
|
15
|
0
48
|
|
1615
|
Aries
|
10
|
32
|
|
|
16
|
0
51
|
|
1616
|
Pisces
|
21
|
12
|
|
|
17
|
0
54
|
|
1617
|
Pisces
|
1
|
49
|
|
|
18
|
0
57
|
|
1618
|
Aquarius
|
12
|
29
|
|
|
19
|
1
0
|
|
1619
|
Capricorn
|
23
|
9
|
|
|
20
|
1
4
|
|
1620
|
Capricorn
|
3
|
49
|
|
|
21
|
1
7
|
|
|
|
|
|
|
|
22
|
1
10
|
|
|
|
|
|
|
|
23
|
1
13
|
|
|
|
|
|
|
|
24
|
1
16
|
|
|
|
|
|
|
|
25
|
1
19
|
|
|
|
|
|
|
|
26
|
1
13
|
|
|
|
|
|
|
|
27
|
1
26
|
|
|
|
|
|
|
|
28
|
1
29
|
|
|
|
|
|
|
|
29
|
1
32
|
|
|
|
|
|
|
|
30
|
1
35
|
CHAP.
XXI
.
To
finde
the
place
of
the
Dragons
head
or
tayle
,
by
the
former
table
.
FInde
out
in
the
former
table
,
the
moneth
next
going
before
the
moneth
giuen
;
finde
out
also
the
day
of
the
moneth
,
Adde
together
the
numbers
of
degrees
and
minutes
answerable
to
that
moneth
and
day
of
the
moneth
,
and
subtract
the
same
out
of
the
place
of
the
Dragons
head
at
the
beginning
of
the
yeare
,
adding
thereto
30.
degr.
(
●●at
is
the
whole
signe
next
going
before
resolued
in
to
degr
.
)
if
the
Sunne
aforesayd
be
greater
then
the
number
of
degr.
shewing
the
place
of
the
Dragons
head
at
the
beginning
of
the
yeare
:
so
shall
you
haue
the
place
of
the
Dragons
head
for
the
time
giuen
.
And
the
point
of
the
Zodiack
opposite
to
this
,
is
the
place
of
the
Dragons
taile
.
Take
for
example
,
The
29.
of
Nouember
1601.
I
find
therefore
against
October
(
the
moneth
going
next
before
Nouember
)
16.
degrees
7.
minutes
and
against
the
29.
day
1.
degree
32.
minutes
,
the
summe
of
both
these
added
together
is
17.
degrees
39.
min.
the
place
of
the
Dragons
head
for
the
beginning
of
the
yeare
1601.
is
11.
deg.
21.
min.
of
Capricorne
,
which
because
they
be
lesse
then
17.
deg.
39.
min.
I
adde
vnto
them
30.
deg.
that
is
the
whole
signe
of
Sagittarie
,
and
the
summe
of
both
is
41.
deg.
12.
min.
out
of
which
subtract
17.
deg.
39.
min.
and
there
shall
remaine
23.
deg.
42.
minutes
of
Sagittarie
;
the
place
of
the
Dragons
head
at
that
time
.
And
the
point
of
the
Zodiacke
which
is
opposite
hereto
(
that
is
the
2●
〈◊〉
42.
minutes
of
Gemini
)
is
the
place
of
the
〈◊〉
tayle
.
CHAP.
XXII
.
To
know
at
what
time
there
shall
be
an
Eclipse
of
the
Moone
.
THe
place
of
the
Dragons
head
being
thus
knowne
,
finde
out
the
same
place
vpon
the
horizon
of
the
Sphaere
,
and
see
what
day
and
moneth
answereth
thereto
finde
out
also
the
place
of
the
full
Moone
,
which
hapneth
next
before
or
after
that
day
,
which
place
if
it
chance
to
bee
within
11.
or
12.
deg.
eyther
before
or
after
that
point
of
the
Zodiack
which
is
opposite
to
the
Dragons
head
,
there
must
needs
be
for
the
most
part
in
Eclipse
of
the
Moone
.
Likewise
if
you
finde
what
day
and
moneth
is
answerable
to
the
place
of
the
Dragons
taile
vpon
the
horizon
of
the
Sphaere
if
the
place
of
the
full
Moone
which
hapneth
next
before
or
after
that
day
chance
to
be
within
11.
or
12.
degrees
of
the
Dragons
head
,
for
the
most
part
there
shall
bee
an
Eclipse
of
the
Moone
.
As
for
example
,
The
20.
of
Ianuarie
last
this
present
yeare
1600.
the
place
of
the
Dragons
head
was
found
(
by
the
former
Chapter
)
to
haue
beene
in
29.
deg.
41.
min.
of
Capricorne
;
whereto
there
answereth
in
the
horizon
the
10.
day
of
Ianuarie
the
place
of
the
full
Moone
hapning
next
after
,
vpon
the
20.
of
the
same
moneth
in
the
morning
must
needs
be
in
the
place
opposite
to
the
place
of
the
Sunne
the
same
20.
〈◊〉
Therefore
because
〈◊〉
Sun
that
day
is
in
9.
deg.
〈◊〉
one
halfe
of
Aquarius
,
therefore
the
place