THE
THEORIQVES
of
the
seuen
Planets
,
shewing
all
their
diuerse
motions
,
and
all
other
accidents
(
called
passions
)
thereunto
belonging
.
SIth
euery
art
hath
his
proper
tearmes
,
without
the
knowledge
whereof
,
no
art
is
easily
learned
:
Minding
therefore
here
to
treat
of
the
Theoriques
of
the
Planets
,
I
thinke
it
best
first
to
set
down
all
the
tearmes
together
with
the
true
significations
thereof
:
which
tearmes
,
though
they
bee
manifold
,
yet
they
may
be
all
reduced
into
seuen
.
For
whatsoeuer
tearme
it
bee
,
it
signifieth
either
a
point
,
a
centre
,
a
line
,
a
circle
,
a
semicircle
,
a
portion
of
a
circle
otherwise
called
an
arche
,
or
an
orbe
,
called
in
Latine
Orbis
,
which
is
as
much
to
say
,
as
a
round
hoope
or
sphere
,
hauing
breadth
and
thickenesse
,
and
sometime
it
is
taken
for
a
circle
.
And
you
see
here
,
that
I
make
a
difference
betwixt
a
point
and
a
centre
;
for
though
euery
centre
is
a
point
,
yet
euery
point
is
not
a
centre
.
Againe
,
I
make
a
difference
betwixt
a
circle
and
an
orbe
;
for
though
they
bee
like
,
in
that
they
both
haue
round
shape
,
yet
they
differ
,
in
that
the
orbe
hath
both
breadth
and
thickenesse
,
and
the
circle
hath
neither
.
But
before
I
define
the
tearmes
belonging
to
the
Theorique
of
anie
Planet
,
I
thinke
it
best
,
according
to
the
method
and
order
vsed
by
Michaell
Mestlyn
,
to
set
downe
foure
principall
intentions
,
meet
to
bee
vsed
in
describing
the
Theorique
of
euerie
Planet
:
of
which
foure
intentions
,
1.
The
first
is
to
shew
of
how
many
particular
orbes
euery
Theorique
consisteth
.
2.
The
second
is
to
shew
towards
what
part
such
orbes
are
moued
,
and
in
what
time
they
make
their
reuolutions
,
and
also
vpon
what
centres
or
poles
they
make
their
regular
mouings
.
3.
The
third
intention
,
is
plainely
to
describe
all
such
points
,
lines
,
arches
,
semicircles
,
and
such
like
things
as
are
needfull
to
be
knowne
for
the
calculating
of
the
mouings
of
any
Planet
.
4.
The
fourth
intention
,
is
to
shew
how
much
latitude
euery
Planet
(
hauing
latitude
)
hath
:
for
euery
Planet
hath
latitude
,
more
or
lesse
,
the
Sunne
onely
excepted
,
which
hath
no
latitude
,
because
he
neuer
departeth
from
the
Eclipticke
line
,
with
whose
Theorique
I
mind
here
first
to
deale
.
Why
deale
you
first
with
the
Theorique
of
the
Sun
?
FOr
foure
causes
.
First
,
because
his
Theorique
is
more
easie
than
all
the
rest
.
Secondly
,
as
well
for
that
he
excelleth
in
dignitie
all
the
other
Planets
,
as
also
for
that
the
mouing
of
all
the
other
Planets
dependeth
vpon
his
mouing
:
which
vnles
it
be
known
,
none
of
the
others
can
be
throughly
known
.
Thirdly
,
for
that
the
mouings
&
reuolutions
of
all
the
rest
of
the
Planets
are
counted
by
his
yearly
reuolutions
.
Fourthly
,
by
the
authoritie
of
Ptolomey
,
and
other
auncient
writers
,
which
in
treating
of
the
Theoriques
,
doe
first
begin
with
the
Theorique
of
the
Sunne
.
NOw
here
followeth
the
first
Intention
,
shewing
by
certain
figures
,
of
how
many
orbes
the
Theorique
of
the
Sunne
consisteth
,
that
is
,
of
three
orbes
,
hereafter
described
,
&
are
contained
in
this
figure
next
following
.
The
first
figure
belonging
to
the
Theorique
of
the
Sunne
,
shewing
his
three
orbes
,
and
their
centres
,
and
also
the
two
points
called
Auges
,
hereafter
defined
.
THough
the
Theorique
of
the
Sun
consisteth
but
of
three
orbes
,
yet
you
see
here
,
that
in
this
figure
there
be
four
orbes
or
circles
,
that
is
,
two
black
,
and
two
white
:
whereof
the
vpper
blacke
circle
,
marked
with
the
letter
D
is
called
the
vpper
deferent
of
the
Auges
;
and
the
lower
blacke
circle
,
marked
with
the
letter
E.
is
called
the
inferior
or
lower
deferent
of
the
Auges
;
and
the
largest
and
greatest
white
circle
,
marked
with
the
letter
C.
is
called
the
Excentricke
or
deferent
of
the
Sunne
,
hauing
the
bodie
of
the
Sunne
fixed
therein
:
and
in
the
middle
white
roundle
are
set
downe
two
prickes
or
centres
,
whereof
that
which
is
marked
with
the
letter
A.
is
the
centre
of
the
world
;
and
the
other
next
aboue
that
,
marked
with
the
letter
B.
is
the
centre
of
the
deferent
of
the
Sun
,
otherwise
called
the
Excentricke
;
and
the
point
which
is
in
the
vpper
lymbe
of
the
deferent
of
the
Sun
,
marked
with
the
letter
F.
is
called
in
the
Arabike
tongue
Aux
,
in
Greeke
Apogaeon
,
in
Latine
Absis
summa
,
that
is
to
say
,
the
highest
point
,
which
I
meane
to
call
in
our
tongue
in
the
singular
number
,
Auge
,
and
in
the
plurall
number
,
Auges
:
the
opposite
point
whereof
,
marked
with
the
letter
G.
is
called
in
Greeke
Perigaeon
,
and
in
Latine
Absis
ima
,
that
is
to
say
,
the
lowest
Auge
.
It
is
also
called
Oppositum
Augis
,
that
is
,
the
point
opposite
to
the
Auge
:
so
as
by
this
figure
you
may
perceiue
,
that
the
point
Auge
is
a
point
in
the
deferent
of
the
Sunne
,
farthest
distant
from
the
centre
of
the
earth
,
and
therfore
is
called
of
some
Longior
longitudo
,
that
is
,
the
farthest
longitude
,
marked
in
the
former
figure
with
the
letter
F
;
and
the
opposite
point
to
that
,
is
called
Propior
longitudo
,
that
is
,
the
nigher
longitude
,
because
it
is
nigher
to
the
centre
of
the
earth
,
and
is
marked
in
the
said
figure
with
the
letter
G.
There
be
also
in
the
said
deferent
,
two
other
points
of
the
meane
longitude
,
whereof
we
shall
speake
hereafter
.
You
see
also
,
that
the
pricke
,
marked
with
the
letter
A.
is
the
centre
of
the
world
;
&
that
the
other
prick
,
marked
with
the
letter
B.
is
the
centre
of
the
deferent
of
the
Sunne
,
which
,
because
it
is
out
of
the
centre
of
the
world
,
and
distant
from
the
same
,
it
is
called
the
centre
of
the
excentricke
:
and
the
distance
betwixt
these
two
centres
,
is
called
in
Latine
excentricita●
;
and
I
likewise
from
henceforth
will
call
such
distance
the
excentricitie
.
Now
describe
the
three
foresaid
circles
or
orbes
,
and
shew
whereto
they
serue
?
THe
first
,
called
the
orbe
excentricke
,
which
in
the
former
figure
is
made
white
,
and
marked
with
the
letter
C.
is
that
which
carieth
the
body
of
the
Sun
,
and
therefore
is
called
in
Latine
Deferens
Solis
,
and
I
will
also
call
it
the
deferent
of
the
Sun
:
in
the
vttermost
circumference
whereof
,
are
set
the
foresaid
two
Auges
,
the
one
right
opposite
to
the
other
,
marked
with
the
letters
F.
G.
as
before
is
said
.
The
other
two
blacke
orbes
,
marked
with
the
letters
D.
E.
are
those
which
carrie
the
Auges
,
&
therfore
are
called
the
deferents
of
the
Auges
,
which
be
two
seuerall
orbes
;
and
yet
to
auoid
Vacuum
,
doe
enclose
one
another
in
such
sort
,
as
the
slenderest
or
narrowest
part
of
the
vppermost
orbe
,
marked
with
the
letter
D.
doth
joine
close
to
the
thickest
or
fullest
part
of
the
nether
orbe
,
marked
with
the
letter
E.
and
the
slenderest
or
narrowest
part
of
the
nether
orbe
,
joyneth
close
to
the
thickest
or
fullest
part
of
the
vpper
orbe
:
and
these
two
orbes
do
contain
within
them
the
orbe
excentrique
,
or
deferent
of
the
Sunne
,
and
also
doe
make
the
whole
sphere
of
the
Sunne
to
be
concentrique
,
that
is
to
say
,
to
haue
all
one
centre
with
the
centre
of
the
world
:
and
yet
in
certaine
respects
,
these
two
orbes
are
also
excentrique
,
that
is
to
say
,
hauing
a
centre
distant
from
the
centre
of
the
world
:
for
the
concaue
superficies
of
the
vppermost
blacke
orbe
,
and
the
convexe
superficies
of
the
nethermost
blacke
orbe
,
beeing
seuerally
taken
,
haue
the
selfe
same
centre
which
the
deferent
of
the
Sunne
hath
,
which
is
the
centre
excentricke
,
marked
with
the
letter
B.
All
which
things
the
former
figure
doth
plainely
shew
.
Wherefore
was
the
deferent
of
the
Sunne
supposed
to
be
excentrique
?
FOr
three
principall
causes
.
First
,
for
that
the
moouing
of
the
Sunne
is
vnequall
,
now
slower
,
now
swifter
.
Secondly
,
for
that
the
bodie
of
the
Sunne
,
by
his
vnequall
distance
from
the
earth
,
seemeth
to
our
sight
somtime
greater
,
and
somtime
lesser
,
the
grossenesse
or
thinnesse
of
the
aire
being
no
cause
thereof
.
Thirdly
,
for
that
the
Sunne
being
in
this
or
that
part
of
the
Zodiake
,
the
eclipse
of
the
Moon
continueth
longer
or
shorter
time
,
so
as
she
abideth
vnder
the
shaddow
of
the
earth
more
one
time
than
another
.
All
which
things
are
salued
by
supposing
an
excentricke
.
Is
the
deferent
of
the
Sunne
,
and
the
circle
excentrique
,
one selfe
thing
?
NO
,
for
though
they
haue
both
one selfe
centre
,
called
the
centre
of
the
excentrique
,
yet
the
circle
excentricke
is
the
circumference
of
a
circle
imagined
to
be
in
the
middle
of
the
deferent
,
&
is
described
by
the
centre
of
the
Sunnes
body
,
deuiding
the
deferent
into
two
equal
parts
or
hemispheres
,
as
you
may
see
in
the
second
figure
next
following
.
The
second
Intention
sheweth
what
moouing
these
orbes
and
circles
before
mentioned
haue
,
and
vpon
what
poles
and
axletrees
they
are
turned
about
.
BEfore
I
come
to
the
declaration
therof
,
it
shall
be
necessary
to
set
downe
one
other
figure
,
containing
the
most
part
of
such
lines
,
points
,
centres
,
circles
,
semicircles
,
and
arches
,
as
doe
belong
to
the
Theorique
of
the
Sunne
,
and
to
shew
what
they
signifie
.
I
say
here
fore
the
most
part
,
because
both
these
&
all
the
rest
shall
be
more
fully
declared
,
when
wee
come
to
the
third
Intention
,
whose
office
is
to
shew
all
such
things
at
the
full
.
¶
The
second
figure
belonging
to
the
Theorique
of
the
Sunne
.
IN
this
figure
,
the
outermost
white
orbe
signifieth
the
Zodiake
,
in
which
are
described
the
characters
of
the
twelue
signes
.
And
the
next
white
orbe
within
that
,
is
the
deferent
of
the
Sunne
,
in
which
is
a
little
circle
,
representing
the
bodie
of
the
Sunne
,
whose
centre
is
marked
with
the
letter
H.
and
the
two
blacke
orbes
are
the
two
deferents
of
the
Auges
of
the
Sunne
before
described
;
and
in
the
middle
white
rundle
are
set
down
the
two
centres
before
described
,
that
is
,
the
centre
of
the
world
,
marked
with
the
letter
A.
and
the
centre
of
the
deferent
of
the
Sunne
marked
with
the
letter
B.
Moreouer
,
in
this
figure
are
drawne
certaine
right
lines
,
whereof
the
long
perpendiculer
line
passing
through
both
the
foresaid
centres
,
marked
with
the
letters
C.
D.
is
called
the
line
of
the
Auges
,
and
the
ouerthwart
line
passing
through
the
centre
of
the
world
to
the
Zodiake
,
marked
with
the
letters
E.
F.
signifieth
the
Axe
tree
of
the
Zodiake
,
whose
outermost
ends
are
the
poles
of
the
eclipticke
.
Then
there
is
another
ouerthwart
right
line
paralell
to
the
foresaid
line
E.
F.
which
passing
through
the
centre
excentrique
extendeth
vnto
the
deferent
of
the
Sunne
,
from
the
one
side
to
the
other
side
thereof
,
whose
outermost
ends
are
the
poles
of
the
said
deferent
,
marked
with
the
letters
K.
L.
Besides
these
three
lines
,
there
are
three
other
lines
,
whereof
that
which
passeth
from
the
centre
of
the
world
to
the
Zodiake
,
marked
with
the
letters
A.
G.
is
called
the
line
of
the
Sunnes
meane
mouing
.
Then
there
is
another
line
paralell
to
that
,
which
passeth
from
the
centre
of
the
deferent
to
the
centre
or
middest
of
the
Suns
bodie
,
marked
with
the
letters
B.
H.
And
the
third
line
passing
from
the
centre
of
the
world
through
the
midst
of
the
Sunnes
bodie
,
euen
to
the
Zodiake
,
is
called
the
line
of
the
Sunnes
true
mouing
,
marked
with
the
letters
A.
H.
I.
There
are
also
in
this
figure
certaine
portions
of
circles
called
arches
,
which
haue
their
proper
significations
,
as
the
arch
of
the
Zodiake
,
contained
betwixt
the
first
point
of
Aries
,
and
the
line
of
the
Auges
,
marked
with
the
letters
E.
C.
is
called
the
Auge
of
the
Sun
in
his
second
signification
,
and
the
arch
contayned
betwixt
E.
and
G.
is
called
the
meane
mouing
of
the
Sun
,
and
the
arch
contained
betwixt
E.
and
I.
is
called
the
true
mouing
of
the
Sunne
,
and
the
arch
contained
betwixt
G.
and
I.
is
called
the
equacion
of
the
Sunne
,
and
the
arch
contained
betwixt
the
line
of
the
meane
moouing
of
the
Sunne
,
and
the
line
of
the
Auges
marked
with
the
letters
C.
G.
is
called
of
some
Argumentum
,
and
of
some
Anomalia
,
that
is
,
the
inequalitie
of
the
Sunnes
moouing
.
All
which
arches
shall
be
more
fully
shewed
and
declared
in
the
third
figure
next
following
.
There
bee
also
in
this
figure
three
little
semicircles
,
whereof
the
two
,
marked
with
the
letters
K.
P.
and
L.
M.
doe
signifie
those
circles
which
the
poles
of
the
excentrique
doe
describe
by
the
mouing
of
the
two
deferents
of
the
Auges
;
and
the
third
semicircle
marked
with
the
letters
B.
N.
signifieth
that
circle
which
the
centre
of
the
excentrique
describeth
by
the
mouing
of
the
said
deferents
of
the
Auges
about
the
centre
of
the
world
,
the
semidiameters
of
all
which
circles
are
equall
.
Doth
the
Theorique
of
the
Sunne
onely
consist
of
the
three
orbes
about
mentioned
,
that
is
,
of
the
deferent
of
the
Sunne
,
and
of
the
two
deferents
of
the
Auges
?
THough
the
auncient
Astronomers
doe
appoint
no
more
but
those
three
,
yet
Copernicus
hauing
found
by
many
obseruations
made
by
himselfe
and
others
since
their
time
,
that
the
Auges
of
the
Sunne
doe
moue
vnequally
,
and
that
the
excentricitie
doth
alter
:
hee
therefore
to
salue
that
apparence
,
dooth
adde
another
orbe
called
the
excentor
of
the
excentrique
;
which
indeed
are
two
shaddowed
orbes
,
enclosing
one
another
like
as
the
two
blacke
orbes
doe
,
the
shape
whereof
you
may
see
plainely
expressed
in
the
sphere
of
Mercurie
,
hereafter
following
.
Now
shew
how
the
foresaid
three
orbes
are
mooued
,
and
first
how
the
excentrique
of
the
Sunne
is
moued
,
and
in
what
time
he
maketh
his
revolution
?
THe
excentrique
or
deferent
of
the
Sunne
is
regularly
moued
vpon
his
owne
centre
,
according
to
the
succession
of
the
signes
right
vnder
the
eclipticke
,
and
maketh
his
revolution
in
the
space
of
one
whole
yeare
,
that
is
in
365
dayes
,
and
almost
sixe
houres
,
and
by
the
revolution
of
this
orbe
is
described
or
limitted
the
Suns
yeare
.
And
you
haue
to
note
,
that
the
tables
of
Alphonsus
and
the
Prutenicall
tables
do
in
a
manner
agree
,
touching
the
daily
moouing
of
this
orbe
,
which
is
i/59
ii/8
iii/19
iiii/37
and
v.
24·
so
as
his
yearely
revolution
containeth
365
dayes
,
5.
houres
.
i/49
ii/15
iii/46
sauing
that
the
tables
of
Alphonsus
doe
faile
in
the
daily
mouing
,
v.
5·
and
thereby
in
the
yearely
revolution
doe
exceed
the
Prutenicall
tables
by
iii/13
and
so
much
is
the
equall
tropicall
yeare
,
according
to
Copernicus
,
counting
the
same
from
the
very
equinoctiall
point
:
but
the
daily
moouing
of
the
Sunne
beeing
counted
from
the
first
starre
of
the
Rams
horne
,
is
i/59
ii/8
iii/11
iiii/22
v.
10·
so
as
his
yearely
revolution
containeth
365
dayes
,
6
houres
,
i/9
and
ii/39
and
this
is
called
the
syderall
yeare
.
The
poles
of
this
orbe
doe
equally
obserue
the
poles
of
the
eclipticke
,
and
therfore
the
centre
of
the
Sunnes
bodie
doth
neuer
swarue
from
the
eclipticke
line
.
Why
doth
not
this
Orbe
also
cary
the
Sunne
equally
about
the
centre
of
the
world
?
BEcause
that
euery
circuler
moouing
that
is
equall
,
maketh
in
equall
time
in
his
circumference
both
equall
arches
and
also
equall
angles
,
vpon
the
centre
of
equacion
;
which
centre
in
this
Theorique
,
is
all
one
with
the
centre
of
the
excentrique
marked
with
B.
though
in
other
Planets
the
centre
of
equacion
is
a
seuerall
centre
by
it selfe
.
And
this
kind
of
mouing
is
only
regular
vpon
one
centre
,
and
not
vpon
many
or
diuerse
centres
,
as
you
may
perceiue
by
the
third
figure
next
following
:
in
which
figure
the
Sun
being
in
his
excentrique
,
and
turning
about
the
centre
B.
is
said
to
be
equall
,
for
whilst
he
descendeth
from
F.
to
H.
on
the
left
hand
of
the
figure
,
he
maketh
the
arch
of
his
excentrique
to
be
F.
H.
and
the
angle
to
be
F.
B.
H.
vpon
his
owne
centre
B.
which
is
an
obtuse
or
blunt
angle
:
but
vpon
the
centre
A.
he
maketh
a
lesser
angle
,
which
is
F.
A.
H.
for
that
is
a
right
angle
;
and
so
by
this
meanes
the
angle
F.
B.
H.
should
be
equall
to
the
angle
F.
A.
H.
that
is
to
say
,
the
greater
to
the
lesser
,
which
is
vnpossible
.
Wherefore
the
angles
made
vpon
A.
the
centre
of
the
world
,
are
not
equall
to
the
angles
made
vpon
the
centre
of
the
equall
mouing
,
marked
with
B.
and
therefore
the
mouing
of
the
Sunne
about
the
centre
of
the
world
,
appeareth
to
be
vnequall
,
sometime
slower
and
sometime
swifter
,
according
to
the
vnequal
arches
of
the
excentrique
,
subtending
equal
angles
in
the
centre
of
the
world
.
How
are
the
deferents
of
the
Auges
moued
?
THey
are
moued
about
the
centre
of
the
world
,
and
vpon
the
poles
of
the
Eclipticke
,
according
to
the
succession
of
the
signes
,
making
by
vertue
of
the
eight
sphere
,
one
revolution
togither
with
the
said
sphere
,
according
to
Alphonsus
,
in
49000
yeares
,
and
by
this
mouing
they
put
forward
the
Auge
of
the
excentrique
by
little
and
little
into
the
next
following
degrees
of
the
Eclipticke
,
and
by
reason
of
the
incredible
slownesse
of
these
orbes
in
their
mouing
,
the
Astronomers
doe
not
agree
in
the
quantitie
of
their
revolution
.
For
Ptolomey
thought
them
to
be
immoouable
,
and
the
followers
of
Alphonsus
thought
their
revolution
to
be
vnequall
,
and
to
be
made
in
49000
yeares
,
as
before
.
But
Copernicus
being
holpen
by
the
obseruations
of
many
ages
,
doth
shew
that
these
orbes
doe
passe
through
the
Zodiake
in
17108
Aegyptian
years
,
and
that
they
passe
through
the
orbe
of
the
fixed
stars
almost
in
50718
Aegyptian
years
;
and
that
the
other
orbe
called
the
excentor
of
the
excentor
,
which
he
himselfe
addeth
to
the
other
orbs
,
doth
make
his
revolution
vpon
his
owne
centre
,
which
is
the
centre
of
a
little
circle
,
contrarie
to
the
succession
of
the
signes
,
in
3434
Aegyptian
yeares
:
and
by
the
mouing
of
this
orbe
,
he
sheweth
that
the
true
Auge
of
the
Sun
creepeth
on
vnequally
,
&
that
the
excentricitie
doth
alter
and
change
.
The
dimension
or
measure
of
the
Sunnes
sphere
.
THe
greatest
excentricitie
of
the
Sunne
,
according
to
the
demonstrations
of
Copernicus
,
contayneth
two
degrees
,
i/50
and
ii/7
such
like
parts
or
degrees
I
say
,
as
the
semidiameter
B.
F.
of
the
excentrique
containeth
sixtie
degrees
.
And
the
least
excentricitie
containeth
but
one
such
part
,
i/55
and
ii/53
And
by
the
demonstrations
of
the
said
Copernicus
,
the
foresaid
semidiameter
B.
F.
dooth
containe
1142
semidiameters
of
the
earth
.
And
A.
B.
in
his
greatest
excentricitie
containeth
almost
48
semidiameters
of
the
earth
.
And
the
said
A.
B.
in
his
least
excentricitie
containeth
almost
37
semidiameters
of
the
earth
,
so
as
when
the
excentricitie
was
greatest
,
and
that
the
Sunne
was
in
his
Auge
,
according
to
the
line
A.
F.
set
downe
in
the
third
next
figure
,
hee
was
then
distant
from
the
centre
of
the
earth
1190
semidiameters
of
the
earth
,
which
distance
Ptolomey
thought
to
be
1210
semidiameters
of
the
earth
.
And
when
the
Sun
was
in
the
point
opposit
to
the
Auge
,
he
was
then
distant
from
the
centre
of
the
earth
,
according
to
the
line
A.
G.
set
down
in
the
said
third
figure
,
1094
semidiameters
of
the
earth
.
But
when
the
excentricitie
is
least
,
as
it
is
in
this
our
age
,
then
the
Sunne
being
in
his
Auge
,
is
distant
from
the
centre
of
the
earth
1179
semidiameters
of
the
earth
,
but
in
these
dayes
the
point
opposit
to
the
Auge
,
approcheth
not
so
nigh
to
the
earth
,
as
it
hath
done
in
times
past
,
for
his
distance
now
contayneth
1105
semidiameters
of
the
earth
,
which
is
further
off
than
the
former
distance
was
,
by
eleuen
semidiameters
of
the
earth
.
And
you
haue
to
note
,
that
one
semidiameter
of
the
earth
contayneth
3436
Italian
myles
,
and
8/21·
of
a
myle
.
The
third
Intention
,
shewing
what
points
,
lines
,
and
arches
are
necessarie
to
be
knowne
touching
the
Theorique
of
the
Sunne
.
THough
I
haue
heretofore
partly
described
such
things
in
the
first
and
second
figures
,
yet
I
mind
once
againe
to
declare
the
same
againe
according
to
Mestlyn
,
who
describeth
euery
thing
,
and
setteth
downe
a
third
figure
,
expressing
the
same
in
such
order
as
followeth
.
Seeing
the
mouing
of
the
Sun
,
by
reason
of
the
orbe
excentrique
,
is
vnequall
,
and
that
the
true
mouing
doth
differ
from
the
meane
mouing
,
for
that
cause
it
is
necessary
to
know
what
the
point
Auge
and
his
opposit
point
is
,
and
their
moouing
:
Also
which
are
the
lines
of
the
meane
mouing
and
true
moouing
of
the
Sun
,
and
what
is
the
yearely
inequalitie
of
such
mouing
,
called
of
Alphonsus
,
argumentum
,
and
what
the
meane
mouing
and
true
moouing
of
the
Sunne
is
,
and
finally
,
what
the
Equacion
is
.
What
is
the
mouing
of
the
point
Auge
,
and
of
his
opposite
point
?
IT
is
an
arch
of
the
Eclipticke
,
contayned
betwixt
the
beginning
of
Aries
,
and
the
line
of
the
Auges
,
which
arch
is
called
of
Purbachius
and
others
the
Auge
of
the
Sunne
,
in
his
second
signification
:
for
Auge
in
the
first
signification
,
is
only
a
point
before
described
in
both
the
former
figures
.
¶
The
third
figure
belonging
to
the
Theorique
of
the
Sunne
.
ALl
the
circles
of
this
figure
are
like
in
signification
to
the
circles
before
set
downe
in
the
second
figure
,
and
in
this
figure
betwixt
the
letter
E.
signifying
here
the
beginning
of
Aries
,
and
the
letter
C.
signifying
the
point
Auge
,
is
contained
the
arch
E.
C.
limitting
the
moouing
of
the
point
Auge
,
counting
from
the
beginning
of
Aries
:
but
Ptolomey
found
in
his
time
,
that
the
said
point
was
in
the
fift
degree
i/30
of
Gemini
,
which
point
in
these
dayes
,
according
to
Copernicus
his
calculation
,
is
almost
in
the
ninth
degree
of
Cancer
.
The
maintainers
of
Alphonsus
his
tables
haue
ouer
boldly
,
as
well
here
as
els
where
,
swarued
from
Ptolomey
:
in
affirming
the
Auge
of
the
Sunne
to
haue
been
in
his
time
contrarie
to
his
owne
obseruations
,
in
the
13
degree
i/30
of
Gemini
,
so
as
in
these
dayes
that
point
ought
to
be
in
the
first
degree
of
Cancer
:
to
whom
no
credite
in
this
matter
is
to
be
giuen
,
because
it
is
contrary
to
all
the
moderne
obseruations
.
What
is
the
line
of
the
meane
mouing
of
the
Sunne
?
IT
is
a
right
line
drawne
from
the
centre
of
the
world
to
the
Eclipticke
,
and
equally
distant
from
another
line
drawne
from
the
centre
of
the
excentrique
to
the
centre
or
middest
of
the
Sunne
,
which
other
line
in
the
Theoriques
of
the
other
Planets
ought
to
be
drawn
from
the
centre
of
equacion
:
but
because
in
the
Theorique
of
the
Sunne
the
centre
of
the
excentrique
,
and
that
of
the
equacion
is
all
one
,
the
one
therefore
may
be
indifferently
taken
for
the
other
:
and
this
line
of
the
meane
moouing
is
marked
in
the
third
figure
with
the
letters
A.
I.
being
paralell
to
the
line
B.
K.
What
is
the
line
of
the
true
mouing
of
the
Sunne
?
IT
is
a
right
line
drawne
from
the
centre
of
the
world
,
through
the
centre
of
the
Sunne
to
the
very
ecliptick
,
represented
here
in
the
third
figure
by
the
letters
A.
K.
What
is
the
arch
of
the
meane
moouing
of
the
Sunne
,
and
also
what
is
the
arch
of
his
true
mouing
?
THe
arch
of
his
mean
mouing
is
an
arch
of
the
eclipticke
contained
betwixt
the
first
point
of
Aries
,
marked
with
the
letter
E.
and
the
line
of
the
mean
mouing
before
described
,
and
this
arch
is
marked
with
the
letters
E.
F.
And
the
arch
of
the
true
mouing
of
the
Sunne
,
is
an
arch
of
the
Eclipticke
,
contained
betwixt
the
beginning
of
Aries
,
and
the
line
of
the
true
moouing
of
the
Sunne
,
which
arch
is
marked
with
the
letters
E.
K.
And
both
these
arches
are
alwayes
to
be
counted
from
the
equinoctiall
point
,
according
to
the
succession
of
the
signes
.
Copernicus
maketh
two
kinds
of
this
true
moouing
of
the
Sunne
,
that
is
,
simple
,
and
compound
,
counting
the
simple
mouing
from
the
first
starte
of
the
Rams
horne
,
as
from
a
beginning
which
is
vnmouable
:
but
he
counteth
the
compound
mouing
from
the
beginning
of
the
vernall
equinoxe
,
which
is
mouable
.
What
is
the
yearely
Anomalia
or
Inequalitie
of
the
Sunnes
mouing
?
IT
is
an
arch
of
the
Eclipticke
,
contained
betwixt
the
line
of
the
Auges
and
the
line
of
the
Suns
moouing
,
according
to
the
succession
of
the
signes
,
and
this
Inequalitie
is
twofold
,
that
is
,
meane
and
true
:
the
meane
,
is
that
which
endeth
at
the
line
of
the
meane
moouing
,
and
is
marked
with
the
letters
C.
I.
And
the
true
Inequalitie
is
that
which
endeth
at
the
line
of
the
true
mouing
of
the
Sunne
,
and
is
marked
with
the
letters
C.
K.
And
this
yearely
Inequalitie
is
called
the
Inequalitie
or
Anomalie
of
the
excentrique
:
but
the
followers
of
Alphonsus
doe
call
it
Argumentum
Solis
.
What
is
the
equacion
of
the
Sunnes
mouing
?
THat
is
an
arch
of
the
Eclipticke
,
contained
betwixt
the
line
of
the
true
moouing
,
and
the
line
of
the
meane
mouing
of
the
Sunne
,
marked
in
the
third
figure
with
the
letters
I.
K.
and
this
arch
doth
make
with
the
centre
of
the
world
the
angle
K.
A.
I.
equall
to
the
angle
A.
H.
B
:
Which
angle
the
line
of
the
true
mouing
together
,
with
the
line
drawne
from
the
centre
of
the
excentrique
to
the
centre
of
the
Sunne
,
dooth
comprehend
.
And
you
haue
to
note
,
that
when
the
Sunne
is
either
in
his
Auge
,
or
in
the
opposite
point
thereof
,
then
there
is
no
such
arch
at
all
,
by
reason
that
the
two
foresaid
lines
of
the
true
and
meane
moouing
doe
at
that
time
meet
and
concurre
in
one
,
making
one selfe
line
,
but
the
said
arch
is
greatest
when
the
Sun
is
in
his
meane
longitude
,
hereafter
defined
.
When
the
Sunne
therefore
descendeth
from
his
Auge
towards
the
point
opposite
of
the
Auge
,
this
arch
to
shew
his
true
place
,
taketh
away
the
equacion
from
the
meane
moouing
.
But
when
the
Sunne
ascendeth
from
the
opposit
point
towards
the
Auge
,
then
this
arch
addeth
so
much
to
the
meane
mouing
.
Wherefore
sith
this
arch
doth
encrease
towards
the
meane
longitude
,
and
going
againe
from
thence
,
is
deminished
;
it
falleth
out
,
that
the
moouing
of
the
Sun
,
which
is
equall
in
his
owne
excentrique
,
appeareth
in
the
centre
of
the
world
to
be
vnequall
,
and
to
be
most
slow
,
the
Sunne
being
in
his
Auge
:
and
the
more
that
he
descendeth
from
thence
,
his
moouing
waxeth
by
little
and
little
the
swifter
.
But
it
is
equall
to
the
meane
mouing
,
when
the
Sunne
is
in
the
meane
longitude
,
but
if
he
be
in
the
point
opposite
to
the
Auge
,
then
his
mouing
is
most
swift
,
and
it
obserueth
the
same
course
,
though
by
a
contrarie
way
,
that
is
,
by
decreasing
,
whilst
the
Sun
ascendeth
from
the
opposit
point
of
the
Auge
towards
the
Auge
.
What
call
you
the
meane
longitude
?
THe
meane
longitude
may
be
taken
two
manner
of
wayes
.
For
first
the
point
of
the
orbe
excentrique
,
in
which
his
equacion
is
greatest
,
is
called
the
meane
longitude
,
of
which
points
there
bee
in
the
excentrique
,
two
:
and
that
meane
longitude
is
bounded
in
the
third
figure
with
the
right
line
A.
H.
K.
which
line
maketh
right
angles
with
the
line
of
the
Auge
in
the
centre
A.
and
in
that
place
is
found
the
angle
A.
H.
B.
or
the
arch
marked
in
the
said
figure
with
the
letters
I.
K.
on
the
left
hand
of
the
figure
,
which
is
the
equacion
in
the
greatest
excentricitie
of
the
Sunne
,
and
that
is
two
degrees
,
i/323
ii/24
but
in
the
least
excentricitie
the
equacion
is
no
more
than
one
degree
,
i/55
ii/41
Secondly
,
the
meane
longitude
is
a
point
of
the
excentrique
,
in
which
the
Sunne
or
any
other
Planet
hath
a
meane
distance
from
the
centre
of
the
world
,
that
is
to
say
,
it
is
in
the
middest
betwixt
the
greatest
and
least
distance
.
For
this
word
longitude
is
generally
taken
for
the
distance
of
any
Planet
from
the
earth
,
which
distance
is
greatest
,
when
the
Planet
is
in
his
Auge
,
and
is
least
when
he
is
in
the
opposite
point
of
the
Auge
:
so
likewise
the
meane
longitude
is
taken
for
that
distance
which
exceedeth
the
least
so
much
as
it
is
exceeded
of
the
greatest
,
and
is
equall
to
the
semidiameter
of
the
excentrique
.
Here
now
should
follow
the
fourth
Intention
,
shewing
the
mou●ng
of
the
Sunne
,
according
to
latitude
:
which
fourth
Intention
,
in
this
Theorique
onely
hath
no
place
,
for
the
Sunne
neuer
swarueth
one
jot
from
the
Eclipticke
line
,
and
therefore
that
line
is
called
the
way
of
the
Sunne
,
by
which
line
all
the
latitudes
and
wanderings
of
the
other
Planets
are
to
be
measured
and
examined
.
And
thus
I
end
with
the
Theorique
of
the
Sunne
.
¶
The
Theorique
of
the
Moone
.
Why
doe
you
deale
with
the
Moone
next
after
the
Sunne
,
sith
she
is
the
lowest
Planet
of
all
?
FOr
three
causes
.
First
,
for
that
the
Moone
though
she
hath
some
more
varietie
in
her
moouing
than
the
Sunne
,
yet
her
Theorique
is
not
so
intricate
as
those
of
the
rest
of
the
Planets
.
Secondly
,
sith
the
Sunne
giueth
light
to
the
world
by
day
,
describing
the
yeares
and
dayes
,
it
is
meet
therfore
,
that
the
Theorique
of
the
Moone
,
which
giueth
light
in
the
night
,
and
describeth
the
months
of
the
year
,
should
follow
next
after
that
of
the
Sunne
.
Thirdly
,
because
all
the
auncient
Astronomers
treating
of
the
Planets
,
doe
place
the
Theorique
of
the
Moone
next
vnto
the
Sunne
,
whom
it
becommeth
vs
very
well
to
follow
therein
.
The
first
Intention
,
shewing
of
how
many
orbes
the
Theorique
of
the
Moone
consisteth
.
IT
consisteth
of
these
fiue
,
whereof
the
first
is
the
Excentrique
,
carrying
the
Epicicle
:
Then
the
two
deferents
of
the
Auges
:
and
the
fourth
is
the
Epicicle
,
carying
the
bodie
of
the
Moone
:
(
but
both
Copernicus
and
Maginus
do
appoint
to
the
Moone
,
two
Epicicles
,
that
is
,
the
first
and
second
Epicicle
,
as
shall
bee
declared
and
demonstrated
hereafter
in
my
extract
out
of
Maginu●
his
Theoriques
:
)
and
the
fift
is
the
Orbe
equant
,
enuironing
all
the
rest
of
the
Orbs.
All
which
Orbs
you
may
see
plainely
set
downe
in
the
figure
next
following
,
and
also
the
two
Centres
,
the
one
of
the
world
,
&
the
other
of
the
excentrique
,
by
helpe
of
eight
letters
,
set
downe
also
in
the
said
figure
,
that
is
,
A.
B.
C.
D.
E.
F.
G.
H.
¶
The
first
figure
belonging
to
the
Theorique
of
the
Moone
.
IN
this
figure
the
letter
A.
signifieth
the
centre
of
the
world
.
And
B.
the
centre
of
the
excentrique
:
which
centre
,
in
going
about
the
centre
of
the
world
,
describeth
a
little
circle
marked
with
the
letters
B.
H.
And
C.
signifieth
the
orbe
excentrique
,
whose
middle
line
being
described
by
the
centre
of
the
Epicicle
,
is
specially
to
be
obserued
in
demonstrating
the
motion
of
the
Moone
.
D.
signifieth
the
vpper
deferent
of
the
Auges
.
E.
signifieth
the
nether
deferent
of
the
Auges
.
F.
signifieth
the
Epicicle
,
whereunto
the
body
of
the
Moone
is
fixed
.
G.
signifieth
the
orbe
equant
,
which
is
the
outermost
white
orbe
,
and
is
otherwise
called
the
circle
or
deferent
of
the
two
nods
or
sections
,
signifying
the
head
and
taile
of
the
Dragon
.
Why
do
the
Astronomers
appoint
vnto
the
Theorique
of
the
Moone
an
orbe
excentrique
?
BEcause
the
equacions
of
the
Epicicle
which
the
excentrique
carrieth
,
are
obserued
to
bee
somewhere
greater
,
and
somewhere
lesser
,
as
shall
be
declared
hereafter
in
the
fift
Figure
belonging
to
the
Theorique
of
the
Moone
.
And
this
apparence
is
to
be
salued
by
supposing
an
excentrique
.
Wherfore
are
the
deferents
of
the
Auges
added
to
the
Theorique
of
the
Moone
?
FOr
the
selfesame
causes
which
are
before
set
downe
in
the
Theorique
of
the
Sunne
.
Why
is
the
Epicicle
supposed
to
bee
needfull
in
this
Theorique
?
FOr
two
causes
:
First
,
because
the
Moone
hath
another
inequalitie
in
her
mouing
,
whereunto
one
onely
excentrique
cannot
supplie
:
for
in
like
and
selfe-same
places
the
motion
of
the
Moone
is
found
to
bee
sometime
swifter
,
and
sometime
flower
.
Secondly
,
because
the
Moone
(
other
things
beeing
like
)
is
obserued
to
be
sometime
higher
from
the
earth
,
and
sometime
lower
,
which
is
to
be
seene
as
well
by
the
apparant
magnitude
of
her
bodie
,
as
also
by
the
continuance
and
quantitie
of
her
Eclipses
.
Why
was
it
needfull
to
adde
to
this
Theorique
the
Orbe
equant
?
FOr
two
causes
:
First
,
that
the
varieties
of
the
Moons
latitude
might
be
salued
thereby
.
Secondly
,
that
the
mouing
of
the
excentrique
,
which
is
found
to
be
irregular
about
his
owne
centre
,
might
be
equated
or
made
equall
by
the
centre
of
this
circle
,
being
as
it
were
the
very
point
of
equacion
,
and
thereof
it
is
called
the
circle
equant
.
Wherefore
is
this
circle
made
to
enuiron
all
the
rest
of
the
orbes
?
THough
as
touching
the
demonstration
of
the
moouings
,
it
maketh
no
great
matter
whether
this
orbe
be
without
or
within
the
rest
of
the
orbes
,
yet
sith
that
by
carrying
about
the
nodes
and
limits
of
the
two
latitudes
of
the
sphere
of
the
Moone
,
and
that
by
this
motion
the
whole
composition
of
the
Moones
sphere
doth
alter
:
it
is
more
meet
that
this
orbe
should
compasse
in
all
the
rest
,
than
to
be
compassed
of
them
.
For
it
is
more
likely
,
that
the
inferiour
orbe
is
mooued
and
turned
about
of
his
superior
,
than
the
superior
of
the
inferior
.
The
second
Intention
,
shewing
towards
what
part
such
orbes
are
moued
,
and
in
what
time
such
orbes
make
their
revolutions
,
and
also
vpon
what
centres
or
poles
they
make
their
regular
mouings
:
and
first
,
how
and
in
what
manner
the
excentrique
of
the
Moone
,
carrying
the
Epicicle
,
is
mooued
.
THe
excentrique
of
the
Moone
is
equally
mooued
about
the
centre
of
the
world
,
according
to
the
succession
of
the
signes
,
and
about
his
owne
poles
,
which
are
distant
on
both
sides
from
the
poles
of
the
Eclipticke
fiue
degrees
,
making
his
revolution
in
the
space
of
one
moneth
,
and
by
this
moouing
it
carrieth
about
the
centre
of
the
Epicicle
equally
through
the
Zodiake
.
And
the
daily
moouing
of
this
excentrique
,
or
of
the
centre
of
the
Epicicle
vnder
the
Zodiake
,
is
13
degrees
,
i/10
ii/35
iii/1
iiii/7
v.
22·
so
as
his
whole
reuolution
is
made
in
27
dayes
,
seuen
houres
,
i/43
ii/5
iii/8
and
so
much
is
the
perodicall
moneth
,
which
is
otherwise
called
of
Iohn
de
Sacro
Busto
the
moneth
of
peragration
,
whereof
I
haue
spoken
in
my
Treatise
of
the
sphere
,
in
the
46
chapter
of
the
first
booke
thereof
.
What
followeth
of
this
inequalitie
of
the
excentrique
?
TWo
things
.
First
,
sith
that
the
Astronomers
by
often
obseruation
haue
found
,
that
the
orbe
excentrick
or
centre
of
the
Epicicle
dooth
equally
turne
about
the
centre
of
the
world
,
it
must
needs
follow
,
that
the
moouing
of
the
said
excentrique
is
vnequall
,
as
well
about
his
owne
centre
,
as
about
any
other
point
,
cleane
contrarie
to
that
which
hath
been
said
touching
the
moouing
of
the
excentrique
,
or
deferent
of
the
Sunne
.
Secondly
,
the
mouing
of
this
excentrique
is
swifter
,
when
the
centre
of
the
epicicle
is
in
the
vpper
part
,
nigh
vnto
the
Auge
;
for
a
greater
portion
thereof
doth
belong
to
the
equall
arches
of
the
Zodiake
,
when
shee
is
nigh
to
the
Auge
,
than
when
she
is
nigh
to
the
opposit
point
of
the
Auge
.
Which
things
doe
plainely
appeare
in
the
third
and
last
figure
belonging
to
the
Theorique
of
the
Sunne
before
described
.
In
which
figure
suppose
the
letters
F.
H.
G.
to
represent
the
excentrique
of
the
Moone
,
whose
moouing
because
it
is
equall
about
the
centre
A.
must
needs
be
vnequall
about
the
centre
B.
Moreouer
,
because
the
medieties
or
halfes
of
the
Zodiake
,
deuided
by
the
right
line
E.
A.
H.
K.
are
turned
about
in
equall
time
,
so
as
the
greater
portion
of
the
excentrique
is
answerable
to
the
vpper
halfe
,
&
the
lesser
portion
to
the
nether
halfe
,
it
easily
appeareth
,
that
the
centre
of
the
Epicicle
maketh
in
his
mouing
a
greater
bent
or
bowt
vpward
,
and
a
lesser
downeward
,
that
is
to
say
,
it
goeth
faster
being
in
the
vpper
halfe
,
than
when
it
is
in
the
nether
halfe
.
How
are
the
deferents
of
the
Auges
of
the
Moone
moued
?
THey
are
equally
moued
,
contrarie
to
the
succession
of
the
signes
about
the
centre
of
the
world
,
&
about
the
same
poles
that
the
excentrique
is
,
and
doe
make
their
revolution
almost
in
32
dayes
.
And
by
this
moouing
they
carry
about
the
point
Auge
,
or
the
whole
line
of
the
Auge
,
equally
through
the
Zodiake
,
contrarie
to
the
succession
of
the
signes
.
And
they
also
cause
the
centre
of
the
excentrique
to
describe
a
little
circle
about
the
centre
of
the
world
,
whose
semidiameter
is
equall
to
the
excentricitie
,
which
little
circle
you
may
see
in
the
first
figure
of
the
Moones
Theorique
,
marked
with
the
letters
B.
H
enuironning
the
centre
of
the
Zodiake
,
marked
with
the
letter
A.
And
the
daily
moouing
of
these
deferents
of
the
Auge
,
contrarie
to
the
succession
of
the
signes
is
eleuen
degrees
,
i/12
ii/18
iii/21
iiii/52
v.
33·
making
one
whole
revolution
in
32
dayes
,
three
houres
,
i/4
ii/38
iii●°
How
and
in
what
manner
is
the
Epicicle
m●ued
or
turned
about
?
THis
Epicicle
beeing
placed
in
the
excentrique
,
and
eleuated
aboue
the
centre
of
the
Zodiake
,
is
moued
in
the
vpper
part
of
the
excentrique
,
contrarie
to
the
succession
of
the
signes
,
and
in
the
nether
part
of
the
said
excentrique
,
according
to
the
succession
of
the
signs
vpon
his
proper
axletree
,
standing
perpendicularly
vpon
the
plane
of
the
excentrique
,
and
being
moued
equally
from
the
meane
Auge
,
maketh
his
revolution
in
27
daies
and
almost
in
13
houres
,
by
which
mouing
the
bodie
of
the
Moone
is
carried
round
about
the
centre
of
the
Epicicle
.
And
the
daily
moouing
of
this
Epicicle
from
the
meane
Auge
,
is
13
degrees
,
i/3
ii/53
iii/56
iiii/23
v/58·
so
as
it
maketh
his
whole
revolution
in
27
dayes
,
13
houres
,
i/18
ii/34
iii/52
But
for
the
better
vnderstanding
of
the
motion
of
the
Epicicle
,
you
haue
to
note
,
that
there
bee
three
speciall
points
belonging
to
the
Epicicle
,
that
is
,
the
meane
Auge
,
the
true
Auge
,
and
the
Touch-point
,
otherwise
called
the
point
of
concauitie
.
How
are
these
three
points
described
?
THe
meane
Auge
is
described
by
a
right
line
,
which
being
drawn
from
that
point
in
the
little
circle
,
which
is
opposite
to
the
centre
of
the
excentrique
,
passeth
through
the
centre
of
the
Epicicle
,
euen
to
the
circumference
thereof
,
marked
in
the
figure
next
following
with
the
letter
M.
The
true
Auge
of
the
Epicicle
is
described
by
a
right
line
,
which
being
drawne
from
the
centre
of
the
world
,
passeth
also
through
the
centre
of
the
Epicicle
,
euen
to
the
circumference
thereof
,
and
is
marked
with
the
letter
V.
The
point
of
concauitie
or
Touch-point
is
described
by
a
right
line
,
which
beeing
drawne
from
the
centre
of
the
excentrique
,
passeth
also
through
the
centre
of
the
Epicicle
,
euen
to
the
circumference
thereof
,
marked
in
the
figure
following
with
the
letter
P.
which
point
is
called
the
point
of
concauitie
,
because
you
must
imagine
,
that
in
the
plane
of
the
excentrique
there
is
a
certaine
concauitie
,
wherein
the
plane
superficies
of
the
Epicicle
is
turned
about
,
which
concauitie
of
it selfe
is
immouable
,
because
it
is
moued
onely
according
vnto
the
motion
of
the
excentrique
:
to
the
plane
of
which
excentrique
,
if
you
attribute
so
much
thicknesse
or
deapth
towards
the
centre
therof
,
as
is
the
diameter
of
the
Epicicle
,
it
must
needs
fall
out
,
that
the
circumference
of
the
Epicicle
will
touch
the
concaue
superficies
of
the
vpper
deferent
of
the
Auges
in
one
onely
point
.
And
therfore
this
point
of
the
Epicicle
may
be
as
well
called
the
Touch-point
,
as
the
point
of
concauitie
:
and
this
point
is
said
to
be
immoouable
,
because
it
neuer
changeth
his
place
,
as
the
other
two
points
,
that
is
,
the
meane
and
true
Auge
of
the
Epicicle
doe
;
which
are
sometime
more
or
lesse
distant
one
from
another
,
the
centre
of
the
Epicicle
being
out
of
the
line
of
the
Auge
of
the
excentrique
;
for
being
in
that
line
,
those
three
point
are
vnited
,
and
doe
meet
all
three
in
one
.
And
the
differing
distance
of
the
meane
and
true
Ange
of
the
Epicicle
,
in
any
place
out
of
the
foresaid
line
,
is
alwaies
to
be
measured
by
the
Touch-point
,
because
it
is
immouable
,
&
not
wandring
as
the
other
two
points
are
,
as
you
shall
more
plainely
perceiue
by
the
figure
next
following
,
and
by
that
which
shall
be
said
hereafter
.
¶
The
second
figure
belonging
to
the
Theorique
of
the
Moone
.
THe
outermost
circle
in
this
figure
signifieth
the
Zodiake
,
whose
centre
is
marked
with
the
letter
A.
and
the
next
inner
great
circle
signifieth
the
excentrique
of
the
Moone
,
whose
centre
is
marked
with
the
letter
B.
which
centre
by
going
about
the
centre
A.
describeth
the
little
circle
B.
C.
which
point
C.
is
the
opposite
point
to
B.
And
the
fiue
little
circles
placed
seuerally
vpon
the
excentrique
,
doe
signifie
euery
where
the
Epicicle
of
the
Moone
,
whose
centres
are
marked
with
these
fiue
letters
,
D.
E.
F.
G.
H.
Again
the
right
lines
,
marked
with
the
letters
B.
P.
passing
through
the
centres
of
all
the
fiue
Epicicles
doe
shew
in
the
circumference
of
the
said
Epicicles
,
the
point
of
concauitie
,
otherwise
called
the
touch
point
,
marked
with
the
letter
P.
And
the
right
lines
,
marked
with
A.
V.
do
shew
the
true
Auge
of
the
Epicicle
,
marked
with
the
letter
V.
and
the
right
lines
,
marked
with
the
letter
C.
M.
doe
shew
the
meane
Auge
of
the
Epicicle
,
marked
with
the
letter
M.
What
conclusions
are
to
be
gathered
out
of
this
Inequalitie
of
the
Epicicle
?
THese
foure
here
following
.
1
First
,
for
so
much
as
it
is
found
by
obseruation
,
that
the
motion
of
the
meane
Auge
of
the
Epicicle
,
marked
with
the
letter
M.
is
regular
and
equall
,
going
euery
day
13
degrees
and
almost
i/4
it
must
needs
follow
that
the
motion
of
the
other
two
points
,
that
is
,
the
true
Auge
of
the
Epicicle
,
marked
with
the
letter
V.
and
the
touch
point
marked
with
P.
is
irregular
and
vnequall
,
because
the
meane
Auge
of
the
Epicicle
is
a
vagarant
point
,
so
called
,
because
it
keepeth
not
alwaies
one
certaine
place
in
the
Epicicle
,
and
yet
is
the
beginning
of
the
motion
of
the
Epicicle
.
2
Secondly
,
if
the
centre
of
the
Epicicle
be
in
the
Auge
or
opposit
Auge
of
the
excentrique
,
then
these
three
points
,
that
is
,
the
Touch-point
,
the
true
Auge
,
and
the
meane
Auge
of
the
Epicicle
be
all
one
,
that
is
to
say
,
doe
concurre
or
meet
all
in
one selfe
line
.
But
if
the
centre
of
the
Epicicle
be
out
of
any
of
the
said
points
,
viz.
out
of
the
Auge
or
opposite
Auge
of
the
excentrique
,
then
they
are
so
seperated
,
as
the
true
Auge
of
the
Epicicle
marked
with
the
letter
V.
is
in
the
middest
betwixt
the
meane
Auge
,
marked
with
M
,
and
the
Touch-point
marked
with
P
,
because
the
centre
of
the
world
is
alwayes
in
the
middest
betwixt
the
centre
of
the
excentrique
and
the
point
C
,
which
point
C
in
the
little
circle
,
is
opposite
to
the
centre
of
the
said
excentrique
,
marked
with
B.
And
the
greatest
distance
of
these
points
is
beneath
the
meane
longitudes
of
the
Excentrique
.
What
those
meane
longitudes
are
,
shall
bee
declared
hereafter
.
3
Thirdly
,
in
that
halfe
of
the
excentrique
,
which
descendeth
from
the
Auge
of
the
said
excentrique
vnto
the
opposite
Auge
of
the
same
,
the
two
Auges
of
the
Epicicle
,
both
true
and
meane
,
marked
with
the
letters
V
and
M
,
doe
goe
before
the
Touch●point
,
in
respect
of
the
motion
of
the
Epicicle
,
which
is
contrarie
to
the
succession
of
the
signes
.
But
in
respect
of
the
motion
of
the
excentrique
,
which
is
alwayes
according
to
the
succession
of
the
signes
,
the
two
points
M
and
V
doe
follow
the
Touch-point
P
,
as
you
may
easily
perceiue
by
the
former
figure
last
set
downe
:
for
the
centre
of
the
Epicicle
being
in
the
Auge
of
the
excentrique
,
marked
with
D
,
or
in
the
opposite
Auge
of
the
same
,
marked
with
G
,
the
three
foresaid
points
are
all
joyned
together
in
one selfe
line
.
But
when
the
Epicicle
descendeth
from
D
to
E
,
then
P
V
and
M
are
seperated
,
and
P
goeth
before
V
and
M
:
and
the
letter
V
being
the
true
Auge
of
the
Epicicle
,
is
in
the
middest
betwixt
P
and
M.
And
such
digression
or
seperation
is
encrased
by
little
and
littl●
vntill
the
centre
of
the
Epicicle
doe
come
to
the
letter
F
,
for
from
thence
they
begin
againe
to
approch
and
to
grow
nigher
together
,
vntill
they
fall
into
the
point
G
,
whereas
they
joyne
againe
,
and
are
all
one
.
But
the
contrarie
happeneth
when
those
points
are
in
the
other
ascending
halfe
of
the
excentrique
,
for
then
M
and
V
doe
goe
before
P
,
proceeding
according
to
the
succession
of
the
signes
.
4
Fourthly
,
the
mouing
of
the
Epicicle
is
swifter
in
the
vpper
part
of
the
excentrique
,
than
in
the
nether
part
thereof
,
for
there
the
meane
Auge
of
the
Epicicle
proceedeth
contrarie
to
the
succession
of
the
●ignes
,
that
is
to
say
,
towards
that
part
into
the
which
the
Epicicle
is
moued
:
but
the
contrarie
happeneth
in
the
lower
part
of
the
excentrique
.
And
you
haue
to
note
,
that
the
Touch-point
P
is
the
measure
of
the
digression
or
seperation
of
both
the
Auges
of
the
Epicicle
,
as
well
true
as
meane
,
because
the
Touch-point
doth
at
no
time
wander
from
his
place
but
remaineth
immoouable
.
The
demonstration
of
this
fourth
conclusion
is
plainly
set
foorth
in
the
former
second
figure
of
the
Moone
,
whereby
you
may
perceiue
,
that
when
the
Epicicle
is
come
to
the
letter
H
,
nigh
vnto
the
meane
longitude
of
the
Excentrique
,
whereas
the
distance
of
the
foresaid
points
M
V
and
P
is
alwayes
greatest
;
then
immediatly
both
the
Auges
,
M
and
V
,
begin
againe
to
approch
vnto
the
Touch-point
P
,
wherefore
M
proceedeth
towards
P
,
contrarie
to
the
succession
of
the
signes
,
vntill
it
meeteth
with
P
in
the
Auge
of
the
excentrique
,
marked
with
the
letter
D.
And
from
thence
M
departeth
againe
from
P
,
contrarie
to
the
succession
of
the
signes
,
vntill
it
arriueth
to
the
other
meane
longitude
of
the
excentrique
,
whereas
it
is
furthest
distant
from
P.
And
by
reason
that
the
Epicicle
is
also
moued
into
that
part
,
it
falleth
out
,
that
the
two
moouings
meeting
in
one selfe
part
,
the
mouing
of
the
Moone
in
the
Epicicle
,
or
rather
the
Epicicle
it selfe
by
following
the
wandering
meane
Auge
,
is
swifter
in
his
gate
.
But
contrariwise
,
in
the
nether
part
of
the
excentrique
,
from
the
place
nigh
vnto
F
(
whereas
the
distance
of
M
P
is
greatest
)
vnto
the
other
place
of
the
greatest
distance
of
the
said
points
nigh
vnto
H
,
the
meane
Auge
of
the
Epicicle
is
mooued
according
to
the
succession
of
the
signs
:
and
there
,
according
to
the
quantitie
of
his
moouing
,
it
taketh
so
much
away
from
the
swiftnesse
of
the
Epicicle
,
as
thereby
the
Epicicle
in
that
place
is
much
more
slower
in
his
gate
.
How
is
the
circle
equant
of
the
Moon
moued
,
which
is
otherwise
called
the
circle
of
the
two
nodes
or
intersections
,
signifying
the
head
and
taile
of
the
Dragon
?
THis
circle
is
equally
moued
,
contrary
to
the
succession
of
the
signs
,
about
the
centre
and
poles
of
the
Eclipticke
,
making
his
revolution
almost
in
19
yeares
:
and
by
the
mouing
of
this
circle
,
the
poles
of
the
deferents
of
the
Auge
are
carried
about
the
poles
of
the
ecliptick
:
and
the
daily
mouing
of
this
orbe
vnder
the
eclipticke
,
is
but
i/3
ii/10
iii/38
iiii/23
and
v.
24·
so
as
it
maketh
his
whole
reuolution
in
6798
daies
,
that
is
to
say
,
in
18
Aegyptian
years
,
228
dayes
,
3
houres
,
i/49
ii/40
and
iii/16
of
an
houre
.
How
is
the
moouing
or
departing
of
the
Moone
from
these
Intersections
called
?
IT
is
called
the
moouing
,
or
rather
the
Anomalie
of
the
Moones
latitude
:
and
the
Moon
,
or
rather
the
centre
of
her
Epicicle
,
maketh
one
returne
to
these
Intersections
in
27
dayes
and
5
houres
,
for
in
that
time
the
Moone
accomplisheth
all
the
varieties
and
changes
of
her
latitude
both
North
and
South
,
and
in
one
day
she
is
seperated
from
these
Intersections
13
d●grees
,
i/1
ii/45
iii/39
iiii/30
and
v/46·
and
maketh
her
returne
to
the
said
Intersections
in
27
dayes
,
5
houres
,
and
ii/36
of
an
houre
.
You
said
before
that
the
motions
of
all
the
other
Planets
were
gouerned
by
the
Sunne
:
Tell
therfore
,
in
what
mouing
of
any
Orbe
belonging
to
the
sphere
of
the
Moone
,
there
appeareth
any
harmonie
or
agreement
of
the
Moone
with
the
Sunne
.
THeir
harmonie
consisteth
in
the
mouing
of
the
deferents
of
the
Auge
of
the
Moone
,
and
in
those
things
which
depend
of
those
deferents
.
For
the
deferents
of
the
Moone
Auge
doe
keepe
such
proportion
with
the
excentrique
of
the
Moone
,
as
looke
how
much
the
line
of
her
meane
mouing
by
the
mouing
of
the
excentrick
is
moued
forward
from
the
line
of
the
meane
mouing
of
the
Sunne
,
according
to
the
succession
of
the
signs
,
beginning
at
the
conjuction
or
opposition
of
the
said
lines
of
the
meane
mouing
,
as
well
of
the
Sunne
as
of
the
Moone
:
so
much
do
those
deferents
carry
backward
the
Auge
of
the
excentrique
from
the
same
line
of
the
meane
mouing
of
the
Sunne
,
contrary
to
the
succession
of
the
signes
,
as
you
shall
more
easily
perceiue
by
this
figure
or
instrument
next
following
,
vsed
by
Reinholdus
in
his
Commentaries
made
vpon
the
Theoriqes
of
Purbachius
,
the
description
and
vse
whereof
here
followeth
.
¶
The
third
figure
belonging
to
the
Theorique
of
the
Moone
.
THis
figure
consisteth
of
certaine
Orbes
and
Circles
,
whereof
some
are
moouable
,
and
some
immouable
.
The
first
lowest
and
greatest
immouable
circle
being
deuided
into
180
parts
,
euery
one
containing
two
degrees
,
which
maketh
in
all
360
degrees
,
signifieth
the
Zodiake
.
And
the
limbe
of
this
circle
is
deuided
into
two
spaces
,
in
the
outermost
whereof
are
set
downe
the
caracters
of
the
twelue
signes
:
and
in
the
innermost
space
are
first
set
down
aboue
on
the
left
hand
nine
little
starres
,
each
one
representing
the
body
of
the
Sunne
,
And
right
vnder
them
are
set
downe
the
first
fiue
aspects
:
the
first
whereof
standing
right
vnder
the
letter
A
,
signifieth
the
Conjunction
of
the
Sunne
and
Moon
,
marked
thus
☌
.
and
next
to
that
on
the
left
hand
,
is
the
Sextile
aspect
,
marked
thus
⚹
.
and
then
the
Quadrat
aspect
,
marked
thus
□
.
and
next
to
that
the
Trine
aspect
marked
thus
△
.
and
then
the
Opposition
,
marked
thus
☍
.
and
these
are
called
the
first
aspects
,
because
they
go
before
the
Full
of
the
Moone
:
and
then
followeth
againe
the
Trine
aspect
,
the
Quadrat
,
the
Sextile
aspect
,
and
the
Conjunction
,
which
are
called
the
second
aspects
,
because
they
chaunce
after
the
Full.
And
the
first
Conjunction
is
placed
right
vnder
the
letter
A
,
which
standing
in
the
very
top
of
the
figure
in
the
outermost
space
of
the
limbe
,
signifieth
the
beginning
of
Aries
.
Moreouer
,
in
the
innermost
space
of
the
limbe
are
set
downe
these
letters
,
viz.
BRCQDPEOFNGMH
,
which
letters
doe
serue
to
shew
the
motion
as
well
of
the
Excentrique
,
as
of
the
Auge
of
the
Moone
.
And
next
to
the
foresaid
Zodiake
are
placed
2
mouable
black
orbes
,
which
are
the
deferents
of
the
Moons
Auge
,
&
opposit
Auge
,
signified
by
the
2
little
tapes
fastened
to
the
vppermost
black
orbe
;
whereof
the
one
tape
is
marked
with
the
letter
X
,
signifying
the
Moons
Auge
,
&
the
other
tape
being
vnmarked
,
signifieth
hir
opposit
Auge
.
Next
betwixt
the
said
two
blacke
orbes
,
is
a
mouable
white
orbe
,
signifying
the
excentrique
or
deferent
of
the
Moones
Epicicle
,
to
which
is
put
a
little
tape
to
shew
the
place
of
the
centre
of
the
Epicicle
,
which
centre
is
marked
with
the
letter
Y
,
and
in
the
circumference
of
the
said
Epicicle
is
fixed
the
body
of
the
Moon
.
And
within
the
Orbe
excentrique
is
another
immoouable
white
orbe
or
roundell
,
the
centre
whereof
is
the
centre
of
the
world
,
marked
with
the
letter
T
,
about
which
is
a
little
circle
described
by
the
centre
of
the
excentrique
of
the
Moone
,
by
turning
round
about
the
centre
of
the
world
,
which
centre
of
the
excentrique
is
marked
with
the
letter
S
,
and
the
opposite
point
to
that
,
is
marked
with
the
letter
V
,
and
the
circumference
of
the
said
little
circle
is
deuided
into
nine
equall
parts
,
marked
with
Arithmeticall
figures
,
as
1.
2.
3.
and
so
forth
to
nine
,
to
shew
the
place
of
the
centre
of
the
excentrique
,
marked
with
S
,
in
euery
aspect
.
For
the
centre
of
the
Moones
Epicicle
being
in
conjunction
with
the
Sunne
,
the
centre
S
is
found
to
be
in
the
vpper
point
of
the
little
circle
,
marked
with
the
figure
1
,
and
being
in
the
first
Sextile
aspect
,
the
centre
S
is
in
the
point
marked
with
the
figure
2
,
and
so
proceedeth
from
point
to
point
,
according
to
the
order
of
the
nine
aspects
,
before
set
downe
.
The
vse
of
this
Figure
or
Instrument
is
plainely
shewed
by
this
one
example
here
following
.
SVppose
therefore
the
Conjunction
of
the
Sun
and
Moone
to
be
vnder
the
letter
A.
wherfore
you
must
place
in
one selfe
line
both
the
Auge
of
the
excentrique
,
marked
with
the
letter
X
,
and
also
the
centre
of
the
Epicicle
,
marked
with
the
letter
Y
,
right
vnder
the
letter
A.
And
because
the
centre
of
the
Epicicle
dooth
mooue
towards
the
left
hand
,
according
to
the
succession
of
the
signes
,
and
that
the
Auge
of
the
Moone
doth
moue
towards
the
right
hand
,
contrary
to
the
succession
of
the
signes
,
you
must
bring
the
centre
Y
to
the
letter
B
,
for
there
will
his
place
be
within
foure
dayes
next
after
the
Conjunction
,
and
there
hauing
staied
the
centre
Y
,
turn
the
Auge
X
towards
the
right
hand
,
euen
to
the
letter
M
,
&
stay
it
there
,
so
shall
you
find
the
midde
bodie
of
the
Sun
,
who
then
followeth
the
Moone
,
to
be
in
the
middest
betwixt
the
two
letters
B
and
M
,
right
ouer
the
Sextile
aspect
;
and
at
that
time
the
Moon
is
said
to
be
in
a
Sextile
aspect
to
the
Sunne
,
for
then
she
is
nigh
to
the
meane
longitudes
,
signified
here
in
this
figure
by
a
white
right
line
,
alwayes
crossing
the
line
of
the
Auges
(
which
is
also
white
)
in
the
centre
of
the
world
with
right
angles
,
and
the
shape
of
the
Moones
light
is
then
horned
,
like
a
sycle
,
called
in
Greeke
Minoides
,
and
in
Latine
Falcata
.
But
at
the
seuenth
day
after
the
Conjunction
,
her
light
will
encrease
somewhat
more
,
wherefore
by
turning
the
centre
Y
to
the
letter
C
,
and
the
Auge
X
to
the
letter
N
,
you
shall
find
the
centre
of
the
Sunne
to
be
in
the
very
midst
betwixt
those
two
letters
,
right
ouer
the
Quadrat
aspect
,
and
the
Moon
to
be
right
in
the
opposit
Auge
,
and
thereby
to
be
in
a
Quadrat
aspect
to
the
Sunne
,
at
which
time
the
shape
of
her
light
is
said
to
be
halfed
,
which
may
be
called
the
halfe
Moone
,
in
Greeke
Diochotomos
,
and
in
Latine
Dimidia
or
Dimidiata
.
But
the
eleuenth
day
after
the
Conjunction
,
she
will
seeme
round
bodied
,
though
not
at
the
full
:
wherfore
you
must
bring
the
centre
Y
to
the
letter
D
,
and
the
Auge
X
to
the
letter
O
,
so
shall
you
find
the
centre
of
the
Sunne
to
be
in
the
middest
betwixt
those
two
letters
,
right
ouer
the
marke
of
the
Trine
aspect
;
for
then
the
Moone
being
againe
in
the
mean
longitude
,
is
said
to
be
in
a
Trine
aspect
to
the
Sunne
,
and
the
shape
of
her
light
is
round
like
a
bowle
,
and
may
be
called
the
whole
Moon
,
though
not
the
full
Moone
,
and
in
Greeke
it
is
called
A●●phichyrtos
,
in
Latine
Vtrinque
gibbosa
.
Againe
,
when
the
Moone
is
fifteene
dayes
old
,
then
bring
both
the
centre
Y
,
and
also
the
Auge
X
to
the
letter
E
,
for
then
you
shall
find
the
Sunne
to
be
right
ouer
the
marke
of
Opposition
,
so
as
the
Moone
is
then
opposite
to
the
Sunne
,
and
then
she
is
at
the
full
,
called
in
Latine
Pleni
Lunium
,
and
in
Greeke
Panselmos
.
But
the
nineteenth
day
of
her
age
the
centre
Y
will
be
in
the
letter
F
,
and
the
Auge
X
in
the
letter
H
,
and
then
the
Moon
is
the
third
time
in
the
mean
longitude
,
and
then
she
is
againe
in
a
Trine
aspect
to
the
Sunne
,
as
she
was
before
at
the
eleuenth
of
her
age
.
And
when
the
Moone
is
two
and
twentie
dayes
old
,
then
the
centre
Y
shall
bee
in
G
,
and
the
Auge
X
in
Q
,
and
then
the
Moone
shall
be
again
in
a
Quadrat
aspect
to
the
Sunne
,
as
she
was
before
when
she
was
seuen
dayes
old
.
And
when
she
is
sixe
and
twentie
dayes
old
,
then
the
centre
Y
shall
bee
in
H
,
and
the
Auge
X
in
R
,
and
then
the
Moone
being
the
fourth
time
in
the
meane
longitude
,
shall
be
in
a
Sextile
aspect
,
as
she
was
before
,
being
but
foure
dayes
old
.
And
when
she
shall
be
thirtie
dayes
old
,
then
the
centre
Y
and
the
Auge
X
shall
meet
together
vnder
A
,
and
so
the
Moone
shall
be
againe
in
Conjunction
with
the
Sunne
.
All
which
things
are
breefely
set
downe
by
Reinholdus
in
this
Table
following
,
consisting
of
seuen
Collums
:
In
the
first
whereof
are
set
down
the
dayes
of
the
Moones
age
during
her
encrease
,
that
is
to
say
,
from
the
Conjunction
to
the
full
,
containing
fifteene
dayes
,
descending
downeward
:
in
the
second
Collum
are
set
the
first
fiue
Aspects
:
and
in
the
third
Collum
the
places
or
points
of
the
Excentrique
.
In
the
fourth
Collum
the
names
of
the
Moones
diuers
shapes
of
lights
,
seruing
as
well
to
her
encrease
as
decrease
.
In
the
fift
Collum
are
set
again
the
places
of
the
Excentrique
.
In
the
sixt
Collum
the
second
Aspects
,
like
to
the
first
.
And
in
the
last
Collum
,
the
dayes
of
the
Moones
age
after
the
full
,
during
her
decrease
or
wane
,
that
is
,
from
15
to
30
,
ascending
vpward
.
The
Table
followeth
in
the
next
Page
.
A
TABLE
SHEWING
THE
DIVERS
SHAPES
OF
THE
MOONE
.
1.
|
2.
|
3.
|
4.
|
5.
|
6.
|
7.
|
The
daies
or
age
of
the
Moone
.
|
The
first
fiue
Aspects
of
the
Moon
.
|
The
places
of
the
Excentrique
|
The
diuers
shapes
and
names
of
the
lights
of
the
Moon
|
The
places
of
the
Excentrique
.
|
The
second
fiue
Aspects
of
the
Moone
.
|
The
dates
.
|
1.
|
☌
|
In
the
Auge
.
|
Coniunctio
,
the
new
Moone
.
|
In
the
Auge
.
|
☌
|
30.
|
4.
|
⚹
.
|
In
the
mean
longitude
of
the
Excentrique
.
|
Falcata
,
the
horned
Moone
.
|
In
the
mean
longitude
of
the
Excentrique
.
|
⚹
.
|
26.
|
7.
|
□
.
|
In
the
opposit
Auge
.
|
Demidiata
,
the
halfe
Moon
.
|
In
the
opposit
Auge
.
|
□
.
|
22.
|
11.
|
△
.
|
In
the
mean
longitude
of
the
Excentrique
.
|
Vtrinquegihbosa
,
almost
round
.
|
In
the
mean
longitude
of
the
Excentrique
.
|
△
.
|
19.
|
15.
|
☍
.
|
In
the
Auge
.
|
Pleni
lunium
,
the
full
Moone
.
|
In
the
Auge
.
|
☍
.
|
15.
|
How
is
this
digression
or
departing
of
the
Moone
from
the
Sunne
,
called
?
IT
is
commonly
called
the
longitude
or
mouing
of
the
Moone
from
the
Sunne
:
and
the
Moone
returneth
again
to
the
Sunne
,
or
rather
ouertaketh
him
in
29
daies
and
one
halfe
day
,
in
which
time
she
accomplisheth
all
her
diuers
illuminations
or
shapes
of
light
,
that
is
to
say
,
she
sustaineth
all
her
aspects
to
the
Sunne
,
and
sheweth
to
the
earth
all
the
diuersities
of
her
lights
and
apparances
.
And
this
month
is
called
the
month
sinodicall
:
for
there
are
two
kinds
of
Lunar
months
,
the
one
periodicall
,
in
which
she
goeth
through
the
whole
Zodiake
,
and
the
other
sinodicall
,
in
which
she
ouertaketh
the
Sunne
;
which
Sacrobust●
calleth
the
moneth
of
Consecution
,
who
maketh
foure
Lunar
moneths
,
that
is
,
the
moneth
of
Peragration
,
the
moneth
of
Apparition
,
the
moneth
Medicinall
,
and
the
moneth
of
Consecution
,
which
are
all
declared
in
the
sixe
and
fortieth
Chapter
of
my
first
booke
of
the
Sphere
.
And
you
haue
to
vnderstand
,
that
the
dayly
moouing
of
the
Moone
from
the
Sunne
,
contayneth
12
degrees
,
i/11
ii/26
iii/41
iiii/29
v58·
and
the
sinodicall
moneth
consisteth
of
29
dayes
,
12
houres
,
i/44
ii/3
iii/11
What
conclusions
doe
accompanie
this
harmonie
of
the
Sun
and
Moone
?
THese
foure
here
following
.
First
,
in
euery
meane
Conjunction
or
Opposition
of
the
Sunne
and
Moone
(
which
meane
Conjunction
or
Opposition
is
said
to
bee
when
the
centre
of
the
Moones
Epicicle
is
either
in
Conjuction
or
in
Opposition
to
the
centre
of
the
Sunne
)
the
centre
of
the
Epicicle
is
found
to
be
in
the
Auge
of
the
Excentrique
,
but
in
euery
Quadrat
aspect
the
centre
of
the
Epicicle
is
in
the
opposit
Auge
of
the
Excentrique
.
Secondly
,
by
this
means
,
in
euery
Conjuction
and
Opposition
,
as
well
the
Excentrique
as
the
Epicicle
,
are
most
swift
in
their
motions
;
but
in
the
quarters
they
are
slowest
,
because
their
Anomalie
or
Inequalitie
is
thereby
altered
,
as
hath
been
said
a
little
before
.
Thirdly
,
the
Moone
in
one
sinodicall
month
passeth
twice
through
the
orbe
Excentrique
.
Fourthly
,
the
centre
of
her
Epicicle
in
one
●inodicall
moneth
describeth
about
the
centre
of
the
world
a
certain
Ovale
figure
,
like
to
this
here
following
:
¶
The
fourth
figure
belonging
to
the
Theorique
of
the
Moone
.
IN
which
Figure
,
the
letter
A
signifieth
the
centre
of
the
world
,
or
of
the
whole
sphere
of
the
Moon
,
and
therfore
at
the
new
Moon
the
centre
of
the
excentrique
is
in
B
,
which
centre
B
,
by
turning
round
about
the
centre
A
,
describeth
a
little
circle
in
the
middest
of
this
figure
,
marked
with
the
letters
DFNKMOR
:
and
the
foure
little
circles
placed
vpon
the
Ovale
circle
,
doe
signifie
the
Epicicle
of
the
Moone
,
the
foure
centres
whereof
are
marked
with
these
foure
letters
,
CIPE
:
and
the
letter
C
signifieth
here
also
the
Auge
of
the
excentrique
,
and
so
doth
the
letter
P
,
but
the
letters
IE
do
each
of
them
signifie
the
opposit
point
of
the
Auge
.
Moreouer
,
the
line
AC
signifieth
here
the
line
of
the
mean
mouing
of
the
Sun
,
from
which
line
when
the
centre
B
departeth
towards
the
right
hand
,
and
commeth
to
the
point
D
,
which
is
in
the
little
circle
,
then
the
centre
of
the
Epicicle
marked
with
C
,
descendeth
on
the
left
hand
to
the
point
E
,
which
is
in
the
Ovale
circle
,
and
then
the
angles
BAD
,
and
BAE
are
equall
through
the
equalitie
of
their
mouings
.
Likewise
,
when
the
centre
of
the
excentrique
commeth
to
the
point
in
the
little
circle
,
marked
with
F
,
the
centre
of
the
Epicicle
is
in
the
point
G.
And
when
the
centre
of
the
excentrique
falleth
into
the
point
H
,
and
there
hath
described
a
quarter
of
the
little
circle
,
then
the
centre
of
the
Epicicle
hath
likewise
made
a
quarter
of
the
Zodiake
,
which
is
90
degrees
,
counting
from
the
line
of
the
meane
mouing
of
the
Sunne
,
wherof
such
distance
of
the
Moone
from
the
Sunne
is
called
a
quarter
,
and
is
found
to
be
in
the
point
1
,
being
then
in
the
opposit
Auge
of
the
excentrique
,
and
so
the
Moone
giueth
light
with
halfe
her
bodie
,
and
is
then
nighest
to
the
earth
.
Againe
,
when
the
centre
of
the
excentrique
commeth
downe
into
K
,
then
the
centre
of
the
Epicicle
departing
from
the
earth
,
commeth
to
the
point
L
:
and
when
the
centre
of
the
excentrique
commeth
to
the
point
M
,
then
the
centre
of
the
Epicicle
is
in
the
point
N.
Lastly
,
when
the
centre
of
the
excentrique
falleth
into
O
,
the
centre
of
the
Epicicle
shall
be
in
P
,
so
as
OP
shall
be
both
in
one
right
line
,
and
thereby
the
centre
of
the
Epicicle
and
the
centre
of
the
excentrique
shall
bee
distant
from
the
Sunne
halfe
a
circle
,
which
is
a
hundred
and
eightie
degrees
,
and
then
the
Moone
shining
with
her
whole
bodie
,
is
opposite
to
the
Sun
.
And
looke
what
course
the
Epicicle
hath
kept
in
the
first
half
of
the
Ovale
circle
during
the
Moones
encrease
,
the
like
course
it
obserueth
in
the
other
halfe
of
the
said
circle
,
whilest
the
Moone
decreaseth
.
How
are
the
Orbes
belonging
to
the
sphere
of
the
Moone
,
to
be
measured
?
AS
the
line
of
the
Auge
marked
with
the
letters
AC
,
or
AP
,
in
the
former
fourth
figure
,
contayneth
60
degrees
or
parts
,
euen
so
the
opposit
Auge
,
marked
with
the
letters
AI
,
or
AQ
,
contayneth
according
to
Ptolomey
of
the
like
degrees
or
parts
,
39
degrees
and
i/22
and
the
semidiameter
of
the
excentrique
,
containeth
49
degrees
,
i/41
and
the
excentricitie
AB
contayneth
10
degrees
,
i/19
and
the
semidiameter
of
the
Epicicle
contayneth
5
degrees
,
i/13
But
if
the
degrees
be
such
,
as
the
semidiameter
of
the
earth
containeth
but
one
degree
or
one
part
thereof
,
then
he
prooueth
by
demonstration
,
that
the
line
of
the
Auge
contayneth
but
59
such
degrees
;
and
the
line
of
the
opposite
Auge
to
contain
no
more
but
38
degrees
and
i/43
and
the
semidiameter
of
the
excentrique
to
containe
48
degrees
,
i/51
ii/30
and
the
excentricitie
to
containe
10
degrees
,
i●●°
ii/30
and
the
semidiameter
of
the
Epicicle
to
containe
5
degrees
,
i/10
And
hereof
it
commeth
to
passe
,
that
the
altitudes
of
the
Moone
are
measured
by
the
semidiameters
of
the
earth
.
For
the
greatest
altitude
of
the
new
of
full
Moon
,
being
then
in
the
Auge
of
the
excentrique
,
is
64
degrees
,
i/10
and
her
least
altitude
when
she
is
in
the
said
Ange
,
is
53
degrees
,
i/50
but
the
greatest
altitude
of
the
Moon
,
being
in
the
beginning
of
any
of
her
quarters
,
and
in
the
opposite
Auge
of
the
excentrique
,
is
43
degrees
,
i/53
and
her
least
altitude
is
then
33
degrees
,
i●●°
of
the
semidiameter
of
the
earth
,
whereof
euery
such
part
is
equall
to
the
semidiameter
of
the
earth
.
And
note
,
that
by
the
altitude
of
the
Moone
is
meant
here
a
right
line
,
extending
from
the
centre
of
the
earth
to
the
centre
of
the
Moone
,
in
what
part
of
heauen
soeuer
she
be
.
But
Copernicus
correcting
these
things
,
in
his
suppositions
or
perticular
propositions
,
prooueth
the
greatest
altitude
of
the
Moone
,
being
either
new
or
full
,
to
containe
65
degrees
,
i●0·
and
her
least
altitude
to
containe
55
degrees
,
i/8
and
being
in
the
beginning
of
any
of
her
quarters
,
her
greatest
altitude
to
containe
68
degrees
,
i/20
and
her
least
altitude
to
containe
52
degrees
,
i/17
Such
degrees
,
I
say
,
whereof
the
semidiameter
of
the
earth
is
but
one
.
The
third
Intention
,
shewing
what
points
,
lines
,
and
arches
are
requisit
to
be
knowne
in
the
Theorique
of
the
Moone
,
which
are
these
here
following
.
-
1.
THe
line
of
the
meane
,
and
also
the
line
of
the
true
mouing
of
the
Moone
.
-
2.
The
meane
and
true
mouing
of
the
Moone
.
-
3.
The
longitude
or
distance
of
the
Moone
from
the
Sunne
.
-
4.
The
doubled
longitude
or
centre
.
-
5.
The
centre
of
the
equalitie
.
-
6.
The
Auge
and
opposit
Auge
of
the
excentrique
.
-
7.
The
Auge
and
opposit
Auge
,
both
meane
and
true
,
and
also
the
Touch-point
,
or
point
of
Concauitie
,
all
three
belonging
to
the
Epicicle
of
the
Moone
.
-
8.
The
Equacion
of
the
Centre
.
-
9.
The
argument
equall
or
meane
.
-
10.
The
argument
equated
.
-
11.
The
Equacion
of
the
Epicicle
.
-
12.
The
diuersitie
of
the
Diameter
.
-
13.
The
proportionall
minutes
:
and
to
these
may
be
added
the
Intersections
,
called
the
head
and
taile
of
the
Dragon
.
Also
the
North
and
South
limit
,
and
the
meane
and
true
mouing
of
the
same
.
And
finally
,
the
meane
&
true
Anomalie
or
Inequalitie
of
the
Moons
latitude
.
What
is
the
line
of
the
meane
mouing
of
the
Moone
?
IT
is
a
right
line
,
which
being
drawne
from
the
centre
of
the
world
,
passeth
through
the
centre
of
the
Epicicle
euen
to
the
Zodiake
.
And
this
line
by
meanes
of
the
regular
moouing
of
the
excentrique
vpon
the
centre
of
the
world
,
is
equally
carried
through
the
Zodiake
,
shewing
the
meane
place
of
the
Moone
,
and
therewith
the
true
place
of
the
centre
of
the
Epicicle
:
which
line
in
the
sixt
figure
hereafter
following
,
is
represented
by
the
letters
M
B
,
which
line
passeth
through
the
centre
of
euery
one
of
the
foure
Epicicles
set
downe
in
the
said
sixt
figure
.
And
this
line
in
the
Theorique
of
the
Sunne
is
threefold
,
whereof
one
proceedeth
from
the
centre
of
the
excentrique
to
the
bodie
of
the
Sunne
,
the
second
.
line
being
equally
distant
from
the
first
,
proceedeth
from
the
centre
of
the
world
to
the
Zodiake
.
The
third
line
proceeding
also
from
the
centre
of
the
world
,
passeth
through
the
bodie
of
the
Sunne
to
the
Zodiake
.
All
which
three
lines
are
before
plainely
set
downe
in
the
second
figure
belonging
to
the
Theorique
of
the
Sun
.
And
these
three
lines
in
this
Theorique
of
the
Moone
,
by
reason
that
the
centre
of
equalitie
,
and
the
centre
of
the
world
is
here
all
one
,
they
doe
make
but
one selfe
line
.
What
is
the
line
of
the
true
mouing
of
the
Moone
?
IT
is
a
right
line
,
which
being
drawne
from
the
centre
of
the
world
,
passeth
through
the
midde
body
of
the
Moone
,
euen
to
the
Zodiake
,
which
the
letters
M
F
C
in
the
sixt
figure
following
doe
shew
.
What
is
the
meane
and
true
mouing
of
the
Moone
?
THe
meane
moouing
of
the
Moone
is
an
arch
of
the
Zodiake
,
which
extendeth
from
the
beginning
of
Aries
,
according
to
the
succession
of
the
signes
,
vnto
the
line
of
the
meane
moouing
of
the
Moone
.
And
the
true
moouing
of
the
Moone
is
an
arch
of
the
Zodiake
,
extending
in
like
manner
from
Aries
to
the
line
of
the
true
moouing
of
the
Moone
.
¶
The
fifth
figure
belonging
to
the
Theorique
of
the
Moone
.
THis
figure
is
vsed
by
Mestelyn
to
shew
the
armonie
of
the
Sunne
and
Moone
,
which
is
alreadie
more
plainely
demonstrated
by
Reinholdus
his
figure
before
set
downe
,
and
it
is
the
third
figure
belonging
to
the
Theorique
of
the
Moon
.
And
the
outermost
circle
of
this
fift
figure
signifieth
the
Zodiake
,
diuided
into
360
degrees
,
and
the
next
greater
circle
is
the
excentrique
of
the
Moone
,
which
carrieth
the
Epicicle
,
whose
centre
is
marked
with
the
letter
F.
And
A
is
the
centre
of
the
Zodiake
:
and
B
is
the
centre
of
the
excentrique
,
which
by
turning
about
the
centre
A
,
describeth
the
little
circle
in
the
middest
of
the
Figure
,
and
the
line
A
F
is
the
line
of
the
meane
mouing
of
the
Moone
,
being
in
G
,
and
the
line
A
B
D
is
the
line
of
the
Moones
Auge
,
or
of
her
excentrique
,
being
in
E
,
and
the
line
A
C
is
the
line
of
the
meane
moouing
of
the
Sunne
,
who
vnlesse
the
Moone
and
he
be
in
Conjunction
or
Opposition
,
is
alwayes
in
the
middest
betwixt
the
Auge
of
the
Moone
,
and
the
centre
of
her
Epicicle
,
as
is
more
plainly
declared
before
in
the
third
figure
.
And
therfore
I
haue
set
down
this
fift
figure
here
,
only
to
shew
the
longitude
&
double
longitude
of
the
Moone
,
and
the
equacion
of
the
centre
,
as
followeth
.
What
is
the
longitude
of
the
Moone
from
the
Sunne
?
IT
is
an
arch
of
the
Zodiake
,
proceeding
according
to
the
succession
of
the
signes
from
the
line
of
the
Suns
meane
mouing
,
to
the
line
of
the
Moones
meane
moouing
,
which
the
arch
C
G
in
the
former
fifth
figure
dooth
shew
.
What
is
the
double
longitude
or
centre
of
the
Moone
?
IT
is
an
arch
of
the
Zodiake
,
proceeding
according
to
the
succession
of
the
signes
,
from
the
Auge
of
the
excentrique
vnto
the
line
of
the
Moones
meane
mouing
,
represented
in
the
former
fift
figure
by
the
letters
E
C
G
,
and
is
called
the
double
longitude
,
because
it
is
double
so
much
as
is
the
distance
of
the
Moone
from
the
Sun
,
represented
in
the
said
figure
by
the
letters
C
G
,
as
you
may
easily
trie
with
your
Compas
.
Alphonsus
and
his
followers
doe
call
it
the
centre
of
the
Moone
,
because
it
dependeth
vpon
the
Auge
of
the
excentrique
,
and
is
answerable
to
that
arch
,
which
in
the
Theorique
of
the
Sunne
is
called
the
yearely
Inequalitie
or
Argument
of
the
Sunne
,
which
is
twofold
,
that
is
,
meane
and
true
,
represented
in
the
third
figure
of
the
Sunnes
Theorique
by
the
letters
C
I
and
C
K.
And
this
double
longitude
is
called
of
Coperni●us
,
Motus
secundi
Epicicli
,
the
moouing
of
the
second
Epicicle
;
which
second
,
and
also
the
first
Epicicle
,
shall
be
declared
hereafter
in
the
eleuenth
chapter
of
my
extract
out
of
Maginus
.
What
is
the
Equacion
of
the
Centre
,
or
of
the
Excentrique
?
IT
is
an
arch
of
the
Epicicle
,
contained
betwixt
the
meane
and
true
Auge
of
the
said
Epicicle
,
represented
in
the
said
fift
figure
of
the
Moone
,
by
the
letters
M
N
:
and
whensoeuer
the
centre
of
the
Epicicle
is
either
in
the
Auge
or
opposite
Auge
of
the
Excentrique
,
then
this
arch
is
no
arch
at
all
.
But
if
the
centre
of
the
Epicicle
be
out
of
those
two
points
,
and
is
found
to
be
in
that
halfe
of
the
Excentrique
which
descendeth
from
the
Auge
towards
the
opposite
point
thereof
,
then
it
addeth
to
the
Inequalitie
of
the
Epicicle
hereafter
defined
,
some
portion
:
but
in
the
other
halfe
it
taketh
so
much
away
from
the
Inequalitie
of
the
Epicicle
,
for
there
the
meane
Auge
of
the
Epicicle
goeth
backward
from
the
true
Auge
thereof
,
contrarie
to
the
succession
of
the
signs
,
towards
that
part
into
which
the
Epicicle
tendeth
;
but
in
the
first
halfe
it
is
cleane
contrarie
.
And
note
,
that
according
to
the
tables
of
Alphonsus
and
of
Ptolomey
,
the
greatest
equacion
of
the
centre
or
excentrique
containeth
13
degrees
,
i/9
but
according
to
the
Prutenicall
Tables
,
it
containeth
no
more
but
●2
degrees
,
i/27
the
difference
whereof
springeth
of
the
diuersitie
of
their
suppositions
.
What
is
the
Anomalia
or
Inequalitie
of
the
Epicicle
,
both
meane
and
true
?
THe
meane
Inequalitie
of
the
Epicicle
,
is
an
Arch
of
the
Epicicle
,
contayned
betwixt
the
meane
Auge
of
the
Epicicle
and
the
midde
bodie
of
the
Moone
,
counted
towards
that
part
whereunto
the
Epicicle
is
moued
:
But
the
true
Inequalitie
is
an
arch
contained
betwixt
the
true
Auge
of
the
Epicicle
,
and
the
midde
bodie
of
the
Moone
.
This
Inequalitie
is
called
of
Ptolomey
,
Anomalia
,
of
Alphonsus
,
Argumentum
;
and
of
Copernicus
,
motus
primi
Epicicli
.
What
is
the
equacion
of
the
Epicicle
,
called
of
Alphonsus
,
Equatio
Argumenti
?
IT
is
an
arch
of
the
Zodiake
,
contained
betwixt
the
line
of
the
meane
mouing
and
the
line
of
the
true
mouing
of
the
Epicicle
.
And
this
arch
is
none
at
all
,
when
the
Moone
is
in
the
true
Auge
,
or
in
the
true
opposit
Auge
of
the
Epicicle
.
And
whilest
the
Moon
passeth
through
the
first
halfe
of
the
Epicicle
,
this
equacion
maketh
the
true
mouing
of
the
Moone
lesser
than
her
meane
moouing
,
and
in
the
other
halfe
of
the
Epicicle
it
maketh
her
true
mouing
greater
than
her
meane
mouing
.
And
this
equacion
of
the
Epicicle
may
be
sometime
greater
,
and
sometime
lesser
,
according
as
the
centre
of
the
Epicicle
is
more
or
lesse
distant
from
the
Auge
of
the
excentrick
,
but
it
is
said
to
be
greatest
when
the
centre
of
the
Epicicle
is
in
the
opposit
Auge
of
the
excentrique
,
and
to
be
least
when
the
centre
of
the
Epicicle
is
in
the
Auge
of
the
said
excentrique
.
But
to
vnderstand
this
and
many
other
things
belonging
to
this
equacion
,
it
shall
be
necessarie
to
set
downe
this
sixt
figure
here
following
,
and
appertaining
to
the
Theorique
of
the
Moone
.
¶
The
sixt
figure
belonging
to
the
Theorique
of
the
Moone
.
THis
figure
as
you
see
consisteth
of
certaine
circles
both
greater
and
lesser
,
and
of
certaine
lines
and
points
,
marked
with
certaine
letters
to
shew
what
they
signifie
.
You
haue
then
to
vnderstand
,
that
the
greatest
and
outermost
circle
of
this
figure
signifieth
the
Zodiake
,
whose
centre
is
marked
with
the
letter
M
:
and
the
circle
that
is
blacker
than
his
fellowes
,
signifieth
the
circle
excentrique
,
which
carrieth
the
Epicicle
of
the
Moone
,
whose
centre
is
marked
with
the
letter
N.
There
be
also
within
the
Zodiake
seuen
other
circles
,
all
drawne
vpon
the
centre
M
,
making
six
equall
spaces
,
euery
space
containing
10
minutes
,
so
as
there
be
in
all
60
minutes
,
which
are
called
the
proportionall
minutes
;
the
vse
whereof
,
and
whereto
they
serue
,
we
shall
shew
here
by
and
by
.
Moreouer
,
there
be
foure
little
circles
,
signifying
the
Epicicle
of
the
Moone
,
euery
one
hauing
his
centre
placed
vpon
the
excentrique
,
marked
with
the
foure
letters
H
I
K
L.
And
the
letters
B
C
set
downe
in
foure
sundry
places
vpon
the
Zodiake
,
right
against
euery
one
of
the
Epicicles
,
doe
signifie
the
arch
of
the
Zodiake
,
which
is
called
the
equacion
of
the
Epicicle
,
which
arch
is
contained
betwixt
the
line
M
B
,
passing
through
the
very
centre
of
the
Epicicle
to
the
Zodiake
,
and
the
line
M
C
passing
through
the
middest
of
the
Moone
,
marked
with
the
letter
F
,
betwixt
which
letter
F
and
the
letter
D
(
set
downe
in
euery
Epicicle
)
is
contayned
an
arch
of
the
Epicicle
,
whereof
the
arch
of
the
Zodiake
B
C
is
said
to
be
the
equacion
.
And
the
foure
letters
H
I
K
L
before
mentioned
,
doe
not
only
signifie
the
centre
of
the
Epicicle
,
but
also
certain
other
points
in
the
excentrique
to
shew
the
encrease
and
decrease
of
the
equacion
of
the
Epicicle
.
For
the
point
H
standing
aboue
,
signifieth
the
Auge
of
the
excentrique
,
in
which
point
whensoeuer
the
centre
of
the
Epicicle
is
found
to
be
,
then
the
equacion
is
least
,
containing
but
4
degrees
,
i/56
ii/20
But
when
the
centre
of
the
Epicicle
is
in
the
point
I
,
then
the
equacion
is
somewhat
greater
:
and
when
it
is
in
the
point
L
,
the
equacion
is
greater
than
that
of
I
,
because
the
more
distant
from
the
Auge
of
the
Excentrique
,
the
greater
is
the
equacion
.
But
when
the
centre
of
the
Epicicle
is
in
the
opposit
Auge
of
the
Excentrique
,
marked
with
the
letter
K
,
then
the
equacion
is
greatest
of
all
,
containing
7
degrees
,
i/40
and
the
difference
betwixt
the
greatest
and
least
equacion
,
is
called
of
Alphonsus
,
Diuersitas
diametri
,
and
of
Ptolomey
,
Excessus
,
because
the
diameter
of
the
Auge
of
the
Excentrique
,
marked
in
this
figure
with
the
letters
M
H
,
dooth
farre
exceed
in
length
the
diameter
of
the
opposite
Auge
of
the
Excentrique
,
marked
with
the
letters
MK
,
as
you
may
easily
trie
with
your
Compas
,
by
applying
the
shortest
diameter
K
M
vnto
the
longest
diameter
M
H
:
the
excesse
or
ouerplus
whereof
is
deuided
as
you
see
into
six
equall
spaces
or
sections
,
euery
one
containing
tenne
minutes
,
through
which
sections
the
seuen
circles
before
mentioned
,
doe
passe
,
making
in
all
sixtie
minutes
;
which
sixtie
minutes
are
not
only
set
downe
in
the
right
line
of
the
Auges
of
the
Excentrique
,
but
also
in
each
halfe
of
the
circumference
of
the
said
Excentrique
,
proceeding
on
both
sides
downeward
from
the
Auge
vnto
the
opposit
Auge
of
the
Excentrique
:
and
these
sixtie
proportionall
minutes
were
inuented
to
know
thereby
how
much
the
equacion
of
the
Epicicle
dooth
encrease
or
decrease
,
according
as
the
centre
of
the
Epicicle
is
more
or
lesse
distant
from
the
Auge
of
the
Excentrique
.
For
if
you
suppose
the
centre
of
the
Epicicle
to
be
in
the
point
I
,
then
like
as
the
diameter
M
I
is
lesser
or
shorter
than
the
diameter
M
H
,
by
twentie
of
the
said
minutes
,
so
the
equacion
of
the
Epicicle
marked
vpon
the
Zodiake
with
B
C
,
is
greater
than
the
equacion
of
the
Epicicle
,
beeing
in
H
,
by
twentie
such
minutes
:
which
excesse
is
marked
with
the
letters
A
C
vpon
the
Zodiake
.
Againe
,
when
the
centre
of
the
Epicicle
is
in
the
point
L
,
then
as
the
diameter
M
L
is
lesser
than
the
diameter
M
H
by
i/40
so
is
the
equacion
of
the
Epicicle
,
marked
with
B
C
,
greater
than
the
equacion
of
the
Epicicle
,
being
in
H
,
by
i/40
which
excesse
is
also
marked
on
the
Zodiake
with
the
letters
A
C.
And
to
speake
breefely
,
the
further
that
the
centre
of
the
Epicicle
is
distant
from
the
Auge
H
,
the
shorter
is
the
diameter
or
right
line
drawne
from
the
centre
M
to
the
centre
of
the
Epicicle
,
and
thereby
the
equacion
of
the
Epicicle
is
the
greater
.
Now
though
these
proportionall
minutes
may
be
described
another
way
,
that
is
,
by
deuiding
the
ouerplus
or
excesse
,
whereby
the
arch
of
the
greatest
equacion
dooth
exceed
the
arch
of
the
least
equacion
into
sixtie
minutes
,
and
thereby
to
know
the
diuersitie
of
euery
equacion
,
in
what
place
soeuer
of
the
Excentrique
the
centre
of
the
Epicicle
is
found
to
bee
(
being
out
of
the
Auge
:
)
yet
I
omit
to
speake
thereof
,
because
the
other
way
before
set
downe
,
is
the
easier
of
the
two
,
and
is
only
the
way
whereby
the
tables
of
calculating
the
said
equacions
are
made
.
The
fourth
Intention
,
shewing
the
twofold
latitude
of
the
Moone
,
and
of
the
head
and
taile
of
the
Dragon
.
THe
latitude
of
the
Moone
is
none
other
thing
but
her
distance
from
the
Eclipticke
line
,
which
distance
is
neuer
aboue
fiue
degrees
.
And
her
latitude
is
twofold
,
that
is
,
Northerne
and
Southerne
.
For
the
deferent
of
the
Moone
in
the
space
of
one
moneth
cutteth
the
Eclipticke
in
two
places
right
opposit
one
to
another
,
and
thereby
the
one
halfe
of
her
deferent
enclineth
towards
the
North
,
and
the
other
halfe
thereof
enclineth
towards
the
South
:
and
those
two
sections
are
called
the
two
nodes
,
the
one
ascendent
,
which
is
the
beginning
of
the
Moones
departing
&
ascending
from
the
Eclipticke
towards
the
North
,
and
the
other
node
is
called
the
node
descendent
,
from
which
node
the
Moon
descendeth
towards
the
South
.
And
as
the
Eclipticke
or
way
of
the
Sunne
is
deuided
into
foure
parts
by
the
four
principall
points
,
that
is
,
the
two
equinoctiall
points
,
and
the
two
solsticiall
points
:
euen
so
the
deferent
of
the
Moone
is
deuided
into
foure
quarters
by
the
two
foresaid
nodes
,
and
by
the
two
limits
of
her
greatest
latitude
.
And
as
the
node
ascendent
sheweth
the
East
,
and
the
node
descendent
the
West
,
so
of
the
two
limits
the
one
sheweth
when
the
Moone
is
farthest
North
,
and
the
other
sheweth
when
she
is
furthest
South
,
as
you
may
plainely
see
by
the
figure
next
following
.
¶
The
seuenth
figure
belonging
to
the
Theorique
of
the
Moone
.
THe
outermost
circle
of
this
figure
drawne
vpon
the
centre
A
,
signifieth
the
Zodiake
,
hauing
the
caracters
of
the
twelue
signes
described
therein
,
and
is
marked
with
the
letters
C
M
N
E
D
,
within
which
circle
are
drawne
two
other
circles
,
crossing
one
another
in
two
points
opposit
,
whereof
that
which
is
drawne
vpon
the
centre
B
,
and
is
marked
with
the
letters
F
I
H
G
,
is
the
excentrique
or
deferent
,
carrying
the
Epicicle
of
the
Moone
.
And
the
other
circle
drawne
vpon
the
centre
A
,
and
marked
with
the
letters
K
I
L
G
,
signifieth
the
eclipticke
or
way
of
the
Sunne
,
and
these
two
circles
are
equall
(
because
their
semidiameters
are
equall
)
crossing
one
another
in
two
points
opposit
:
whereof
that
Intersection
which
is
on
the
right
hand
,
is
called
the
node
ascendent
or
head
of
the
Dragon
,
figured
thus
☊
,
and
that
on
the
left
hand
is
called
the
node
decendent
or
tail
of
the
Dragon
,
figured
thus
☋
,
and
the
limits
are
marked
with
the
two
letters
F
H
,
whereof
the
letter
F
signifieth
the
North
limit
,
and
H
the
South
limit
.
And
you
haue
to
note
,
that
the
head
of
the
Dragon
hath
two
motions
or
mouings
,
the
one
meane
and
the
other
true
.
His
meane
mouing
is
an
arch
of
the
Zodiake
,
extending
from
the
beginning
of
Aries
,
marked
in
the
former
Figure
with
the
letter
C
,
contrarie
to
the
succession
of
the
signes
by
the
mouing
of
the
orbe
equant
vnto
the
letter
D
,
shewing
the
place
of
the
head
of
the
Dragon
in
the
Zodiake
,
whereunto
the
line
A
G
doth
point
,
which
arch
is
marked
with
the
letters
C
D.
Againe
,
his
true
moouing
is
an
arch
of
the
Zodiake
,
extending
according
to
the
succession
of
the
signes
,
from
the
beginning
of
Aries
vnto
the
head
of
the
Dragon
.
And
this
arch
is
marked
with
the
letters
C
M
N
E
D
,
which
two
arches
being
added
together
,
doe
make
vp
the
whole
Zodiake
,
and
the
selfesame
moouings
are
also
incident
to
the
other
three
points
,
that
is
,
to
the
taile
of
the
Dragon
,
and
to
the
two
limits
.
¶
Of
the
Inequalitie
of
the
Moones
latitude
both
meane
and
true
.
What
is
the
Inequalitie
or
Anomalie
of
her
latitude
?
IT
is
an
arch
of
the
Zodiake
,
extending
according
to
the
succession
of
the
signes
,
from
the
Dragons
head
vnto
the
place
of
the
Moone
:
which
if
it
be
her
meane
place
,
then
such
arch
is
called
the
meane
Inequalitie
of
her
latitude
:
but
if
it
be
the
true
place
of
the
Moone
,
then
that
arch
is
called
the
true
Inequalitie
of
her
latitude
.
How
to
know
her
meane
and
true
place
hath
been
shewed
before
.
But
you
haue
to
note
,
that
though
the
followers
of
Alphonsus
doe
make
this
arch
of
latitude
to
begin
at
the
Dragons
head
:
euen
as
the
Eclipticke
is
said
to
begin
at
the
vernall
Equinoctiall
point
:
yet
Ptolomey
and
Copernicus
,
and
also
the
Prutenicall
Tables
,
doe
make
the
said
arch
to
begin
at
the
North
limit
of
the
Moones
latitude
,
and
so
to
extend
,
according
to
the
succession
of
the
signes
:
by
helpe
of
which
arch
the
latitude
of
the
Moone
is
alwayes
to
be
found
in
the
said
Tables
.
❧
The
Theorique
of
the
three
Superior
Planets
,
that
is
,
Saturne
,
Iupiter
,
and
Mars
.
Why
are
these
three
called
the
Superior
Planets
?
BEcause
they
are
placed
aboue
the
Sun
:
euen
as
the
other
three
Planets
,
that
is
,
Venus
,
Mercurie
,
and
the
Moone
,
are
called
the
Inferior
Planets
,
because
they
are
placed
vnder
the
Sunne
,
who
is
cheefe
gouernour
of
them
all
.
The
Theorique
of
which
three
superior
Planets
,
we
thinke
it
best
here
to
describe
next
after
the
Moone
,
because
that
though
they
be
subject
to
more
diuersities
of
mouings
than
either
the
Sunne
or
Moone
,
yet
to
fewer
than
Venus
or
Mercurie
.
Why
are
these
three
Planets
ioined
together
all
in
one
Theorique
?
BEcause
in
the
qualitie
of
their
moouings
,
as
well
according
to
longitude
as
latitude
,
they
be
like
,
differing
only
in
quantitie
,
and
their
orbes
haue
like
vniformitie
,
and
therefore
may
be
very
well
described
in
one selfe
Theorique
.
The
first
Intention
,
shewing
how
many
orbes
doe
belong
to
the
Theorique
of
euery
one
of
these
Planets
.
VIZ.
Foure
orbes
,
and
one
circle
,
that
is
,
the
Excentrique
carrying
the
Epicicle
,
then
the
two
deferents
of
the
Auge
and
opposit
Auge
of
the
Excentrique
,
and
the
Epicicle
carrying
the
body
of
the
Planet
,
whereto
is
added
the
circle
Equant
:
all
which
are
set
downe
in
the
Figure
next
following
.
¶
The
first
figure
of
the
three
vpper
Planets
.
THis
figure
as
you
see
is
also
enuironed
with
a
great
circle
,
signifying
here
the
orbe
which
carrieth
the
two
sections
,
called
the
head
and
taile
of
the
Dragon
,
and
is
the
outermost
circle
of
all
,
marked
with
the
letter
M
,
whose
centre
is
the
letter
A
,
which
is
the
centre
of
the
world
.
And
next
to
that
are
the
two
blacke
deferents
of
the
Auges
,
whereof
the
vpper
deferent
is
marked
with
D
,
and
the
nether
deferent
with
E
,
both
which
are
in
diuers
respects
concentrique
with
the
centre
of
the
world
,
and
also
excentrique
:
and
within
those
two
deferents
is
placed
the
Excentrique
which
carrieth
the
Epicicle
,
and
the
centre
of
the
excentrique
is
marked
with
the
letter
B
,
and
the
little
circle
aboue
is
the
Epicicle
,
whose
centre
is
F
,
which
centre
by
turning
round
about
vpon
the
plane
of
the
Excentrique
,
describeth
in
the
very
middest
thereof
a
circle
marked
with
the
letter
C
,
which
circle
is
crossed
in
two
points
opposit
by
another
circle
,
called
the
circle
equant
,
marked
with
the
letter
G
,
whose
centre
is
marked
with
the
letter
H.
Why
are
these
foure
orbes
placed
in
this
Theorique
of
the
three
vpper
Planets
?
THe
Excentrique
is
needfull
as
well
to
shew
their
vnequall
distances
from
the
earth
,
as
also
for
that
the
equacions
of
their
Epicicles
are
sometime
greater
,
and
sometime
lesser
,
as
hath
ben
demonstrated
before
in
the
sixt
figure
of
the
Moon
.
And
the
two
deferents
of
the
Auges
are
here
placed
for
the
selfesame
causes
that
are
before
declared
.
Againe
,
the
Epicicle
is
necessarily
supposed
,
because
it
is
well
knowne
by
often
obseruation
,
that
euery
one
of
these
three
Planets
in
like
and
selfesame
places
of
his
Excentrique
is
found
to
haue
diuerse
and
sundry
motions
,
whereof
they
are
said
to
be
sometime
swift
and
sometime
slow
,
now
stationarie
and
now
retrograde
;
moreouer
,
they
are
sometime
nigher
to
the
earth
,
and
sometime
further
off
,
as
manifestly
appeareth
by
the
mutabilitie
of
their
apparant
greatnesse
:
all
which
apparences
are
salued
,
by
supposing
an
Epicicle
.
Wherefore
is
the
circle
equant
added
to
this
Theorique
?
BEcause
the
conuersions
of
the
Excentriques
and
of
the
Epicicles
of
these
three
Planets
are
not
obserued
to
be
equated
to
their
owne
centres
,
but
to
some
other
point
,
which
point
is
called
the
centre
equant
,
marked
in
the
former
figure
with
the
letter
H
:
and
because
it
is
not
needfull
to
appoint
to
that
centre
any
peculiar
orbe
,
sith
there
is
no
vse
thereof
,
the
Astronomers
thinke
it
sufficient
onely
to
describe
about
that
centre
a
circle
vpon
the
Plane
of
the
Excentrique
,
equall
to
the
circle
Excentrique
in
euery
respect
;
for
hauing
both
equall
semidiameters
,
as
I
said
before
,
they
must
needs
be
equall
.
Hath
the
Orbe
which
carrieth
the
two
nodes
,
no
vse
in
this
Theorique
?
YEs
,
they
may
be
vsed
as
well
in
the
Theorique
of
these
Planets
,
as
in
the
rest
.
And
yet
because
the
varieties
of
the
latitudes
are
obserued
to
proceed
equally
according
to
the
succession
of
the
signes
,
together
with
the
Auges
,
the
office
of
carrying
the
Nodes
,
is
most
commonly
by
the
Astronomers
appointed
to
the
two
deferents
of
the
Auges
,
so
as
this
orbe
in
this
Theorique
hauing
none
other
vse
,
is
not
thought
so
needfull
.
The
second
Intention
,
shewing
towards
what
part
such
Orbes
are
moued
,
and
in
what
time
they
make
their
reuolutions
,
and
also
vpon
what
centres
or
poles
they
make
their
regular
mouings
:
and
first
of
all
,
how
and
in
what
manner
the
Excentriques
,
carying
the
Epicicles
of
these
Planets
,
are
mooued
.
THe
Excentrique
of
euery
one
of
these
Planets
,
is
moued
according
to
the
succession
of
the
signes
,
vpon
his
owne
proper
poles
,
declining
vnequally
on
both
sides
from
the
poles
of
the
Eclipticke
,
and
yet
it
moueth
equally
about
the
centre
of
the
circle
equant
:
and
the
Excentrique
of
Saturne
is
commonly
said
to
make
his
reuolution
in
thirtie
yeares
,
and
the
Excentrique
of
Iupiter
in
twelue
yeares
,
and
that
of
Mars
almost
in
two
yeares
.
How
much
is
the
precise
dayly
motion
and
perfect
reuolution
of
euery
one
of
these
Excentriques
?
TO
vnderstand
this
the
better
,
you
had
need
to
remember
Coper●icus
his
diuision
of
the
beginning
of
mouing
before
mentioned
,
which
is
twofold
,
the
one
compound
,
and
the
other
simple
.
The
compound
moouing
is
to
be
accounted
from
the
vernall
equinoctiall
point
,
which
point
of
beginning
is
vnstable
:
and
the
simple
moouing
is
to
be
counted
from
the
first
starre
of
the
Rams
horne
,
called
of
the
Astronomers
,
The
firme
and
stable
point
,
or
beginning
of
moouing
:
wherefore
if
you
count
from
the
Equinoctiall
point
,
then
the
daily
mouing
of
the
Ex●●ntrique
of
Saturne
containeth
i/2
ii/0
iii/35
iiii/33
v/2·
that
of
Iupiter
,
i/4
ii/59
iii/15
iiii/49
v/53·
and
that
of
Mars
,
i/31
ii/26
iii/39
iiii/14
v/6·
And
one
whole
reuolution
of
Saturne
,
counting
from
the
Equinoctiall
point
,
contayneth
29
Aegyptian
yeares
,
161
dayes
,
22
houres
,
i/28
ii●°
iii/22
And
the
re●olution
of
Iupiter
,
counting
also
from
the
Aequinoctiall
point
,
containeth
11
Aegyptian
years
,
315
dayes
,
15
houres
,
i/●.
ii/10.
iii/30.
And
that
of
Mars
containeth
one
Aegyptian
yeare
,
321
dayes
,
22
houres
,
i/19
ii/49
iii/48
But
if
you
count
their
mouing
from
the
first
star
of
the
Rams
horne
,
then
the
Excentriques
of
these
Planets
will
not
make
their
reuolutions
so
soone
,
but
bee
somewhat
longer
in
returning
to
that
first
point
of
moouing
,
for
the
excentrique
of
Saturne
will
then
make
his
reuolution
in
29
Aegyptian
yeares
,
174
dayes
,
4
houres
,
i/58
ii/25
iii/30
And
that
of
Iupiter
in
11
Aegyptian
yeares
,
317
dayes
,
14
houres
,
i/49
ii/31
iii/56
And
that
of
Mars
in
one
Aegyptian
yeare
,
321
dayes
,
23
houres
,
i/31
ii/56
iii/49
In
what
place
is
the
centre
of
the
circle
equant
to
bee
found
?
IN
the
line
of
the
Auge
of
the
excentrique
towards
the
same
Auge
,
whose
distance
from
the
centre
of
the
world
is
double
to
the
excentricitie
of
the
excentrique
:
which
excentricitie
is
the
space
contained
betwixt
the
centre
of
the
world
,
and
the
centre
of
the
excentrique
.
What
followeth
vpon
this
Inequalitie
or
Irregularitie
of
the
Excentriques
?
WE
haue
shewed
you
before
in
the
Theorique
of
the
Moone
,
that
the
centre
of
equalitie
is
towards
the
opposit
Auge
of
her
Excentrique
,
and
is
all
one
with
the
centre
of
the
earth
,
and
thereby
the
mouing
of
her
excentrique
,
whilest
her
Epicicle
mooueth
towards
the
Auge
,
is
the
swifter
.
But
because
in
this
Theorique
of
the
three
Planets
,
the
centre
of
the
equant
is
towards
the
Auge
of
the
Excentrique
,
the
Excentrique
therfore
moueth
the
more
slowly
;
for
a
lesser
portion
of
the
Excentrique
belongeth
to
the
vpper
halfe
of
the
circle
equant
,
and
a
greater
portion
thereof
is
due
to
the
nether
halfe
of
the
circle
equant
,
as
plainely
appeareth
by
the
former
figure
:
for
if
you
draw
a
right
line
through
the
centre
of
the
equant
,
so
as
it
may
cut
the
line
of
the
Auge
with
right
angles
,
it
will
deuide
the
circle
equant
into
two
equall
semicircles
,
but
it
will
deuide
the
Excentrique
into
two
vnequall
portions
,
whereof
the
vppermost
is
the
lesser
,
and
the
nethermost
the
greater
.
And
sith
the
mouing
of
the
Excentrique
is
equall
about
the
centre
of
the
equant
,
and
that
these
vnequall
portions
of
the
Excentrique
do
turne
about
the
said
centre
in
equall
time
,
it
must
needs
moue
more
slowly
aboue
,
and
more
quickly
beneath
.
How
are
the
deferents
of
the
Auges
moued
?
THey
are
mooued
according
to
the
succession
of
the
signes
,
about
the
centre
and
poles
of
the
Eclipticke
,
by
vertue
of
the
eighth
sphere
,
&
according
to
Alphonsus
doe
make
their
whole
reuolution
in
49000
yeares
,
by
which
moouing
they
put
forward
by
little
and
little
the
Auges
of
the
Excentriques
.
How
and
in
what
manner
are
the
Epicicles
of
these
Planets
mooued
?
THey
are
moued
in
their
vpper
part
according
to
the
succession
of
the
signes
,
and
in
their
nether
part
contrarie
to
the
succession
of
the
signes
,
which
is
cleane
contrary
to
the
mouing
of
the
Moones
Epicicle
before
declared
.
And
euery
one
of
these
Epicicles
is
equally
mooued
from
his
meane
Auge
,
vpon
his
owne
proper
axletree
,
which
is
also
mouable
,
standing
vpon
the
plane
of
the
Excentrique
obliquely
or
slopewise
,
and
not
perpendicularly
.
And
the
Epicicles
of
Saturne
and
Iupiter
doe
go
about
in
the
space
of
one
yeare
and
a
few
daies
more
,
but
the
Epicicle
of
Mars
goeth
about
in
a
little
more
than
two
yeares
:
and
by
this
moouing
euery
Epicicle
carrieth
about
with
him
the
bodie
of
his
proper
Planet
.
What
is
the
daily
mouing
and
also
the
periodicall
reuolution
of
euery
one
of
these
Epicicles
?
THe
daily
mouing
of
the
Epicicle
of
Saturne
,
is
i/57
ii/7
ii/●4·
iii/4
v/22·
and
that
of
Iupiter
,
is
i/54
ii/9
iii/3
iiii/●7·
v/31·
and
that
of
Mars
,
is
i/27
ii/41
iii/40
iiii/23
v/19·
So
as
the
Epicicle
of
Saturne
maketh
one
period
in
378
dayes
,
which
is
one
yeare
,
13
dayes
,
and
6
houres
,
i/24
ii/57
iii/26
And
the
Epicicle
of
Iupiter
maketh
one
period
in
398
dayes
,
which
is
one
yeare
,
33
daies
,
and
21
houres
,
i/13
ii/15
iii/33
And
the
Epicicle
of
Mars
maketh
one
period
in
779
dayes
,
which
is
two
yeares
,
49
daies
,
22
houres
,
i/28
i●9·
iii/49
How
is
the
meane
Auge
of
euery
one
of
these
Epicicles
described
?
BY
a
right
line
drawne
from
the
centre
of
the
circle
equant
through
the
centre
of
the
Epicicle
,
euen
to
the
circumference
thereof
,
making
there
a
point
marked
in
the
figure
next
following
with
the
letter
M
,
which
is
furthest
distant
from
the
centre
of
the
equant
.
And
the
centre
of
the
equant
gouerneth
the
moouing
as
well
of
the
Epicicle
,
as
of
the
Excentrique
,
as
you
may
plainely
see
by
this
figure
following
.
¶
The
second
figure
belonging
to
the
Theorique
of
the
three
superior
Planets
.
THis
figure
consisteth
of
diuerse
circles
and
centres
,
lines
,
and
points
,
whereof
the
outermost
circle
signifieth
the
Zodiake
,
whose
centre
is
marked
with
the
letter
A
,
and
of
the
two
greater
circles
drawne
within
that
,
cutting
one
another
in
two
points
opposit
,
the
one
is
the
circle
equant
,
whose
centre
is
marked
with
the
letter
C
,
and
the
other
is
the
Excentrique
,
whose
centre
is
marked
with
the
letter
B
,
and
the
Auge
of
the
Excentrique
is
marked
with
the
letter
D
,
and
the
opposit
Auge
therof
is
marked
with
the
letter
E
:
and
the
foure
lesser
circles
placed
vpon
the
Excentrique
,
are
Epicicles
,
whereof
two
haue
their
centres
,
marked
with
the
letter
H
,
as
well
on
the
right
hand
as
on
the
left
hand
of
the
figure
,
for
the
right
line
C
H
M
dooth
point
to
the
meane
Auge
of
the
Epicicle
,
marked
with
the
letter
M
on
both
sides
of
the
figure
,
and
the
right
line
A
H
V
doth
point
to
the
true
Auge
of
the
Epicicle
,
marked
likewise
on
both
sides
of
the
figure
with
the
letter
V
,
and
the
right
line
B
H
P
sheweth
the
Touch-point
,
marked
also
on
both
sides
of
the
figure
with
the
letter
P
,
which
is
alwaies
in
the
middest
betwixt
the
meane
and
true
Auge
of
the
Epicicle
,
being
out
of
the
line
of
the
Auges
.
Now
what
the
other
letters
set
downe
in
the
outside
of
this
figure
doe
signifie
,
shall
be
shewed
when
we
come
to
describe
the
points
,
lines
,
and
arches
,
belonging
to
this
Theorique
.
What
conclusions
doe
follow
vpon
this
Inequalitie
of
the
Epicicle
?
1.
THese
foure
:
First
,
the
moouing
of
the
Planet
to
any
other
point
in
the
circumference
of
the
Epicicle
,
than
to
the
meane
Auge
of
the
Epicicle
and
to
the
opposit
Auge
,
is
vnequall
.
2.
Secondly
,
when
the
centre
of
the
Epicicle
is
either
in
the
Auge
or
opposit
Auge
of
the
Excentrique
,
then
the
three
points
,
that
is
,
the
mean
Auge
,
the
true
Auge
,
and
the
Touch-points
are
all
vnited
,
and
doe
meet
in
one selfe
line
:
but
beeing
out
of
the
line
of
the
Auge
,
they
are
so
seuered
,
as
the
Touch-point
is
in
the
middest
betwixt
the
meane
and
true
Auge
of
the
Epicicle
,
because
that
the
centre
of
the
Excentrique
is
in
the
middest
betwixt
the
centre
of
the
Equant
,
and
the
centre
of
the
Eclipticke
.
3.
Thirdly
,
in
the
descending
halfe
of
the
excentrique
from
the
Auge
towards
the
opposit
Auge
thereof
,
that
is
from
D
to
E
,
the
meane
Auge
of
the
Epicicle
,
marked
with
M
,
goeth
before
the
Touch-point
,
marked
with
P
,
according
to
the
succession
of
the
signes
;
and
the
true
Auge
of
the
Epicicle
followeth
the
said
Touch-point
,
according
to
the
succession
of
the
signes
.
But
in
the
other
ascending
halfe
of
the
Excentrique
,
the
true
Auge
of
the
Epicicle
beeing
out
of
the
line
of
the
Auges
of
the
Excentrique
,
alwayes
enclineth
from
the
Touch-point
towards
the
Auge
of
the
Excentrique
,
and
the
meane
Auge
of
the
Epicicle
enclineth
towards
the
opposit
Auge
of
the
Excentrique
.
4.
Fourthly
,
in
the
vpper
part
of
the
Excentrique
the
mouing
of
the
Planet
is
swifter
than
in
the
lower
part
of
the
Excentrique
,
because
that
the
meane
Auge
of
the
Epicicle
goeth
in
the
vpper
part
of
the
Excentrique
,
according
to
the
succession
of
the
signes●
.
But
in
the
other
nether
halfe
of
the
Excentrique
,
the
moouing
of
the
Planet
is
slower
,
going
there
contrarie
to
the
succession
of
the
signe
.
What
harmonie
is
there
betwixt
the
mouing
of
the
Sunne
,
and
the
mouings
of
the
three
superior
Planets
,
and
wherof
dependeth
such
harmonie
▪
IT
chiefely
dependeth
vpon
the
periodical
reuolutions
and
mouings
of
their
Epicicles
:
for
it
is
well
known
by
good
obseruation
,
that
in
euery
meane
conjunction
of
the
Sunne
with
any
of
the
said
three
Planets
,
the
Planet
it selfe
is
in
the
meane
Auge
of
his
Epicicle
;
and
in
euery
meane
opposition
of
the
Sunne
with
any
of
the
said
three
Planets
,
the
Planet
it selfe
is
in
the
meane
opposit
Auge
of
his
Epicicle
:
and
in
any
other
place
look
how
much
the
meane
place
of
the
Sunne
is
distant
from
the
meane
place
of
the
Planet
,
so
much
is
the
Planet
it selfe
distant
from
the
meane
Auge
of
the
Epicicle
,
as
you
shall
easily
perceiue
by
this
figure
following
.
What
meane
Conjunction
or
Opposition
is
,
shall
be
declared
hereafter
in
the
second
booke
,
treating
of
the
passions
of
the
Planets
.
¶
The
third
figure
belonging
to
the
Theorique
of
the
three
superior
Planets
.
THis
figure
as
you
see
consisteth
of
two
seuerall
circles
,
wherof
the
lesser
circle
which
standeth
aboue
,
signifieth
the
Epicicle
,
carrying
the
Planet
,
whose
centre
is
marked
with
the
letter
B.
And
the
greater
circle
beneath
,
is
the
deferent
of
the
Sunne
.
In
each
of
which
circles
are
set
downe
the
caracters
of
the
fiue
Aspects
,
whereof
in
both
circles
,
that
of
the
Conjunction
is
placed
aboue
,
and
that
of
the
Opposition
beneath
:
and
on
each
hand
on
both
sides
are
placed
the
caracters
of
the
other
three
aspects
,
that
is
,
the
Sextile
,
the
Quadrat
,
and
the
Trine
aspect
.
The
letters
set
downe
on
both
sides
of
either
circle
,
doe
serue
to
shew
the
points
of
moouing
,
as
well
of
the
Sunne
in
his
deferent
,
as
of
the
Planet
in
his
Epicicle
:
for
when
the
Sunne
by
his
meane
mouing
is
in
the
point
C
of
his
deferent
,
and
the
Planet
in
the
meane
Auge
of
his
Epicicle
,
marked
with
D
,
then
are
both
their
meane
mouings
joined
in
one selfe
line
,
and
so
be
in
a
Conjunction
.
And
as
the
Sun
departing
from
thence
to
the
point
E
,
set
downe
on
the
left
hand
of
his
deferent
,
hath
gone
a
sixt
part
of
his
deferent
,
and
thereby
is
in
the
first
Sextile
aspect
:
so
the
Planet
departing
from
the
meane
Auge
of
his
Epicicle
,
and
comming
to
the
point
F
,
hath
gone
also
a
sixt
part
of
his
Epicicle
,
and
is
thereby
in
the
first
Sextile
aspect
:
and
when
the
Sunne
commeth
to
the
point
G
,
and
the
Planet
to
the
point
H
,
then
they
are
both
in
a
Quadrat
aspect
:
and
when
the
Sunne
commeth
to
the
point
I
,
and
the
Planet
to
the
point
K
,
then
are
they
both
in
a
Trine
aspect
:
and
when
the
Sunne
is
in
the
point
L
,
and
the
Planet
in
the
point
M
,
then
they
are
just
opposit
one
to
another
,
being
both
in
one selfe
line
:
and
in
departing
from
thence
,
they
obserue
like
order
in
going
through
the
other
halfe
of
their
circles
,
vntill
they
come
againe
to
be
in
a
Conjunction
,
as
the
letters
N
P
R
on
the
right
hand
,
being
the
halfe
of
the
Sunnes
deferent
,
and
the
letters
O
Q
S
on
the
right
hand
,
being
the
halfe
of
the
Epicicle
,
do
shew
.
Of
this
harmonie
doe
follow
three
conclusions
.
1.
FIrst
one
period
of
the
Epicicle
is
justly
accomplished
in
so
much
time
as
passeth
betwixt
two
Conjunctions
of
the
Sunne
and
of
the
Planet
.
2.
Secondly
,
looke
how
many
degrees
the
Sunne
by
his
meane
mouing
is
distant
from
the
meane
moouing
of
the
Planet
,
so
much
doth
the
Planet
depart
from
the
meane
Auge
of
his
Epicicle
.
And
therefore
the
meane
mouing
of
the
centre
of
the
Epicicle
,
and
the
meane
mouing
of
the
Planet
in
his
Epicicle
,
being
joyned
together
,
are
equall
to
the
meane
mouing
of
the
Sunne
.
3.
Thirdly
,
of
this
way
may
be
gathered
,
that
the
Epicicle
and
the
Excentrique
as
touching
their
swiftnesse
and
slownesse
of
gate
in
making
their
periodicall
reuolutions
,
are
cleane
contrary
one
to
another
,
for
in
those
places
whereas
the
mouing
of
the
Excentrique
is
slowest
,
there
the
mouing
of
the
Epicicle
is
swiftest
,
and
yet
their
mouings
being
all
joyned
together
,
are
equall
to
the
mouing
of
the
Sunne
.
What
measure
doth
Ptolomey
appoint
to
euery
one
of
their
Orbes
?
THeir
measures
doe
depend
of
the
semidiameter
of
the
Excentrique
,
which
is
supposed
to
containe
60
parts
or
degrees
,
and
of
such
like
parts
the
excentricitie
of
the
excentrique
of
Saturne
containeth
3
degrees
,
i/25
and
that
of
Iupiter
2
degrees
,
i/45
and
that
of
Mars
6
degrees
,
i/0
Againe
,
the
excentricitie
of
the
equant
of
Saturne
containeth
6
degrees
,
i/50
and
that
of
Iupiter
containeth
5
degrees
,
i/30
and
that
of
Mars
12
degrees
,
i/0
And
the
semidiameter
of
the
Epicicle
of
Saturne
containeth
6
degrees
,
i/30
and
that
of
Iupiter
11
degrees
,
i/30
and
that
of
Mars
39
degrees
,
i/30
And
the
least
altitude
from
the
earth
of
Saturne
,
is
50
degrees
,
i/5
and
that
of
Iupiter
is
45
degrees
,
i/45
and
that
of
Mars
is
14
degrees
,
i/30
And
the
greatest
altitude
from
the
earth
of
Saturne
is
69
degrees
,
i/55
and
that
of
Iupiter
is
74
degrees
,
I●15
.
and
that
of
Mars
is
105
degrees
,
i30
.
The
third
Intention
,
shewing
what
points
,
lines
,
and
arch●s
are
necessarie
to
be
knowne
in
the
Theoriques
of
the
three
vpper
Planets
,
which
are
these
here
following
.
-
1.
FIrst
,
the
Auge
and
opposit
Auge
as
well
of
the
Excentrique
,
as
of
the
circle
equant
.
-
2.
The
lines
of
the
meane
and
true
mouing
of
the
Epicicle
,
and
of
the
Planet
.
-
3.
The
meane
and
true
mouing
of
the
Epicicle
,
and
of
the
Planet
.
-
4.
The
Inequalitie
or
centre
of
the
Excentrique
,
both
meane
and
true
.
-
5.
The
meane
and
true
Auge
of
the
Epicicle
.
-
6.
The
equacion
of
the
Excentrique
,
or
of
the
centre
,
as
well
in
the
Excentrique
as
in
the
Epicicle
.
-
7.
The
inequalitie
of
commutation
or
argument
,
both
meane
and
true
.
-
8.
The
equacion
of
the
argument
.
-
9.
The
meane
longitude
.
-
10.
The
excesse
of
the
longer
longitude
.
-
11.
The
excesse
of
the
nigher
longitude
.
-
12.
The
proportionall
minutes
both
nigher
and
more
remote
.
-
13.
The
diameter
of
the
Auges
.
-
14.
The
diameter
of
the
mean
longitude
in
the
Epicicle
.
-
15.
The
vpper
and
nether
halfe
of
the
Epicicle
.
-
16.
The
orientall
and
occidentall
halfe
of
the
Epicicle
,
the
descriptions
of
all
which
things
do
here
follow
.
But
first
as
touching
the
Auges
and
opposit
Auges
,
as
well
of
the
Excentrique
as
of
the
Equant
,
they
are
alreadie
before
described
.
The
line
of
the
meane
moouing
of
the
Planet
or
of
his
Epicicle
,
is
a
right
line
drawne
from
the
centre
of
the
world
to
the
Zodiake
,
and
is
a
paralell
or
equally
distant
to
another
line
,
drawne
from
the
centre
of
the
Equant
,
and
passing
through
the
centre
of
the
Epicicle
.
Of
which
two
lines
,
the
first
is
marked
in
the
second
Figure
on
the
right
hand
thereof
,
with
the
letters
A
I
,
and
the
other
line
is
marked
on
the
same
hand
with
the
letters
C
H.
But
the
line
of
the
true
mouing
of
the
Epicicle
,
is
a
right
line
drawne
from
the
centre
of
the
world
through
the
centre
of
the
Epicicle
euen
to
the
Zodiake
,
represented
on
both
hands
of
the
said
figure
with
the
letters
A
K.
Now
the
line
of
the
true
mouing
of
the
Planet
,
is
a
right
line
drawne
from
the
centre
of
the
world
through
the
bodie
of
the
Planet
vnto
the
Zodiake
,
signified
by
the
letters
A
L
set
down
on
both
sides
of
the
said
second
figure
.
But
if
the
Planet
be
either
in
the
true
Auge
or
opposit
Auge
of
the
Epicicle
,
then
the
two
lines
AK
and
AL
are
vnited
.
But
if
the
centre
of
the
Epicicle
be
either
in
the
Auge
or
opposit
Auge
of
the
Excentrique
,
that
is
either
in
D
or
E
,
then
the
three
lines
AI
,
AK
,
and
CHM
,
are
all
one
.
The
meane
mouing
of
the
Planet
or
of
his
Epicicle
,
is
an
arch
of
the
Zodiake
,
extending
from
the
vernall
Aequinoctiall
point
,
according
to
the
succession
of
the
signes
vnto
the
line
of
the
meane
mouing
of
the
Planet
or
Epicicle
,
marked
in
the
said
figure
with
the
letters
N
F
I
,
proceeding
towards
the
left
hand
.
The
true
moouing
of
the
Epicicle
is
an
arch
of
the
Zodiake
,
extending
according
to
the
succession
of
the
signes
from
the
said
Aequinoctiall
point
to
the
line
of
the
true
mouing
of
the
Epicicle
,
marked
with
the
letters
N
F
K.
But
the
true
mouing
of
the
Planet
is
an
arch
of
the
Zodiake
,
extending
in
like
manner
from
the
Aequinoctiall
point
to
the
line
of
the
true
mouing
of
the
Planet
,
marked
in
the
said
figure
with
the
letters
N
F
L.
And
remember
,
that
the
letter
N
alwaies
signifieth
the
vernall
Aequinoctiall
point
,
whereto
is
set
the
caracter
of
Aries
.
Of
the
Inequalitie
of
the
Excentrique
,
both
meane
and
true
.
THe
mean
Inequalitie
of
the
Excentrique
is
an
arch
of
the
Zodiake
,
extending
according
to
the
succession
of
the
signes
,
from
the
line
of
the
Auge
of
the
Excentrique
vnto
the
line
of
the
meane
moouing
of
the
Planet
or
Epicicle
:
which
Inequalitie
the
followers
of
Alphonsus
do
call
Centrum
medium
,
marked
on
the
left
hand
of
the
foresaid
figure
with
the
letters
F
I.
But
the
true
Inequalitie
of
the
Excentrique
is
an
arch
of
the
Zodiake
,
extending
according
to
the
succession
of
the
signes
,
from
the
line
of
the
Auge
of
the
Excentrique
vnto
the
line
of
the
true
mouing
of
the
Epicicle
;
which
arch
is
marked
on
the
left
hand
in
the
said
figure
with
the
letters
F
K.
What
is
the
equaction
of
the
Excentrique
?
IT
is
an
arch
of
the
Excentrique
,
contained
betwixt
the
line
of
the
meane
mouing
and
the
line
of
the
true
mouing
of
the
Epicicle
,
and
is
marked
on
both
sides
of
the
foresaid
figure
with
the
letters
I
K.
What
is
the
Equacion
of
the
centre
in
the
Epicicle
?
IT
is
an
arch
of
the
Epicicle
contained
betwixt
the
meane
and
true
Auge
of
the
Epicicle
,
and
is
marked
on
both
hands
of
the
said
figure
with
the
letters
V
M.
But
this
arch
is
no
arch
,
when
the
centre
of
the
Epicicle
is
in
the
Auge
of
the
Excentrique
,
and
it
is
greatest
when
the
centre
of
the
Epicicle
is
in
any
of
the
two
meane
longitudes
.
And
you
haue
to
note
,
that
the
equacion
of
the
centre
in
the
Excentrique
,
and
the
equacion
of
the
centre
in
the
Epicicle
are
alwaies
like
.
Moreouer
,
whilest
the
Epicicle
descendeth
in
the
one
halfe
of
the
Excentrique
from
the
Auge
of
the
Excentrique
,
marked
with
D
,
towards
the
opposit
Auge
thereof
marked
with
E
,
this
equacion
is
taken
away
from
the
meane
Inequalitie
of
the
Excentrique
,
and
is
added
to
the
mean
argument
(
which
is
here
by
and
by
defined
)
so
as
it
may
make
therby
and
in
that
place
,
as
well
the
equated
Inequalitie
of
the
Excentrique
,
as
the
equated
argument
.
But
whilest
the
Epicicle
ascendeth
in
the
other
halfe
of
the
Excentrique
,
it
is
cleane
contrary
:
for
when
the
right
line
AHV
in
the
foresaid
second
figure
falleth
into
the
two
paralels
A
I
and
C
H
M
,
it
maketh
the
two
angles
I
A
H
and
M
H
V
to
be
equall
.
And
to
the
two
equall
angles
doe
belong
two
like
arches
,
represented
in
the
said
figure
by
the
letters
I
K
,
and
V
M
,
which
arches
or
equacions
are
not
to
be
added
or
subtracted
both
together
.
But
when
the
one
is
added
,
the
other
is
always
to
be
taken
away
,
because
the
one
cleaueth
to
the
end
,
and
the
other
to
the
beginning
of
their
circles
,
tending
towards
one selfe
part
.
What
is
the
meane
and
true
argument
?
THe
meane
argument
is
an
arch
of
the
Epicicle
,
contained
betwixt
the
meane
Auge
thereof
,
and
the
body
of
the
Planet
,
to
be
counted
towards
that
part
whereinto
to
the
Epicicle
is
mooued
:
which
arch
is
represented
in
the
said
second
figure
by
the
letters
M
L.
And
the
true
argument
is
an
arch
of
the
Epicicle
,
contained
betwixt
the
true
Auge
of
the
Epicicle
and
the
body
of
the
Planet
,
marked
in
the
foresaid
figure
with
the
letters
V
L.
What
is
the
equacion
of
the
Epicicle
,
or
of
the
argument
?
IT
is
an
arch
of
the
Zodiake
,
contained
betwixt
the
line
of
the
true
mouing
of
the
Epicicle
,
and
the
line
of
the
true
mouing
of
the
Planet
,
marked
in
the
foresaid
second
figure
with
the
letters
K
L
:
and
this
arch
is
no
arch
when
the
Planet
is
either
in
the
true
Auge
or
in
the
true
opposit
Auge
of
the
Epicicle
.
And
it
is
greatest
when
the
Planet
is
in
the
line
,
which
being
drawne
from
the
centre
of
the
world
,
toucheth
in
one
point
the
outside
of
the
Epicicle
,
which
line
is
marked
in
the
foresaid
second
figure
on
the
left
hand
therof
,
with
the
letters
A
L
,
and
on
the
right
hand
,
with
the
letters
A
I.
And
note
,
that
when
the
Planet
is
in
the
first
halfe
of
the
Epicicle
,
descending
from
the
true
Auge
to
the
opposit
Auge
,
it
addeth
this
equacion
to
the
true
moouing
of
the
Epicicle
,
but
in
the
other
halfe
of
the
Epicicle
it
taketh
so
much
away
.
BVt
now
for
the
better
vnderstanding
of
the
equacions
both
least
and
greatest
of
all
the
three
superior
Planets
,
and
of
all
the
other
tearmes
belonging
to
the
said
three
Planets
,
it
shall
be
necessarie
to
set
downe
this
other
figure
here
following
.
¶
The
fourth
figure
belonging
to
the
Theoriques
of
the
three
vpper
Planets
.
THis
figure
differeth
not
much
from
the
sixt
figure
belonging
to
the
Theorique
of
the
Moon
before
set
downe
,
for
the
outermost
circle
of
this
figure
signifieth
as
well
here
as
there
the
Zodiake
,
whose
centre
is
marked
with
the
letter
A
:
and
the
inner
blacker
circle
signifieth
the
Excentrique
,
carrying
the
Epicicle
of
any
of
the
three
vpper
Planets
,
whose
centre
is
marked
with
the
letter
B
:
and
aboue
that
centre
is
placed
the
centre
of
the
circle
Equant
,
marked
with
the
letter
C.
but
the
circle
it selfe
cannot
fitly
be
made
here
,
because
it
must
be
equall
in
euery
respect
to
the
Excentrique
,
as
hath
been
said
before
.
And
each
one
of
the
fiue
little
circles
,
placed
vpon
the
Excentrique
,
doth
signifie
the
Epicicle
whereto
the
body
of
any
of
the
three
Planets
is
fixed
.
And
the
7
halfe
circles
making
6
spaces
,
euery
space
containing
ten
minutes
,
as
well
aboue
as
beneath
the
centre
A
,
doe
shew
the
proportionall
minutes
,
which
are
partly
described
before
in
the
sixt
figure
of
the
Moone
,
and
shall
be
more
fully
againe
described
here
.
Now
,
as
touching
the
rest
of
the
letters
placed
as
wel
within
the
figure
,
as
round
about
the
same
,
we
come
now
to
shew
their
significations
:
for
the
letters
E
F
G
H
do
signifie
the
Excentrique
,
whose
Auge
is
marked
with
the
letter
E
,
and
his
opposit
Auge
with
the
letter
G.
A
description
of
the
meane
longitudes
.
MOreouer
,
there
is
a
point
in
the
middest
betwixt
the
centre
A
and
the
centre
B
,
marked
with
the
letter
I
,
through
which
point
is
drawne
a
right
line
,
marked
with
the
letters
F
I
H
,
which
falling
perpendicularly
vpon
the
line
E
A
G
,
crosseth
the
same
in
the
point
I
with
right
angles
,
and
thereby
sheweth
the
two
meane
longitudes
in
the
Excentrique
,
marked
with
the
letters
F
H
,
in
which
two
places
the
centre
of
the
Epicicle
is
alwaies
equally
distant
as
well
from
the
centre
B
,
as
from
the
centre
A.
And
therefore
those
two
points
doe
shew
the
meane
longitudes
.
And
when
the
centre
of
the
Epicicle
commeth
to
any
of
those
two
points
,
then
the
greatest
equacion
of
the
Excentrique
of
Saturne
is
6
degrees
,
i/30
ii/30
and
that
of
Iupiter
is
5
degrees
,
i/14
and
that
of
Mars
is
11
degrees
,
i/6
But
when
the
centre
of
the
Epicicle
is
in
the
Auge
of
the
Excentrique
,
marked
with
E
,
then
the
arch
Q
R
sheweth
the
greatest
equacion
for
Saturne
to
be
5
degrees
,
i/55
ii/33
and
for
Iupiter
10
degrees
,
i/30
ii/15
and
for
Mars
36
degrees
,
i/54
ii/20
And
when
the
centre
of
the
Epicicle
is
in
the
opposit
Auge
of
the
Excentrique
,
marked
with
G
,
then
the
arch
QT
sheweth
the
greatest
equacion
for
Saturne
to
be
6
degrees
,
i/38
ii/40
and
for
Iupiter
11
degrees
,
i/31
ii/30
and
for
Mars
46
degrees
,
i/38
ii/15
What
be
the
excesses
of
the
longer
and
nigher
longitudes
?
BEfore
I
define
what
they
be
,
it
shall
not
be
amisse
to
aduertise
you
,
that
both
Ptolomey
,
Purbachius
,
and
the
followers
of
Alphonsus
,
in
counting
or
measuring
the
equacions
of
the
Epicicle
of
the
Moone
,
or
of
the
argument
(
as
they
tearme
it
)
they
haue
regard
onely
to
the
excesse
of
the
longer
and
shorter
diameter
of
the
Auges
of
the
Excentrique
,
which
excesse
they
call
the
diuersitie
of
the
diameter
;
which
is
plainely
described
before
in
the
sixt
figure
belonging
to
the
Theorique
of
the
Moone
,
and
therefore
resort
thereunto
,
that
you
may
the
better
beare
it
in
mind
.
But
in
the
other
Planets
they
make
two
excesses
,
whereof
they
call
the
one
the
excesse
of
the
longer
longitude
,
and
the
other
the
excesse
of
the
nigher
longitude
.
The
excesse
of
the
longer
longitude
,
is
an
arch
of
the
Zodiake
,
shewing
the
equacion
of
the
Epicicle
,
when
the
centre
therof
is
in
any
of
the
two
meane
longitudes
,
marked
in
the
Excentrique
on
the
right
hand
with
the
letter
H
,
and
on
the
left
hand
with
the
letter
F
:
for
then
the
foresaid
arch
of
the
Zodiake
is
greater
than
that
which
sheweth
the
equacion
of
the
Epicicle
,
his
centre
being
in
the
Auge
of
the
Excentrique
,
marked
with
E.
But
when
the
centre
of
the
Epicicle
is
in
the
opposit
Auge
of
the
Excentrique
,
then
the
foresaid
arch
of
the
Zodiake
which
is
right
against
the
meane
longitude
,
marked
with
H
,
is
lesser
than
the
arch
of
the
Zodiake
,
which
representeth
the
equacion
of
the
Epicicle
,
his
centre
being
in
the
said
opposit
Auge
of
the
Excentrique
,
and
therefore
is
called
the
excesse
of
the
nigher
longitude
.
And
of
these
two
excesses
doe
rise
two
sorts
of
proportionall
minutes
,
that
is
,
the
longer
and
the
nigher
.
All
which
things
you
shall
better
vnderstand
,
by
helpe
of
the
last
fourth
Figure
:
in
which
figure
the
arch
marked
with
the
letters
Q
R
S
on
the
right
hand
of
the
said
figure
is
the
arch
of
the
Zodiake
,
representing
the
equacion
of
the
Epicicle
when
his
centre
is
in
the
point
H
,
signifying
the
meane
longitude
of
the
Excentrique
,
which
arch
is
greater
than
the
arch
marked
with
Q
R
,
in
the
top
of
the
Figure
,
shewing
the
equacion
of
the
Epicicle
,
when
his
centre
is
in
the
Auge
of
the
Excentrique
,
marked
with
E
,
by
so
much
as
that
little
portion
of
the
Zodiake
,
marked
on
the
right
hand
of
the
figure
with
the
letters
R
S
,
doth
shew
,
as
you
may
easily
trie
with
your
Compasses
.
And
the
said
arch
Q
R
S
is
lesser
than
the
arch
Q
T
,
standing
in
the
lowest
part
of
the
figure
,
whe●eas
the
centre
of
the
Epicicle
is
in
the
opposit
Auge
of
the
Excentrique
,
marked
with
the
letter
G
,
by
so
much
as
the
letters
ST
on
the
right
hand
do
shew
,
so
as
in
this
figure
the
letters
R
S
on
the
right
hand
doe
shew
the
excesse
of
the
longer
longitude
,
and
the
letters
ST
on
the
same
hand
doe
shew
the
excesse
of
the
nigher
longitude
:
of
which
two
excesses
doe
spring
the
two
kinds
of
proportionall
minutes
before
mentioned
,
which
doe
serue
to
shew
how
much
euery
equacion
of
the
Epicicle
is
greater
or
lesser
than
another
,
when
the
centre
of
the
Epicicle
is
in
any
other
place
of
the
Excentrique
,
and
is
clean
out
of
the
Auge
or
opposit
Auge
,
and
also
out
of
the
meane
longitude
of
the
Excentrique
.
And
as
in
the
sixt
figure
of
the
Moone
the
equacions
of
the
Epicicle
in
euery
place
of
the
Excentrique
(
his
centre
being
neither
in
the
Auge
nor
in
the
opposite
Auge
of
the
Excentrique
)
is
knowne
by
the
proportionall
minutes
,
for
that
as
well
the
excesse
of
the
longest
,
as
the
excesse
of
the
shortest
diameter
of
the
Auges
of
the
Excentrique
is
each
of
them
there
diuided
into
sixtie
minutes
:
so
here
likewise
the
said
proportionall
minutes
are
found
out
by
deuiding
the
difference
or
ouerplus
that
is
betwixt
the
diameter
of
the
meane
longitude
,
and
the
longest
diameter
of
the
Auge
of
the
Excentrique
into
60
minutes
;
and
also
by
deuiding
into
60
minutes
the
ouerplus
or
difference
that
is
betwixt
the
diameter
of
the
meane
longitude
and
the
shortest
diameter
of
the
Auges
of
the
Excentrique
,
as
you
may
plainely
perceiue
by
the
last
fourth
figure
,
wherein
as
the
line
A
E
signifying
the
longer
diameter
of
the
Auges
of
the
Excentrique
,
exceedeth
in
length
the
diameter
of
the
meane
longitude
,
marked
on
the
right
hand
with
A
H
,
and
on
the
left
hand
with
A
F
,
by
a
third
part
and
somewhat
more
(
which
excesse
or
ouerplus
is
deuided
into
60
minutes
:
)
euen
so
the
difference
or
ouerplus
,
whereby
the
diameter
A
H
or
A
F
exceedeth
the
shorter
diameter
of
the
Auges
of
the
Excentrique
,
marked
with
the
letters
A
G
,
is
also
deuided
into
60
minutes
;
of
which
the
first
i/60
are
called
the
longer
proportionall
minutes
,
and
the
last
i/60
are
called
the
nigher
proportional
minutes
,
because
they
are
nigher
to
the
centre
of
the
earth
.
And
according
as
any
other
right
line
drawne
from
A
the
centre
of
the
world
to
the
centre
of
the
Epicicle
,
being
in
any
other
place
of
the
Excentrique
,
out
of
the
Auge
or
opposit
Auge
of
the
Excentrique
,
or
out
of
the
mean
longitudes
,
is
longer
or
shorter
;
so
doth
the
equacion
of
the
Epicicle
encrease
or
decrease
:
For
as
by
supposing
the
centre
of
the
Epicicle
to
be
in
the
point
K
of
the
Excentrique
,
you
shall
find
the
right
line
A
K
to
be
longer
than
the
line
A
H
by
40
minutes
;
euen
so
the
equacion
of
the
Epicicle
in
K
,
marked
with
Q
S
,
is
lesser
than
the
equacion
of
the
Epicicle
in
the
point
H
,
marked
also
with
Q
S
,
by
40
of
such
minutes
,
as
the
little
arch
R
S
,
signifying
the
excesse
of
the
longer
longitude
,
doth
containe
60
minutes
.
Likewise
,
as
the
line
A
L
is
shorter
than
the
line
A
H
by
40
minutes
,
euen
so
the
equacion
of
the
Epicicle
,
marked
with
Q
S
(
his
centre
beeing
in
L
)
is
greater
than
the
equacion
of
the
said
Epicicle
,
marked
also
with
Q
S
,
his
centre
beeing
in
the
point
H
,
by
40
of
such
minutes
,
as
the
arch
S
T
,
signifying
the
nigher
longitude
,
dooth
containe
60
minutes
.
And
remember
here
,
that
in
seeking
in
this
figure
to
know
the
length
of
the
line
A
K
by
the
minutes
,
you
must
put
the
firme
foot
of
your
Compas
in
the
centre
A
,
and
the
moouable
foot
in
the
point
L
,
and
so
to
draw
the
moouable
foot
from
thence
to
the
line
A
H
Q
,
vpon
which
line
the
numbers
of
the
60
proportionall
minutes
are
set
downe
:
and
to
know
the
length
of
the
line
A
L
,
you
must
fit
your
Compasses
to
A
L
,
and
then
draw
the
mouable
foot
to
the
line
A
G
Q
,
vpon
which
line
are
also
set
downe
the
60
proportionall
minutes
,
in
like
manner
as
they
are
vpon
the
line
A
H
Q
,
sauing
that
in
the
line
A
H
Q
the
said
60
minutes
are
to
be
counted
from
H
towards
Q
,
and
in
the
line
A
G
Q
they
proceed
vpward
from
Q
to
G
,
according
as
the
inferior
halfe
circles
doe
shew
.
And
after
this
manner
you
must
deale
,
to
know
the
length
of
any
other
line
drawne
from
the
centre
A
to
any
other
point
of
the
Excentrique
,
whereinto
the
centre
of
the
Epicicle
chaunceth
to
fall
;
considering
alwayes
whether
such
line
be
either
longer
or
shorter
than
the
line
A
H
,
passing
through
the
point
of
the
meane
longitude
,
to
the
intent
you
may
know
thereby
how
to
applie
the
length
of
euery
line
to
the
right
number
of
the
proportionall
minutes
belonging
to
the
same
.
But
you
haue
to
note
,
that
neither
Copernicus
nor
the
Prutenicall
tables
doe
make
any
more
kinds
of
excesses
or
proportionall
minutes
,
but
that
onely
which
is
plainly
declared
before
in
the
sixt
figure
of
the
Moone
.
What
is
the
diameter
of
the
Auges
in
the
Epicicle
?
IT
is
a
right
line
passing
through
the
centre
of
the
Epicicle
,
and
also
through
the
true
Auge
and
the
true
opposit
Auge
of
the
said
Epicicle
:
which
line
deuideth
the
plane
of
the
Epicicle
into
two
equall
hal●es
,
whereof
the
one
is
called
the
Orientall
halfe
,
and
the
other
the
Occidentall
halfe
,
hereafter
described
in
the
sixt
figure
.
What
is
the
diameter
of
the
mean
longitudes
in
the
Epicicle
?
IT
is
a
right
line
drawne
through
the
centre
of
the
Epicicle
,
erected
perpendicularly
vpon
the
diameter
of
the
true
Auges
of
the
said
Epicicle
next
before
defined
:
and
when
the
Planet
falleth
into
this
line
,
it
sheweth
the
meane
distance
that
is
betwixt
the
greatest
longitude
in
the
Auge
of
the
Epicicle
,
and
the
least
longitude
in
the
opposit
Auge
of
the
said
Epicicle
,
and
thereof
is
called
the
diameter
of
the
meane
longitudes
.
And
this
line
deuideth
also
the
plane
of
the
Epicicle
into
two
halfes
,
that
is
,
the
vpper
halfe
,
and
the
nether
halfe
.
The
vpper
halfe
is
that
which
is
aboue
the
diameter
of
the
meane
longitudes
,
and
is
farthest
from
the
earth
:
and
the
lower
or
nether
halfe
is
beneath
the
said
diameter
,
and
is
nigher
to
the
earth
.
What
is
the
Orientall
and
Occidentall
halfe
of
the
Epicicle
?
THe
Orientall
halfe
is
that
,
which
being
contained
betwixt
the
Auge
and
opposit
Auge
,
looketh
towards
the
East
:
and
the
other
halfe
looking
towards
the
West
,
is
called
the
Occidentall
halfe
.
And
you
haue
to
note
,
that
as
well
in
these
three
Planets
,
as
in
the
other
two
Planets
next
following
,
that
is
,
Venus
and
Mercurie
,
the
first
halfe
of
the
Epicicle
is
Orientall
,
and
the
later
halfe
Occidentall
:
but
in
the
Moone
the
later
halfe
of
her
Epicicle
is
Orientall
,
and
the
first
halfe
thereof
is
Occidentall
,
For
the
Epicicle
of
euery
one
of
the
foresaid
fiue
Planets
going
from
the
Auge
,
in
his
vpper
part
,
according
to
the
succession
of
the
signes
,
carrieth
the
Planet
first
into
the
Orientall
halfe
:
but
in
the
Moon
it
is
cleane
contrarie
.
The
fourth
Intention
,
shewing
the
twofold
latitude
of
the
three
vpper
Planets
,
and
wherein
their
latitude
differeth
from
the
latitude
of
the
Moone
.
THe
latitude
of
the
Moone
is
simple
,
hauing
onely
respect
to
the
distance
of
her
Excentrique
or
Deferent
,
from
the
Eclipticke
line
;
whose
greatest
distance
from
thence
,
either
toward
the
North
or
South
,
is
but
fiue
degrees
,
as
hath
been
said
before
,
by
reason
that
the
poles
of
her
Excentrique
are
distant
from
the
poles
of
the
Ecliptick
no
more
but
fiue
degrees
.
But
the
latitude
of
the
three
vpper
Planets
is
to
be
considered
two
manner
of
waies
:
First
,
according
to
the
distance
of
any
of
their
excentriques
from
the
Eclipticke
:
and
secondly
,
according
to
the
distance
of
any
of
their
Epicicles
from
the
Excentrique
thereof
,
which
two
kinds
of
latitude
Purbachius
describeth
the
first
in
this
manner
:
The
first
(
sayth
he
)
chaunceth
by
reason
that
the
plane
or
superficies
of
the
Excentrique
of
the
Planet
declineth
from
the
plane
of
the
Eclipticke
in
two
parts
opposit
,
the
greatest
distance
of
such
declination
remaining
alwaies
invariable
like
as
in
the
Moone
,
and
yet
the
two
Nodes
or
Intersections
,
that
is
to
say
,
the
node
ascendent
and
descendent
,
otherwise
called
the
head
and
taile
of
the
Dragon
,
are
not
moued
contrary
to
the
succession
of
the
signes
(
as
in
the
Moone
)
but
according
to
the
mouing
of
the
eighth
sphere
,
so
as
the
Auges
of
the
deferents
of
those
Nodes
do
describe
on
the
North
side
,
paralell
circumferences
that
be
equally
distant
from
the
Eclipticke
:
and
though
such
Auges
be
alwaies
septentrionall
,
yet
notwithstanding
those
Auges
be
not
in
all
the
three
planets
the
very
points
or
limits
of
the
greatest
latitude
of
their
deferents
from
the
Eclipticke
;
yea
that
falleth
out
only
in
Mars
,
the
Auge
of
whose
excentrique
doth
most
decline
from
the
Eclipticke
to
the
North
;
but
in
Saturne
the
point
or
limit
of
his
greatest
latitude
goeth
before
the
Auge
of
his
excentrique
,
contrary
to
the
succession
of
the
signes
,
and
is
distant
from
his
Auge
50
degrees
;
and
in
Iupiter
such
point
goeth
after
the
Auge
of
his
excentrique
according
to
the
succession
of
the
signs
,
and
is
distant
from
his
Auge
20
degrees
.
All
which
things
you
shall
more
plainly
perceiue
by
this
figure
here
following
,
set
downe
by
Reinholdus
in
his
Comment
vpon
Purbacchius
.
¶
The
fifth
figure
of
the
three
superior
Planets
.
IN
this
figure
the
letter
D
signifieth
the
centre
of
the
world
,
whereupon
is
drawne
a
circle
signifying
the
plane
of
the
Eclipticke
:
and
the
said
point
D
,
representeth
also
both
the
poles
of
the
Eclipticke
.
And
vpon
the
point
C
is
drawn
another
circle
,
signifying
the
plane
or
superficies
of
the
excentrique
,
marked
in
the
vpper
part
with
the
letters
A
B
E
,
enclining
as
you
see
towards
the
plane
of
the
Eclipticke
.
And
because
the
two
planes
,
that
is
,
the
plane
of
the
Excentrique
&
the
plane
of
the
Eclipticke
doe
crosse
or
cut
one
another
in
the
very
centre
of
the
world
,
marked
with
D
;
and
because
the
Auges
of
the
three
Planets
are
all
distant
from
the
Eclipticke
towards
the
North
;
therefore
the
centres
of
their
Excentriques
must
needs
be
also
Northerly
,
and
out
of
the
centre
of
the
Eclipticke
:
so
as
the
centre
of
the
Excentrique
for
Saturne
,
is
to
be
found
in
the
line
A
D
,
and
for
Mars
,
in
the
line
B
D
,
and
for
Iupiter
,
in
the
line
E
D.
And
the
Auge
of
Saturne
is
marked
with
A
,
and
that
of
Mars
with
B
,
and
that
of
Iupiter
with
E.
Moreouer
,
the
right
line
,
marked
with
the
letters
B
F
C
G
H
,
representeth
the
plane
of
the
greatest
circle
,
passing
as
well
through
the
poles
of
the
Eclipticke
,
as
also
through
that
right
line
,
which
passing
through
the
centre
of
the
world
is
erected
with
right
angles
vpon
the
plane
of
the
excentrique
:
For
this
plane
of
the
greatest
circle
doth
deuide
the
arches
,
as
well
of
the
Excentrick
,
as
also
of
the
Eclipticke
,
two
manner
of
wayes
:
which
arches
are
distinguished
in
this
figure
by
the
two
vsuall
caracters
,
signifying
the
two
nodes
,
otherwise
called
the
head
and
taile
of
the
Dragon
:
and
either
of
the
two
distances
,
F
B
,
or
G
H
,
sheweth
the
greatest
declination
of
the
two
planes
,
And
finally
,
the
point
B
is
the
limit
of
the
North
latitude
,
and
G
the
limit
of
the
South
latitude
of
any
of
the
three
Planets
.
Thus
you
may
perceiue
,
that
the
Auge
of
the
Excentrique
of
Mars
is
alwayes
in
the
North
limit
,
and
his
opposite
Auge
in
the
South
limit
,
but
the
Auge
of
Iupiters
Excentrique
,
marked
in
the
former
Figure
with
E
,
goeth
before
the
North
limit
B
,
that
is
to
say
,
the
centre
of
Iupiters
Epicicle
commeth
to
the
Auge
of
his
Excentrique
,
before
that
it
arriueth
to
the
North
limit
.
And
finally
,
the
Auge
of
Saturne
his
Excentrique
,
marked
in
the
said
figure
with
A
,
followeth
after
the
North
limit
,
so
as
the
centre
of
his
Epicicle
arriueth
to
the
North
limit
,
before
it
commeth
to
the
Auge
of
his
Excentrique
.
And
the
followers
of
Alphonsus
do
make
the
Node
ascendent
of
Mars
to
be
at
this
day
in
the
sixteenth
degree
of
Taurus
,
and
his
Node
descendent
to
be
in
the
sixteenth
degree
of
Scorpio
:
and
the
Node
ascendent
of
Iupiter
to
bee
in
the
14
degree
of
Cancer
,
and
his
Node
descendent
to
be
in
the
14
degree
of
Capricorne
,
and
his
North
limit
to
be
in
the
14
degree
of
Libra
.
And
the
Node
ascendent
of
Saturne
to
be
in
the
24
degree
of
Cancer
,
and
his
Node
descendent
to
be
in
the
24
degree
of
Capricorne
,
because
his
North
limit
is
in
the
24
degree
of
Libra
,
so
as
there
is
no
great
difference
betwixt
Saturne
and
Iupiter
,
touching
their
limits
.
And
partly
hereby
,
and
partly
by
that
which
followeth
hereafter
,
it
shall
manifestly
appeare
that
Saturne
whilest
he
passeth
through
the
one
halfe
of
the
Zodiake
,
counting
from
the
24
degree
of
Cancer
vnto
the
24
degree
of
Capricorne
,
he
hath
alwaies
North
latitude
;
and
whilest
he
passeth
through
the
other
halfe
of
the
Zodiake
,
he
hath
alwaies
South
latitude
.
Wherefore
considering
that
he
maketh
his
whole
reuolution
in
thirtie
yeares
,
he
hath
continually
during
the
space
of
15
yeares
North
latitude
,
and
during
the
other
15
yeares
South
latitude
:
and
the
like
is
to
be
judged
of
Iupiter
and
Mars
,
according
to
the
time
of
their
entire
reuolutions
;
for
Iupiter
maketh
his
reuolution
in
12
yeares
,
and
Mars
in
2
yeares
.
But
Mestlyn
following
Copernicus
,
setteth
down
the
places
of
the
North
limit
and
Node
ascendent
of
euery
one
of
the
three
vpper
Planets
in
this
manner
,
that
is
to
say
,
the
North
limit
of
♄
to
be
in
these
daies
in
the
9
degree
,
i10°
of
m
,
and
that
of
♃
to
be
in
the
26
degree
,
i40°
of
♎
,
and
that
of
♂
to
be
in
the
28
degree
,
i24°
of
♎
Againe
,
the
node
ascendent
of
♄
to
be
in
the
9
degree
,
i10°
of
♌
,
and
that
of
♃
to
be
in
the
26
degree
,
i40°
of
69
,
and
that
of
♂
to
be
in
the
28
degree
,
i24°
of
♉
.
And
as
for
the
South
limit
and
the
node
descendent
of
euery
Planet
,
each
one
doth
occupie
in
the
Zodiake
such
degree
and
minutes
as
is
opposit
to
the
place
of
the
North
limit
,
and
of
the
node
ascendent
of
euery
one
of
the
said
Planets
before
set
downe
.
And
Mestlyn
sayth
,
That
as
the
greatest
latitude
of
the
Moone
either
North
or
South
from
the
Eclipticke
,
is
only
fiue
degrees
,
so
he
appointeth
to
the
greatest
latitude
of
the
Excentrique
of
♄
from
the
Eclipticke
but
2
degrees
,
i30°
and
to
that
of
♃
1
degree
,
i30°
and
to
that
of
♂
1
degree
,
i0°
Now
to
shew
the
second
manner
of
latitude
belonging
to
the
three
vpper
Planets
,
caused
by
the
enclining
of
the
true
Auge
of
the
Epicicle
from
the
Excentrique
,
I
mind
therin
to
follow
Mes●lyn
,
who
affirmeth
that
kind
of
latitude
to
be
twofold
,
whereof
the
one
is
called
Inclination
,
and
the
other
Reflexion
:
neither
of
them
being
fixed
,
but
mutable
,
and
yet
proportionable
to
the
period
of
their
Excentriques
,
for
the
better
vnderstanding
whereof
he
setteth
down
this
figure
following
.
¶
The
sixt
figure
belonging
to
the
three
vpper
Planets
.
IN
which
figure
the
centre
A
is
the
centre
of
the
world
,
whereupon
is
drawne
the
outermost
circle
,
signifying
the
plane
of
the
Zodiake
,
marked
with
the
letters
B
C
D
E
,
passing
through
the
poles
of
the
Ecliptique
,
marked
with
the
letters
C
E.
Then
vpon
the
centre
F
is
drawn
another
circle
,
signifying
the
plane
of
the
Excentrique
,
marked
with
the
letters
G
H
I
K
,
passing
through
the
poles
of
the
Excentrique
,
marked
with
the
letters
M
O
,
and
also
through
the
North
limit
,
marked
with
L
,
and
through
the
South
limit
,
marked
with
N
;
and
the
two
little
circles
placed
vpon
the
Excentrique
,
each
of
them
signifieth
the
Epicicle
.
And
you
haue
to
note
,
that
the
plane
of
the
motion
of
the
said
Excentrique
is
signified
here
by
the
right
line
,
marked
with
the
letters
L
F
N
,
which
cutteth
the
Eclipticke
in
the
centre
A
;
so
as
when
the
centre
of
the
Epicicle
is
in
L
,
it
hath
then
his
greatest
North
latitude
,
likewise
being
in
N
,
it
hath
his
greatest
South
latitude
:
and
by
this
Figure
you
may
perceiue
,
that
the
one
pole
of
the
Excentrique
is
more
distant
from
the
pole
of
the
Eclipticke
than
the
other
,
for
O
is
more
distant
from
K
,
than
H
from
M.
The
signification
of
the
rest
of
the
letters
wherwith
the
Epicicles
are
marked
,
shall
be
declared
hereafter
.
In
the
meane
time
we
will
speake
first
of
the
latitude
,
called
the
Inclination
of
the
Epicicle
,
in
Greeke
En●lysis
,
which
causeth
the
diameter
of
the
Auges
of
the
Epicicle
to
decline
on
both
sides
of
the
plane
of
the
Excentrique
,
that
is
to
say
,
as
well
inwardly
as
outwardly
,
in
maner
and
forme
following
:
for
when
the
centre
of
the
Epicicle
is
in
any
of
the
two
Nodes
,
the
diameter
of
the
Auges
doth
not
decline
at
all
either
from
the
Excentrique
orfrom
the
plane
of
the
Eclipticke
,
because
then
it
falleth
just
into
their
mutuall
fection
.
But
when
the
centre
of
the
Epicicle
departeth
from
any
of
the
Nodes
,
then
in
the
vpper
halfe
of
the
Excentrique
,
containing
the
Auge
of
the
Epicicle
,
the
foresaid
diameter
of
the
Auges
declineth
inwardly
from
the
Excentrique
towards
the
plane
of
the
Eclipticke
,
and
yet
arriueth
not
to
the
same
.
But
when
the
centre
of
the
Epicicle
is
in
the
nether
halfe
of
the
Excentrique
,
containing
the
opposit
Auge
of
the
Epicicle
,
the
diameter
of
the
Auges
declineth
outwardly
from
the
Excentrick
towards
the
Eclipticke
,
and
yet
arriueth
not
to
the
same
.
And
the
greatest
declination
of
this
diameter
is
when
the
centre
of
the
Epicicle
is
in
any
of
the
limits
;
and
yet
such
declination
is
no
where
so
great
,
as
that
being
out
of
the
Nodes
,
it
can
reach
vnto
the
Eclipticke
:
and
this
declination
maketh
his
reuolution
vpon
the
diameter
of
the
mean
longitudes
.
The
most
part
of
which
things
you
may
see
plainely
set
foorth
in
the
sixt
figure
before
described
,
in
which
both
the
Epicicles
are
marked
with
the
letters
P
Q
R
,
whereof
P
signifieth
in
either
of
the
Epicicles
the
Auge
,
and
R
signifieth
the
opposit
Auge
of
the
Epicicle
,
and
the
arch
P
Q
signifieth
the
greatest
Inclination
of
the
diameter
of
those
Auges
to
the
Excentrique
.
So
as
when
the
centre
of
the
Epicicle
is
in
the
North
limit
marked
with
L
,
the
foresaid
Auge
P
declineth
inwardly
from
the
plane
of
the
Excentrique
towards
the
Eclipticke
,
and
R
the
opposit
Auge
fleeth
outwardly
from
the
Eclipticke
.
But
when
the
centre
of
the
Epicicle
is
in
the
South
limit
,
marked
with
N
,
then
the
Auge
P
being
on
the
other
side
of
the
Excentrique
,
declineth
againe
towards
the
Eclipticke
,
and
R
the
opposit
Auge
occupieth
the
opposit
place
to
P.
And
you
haue
to
vnderstand
,
that
the
greatest
declination
here
signified
by
the
arch
P
Q
for
♄
containeth
4
degrees
,
i30°
and
for
♃
2
degrees
,
i30°
and
for
♂
2
degrees
,
i15°
And
to
the
intent
that
you
may
the
better
conceiue
all
the
varietie
of
the
foresaid
Inclination
,
Mestlyn
setteth
downe
this
other
Figure
here
next
following
,
which
also
serueth
to
demonstrat
the
second
kind
of
latitude
,
called
Reflexion
,
in
Greeke
Loxasis
,
hereafter
by
him
plainely
described
.
¶
The
seuenth
figure
belonging
to
the
The●rique
of
the
three
vpper
Planets
.
IN
this
figure
vpon
the
centre
F
,
signifying
the
centre
of
the
world
,
is
drawne
a
great
circle
,
which
signifieth
the
whole
sphere
of
the
Planet
,
whose
poles
are
marked
with
D
E
,
whereof
D
is
the
North
pole
,
and
E
the
South
pole
.
And
within
this
circle
are
drawne
two
other
oblique
circles
of
shape
,
ovale
;
whereof
the
outermost
marked
with
the
letters
A
B
C
,
signifieth
the
Ecliptick
:
and
the
inward
circle
signifieth
the
Excentrique
,
whereon
are
placed
foure
Epicicles
,
the
highest
whereof
hath
his
centre
marked
with
G
,
signifying
here
the
North
limit
;
and
the
centre
of
the
lowest
Epicicle
is
marked
with
N
,
signifying
the
South
limit
;
and
the
centre
of
the
Epicicle
on
your
right
hand
is
marked
with
M
,
signifying
the
Node
ascendent
;
and
the
centre
of
the
Epicicle
on
your
left
hand
is
marked
with
O
,
signifying
the
Node
descendent
.
Moreouer
,
euery
Epicicle
is
crossed
with
two
diameters
,
whereof
that
which
is
marked
with
H
K
,
doth
signifie
in
euery
Epicicle
the
line
of
the
Auges
of
the
Epicicle
,
that
is
to
say
,
H
the
Auge
,
and
K
the
opposit
Auge
;
and
the
other
diameter
marked
with
I
L
,
signifieth
the
line
of
the
meane
longitudes
.
Wherfore
whensoeuer
the
centre
of
the
Epicicle
is
in
the
Node
ascendent
,
marked
with
M
,
then
there
is
no
Inclination
of
the
diameter
of
the
Auges
,
because
it
falleth
into
the
common
Intersection
,
as
well
of
the
Excentrique
as
of
the
Eclipticke
:
but
the
more
that
the
diameter
of
the
Auges
departeth
from
thence
towards
the
North
limit
,
the
more
it
falleth
vpon
the
line
of
the
meane
longitudes
,
marked
with
I
L
,
insomuch
,
as
when
it
arriueth
to
the
North
limit
,
marked
with
G
,
the
inclination
then
is
greatest
,
and
the
line
of
the
Auge
falleth
directly
and
perpendicularly
vpon
the
line
of
the
meane
longitudes
,
and
from
thence
the
inclination
decreaseth
,
vntil
the
diameter
of
the
Auges
arriueth
to
the
Node
descendent
,
marked
with
O
,
in
which
point
it
hath
againe
no
declination
.
But
departing
from
thence
towards
N
,
the
inclination
of
this
diameter
goeth
vnto
the
other
side
of
the
Excentrique
.
For
as
the
Auge
of
the
Epicicle
passing
first
from
M
through
G
into
O
,
declineth
from
the
plane
of
the
Excentrique
towards
E
the
South
pole
:
euen
so
departing
from
O
,
and
passing
through
N
to
M
,
it
declineth
towards
D
the
North
pole
:
and
so
the
Auge
H
is
found
againe
to
encline
to
the
Eclipticke
:
and
K
the
opposite
Auge
to
flee
from
the
same
vntill
it
hath
his
greatest
declination
,
which
is
in
the
point
N
,
and
from
thence
it
returneth
to
M
,
&
there
again
hath
no
declination
at
all
.
Of
the
second
latitude
,
caused
by
the
Epicicle
,
called
the
Reflexion
.
BY
this
Reflexion
the
diameter
of
the
meane
longitudes
of
the
Epicicle
,
marked
in
the
former
seuenth
figure
with
the
letters
I
L
,
reflecteth
or
turneth
backward
,
as
well
within
as
without
the
plane
of
the
Excentrique
,
sauing
that
when
the
centre
of
the
Epicicle
is
in
any
of
the
limits
,
for
then
this
diameter
falleth
just
and
wholly
vpon
the
plane
of
the
Excentrique
,
but
when
the
centre
of
the
Epicicle
departeth
from
any
of
the
limits
,
then
the
Occidentall
halfe
of
this
diameter
turneth
inwardly
within
the
plane
,
as
well
of
the
Excentrique
as
of
the
Eclipticke
;
and
the
Orientall
halfe
of
the
said
diameter
turneth
outwardly
,
that
is
,
on
the
outside
of
both
the
said
planes
.
What
the
Occidentall
and
Orientall
halfe
is
,
hath
beene
described
before
in
the
third
Intention
.
And
note
,
that
the
greatest
reflexion
of
this
diameter
chanceth
when
the
centre
of
the
Epicicle
is
in
any
of
the
Nodes
,
which
greatest
reflexion
for
Saturne
,
is
2
degrees
,
i30°
and
for
Iupiter
one
degree
,
i30°
and
for
Mars
one
degree
,
i0°
And
this
greatest
reflexion
is
like
vnto
the
greatest
obliquitie
or
latitude
of
the
Excentrique
from
the
Eclipticke
,
as
is
before
set
downe
.
Moreouer
,
you
haue
to
note
,
that
as
in
the
former
kind
of
latitude
,
called
Inclination
,
the
diameter
of
the
Auges
of
the
Epicicle
maketh
his
reuolution
vpon
the
diameter
of
the
meane
longitudes
;
so
in
this
second
kind
of
latitude
called
Reflexion
,
the
diameter
of
the
mean
longitudes
maketh
his
reuolution
vpon
the
diameter
of
the
Auges
.
And
for
the
better
vnderstanding
of
that
which
hath
been
said
here
touching
the
reflexion
of
the
diameter
of
the
meane
longitudes
,
marke
well
the
former
seuenth
figure
,
in
which
you
may
see
,
that
when
the
centre
of
the
Epicicle
is
in
the
North
limit
,
marked
with
G
,
the
diameter
of
the
meane
longitudes
,
marked
with
I
L
,
lieth
full
vpon
the
plane
of
the
Excentrique
,
without
any
reflexion
.
But
when
the
centre
departeth
from
thence
,
then
the
Occidentall
halfe
of
the
said
diameter
,
contained
betwixt
the
centre
and
the
letter
L
,
bendeth
inwardly
towards
the
South
pole
,
and
this
Occidentall
halfe
still
remaineth
within
the
Eclipticke
and
within
the
Excentrique
,
vntill
the
centre
of
the
Epicicle
falleth
into
the
Node
descendent
,
marked
with
O
,
in
which
place
the
said
diameter
hath
his
greatest
reflexion
,
and
euen
there
is
vnited
to
the
plane
of
the
Eclipticke
.
And
the
centre
of
the
Epicicle
departing
from
thence
the
said
Occidentall
halfe
,
remaining
out
of
the
Eclipticke
and
out
of
the
Excentrique
,
approcheth
againe
to
the
plane
of
the
Excentrique
,
and
is
vnited
to
the
same
in
the
point
N
:
but
in
the
other
Orientall
halfe
it
happeneth
cleane
contrarie
.
What
conclusions
doe
follow
vpon
these
two
kinds
of
latitudes
,
called
the
Inclination
and
Reflexion
.
1.
THese
seuen
here
following
:
for
first
,
whensoeuer
the
centre
of
the
Epicicle
is
in
any
of
the
Nodes
,
then
the
whole
plane
of
the
Epicicle
falleth
into
the
plane
of
the
Eclipticke
,
for
then
the
diameter
of
the
Auges
of
the
Epicicle
is
also
there
,
hauing
no
Inclination
at
all
.
And
then
there
is
also
the
diameter
of
the
meane
longitudes
of
the
Epicicle
,
whose
obliquite
from
the
Excentrique
,
is
alwaies
so
much
as
is
the
obliquite
of
the
Excentrique
from
the
Eclipticke
.
But
the
Epicicle
is
neuer
vnited
to
the
plane
of
the
Excentrique
,
because
neither
of
the
foresaid
diameters
doe
decline
both
at
once
from
the
plane
of
the
Excentrique
.
2.
Secondly
,
the
centre
of
the
Epicicle
being
in
any
of
the
Nodes
,
the
axletree
of
the
Epicicle
standeth
perpendicularly
vpon
the
axletree
of
the
Eclipticke
,
from
which
it
is
then
equally
distant
.
But
it
is
not
equally
distant
to
the
axletree
of
the
Excentrique
.
3.
Thirdly
,
hereof
may
be
gathered
,
that
the
planes
of
the
Excentriques
and
of
the
Epicicles
doe
cut
one
another
alwaies
in
a
diuers
diameter
,
for
in
the
two
nodes
such
section
is
made
vpon
the
diameter
of
the
Auges
,
but
in
the
two
limits
such
section
is
made
vpon
the
diameter
of
the
meane
longitudes
:
and
in
all
other
meane
places
betwixt
the
said
nodes
and
limits
,
such
section
chanceth
somtime
in
one
place
,
&
somtime
in
another
.
4.
Fourthly
,
the
line
of
the
mutuall
section
,
whereas
the
Epicicle
and
the
Excentrique
doe
cut
one
another
,
doth
wander
through
the
plane
of
the
Epicicle
in
such
sort
,
as
the
one
halfe
of
the
Epicicle
looking
vp
towards
the
North
limit
,
declineth
from
the
plane
of
the
Excentrique
towards
the
South
.
And
the
other
halfe
approching
nigher
to
the
South
limit
,
declineth
from
the
Excentrique
towards
the
North
,
as
you
may
plainely
perceiue
by
the
former
seuenth
figure
,
in
which
,
that
halfe
of
the
Epicicle
which
looketh
towards
the
North
limit
,
marked
with
G
,
is
the
vpper
halfe
of
the
Epicicle
,
marked
with
the
letters
L
H
I
:
but
when
that
halfe
commeth
vnto
the
Node
descendent
,
marked
with
O
,
then
it
is
called
the
Occidentall
halfe
,
marked
with
the
letters
K
L
H
:
and
when
it
is
come
to
the
South
limit
,
marked
with
N
,
then
it
is
called
the
inferior
or
nether
halfe
,
marked
with
the
letters
I
K
L
:
But
when
that
halfe
arriueth
to
the
Node
ascendent
,
marked
with
M
,
then
it
is
called
the
Orientall
halfe
,
and
is
marked
with
the
letters
H
I
K.
And
the
other
halfe
of
the
Epicicle
declining
from
the
plane
of
the
Excentrique
towards
the
North
pole
,
looketh
towards
the
South
limit
.
5.
Fifthly
,
when
the
Planet
is
in
the
vpper
halfe
of
the
Epicicle
,
in
which
the
Auge
is
,
then
he
alwaies
walketh
betwixt
the
Eclipticke
and
the
Excentrique
:
but
when
he
is
in
the
nether
halfe
,
he
goeth
cleane
without
them
both
.
6.
Sixtly
,
the
diameter
of
the
Auge
being
in
the
vpper
halfe
of
the
Epicicle
,
and
out
of
the
Nodes
,
declineth
towards
the
Eclipticke
,
and
being
againe
in
the
nether
halfe
,
departeth
from
the
Eclipticke
towards
that
part
whereunto
the
Excentrique
declineth
.
Hereof
it
must
needs
follow
,
that
the
Planet
whilest
he
is
in
the
Orientall
halfe
,
encreaseth
his
latitude
,
and
in
the
Occidentall
halfe
deminisheth
the
same
,
but
yet
so
,
as
his
latitude
from
the
Node
ascendent
to
the
Node
descendent
,
is
alwaies
Northerly
,
and
from
thence
to
the
node
ascendent
it
is
alwaies
Southerly
.
What
be
the
greatest
latitudes
of
the
three
Planets
,
as
well
in
the
North
and
South
limit
,
as
also
in
the
North
and
South
true
Auges
of
the
Epicicle
?
ACcording
to
the
tables
of
Alpho●sus
,
when
the
Planet
is
in
the
North
limit
of
the
Excentrique
,
and
also
in
the
North
true
Auge
of
the
Epicicle
,
then
the
greatest
North
latitude
for
Saturne
is
2
degrees
,
i3
.
for
Iupiter
1
degree
,
i5
.
and
for
Mars
only
i5
.
And
when
the
Planet
is
in
the
North
limit
of
the
Excentrique
,
&
therwith
in
the
North
opposit
Auge
of
the
Epicicle
,
then
the
greatest
North
latitude
for
Saturne
is
3
degrees
,
i3
.
for
Iupiter
2
degrees
,
i5
.
and
for
Mars
4
degrees
,
i21
.
But
when
the
Planet
is
in
the
South
limit
of
the
Excentrique
,
and
therewith
in
the
South
true
Auge
of
the
Epicicle
,
then
the
greatest
South
latitude
for
Saturne
is
two
degrees
,
i5
.
for
Iupiter
1
degree
,
i4
.
and
for
Mars
only
i2
.
And
if
the
Planet
be
in
the
South
limit
of
the
Excentrique
,
and
therewith
in
the
South
opposit
Auge
of
the
Epicicle
,
then
the
greatest
South
latitude
for
Saturne
is
3
degrees
,
i1
.
for
Iupiter
2
degrees
,
i8
.
and
for
Mars
7
degrees
,
i30
.
But
betwixt
Alphonsus
his
tables
and
the
Prutenicall
tables
there
is
some
difference
,
for
the
Prutenicall
tables
when
the
Planet
is
in
the
North
Auge
of
the
Epicicle
,
doe
allow
for
the
greatest
North
latitude
of
Saturne
2
degrees
,
i3
.
for
Iupiter
1
degree
,
i6
.
and
for
Mars
i5
.
Againe
,
the
Planet
being
in
the
North
opposit
Auge
,
they
allow
for
the
greatest
North
latitude
of
Saturne
3
degrees
,
i2
.
for
Iupiter
2
degrees
,
i4
.
and
for
Mars
4
degrees
,
i/30
.
and
when
the
Planet
is
in
the
South
true
Auge
of
the
Epicicle
,
they
allow
for
the
greatest
South
latitude
of
Saturne
2
degrees
,
i2
.
for
Iupiter
1
degree
,
i5
.
and
for
Mars
i4
.
Againe
,
when
the
Planet
is
in
the
South
opposit
Auge
of
the
Epicicle
,
they
allow
for
the
greatest
South
latitude
of
Saturne
3
degrees
,
i5
.
for
Iupiter
2
degrees
,
i7
.
and
for
Mars
6
degrees
,
i50
.
The
seuenth
Conclusion
.
THe
diameter
of
the
meane
longitudes
,
and
the
diameter
of
the
mutuall
sections
of
the
Epicicle
and
of
the
Excentrique
,
are
alwaies
in
a
manner
equally
distant
to
the
diameter
of
the
section
of
the
Excentrique
and
of
the
Eclipticke
,
and
thereby
are
equally
distant
also
,
in
a
manner
to
the
Eclipticke
it selfe
.
I
say
here
in
a
manner
,
because
that
neither
of
the
foresaid
diameters
being
out
of
the
limits
or
nodes
,
are
justly
equally
distant
from
the
Eclipticke
,
yet
the
difference
is
so
small
,
as
it
is
scant
sensible
,
and
therefore
may
be
taken
for
one
simple
latitude
,
whereby
the
plane
of
the
Epicicle
,
which
in
the
Nodes
is
vnited
to
the
Eclipticke
,
maketh
the
diameter
,
which
is
paralell
to
the
line
drawne
through
both
the
limits
to
decline
vpon
that
diameter
,
which
is
a
paralell
to
a
right
line
drawne
through
both
the
Nodes
,
which
the
former
seuenth
figure
plainly
sheweth
:
for
when
the
Epicicle
is
either
in
M
or
in
O
,
then
the
diameter
of
Inclination
,
marked
with
I
L
,
is
paralell
to
the
line
G
F
N
,
drawne
through
the
two
limits
,
and
also
through
the
centre
F.
But
when
the
Epicicle
is
in
G
or
N
,
then
the
diameter
HK
,
looking
vpward
,
is
all
one
with
the
line
G
F
N.
Againe
,
the
Epicicle
being
in
M
and
O
,
such
declination
is
made
vpon
the
ouerthwart
diameter
H
K
,
which
then
is
all
one
with
the
line
drawne
through
the
Nodes
,
marked
with
the
letters
O
F
M
:
but
the
Epicicle
being
in
G
or
N
,
the
same
Inclination
is
made
vpon
the
diameter
I
L
,
being
paralell
to
the
line
O
F
M
,
so
as
in
the
meane
places
that
are
betwixt
the
limits
and
the
Nodes
,
the
enclining
diameter
looketh
vpward
,
and
that
diameter
whereupon
the
Inclination
is
made
,
is
alwayes
transverse
or
ouerthwart
.
From
hence
the
Astronomers
doe
calculate
the
latitudes
of
these
three
Planets
,
hauing
regard
onely
to
the
position
or
placing
of
the
Epicicles
in
the
two
limits
,
and
by
the
proportionall
minutes
doe
find
out
the
equacion
in
euery
other
place
or
position
,
according
as
the
said
Position
is
more
or
lesse
distant
from
the
limits
,
or
from
the
Eclipticke
.
¶
The
Theorique
of
Mercurie
.
The
first
Intention
belonging
to
the
Theorique
of
Mercurie
,
shewing
of
what
and
how
many
orbes
his
Theorique
consisteth
.
THis
Theorique
consisteth
of
seuen
Orbes
,
that
is
,
the
Excentrique
,
the
two
deferents
,
carrying
the
Auge
of
the
Equant
,
the
excentor
of
the
Excentrique
,
the
Epicicle
,
the
circle
Equant
,
and
the
circle
of
the
Nodes
,
as
this
figure
sheweth
.
¶
The
first
figure
belonging
to
the
Theorique
of
Mercurie
.
IN
which
figure
the
letter
A
signifieth
the
centre
of
the
world
,
and
B
the
centre
of
the
Excentrique
,
and
C
signifieth
the
Orbe
Excentrique
,
which
is
a
white
orbe
:
and
the
two
blacke
orbes
,
marked
with
the
letters
D
E
,
are
the
two
deferents
of
the
Auge
of
the
Excentrique
,
and
the
letter
F
signifieth
the
centre
of
the
Epicicle
,
in
whose
circumference
the
starre
of
Mercurie
is
turned
about
:
and
the
letter
G
signifieth
the
circle
Equant
,
whose
centre
is
marked
with
the
letter
H
,
in
the
line
of
the
Auge
,
a
little
aboue
the
centre
A.
And
B
H
is
the
diameter
of
the
little
circle
,
which
little
circle
is
almost
in
the
midst
of
the
foresaid
first
figure
,
and
the
centre
of
that
little
circle
is
marked
with
the
letter
I
,
in
the
circumference
of
which
little
circle
is
carried
about
the
centre
of
the
Excentrique
,
marked
with
B.
And
the
letter
I
is
also
the
centre
of
the
Orbe
called
Excentrus
excentri
,
which
indeed
are
two
orbes
going
close
together
,
marked
with
the
letters
L
and
K
,
and
are
shaddowed
with
little
lines
;
and
these
two
orbes
doe
containe
within
the
compasse
thereof
the
whole
orbe
Excentrique
,
which
carrieth
the
Epicicle
of
Mercurie
.
And
the
outermost
circle
of
all
,
marked
with
M
,
signifieth
here
the
deferent
of
the
nodes
.
Wherefore
is
the
excentor
of
the
Excentrique
added
to
the
sphere
of
Mercurie
?
BEcause
hee
hath
a
peculiar
varietie
in
his
moouing
,
not
common
to
the
other
Planets
,
for
his
equacions
in
departing
from
the
Sunne
,
are
found
to
be
least
but
once
,
and
to
be
greatest
twice
,
as
though
he
ascended
but
once
to
the
Auge
,
and
descended
twice
to
the
opposit
Auge
:
which
things
are
salued
by
adding
this
orbe
to
his
Theorique
.
And
all
the
rest
of
the
orbes
are
placed
in
this
Theorique
for
the
selfesame
causes
that
are
before
declared
.
How
and
in
what
manner
is
the
Excentrique
of
Mercurie
mooued
?
IT
is
moued
in
like
manner
as
is
the
Excentrique
of
Venus
,
according
to
the
succession
of
the
signes
,
vpon
his
owne
axletree
and
proper
poles
,
vagarant
together
with
the
poles
of
the
deferents
of
the
Auges
,
and
that
equally
about
the
centre
of
the
circle
Equant
,
making
one
period
in
the
space
of
one
yeare
precisely
together
with
the
Excentrique
of
the
Sunne
.
Where
is
the
centre
of
Mercurie
his
circle
Equant
to
bee
found
,
about
the
which
his
Excentrique
goeth
regularly
?
THe
centre
of
Mercurie
his
Equant
is
in
the
line
of
the
mean
Auge
,
in
the
very
middest
betwixt
the
centre
of
the
world
and
the
centre
of
that
orbe
which
is
called
the
excentor
of
the
Excentrique
:
for
it
occupieth
the
lowest
part
of
the
little
circle
,
described
by
the
centre
of
the
Excentrique
,
and
this
centre
of
the
Equant
is
marked
in
the
former
figure
with
the
letter
H.
How
many
Auges
do
belong
to
the
Excentrique
of
Mercury
?
TWo
,
that
is
,
the
true
Auge
and
the
mean
Auge
.
The
true
Auge
is
in
the
Excentrique
,
described
by
a
right
line
drawne
from
the
centre
of
the
world
through
the
centre
of
the
Excentrique
:
and
this
Auge
by
reason
that
the
centre
of
the
Excentrique
goeth
round
about
the
little
circle
,
is
not
stable
,
nor
keepeth
alwaies
one
place
.
But
the
meane
Auge
belonging
as
well
to
the
Excentrique
as
also
to
the
circle
Equant
,
is
described
by
a
right
line
,
drawne
from
the
centre
of
the
world
throgh
the
centre
of
the
Excentrique
,
and
also
through
the
centre
of
the
Equant
,
both
which
centres
are
in
one selfe
line
.
And
this
meane
Auge
is
the
rule
of
the
true
Auge
,
because
it
remaineth
fixed
vnder
the
deferents
of
the
Auges
.
And
therefore
these
two
deferents
of
the
Auges
are
also
said
to
carry
about
this
Auge
of
the
Equant
.
What
is
to
be
gathered
hereof
?
THat
the
Excentrique
of
Mercurie
,
like
as
that
of
the
Moone
,
is
swifter
in
his
vpper
part
towards
the
Auge
,
than
in
his
nether
part
:
for
there
the
centre
of
the
Equant
approcheth
nigher
vnto
the
opposit
Auge
,
than
to
the
Auge
.
How
are
the
deferents
moued
,
that
doe
carry
the
Auge
of
the
Equant
,
otherwise
called
the
meane
Auge
?
THey
are
moued
according
to
the
succession
of
the
signes
,
about
the
centre
of
the
world
,
vpon
their
proper
poles
,
both
on
this
side
and
beyond
the
vagarant
poles
of
the
Eclipticke
,
by
vertue
of
the
eigth
heauen
,
making
their
reuolution
together
with
that
heauen
according
to
the
Alphonsynes
doctrine
,
in
49000.
yeares
:
and
by
this
mouing
the
Auge
and
opposit
Auge
of
the
Equant
are
put
forward
.
And
this
instabilitie
of
the
poles
of
the
deferents
,
doe
also
make
the
poles
of
eyther
Excentrique
to
wander
on
both
sides
of
the
Eclipticke
.
Ptolomey
in
his
time
found
the
Auge
of
Mercuries
Equant
to
be
in
the
10
degree
of
Libra
,
thinking
that
according
to
the
obseruations
of
the
former
times
,
the
said
Auge
,
together
with
the
sphere
of
the
fixed
starres
,
went
but
one
degree
in
a
hundred
yeares
.
But
according
to
Copernicus
his
obseruations
,
the
said
Auge
is
found
to
be
in
the
beginning
of
Sagittarius
:
Whereby
he
gathereth
,
That
the
said
Auge
vnder
the
sphere
of
the
fixed
starres
,
maketh
one
degree
in
63
yeares
(
so
as
the
motion
of
that
Auge
is
equall
:
)
and
according
to
these
obseruations
,
it
maketh
his
whole
reuolution
vnder
the
Orbe
of
the
fixed
starres
,
in
22405
Aegyptian
yeares
,
but
vnder
the
Zodiake
it
maketh
his
period
in
11995
Aegyptian
yeares
,
which
lacketh
but
fiue
yeares
of
12000
Aegyptian
yeares
.
And
the
tables
of
Alphonsus
cleane
contrarie
to
the
manifold
obseruations
of
Ptolomey
doe
make
the
Auge
of
Mercurie
to
haue
been
in
his
time
in
the
12
degree
i40°
of
Libra
,
according
to
which
account
,
it
ought
to
be
in
these
dayes
in
the
first
degree
and
i12°
of
Scorpio
.
How
is
the
excentor
of
the
Excentrique
moued
?
IT
is
equally
mooued
contrarie
to
the
succession
of
the
signes
,
about
his
owne
centre
,
which
is
also
the
centre
of
the
little
circle
,
and
vpon
his
owne
axeltree
and
proper
poles
vagarant
,
together
with
the
poles
of
the
two
deferents
that
doe
carry
the
Auge
of
the
Equant
:
and
it
maketh
his
period
in
the
space
of
one
yeare
,
in
which
time
the
Excentrique
also
goeth
once
about
the
line
of
the
Auge
.
And
you
haue
to
note
,
that
the
excentor
of
the
Excentrique
,
as
the
Excentrique
it selfe
,
do
both
returne
in
like
time
to
the
line
of
the
Auge
,
that
is
to
say
,
the
excentor
contrarie
to
the
succession
of
the
signes
,
and
the
Excentrique
according
to
the
succession
of
the
signes
,
both
I
say
in
the
space
of
365
dayes
,
6
houres
,
i33°
ii8°
and
iii35°
What
conclusions
doe
follow
of
the
mouing
of
this
Orbe
?
DIuerse
,
but
specially
these
three
here
following
.
1.
First
,
that
the
centre
of
the
Excentrique
is
caried
about
the
circumference
of
the
little
circle
.
2.
Secondly
,
that
the
excentricitie
of
the
Excentrique
is
sometime
changed
,
for
many
times
it
is
threefold
so
much
as
is
the
excentricitie
of
the
Equant
,
and
specially
when
the
centre
of
the
Excentrique
is
in
the
top
of
the
little
circle
;
but
when
the
centre
of
the
Excentrique
is
in
the
lowest
part
of
the
litle
circle
,
then
the
excentricitie
of
the
Excentrick
is
equal
to
the
excentricitie
of
the
equant
.
3.
Thirdly
,
that
the
Auge
and
opposit
Auge
of
the
Excentrique
is
turned
about
the
Auge
&
opposit
Auge
of
the
Equant
,
as
well
contrarie
as
also
according
to
the
succession
of
the
signes
,
and
yet
doth
neuer
ex●eed
his
bounds
,
that
is
to
say
,
the
twelfth
part
of
the
Zodiake
.
Now
for
the
better
vnderstanding
of
this
which
hath
ben
and
shall
be
said
hereafter
,
all
those
that
doe
write
of
the
Theoriques
doe
set
downe
this
figure
here
following
.
¶
The
second
figure
belonging
to
the
Theorique
of
Mercurie
.
THis
figure
as
you
see
consisteth
of
diuers
circles
,
some
greater
,
some
lesser
;
and
of
diuers
right
lines
,
some
longer
,
some
shorter
:
and
of
the
circular
lines
there
is
one
that
hath
a
shape
Ovale
,
like
to
an
egge
;
and
there
be
two
others
,
the
one
like
to
a
halfe
Moone
,
and
the
other
like
to
an
Oyster
shell
or
Cockle
shell
:
all
which
things
,
whereto
they
serue
and
what
they
signifie
,
shall
be
here
declared
by
helpe
of
the
letters
therein
contained
:
for
the
double
,
round
,
and
greatest
circle
being
deuided
into
twelue
equall
parts
,
marked
with
Arithmeticall
figures
,
signifieth
the
circle
Equant
,
whose
Auge
is
marked
aboue
with
the
letter
A
,
and
his
opposit
Auge
being
beneath
,
is
marked
with
the
letter
B
,
and
the
line
A
B
is
the
line
of
the
Auges
,
which
passeth
through
these
three
centres
,
that
is
,
the
centre
of
the
world
marked
with
the
letter
C
,
the
centre
of
the
Equant
marked
with
the
letter
D
,
and
the
centre
of
the
little
middle
circle
marked
with
the
letter
E
,
which
little
circle
is
made
by
the
turning
of
the
centre
of
the
Excentrique
about
the
centre
E
,
and
therefore
when
the
centre
of
the
Excentrique
commeth
to
the
very
top
of
the
little
circle
,
marked
with
the
letter
F
,
then
is
his
excentricitie
three
times
as
much
as
is
the
excentricitie
of
the
equant
,
which
lieth
betwixt
D
and
C
,
for
Ptolomey
found
the
right
line
D
C
to
be
equall
vnto
the
semidiameter
of
the
said
little
circle
.
But
when
the
centre
of
the
Excentrique
falleth
downe
from
F
to
D
,
his
excentricitie
is
least
of
all
,
and
there
the
Excentrique
is
also
vnited
to
the
Equant
it self
,
and
the
Auge
also
of
the
Excentrique
falleth
into
the
line
A
B
:
but
if
the
centre
of
the
Excentrique
doth
fall
from
that
line
into
any
other
part
of
the
circumference
of
the
said
little
circle
,
then
his
Auge
doth
wander
either
into
the
West
part
going
contrarie
to
the
succession
of
the
signes
,
or
els
into
the
East
part
,
going
according
to
the
succession
of
the
signes
;
as
suppose
the
centre
of
the
Excentrique
to
be
in
the
point
marked
with
P
in
the
litle
middle
circle
on
the
right
hand
,
then
his
Auge
will
be
in
G
,
and
his
opposit
Auge
in
L
:
and
if
his
centre
be
in
O
,
then
his
Auge
shall
be
in
I
,
and
his
opposit
Auge
in
M:
and
if
his
centre
be
in
R
,
then
his
Auge
will
be
in
S
,
and
his
opposit
Auge
in
T
:
but
if
his
centre
be
in
V
,
then
his
Auge
will
be
in
X
,
and
his
opposit
Auge
in
Y
:
so
likewise
if
his
centre
be
in
Z
,
his
Auge
will
be
in
a
,
and
his
opposit
Auge
in
d
:
and
if
his
centre
be
in
C
,
then
his
Auge
will
be
in
B
,
and
his
opposit
Auge
in
E.
And
the
outermost
bounds
of
the
wanderings
of
the
Auges
are
the
two
letters
G
and
I
:
and
the
bounds
of
the
wanderings
of
the
opposit
Auges
are
the
two
letters
L
and
M
,
which
bounds
doe
limit
these
foure
angles
,
that
is
,
G
C
A
,
I
C
A
,
L
C
B
,
and
M
C
B.
To
euery
one
of
which
angles
in
the
circular
concentrique
dooth
answere
one
whole
signe
of
the
Zodiake
,
which
Mestelyn
dooth
proue
by
certaine
propositions
of
E●clides
first
booke
,
which
for
breuitie
I
here
omit
.
You
haue
also
to
note
,
that
the
foresaid
Auge
describeth
the
vpper
circle
,
made
in
a
manner
like
a
halfe
Moone
,
marked
with
the
letters
N
S
G
X
A
B
I
a
:
and
the
opposit
Auge
describeth
the
nether
circle
,
made
like
an
Oyster
shell
,
marked
with
the
letters
Q
T
L
Y
B
e
M
d
,
and
vpon
the
long
Ovale
circle
are
placed
two
little
circles
,
of
each
hand
one
,
signifying
the
Epicicle
of
Mercurie
,
whose
centres
are
marked
with
the
letters
K
and
H
:
for
the
centre
of
his
Epicicle
describeth
the
said
Ovale
figure
,
but
not
altogether
like
vnto
the
Ovale
figure
of
the
Moon
,
as
shall
be
shewed
hereafter
.
In
the
meane
time
you
haue
to
note
,
that
when
the
centre
of
the
Excentrique
is
in
the
top
of
the
little
circle
,
marked
with
F
,
then
the
Epicicle
is
furthest
distant
from
the
earth
,
because
he
is
then
in
the
Auge
.
But
when
the
Epicicle
is
come
downe
in
the
Ovale
figure
vnto
the
point
H
,
and
the
centre
of
the
Excentrique
is
also
come
downe
in
the
little
circle
vnto
the
point
P
,
hauing
made
a
third
part
of
that
circle
,
euen
as
the
Epicicle
hath
made
a
third
part
of
the
Equant
,
then
the
Epicicle
is
nighest
vnto
the
earth
.
But
when
the
centre
of
the
Excentrique
is
come
downe
to
the
point
D
,
and
the
Epicicle
is
come
to
the
opposit
Auge
,
marked
with
B
,
then
he
is
more
distant
from
the
earth
,
than
when
he
was
in
the
point
H
,
the
demonstration
whereof
I
here
omit
:
and
the
Epicicle
beeing
come
to
the
opposit
Auge
,
hath
then
passed
through
the
whole
excentor
of
the
Excentrique
,
and
hath
made
one
period
,
and
doth
the
like
in
the
other
halfe
:
whereby
you
may
gather
first
,
that
the
centre
of
the
Epicicle
in
making
one
period
dooth
passe
twice
through
the
excentor
of
the
Excentrique
:
secondly
,
that
the
said
centre
of
the
Epicicle
in
making
one
reuolution
,
is
but
once
in
the
Auge
of
the
Excentrique
,
at
which
time
he
is
most
distant
from
the
earth
.
But
being
in
the
very
opposit
Auge
,
he
is
not
so
nigh
vnto
the
earth
,
as
when
he
is
in
the
other
two
points
before
mentioned
,
each
of
which
points
is
distant
120
degrees
from
the
Auge
of
the
Equant
,
and
in
those
points
is
nearest
to
the
earth
.
Thirdly
,
that
the
centre
of
the
Epicicle
,
by
these
manifold
motions
,
describeth
the
said
Ovale
figure
,
which
notwithstanding
is
not
like
in
many
respects
vnto
the
Ovale
figure
of
the
Moone
;
how
and
wherefore
,
we
come
now
to
shew
.
A
comparison
shewing
in
what
things
the
Moone
and
Mercurie
by
their
motions
do
agree
or
differ
,
in
describing
their
Ovale
figures
:
and
first
,
they
agree
in
these
things
following
.
FOr
looke
how
much
the
Excentrique
of
either
Planet
dooth
proceed
according
to
the
succession
of
the
signes
,
that
is
to
say
,
the
Excentrique
of
the
Moone
from
the
line
of
the
mean
mouing
of
the
Sun
,
and
the
Excentrique
of
Mercurie
from
the
line
of
the
meane
Auge
;
so
much
doe
the
orbes
of
vnequall
thickenesse
reuert
contrarie
to
the
succession
of
the
signes
,
that
is
to
say
,
the
two
deferents
carrying
the
Auge
of
the
Moone
,
and
the
excentor
of
the
Excentrique
of
Mercurie
doe
make
like
circuits
as
well
to
the
foresaid
lines
,
as
to
their
opposit
parts
.
Secondly
,
the
centre
of
either
of
their
Excentriques
by
the
going
backward
of
the
said
orbes
,
describeth
about
the
centres
of
the
same
orbes
a
little
circle
.
Thirdly
,
whilest
the
Excentrique
maketh
one
period
to
the
foresaid
lines
,
the
centre
of
the
Epicicle
of
either
Planet
goeth
twice
about
the
foresaid
orbes
.
Wherfore
it
followeth
of
necessitie
,
that
the
Epicicle
in
euery
reuolution
is
twice
nighest
,
and
twice
furthest
off
from
the
centre
of
the
little
circle
:
and
by
this
meanes
,
the
Epicicle
of
either
Planet
in
making
one
period
describeth
with
his
centre
the
figure
Ovale
.
Thus
much
touching
their
likenesse
or
agreement
in
describing
the
figure
Ovale
of
either
Planet
.
Now
we
will
shew
you
wherein
they
disagree
in
making
the
figure
Ovale
.
The
centre
of
the
little
circle
in
the
sphere
of
the
Moone
,
is
also
the
centre
of
the
world
;
but
in
the
sphere
of
Mercurie
al
that
little
circle
is
excentricall
,
because
that
in
Mercurie
it
is
described
by
an
orbe
which
is
excentricall
,
and
in
the
sphere
of
the
Moone
it
is
described
by
those
orbs
,
which
in
some
respect
are
concentricall
.
Wherefore
the
Auge
of
the
Moone
dooth
wander
equally
throughout
the
whole
Zodiake
:
but
the
Auge
of
Mercurie
is
turned
and
wrythed
on
each
side
of
his
meane
Auge
:
and
by
his
turning
and
wandering
,
now
on
this
side
,
and
now
on
that
side
,
both
the
Auge
and
also
the
opposit
Auge
doe
each
of
them
make
a
figure
that
wrieth
in
and
out
,
and
that
which
the
Auge
maketh
,
is
marked
in
the
former
figure
with
the
letters
N
S
G
X
A
b
I
a
,
almost
like
to
a
halfe
Moone
;
and
that
which
the
opposit
Auge
maketh
,
is
marked
with
these
letters
,
Q
T
L
Y
B
e
M
d
,
much
like
to
an
Oyster
shell
,
as
hath
beene
said
before
.
Whereof
it
followeth
,
that
the
Auge
of
the
Moone
is
onely
moued
contrarie
to
the
succession
of
the
signes
.
But
the
Auges
of
Mercurie
doth
sometime
proceed
by
a
reciprocke
mouing
according
to
the
succession
of
the
signes
.
Moreouer
,
the
excentricitie
of
the
Moone
in
a
whole
period
is
neuer
changed
,
but
abideth
alwaies
one
and
the
same
:
but
the
excentricitie
of
Mercurie
is
continually
changed
.
Againe
,
the
Moone
in
euery
her
reuolution
falleth
twice
into
the
Auge
,
and
twice
into
the
opposit
Auge
,
by
meanes
whereof
she
is
twice
furthest
from
the
earth
,
and
twice
nighest
to
the
same
;
and
the
limits
of
those
distances
is
a
just
quarter
of
a
circle
one
from
another
,
which
is
90
degrees
.
But
Mercurie
falleth
neither
into
the
Auge
nor
opposit
Auge
but
once
only
,
and
he
is
furthest
distant
from
the
earth
when
he
is
in
the
Auge
.
But
he
is
nighest
to
the
earth
twice
(
not
when
he
is
in
the
opposit
Auge
)
but
in
two
places
,
each
of
them
being
distant
on
either
side
from
the
Auge
the
third
part
of
a
circle
,
which
is
120
degrees
.
Finally
,
the
Epicicle
of
the
Moone
describeth
a
figure
,
more
like
to
a
figure
Lenticular
,
than
to
a
figure
Ovale
.
And
the
Epicicle
of
Mercurie
describeth
a
figure
more
Ovale
than
otherwise
,
the
cause
whereof
is
,
for
that
the
centre
of
the
Moones
Equant
(
about
which
her
Excentrique
maketh
his
regular
motion
)
is
also
the
centre
of
the
little
circle
.
But
the
centre
of
Mercuries
Equant
is
resident
in
the
lowest
part
of
the
said
little
circle
,
notwithstanding
each
figure
is
commonly
called
an
Ovale
figure
.
How
and
in
what
maner
is
the
Epicicle
of
Mercurie
moued
?
THe
Epicicle
of
Mercurie
in
the
vpper
part
is
mooued
according
to
the
succession
of
the
signes
,
and
in
the
nether
part
contrarie
to
the
succession
of
the
signes
,
about
his
owne
moouable
axletree
,
standing
slopewise
vpon
the
plane
of
the
Excentrique
.
And
it
is
equally
moued
from
the
meane
Auge
,
making
his
reuolution
almost
in
4
months
,
and
his
daily
moouing
containeth
3
degrees
,
i6°
ii●4
iii14°
iiii5°
v16°
so
as
it
maketh
one
period
in
115
dayes
,
21
houres
,
i●°
ii20°
iii54°
How
is
the
meane
Auge
of
this
Epicicle
described
?
IT
is
described
by
a
right
line
drawn
from
the
centre
of
the
Equant
,
and
passing
through
the
centre
of
the
Epicicle
,
euen
to
the
circumference
thereof
.
What
conclusions
are
to
be
gathered
hereof
?
FIrst
,
that
the
Epicicle
of
Mercurie
,
contrarie
to
that
which
happeneth
in
the
three
vpper
Planets
,
and
also
in
Venus
,
is
slower
of
gate
in
the
vpper
part
of
the
Excentrique
,
&
quicker
of
gate
in
the
lower
part
of
the
Excentrique
,
because
the
centre
of
the
Equant
in
this
Theorique
of
Mercurie
approcheth
nigher
to
the
opposite
Auge
,
but
in
the
other
Planets
last
named
,
the
centre
of
their
Equant
approcheth
nigher
to
the
Auge
.
Secondly
,
when
the
centre
of
the
Epicicle
is
in
the
line
of
the
Auges
,
then
both
the
meane
and
true
Auge
of
the
Epicicle
,
and
also
the
point
of
concauitie
are
all
three
vnited
together
in
one selfe
line
,
yea
,
the
meane
Auge
and
also
the
point
of
concauitie
are
again
vnited
,
when
the
centre
of
the
Epicicle
is
in
any
of
the
two
points
of
next
approch
to
the
earth
,
marked
in
the
former
second
figure
with
the
letters
H
K
:
and
from
thence
aboue
those
points
of
next
approch
towards
the
Auge
of
the
Excentrique
,
the
meane
Auge
of
the
Epicicle
is
alwayes
in
the
middest
betwixt
the
true
Auge
and
the
point
of
concauitie
.
But
beneath
the
foresaid
points
of
next
approch
towards
the
opposit
Auge
of
the
Excentrique
,
the
point
of
concauitie
is
in
the
middest
of
the
meane
and
true
Auge
of
the
Epicicle
:
the
demonstration
whereof
for
breuitie
sake
I
doe
here
omit
.
What
harmonie
or
agreement
is
there
betwixt
Mercurie
and
the
Sunne
?
MErcurie
as
well
as
Venus
,
in
the
periodicall
mouing
of
their
Excentrique
,
dooth
follow
the
Sunne
:
for
the
reuolution
of
Mercurie
agreeth
most
exactly
with
the
Excentrique
of
the
Sunne
.
And
hereto
you
may
also
adde
,
that
the
excentor
of
the
Excentrique
of
Mercurie
,
maketh
his
reuolution
together
with
the
Excentrique
of
the
Sunne
,
not
simply
,
but
in
hauing
respect
to
the
mean
Auge
of
Mercurie
,
or
of
the
Equant
:
yea
,
and
moreouer
according
to
the
late
obseruations
and
speciall
conclusions
touching
the
orbes
of
the
Sunne
(
whereof
we
haue
spoken
before
in
the
Theorique
of
the
Sunne
)
Mercurie
touching
so
much
as
appertaineth
to
his
moouing
according
to
longitude
,
agreeth
with
the
Theorique
of
the
Sunne
,
both
in
number
and
in
like
disposition
or
placing
of
the
orbes
,
and
also
in
the
qualitie
of
the
mouing
of
the
said
orbes
.
For
according
to
Copernicus
,
there
is
in
both
Theoriques
an
excentor
of
the
Excentrique
,
going
contrarie
to
the
succession
of
the
signes
,
whereby
the
meane
Auge
is
on
both
sides
most
distant
from
the
true
Auge
,
and
causeth
the
excentricitie
to
be
mutable
.
What
conclusions
doe
follow
of
this
harmonie
?
THese
here
following
:
for
first
you
haue
to
note
,
that
the
Sunne
and
Mercurie
,
and
also
Venus
,
are
alwayes
joyned
together
in
their
meane
moouing
:
and
as
they
haue
all
three
one selfe
meane
moouing
,
so
they
must
needs
haue
also
one selfe
line
of
their
meane
moouing
.
And
hereof
it
followeth
,
that
neither
Mercurie
nor
Venus
can
depart
from
the
Sunne
any
further
than
the
bignesse
of
their
Epicile
will
suffer
them
.
Moreouer
,
look
how
much
the
Sun
proceedeth
forward
from
the
mean
Auge
of
Mercurie
:
so
much
the
centre
of
Mercuries
Excentrique
goeth
backward
in
the
little
circle
.
How
are
the
Orbes
belonging
to
the
sphere
of
Mercurie
to
be
measured
?
OF
such
like
parts
as
the
semidiameter
of
the
Excentrique
,
marked
with
the
letters
D
A
,
or
with
P
H
,
in
the
former
figure
,
containeth
60
parts
,
the
excentricitie
of
the
Equant
,
marked
in
the
said
figure
with
the
letters
C
D
,
containeth
according
to
Ptolomey
three
parts
,
and
the
greatest
excentricitie
of
the
Excentrique
,
marked
with
the
letters
C
F
,
containeth
9
such
parts
.
And
the
line
of
the
Auge
,
marked
with
C
N
,
containeth
69
such
parts
or
degrees
.
And
the
line
of
the
opposit
Auge
marked
with
C
Q
,
(
such
as
it
is
then
)
containeth
51
degrees
.
But
when
the
centre
of
the
Epicicle
is
in
the
very
opposit
Auge
it selfe
,
marked
with
D
,
then
the
line
of
the
said
opposit
Auge
,
marked
with
C
B
,
containeth
57
parts
.
But
the
line
of
the
nighest
approch
,
marked
on
the
left
side
of
the
former
figure
with
C
H
,
and
on
the
right
side
with
C
K
,
is
said
to
containe
55
degrees
,
and
i3°
and
so
the
semidiameter
of
the
Epicicle
containeth
22
degrees
and
i30°
Hereof
it
followeth
,
that
the
greatest
distance
of
Mercurie
being
placed
in
the
Auge
of
his
Excentrique
and
of
his
Epicicle
,
containeth
91
degrees
and
i30°
and
if
his
excentricitie
did
continue
alwayes
fixed
and
vnmoouable
,
the
altitude
of
Mercurie
being
in
the
opposit
Auges
of
those
orbes
,
should
be
28
degrees
,
and
i30°
And
though
that
Mercurie
himselfe
with
his
bodie
doe
neuer
descend
so
farre
,
for
such
causes
as
are
before
declared
,
yet
it
is
necessarie
that
this
capacitie
be
attributed
to
his
orbe
.
And
when
Mercurie
is
in
any
of
the
points
of
nighest
approch
,
then
his
least
altitude
is
33
degrees
and
i4°
.
The
third
Intention
,
shewing
what
points
,
lines
,
and
arches
are
meet
to
be
knowne
in
the
Theorique
of
Mercurie
.
IN
all
these
things
Mercurie
agreeth
with
Venus
and
with
the
three
vpper
Planets
,
which
being
alreadie
set
downe
in
those
Theoriques
,
need
not
here
againe
to
be
rehearsed
,
&
therfore
resort
to
the
third
Intention
,
as
well
of
the
three
vpper
Planets
,
as
to
that
of
Venus
.
In
the
tables
as
well
of
Ptolomey
,
as
in
those
of
Alphonsus
and
of
their
followers
,
the
equacions
of
the
arguments
are
counted
at
that
place
of
the
Excentrique
,
in
which
the
distance
of
the
centre
of
the
Epicicle
from
the
earth
is
equall
vnto
the
semidiameter
of
the
Excentrique
.
And
to
these
equacions
may
be
added
the
excesse
of
the
longer
longitude
,
and
also
the
excesse
of
the
nigher
longitude
,
not
that
when
the
Planet
is
in
the
very
opposite
Auge
,
but
when
he
is
in
any
of
the
two
points
of
nighest
approch
.
To
these
equacions
also
may
be
referred
the
proportionall
minutes
both
longer
and
nigher
.
The
equacions
of
the
Parallax
or
of
the
Epicicle
which
are
set
downe
in
the
Prutenicall
tables
,
do
appertaine
to
the
Auge
of
the
Equant
.
But
the
excesse
do
belong
to
the
points
of
next
approch
,
marked
in
the
second
figure
with
the
letters
H
K.
What
this
word
Parallax
doth
signifie
,
shall
be
declared
hereafter
.
And
you
haue
to
vnderstand
,
that
the
greatest
equacion
of
the
centre
containeth
3
degrees
,
i/0
ii/30
and
that
the
greatest
equacion
of
the
argument
,
when
the
centre
of
the
Epicicle
is
in
the
Auge
of
the
Excentrique
,
containeth
19
degrees
,
i/3
ii/6
But
when
the
Epicicle
is
in
any
of
the
2
points
of
next
approch
,
then
it
containeth
23
degrees
,
i/51
ii/40
The
fourth
Intention
,
shewing
the
latitudes
,
as
well
of
Venus
as
of
Mercurie
,
and
wherin
they
do
agree
or
disagree
.
IN
qualitie
these
two
Planets
are
most
like
,
for
looke
in
what
maner
the
Excentrique
of
Venus
doth
decline
towards
the
Ecliptick
,
or
her
Epicicle
to
the
Excentrique
;
in
like
manner
dooth
the
Excentrique
and
the
Epicicle
of
Mercurie
make
their
declination
,
but
yet
with
this
difference
,
that
looke
in
what
sort
those
two
circles
in
the
Theorique
of
Venus
do
decline
towards
the
North
,
in
like
sort
the
said
two
circles
in
the
Theorique
of
Mercurie
doe
decline
towards
the
South
.
How
manifold
is
the
latitude
of
these
two
Planets
?
THreefold
,
whereof
one
dependeth
vpon
the
moouable
obliquitie
or
slopenesse
of
the
Excentrique
,
and
the
other
two
latitudes
doe
depend
of
the
inclinations
of
the
Epicicles
,
which
inclinations
are
also
twofold
and
mouable
,
whereof
the
one
in
Greeke
is
called
Engclysis
,
and
the
other
Loxosis
,
as
shall
be
declared
hereafter
.
What
manner
of
latitude
is
that
which
the
Excentrique
of
either
Planet
causeth
?
WE
haue
said
before
,
that
the
poles
of
the
deferents
of
the
Auges
doe
wander
both
beyond
and
also
on
this
side
of
the
poles
of
the
Eclipticke
,
and
therefore
the
plane
of
the
Excentrique
hath
obliquitie
or
slopenesse
,
and
yet
not
fixed
as
in
the
other
vpper
Planets
but
moouable
.
And
as
well
the
mutuall
section
,
as
the
swaying
of
the
planes
of
the
Excentrique
and
of
the
Eclipticke
is
made
vpon
the
diameter
of
the
world
,
standing
with
right
angles
vpon
the
line
of
the
Auge
,
and
therefore
the
diameter
which
gouerneth
this
declination
,
is
the
line
of
the
Auge
and
of
his
opposit
Auge
.
And
by
this
meanes
it
falleth
out
,
that
the
Auge
and
opposit
Auge
,
or
rather
the
each
halfe
of
the
plane
of
the
whole
Theorique
doth
sway
from
the
Eclipticke
,
now
towards
the
North
,
and
now
towards
the
South
,
but
the
nodes
of
such
swaying
are
alwaies
distant
from
the
Auge
one
whole
quarter
of
the
Zodiake
:
and
this
moouing
of
latitude
is
commonly
called
the
declination
of
the
Excentrique
.
What
proportion
doth
the
swaying
of
the
declination
of
the
Excentrique
,
as
well
of
Mercurie
as
of
Venus
obserue
in
the
making
of
their
periods
?
THis
here
following
:
for
when
the
centre
of
the
Epicicle
is
either
in
the
Node
ascendent
or
descendent
,
all
the
whole
plane
of
the
Excentrique
doth
fall
into
the
Eclipticke
;
for
though
the
centre
of
Mercurie
his
Epicicle
doth
neuer
ascend
to
the
North
,
nor
the
centre
of
the
Epicicle
of
Venus
to
the
South
,
yet
we
may
call
the
one
node
ascendent
,
and
the
other
descendent
,
as
well
for
the
likenesse
or
proportion
that
is
betwixt
those
two
Planets
&
the
other
Planets
,
as
also
for
that
the
one
node
is
in
the
ascendent
halfe
of
the
Excentrique
towards
the
Auge
,
&
the
other
node
is
in
the
descendent
halfe
of
the
Excentrique
towards
the
opposit
Auge
.
But
if
the
centre
of
the
Epicicle
be
in
the
vpper
halfe
aboue
the
diameter
of
the
section
or
swaying
towards
the
Auge
,
then
the
Auge
,
or
rather
the
whole
vpper
half
of
the
Excentrique
doth
decline
from
the
Eclipticke
,
that
is
to
say
,
in
Venus
towards
the
North
,
and
in
Mercurie
towards
the
South
.
But
if
the
centre
of
the
Epicicle
be
in
the
nether
halfe
,
then
the
Auge
of
Venus
declineth
towards
the
South
,
and
the
opposit
Auge
towards
the
North
:
but
in
Mercurie
it
is
cleane
contrarie
,
and
the
greatest
declination
is
when
the
centre
of
the
Epicicle
is
either
in
the
Auge
or
opposit
Auge
of
the
Excentrique
.
What
conclusions
may
be
gathered
hereof
?
FIrst
,
that
the
Auges
are
not
alwaies
found
to
be
in
the
North
nor
in
the
South
,
as
it
chanceth
in
the
three
vpper
Planets
,
but
sometime
in
the
one
place
,
and
sometime
in
the
other
.
Secondly
,
that
the
centre
of
Venus
her
Epicicle
doth
neuer
arriue
vnto
the
South
,
nor
the
centre
of
Mercuries
Epicicle
to
the
North
:
for
this
swaying
is
of
such
manner
,
as
that
halfe
of
the
Excentrique
,
into
which
the
Epicicle
at
any
time
entreth
,
doth
by
and
by
begin
to
decline
into
the
said
North
part
for
Venus
,
and
into
the
South
part
for
Mercurie
:
and
this
Inclination
of
the
Excentriques
,
causeth
that
the
North
latitudes
of
Venus
be
alwaies
greater
than
her
South
latitudes
;
but
in
Mercurie
it
is
cleane
contrarie
.
And
you
haue
to
note
,
that
the
greatest
angle
or
section
of
the
Excentrique
and
Eclipticke
,
is
for
Venus
,
i/10
and
for
Mercurie
,
i/45
But
for
the
better
vnderstanding
,
as
well
of
this
that
hath
been
said
before
,
as
of
that
which
is
to
be
said
hereafter
touching
the
foresaid
latitudes
,
it
shall
be
needfull
to
set
down
this
figure
here
following
.
¶
The
third
figure
shewing
the
latitudes
of
the
said
two
Planets
.
THis
figure
,
made
somewhat
like
to
a
Butterflie
,
with
her
wings
spread
open
,
containeth
three
seuerall
planes
of
orbes
,
cutting
one
another
in
the
diameter
of
the
world
,
which
passeth
through
the
centre
of
the
world
,
marked
here
with
A
:
which
three
planes
doe
represent
no
more
but
one
onely
plane
,
that
is
,
the
Excentrique
of
Venus
or
of
Mercurie
,
to
shew
the
diuerse
positions
or
placings
of
the
said
Excentrique
,
caused
by
the
latitude
of
their
inclination
.
And
ye
haue
to
vnderstand
,
that
the
middlemost
of
these
three
planes
or
orbes
,
marked
with
the
letters
L
K
M
T
,
and
containing
therein
foure
Epicicles
,
doth
signifie
,
that
the
Excentrique
being
in
either
of
the
two
points
K
or
T
,
is
vnited
to
the
Eclipticke
:
but
the
other
two
planes
,
whereof
the
first
hauing
the
line
of
the
Auge
drawne
through
the
limits
of
the
greatest
declination
,
marked
with
the
letters
B
C
,
and
the
second
plane
hauing
a
line
marked
with
Q
P
,
dooth
signifie
the
declination
of
the
Excentrique
from
the
Epicicle
.
Moreouer
,
in
this
figure
the
two
planes
B
C
,
and
Q
P
,
hard
by
the
mutuall
section
which
is
nigh
vnto
K
and
T
,
are
cut
off
,
not
for
that
such
orbes
are
to
be
cut
off
indeed
;
but
that
by
this
means
the
Epicicles
being
in
K
or
T
,
might
be
the
better
seene
in
the
middlemost
plane
,
marked
with
the
letters
L
K
M
T.
You
see
also
,
that
in
this
figure
the
circumference
of
euery
one
of
the
foure
Epicicles
is
marked
with
these
four
letters
,
G
H
F
I
,
but
yet
placed
in
diuerse
order
,
according
to
the
diuers
mouing
of
the
Epicicle
.
And
you
haue
to
note
,
that
when
the
centre
of
any
of
those
Epicicles
is
in
the
Node
ascendent
,
marked
with
K
,
then
the
plane
of
the
Excentrique
,
whose
diameter
by
passing
through
the
Auge
L
,
and
the
opposit
Auge
M
,
is
the
line
L
A
M
,
wholly
vnited
to
the
Eclipticke
,
hauing
no
declination
at
all
,
whereby
the
axletree
of
the
said
plane
,
marked
with
N
O
,
hangeth
perpendicularly
vpon
the
plane
of
the
Eclipticke
.
But
when
the
centre
of
the
Epicicle
ascendeth
from
the
Node
K
towards
the
Auge
of
the
Excentrique
,
marked
with
B
,
then
the
vpper
part
of
the
Excentrique
dooth
by
and
by
decline
from
the
Eclipticke
towards
the
North
for
Venus
,
and
towards
the
South
for
Mercurie
;
as
when
the
centre
of
the
Epicicle
is
in
the
Auge
B
,
for
then
the
diameter
B
A
C
,
or
rather
the
whole
vpper
halfe
of
the
Excentrique
is
found
to
be
on
this
side
of
the
Eclipticke
,
and
the
inferiour
part
of
the
Excentrique
to
be
beyond
the
Eclipticke
,
and
the
axletree
of
the
Excentrique
is
then
the
line
D
E.
But
when
the
centre
of
the
Epicicle
is
come
downe
to
the
Node
descendent
,
marked
with
T
,
then
the
plane
of
the
Excentrique
is
vnited
again
to
the
Eclipticke
,
and
the
right
line
L
A
M
is
againe
the
diameter
of
the
Auge
.
But
when
the
Epicicle
is
once
passed
the
Node
descendent
,
marked
with
T
,
then
the
vpper
part
of
the
Excentrique
which
was
before
on
this
side
of
the
Eclipticke
,
beginneth
now
to
decline
beyond
the
Eclipticke
,
wherefore
the
lower
part
of
the
Excentrique
beginneth
now
to
haue
the
same
declination
which
the
vpper
part
had
before
,
that
is
to
say
,
towards
the
North
for
Venus
,
and
towards
the
South
for
Mercurie
.
And
therefore
the
centre
of
the
Epicicle
being
in
the
opposit
Auge
,
marked
with
P
,
the
position
of
the
Excentrique
is
the
line
P
A
Q
,
and
the
axletree
thereof
,
is
the
line
R
S.
It
appeareth
therefore
,
when
the
centre
of
the
Epicicle
is
in
any
of
the
Nodes
,
either
K
or
T
,
that
then
the
Excentrique
is
vnited
to
the
Eclipticke
.
But
if
the
centre
of
the
Epicicle
be
out
of
those
Nodes
,
then
as
well
towards
the
Auge
B
,
as
towards
the
opposit
Auge
P
,
the
Excentrique
hath
the
like
latitude
as
before
,
that
is
,
North
latitude
for
Venus
,
and
South
latitude
for
Mercurie
.
And
therefore
the
centre
of
the
Epicicle
doth
not
goe
beyond
the
Eclipticke
,
either
towards
C
or
Q.
What
manner
of
latitudes
haue
the
Epicicles
,
as
well
of
Venus
as
of
Mercurie
?
THe
planes
of
their
Epicicles
,
whose
axletrees
we
haue
said
before
to
be
oblique
or
sloping
to
the
Excentriques
vpon
the
two
diameters
,
that
is
to
say
,
vpon
the
diameter
of
the
Auges
,
and
vpon
the
diameter
of
the
meane
longitudes
are
enclined
and
swaied
on
both
sides
of
their
Excentriques
,
and
yet
proportionally
answerable
to
the
periods
of
their
Excentriques
.
How
is
the
first
diameter
,
passing
through
the
Auges
,
declined
?
THe
diameter
of
the
Auges
declineth
on
both
hands
from
the
plane
of
the
Excentrique
,
in
such
sort
as
followeth
:
for
when
the
centre
of
the
Epicicle
is
in
any
of
the
limits
,
that
is
to
say
,
either
in
the
Auge
or
opposit
Auge
of
the
Excentrique
,
marked
in
the
former
figure
with
B
P
,
then
the
diameter
of
the
Auges
haue
no
declination
at
all
,
because
it
falleth
just
into
the
plane
of
the
Excentrique
;
but
the
declination
thereof
is
greatest
,
when
the
centre
of
the
Epicicle
is
in
any
of
the
two
Nodes
,
yet
with
such
difference
,
as
the
inclination
of
this
diameter
,
or
rather
of
the
one
halfe
of
the
plane
of
the
Epicicle
being
made
in
the
descending
halfe
of
the
Excentrique
,
is
for
Venus
Northward
,
and
for
Mercurie
Southward
:
but
in
the
ascending
halfe
of
the
Excentrique
,
the
halfe
of
this
diameter
for
Venus
is
Southward
,
and
for
Mercurie
Northward
.
And
this
declination
is
made
vpon
the
diameter
of
the
meane
longitudes
,
which
the
former
figure
dooth
plainely
shew
:
for
the
Epicicle
being
in
B
or
P
,
which
are
the
two
limits
,
the
declination
of
the
diameter
of
the
Auges
is
nothing
at
all
.
But
the
centre
of
the
Epicicle
being
in
T
,
which
is
the
Node
descendent
,
the
vpper
part
of
this
diameter
,
marked
with
T
G
,
declineth
from
the
plane
of
the
Excentrique
Northward
for
Venus
,
and
Southward
for
Mercurie
:
but
the
lower
halfe
,
marked
with
T
F
,
enclineth
contrariwise
,
that
is
to
say
,
Southward
for
Venus
,
and
Northward
for
Mercurie
.
And
because
that
the
declination
is
greatest
when
the
Epicicle
is
in
any
of
the
Nodes
,
then
the
aforesaid
diameter
beginneth
againe
to
approch
vnto
the
plane
of
the
Excentrique
,
and
in
the
limit
P
is
vnited
againe
to
the
plane
of
the
Excentrique
,
and
from
thence
the
vpper
part
of
the
said
diameter
declineth
beyond
the
plane
of
the
Excentrique
to
the
other
side
,
and
the
inferior
part
to
this
side
.
Wherefore
the
Auge
of
the
Epicicle
,
marked
with
G
,
being
in
the
point
K
,
which
before
was
for
Venus
Northward
,
is
now
Southward
,
and
for
Mercurie
cleane
contrarie
.
The
greatest
angle
of
this
Inclination
of
the
plane
of
the
Epicicle
vnto
the
Excentrique
,
is
demonstrated
by
Ptolomey
and
Copernicus
,
to
be
for
Venus
two
degrees
,
and
i/30
and
for
Mercurie
6
degrees
,
and
i/15
To
these
from
the
Auge
of
the
Epicicle
to
the
centre
of
the
world
,
doe
agree
for
Venus
one
degree
,
and
i/3
and
for
Mercurie
one
degree
,
and
i/46
But
from
the
opposit
Auge
of
the
Epicicle
to
the
centre
of
the
world
,
it
is
for
Venus
6
degrees
,
and
i/22
and
for
Mercurie
4
degrees
,
and
i/5
Hitherto
of
the
first
manner
of
the
declination
of
the
Epicicles
from
their
Excentriques
,
called
in
Latine
Inclinatio
,
or
Deviatio
,
in
Greeke
Engclisis
.
Now
shew
in
what
manner
the
other
diameter
,
passing
through
the
meane
longitudes
of
the
Epicicle
,
maketh
his
declination
?
THis
kind
of
declination
of
the
Epicicle
,
is
commonly
called
the
reflection
,
in
Greeke
Loxosis
,
because
it
maketh
the
diameter
of
the
meane
longitudes
to
reflect
on
both
sides
from
the
plane
of
the
Excentrique
in
such
manner
as
followeth
:
for
while
the
centre
of
the
Epicicle
is
in
any
of
the
Nodes
,
which
is
distant
a
just
quarter
of
the
Zodiake
from
the
Auge
or
opposit
Auge
,
then
the
reflection
of
this
diameter
is
nothing
at
all
,
because
then
it
falleth
wholly
into
the
plane
of
the
Excentrique
;
but
such
reflection
is
greatest
,
when
the
centre
of
the
Epicicle
is
in
any
of
the
limits
,
or
in
the
Auge
or
opposit
Auge
.
And
yet
with
such
difference
,
as
the
reflection
of
the
halfe
of
this
diameter
,
called
the
Orientall
halfe
of
the
Epicicle
,
may
be
in
the
vpper
halfe
of
the
Excentrique
,
Northward
for
Venus
,
and
Southward
for
Mercurie
.
But
in
the
lower
halfe
of
the
Excentrique
,
the
said
Orientall
halfe
of
the
Epicicle
reflecteth
for
Venus
towards
the
South
,
and
for
Mercurie
towards
the
North.
And
this
reflection
is
made
vpon
the
diameter
of
the
Auges
,
all
which
things
the
former
figure
dooth
plainely
shew
.
For
when
the
centre
of
the
Epicicle
is
in
K
or
T
,
which
be
the
two
Nodes
,
then
the
diameter
of
the
mean
longitudes
,
marked
with
H
I
,
hath
no
reflection
at
all
,
but
lieth
whole
vpon
the
plane
of
the
Excentrique
,
as
you
may
see
in
the
Node
ascendent
,
marked
with
K
:
but
in
the
vpper
part
of
the
Excentrique
towards
the
Auge
,
when
the
centre
of
the
Epicicle
is
in
the
Auge
B
,
then
the
Orientall
halfe
of
the
diameter
H
I
,
marked
in
the
highest
Epicicle
of
this
figure
with
the
letters
H
B
,
or
els
the
Orientall
halfe
of
the
said
highest
Epicicle
,
marked
with
the
letters
G
H
F
,
doth
reflect
from
the
plane
of
the
Excentrique
for
Venus
Northward
,
and
for
Mercurie
Southward
.
But
the
Occidentall
halfe
of
the
said
diameter
,
marked
with
B
I
,
or
that
halfe
of
the
Epicicle
marked
with
F
I
G
,
doth
reflect
cleane
contrarie
,
that
is
to
say
,
for
Venus
towards
the
South
,
and
for
Mercurie
towards
the
North.
And
when
the
reflection
is
greatest
,
then
this
diameter
approcheth
the
Eclipticke
,
and
falleth
into
the
same
in
the
point
T
,
that
is
to
say
,
in
the
Node
descendent
.
And
departing
from
thence
downeward
towards
the
limit
P
,
the
said
halfe
of
the
diameter
reflecteth
on
the
other
side
beyond
the
Eclipticke
,
and
then
the
Occidentall
halfe
succeedeth
,
which
as
when
it
was
in
the
vpper
part
of
the
Excentrique
,
was
for
Venus
South
,
and
for
Mercurie
North
:
so
now
by
going
from
T
to
P
,
and
so
to
K
,
it
is
made
for
Venus
Northward
,
and
for
Mercurie
Southward
.
And
the
greatest
angle
of
the
reflection
of
this
diameter
vnto
the
Excentrique
,
is
demonstrated
to
be
for
Venus
3
degrees
,
i/30
&
for
Mercurie
7
degrees
:
and
to
these
doe
agree
at
the
centre
of
the
world
the
latitudes
for
Venus
to
be
2
degrees
,
i/30
and
as
much
for
Mercurie
.
Notwithstanding
,
because
Mercurie
hath
a
greater
excentricitie
,
this
angle
in
the
Auge
of
the
Excentrique
,
hath
to
the
centre
of
the
world
two
degrees
,
ii/15
and
in
the
opposite
Auge
of
the
said
Excentrique
,
it
hath
2
degrees
,
ii/45
What
conclusions
are
to
be
gathered
of
the
inclinations
and
reflections
of
the
Epicicles
?
1.
THese
here
following
:
First
,
the
plane
of
the
Epicicle
is
neuer
vnited
with
the
plane
of
the
Excentrique
or
of
the
Eclipticke
,
by
reason
of
the
continuall
inclinations
of
the
one
or
of
the
other
diameter
.
And
therefore
the
axletree
of
the
Epicicle
is
neuer
perpendicular
to
any
of
those
planes
.
2.
Secondly
,
the
declinations
of
the
diameter
of
the
Auges
,
and
of
the
meane
longitudes
of
the
Epicicle
of
these
two
Planets
,
that
is
to
say
,
of
Venus
and
Mercurie
,
are
contrarie
to
the
declinations
of
the
three
vpper
Planets
,
for
there
the
declinations
of
the
diameters
of
the
Auges
are
greatest
in
the
limits
,
&
nothing
in
the
nodes
,
but
the
declinations
of
the
said
diameters
in
these
two
Planets
are
greatest
in
the
nodes
,
and
nothing
in
the
limits
.
Againe
,
the
reflections
in
the
three
vpper
Planets
are
greatest
in
the
nodes
,
and
nothing
in
the
limits
,
wheras
in
these
two
Planets
the
reflections
are
greatest
in
the
limits
,
and
nothing
in
the
nodes
.
3.
Thirdly
,
the
planes
of
the
Excentriques
and
Epicicles
of
these
two
Planets
doe
cut
one
another
in
diuers
diameters
:
for
in
the
nodes
such
section
is
made
in
the
diameter
of
the
meane
longitudes
,
but
in
the
limits
the
same
section
is
made
in
the
diameter
of
the
Auges
;
and
in
the
meane
places
such
section
chanceth
sometime
in
one
place
,
and
sometime
in
another
,
betwixt
the
said
diameters
:
but
the
said
section
in
the
three
vpper
Planets
,
obserueth
contrarie
order
,
as
hath
been
said
before
.
4.
Fourthly
,
the
line
of
the
mutuall
section
of
the
Epicicle
and
of
the
Excentrique
doth
wander
through
the
plane
of
the
Epicicle
in
such
sort
,
as
the
one
halfe
of
the
said
plane
departeth
from
the
plane
of
the
Excentrique
for
Venus
towards
the
North
,
and
for
Mercurie
towards
the
South
:
so
the
other
halfe
of
the
said
plane
declineth
cleane
contrarie
,
that
is
to
say
,
for
Venus
towards
the
South
,
and
for
Mercurie
towards
the
North
:
but
in
the
three
vpper
Planets
such
line
of
mutuall
section
obserueth
a
contrarie
order
.
By
these
conclusions
it
is
manifest
,
that
the
latitude
of
Mercurie
and
Venus
hath
three
variations
,
the
first
by
reason
of
the
moouable
obliquitie
of
the
Excentrique
:
the
second
by
reason
of
the
mouable
declinations
of
the
Epicicle
:
and
the
third
by
reason
of
the
moouable
reflections
of
the
said
Epicicle
.
All
which
things
you
may
the
more
easily
perceiue
by
the
former
figure
,
for
the
Epicicle
being
in
the
Node
ascendent
,
marked
with
K
,
the
diameter
of
the
meane
longitudes
,
marked
with
H
I
,
is
in
the
very
plane
of
the
Excentrique
:
but
the
diameter
of
the
Auges
of
the
said
Epicicle
,
marked
with
FG
,
hath
then
greatest
declination
,
so
as
the
whole
nether
halfe
of
the
said
Epicicle
,
marked
with
the
letters
H
F
I
,
looking
towards
the
Node
descendent
,
is
for
Venus
Northward
,
and
for
Mercurie
Southward
.
And
the
vpper
halfe
of
the
said
Epicicle
,
marked
with
the
letters
I
G
H
,
being
partly
hidden
from
our
sight
,
by
reason
that
it
is
vnder
the
Excentrique
,
is
for
Venus
Southerly
,
and
for
Mercurie
Northerly
:
and
the
d●ameter
of
the
section
,
marked
with
H
I
,
is
aparalell
to
the
line
of
the
Auge
of
the
Excentrique
,
which
line
is
marked
with
these
letters
,
L
A
M
,
whereof
L
signifieth
the
Auge
,
and
M
the
opposit
Auge
of
the
Excentrique
,
and
A
the
centre
of
the
world
:
so
in
the
other
Node
,
marked
with
T
,
the
selfesame
diameter
H
I
is
in
the
meane
longitudes
,
but
there
the
vpper
halfe
of
the
Epicicle
,
marked
with
the
leters
I
G
H
,
looking
towards
the
same
part
as
before
,
is
then
for
Venus
towards
the
North
,
and
for
Mercurie
towards
the
South
.
But
the
lower
halfe
of
the
Epicicle
,
marked
with
the
letters
H
F
I
,
(
whereof
some
part
is
now
againe
hidden
and
couered
as
it
were
with
the
plane
of
the
Excentrique
)
is
for
Venus
towards
the
South
,
and
for
Mercurie
towards
the
North.
The
like
and
the
same
dooth
chance
when
the
centre
of
the
Epicicle
is
either
in
the
Auge
B
,
or
the
opposit
Auge
P
;
for
in
those
places
the
diameters
of
the
Auges
,
marked
with
F
G
,
hauing
no
declination
,
the
Epicicles
are
diuided
,
and
the
diameters
H
I
haue
their
greatest
reflection
:
and
yet
after
the
same
manner
as
before
,
that
is
,
when
the
East
halfe
is
in
B
,
and
the
West
halfe
in
P
,
which
letters
doe
signifie
as
well
the
two
limits
,
that
is
,
B
the
North
limit
,
and
P
the
South
limit
,
as
the
two
Auges
;
for
here
againe
the
one
halfe
of
the
Epicicle
is
wholly
to
be
seene
,
in
which
whilest
it
goeth
towards
the
Node
descendent
,
Venus
is
Northward
,
and
Mercurie
Southward
.
But
the
other
halfe
of
the
Epicicle
,
(
which
the
plane
of
the
Excentrique
dooth
partly
hide
and
couer
)
dooth
reflect
or
turne
backward
on
the
the
other
side
from
the
Excentrique
.
And
euen
so
it
fareth
in
like
manner
in
all
the
meane
places
that
are
betwixt
the
limits
and
the
nodes
.
And
here
endeth
the
first
booke
of
the
Theoriques
.
The
second
Booke
or
Part
,
treating
of
the
Passions
or
Accidents
of
the
Planets
.
HAuing
sufficiently
spoken
of
the
three
seuerall
latitudes
,
belonging
as
well
to
Venus
as
to
Mercurie
,
I
mind
here
to
make
an
end
of
the
first
part
of
the
Theoriques
;
wherein
haue
been
plainely
declared
all
the
diuerse
motions
of
the
Planets
,
as
well
according
to
their
longitude
as
latitude
:
and
so
now
to
proceed
to
the
second
part
,
wherein
wee
haue
to
treat
of
the
passions
,
qualities
,
or
accidents
of
the
Planets
;
of
which
,
though
Purbachius
maketh
fiue
kinds
,
counting
their
motions
according
to
latitude
to
be
one
of
those
fiue
:
yet
me
thinkes
that
Mestelyn
hath
more
reason
to
make
but
foure
generall
kinds
,
sith
the
latitude
of
euery
Planet
,
that
hath
latitude
,
is
rather
a
principall
part
of
his
motion
than
a
passion
:
for
all
their
motions
are
either
according
to
longitude
,
or
to
latitude
,
and
therefore
minding
herein
to
follow
Mestelyn
,
I
will
set
downe
but
foure
kinds
of
passions
,
as
he
dooth
,
which
doe
grow
of
foure
seuerall
comparisons
.
First
,
by
comparing
the
moouing
of
the
Epicicle
of
any
Planet
together
with
the
mouing
of
his
Excentrique
.
Secondly
,
by
comparing
the
moouing
of
the
Planets
one
to
another
.
Thirdly
,
by
comparing
their
moouings
to
the
Sunne
.
And
fourthly
,
by
comparing
their
moouings
or
rather
places
to
the
centre
of
the
world
and
to
the
globe
of
the
earth
,
euery
one
whereof
containeth
certaine
speciall
kinds
of
passions
or
accidents
,
hereafter
declared
.
What
speciall
accidents
doe
belong
to
the
first
generall
kind
,
consisting
of
the
comparison
of
the
mouing
of
the
Epicicle
to
the
mouing
of
his
Excentrique
?
BY
this
passion
the
Planets
are
said
to
be
sometime
direct
,
sometime
retrograde
,
and
somtime
stationarie
;
which
three
accidents
doe
belong
onely
vnto
the
fiue
Planets
,
the
Sunne
and
Moone
not
beeing
reckoned
.
Moreouer
,
they
are
said
to
be
sometime
swift
,
sometime
slow
,
and
sometime
in
a
meane
.
Sometime
also
they
are
said
to
be
either
encreased
or
deminished
in
number
,
and
sometime
to
be
ascendent
,
and
sometime
descendent
.
When
is
any
Planet
said
to
be
direct
,
retrograde
,
or
stationarie
?
IT
is
said
to
be
direct
,
when
the
line
of
the
true
mouing
of
the
Planet
,
drawne
from
the
centre
of
the
world
through
the
midde
bodie
of
the
Planet
,
proceedeth
forward
according
to
the
succession
of
the
signes
,
following
the
line
of
the
true
mouing
of
the
centre
of
his
Epicicle
,
which
goeth
alwaies
according
to
the
succession
of
the
signes
.
And
it
is
said
to
be
retrograde
,
when
the
line
of
the
true
mouing
of
the
Planet
goeth
more
backward
,
contrarie
to
the
succession
of
the
signes
,
than
the
line
of
the
true
moouing
of
the
centre
of
the
Epicicle
proceedeth
forward
according
to
the
succession
of
the
signes
.
And
it
is
said
to
be
stationarie
,
when
both
these
lines
are
drawne
to
the
Zodiake
with
an
equall
moouing
into
diuerse
parts
of
heauen
,
so
as
the
line
of
the
Planets
true
moouing
maketh
as
great
an
arch
of
the
Zodiake
in
going
backward
contrarie
to
the
succession
of
the
signs
,
as
the
line
of
the
true
mouing
of
the
centre
of
the
Epicicle
maketh
,
in
proceeding
forward
according
to
the
succession
of
the
signes
,
for
then
the
Planet
for
a
while
seemeth
to
stand
still
,
and
not
to
be
mooued
from
his
place
,
and
thereof
is
said
to
be
stationarie
,
like
to
any
of
the
fixed
starres
.
And
you
haue
to
vnderstand
,
that
these
diuersities
of
motions
vnder
the
Zodiake
proceedeth
of
the
mouing
of
the
Epicicle
,
which
in
his
vpper
part
carrieth
the
Planet
according
to
the
succession
of
the
signs
,
and
in
his
nether
part
carrieth
the
same
contrarie
to
the
succession
of
the
signes
,
called
his
retrogradation
.
In
which
inferior
or
nether
part
of
the
Epicicle
are
the
two
points
of
station
.
But
for
the
better
vnderstanding
of
that
which
hath
been
said
touching
the
direction
,
retrogradation
,
and
station
of
any
Planet
,
it
shall
be
needfull
to
set
downe
this
figure
here
following
,
together
with
the
description
thereof
,
the
signification
of
whose
parts
the
letters
doe
shew
as
you
may
see
in
the
page
next
following
.
¶
The
first
figure
of
the
second
Booke
.
IN
this
figure
the
letter
A
standing
at
the
nether
end
of
the
right
lines
,
signifieth
the
centre
of
the
world
,
from
whence
all
the
said
right
lines
are
drawne
to
the
Zodiake
:
and
B
signifieth
the
centre
of
the
Epicicle
:
&
the
middle
right
line
A
B
passing
through
the
true
Auge
of
the
Epicicle
,
marked
with
C
,
dooth
shew
the
true
place
of
the
said
Auge
vnder
the
Zodiake
,
marked
with
the
letter
D
:
and
the
letter
E
sheweth
the
true
opposit
Auge
of
the
Epicicle
:
and
the
highest
arch
aboue
,
containing
certaine
degrees
of
diuision
,
signifieth
a
portion
of
the
Zodiake
:
and
the
two
outermost
lines
,
A
F
G
,
and
A
H
I
,
be
lines
of
contingence
,
touching
the
Epicicle
in
the
two
points
,
marked
with
H
and
F
:
and
the
two
inner
right
lines
,
marked
with
the
letters
A
N
,
and
A
L
,
drawne
from
the
centre
A
through
the
two
points
of
station
,
marked
with
K
and
M
,
do
shew
in
the
Zodiake
the
retrogradation
,
marked
with
the
letters
L
N
:
and
the
two
points
H
F
doe
deuide
the
Epicicle
into
two
parts
or
halfes
,
whereof
the
one
is
called
the
vpper
halfe
,
marked
with
the
letters
H
C
F
,
and
the
other
the
nether
halfe
,
marked
with
the
letters
F
E
H.
And
as
the
point
F
sheweth
the
Orientall
or
East
part
,
so
H
sheweth
the
Occidentall
or
West
part
:
and
euery
one
of
the
fiue
Planets
in
the
vpper
halfe
of
the
Epicicle
,
marked
with
H
C
F
,
is
said
to
goe
from
H
to
F
,
according
to
the
succession
of
the
signes
,
describing
the
arch
of
the
Zodiake
,
marked
with
I
D
G
,
which
is
called
his
direction
or
progression
:
but
in
the
lower
halfe
,
marked
with
F
E
H
,
the
Planet
is
said
to
goe
contrarie
to
the
succession
of
the
signs
,
called
his
retrogradation
:
and
when
he
is
in
any
of
the
two
points
,
marked
with
K
M
,
then
he
is
said
to
be
stationarie
;
whereof
the
point
K
is
the
point
of
the
first
station
,
whereas
the
Planet
beginneth
first
to
be
retrograde
,
and
M
is
the
point
of
the
second
station
,
whereas
the
Planet
endeth
his
retrogradation
,
and
beginneth
his
progression
:
which
two
points
are
alwaies
beneath
the
two
Touch-points
F
H
,
towards
the
opposit
Auge
of
the
Epicicle
,
marked
with
E
,
from
which
the
two
points
of
station
are
alwaies
equally
distant
,
and
also
from
the
true
Auge
of
the
Epicicle
.
And
the
letters
C
F
K
doe
shew
the
arch
of
the
first
station
,
which
arch
is
otherwise
called
the
first
station
in
the
second
signification
;
and
C
F
K
M
doe
shew
the
arch
of
the
second
station
,
otherwise
called
the
second
station
in
the
second
signification
:
and
the
letters
M
H
C
F
K
,
doe
shew
the
arch
of
progression
,
and
KM
doe
shew
the
arch
of
retrogradation
.
But
you
haue
to
note
,
that
though
the
two
points
of
station
are
alwaies
equally
distant
as
well
from
the
opposit
Auge
,
as
from
the
Auge
of
the
Epicicle
,
yet
such
distance
is
not
alwaies
of
like
qualitie
,
neither
is
the
arch
of
their
progression
,
nor
the
arch
of
their
retrogradation
alwaies
of
one
bignesse
,
but
do
alter
and
that
for
four
causes
:
First
,
for
that
the
Epicicle
through
the
moouing
of
his
Excentrique
is
sometime
nigher
and
sometime
further
off
from
the
centre
of
the
earth
:
for
the
nigher
that
the
epicicle
is
to
the
earth
,
the
more
are
the
stational
points
distant
from
the
true
opposit
Auge
of
the
Epicicle
in
all
the
fiue
Planets
,
sauing
in
Mercurie
.
The
second
cause
may
be
the
diuerse
magnitude
of
the
Epicicle
,
being
compared
to
his
Excentrick
,
for
the
stationall
points
of
a
greater
Epicicle
do
approch
nigher
vnto
the
opposit
Auge
,
than
the
stationall
points
of
a
lesser
Epicicle
doe
.
The
third
cause
is
the
periodicall
slownesse
or
swiftnesse
of
the
Epicicle
,
being
compared
to
the
periodicall
mouing
of
his
Excentrique
,
for
the
slower
reuolution
of
the
Epicicle
maketh
the
stationall
points
to
be
nigher
to
the
opposit
Auge
of
the
Epicicle
,
and
therby
as
well
the
arch
of
progression
as
of
retrogradation
doe
encrease
and
decrease
.
Fourthly
,
the
diuersities
of
their
excentricities
may
cause
the
stationall
points
to
alter
in
their
distances
from
the
opposit
Auge
of
the
Epicicle
.
Wherefore
is
the
Moone
and
Sunne
exempted
from
these
passions
?
THe
Sunne
hath
no
Epicicle
,
and
though
the
Moon
hath
an
Epicicle
,
yet
she
is
neither
said
to
be
stationarie
nor
retrograde
,
by
meanes
of
the
swiftnesse
of
the
centre
of
her
Epicicle
,
which
maketh
euery
day
a
greater
arch
of
the
Zodiake
,
according
●n
the
succession
of
the
signes
,
than
she
can
goe
backward
,
because
her
Epicicle
is
both
small
and
slow
in
her
gate
.
And
though
Saturne
hath
a
very
small
Epicicle
,
yet
the
swiftnes
therof
doth
supplie
that
want
,
and
thereby
he
is
both
stationarie
and
retrograde
,
and
so
are
the
other
foure
Planets
,
viz.
Iupiter
,
Mars
,
Venus
,
and
Mercurie
.
When
are
the
Planets
said
to
be
swift
,
slow
,
or
in
a
meane
?
THey
are
said
to
be
swift
,
when
their
true
moouing
is
quicker
,
according
to
the
succession
of
the
signes
,
than
their
meane
moouing
is
:
and
they
are
said
to
bee
slow
,
when
their
true
mouing
is
slower
(
according
to
the
succession
of
the
signes
)
than
their
meane
moouing
is
:
and
they
are
said
to
be
in
a
meane
,
when
their
true
moouing
(
according
to
the
succession
of
the
signes
)
is
equall
vnto
their
meane
mouing
.
When
are
Planets
said
to
bee
encreased
or
deminished
in
number
?
THey
be
encreased
when
the
line
of
the
true
mouing
goeth
(
according
to
the
succession
of
the
signes
)
before
the
line
of
their
meane
mouing
.
And
they
are
said
to
be
deminished
in
number
,
when
the
line
of
their
true
moouing
dooth
follow
after
the
line
of
their
meane
moouing
.
When
is
any
Planet
said
to
be
ascendent
or
descendent
?
HE
is
said
to
be
as●endent
,
whilest
he
ascendeth
from
the
opposit
Auge
of
his
Epicicle
to
the
Auge
therof
:
and
he
is
said
to
be
descendent
,
whilest
he
descendeth
in
the
other
halfe
of
the
Epicicle
from
the
Auge
to
the
opposit
Auge
of
his
said
Epicicle
.
The
second
generall
kind
of
passions
,
rising
of
the
comparison
made
by
comparing
the
mouing
of
euery
Planet
one
to
another
,
comprehending
the
fiue
Aspects
of
the
Planets
,
which
be
these
here
following
.
THat
is
to
say
,
their
Conjunction
,
their
Sextile
aspect
,
their
Quadrile
aspect
,
their
Trine
aspect
,
and
their
Opposition
:
whose
caracters
are
here
set
down
,
together
with
the
definition
of
euery
such
Aspect
.
1.
The
Conjunction
,
marked
thus
●
.
is
when
two
Planets
are
both
in
one selfe
signe
,
and
in
one selfe
degree
,
which
aspect
in
Greeke
is
called
Synodos
.
2.
The
Sextile
aspect
,
marked
thus
*
,
is
when
two
Planets
are
distant
one
from
another
by
a
sixt
part
of
the
Zodiake
,
that
is
to
say
,
by
two
whole
signs
,
or
60
degrees
,
which
aspect
is
called
in
Greeke
Exagon●s
.
3.
The
Quadrile
aspect
,
marked
thus
●
,
is
when
two
Planets
are
distant
the
one
from
the
other
three
whole
signes
,
or
90
degrees
of
the
Zodiake
,
and
is
called
in
Greeke
Tetragonos
.
4.
The
Trine
aspect
,
marked
thus
●
,
is
when
two
Planets
are
distant
the
one
from
the
other
by
foure
whole
signes
or
120
degrees
of
the
Zodiake
,
and
is
called
in
Greeke
Trigonos
.
5.
The
Opposition
,
marked
thus
☍
,
is
when
two
Planets
are
right
opposit
the
one
to
the
other
,
and
are
distant
the
one
from
the
other
by
six
whole
signes
or
180
degrees
of
the
Zodiake
,
and
is
called
in
Greeke
Diametros
,
that
is
to
say
,
a
diametrall
aspect
,
as
when
one
is
right
against
another
in
a
right
line
.
But
you
haue
to
vnderstand
,
that
Ptolomey
comprehendeth
as
well
the
Opposition
as
Conjunction
of
any
two
Planets
,
but
especially
of
the
Sunne
and
Moone
,
vnder
this
Greeke
name
Syzigias
.
And
you
haue
to
note
,
that
three
of
these
aspects
,
that
is
,
the
Sextile
,
Quadrile
,
and
Trine
aspect
,
are
said
to
be
double
,
because
they
looke
two
manner
of
waies
,
that
is
,
towards
the
left
hand
,
called
the
sinister
aspect
,
and
towards
the
right
hand
called
the
dexter
aspect
.
The
direction
of
the
sinister
aspect
is
according
to
the
succession
of
the
twelue
signs
,
which
succession
beginneth
at
Aries
,
and
so
proceedeth
forward
to
Taurus
,
Gemini
,
and
Cancer
,
and
so
forth
to
the
last
point
of
Pisces
.
But
the
direction
of
the
dexter
aspect
is
contrarie
to
the
succession
of
the
signes
,
looking
backward
from
Aries
towards
Pisces
,
Aquarius
,
Capricornus
,
and
so
forth
to
the
last
point
of
Taurus
.
As
for
example
,
if
one
Planet
be
in
the
beginning
of
Aries
,
and
another
in
the
beginning
of
Gemini
,
those
two
Planets
do
looke
one
to
another
with
a
sinister
Sextile
aspect
.
But
if
the
one
Planet
be
in
Aries
,
as
before
,
and
the
other
in
Aquarius
,
then
they
looke
one
to
another
with
a
dexter
Sextile
aspect
,
as
you
may
see
by
this
figure
following
,
which
dooth
plainely
shew
as
well
those
aspects
as
all
the
other
aspects
before
mentioned
;
it
sheweth
also
with
what
aspect
euery
one
of
the
twelue
signes
doe
regard
one
another
.
¶
The
figure
of
Aspects
.
BVt
you
haue
to
vnderstand
,
that
all
the
Planets
doe
not
regard
or
behold
one
another
with
all
the
foresaid
fiue
aspects
,
for
though
the
three
vpper
Planets
and
the
Moone
may
behold
one
another
,
or
any
of
the
rest
with
euery
one
of
the
said
fiue
Aspects
,
yet
Venus
and
Mercurie
cannot
so
doe
,
for
Venus
is
neuer
distant
from
the
Sunne
aboue
48
degrees
,
nor
Mercurie
aboue
29
degrees
:
and
yet
they
may
bee
distant
one
from
another
by
a
Sextile
aspect
.
And
of
the
foresaid
aspects
,
some
are
said
to
be
meane
,
and
some
to
be
true
,
and
specially
their
Conjunctions
and
Oppositions
,
whereof
the
Astronomers
doe
not
make
any
great
account
,
but
onely
of
the
Conjunctions
and
Oppositions
belonging
to
the
Sunne
and
Moone
,
which
two
Planets
the
Astronomers
doe
call
in
Latine
Luminaria
,
that
is
to
say
,
The
two
cheefe
lights
:
the
knowledge
of
whose
meane
and
true
Conjunctions
and
Oppositions
,
is
necessarie
,
for
the
better
vnderstanding
of
their
Eclipses
.
When
are
their
Coniunctions
and
Oppositions
said
to
bee
meane
or
true
?
THey
are
said
to
be
meane
,
when
the
two
lines
of
both
their
meane
mouings
doe
meet
in
one selfe
point
of
the
Zodiake
,
and
doe
make
one selfe
line
.
And
they
are
said
to
bee
true
,
when
the
two
lines
of
their
true
moouings
doe
meet
and
make
both
one selfe
line
in
one selfe
degree
of
the
Zodiake
,
and
their
Oppositions
are
either
meane
or
true
,
according
as
the
said
lines
doe
meet
in
the
opposit
points
of
the
Zodiake
.
And
the
true
Conjunctions
of
the
said
two
lights
are
said
to
bee
true
,
sometime
according
to
longitude
onely
,
as
when
the
foresaid
true
lines
doe
meet
in
one selfe
point
onely
according
to
longitude
:
for
the
Moone
doth
oftentimes
wander
from
the
Eclipticke
line
,
and
therefore
though
the
line
of
her
true
mouing
doe
meet
with
the
line
of
the
Sunnes
true
moouing
in
one selfe
point
vnder
the
Zodiake
(
the
Moone
hauing
then
latitude
)
yet
that
is
according
to
longitude
only
:
but
if
those
two
lines
doe
meet
when
the
Moone
hath
no
latitude
,
but
is
right
vnder
the
Eclipticke
line
,
then
such
Conjunction
is
both
according
to
latitude
,
and
also
according
to
longitude
,
which
is
called
a
Corporall
or
Eclipticall
Conjunction
.
And
the
like
is
to
be
said
of
their
true
Oppositions
,
when
the
said
lines
doe
meet
in
like
manner
in
the
opposit
points
of
the
Zodiake
.
Moreouer
,
you
haue
to
note
,
that
the
true
Conjunctions
may
differ
from
the
meane
Conjunctions
by
reason
of
time
,
for
sometime
the
one
may
go
before
or
after
the
other
,
and
sometime
meet
both
at
one
instant
.
They
may
meet
both
at
one
instant
two
manner
of
waies
:
First
,
when
the
Sunne
or
Moon
are
in
the
Auge
or
opposit
Auge
of
their
Excentriques
,
or
when
the
one
is
in
the
Auge
,
and
the
other
in
the
opposit
Auge
,
for
then
the
foresaid
lines
of
their
meane
and
true
mouings
are
all
one
.
Secondly
,
they
doe
meet
at
one
instant
,
when
the
equacions
of
their
arguments
are
equall
and
of
like
qualitie
,
which
is
to
bee
knowne
by
the
Prutenicall
tables
.
But
the
true
Conjunctions
and
Oppositions
doe
goe
before
the
mean
Conjunctions
or
Oppositions
,
when
at
the
time
of
the
mean
Conjunction
and
Opposition
the
place
of
the
Sunne
is
before
the
place
of
the
Moone
.
And
the
true
Conjunctions
and
Oppositions
doe
follow
the
meane
,
when
at
the
time
of
the
meane
Conjunction
and
Opposition
the
place
of
the
Moone
is
before
the
place
of
the
Sunn●
.
The
like
is
to
be
said
also
touching
their
quarters
,
both
meane
and
true
.
And
you
haue
to
note
,
that
one
whole
period
betwixt
euery
two
Conjunctions
or
Oppositions
of
the
Sunne
and
Moone
dooth
containe
a
Synodicall
month
,
which
is
29
daies
and
a
halfe
,
The
third
generall
kind
of
Passions
,
made
by
comparing
of
the
mouings
of
all
the
six
Planets
,
vnto
the
Sunne
,
containeth
these
three
speciall
kinds
of
Passions
here
following
.
1.
FOr
first
they
are
said
to
be
either
encreased
or
decreased
in
light
,
or
els
to
be
combust
,
called
in
Greeke
Hyppaugi
,
that
is
to
say
,
hidden
or
couered
with
the
beames
of
the
Sun
,
so
as
they
cannot
yeeld
their
light
.
2.
Secondly
,
they
are
said
to
bee
Orientall
or
Occidentall
.
3.
Thirdly
,
to
haue
diuerse
kinds
of
rising
and
setting
,
like
as
the
fixed
starres
haue
,
that
is
to
say
,
they
rise
or
set
sometime
Cosmice
,
sometime
Achronice
,
and
sometime
Helyace
;
of
which
three
Poeticall
kinds
of
rising
and
setting
,
though
I
haue
somewhat
spoken
before
in
my
first
booke
of
the
Sphere
,
chap.
35.
yet
I
wil
declare
the
same
here
once
againe
more
at
the
full
,
according
to
Maginus
,
who
doth
set
them
downe
in
such
manner
as
hereafter
followeth
.
Shew
how
and
when
these
Passions
doe
chance
?
THe
Planets
are
said
to
be
encreased
in
light
,
when
after
that
any
of
them
hath
been
in
Conjunction
with
the
Sunne
,
either
the
Sunne
departeth
from
that
Planet
,
or
the
Planet
departeth
from
the
Sunne
,
vntill
it
be
at
his
furthest
distance
from
the
Sunne
.
And
it
is
said
to
bee
deminished
in
light
,
when
after
such
furthest
distance
either
the
Planet
approcheth
to
the
Sunne
,
or
the
Sunne
to
the
Planet
.
And
it
is
said
to
be
combust
,
when
the
Planet
is
hidden
vnder
the
beames
of
the
Sunne
,
so
as
it
cannot
yeeld
his
light
,
as
is
before
said
.
Secondly
,
all
starres
are
said
to
be
Orientall
or
Matutine
,
when
they
rise
before
the
Sunne
;
and
they
are
said
to
bee
Occidentall
,
when
they
goe
downe
after
the
Sunne
;
and
yet
with
some
difference
as
Maginus
sayth
:
for
the
three
vpper
Planets
(
that
is
to
say
)
Saturne
,
Iupiter
,
and
Mars
,
are
said
to
bee
Orientall
,
Matutine
,
and
to
goe
before
the
Sunne
from
the
time
of
their
being
in
Conjunction
with
the
Sunne
,
vntill
they
come
to
be
in
Opposition
to
the
Sunne
,
as
well
when
they
are
seene
,
as
not
seene
:
and
this
happeneth
whilest
any
of
those
three
Planets
descendeth
from
the
Auge
of
his
Epicicle
through
the
meane
longitudes
vnto
the
opposit
Auge
of
the
said
Epicicle
:
but
the
two
inferior
Planets
,
that
is
,
Venus
and
Mercurie
,
are
said
to
be
Orientall
,
Matutine
,
and
to
goe
before
the
Sun
,
when
either
of
them
ascendeth
from
the
opposit
Auge
of
his
Epicicle
vnto
the
Auge
of
the
said
Epicicle
,
which
you
may
euidently
see
by
the
first
figure
of
this
second
book
.
But
as
for
the
Moone
,
she
is
said
to
be
Orientall
,
Matutine
,
and
to
goe
before
the
Sunne
,
during
the
time
of
her
wane
or
decrease
.
Againe
,
the
three
vpper
Planets
are
said
to
be
Occidentall
,
Vespertine
,
and
to
follow
the
Sunne
from
their
being
in
Opposition
with
the
Sunne
,
vntill
they
come
againe
to
be
in
Conjunction
with
the
Sunne
;
which
chanceth
whilest
any
of
them
is
carried
from
the
opposite
Auge
of
the
Epicicle
through
the
meane
longitudes
,
vnto
the
Auge
of
the
same
Epicicle
.
But
Venus
and
Mercurie
are
said
to
be
Occidentall
,
Vespertine
,
and
to
follow
the
Sunne
,
whilest
either
of
them
descendeth
from
the
Auge
of
their
Epicicle
vnto
the
opposit
Auge
of
the
same
.
But
as
for
the
Moone
,
shee
is
said
to
be
Occidentall
,
Vespertine
,
and
to
follow
the
Sun
all
the
time
that
she
is
in
her
encrease
.
Now
you
haue
to
vnderstand
,
that
the
rising
and
going
downe
of
the
fixed
starres
,
as
well
Matutine
as
Vespertine
,
is
twofold
,
that
is
,
true
and
apparent
.
The
Matutine
rising
is
said
to
be
true
,
when
the
starre
riseth
together
with
the
Sunne
in
one selfe
point
of
the
Eclipticke
,
and
at
one selfe
instant
,
at
which
time
the
star
remaineth
hidden
vnder
the
beames
of
the
Sunne
:
but
such
Matutine
rising
is
said
to
be
apparent
,
when
the
starre
hauing
been
hidden
a
little
before
with
the
beames
of
the
Sunne
,
doth
get
out
from
thence
,
so
as
in
the
morning
it
may
bee
seene
,
which
chanceth
when
the
Sunne
goeth
from
the
starre
.
Again
,
the
Vespertine
rising
is
said
to
be
true
,
when
the
starre
is
right
opposite
in
any
part
of
the
Eclipticke
to
the
Sunne
,
at
the
time
of
his
going
downe
,
and
is
so
much
eleuated
aboue
the
Horizon
,
as
after
the
euening
twilight
it
may
be
seene
:
but
such
Vespertine
rising
is
said
to
be
apparent
,
when
the
starre
in
the
euening
after
Sun
setting
,
dooth
shine
,
and
beginneth
to
appeare
in
the
West
.
Now
the
Matutine
going
downe
of
any
starre
is
said
to
be
true
,
when
the
starre
goeth
downe
at
such
time
as
the
Sunne
riseth
,
and
is
in
the
opposit
point
of
the
Eclipticke
,
to
the
Sunne
.
But
the
Matutine
going
downe
is
said
to
be
apparent
,
when
the
starre
at
the
rising
of
the
Sunne
(
which
a
little
before
night
haue
been
seene
)
is
now
hidden
vnder
the
beames
of
the
Sunne
.
Moreouer
,
the
Vespertine
going
downe
of
any
starre
is
said
to
be
true
,
when
it
goeth
downe
together
with
the
Sunne
at
one selfe
instant
.
And
such
Vespertine
going
downe
is
said
to
be
apparent
,
when
the
starre
at
the
going
downe
of
the
Sunne
is
hidden
,
which
a
little
before
might
haue
been
seene
,
and
so
continueth
hidden
vntill
the
morning
,
vntill
it
may
get
from
vnder
the
beames
of
the
Sunne
.
Out
of
this
difference
of
rising
and
going
downe
of
the
Planets
may
be
gathered
these
6
rules
here
folowing
.
1.
First
,
that
the
three
vpper
Planets
,
the
Moone
,
and
also
the
fixed
starres
are
subject
to
the
true
rising
&
setting
as
well
Matutine
as
Vespertine
;
but
neither
the
apparent
rising
Vespertine
,
nor
the
apparent
setting
Matutine
doe
belong
to
any
of
them
,
but
only
to
the
Moone
,
which
notwithstanding
suffereth
neither
the
apparent
rising
Matutine
,
nor
the
apparent
rising
Vespertine
.
2.
Secondly
,
though
Venus
and
Mercurie
be
subject
to
the
apparent
rising
and
setting
,
as
well
Matutine
as
Vespertine
,
yet
they
cannot
haue
the
true
Matutine
setting
,
or
the
true
Vespertine
rising
.
3.
Thirdly
,
of
all
the
fixed
starres
and
of
the
three
vpper
Planets
,
their
true
rising
and
setting
Matutine
,
are
before
their
apparent
rising
and
setting
Matutine
:
but
their
true
Vespertine
rising
and
setting
are
after
their
apparent
rising
and
setting
.
4.
Fourthly
,
in
the
two
inferior
Planets
,
that
is
,
Venus
and
Mercurie
,
their
apparent
Matutine
and
Vespertine
rising
are
after
their
true
Matutine
and
Vespertine
setting
;
but
their
apparent
Matutine
and
Vespertine
setting
are
before
their
true
Matutine
and
Vespertine
rising
.
5.
Fiftly
,
the
apparent
Matutine
rising
of
the
Moone
doth
follow
her
true
Matutine
rising
,
and
contrarie
her
apparent
Matutine
setting
,
doth
go
before
her
true
Matutine
setting
.
6.
Sixtly
,
it
is
meet
that
there
bee
some
distance
of
space
betwixt
any
starre
and
the
Sunne
,
whereby
they
should
either
appeare
to
bee
out
of
the
beames
of
the
Sunne
,
or
else
to
be
hidden
vnder
the
Sunne
.
And
this
distance
is
not
of
like
quantitie
in
euery
starre
,
but
varieth
according
to
the
greatnesse
or
littlenesse
of
the
starre
,
for
the
greater
and
more
lightsome
that
the
starre
is
,
the
lesser
time
it
staies
vnder
the
beams
of
the
Sunne
.
And
the
limits
of
the
quantitie
of
distance
that
do
belong
to
euery
starre
,
as
well
to
the
fixed
starres
as
to
the
Planets
,
are
to
be
found
in
a
great
circle
,
passing
both
through
the
bodie
of
the
Sunne
,
and
also
through
the
pole
of
the
Horizon
.
For
to
euery
limit
the
Astronomers
doe
appoint
his
proper
arch
of
quantitie
,
called
of
them
the
arch
of
vision
.
Define
what
that
arch
is
.
THe
Arch
of
Vision
,
is
that
portion
of
the
Verticall
circle
that
is
comprehended
betwixt
the
Horizon
and
the
Sunne
,
at
such
time
as
the
starre
first
beginneth
to
appeare
,
or
els
ceaseth
to
bee
seene
:
which
arches
of
vision
in
fixed
starres
are
greater
or
lesser
,
according
to
the
magnitude
of
the
said
starres
,
for
to
those
starres
,
that
be
of
the
first
bignesse
,
they
make
the
arch
of
vision
to
containe
12
degrees
,
and
to
those
of
the
second
bignesse
13
degrees
,
and
to
those
of
the
third
bignesse
14
degrees
,
and
to
those
of
the
fourth
bignesse
15
degrees
,
and
to
those
of
the
fift
bignesse
,
16
degrees
,
and
to
those
of
the
sixt
bignesse
17
degrees
,
and
to
the
least
fixed
stars
of
all
,
they
appoint
18
degrees
,
which
18
degrees
is
the
beginning
as
well
of
the
day
light
in
the
morning
,
as
of
the
twilight
in
the
euening
:
for
when
the
Sunne
is
departed
from
the
Horizon
18
degrees
,
either
vpward
or
downeward
,
it
beginneth
to
waxe
day
light
in
the
morning
,
or
twilight
in
the
euening
.
Now
as
touching
the
quantitie
of
the
said
arch
of
vision
belonging
to
euery
one
of
the
fiue
Planets
,
they
appoint
to
Saturne
11
degrees
,
to
Iupiter
10
degrees
,
to
Mars
11
degrees
,
½
.
to
Venus
5
degrees
,
and
to
Mercurie
10
degrees
:
so
as
by
knowing
the
degree
of
the
Ecl●pticke
,
wherewith
any
starre
riseth
or
goeth
downe
,
and
also
the
arch
of
vision
,
together
with
the
angle
of
section
,
whereas
the
Eclipticke
and
Horizon
doe
crosse
one
another
in
one selfe
part
,
you
shall
know
what
time
the
starre
spendeth
in
his
rising
or
setting
.
And
for
the
better
vnderstanding
of
the
said
arch
of
vision
,
Maginus
setteth
downe
this
figure
here
following
,
together
with
the
description
thereof
,
by
helpe
of
certaine
letters
therein
contained
▪
¶
The
figure
shewing
the
arch
of
vision
.
THis
figure
as
you
see
consisteth
of
two
whole
circles
being
of
like
greatnesse
,
and
also
it
containeth
the
portion
of
a
great
circle
.
The
whole
circle
,
marked
with
G
E
C
,
signifieth
the
Horizon
,
whose
pole
or
Zenith
is
marked
with
the
letter
A
:
and
the
other
whole
circle
,
marked
with
the
letters
F
E
D
,
signifieth
the
Eclipticke
,
whose
pole
is
marked
with
the
letter
B
:
and
the
letter
D
sheweth
the
place
of
the
Sunne
,
being
hidden
beneath
the
Horizon
.
And
imagine
the
place
of
the
starre
his
appearing
or
departing
to
be
in
C
,
in
the
very
Horizon
it selfe
.
Now
the
portion
of
the
great
circle
,
drawne
through
the
Verticall
point
of
the
Horizon
,
and
also
through
the
bodie
of
the
Sunne
,
is
marked
with
the
letters
A
C
D.
And
the
arch
C
D
is
the
arch
of
vision
.
But
now
you
haue
to
vnderstand
,
that
the
Moone
obserueth
not
like
law
or
order
of
hi●
appearing
,
after
that
she
hath
been
in
Conjunction
with
the
Sunne
.
For
though
the
auncient
Astronomers
,
as
Theon
,
Alexandrinus
,
Alfraganius
,
Albategnus
,
and
others
,
doe
appoint
to
her
arch
of
vision
twelue
degrees
of
the
Aequinoctiall
,
yet
that
is
not
alwaies
certaine
,
but
sometime
more
,
and
sometime
lesse
,
sith
the
Moone
doth
shew
her selfe
sometime
sooner
and
sometime
later
after
her
Conjunction
with
the
Sunne
,
and
that
for
three
causes
or
respects
,
first
by
reason
of
the
inclination
of
the
Zodiake
to
the
Horizon
,
for
whilest
she
is
in
the
ascending
halfe
of
the
Zodiake
,
which
is
from
the
beginning
of
Capricorn
to
the
end
of
Gemini
,
which
is
the
halfe
of
long
discension
,
she
appeareth
sooner
aboue
the
Horizon
,
than
when
she
is
in
the
other
halfe
of
short
discension
,
which
is
from
Cancer
to
Capricorne
,
because
the
Moone
goeth
downe
later
and
not
before
that
the
Sunne
be
deeply
hidden
vnder
the
Horizon
,
making
thereby
a
greater
twilight
.
The
second
cause
is
the
latitude
of
the
Moone
from
the
Ecliptick
,
for
the
more
North
latitude
she
hath
,
the
more
slowly
she
goeth
downe
,
and
therby
is
the
sooner
seene
,
and
specially
to
those
that
dwell
betwixt
the
Tropicke
of
Cancer
,
and
the
circle
Artique
.
The
third
cause
is
the
swiftnesse
of
her
true
mouing
,
for
in
her
swift
mouing
she
is
sooner
seene
than
in
her
slow
moouing
.
And
when
all
those
three
causes
do
concurre
,
it
is
possible
that
she
may
bee
seene
the
selfesame
day
that
the
change
is
,
albeit
that
seldome
chanceth
,
and
that
onely
in
those
places
,
whose
latitude
is
very
farre
Northerne
.
But
if
two
of
the
foresaid
causes
doe
concurre
,
then
she
may
be
seene
the
next
day
after
her
Conjunction
with
the
Sunne
:
if
there
be
no
more
but
one
cause
,
then
she
is
commonly
seene
the
third
day
after
the
change
.
But
if
she
be
in
the
descending
halfe
of
the
Zodiake
,
and
haue
therewith
South
latitude
,
and
is
slow
of
gate
,
there
may
passe
foure
daies
before
she
appeareth
.
Here
also
it
is
meet
to
speake
of
the
diuersitie
of
her
shape
,
according
as
she
is
distant
from
the
Sunne
,
as
well
in
her
increase
as
decrease
:
for
during
her
increase
,
shee
followeth
the
Sunne
,
and
turneth
her
hornes
from
the
Sunne
towards
the
East
,
and
her
lightsome
part
to
the
Sunne
,
and
riseth
aboue
the
Horizon
immediatly
after
the
Sunne
is
set
.
But
during
her
decrease
,
which
is
from
the
full
vnto
the
change
,
she
goeth
before
the
Sunne
,
and
turneth
her
hornes
towards
the
West
,
and
riseth
in
the
morning
before
the
Sunne
.
And
as
for
the
diuers
names
which
she
hath
both
in
Greeke
and
Latine
,
according
to
hir
diuers
aspects
to
the
Sunne
,
are
plainly
set
down
before
in
a
table
made
by
Reinholdus
,
which
table
immediatly
followeth
the
third
figure
belonging
to
the
Theorique
of
the
Moone
;
and
therefore
I
would
wish
you
to
resort
thereunto
,
because
I
thinke
it
superfluous
to
repeat
it
againe
here
.
Notwithstanding
loe
here
the
figure
which
is
commonly
vsed
to
shew
the
diuerse
shapes
of
her
light
,
as
well
in
her
encrease
as
decrease
.
The
fourth
generall
kind
of
passions
of
the
Planets
,
that
do●
chance
by
comparing
their
mouings
vnto
the
globe
of
the
earth
.
BVt
you
haue
to
vnderstand
,
that
the
passions
rising
of
this
comparison
,
are
not
so
properly
incident
to
all
the
Planets
,
as
to
the
Moone
;
because
that
the
greatnesse
of
the
earth
is
not
to
be
esteemed
in
respect
of
the
other
Planets
,
or
at
the
least
not
with
any
great
sensibilitie
or
affection
.
Shew
what
passions
the
Moone
hath
to
the
earth
,
or
the
earth
to
the
Moone
?
THese
three
here
following
:
for
first
the
greatnesse
of
the
earth
doth
not
suffer
the
true
place
of
the
Moone
to
be
all
one
with
her
visible
place
.
Secondly
,
the
earth
sometime
taketh
away
the
light
of
the
Sunne
from
the
Moone
,
and
so
causeth
her
to
be
eclipsed
.
Thirdly
,
the
Moone
with
her
apparent
magnitude
taketh
away
the
light
of
the
Sun
,
causing
the
same
in
some
parts
of
the
earth
to
be
eclipsed
.
And
hereof
dependeth
the
whole
doctrine
of
the
Eclipses
,
whereof
we
shal
treat
hereafter
.
In
the
meane
time
shew
what
is
the
true
place
,
and
also
what
is
the
visible
place
of
the
Moone
,
or
of
any
other
starre
?
THe
true
place
of
the
Moone
or
of
any
other
starre
,
is
apoint
in
the
outermost
heuen
,
determined
by
a
right
line
beeing
drawne
from
the
very
centre
of
the
earth
through
the
bodie
of
the
Moone
or
starre
,
vnto
the
said
outermost
heauen
.
And
the
visible
place
to
our
sight
,
is
a
point
in
the
outermost
heauen
,
determined
by
a
right
line
passing
through
the
body
of
the
Moone
or
star
from
our
eie
vnto
the
said
heauen
,
whilest
we
stand
vpon
the
vpper
face
of
the
earth
to
behold
the
starre
.
And
the
distance
or
portion
of
circle
contained
betwixt
those
two
points
,
is
called
in
Greeke
Paralaxis
,
which
in
English
may
be
called
the
diuersitie
of
Aspects
.
All
which
things
you
may
see
plainly
expressed
in
this
figure
following
.
THis
figure
as
you
see
is
made
like
a
Quadrant
:
the
nether
right
line
whereof
,
commonly
called
the
Base
,
signifieth
the
Horizon
,
and
the
perpendicular
right
line
falling
vpon
the
same
,
and
making
therewith
a
right
angle
,
is
the
axletree
of
the
Horizon
:
and
the
said
right
angle
,
marked
with
the
letter
A
,
signifieth
the
centre
of
the
earth
,
whose
halfe
globe
,
made
like
a
halfe
circle
,
is
drawne
vpon
the
said
centre
,
and
the
short
line
,
marked
with
the
letters
A
B
,
signifieth
the
semidiameter
of
the
earth
,
&
the
letter
F
signifieth
the
Zenith
,
from
which
F
to
G
is
drawn
the
arch
of
the
Quadrant
,
signifying
here
the
Verticall
circle
.
And
you
haue
to
vnderstand
,
that
the
right
line
that
is
drawn
from
A
throgh
the
bodie
of
the
Moone
,
marked
with
the
letter
C
vnto
the
point
D
,
set
downe
in
the
arch
of
the
Quadrant
or
Verticall
circle
,
sheweth
the
true
place
of
the
Moone
:
and
the
right
line
drawne
from
B
,
through
the
bodie
of
the
Moone
vnto
the
point
of
the
foresaid
arch
,
marked
with
E
,
sheweth
the
apparent
place
of
the
Moone
visible
to
our
sight
from
the
vpper
face
of
the
earth
:
and
the
little
arch
contained
betwixt
D
and
E
,
is
the
Parallax
or
diuersitie
of
Aspects
.
And
you
haue
to
note
,
that
the
apparent
or
visible
place
of
the
Moone
is
alwayes
lower
in
the
heauen
,
than
her
true
place
,
vnlesse
the
Moone
doe
chance
to
be
in
the
right
line
of
the
Zenith
,
for
then
there
is
no
Parallax
at
all
,
because
both
the
lines
and
places
do
concurre
and
meet
in
one
,
as
the
two
lines
A
B
and
B
F
doe
shew
,
making
both
one selfe
line
:
and
the
further
that
the
Moone
is
distant
from
the
earth
,
the
lesser
is
the
Parallax
,
and
the
nigher
that
shee
is
to
the
earth
,
the
greater
Parallax
she
hath
.
But
the
true
quantitie
of
her
Parallax
in
euery
place
is
to
be
learned
by
the
Prutenicall
tables
.
And
you
haue
to
vnderstand
,
that
the
Astronomers
doe
make
the
Parallax
of
the
Moone
to
be
threefold
,
that
is
,
first
simple
,
then
according
to
longitude
,
and
thirdly
according
to
latitude
.
For
if
you
haue
onely
respect
to
the
Verticall
circle
,
then
it
is
said
to
be
simple
,
which
is
before
defined
:
but
if
you
haue
respect
to
the
Zodiake
,
then
it
is
said
to
be
sometime
according
to
longitude
,
and
sometime
according
to
latitude
.
What
is
the
Parallax
according
to
longitude
?
IT
is
an
arch
of
the
Eclipticke
,
intercepted
or
contained
betwixt
two
great
circles
drawn
through
the
poles
of
the
said
Eclipticke
;
so
as
the
one
circle
dooth
passe
through
the
true
place
of
the
Planet
,
and
the
other
great
circle
passeth
through
the
apparent
or
visible
place
of
the
said
Planet
.
What
is
the
Parallax
according
to
latitude
?
IT
is
an
arch
of
a
great
circle
,
falling
perpendicularly
vpon
the
Eclipticke
,
and
is
drawne
either
through
the
true
place
,
or
els
through
the
apparent
and
visible
place
of
the
Moone
,
which
arch
is
intercepted
betwixt
two
circles
,
paralels
to
the
Eclipticke
,
whereof
the
one
passeth
through
the
true
place
,
and
the
other
through
the
apparent
place
of
the
Moone
.
For
the
better
vnderstanding
of
all
which
things
,
it
shall
be
necessarie
to
set
down
here
once
againe
the
Quadrant
before
described
,
together
with
his
proper
letters
of
signification
;
and
then
to
adde
to
the
said
Quadrant
the
Eclipticke
line
,
and
also
the
two
circles
which
are
paralels
to
the
same
;
and
thirdly
,
the
two
circles
that
are
drawne
from
the
pole
of
the
Zodiake
,
so
as
the
one
may
passe
through
the
true
place
,
and
the
other
through
the
apparent
place
of
the
Moon
:
all
which
things
this
figure
plainely
sheweth
.
A
figure
shewing
all
the
three
kinds
of
Paralaxes
.
The
description
of
the
figure
.
FIrst
the
Quadrant
of
this
figure
,
together
with
his
former
letters
,
doe
shew
the
simple
Parallax
,
otherwise
called
of
some
the
mixt
Parallax
,
because
it
comprehendeth
both
the
other
two
Parallaxes
,
vnto
which
Quadrant
is
added
first
the
Eclipticke
line
,
deuided
into
degrees
,
and
is
signified
by
the
letters
I
H
:
the
arch
whereof
,
marked
with
K
L
,
intercepted
betwixt
the
true
and
apparent
place
of
the
Moone
,
sheweth
the
Parallax
according
to
longitude
:
then
the
two
circles
,
Paralels
to
the
Eclipticke
,
which
are
marked
with
the
letters
N
M
,
and
Q
P
,
through
which
two
Paralels
,
and
also
through
the
Eclipticke
are
drawne
from
the
pole
of
the
Zodiake
,
marked
with
S
,
two
great
circles
,
whereof
the
one
passeth
through
the
true
place
of
the
Moone
,
marked
with
S
D
R
,
and
the
other
passeth
through
the
apparent
place
of
the
Moone
,
marked
with
S
O
E
:
so
as
each
of
the
arches
,
intercepted
betwixt
the
foresaid
Paralels
,
that
is
to
say
,
either
D
R
or
O
E
,
signifieth
the
Parallax
according
to
latitude
;
and
the
Diagonall
arch
,
marked
with
the
letters
D
E
,
doe
shew
the
simple
or
mixt
Parallax
.
How
the
two
Parallaxes
of
longitude
and
latitude
are
to
bee
compared
together
.
TO
doe
this
,
it
is
first
necessarie
to
know
what
the
90
degree
of
the
Moon
is
,
which
is
a
point
in
the
Eclipticke
,
deuiding
that
semicircle
of
the
Eclipticke
,
which
is
aboue
the
Horizon
,
into
two
equall
Quadrants
,
and
is
in
the
very
middest
of
the
said
semicircle
betwixt
East
and
West
:
and
this
point
is
readily
found
by
helpe
of
a
celestiall
globe
,
in
manner
and
forme
following
.
For
first
hauing
set
the
globe
at
our
latitude
,
which
is
52
,
suppose
the
Moone
to
be
in
the
first
point
of
Taurus
:
here
if
you
bring
that
point
to
the
mouable
Meridian
,
you
shal
find
,
that
the
17
of
Leo
then
riseth
aboue
the
Horizon
,
and
that
the
17
of
Aquarius
goeth
downe
beneath
the
Horizon
,
which
is
the
one
halfe
of
the
Eclipticke
;
of
which
halfe
,
by
counting
90
degrees
from
the
East
point
,
that
is
,
from
the
17
of
Leo
,
and
so
forward
,
you
shall
find
,
that
the
17
of
Taurus
is
the
middle
point
or
90
degree
,
and
the
same
to
be
nigher
to
the
South
than
to
the
East
.
Now
how
to
compare
together
the
two
foresaid
Parallaxes
,
these
fiue
rules
following
doe
shew
.
1.
First
,
if
the
Moon
be
in
the
90
degree
of
the
Eclipticke
aboue
the
Horizon
,
then
there
is
no
Parallax
of
longitude
,
but
only
of
latitude
.
2.
Secondly
,
when
the
Eclipticke
passeth
through
the
Zenith
,
there
is
no
Parallax
of
latitude
,
but
onely
of
longitude
.
3.
Thirdly
,
when
the
Eclipticke
passeth
not
through
the
Zenith
,
the
two
foresaid
Parallaxes
shall
be
differing
one
from
another
,
and
shall
not
fall
one
into
another
.
4.
Fourthly
,
to
those
that
haue
more
latitude
than
30
degrees
,
the
Moone
alwaies
appeareth
more
to
the
South
,
because
her
Parallaxes
doe
alwaies
fall
more
Southerly
.
5.
Fiftly
,
the
Moone
from
her
rising
vntill
she
come
to
the
90
degree
,
appeareth
more
Eastward
:
but
from
the
90
degree
to
her
setting
,
she
appeareth
more
Westward
,
as
the
globe
plainely
sheweth
.
How
to
know
whether
the
Moone
be
in
the
90
degree
,
or
not
.
YOu
shall
know
this
by
obseruing
the
hornes
of
the
Moon
,
for
if
both
the
tips
of
the
horns
of
the
Moon
doe
rightly
hang
one
ouer
another
by
a
perpendicular
line
,
then
the
Moone
is
in
the
90
degree
of
the
Ecliptick
aboue
the
Horizon
:
but
if
the
vpper
horne
doe
more
encline
to
the
East
than
the
nether
horne
doth
,
then
the
Moone
is
short
of
the
90
degree
.
But
if
the
vpper
horn
be
more
to
the
West
,
then
the
Moone
is
past
the
90
degree
.
And
here
I
end
with
the
description
of
the
Parallax
,
and
all
the
kinds
thereof
:
minding
now
to
treat
of
the
Eclipses
of
the
Sunne
and
Moone
,
which
are
meet
to
be
accounted
amongst
the
cheefest
Passions
of
these
two
Planets
.
❀
Of
the
Eclipses
of
the
Sunne
and
Moone
,
and
first
of
the
Moone
.
THough
this
word
Eclipse
may
be
generally
taken
for
the
hiding
or
darkening
of
any
star
from
our
sight
,
yet
here
it
is
cheefely
to
be
referred
to
the
Eclipse
of
the
Sunne
or
Moone
,
which
is
the
depriuing
of
their
light
from
the
sight
of
vs
that
dwell
here
vpon
the
earth
:
but
first
wee
will
treat
of
the
Eclipse
of
the
Moone
,
and
shew
how
and
when
it
chanceth
.
The
Moon
hauing
no
light
of
it selfe
,
but
onely
from
the
Sunne
,
is
neuer
eclipsed
,
but
when
the
earth
is
betwixt
her
and
the
Sunne
,
which
cannot
chance
,
but
when
the
Moone
is
at
the
full
,
and
diametrally
opposit
to
the
Sunne
:
and
also
when
such
Opposition
is
either
in
the
head
or
taile
of
the
Dragon
,
or
somewhat
nigh
therunto
,
which
are
nothing
els
but
two
sections
of
two
circles
,
that
is
,
the
Eclipticke
and
the
deferent
of
the
Moone
,
cutting
one
another
in
two
opposite
points
,
otherwise
called
the
two
Nodes
,
which
are
before
described
in
the
Theorique
of
the
Moone
,
and
are
also
plainely
declared
in
the
first
part
of
my
sphere
,
chap.
15.
But
for
so
much
as
there
be
many
other
needfull
things
to
be
knowne
touching
those
two
Eclipses
,
I
mind
here
to
treat
thereof
more
at
large
.
And
first
of
the
Eclipse
of
the
Moone
,
shewing
first
the
causes
why
her
eclipse
is
not
alwaies
after
one
maner
.
Secondly
,
what
shape
the
shaddow
of
the
earth
hath
at
the
time
of
her
Eclipse
,
and
how
many
kinds
of
shaddowes
there
be
.
Thirdly
,
how
many
waies
she
may
be
said
to
be
eclipsed
,
either
totally
or
in
part
.
Fourthly
,
which
be
the
bounds
,
within
which
she
being
at
the
full
,
may
be
eclipsed
.
Fiftly
,
how
many
points
or
digits
she
may
be
eclipsed
.
Sixtly
,
what
things
are
to
be
considered
touching
the
durance
or
continuance
of
her
Eclipse
,
&
how
they
are
defined
.
And
lastly
,
at
what
part
the
Moone
beginneth
to
bee
eclipsed
,
and
from
what
part
her
light
is
to
her
againe
restored
.
The
causes
why
the
Eclipse
of
the
Moone
is
not
alwaies
after
one
maner
,
but
variable
as
well
in
magnitude
as
in
continuance
,
are
these
foure
here
following
.
1.
The
first
cause
is
the
vnequall
latitude
of
the
Moon
,
for
sometime
her
latitude
is
very
little
or
nothing
at
all
,
and
then
is
her
eclipse
greater
in
magnitude
,
and
longer
in
continuance
:
and
sometime
her
latitude
is
so
great
,
that
she
commeth
but
a
very
little
within
the
shaddow
of
the
earth
,
and
thereby
looseth
but
a
small
portion
of
her
light
:
and
sometimes
she
commeth
not
within
the
compasse
of
the
shaddow
of
the
earth
at
all
,
and
so
she
is
not
eclipsed
.
For
this
is
a
generall
rule
,
that
when
the
latitude
of
the
Moone
,
at
the
time
of
the
true
Opposition
of
the
Moone
and
Sunne
is
lesser
than
the
summe
of
the
two
semidiameters
,
that
is
,
of
the
shaddow
and
of
the
Moones
bodie
,
being
added
together
,
there
will
be
an
Eclipse
of
the
Moone
.
And
the
greater
and
more
that
the
excesse
of
those
two
semidiameters
of
the
Moon
and
of
the
shaddow
is
than
her
latitude
,
the
greater
and
longer
will
the
Eclipse
be
.
And
if
the
summe
of
those
two
semidiameters
bee
just
equall
vnto
the
latitude
of
the
Moone
,
then
she
shall
onely
touch
the
shaddow
,
and
so
passe
without
any
Eclipse
.
2.
The
second
cause
of
the
change
or
variable
shape
of
the
eclipse
of
the
Moone
,
is
the
vnequall
thickenesse
of
the
shaddow
of
the
earth
:
for
the
higher
that
the
shadow
of
the
earth
ariseth
,
the
more
narrow
it
groweth
,
ending
with
a
sharpe
point
,
because
the
bodie
of
the
Sun
is
greater
than
the
bodie
of
the
earth
,
and
therefore
the
shaddow
cannot
be
of
any
other
shape
than
Conicall
:
for
there
be
three
kinds
of
shaddowes
,
that
is
,
Conicall
,
Cylindricall
,
and
Calathoidall
.
The
shaddow
Conicall
is
that
which
endeth
with
a
sharpe
point
.
The
Cylindricall
is
of
like
bignesse
euerywhere
,
like
a
round
pillar
.
And
the
Calathoidall
shadow
,
the
further
it
extendeth
,
the
greater
it
is
,
like
a
cup
or
bowle
,
that
is
narrow
at
the
bottome
and
broad
at
the
brim
;
of
which
shape
that
shaddow
taketh
his
name
,
for
Calathos
in
Greeke
is
as
much
to
say
as
a
cup
:
as
these
three
figures
doe
plainely
shew
.
Conicall
.
Cylindricall
.
Calathoidall
.
ANd
it
is
to
be
noted
,
that
when
the
Moone
is
in
the
lower
part
of
her
Epicicle
neare
vnto
the
opposite
Auge
thereof
,
her
Eclipse
continueth
longer
than
it
doth
when
she
is
neer
vnto
the
Auge
of
her
said
Epicicle
.
3.
The
third
cause
is
the
variable
thickenesse
of
the
shaddow
which
the
earth
yeeldeth
,
according
as
the
Sun
is
either
in
the
Auge
or
opposit
Auge
of
his
Excentrick
,
as
you
may
easily
perceiue
by
this
figure
following
,
consisting
of
three
circles
and
certaine
right
lines
.
4.
The
fourth
cause
of
the
varietie
of
her
Eclipses
is
her
vnequall
mouing
in
her
true
motion
,
either
swift
or
slow
,
for
when
she
is
in
her
swift
motion
,
the
continuance
of
her
Eclipse
must
needs
be
shorter
than
when
she
is
in
her
slow
motion
.
And
to
know
her
hourely
motion
,
either
meane
or
true
,
is
to
be
found
by
the
Prutenicall
tables
.
But
now
though
her
Eclipse
be
thus
variable
,
as
you
see
,
yet
such
varietie
may
be
brought
into
two
cheefe
heads
,
that
is
,
when
she
is
said
to
be
totally
,
or
partly
,
eclipsed
;
whereof
we
come
now
to
speake
.
The
totall
Eclipse
of
the
Moone
is
twofold
,
that
is
,
either
without
any
continuance
of
time
,
or
els
with
some
continuance
of
time
.
In
the
former
,
so
soone
as
she
hath
lost
her
whole
light
,
she
presently
beginneth
to
recouer
the
same
again
:
but
in
the
latter
,
she
being
wholly
eclipsed
,
the
same
continueth
some
quantitie
of
time
.
The
first
way
chanceth
when
the
latitude
of
the
Moone
and
the
semidiameter
of
her
bodie
being
both
added
together
,
the
summe
thereof
is
equall
vnto
the
semidiameter
of
the
earth
,
as
this
figure
plainely
sheweth
.
¶
The
first
figure
belonging
to
the
Eclipse
of
the
Moone
.
IN
which
figure
,
the
great
blacke
circle
signifieth
the
shaddow
of
the
earth
,
and
the
three
lesser
circles
being
all
of
like
bignesse
,
each
of
them
representeth
the
body
of
the
Moon
:
and
what
the
right
lines
doe
signifie
,
the
letters
doe
shew
:
for
the
letters
B
D
doe
represent
the
semidiameter
of
the
shaddow
of
the
earth
,
when
the
Moone
is
eclipsed
:
and
B
K
sheweth
the
latitude
of
the
Moone
from
the
Eclipticke
,
which
Eclipticke
is
marked
with
the
letters
A
C.
Now
K
D
signifieth
the
semidiameter
of
the
Moons
bodie
,
and
the
letter
I
sheweth
the
centre
of
her
bodie
in
the
beginning
of
her
Eclipse
,
and
the
letter
H
the
centre
of
her
body
at
the
end
of
her
Eclipse
.
And
the
right
line
I
K
H
signifieth
the
way
of
the
Moon
during
the
time
of
her
Eclipse
.
Here
for
so
much
as
the
two
semidiameters
D
K
,
and
K
B
,
being
both
added
together
,
are
equall
vnto
B
D
,
which
is
the
semidiameter
of
the
shaddow
,
you
may
perceiue
,
that
the
Moone
being
in
the
point
I
,
began
to
loose
her
light
by
little
and
little
,
vntill
she
came
to
the
point
K
,
and
there
was
wholly
darkened
,
from
whence
she
presently
began
again
without
any
stay
to
recouer
her
light
,
vntill
she
came
to
the
point
H
,
whereas
she
is
fully
restored
againe
to
her
light
.
The
second
kind
of
totall
Eclipses
of
the
Moone
,
is
when
she
is
wholly
eclipsed
,
and
the
same
continueth
some
quantitie
of
time
,
which
alwaies
happeneth
when
the
semidiameter
of
the
shaddow
of
the
earth
in
the
place
of
the
Eclipse
,
is
greater
than
the
latitude
of
the
Moone
and
of
her
bodily
semidiameter
being
both
added
together
:
as
this
second
figure
next
following
plainly
sheweth
.
¶
The
second
figure
belonging
to
the
Eclipse
of
the
Moone
.
IN
which
figure
,
suppose
the
semidiameter
of
the
shaddow
of
the
earth
in
the
place
of
the
Eclipse
to
be
the
line
BK
,
and
the
line
B
D
to
bee
the
latitude
of
the
Moone
at
the
time
of
the
middle
of
the
Eclipse
from
the
Eclipticke
,
marked
with
the
letters
A
C
,
and
the
line
R
D
to
bee
the
semidiameter
of
the
Moon
,
&
H
I
to
be
the
way
of
the
Moon
in
the
time
of
her
darkenesse
,
and
I
to
be
the
place
of
the
beginning
of
her
Eclipse
,
and
H
the
ending
of
the
Eclipse
,
and
M
her
place
when
she
is
wholly
darkened
,
and
L
her
place
when
she
beginneth
to
recouer
her
light
againe
.
Now
you
see
,
that
when
she
commeth
to
the
point
M
,
shee
is
wholly
eclipsed
,
like
as
she
is
also
when
she
commeth
to
the
point
L
,
and
because
she
spendeth
some
quantitie
of
time
in
going
from
M
to
L
,
and
is
wholly
darkened
,
therfore
is
this
called
a
Totall
Eclipse
with
continuance
.
Thus
much
touching
the
Totall
Ecllipse
of
the
Moone
,
now
we
will
speake
of
the
Partiall
Eclipse
of
the
Moone
.
The
Partiall
Eclipse
is
when
some
part
of
the
Moone
is
darkened
,
and
not
the
whole
:
and
of
this
Partiall
Eclipse
there
are
three
sorts
.
The
first
is
,
when
halfe
of
the
Moones
diameter
is
darkened
,
and
the
other
halfe
keepeth
still
her
light
,
which
happeneth
when
the
latitude
of
the
Moone
is
equall
vnto
the
semidiameter
of
the
shaddow
of
the
earth
in
the
place
of
the
Eclipse
,
as
you
may
perceiue
by
this
third
figure
next
following
.
¶
The
third
figure
belonging
to
the
Eclipse
of
the
Moone
.
IN
which
figure
,
B
D
signifying
the
latitude
of
the
Moone
from
the
Eclipticke
A
C
,
is
just
equall
vnto
the
semidiameter
of
the
shaddow
of
the
earth
,
marked
also
with
B
D.
The
second
sort
of
partiall
Eclipse
of
the
Moone
,
is
when
a
lesser
part
than
the
semidiameter
of
the
Moone
is
darkened
,
which
happeneth
when
her
latitude
is
more
than
the
semidiameter
of
the
shaddow
of
the
earth
,
as
you
may
see
by
this
fourth
figure
.
¶
The
fourth
figure
belonging
to
the
Eclipse
of
the
Moone
.
IN
which
figure
B
K
signifieth
the
semidiameter
of
the
shaddow
,
and
B
D
signifieth
the
latitude
of
the
Moon
:
now
for
that
B
D
is
more
than
B
K
,
you
see
that
there
is
but
a
little
of
her
light
taken
away
by
the
shaddow
of
the
earth
.
The
third
sort
of
Partiall
Eclipses
is
,
when
more
than
the
semidiameter
of
the
Moone
is
darkened
:
which
happeneth
when
the
latitude
of
the
Moone
is
lesse
than
the
semidiameter
of
the
shaddow
of
the
earth
,
as
you
may
see
by
this
fift
figure
.
¶
The
fift
figure
belonging
to
the
Eclipse
of
the
Moone
.
IN
which
figure
,
B
D
signifying
the
latitude
of
the
Moone
,
is
lesse
than
B
K
,
representing
here
the
semidiameter
of
the
shaddow
,
and
therefore
more
than
the
semidiameter
of
the
Moone
is
eclipsed
.
How
to
know
the
bounds
or
limits
,
whereby
is
easily
knowne
what
kind
of
Eclipse
of
the
Moone
will
happen
when
she
is
at
the
full
.
THe
limits
are
most
certainely
knowne
by
the
latitude
of
the
Moone
at
the
time
of
her
true
opposition
to
the
Sunne
:
for
if
you
find
the
latitude
of
the
Moone
by
the
Prutenicall
tables
,
or
otherwise
,
to
be
more
than
the
summe
of
the
semidiameters
of
the
shaddow
and
of
the
Moon
being
added
together
,
then
there
will
be
no
Eclipse
at
that
full
,
but
if
the
latitude
of
the
Moone
be
lesse
than
the
summe
of
the
two
said
semidiameters
added
together
,
you
may
be
sure
,
that
the
Moon
will
be
eclipsed
at
her
full
:
so
that
the
tearmes
or
bounds
of
the
Eclipses
are
knowne
by
comparing
the
latitude
of
the
Moone
with
the
summe
of
the
foresaid
two
semidiameters
being
added
together
.
The
least
summe
of
which
two
semidiameters
,
that
is
to
say
,
of
the
Moone
and
of
the
shaddow
of
the
earth
is
i/53
ii/53
which
is
,
when
the
Moone
is
in
the
Auge
of
her
Epicicle
,
and
the
Sun
in
the
opposit
Auge
of
his
Excentrique
,
and
that
in
his
least
excentricitie
.
But
the
greatest
summe
of
the
said
apparent
diameters
that
can
bee
,
is
one
degree
,
i/7
ii/5
which
happeneth
when
the
Moone
is
in
the
opposite
Auge
of
her
Epicicle
,
and
the
Sunne
in
the
Auge
of
his
Excentrique
,
and
that
in
his
greatest
excentricitie
.
And
hereof
you
may
gather
these
three
rules
.
First
,
if
the
latitude
of
the
Moone
at
the
time
of
her
true
opposition
to
the
Sunne
be
lesse
than
i/53
ii/53
shee
must
needs
be
eclipsed
.
Secondly
,
if
her
latitude
be
more
than
i/67
ii/52
shee
cannot
be
eclipsed
at
the
Full.
Thirdly
,
if
her
latitude
be
more
than
i/53
ii/5
and
lesse
than
i/67
ii/52
then
she
may
happen
to
be
eclipsed
,
but
not
necessarily
.
And
these
bounds
or
limits
may
also
be
determined
by
the
distance
of
the
Moone
from
any
of
the
two
Nodes
,
that
is
,
from
the
head
or
taile
of
the
Dragon
,
which
distance
is
neuer
lesse
than
10
degrees
,
i/22
neither
at
any
time
greater
than
13
degrees
,
i/5
which
bounds
or
limits
are
set
downe
by
Ptolomey
thus
.
If
the
distance
of
the
Moone
at
the
time
of
her
true
Opposition
from
either
of
the
two
Nodes
,
be
lesse
than
12
degrees
,
i/12
or
if
the
said
distance
of
the
Moone
from
either
of
the
said
Nodes
at
the
time
of
her
meane
Opposition
,
bee
lesse
than
15
degrees
,
and
i/12
(
the
said
distance
being
reckoned
either
according
to
the
succession
of
the
signes
,
or
contrarie
to
the
succession
of
the
signes
,
vpon
the
Eclipticke
)
then
the
Moone
may
be
eclipsed
.
Of
the
twelue
Digits
,
whereinto
the
bodie
of
the
Moone
is
wont
to
be
deuided
,
to
know
thereby
how
much
at
any
Full
she
is
eclipsed
.
THough
that
the
diameters
of
the
Moone
and
of
the
shaddow
may
bee
accounted
by
degrees
and
minutes
,
yet
notwithstanding
,
the
magnitude
or
greatnesse
of
her
Eclipses
is
vsually
reckoned
by
digits
,
or
ynches
,
by
deuiding
the
diameter
of
her
body
into
12
equal
parts
,
because
her
diameter
appeareth
to
our
sight
as
it
were
a
foot
in
length
:
and
therefore
as
the
foot
is
deuided
into
12
ynches
,
so
is
the
diameter
of
the
Moone
supposed
to
be
also
deuided
into
12
parts
,
which
parts
are
called
digits
or
points
,
and
by
them
is
the
greatnesse
of
her
Eclipse
determined
,
and
therefore
they
bee
called
Eclipticall
digits
or
points
.
And
although
that
the
diameter
of
the
Moone
is
deuided
but
into
12
digits
,
yet
neuerthelesse
the
Eclipse
of
the
Moone
may
sometimes
happen
to
be
very
neer
23
digits
,
by
reason
of
the
thicknesse
of
the
shaddow
of
the
earth
,
whose
semidiameter
sometime
exceedeth
the
diameter
of
the
Moone
,
and
such
excesse
is
wont
to
be
deuided
also
into
12
such
parts
as
is
the
diameter
of
the
Moone
,
and
so
the
Moon
may
be
eclipsed
more
than
12
points
,
as
you
may
more
plainly
perceiue
by
this
sixt
figure
next
following
.
¶
The
sixt
figure
belonging
to
the
Eclipse
of
the
Moone
.
IN
which
figure
,
the
letters
DK
representeth
the
semidiameter
of
the
shaddow
,
and
R
S
the
diameter
of
the
Moon
at
the
time
of
her
greatest
darkenesse
.
Now
supposing
the
said
R
S
to
bee
deuided
into
12
equall
parts
,
the
said
12
parts
are
called
the
Eclipticall
digits
:
&
for
that
some
part
of
the
semidiameter
of
the
shadow
,
namely
,
S
K
,
extendeth
further
than
R
S
,
which
is
the
diameter
of
the
Moone
,
the
ouerplus
SK
is
supposed
also
to
be
deuided
in
this
Eclipse
into
certaine
equal
parts
,
namely
into
three
such
parts
,
as
the
diameter
of
the
Moone
containeth
12
,
so
as
the
eclipticall
digits
in
this
Eclipse
are
15
:
for
you
may
easily
perceiue
,
that
if
the
semidiameter
of
the
Moone
were
longer
by
three
digits
than
it
is
,
yet
it
might
be
wholly
eclipsed
:
and
as
you
see
the
number
of
eclipticall
digits
in
this
Eclipse
to
be
15
:
euen
so
the
number
of
the
said
digits
may
amount
sometime
to
be
22
digits
and
51
minutes
.
For
you
may
remember
that
I
said
before
,
that
the
summe
of
the
semidiameter
of
the
Moone
and
of
the
shaddow
being
added
together
,
may
sometimes
happen
to
be
i/69
ii/52
when
the
Sunne
is
in
his
greatest
excentricitie
,
and
in
the
Auge
of
his
Excentrique
,
and
the
Moone
in
the
opposite
Auge
of
her
Epicicle
:
at
which
time
the
semidiameter
of
the
Moone
,
is
i17
ii/49
and
so
consequently
her
whole
diameter
is
i/35
ii/38
then
say
by
the
rule
of
proportion
,
if
i/35
ii/38
are
equall
vnto
12
digits
,
what
shall
i/67
ii/52
be
equall
vnto
?
so
shall
you
find
the
fourth
proportionall
number
to
be
22
digits
and
51
minutes
:
and
this
is
the
greatest
number
of
Eclipticall
digits
,
that
any
Eclipse
of
the
Moone
can
haue
.
And
the
more
Eclipticall
digits
that
any
Eclipse
hath
,
the
longer
is
the
time
of
durance
or
continuance
thereof
.
Of
the
continance
of
the
Moones
Eclipse
,
what
it
is
,
and
how
many
things
are
wont
by
the
Astronomers
to
be
considered
therein
.
THe
continuance
of
the
Eclipse
is
that
space
of
time
which
she
spendeth
in
going
from
the
very
beginning
of
the
Eclipse
to
the
middest
of
the
same
,
whereas
she
is
most
darkened
.
And
these
fiue
things
are
woont
therin
to
be
considered
,
that
is
,
the
minutes
of
Incidence
,
the
minutes
of
the
halfe
continuance
,
the
time
of
Incidence
,
the
time
of
halfe
continuance
,
and
the
halfe
continuance
it selfe
.
1.
And
first
you
haue
to
note
,
that
the
minutes
of
Incidence
are
accounted
in
partiall
Eclipses
after
one
way
,
and
in
totall
Eclipses
with
continuance
another
way
:
for
in
partiall
Eclipses
&
also
in
totall
Eclipses
without
continuance
,
the
minutes
of
Incidence
are
said
to
be
the
arch
of
the
Moones
way
which
she
maketh
in
her
mouing
of
longitude
from
the
beginning
of
her
Eclipse
to
the
midst
thereof
,
where
she
is
fully
darkened
,
as
appeareth
by
the
third
,
fourth
,
and
fift
figures
of
partiall
Eclipses
before
set
down
:
in
all
which
,
the
point
L
signifieth
the
place
of
the
Moone
at
the
beginning
of
her
Eclipse
,
and
the
point
D
the
place
of
the
Moon
at
the
middle
of
her
Eclipse
.
Now
the
arch
of
her
way
from
L
to
D
,
is
called
the
minutes
of
Incidence
,
for
so
long
her
light
decreaseth
by
little
and
little
,
vntill
so
much
be
taken
away
,
as
can
be
in
any
of
those
partiall
Eclipses
.
But
if
the
Eclipse
be
totall
,
without
any
continuance
,
as
in
the
first
figure
,
then
the
way
of
her
motion
in
going
from
the
point
I
vnto
the
point
K
,
where
she
is
wholly
darkened
,
is
called
the
scruples
of
Incidence
.
But
if
the
totall
Eclipse
haue
any
continuance
,
then
the
minutes
or
scruples
of
Incidence
are
that
portion
of
the
Ecliptick
,
throgh
which
the
Moon
goeth
from
the
very
beginning
of
her
Eclipse
,
vntill
the
time
that
she
be
wholly
eclipsed
,
as
in
the
second
&
last
figures
the
letter
I
signifieth
the
point
,
in
which
the
Moon
is
at
the
beginning
of
her
Eclipse
,
and
M
the
point
in
which
she
is
fully
darkened
:
and
the
arch
I
M
is
called
the
minutes
or
scruples
of
Incidence
,
and
these
minutes
in
the
end
of
the
Eclipse
are
called
minutes
of
repletion
,
as
in
the
third
,
fourth
,
and
fift
figures
,
the
arch
of
the
Moons
way
,
namely
D
M
,
or
K
H
in
the
first
figure
,
or
L
H
in
the
second
and
last
figures
,
doe
shew
:
which
minutes
of
repletion
are
reckoned
from
the
very
time
of
the
beginning
of
her
clearing
vnto
the
time
that
she
hath
fully
recouered
her
whole
light
:
and
the
minutes
or
scruples
of
repletion
are
equall
to
the
minutes
or
scruples
of
Incidence
.
2.
The
second
thing
which
is
considered
in
accounting
of
the
continuance
of
Eclipses
,
is
the
scruples
of
halfe
continuance
,
which
is
nothing
els
but
the
arch
which
the
Moone
maketh
in
going
from
the
Sunne
,
from
the
time
of
her
whole
darkenesse
vnto
the
very
middle
of
the
Eclipse
:
from
which
middle
Eclipse
,
the
Moone
going
still
forward
vntill
she
begin
againe
to
recouer
her
light
,
the
said
arch
is
called
the
scruples
of
Emersion
,
as
in
the
second
and
last
figures
the
arch
M
D
doth
shew
,
whereof
M
representeth
the
place
in
which
shee
looseth
her
whole
light
,
vntill
she
come
to
the
point
D
,
which
signifieth
her
place
when
she
is
in
the
middle
of
her
Eclipse
,
or
in
her
diametrall
Opposition
to
the
Sunne
.
And
this
is
called
the
scruples
of
halfe
continuance
:
but
the
arch
of
her
motion
from
D
to
L
,
where
she
beginneth
again
to
receiue
her
light
,
is
called
the
minutes
of
Emersion
,
and
these
minutes
of
Emersion
are
equall
vnto
the
scruples
of
halfe
continuance
,
as
the
scruples
of
Repletion
were
equall
vnto
the
minutes
of
Incidence
.
3.
The
third
thing
to
be
considered
in
accounting
the
Eclipse
of
the
Moon
,
is
the
time
of
Incidence
:
which
is
nothing
els
but
the
very
time
which
the
Moon
spendeth
in
going
of
the
minutes
of
Incidence
,
or
the
time
of
Incidence
is
that
portion
of
time
which
the
Moon
spendeth
in
mouing
from
the
beginning
of
the
Eclipse
vnto
the
point
where
she
is
most
darkened
(
if
the
Eclipse
be
partiall
)
as
in
the
third
,
fourth
,
and
fift
figures
,
the
time
which
the
Moone
spendeth
in
her
mouing
from
the
point
L
,
where
she
beginneth
to
bee
eclipsed
vnto
the
point
D
,
where
her
darkenesse
is
greatest
,
is
called
the
time
of
Incidence
.
Likewise
if
the
Eclipse
be
totall
,
the
time
which
shee
spendeth
in
moouing
from
the
beginning
of
the
Eclipse
,
vnto
the
point
in
which
she
is
wholly
obscured
,
as
in
the
first
figure
the
time
which
she
spendeth
vnto
her
mouing
from
the
point
I
vnto
the
point
K
,
so
the
time
which
she
spendeth
in
going
from
I
to
D
,
in
the
second
and
last
figures
is
called
the
time
of
Incidence
.
4.
The
fourth
thing
to
be
considered
,
is
the
time
of
halfe
continuance
,
which
is
that
quantitie
of
time
which
the
Moone
spendeth
in
her
moouing
from
the
point
in
which
she
looseth
her
whole
light
,
vnto
the
point
of
the
middle
Eclipse
,
as
in
the
second
and
last
figures
the
time
which
she
spendeth
in
going
from
the
point
M
to
the
point
D
,
is
called
the
time
of
halfe
continuance
.
And
the
time
which
she
spendeth
in
her
mouing
from
D
to
L
,
in
the
said
second
and
last
figures
is
called
the
time
of
her
Emersion
:
which
time
is
equall
vnto
the
time
of
halfe
continuance
,
sauing
that
the
variable
motion
of
the
Moone
beeing
swifter
in
the
one
than
in
the
other
,
may
make
a
little
difference
,
which
in
so
short
a
time
cannot
be
sensible
.
And
in
like
manner
,
the
time
of
Repletion
is
equall
vnto
the
time
of
Incidence
,
vnlesse
the
varietie
of
her
motion
doe
make
a
little
vnsensible
difference
.
5.
The
last
thing
that
is
to
be
considered
in
the
continuance
of
the
Eclipse
,
is
the
half
time
of
durance
,
which
is
nothing
els
but
the
time
which
the
Moone
spendeth
in
going
from
the
point
in
which
she
began
to
be
eclipsed
,
vnto
the
point
of
the
middle
Eclipse
:
and
this
time
is
equall
to
the
time
of
Incidence
in
Partiall
Eclipses
,
as
in
the
third
,
fourth
,
and
fifth
figures
,
the
time
which
she
spendeth
in
going
from
L
to
D
,
is
the
time
of
halfe
durance
:
and
likewise
the
time
which
she
spendeth
in
her
mouing
from
I
to
K
in
the
first
figure
,
is
the
time
of
halfe
durance
:
but
if
the
Eclipse
be
totall
with
continuance
,
then
is
the
time
of
halfe
durance
equall
vnto
the
time
of
Incidence
,
and
also
to
the
time
of
halfe
continuance
,
being
both
added
together
.
Furthermore
,
you
haue
to
note
,
that
the
Eclipse
of
the
Moone
dooth
alwayes
begin
on
the
East
side
of
her
bodie
(
I
call
that
the
East
side
which
is
towards
the
East
)
for
sith
that
her
motion
is
from
West
to
East
,
and
that
very
swift
,
in
respect
of
the
Sunne
or
of
the
shaddow
of
the
earth
,
it
must
needs
follow
,
that
the
East
side
of
her
bodie
first
toucheth
the
shaddow
in
the
beginning
of
her
Eclipse
,
and
so
continueth
her
mouing
through
the
said
shaddow
,
leauing
the
same
behind
her
on
the
West
side
of
her
bodie
.
And
although
that
this
be
true
in
all
Eclipses
of
the
Moone
,
yet
in
partiall
Eclipses
,
if
the
latitude
〈◊〉
if
the
Moone
be
North
,
then
is
the
South
part
of
her
bodie
darkened
,
but
if
her
latitude
be
South
,
then
is
the
North
part
of
her
bodie
darkened
.
And
note
,
that
whensoeuer
any
Eclipse
doth
happen
the
said
Eclipse
may
be
seene
of
all
them
,
aboue
whose
Horizon
she
is
in
the
time
of
her
Eclipse
,
and
that
at
one selfe
instant
or
moment
of
time
,
be
it
the
beginning
,
middle
,
or
ending
of
any
such
Eclipse
:
but
it
is
not
so
in
the
Eclipse
of
the
Sunne
,
neither
can
any
other
of
the
Planers
be
eclipsed
or
darkened
by
the
shaddow
of
the
earth
,
because
the
same
shaddow
reacheth
not
so
high
as
any
of
the
three
higher
Planets
are
:
and
as
for
Venus
and
Mercurie
,
their
place
is
alwaies
so
nigh
vnto
the
place
of
the
Sunne
,
as
they
cannot
be
eclipsed
at
any
time
.
Thus
much
touching
the
Eclipse
of
the
Moone
,
and
now
I
will
speake
of
the
Eclipse
of
the
Sunne
.
Of
the
Eclipse
of
the
Sunne
,
how
and
when
it
chanceth
.
THe
Eclipse
of
the
Sunne
is
nothing
but
the
darkening
or
depriuing
of
his
light
from
our
sight
,
caused
by
the
interposition
of
the
bodie
of
the
Moon
betwixt
the
bodie
of
the
Sunne
and
the
bodie
of
the
earth
:
and
this
Eclipse
neuer
happeneth
but
when
the
Moone
and
the
Sunne
are
in
a
visible
Conjunction
.
For
you
haue
to
note
,
that
there
be
three
kinds
of
Conjunctions
,
that
is
,
meane
,
true
and
visible
,
or
apparent
to
our
sight
.
What
the
meane
and
true
Conjunction
is
,
hath
been
before
defined
:
and
it
is
called
a
visible
Conjunction
,
when
a
right
line
being
drawn
from
our
eye
or
sight
,
passeth
through
the
centre
of
the
Moone
vnto
the
centre
of
the
Sunne
,
whereby
the
said
two
Planets
appeare
to
our
sight
to
bee
in
one selfe
degree
〈…〉
,
that
is
to
say
,
in
one selfe
point
of
the
Eclipticke
.
For
although
that
the
centre
of
the
Moone
bee
betwixt
the
centre
of
the
Sunne
and
the
centre
of
the
earth
at
euery
true
Conjunction
,
and
also
neere
to
any
of
the
Nodes
,
yet
perhaps
it
shall
appeare
no
Eclipse
to
our
sight
,
because
the
two
Planets
be
not
in
a
visible
Conjunction
,
as
haue
been
demonstrated
before
,
when
we
did
speake
of
the
Parallax
,
whereupon
cheefely
dependeth
the
knowledge
of
the
Eclipses
:
neither
can
the
body
of
the
Moone
,
being
farre
lesser
than
the
earth
,
possibly
shaddow
at
any
time
all
the
earth
:
and
the
body
of
the
Sun
is
farre
bigger
than
either
of
them
both
,
by
reason
whereof
,
the
Eclipse
of
the
Sunne
may
chance
to
one
part
of
the
earth
,
and
not
to
another
:
neither
can
any
Eclipse
of
the
Sunne
or
Moone
chance
,
but
when
those
two
Planets
are
either
in
the
head
or
taile
of
the
Dragon
,
or
els
very
nigh
the
same
.
All
which
things
you
shal
better
vnderstand
by
this
figure
here
following
.
¶
The
first
figure
belonging
to
the
Eclipse
of
the
Sunne
.
THis
figure
as
you
see
consisteth
of
certaine
circles
,
both
greater
and
lesser
,
and
of
certain
right
lines
:
in
which
figure
,
the
highest
circle
signifieth
the
bodie
of
the
Sunne
,
whose
centre
is
marked
with
the
letter
P
:
and
the
middle
lesser
circle
beneath
that
,
made
most
part
blacke
,
signifieth
the
bodie
of
the
Moon
eclipsed
,
whose
centre
is
marked
with
the
letter
C
,
and
the
diameter
thereof
is
marked
with
the
letters
L
K
:
and
the
lowest
lesser
circle
representeth
the
bodie
of
the
earth
,
whose
centre
is
marked
with
the
letter
A
:
and
the
two
great
circles
,
crossing
one
another
in
two
points
opposit
,
that
is
to
say
,
in
C
,
where
also
would
be
set
the
caracter
of
the
Dragons
head
;
and
in
the
other
crosse
point
opposit
,
is
set
the
caracter
of
the
Dragons
taile
;
of
which
two
circles
,
the
one
is
called
the
deferent
of
the
Moon
,
and
the
other
the
Eclipticke
.
Now
what
the
right
lines
doe
signifie
,
the
letters
doe
shew
:
for
the
two
outermost
right
lines
,
F
H
,
and
G
I
,
doe
signifie
the
outermost
beames
of
the
Sunne
,
which
doe
fall
vpon
the
earth
:
but
the
two
inner
lines
F
L
,
and
G
K
,
do
signifie
the
beames
of
the
Sunne
which
do
fall
vpon
the
Moone
:
which
two
lines
being
drawne
out
in
length
,
do
concurre
and
meet
in
the
point
A
,
representing
the
centre
of
the
earth
,
and
thereby
doe
make
the
cone
to
be
F
A
G
,
the
axle●●●e
of
which
cone
,
is
the
right
line
P
A
:
and
the
little
shaddowed
cone
,
marked
with
the
letters
L
K
A
,
signifieth
the
cone
of
the
Moones
shaddow
at
the
time
of
a
true
Conjunction
,
when
the
Sunne
is
eclipsed
;
the
axle●ee
of
which
little
cone
is
signified
by
the
line
C
A
:
and
the
two
lines
,
K
E
,
and
L
D
,
do
signifie
the
outermost
sides
of
the
Moones
shaddow
,
falling
vpon
the
earth
in
the
two
points
D
and
E.
Now
hereby
you
may
perceiue
,
that
those
people
which
haue
their
dwelling
betwixt
D
and
E
,
are
wholly
depriued
of
the
light
of
the
Sun
:
but
those
that
dwell
betwixt
E
and
I
,
or
betwixt
D
and
H
,
do
still
retaine
the
light
of
the
Sunne
.
Moreouer
,
the
Sunne
is
to
some
inhabitants
of
the
earth
totally
eclipsed
,
and
to
some
partly
,
and
to
some
nothing
at
all
,
as
this
figure
next
following
doth
plainely
shew
.
¶
The
sec●nd
figure
belonging
to
the
Eclipse
of
the
Sunne
,
with
the
description
thereof
.
THis
figure
as
you
see
consisteth
of
three
circles
and
certaine
right
lines
:
of
which
circles
,
the
highest
and
greatest
representeth
the
body
of
the
Sunne
,
whose
centre
is
marked
with
P
:
and
the
middle
little
circle
,
made
almost
all
blacke
,
signifieth
the
body
of
the
Moone
,
whose
centre
is
marked
with
the
letter
C
,
and
her
semidiameter
with
C
B
,
and
her
whole
diameter
with
L
K
,
and
the
small
vpper
portion
of
her
bodie
,
made
white
,
is
that
which
is
lightened
by
the
Sunne
,
all
the
rest
of
her
bodie
beeing
darkened
.
The
third
and
lowest
circle
being
greater
than
that
of
the
Moone
,
signifieth
the
body
of
the
earth
,
whose
centre
is
marked
with
A
,
and
the
semidiameter
thereof
with
A
E.
Now
as
touching
the
signification
of
the
right
lines
,
the
letters
thereto
belonging
doe
shew
:
for
the
outermost
lines
marked
with
Q
K
,
and
O
L
,
doe
signifie
the
outermost
beames
of
the
Sunne
that
doe
fall
vpon
the
bodie
of
the
Moone
,
concurring
or
meeting
in
the
point
I
,
enclosing
the
Conicall
shaddow
of
the
Moone
,
marked
with
the
letters
L
K
I
,
the
axletree
of
which
Conicall
shaddow
is
the
middle
line
C
I
,
for
to
those
that
dwell
vpon
the
earth
vnder
the
point
I
,
the
Sunne
is
totally
eclipsed
,
and
to
those
that
dwell
vnder
the
point
N
,
he
is
partly
eclipsed
,
and
partly
not
,
and
to
those
that
dwell
betwixt
N
and
H
,
he
is
not
eclipsed
at
all
.
Againe
,
the
Moone
is
not
alwaies
right
vnder
the
Eclipticke
line
,
as
the
Sunne
is
,
and
therefore
her
shaddow
at
the
time
of
the
Eclipse
cannot
point
to
the
centre
of
the
earth
,
as
it
doth
when
she
is
in
either
of
the
two
Nodes
:
but
sometime
Northward
and
sometime
Southward
from
the
centre
of
the
earth
,
according
as
her
latitude
is
either
Northerly
or
Southerly
:
so
likewise
her
said
shaddow
after
euery
true
Conjunction
will
point
Eastward
,
and
before
a
true
Conjunction
Westward
.
And
further
you
haue
to
note
,
that
the
true
and
visible
Conjunctions
doe
neuer
happen
together
,
except
the
true
Conjunction
of
the
Sunne
and
Moone
chance
to
be
in
the
90
degree
,
which
what
it
is
,
is
before
declared
,
for
in
the
90
degree
there
is
no
Parallax
at
all
.
But
in
all
other
places
,
the
true
and
visible
places
doe
differ
,
and
the
visible
Conjunction
is
before
the
true
Conjunction
,
if
the
said
true
Conjunction
be
in
the
East
part
of
the
Zodiake
,
that
is
,
betwixt
the
Sunne
rising
and
the
90
degree
.
But
if
the
true
Conjunction
be
in
the
West
part
of
the
Zodiake
,
that
is
,
betwixt
the
90
degree
and
the
Sunne
setting
,
then
the
true
Conjunction
is
before
the
visible
Conjunction
.
And
generally
,
the
further
that
the
true
Conjunction
is
from
the
90
degree
,
the
greater
is
the
difference
betwixt
the
true
Conjunction
and
the
visible
Conjunction
,
which
things
are
before
fully
declared
,
whereas
I
speake
of
the
Parallax
,
and
by
help
of
the
celestiall
globe
are
easily
perceiued
.
Of
the
varietie
of
the
Solar
Eclipses
,
and
why
they
be
not
alwaies
like
,
but
doe
differ
as
well
in
magnit●de
as
in
time
of
continuance
.
OF
this
varietie
there
be
foure
causes
.
1.
First
,
the
vnequall
apparent
latitude
of
the
Moone
:
for
the
greater
that
the
latitude
of
the
Moon
is
,
the
lesser
and
shorter
is
the
Eclipse
of
the
Sunne
:
but
the
lesser
that
her
latitude
is
,
the
greater
and
longer
is
the
Eclipse
of
the
Sunne
.
For
this
is
a
generall
true
rule
,
that
if
the
apparent
latitude
of
the
Moone
at
the
time
of
the
visible
Conjunction
be
greater
than
the
summe
of
the
two
semidiameters
of
the
Sun
and
of
the
Moone
,
being
both
added
together
,
then
the
Sunne
shall
not
be
eclipsed
at
the
visible
Conjunction
:
but
if
the
apparent
latitude
of
the
Moone
be
lesse
than
the
summe
of
the
two
said
semidiameters
,
being
added
together
,
then
shal
the
Sunne
be
eclipsed
at
that
visible
Conjunction
:
and
the
greater
that
the
difference
betwixt
the
summe
of
the
two
semidiameters
,
and
the
Moones
latitude
is
,
the
greater
is
the
Eclipse
of
the
Sunne
.
2.
The
second
cause
of
the
varieties
of
the
Eclipse
of
the
Sunne
,
is
the
vnequall
distance
as
well
of
the
Sunne
as
of
the
Moone
,
from
the
earth
:
for
the
changing
of
their
distances
from
the
earth
,
maketh
the
diameters
of
their
bodies
to
appeare
greater
or
lesser
.
For
the
neerer
that
they
approch
to
the
earth
,
the
greater
do
their
diameters
appeare
vnto
vs
:
for
when
the
Sunne
is
in
the
Auge
of
his
Excentrique
,
and
therewith
in
his
greatest
excentricitie
,
the
semidiameter
of
his
shaddow
is
i15°
ii40°
But
if
he
be
in
his
greatest
excentricitie
,
and
in
the
opposit
Auge
of
his
Excentrique
,
then
his
semidiameter
is
i17°
ii2°
which
is
greater
than
it
was
before
by
i1°
ii/22
And
if
the
Sunne
be
in
his
least
excentricitie
(
as
it
is
almost
in
these
our
dayes
)
and
also
in
his
Auge
,
then
his
semidiameter
is
i15°
ii49°
but
being
in
the
opposit
Auge
of
his
Excentrique
,
then
his
semidiameters
is
ii/16
i2°
which
is
greater
than
it
was
before
by
i1°
ii3°
Likewise
,
when
the
Moone
is
in
her
Auge
,
whether
it
bee
at
her
Conjunction
with
the
Sunne
,
or
at
her
Opposition
to
the
Sunne
,
her
semidiameter
is
but
i15°
ii0°
but
being
in
her
opposit
Auge
,
her
semidiameter
will
be
i17°
ii49°
which
is
greater
than
it
was
before
by
i2°
ii49°
whereby
it
happeneth
,
that
sometime
the
whole
bodie
of
the
Sunne
seemeth
to
be
darkened
,
and
at
other
times
but
some
part
of
his
bodie
,
and
that
either
at
some
side
thereof
,
or
els
in
the
very
middest
of
his
bodie
,
and
then
there
appeareth
round
about
him
a
narrow
bright
circle
,
which
we
commonly
call
a
borrough
,
all
the
other
part
in
the
midst
of
his
body
being
darkened
.
3.
The
third
cause
of
the
varietie
of
the
Solar
Eclipses
,
is
the
twofold
inequalitie
of
the
Moones
motion
,
whereof
the
first
dependeth
vpon
the
motion
of
her
Epicicle
,
whereby
she
is
sometimes
swift
,
and
sometimes
slow
of
ga●e
.
And
the
second
inequalitie
of
her
motion
happeneth
by
reason
of
her
Parallax
,
which
maketh
her
motion
to
appeare
variable
euery
houre
,
and
thereby
her
apparent
motion
is
also
sometime
swift
&
sometimes
slow
.
And
it
happeneth
,
that
not
onely
the
time
of
the
continuance
of
the
Eclipse
altereth
,
but
also
the
time
of
Incidence
is
made
to
be
vnequall
vnto
the
time
of
repletion
.
4.
The
fourth
cause
of
the
inequalitie
of
the
Sunnes
Eclipses
,
is
the
small
quantitie
of
the
body
of
the
Moon
,
in
respect
of
the
Sunne
,
or
of
the
Earth
,
and
the
small
distance
of
the
Moone
from
the
Earth
:
for
by
these
two
meanes
neither
can
the
Solar
Eclipses
appeare
of
a
like
bignesse
in
all
places
in
which
they
may
be
seene
,
neither
yet
can
the
said
Eclipses
be
seene
at
one
time
in
all
places
of
the
earth
,
as
was
shewed
before
.
Lastly
,
by
these
two
meanes
it
happeneth
that
the
Eclipse
of
the
Sunne
appeareth
not
at
one selfe
time
in
diuers
places
,
and
it
beginneth
sooner
to
them
which
dwell
Westward
,
than
to
those
which
dwel
Eastward
,
in
such
sort
,
as
the
said
Eclipse
of
the
Sunne
will
be
ended
in
one
place
before
it
begin
in
another
.
And
thus
much
touching
the
causes
of
the
varietie
of
the
Eclipses
of
the
Sunne
.
Of
the
two
speciall
kinds
of
Solar
Eclipses
,
that
is
,
totall
and
partiall
.
THe
Totall
Eclipse
is
when
the
Sunne
is
wholly
darkened
,
or
seemeth
to
vs
to
haue
lost
his
whole
light
,
and
this
Eclipse
is
alwaies
without
continuance
,
which
happeneth
when
the
Moone
hath
no
apparent
latitude
at
the
time
of
the
visible
Conjunction
,
as
this
figure
plainly
sheweth
.
¶
The
third
figure
belonging
to
the
Solar
Eclipse
.
IN
which
figure
,
suppose
the
letter
A
to
be
the
centre
of
the
Sunnes
body
,
and
the
line
A
H
to
bee
the
semidiameter
of
his
body
,
and
D
B
to
be
the
Eclipticke
line
,
and
A
B
to
be
the
semidiameter
of
the
circle
,
in
which
the
Moone
is
at
the
beginning
and
ending
of
the
Eclipse
,
and
the
line
F
G
to
be
the
way
of
the
Moones
motion
,
during
the
time
of
the
Eclipse
,
crossing
the
line
D
B
in
the
point
A
,
which
point
A
may
also
signifie
the
head
or
taile
of
the
Dragon
,
and
the
letter
F
signifieth
the
South
latitude
,
and
G
the
North
latitude
:
and
the
point
F
doth
also
signifie
the
centre
of
the
Moone
at
the
beginning
,
and
G
the
centre
of
the
Moone
at
the
ending
of
the
Eclipse
,
and
the
line
R
F
or
G
S
doth
signifie
the
semidiameter
of
the
body
of
the
Moone
.
Now
you
see
,
that
the
Moone
by
her
motion
commeth
by
little
and
little
to
shaddow
the
light
of
the
Sunne
vntill
she
haue
mooued
from
the
point
F
,
where
the
Eclipse
began
,
vnto
the
point
A
,
where
his
whole
light
is
taken
away
;
and
then
without
any
stay
she
moueth
on
forward
from
the
point
A
vnto
G
,
where
the
Eclipse
endeth
.
And
although
it
falleth
out
sometimes
,
that
the
Moone
dooth
shaddow
more
than
the
body
of
the
Sun
(
which
is
very
seldome
or
neuer
,
although
it
may
so
happen
)
yet
doth
the
totall
darkenesse
continue
so
little
a
time
,
as
it
is
insensible
:
and
therefore
the
totall
Eclipse
of
the
Sunne
is
alwaies
without
continuance
.
Of
the
Partiall
Eclipse
of
the
Sunne
.
THe
Partiall
Eclipse
of
the
Sunne
is
when
some
part
of
the
Sunnes
light
is
taken
away
,
and
not
all
his
bodie
darkened
;
and
of
this
kind
there
are
three
sorts
.
1.
The
first
is
,
when
the
semidiameter
of
the
Sunne
is
darkened
:
which
happeneth
when
the
apparent
latitude
of
the
Moone
is
equall
vnto
her
apparent
semidiameter
.
2.
The
second
sort
is
when
more
than
the
semidiameter
of
the
Sunne
is
darkened
,
which
happeneth
when
the
apparent
latitude
of
the
Moone
is
lesse
than
the
apparent
semidiameter
of
her
bodie
.
3.
The
third
,
is
when
lesse
than
the
semidiameter
of
the
bodie
of
the
Sunne
is
darkened
,
which
happeneth
when
the
apparent
latitude
of
the
Moon
is
greater
than
the
apparent
semidiameter
of
her
bodie
.
Of
all
which
three
kinds
,
I
haue
set
an
example
in
these
three
figures
here
following
.
¶
Three
figures
shewing
the
three
kinds
of
the
Sunnes
Partiall
Eclipses
.
OF
which
figures
,
the
first
sheweth
the
first
kind
of
Partiall
Eclipse
,
the
second
figure
sheweth
the
second
kind
,
and
the
third
figure
sheweth
the
last
kind
of
Partiall
Eclipses
.
In
euery
of
which
figures
,
the
letter
A
signifieth
the
centre
of
the
Sunne
,
and
the
semidiameter
of
his
bodie
is
the
right
line
A
B
,
and
vpon
the
centre
A
is
drawne
a
great
circle
,
marked
with
the
letters
C
S
D
L
,
whereof
the
letter
C
signifieth
the
North
,
D
the
South
,
L
the
West
,
and
S
the
East
:
vnto
which
circle
when
the
Moone
commeth
on
the
West
part
,
the
Eclipse
of
the
Sunne
beginneth
;
and
it
endeth
when
the
Moone
commeth
to
the
said
circle
on
the
East
side
.
And
the
right
line
S
L
signifieth
the
Eclipticke
line
,
and
the
right
line
H
I
signifieth
the
deferent
of
the
Moone
:
and
the
point
marked
with
the
letter
E
,
signifieth
the
place
of
the
Moone
at
the
beginning
of
the
Eclipse
,
and
G
her
place
at
the
ending
of
the
Eclipse
,
and
F
her
place
at
the
middle
of
the
Eclipse
,
or
at
the
time
of
her
greatest
darkenesse
:
and
the
right
line
F
V
in
the
second
figure
is
the
semidiameter
of
the
Moone
at
the
time
of
her
greatest
darkenesse
.
The
caracters
of
the
Nodes
on
the
East
or
West
side
of
any
of
the
foresaid
figures
doe
shew
what
way
the
head
or
taile
of
the
Dragon
doth
stand
,
and
to
which
of
the
Nodes
the
Eclipse
is
nearest
.
Of
the
bounds
or
limits
of
the
Solar
Eclipses
.
ANd
now
that
you
know
the
seuerall
kinds
of
Eclipses
,
it
will
not
be
hard
to
judge
which
of
them
will
happen
at
the
time
of
any
Eclipse
of
the
Sunne
,
especially
if
you
know
the
bounds
or
limits
within
which
the
Eclipse
of
the
Sunne
must
needs
be
before
hee
can
bee
eclipsed
:
which
bounds
cannot
bee
better
determined
,
than
by
the
apparent
latitude
of
the
Moone
;
for
if
the
said
latitude
be
more
than
the
two
semidiameters
of
the
Sunne
and
of
the
Moone
being
both
added
together
,
it
is
impossible
that
the
Sunne
should
be
eclipsed
at
that
Conjunction
:
but
if
the
apparent
latitude
be
lesse
than
the
said
two
semidiameters
,
then
may
the
Sun
be
eclipsed
:
and
the
least
summe
of
the
two
semidiameters
of
the
Sunne
and
Moone
that
can
be
(
which
is
when
both
the
Sunne
and
Moone
are
in
the
Auges
of
their
orbes
,
and
the
Sunne
in
his
greatest
excentricitie
)
is
i30
.
ii40
.
and
the
greatest
summe
of
the
said
two
semidiameters
that
can
be
,
is
but
i34
.
ii1
.
from
hence
you
may
gather
these
three
rules
here
following
.
1.
First
,
if
the
apparent
latitude
of
the
Moone
at
the
time
of
the
visible
Conjunction
be
lesse
than
i30
.
ii40
.
it
cannot
be
but
that
the
Sunne
must
be
eclipsed
.
2.
Secondly
,
if
the
apparent
latitude
of
the
Moone
at
the
time
of
the
visible
Conjunction
be
more
than
i30
.
ii40
.
and
lesse
than
i34
.
ii31
.
it
may
bee
that
the
Sunne
shall
be
eclipsed
in
some
part
at
the
time
of
the
visible
Conjunction
.
3.
Thirdly
,
if
the
apparent
latitude
of
the
Moone
be
more
than
i34
.
ii51
.
the
Sun
cannot
loose
any
of
his
light
.
But
Ptolomey
determineth
the
said
bounds
of
the
Solar
Eclipses
by
the
distance
of
the
Moone
from
either
of
the
two
Nodes
:
for
if
the
Moon
be
distant
from
either
of
the
Nodes
20
degrees
,
i40
.
towards
the
North
,
or
11
degrees
,
i20
.
towards
the
South
at
the
time
of
the
meane
Conjunction
,
then
it
may
fall
out
that
the
Sunne
shall
be
eclipsed
:
but
if
she
be
further
distant
from
the
said
Nodes
at
the
time
of
the
meane
Conjunction
,
then
cannot
the
Sunne
be
eclipsed
.
And
note
,
that
Ptolomey
maketh
the
North
bounds
bigger
than
the
Southerne
bounds
,
because
of
the
Parallax
.
And
this
distance
from
the
Nodes
may
be
reckoned
either
according
to
the
succession
or
contrarie
to
the
succession
of
the
signes
.
Of
the
Eclipticall
digits
belonging
to
the
Solar
Eclipses
.
AS
the
Eclipticall
digits
of
the
Moone
were
12
,
so
likewise
are
there
12
Eclipticall
digits
of
the
Eclipse
of
the
Sunne
;
but
the
Eclipse
of
the
Sunne
can
neuer
exceed
12
digits
and
15
minutes
:
for
the
greatest
apparent
semidiameter
of
the
Moon
is
but
i17
.
ii49
.
and
the
least
apparent
semidiameter
of
the
Sunne
is
i15
.
ii40
.
which
two
semidiameters
if
you
adde
together
,
the
summe
will
be
i33
.
ii29
.
Then
hauing
doubled
the
least
semidiameter
of
the
Sunne
,
which
is
i15
.
ii40
.
the
summe
will
be
i31
.
ii20
.
which
is
the
least
apparent
semidiameter
of
the
Sun
:
then
say
by
the
rule
of
proportion
,
if
i31
.
ii20
.
be
equall
to
12
digits
,
to
what
or
how
much
shall
i33
.
ii29
.
be
equall
?
so
shal
you
find
the
fourth
proportionall
number
to
be
very
neare
12
digits
and
50
minutes
:
and
this
is
the
greatest
number
of
Eclipticall
digits
that
any
Eclipse
of
the
Sunne
can
haue
.
And
this
may
happen
when
the
Sunne
is
in
the
Auge
of
his
Excentrique
,
and
in
his
greatest
excentricitie
:
and
the
Moone
in
her
opposit
Auge
,
and
therewith
in
such
places
as
are
situated
within
the
compasse
of
the
Moones
shaddow
,
the
diameter
of
which
shaddow
may
at
that
time
be
very
neare
280
miles
in
length
of
our
English
miles
,
or
70
Germane
miles
,
within
which
compasse
whosoeuer
dwelleth
,
may
loose
the
whole
light
of
the
Sunne
at
that
Eclipse
.
And
you
shall
know
the
number
of
the
Eclipticall
digits
by
the
62
precept
of
the
Prutenicall
tables
.
And
many
times
it
may
fall
out
,
that
although
the
Moone
haae
no
apparent
latitude
,
yet
the
Eclipse
of
the
Sunne
will
not
be
so
great
,
for
if
the
Moon
be
in
her
Auge
,
and
the
Sunne
in
the
opposit
Auge
of
his
Excentrique
,
and
therewith
in
his
least
excentricitie
,
the
number
of
the
Eclipticall
digits
can
be
no
more
but
11
degrees
,
and
15
minutes
,
so
as
the
Sunne
will
appear
to
haue
lost
his
light
in
the
very
midst
;
and
round
about
that
Eclipse
will
appeare
a
little
circle
as
it
were
three
quarters
of
an
inch
in
breadth
.
All
which
things
touching
the
Eclipticall
digits
,
will
not
be
hard
to
conceiue
,
if
you
remember
what
was
spoken
of
this
matter
in
the
Eclipses
of
the
Moone
.
What
things
are
to
be
considered
touching
the
continuance
of
the
Solar
Eclipse
.
IN
accounting
the
continuance
of
the
Eclipse
of
the
Sunne
,
the
Astronomers
doe
only
obserue
two
things
.
1.
The
first
is
the
scruples
of
Incidence
,
which
are
nothing
els
but
the
way
or
arch
of
the
circle
of
the
Moones
deferent
,
in
which
she
goeth
from
the
beginning
of
the
Eclipse
vnto
the
middle
of
the
same
:
which
in
the
three
last
figures
is
signified
by
the
line
E
F.
2.
The
second
thing
which
they
vsually
obserue
,
is
the
time
of
Incidence
,
which
is
nothing
els
but
the
quantitie
of
time
which
the
Moone
spendeth
whilest
she
is
in
going
of
the
said
minutes
of
Incidence
:
both
which
two
things
you
shall
easily
find
,
as
also
the
minutes
of
repletion
,
by
the
63
precept
of
the
Prutenicall
tables
.
And
as
the
Eclipse
of
the
Moone
doth
begin
on
the
East
side
of
her
bodie
and
endeth
on
the
West
side
thereof
,
euen
so
the
Eclipse
of
the
Sunne
beginneth
on
the
West
side
of
his
bodie
,
and
endeth
on
the
East
;
which
happeneth
by
the
motion
of
the
Moone
,
which
motion
is
from
West
to
East
:
and
if
the
Eclipse
of
the
Sun
be
partiall
,
and
the
apparent
latitude
of
the
Moone
be
North
,
then
is
the
North
side
of
the
Sunne
eclipsed
,
and
the
South
side
retaineth
still
his
light
:
but
if
her
apparent
latitude
be
South
,
then
is
the
South
side
of
the
Sunne
darkened
,
and
the
North
side
keepeth
still
his
light
.
And
this
is
a
generall
obseruation
,
that
no
Eclipse
of
the
Sun
is
vniuersall
(
except
that
which
was
against
nature
at
the
death
of
Christ
)
but
alwaies
perticular
,
that
is
,
it
may
be
seene
in
some
few
places
,
but
not
in
all
places
of
the
world
:
neither
doth
it
begin
or
end
in
all
places
at
one selfe
instant
,
neither
dooth
it
appeare
in
all
places
of
one selfe
bignesse
,
or
of
one
shape
,
but
in
one
place
is
totall
,
and
in
another
place
at
the
same
time
Partiall
,
and
in
other
places
againe
there
appeareth
no
Eclipse
at
all
.
The
causes
of
which
diuersitie
haue
been
before
declared
.
How
to
find
out
the
quantities
,
encreasing
,
decreasing
,
beginning
,
and
ending
of
the
Suns
Eclipses
,
without
any
offence
of
your
eiesight
.
HAuing
learned
by
the
Ephemerides
,
or
by
some
other
Almanacke
at
what
time
the
Eclipse
shall
be
,
resort
to
some
tower
or
high
loft
,
the
higher
the
better
,
and
see
that
the
place
whereas
you
would
make
your
obseruation
,
be
without
light
,
and
so
darke
,
as
you
can
possibly
make
it
,
leauing
only
a
litle
hole
or
rift
,
through
which
the
beames
of
the
Sunne
may
streeke
through
:
and
vpon
the
pauement
or
on
the
wall
that
looketh
right
against
that
hole
or
rift
,
behold
what
light
the
Sunne
yeeldeth
,
for
that
light
will
represent
the
true
shape
of
the
Sunne
at
that
present
,
and
plainely
shew
so
much
portion
to
be
wanting
from
the
lightsome
circle
,
as
the
Moone
comming
betwixt
the
Sunne
&
the
earth
,
doth
take
away
from
our
sight
.
Wherefore
if
you
deuide
the
diameter
of
the
said
lightsome
circle
into
12
parts
or
points
,
which
the
Astronomers
doe
call
digits
,
you
shall
find
out
all
the
things
aboue
mentioned
,
without
looking
vp
to
the
heauen
.
The
Methodicall
doctrine
of
the
Eclipses
,
set
downe
by
Reinoldus
in
his
Commentarie
vpon
Purbachius
.
FIrst
Ptolomey
found
out
the
true
latitude
of
the
Moone
,
and
deuided
the
same
from
her
apparent
latitude
,
as
he
teacheth
in
the
12
chapter
of
his
fift
booke
:
for
in
the
Eclipses
of
the
Moone
it
is
very
necessarie
to
haue
knowledge
both
of
her
true
latitude
,
and
also
of
her
apparent
latitude
,
for
the
Eclipse
of
the
Sunne
without
hauing
knowledge
of
her
apparent
latitude
,
and
of
her
Parallaxes
,
can
neuer
be
well
foreknowne
:
and
by
this
he
did
not
only
judge
of
other
things
,
but
also
by
a
Geometricall
way
found
,
that
the
greatest
distance
of
the
Moon
from
the
earth
,
she
being
either
at
the
change
or
at
the
full
,
did
contain
64
semidiameters
of
the
earth
,
and
one
sixt
part
.
Moreouer
,
by
other
obseruations
hee
did
know
the
proportions
of
the
semidiameters
,
as
well
of
the
Moones
excentrique
,
and
of
her
Epicicle
,
as
also
of
her
excentricitie
.
Then
by
other
obseruations
hee
sought
out
the
quantities
of
the
apparent
diameters
of
the
Sunne
,
of
the
Moone
,
and
of
the
shaddow
,
as
well
at
the
new
Moone
,
as
at
the
full
,
in
manner
and
forme
following
:
for
first
by
the
helpe
of
an
instrument
,
hauing
a
Diopter
,
he
found
the
Sunne
and
Moone
to
be
in
one
selfe
angle
when
shee
was
most
distant
from
the
earth
.
Then
he
attributed
to
the
Moone
two
Eclipses
,
in
the
one
whereof
,
when
her
latitude
was
i48
.
ii30
.
the
shaddow
darkened
one
quarter
of
her
diameter
:
and
in
the
other
Eclipse
,
the
shaddow
darkened
the
one
halfe
of
her
diameter
,
when
as
her
latitude
was
i40
.
ii40
.
and
in
either
of
the
Eclipses
the
Moone
was
very
nigh
to
the
height
of
her
Epicicle
.
Hereof
it
manifestly
appeared
,
that
a
quarter
of
the
Moones
diameter
,
when
she
was
most
distant
from
the
earth
,
contained
in
heauen
according
to
our
aspect
,
i/57
.
ii/0●.
which
being
reckoned
foure
times
,
doe
shew
that
the
diameter
of
the
Moone
was
at
that
time
i31
.
ii20
.
whereunto
the
obserued
diameter
of
the
Sunne
was
then
equall
:
and
the
semidiameter
of
the
shaddow
in
the
later
Eclipse
did
appeare
to
be
i40
.
ii40
.
for
the
centre
of
the
Moones
body
did
then
touch
the
outermost
brim
of
the
shaddow
.
Hereby
it
likewise
appeareth
,
that
the
diameter
of
the
shaddow
hath
such
proportion
to
the
diameter
of
the
Moones
body
,
as
13
hath
to
5
,
and
keepeth
the
selfe-same
proportion
in
all
other
Eclipses
of
the
Moone
:
and
though
it
most
manifestly
appeareth
by
this
,
that
the
diameter
of
the
shadow
doth
exceed
in
greatnesse
the
diameter
of
the
Moone
,
yet
it
followeth
not
by
&
by
therof
,
that
the
Moone
is
lesser
than
the
earth
.
Now
therfore
Ptolomey
by
comparing
according
to
the
doctrine
of
plaine
triangles
,
the
semidiameters
of
the
Moone
and
of
the
shadow
together
with
the
distance
of
the
said
Moon
,
being
measured
by
the
semidiameters
of
the
earth
,
hee
found
the
semidiameter
of
the
Moone
only
to
containe
i17
.
ii●3
.
and
the
semidiameter
of
the
shaddow
to
contain
i45
.
and
ii38
.
such
like
minutes
,
I
say
,
as
the
semidiameter
of
the
earth
hath
60.
And
therefore
it
appeareth
hereby
,
that
either
of
the
semidiameters
,
that
is
,
of
the
Moon
,
or
of
the
shaddow
,
is
lesse
than
the
semidiameter
of
the
earth
:
for
the
semidiameter
of
the
earth
is
almost
in
like
proportion
to
the
semidiameter
of
the
shaddow
,
as
4
is
to
3
,
and
being
compared
to
the
semidiameter
of
the
Moone
,
it
is
almost
in
such
proportion
,
as
17
is
to
5
:
whereof
it
followeth
necessarily
,
that
the
shaddow
of
the
earth
is
Conicall
,
that
is
,
round
,
growing
to
a
sharpe
point
,
and
therefore
the
Sunne
must
needs
be
greater
than
the
earth
.
Neither
could
any
right
judgement
haue
been
made
touching
the
quantities
of
the
said
three
bodies
,
that
is
,
the
Sunne
,
the
Moone
,
and
the
earth
,
vnlesse
that
the
Parallaxes
of
the
Moone
had
first
shewed
the
distance
of
the
Moone
from
the
earth
,
the
said
distance
being
measured
by
the
semidiameters
of
the
earth
.
For
if
you
suppose
the
distance
betwixt
the
Moone
and
the
earth
to
be
48
semidiameters
of
the
earth
,
you
shall
find
that
the
semidiameter
of
the
shaddow
will
be
altogether
equall
to
the
semidiameter
of
the
earth
,
and
so
the
shaddow
shall
be
Cylindricall
,
that
is
to
say
,
in
all
parts
round
like
a
pillar
.
And
if
you
suppose
the
said
distance
of
the
Moone
from
the
earth
to
be
greater
,
as
to
be
170
semidiameters
of
the
earth
,
then
the
semidiameter
of
the
shaddow
(
the
Moone
being
in
Transit●
)
will
contain
two
semidiameters
of
the
earth
,
and
so
the
shaddow
shall
be
Calathoidall
,
that
is
to
say
,
like
a
cup
or
top
,
extending
together
with
his
length
in
breadth
and
widenesse
more
and
more
infinitely
.
All
which
three
shapes
of
shaddows
are
before
plainely
set
forth
in
their
figures
.
By
this
Ptolomey
doth
proue
,
that
the
distance
of
the
Sun
from
the
centre
of
the
earth
,
containeth
1270
semidiameters
of
the
earth
,
and
that
the
semidiameter
of
the
Suns
bodie
containeth
fiue
such
semidiameters
and
a
halfe
,
as
the
earth
hath
,
and
that
the
diameter
of
the
Sun
to
the
diameter
of
the
earth
is
in
such
proportion
as
is
11
to
2.
Finally
,
he
proueth
the
axletree
of
the
shaddow
to
contain
268
such
semidiameters
as
the
earth
hath
.
Wherefore
according
to
the
opinion
of
Ptol●mey
,
the
excentricitie
of
the
Sunne
should
containe
48
semidiameters
of
the
earth
,
and
almost
one
fourth
part
.
Now
by
knowing
the
diameters
of
the
three
bodies
,
it
is
easie
to
find
out
their
proportions
:
for
by
the
last
proposition
of
Euclide
his
twelfth
booke
,
looke
what
proportion
is
betwixt
the
diameters
of
any
two
spheres
,
the
same
proportion
beeing
tripled
,
is
the
proportion
betwixt
the
said
two
spheres
.
And
therefore
because
the
diameter
of
the
Sunne
is
to
the
diameter
of
the
earth
in
like
proportion
,
as
11
is
to
2
,
the
same
proportion
being
tripled
,
shall
be
1331
to
8
,
so
as
the
body
of
the
Sunne
doth
containe
the
body
of
the
earth
166
times
and
almost
one
halfe
.
In
like
maner
you
shall
find
the
bodie
of
the
Moone
to
be
almost
the
40
part
of
the
body
of
the
earth
:
for
the
diameter
of
the
earth
to
the
diameter
of
the
Moon
is
in
such
proportion
as
is
17
to
5
,
so
as
the
body
of
the
earth
containeth
the
body
of
the
Moone
almost
40
times
,
as
was
said
before
.
And
the
body
of
the
Sunne
containeth
the
bodie
of
the
Moone
almost
6600
times
.
The
proportions
of
which
three
bodies
are
these
numbers
here
following
,
that
is
to
say
,
for
the
Sunne
6539203
,
and
for
the
Earth
39304
,
and
for
the
Moone
1000.
A
breefe
Extract
of
Maginus
his
Theoriques
,
shewing
all
the
definitions
of
such
names
and
motions
as
are
needfull
to
be
knowne
for
the
calculating
of
the
places
of
any
of
the
seuen
Planets
,
or
other
motions
of
any
Heauen
whatsoeuer
,
that
are
to
be
found
out
by
the
Prutenicall
Tables
.
TO
auoid
the
Paradoxicall
supposition
of
Copernicus
,
supposing
the
Earth
to
mooue
,
and
the
Sunne
to
stand
still
in
the
middest
of
heauen
,
Maginus
is
fain
to
suppose
that
there
be
three
mouable
heauens
aboue
the
eight
heauen
,
and
so
maketh
in
all
eleuen
mouable
heauens
,
which
is
one
more
than
all
the
other
Astronomers
haue
heretofore
set
downe
.
And
he
calleth
the
highest
or
eleuenth
heauen
,
the
first
mouable
,
describing
the
same
as
hereafter
followeth
:
next
to
which
is
placed
in
his
Theoriques
the
tenth
heauen
,
then
the
ninth
and
eight
heauen
,
and
vnder
that
,
the
seuen
Planets
,
that
is
,
first
Saturne
,
then
Iupiter
,
Mars
,
Sol
,
Venus
,
Mercurie
,
and
Luna
,
which
is
the
lowest
heauen
of
all
.
Of
which
his
Theoriques
I
thought
good
to
make
a
breefe
Extract
,
because
that
more
tearmes
belonging
to
the
Prutenicall
Tables
are
therein
both
defined
and
demonstrated
,
than
are
set
downe
either
by
Purbachius
or
by
Mes●elyn
in
their
Theoriques
.
And
according
to
the
number
of
this
eleuen
Heauens
,
I
haue
deuided
this
Extract
into
11
chapters
.
CHAP.
I.
The
description
of
the
eleuenth
Heauen
or
first
mouable
,
together
with
such
definitions
as
are
contained
therein
.
THe
first
mouable
is
the
greatest
or
highest
heauen
,
which
carieth
all
the
inferior
heauens
round
about
from
East
to
West
in
24
houres
.
The
concaue
superficies
whereof
is
imagined
to
be
traced
with
certaine
circles
,
whereof
some
be
greater
and
some
lesser
.
2.
The
greater
circles
cheefely
seruing
for
our
purpose
,
are
these
,
the
Aequinoctiall
,
the
Eclipticke
,
and
the
two
Colures
,
the
one
called
the
Colure
of
the
Equinoxes
,
and
the
other
the
Colure
of
the
Solstices
.
3.
The
Aequinoctiall
is
a
great
circle
supposed
to
be
in
the
convex
superficies
of
the
first
mouable
,
deuiding
the
same
superficies
into
two
equall
parts
,
the
poles
of
which
circle
are
the
poles
of
the
world
,
vpon
which
poles
the
said
first
mouable
continually
mooueth
,
making
his
reuolution
in
24
houres
.
4.
The
Eclipticke
of
the
first
mouable
is
also
a
great
circle
,
deuiding
the
superficies
thereof
into
two
equall
parts
,
&
cutteth
the
Aequinoctiall
in
two
opposit
points
,
which
points
are
called
the
Equinoxes
,
one
of
them
being
called
the
Vernall
Equinox
,
and
the
other
the
Autumnall
Equinox
:
and
the
poles
of
this
Eclipticke
are
alwaies
distant
from
the
poles
of
the
world
23
degrees
,
i/40
and
doe
neuer
alter
.
And
this
Eclipticke
is
called
the
meane
Eclipticke
.
5.
The
Colure
of
the
Equinoxes
,
is
a
great
circle
passing
through
the
two
Equinoxes
,
and
the
two
poles
of
the
world
.
6.
The
Colure
of
the
Solstices
,
is
also
a
great
circle
deuiding
the
superficies
of
the
first
moouable
into
two
equall
parts
,
and
is
drawne
both
through
the
poles
of
the
world
,
and
also
through
the
poles
of
the
meane
Eclipticke
.
CHAP.
II.
Of
the
tenth
Heauen
.
THe
tenth
Heauen
is
a
great
Orbe
next
vnto
the
first
mouable
,
hauing
contrarie
motion
to
the
first
moouable
,
that
is
,
from
West
to
East
vpon
the
poles
of
the
Eclipticke
of
the
first
moouable
or
meane
Eclipticke
,
and
maketh
his
reuolution
in
3434
Aegyptian
yeares
,
and
10
daies
.
In
which
,
imagine
the
letter
A
to
be
the
pole
of
the
meane
Eclipticke
of
the
first
moouable
,
and
also
the
pole
of
the
tenth
heauen
,
about
which
pole
the
tenth
sphere
maketh
his
reuolution
in
3434
Aegyptian
yeares
,
and
10
daies
.
And
vpon
the
point
A
imagine
also
a
lesser
circle
to
be
drawne
,
whose
semidiameter
is
A
B
,
containing
in
length
i●°
and
imagine
the
same
lesser
circle
to
be
the
circle
B
D
F
,
in
the
circumference
whereof
,
suppose
the
centre
of
another
lesser
circle
equall
to
that
,
to
be
placed
in
the
point
D
,
and
let
the
semidiameter
of
the
said
second
lesser
circle
be
D
E
,
containing
in
length
i/6
the
centre
of
which
second
circle
,
viz.
D
,
you
must
suppose
neuer
to
change
his
place
,
but
to
mooue
about
the
pole
A
,
as
the
tenth
heauen
mooueth
about
the
same
pole
A.
And
so
likewise
suppose
the
second
little
circle
A
H
E
to
be
fastened
to
the
first
,
so
as
the
said
second
circle
hath
no
other
motion
but
that
which
the
centre
D
hath
,
and
imagine
the
right
perpendicular
line
C
G
to
be
part
of
the
Solisticiall
colure
of
the
first
mouable
;
which
Colure
the
circumference
of
the
second
little
circle
A
H
E
will
cut
in
some
one
point
or
other
,
as
in
the
point
H
,
the
place
of
which
intersection
wheresoeuer
that
happeneth
vpon
the
line
C
G
,
is
the
pole
of
the
Eclipticke
of
the
tenth
heauen
,
whose
pole
doth
continually
alter
his
place
,
and
therefore
the
place
of
the
Eclipticke
of
the
said
tenth
heauen
,
must
needs
alter
,
being
sometimes
farre
from
the
meane
Eclipticke
,
and
sometimes
neare
vnto
it
,
and
sometimes
vnited
therewith
.
But
the
greatest
distance
that
can
be
betwixt
the
two
Ecliptickes
,
is
i/12
according
to
the
greatest
distance
which
is
betwixt
the
poles
of
the
Eclipticke
,
&
the
poles
of
the
first
moouable
:
for
the
poles
of
the
Eclipticke
of
the
tenth
heauen
can
neuer
exceed
i/12
and
the
Ecliptick
of
this
tenth
heauen
is
called
the
true
Eclipticke
,
whose
poles
doe
differ
from
the
poles
of
the
meane
Eclipticke
i/12
as
haue
been
said
before
.
3.
And
such
distance
is
called
the
equacion
of
the
obliquitie
of
the
Eclipticke
,
which
the
former
figure
doth
plainely
demonstrate
:
for
the
letter
A
is
supposed
to
be
the
pole
of
the
meane
Eclipticke
,
and
H
the
pole
of
the
true
Eclipticke
:
and
this
equacion
of
the
obliquitie
is
to
be
found
in
the
16
Cannon
of
the
Prutenicall
tables
,
by
helpe
of
which
equacion
or
Prosthapherisis
,
you
may
find
at
any
time
the
obliquitie
of
the
true
Eclipticke
,
as
is
taught
in
the
13
precept
of
the
said
tables
.
But
now
because
the
said
Prosthapherisis
cannot
bee
found
but
by
the
Anomalia
of
the
obliquitie
,
you
are
to
know
first
what
that
Anomalia
is
,
which
the
foresaid
figure
dooth
also
shew
.
In
which
figure
,
you
must
suppose
the
right
line
A
E
to
be
the
diameter
of
the
second
lesser
circle
,
the
one
end
whereof
is
alwaies
fixed
in
the
point
A
:
and
the
other
end
marked
with
E
,
by
the
motion
of
the
tenth
heauen
,
describeth
the
great
circle
C
E
G.
4.
And
this
circle
is
called
the
circle
of
Anomalia
of
the
obliquitie
of
the
true
Eclipticke
.
5.
And
the
arch
or
portion
of
this
circle
,
marked
with
the
letters
C
E
,
is
the
Anomalia
of
the
obliquitie
of
the
true
Eclipticke
:
the
motion
of
which
Anomalia
you
shall
find
at
any
time
by
the
Prutenicall
tables
in
the
14
Cannon
vnder
the
title
Anomalia
Aequinoctiorum
in
such
order
as
the
eight
precept
teacheth
.
CHAP.
III.
Of
the
ninth
Heauen
.
THe
ninth
Heauen
is
a
sphere
situated
next
and
immediatly
vnder
the
tenth
heauen
:
the
motion
of
which
ninth
sphere
is
from
North
to
South
vpon
his
proper
poles
,
which
are
fixed
in
the
two
Aequinoctiall
points
,
called
the
true
Aequinoctiall
points
of
the
tenth
heauen
,
about
which
poles
he
maketh
his
reuolution
in
1717
Aegyptian
yeares
and
5
daies
.
In
this
sphere
are
imagined
certaine
circles
both
greater
and
lesser
to
be
drawne
,
as
in
the
former
two
heauens
:
but
the
greater
circles
whereof
we
shall
haue
most
vse
,
are
these
,
that
is
,
the
Eclipticke
and
the
Aequinoctiall
.
2.
The
Eclipticke
of
this
ninth
sphere
is
alwaies
in
the
plane
of
the
Eclipticke
of
the
tenth
sphere
,
and
therfore
doth
not
differ
from
the
true
Eclipticke
,
because
it
neuer
swarueth
from
the
same
:
but
the
Aequinoctiall
line
of
this
ninth
sphere
is
mouable
,
according
as
the
two
Aequinoctiall
points
in
which
it
crosseth
the
true
Eclipticke
,
are
moouable
,
being
caried
both
backward
and
forward
,
and
sometimes
are
conjoined
together
with
the
Aequinoctiall
points
of
the
tenth
heauen
,
and
sometimes
againe
are
remooued
from
the
said
true
Aequinoctiall
points
of
the
tenth
sphere
,
and
the
greatest
distance
that
the
said
two
points
can
haue
from
the
Aequinoctiall
points
of
the
tenth
sphere
is
1
degree
,
i/12
ii/22
iii/30
IN
which
,
the
point
A
signifieth
the
Vernall
Aequinoctiall
point
,
as
well
of
the
tenth
heauen
,
as
of
the
first
mouable
,
which
point
we
will
hereafter
call
the
true
vernall
Aequinox
,
in
which
point
one
of
the
poles
of
the
ninth
sphere
is
supposed
to
be
fixed
,
and
the
other
pole
is
in
the
opposit
point
,
which
is
the
true
Autumnall
Aequinoctiall
point
.
Now
vpon
the
centre
A
imagine
a
little
circle
to
be
drawne
,
whose
semidiameter
is
A
B
,
containing
in
length
vpon
the
superficies
of
the
said
ninth
sphere
,
i●5·
ii/41
iii/15
and
in
the
same
convex
superficies
imagine
a
second
little
circle
to
be
drawne
,
equall
vnto
the
former
,
the
centre
of
which
second
circle
is
in
the
circumference
of
the
first
little
circle
,
viz.
in
the
point
C
,
the
semidiameter
whereof
is
C
D
,
containing
in
length
i/35
ii/41
ii/15
so
shall
the
whole
diameter
A
D
containe
in
length
1
degree
,
i/11
ii/22
iii/30
and
suppose
the
right
line
K
G
to
be
the
true
Eclipticke
,
and
the
right
ouerthwart
line
I
F
to
be
the
AEquinoctiall
line
of
the
tenth
heauen
and
also
of
the
first
mouable
.
Now
the
circumference
of
the
second
little
circle
wil
crosse
the
true
Eclipticke
K
G
in
some
one
point
or
other
,
as
in
the
point
E
,
which
point
of
Intersection
,
wheresoeuer
it
happeneth
to
be
,
is
the
place
of
the
Vernall
Aequinoctiall
point
of
the
ninth
sphere
:
which
Vernall
Aequinoctiall
point
we
will
henceforth
call
the
meane
Equinox
,
as
the
point
A
is
the
true
Equinox
.
So
that
hereby
you
may
perceiue
,
that
the
meane
Equinox
is
nothing
els
but
that
point
in
which
the
Aequinoctiall
line
of
the
ninth
sphere
crosseth
the
Eclipticke
line
of
the
said
ninth
sphere
or
true
Eclipticke
.
3.
The
Prosthapheresis
of
the
Equinox
is
the
distance
which
is
betwixt
the
true
and
meane
Equinox
,
as
is
the
line
A
E
:
and
this
Prosthapheresis
you
shall
find
in
the
16
Cannon
,
vnder
the
title
Praecessionis
Aequinoctiorum
,
the
manner
of
finding
whereof
is
taught
in
the
10
Precept
.
But
because
the
said
Prosthapheresis
cannot
bee
found
but
by
helpe
of
the
Anomalia
of
the
Equinox
.
4.
I
will
therefore
shew
what
the
said
Anomalia
of
the
Equinox
is
.
For
the
vnderstanding
whereof
,
resort
to
the
former
figure
,
in
which
you
see
how
the
tip
or
extreame
point
of
the
diameter
of
the
second
circle
,
viz.
the
point
D
describeth
by
his
motion
,
that
is
,
by
the
motion
of
the
ninth
sphere
,
the
circle
D
F
G
H
I
K
L
,
which
circle
is
called
the
circle
of
Anomalia
,
wherein
the
motion
of
the
Anomalia
is
alwaies
reckoned
:
and
the
distance
betwixt
the
point
L
and
the
point
D
,
is
the
Anomalia
of
the
Equinox
it selfe
,
and
is
alwaies
double
vnto
the
Anomalia
of
the
obliquitie
of
the
true
Eclipticke
,
and
therefore
we
vse
to
doe
no
more
but
to
double
the
Anomalia
of
the
said
obliquitie
,
otherwise
called
the
simple
Anomalia
,
which
is
to
be
found
by
the
14
Cannon
,
vnder
the
title
,
Anomalia
Aequinoctiorum
,
in
such
order
as
the
eight
Precept
teacheth
.
CHAP.
IIII.
Of
the
eight
Heauen
.
1.
THe
eight
Heauen
is
situated
vnder
the
ninth
Heauen
,
and
moueth
from
West
to
East
contrarie
to
the
motion
of
the
first
moouable
,
vpon
the
poles
of
the
true
Eclipticke
,
making
his
reuolution
in
25816
Aegyptian
yeares
,
and
dependeth
wholly
vpon
the
meane
Equinox
.
2.
In
this
sphere
are
imagined
also
an
Aequinoctiall
and
an
Ecliptick
line
:
and
the
Ecliptick
line
of
this
Heauen
is
alwaies
in
the
same
plane
with
the
Ecliptick
of
the
9
and
10
Heauens
,
and
swarueth
not
from
the
true
Ecliptick
at
all
.
But
the
Aequinoctiall
points
of
this
sphere
do
moue
from
the
true
Equinoxes
,
sometimes
forward
,
and
sometimes
times
backward
,
euen
as
the
meane
Equinox
of
the
ninth
sphere
moueth
.
3.
This
sphere
is
apparent
to
the
eye
,
by
reason
of
the
multitude
of
starres
which
are
therein
:
the
moouing
of
all
which
starres
,
and
all
other
the
inferior
lights
,
is
accounted
or
reckoned
from
the
first
starre
of
the
Rams
horne
,
as
from
a
visible
beginning
,
although
the
same
be
vnstable
,
by
reason
of
the
changeable
moouing
of
the
Precession
of
the
meane
Vernall
Equinox
.
As
for
example
,
suppose
in
this
figure
the
line
K
G
to
be
the
true
Eclipticke
,
and
I
F
to
be
the
Aequinoctiall
of
the
first
moouable
,
crossing
one
another
in
the
point
A
,
which
representeth
the
true
Equinox
,
vnto
which
point
when
the
Sunne
commeth
,
it
is
Equinox
throughout
all
the
world
:
and
suppose
M
to
be
the
first
star
of
the
Rams
horn
,
through
which
a
right
perpendicular
line
passeth
,
signifying
a
great
circle
drawne
through
the
first
starre
of
the
Rams
horne
,
&
also
through
the
poles
of
the
true
Eclipticke
:
and
suppose
L
H
to
be
another
great
circle
drawne
through
the
true
Aequinoctiall
point
A
,
and
through
the
poles
of
the
true
Eclipticke
,
so
shall
M
A
be
the
true
Precession
of
the
Vernall
Equinox
.
In
like
manner
suppose
the
line
D
E
to
bee
another
great
circle
,
passing
through
the
point
E
,
signifying
the
meane
Equinox
,
and
also
through
the
poles
of
the
true
Eclipticke
,
so
as
the
arch
of
the
true
Eclipticke
,
which
is
comprehended
betwixt
M
and
E
,
is
the
meane
Precession
of
the
vernall
Equinox
.
And
this
meane
Precession
is
readily
found
by
the
14
Cannon
,
as
the
8
Precept
teacheth
,
and
the
title
thereof
in
the
said
14
Cannon
,
is
Praecessionis
Aequinoctiorum
.
But
the
true
Precession
is
to
be
found
by
helpe
of
the
Prosthapheresis
,
which
was
defined
in
the
third
definition
of
the
third
chapter
.
And
although
that
there
be
many
other
circles
both
great
and
little
,
which
the
Astronomers
vse
,
as
the
circles
of
Positions
,
Azimuths
,
and
many
others
,
yet
will
I
only
speake
of
such
circles
,
arches
,
and
points
in
the
Heauen
as
are
belonging
to
our
present
purpose
(
because
I
haue
spoken
of
the
others
in
my
sphere
)
shewing
what
is
the
longitude
,
latitude
,
and
declination
of
any
star
or
point
in
this
Heauen
.
5.
The
longitude
of
any
starre
is
an
arch
of
the
Eclipticke
,
comprehended
betwixt
the
true
Vernall
Equinox
,
and
the
circle
of
latitude
of
the
said
starre
or
point
.
6.
The
circle
of
latitude
is
a
great
circle
passing
through
the
poles
of
the
true
Eclipticke
and
the
centre
of
the
starre
.
Of
which
circle
,
that
part
which
is
betwixt
the
centre
of
the
starre
and
the
true
Eclipticke
,
is
called
the
latitude
of
the
starre
.
7.
The
circle
of
declination
is
a
great
circle
,
passi●g
through
the
poles
of
the
world
,
and
through
the
centre
of
any
starre
or
other
point
in
the
firmament
:
and
that
part
of
this
circle
which
is
contained
betwixt
the
said
starre
and
the
true
Aequinoctiall
line
,
is
called
the
declination
of
the
starre
.
CHAP.
V.
Of
the
seuenth
Heauen
,
that
is
,
the
heauen
of
Saturne
.
1.
THe
seuenth
Heauen
is
situated
next
vnder
the
eight
Heauen
or
Sphere
,
and
mooueth
from
West
to
East
,
and
is
onely
proper
to
Saturne
,
which
is
the
highest
Planet
:
whose
orbes
and
motions
thereof
,
this
figure
here
following
doth
plainely
shew
.
¶
The
first
figure
belonging
to
the
Theorique
of
Saturne
,
together
with
the
description
thereof
.
In
this
figure
,
consisting
of
certain
circles
&
right
lines
,
you
see
that
the
three
outermost
great
circles
drawn
vpon
the
p●int
A
,
signifying
the
centre
of
the
world
,
do
enclose
two
w●●●te
seuerall
spaces
,
and
in
each
space
are
set
down
the
caracters
of
the
12
signes
:
of
which
two
spaces
,
the
outermost
representeth
the
Eclipticke
both
of
the
10
and
9
Heauen
,
the
beginning
of
which
Ecliptick
is
marked
on
the
right
hand
with
the
letter
D
,
signifying
the
true
Vernall
Equinox
:
and
the
next
space
vnder
that
representeth
the
Eclipticke
of
the
eight
Heauen
,
whose
beginning
is
marked
with
a
little
starre
,
●ignifying
the
first
starre
of
the
Rams
horne
.
2.
And
the
two
blacke
orbes
doe
represent
the
deferents
of
the
Auge
,
which
Auge
is
marked
with
the
letter
I
,
&
the
opposit
Auge
with
the
letter
R
,
which
deferents
doe
moue
regularly
,
and
doe
make
their
reuolution
in
35333
Aegyptian
yeares
:
and
betwixt
the
two
balcke
orbes
is
another
white
orbe
,
signifying
the
orbe
Excentrique
,
drawne
vpon
his
owne
centre
,
marked
with
the
letter
B
,
in
the
middest
of
which
broad
white
circle
is
another
circle
described
by
the
centre
of
the
Epicicle
,
marked
with
the
letter
E
,
vpon
which
point
E
is
drawne
a
little
circle
,
signifying
the
Epicicle
it selfe
,
which
carrieth
the
body
of
the
Planet
,
in
the
circumference
wherof
is
a
little
starre
,
representing
the
body
of
Saturne
.
You
see
also
that
there
is
another
circle
which
crosseth
the
foresaid
middle
circle
of
the
Excentrique
in
two
points
opposit
,
drawne
vpon
his
owne
centre
,
marked
with
C
,
and
is
called
the
circle
Equant
.
The
motions
of
which
circles
,
and
also
the
significations
of
the
right
lines
and
arches
in
this
figure
contained
,
are
by
helpe
of
the
letters
hereafter
declared
:
for
the
right
line
which
is
drawne
from
the
point
A
vnto
the
point
I
,
and
so
foorth
to
the
Eclipticke
,
is
called
the
line
of
Auge
:
and
the
point
or
degree
of
the
Eclipticke
,
into
which
the
line
of
the
Auge
falleth
,
is
called
the
place
of
the
Auge
,
which
for
example
sake
suppose
to
be
in
the
first
point
of
Gemini
,
marked
with
the
letter
F.
And
the
arch
comprehended
betwixt
the
point
F
and
the
first
starre
of
the
Rams
horne
,
signified
by
the
little
starre
set
downe
on
the
right
hand
in
the
true
Eclipticke
is
called
the
meane
motion
of
the
Auge
.
And
the
right
line
A
B
is
called
the
excentricitie
of
the
Excentrique
,
containing
in
length
3
degrees
,
i/25
and
the
right
line
A
C
is
the
excentricitie
of
the
circle
Equant
,
containing
in
length
6
degrees
,
i/50
3.
The
Auge
is
that
point
in
the
superficies
of
the
Excentrique
which
is
furthest
distant
from
the
centre
of
the
world
,
marked
with
the
letter
1.
But
the
opposit
Auge
is
that
point
in
the
superficies
of
the
said
Excentrique
,
which
is
nearest
vnto
the
centre
of
the
world
,
marked
with
the
letter
R.
4.
The
place
of
each
point
is
shewed
by
a
right
line
drawne
through
the
centre
of
the
world
&
also
through
the
Auge
of
the
Excentrique
vnto
the
Zodiake
of
the
eight
Heauen
,
marked
with
the
caracters
of
the
twelue
signes
,
and
the
line
so
drawne
,
is
called
the
line
of
Auge
.
5.
The
meane
motion
of
the
Auge
is
an
arch
of
the
Eclipticke
,
proceeding
from
the
first
starre
of
the
Rams
horne
vnto
the
place
of
the
Auge
,
and
is
found
in
such
order
as
is
shewed
in
the
eight
Precept
,
by
helpe
of
the
13
and
14
Cannons
in
that
Colume
,
whose
title
is
Apogaea
Saturni
.
6.
But
the
true
motion
of
the
Auge
is
an
arch
of
the
Eclipticke
,
beginning
at
the
true
Vernall
Equinox
,
and
ending
at
the
place
of
the
Auge
:
the
manner
how
to
find
the
same
,
is
shewed
in
the
33
Precept
.
7.
The
orbe
Excentrique
,
is
an
orbe
of
one
equall
thicknesse
,
compassing
the
centre
of
the
world
,
in
which
Excentrique
the
Epicicle
is
alwaies
caried
,
and
maketh
his
reuolution
in
29
Aegyptian
yeares
,
183
dayes
,
and
almost
5
houres
,
the
Diurnall
motion
thereof
is
i/2
ii/0
iii/21
iiii/16
almost
.
8.
The
centre
of
the
Excentrique
,
marked
with
B
,
is
a
point
in
the
middle
of
the
Excentrique
,
from
which
all
right
lines
that
are
drawn
vnto
the
concauitie
of
the
Excentrique
,
are
equall
.
9.
The
distance
betwixt
which
centre
and
the
centre
of
the
world
is
called
the
excentricitie
of
the
Excentrique
:
and
the
distance
betwixt
the
two
said
centres
,
that
is
,
of
the
world
and
of
the
Excentrique
,
is
3
degrees
,
i/25
10.
The
circle
Equant
is
a
circle
described
vpon
the
point
C
in
the
plane
of
the
Excentrique
,
in
regard
of
the
centre
wherof
,
the
motion
as
well
of
the
Excentrique
as
of
the
Epicicle
,
is
regular
and
equall
.
And
this
circle
is
sometimes
called
the
circle
of
equalitie
,
sometimes
the
Equator
,
and
other
times
the
Excentricall
Equator
,
the
distance
of
the
centre
whereof
is
from
the
centre
of
the
Excentrique
3
degree
,
i/25
and
from
the
centre
of
the
world
6
degrees
,
i/50
and
this
distance
from
the
centre
of
the
world
is
called
the
Excentricitie
of
the
circle
Equant
.
11.
The
Epicicle
is
a
little
orbe
,
whose
centre
is
marked
with
the
letter
E
,
which
the
Excentrique
carrieth
about
,
which
Epicicle
notwithstanding
hath
his
proper
motion
,
for
the
higher
part
thereof
hath
his
moouing
according
to
the
succession
of
the
signes
,
and
the
lower
part
contrarie
to
the
succession
of
the
signes
.
The
daily
motion
of
the
Epic●cle
about
his
owne
centre
,
is
i/57
ii/7
iii/44
and
maketh
one
ent●e
reuolution
in
378
dayes
,
21
houres
,
i/36
12.
But
because
that
the
accounting
of
the
motions
by
the
circle
Equant
is
troublesome
,
therefore
the
Astronomers
doe
vse
to
reckon
the
fame
vpon
the
Eclipticke
,
by
imposing
a
line
to
be
drawne
from
the
centre
of
the
world
vnto
the
Eclipticke
,
in
such
sort
,
as
the
same
may
be
paralel
vnto
the
line
before
drawne
:
as
in
the
foresaid
figure
,
the
line
A
G
being
paralell
vnto
the
line
C
E
,
is
called
the
line
o●
the
meane
moouing
of
the
Epicicle
or
of
the
Planet
.
13.
The
meane
Anomalia
of
the
Excentrique
is
an
arch
of
the
Ecliptick
,
beginning
at
the
line
of
the
Auge
,
and
so
proceeding
according
to
the
succession
of
the
signes
,
vntill
at
end
at
the
line
of
the
meane
moouing
,
as
in
the
foresaid
figure
the
line
A
F
is
the
line
of
the
Auge
,
and
A
G
is
the
line
of
the
meane
moouing
.
Now
the
arch
of
the
Eclipticke
,
which
is
comprehended
betwixt
the
two
lines
,
A
F
,
and
A
G
,
that
is
to
say
,
the
arch
F
G
is
called
the
meane
Anomalia
of
the
Excentrique
,
and
of
some
it
is
called
the
meane
or
equall
centre
.
14.
But
if
the
said
arch
bee
reckoned
from
the
first
starre
of
the
Rams
horne
,
vnto
the
line
of
the
meane
mouing
,
marked
with
A
G
,
then
the
said
arch
is
called
the
equ●ll
motion
of
longitude
,
which
you
may
find
by
the
Tables
at
any
time
,
supposed
by
the
13
and
14
Cannons
in
the
Colume
,
whose
title
is
Longitudinis
Saturni
,
in
such
order
as
is
shewed
in
the
eight
Precept
.
The
equall
or
meane
moouing
of
the
longitude
of
Saturne
,
is
daily
i/2
ii/0
iii/27
iiii/18
and
the
yearely
motion
thereof
is
12
degrees
,
i/12
ii/46
iii/4
and
the
whole
reuolution
is
in
29
Aegyptian
yeares
,
174
dayes
,
4
houres
,
i/58
ii/24
for
in
that
time
it
returneth
to
the
first
starre
of
the
Rams
horne
.
15.
The
line
of
the
true
mouing
of
the
Epicicle
is
a
right
line
drawne
from
the
centre
of
the
world
,
passing
through
the
centre
of
the
Epicicle
vnto
the
Eclipticke
,
as
in
the
foresaid
figure
the
right
line
A
E
L
is
called
the
line
of
the
true
motion
of
the
Epicicle
.
16.
The
true
or
coequated
Anomalia
of
the
Excentrique
(
which
is
called
by
the
Alphonsines
the
true
centre
)
is
an
arch
of
the
Eclipticke
,
beginning
at
the
place
of
the
Auge
of
the
Excentrique
,
and
endeth
at
the
true
place
of
the
centre
of
the
Epicicle
,
as
in
the
foresaid
Figure
the
arch
F
L
is
the
true
Anomalia
of
the
Excentrique
.
17.
The
true
motion
of
the
longitude
of
the
Epicicle
is
an
arch
of
the
Eclipticke
,
beginning
at
the
first
starre
of
the
Rams
horne
,
and
endeth
at
the
true
place
of
the
centre
of
the
Epicicle
,
as
in
the
foresaid
figure
,
the
arch
from
the
Rams
horne
,
marked
with
a
little
starre
in
the
Eclipticke
of
the
eight
sphere
,
to
L
,
is
called
the
true
mouing
of
the
longitude
of
the
Epicicle
.
18.
The
Prosthapheresis
or
Equacion
of
the
centre
,
is
the
difference
betwixt
the
meane
Anomalia
and
the
coequated
Anomalia
of
the
Excentrique
,
or
the
difference
betwixt
the
equall
mouing
and
the
true
moouing
of
longitude
.
As
the
arch
L
G
is
called
the
equacion
of
the
centre
,
and
this
equacion
is
neuer
greater
than
6
degrees
,
i/30
ii/30
and
is
alwaies
greatest
when
the
equall
mouing
of
the
centre
of
the
Epicicle
from
the
Auge
of
the
Excentrique
,
is
11
Sex
.
33
degrees
,
whether
the
same
bee
reckoned
according
to
the
succession
of
the
signes
,
or
contrarie
to
the
succession
of
the
signes
:
and
from
thence
it
decreaseth
vntill
the
line
of
the
said
mean
moouing
commeth
into
the
line
of
the
opposite
Auge
.
The
finding
of
which
Equacion
is
taught
in
the
34
Precept
,
by
helpe
of
the
19
Cannon
in
the
Colume
,
whose
title
is
Eccentrici
,
and
is
to
be
added
or
subtracted
according
as
the
words
Subtrahe
and
Adde
at
the
head
or
foot
of
the
said
Colume
,
doe
shew
.
19.
The
two
points
in
which
the
Prosthapheresis
of
the
Excentrique
is
greatest
,
are
called
the
meane
longitude
of
the
Excentrique
:
and
these
two
points
are
shewed
by
a
right
line
perpendicularly
drawne
vpon
the
line
of
Auge
,
and
passing
through
the
middle
space
of
the
distance
betwixt
the
centre
of
the
world
and
the
centre
of
the
Excentrique
,
as
in
the
former
figure
,
in
which
the
point
A
signifieth
the
centre
of
the
world
,
and
the
point
B
the
centre
of
the
Excentrique
.
Now
if
the
space
B
A
be
deuided
into
two
equall
parts
,
as
in
the
point
Q
,
and
through
the
same
point
Q
a
right
line
be
drawne
,
crossing
the
line
A
F
with
right
angles
,
and
is
produced
as
well
towards
the
right
hand
as
towards
the
left
,
vnto
the
two
points
of
the
circumference
of
the
Excentrique
,
marked
with
the
two
letters
T
and
V
,
the
said
two
points
T
and
V
are
called
the
meane
longitudes
of
the
Excentrique
:
in
which
meane
longitudes
the
centre
of
the
Epicicle
is
,
when
the
equall
motion
of
Saturnes
longitude
is
93
degrees
or
267
degrees
.
20.
The
meane
Auge
of
the
Epicicle
is
a
point
in
the
circumference
of
the
Epicicle
,
which
is
furthest
distant
from
the
centre
of
the
circle
Equant
:
and
this
point
is
found
by
drawing
a
right
line
from
the
centre
of
the
circle
Equant
vnto
the
circumference
of
the
Epicicle
,
through
the
centre
of
the
said
Epicicle
,
as
in
the
former
figure
the
right
line
C
E
being
produced
vnto
the
circumference
of
the
Epicicle
,
sheweth
the
meane
Auge
of
the
Epicicle
to
be
in
the
point
H.
21.
The
true
Auge
of
the
Epicicle
is
a
point
in
the
circumference
of
the
Epicicle
,
which
is
furthest
distant
from
the
centre
of
the
world
,
and
is
found
by
drawing
a
right
line
from
the
centre
of
the
world
vnto
the
centre
of
the
Epicicle
,
and
produced
vnto
the
circumference
therof
,
as
the
right
line
A
E
being
produced
vnto
the
circumference
of
the
Epicicle
,
meeteth
with
the
same
circumference
in
the
point
K
,
which
is
therefore
called
the
true
Auge
of
the
Epicicle
.
22.
The
Touch
point
is
a
point
in
the
circumference
of
the
Epicicle
,
which
is
furthest
distant
from
the
centre
of
the
Excentrique
,
and
is
determined
by
a
right
line
drawn
from
the
centre
of
the
Excentrique
vnto
the
centre
of
the
Epicicle
,
and
so
produced
vnto
the
circumference
of
the
Epicicle
:
as
if
the
line
B
E
bee
produced
vnto
the
circumference
of
the
Epicicle
,
viz.
vnto
the
point
N
,
the
said
point
N
is
called
the
Touch
point
of
the
Epicicle
.
23.
The
Anomalia
of
commutation
is
an
arch
of
the
Epicicle
,
beginning
at
the
meane
Auge
of
the
Epicicle
,
and
ending
at
the
place
of
the
Planet
in
the
Epicicle
:
and
this
arch
is
alwaies
reckoned
,
according
as
the
Planet
moueth
.
As
the
arch
H
*
of
the
Epicicle
is
called
the
Anomalia
of
commutation
,
and
is
otherwise
called
of
some
the
meane
Anomalia
of
the
orbe
or
Epicicle
,
and
of
others
the
meane
argument
:
the
finding
of
the
Anomalia
of
Commutation
is
taught
in
the
8
Precept
,
by
helpe
of
the
13
and
14
Cannons
in
his
proper
Collum
,
whose
title
is
Anomalia
comutationis
Satura●
.
24.
The
coequated
Anomalia
of
Commutation
is
an
arch
of
the
Epicicle
,
beginning
at
the
true
Auge
of
the
Epicicle
,
and
ending
at
the
place
of
the
Planet
in
his
Epicicle
.
As
the
arch
K
N
H
is
called
the
coequated
Anomalia
of
Commutation
:
which
some
call
the
true
Anomalia
of
the
Orbe
,
and
others
call
it
the
true
Argument
.
25.
The
Prosthapheresis
or
equacion
of
the
centre
in
the
Epicicle
,
is
an
arch
of
the
Epicicle
,
which
is
comprehended
betwixt
the
meane
and
true
Auge
of
the
Epicicle
:
as
in
the
former
figure
the
point
K
is
the
true
Auge
,
and
the
point
H
is
the
meane
Auge
of
the
Epicicle
,
the
distance
betwixt
which
two
Auges
is
the
arch
K
N
H
,
and
that
is
the
equacion
of
the
centre
in
the
Epicicle
:
and
this
equacion
is
alwaies
equall
vnto
the
equacion
of
the
centre
,
before
defined
in
the
18
definition
of
this
chapter
:
Only
this
rule
is
generally
to
be
obserued
,
that
if
the
Prosthapheresis
were
added
in
the
coequating
of
the
Anomalia
of
the
Excentrique
,
the
same
Prosthapheresis
must
be
subtracted
in
the
coequating
of
the
Anomalia
of
Commutation
:
and
so
againe
if
it
bee
subtracted
in
the
former
,
then
it
must
be
added
in
the
latter
.
26.
The
line
of
the
true
motion
of
the
Planet
is
a
right
line
drawne
from
the
centre
of
the
world
vnto
the
Eclipticke
,
through
the
centre
of
the
Planet
.
As
in
the
former
figure
the
right
line
A
*
S
is
called
the
line
of
the
true
motion
of
the
Planet
.
27.
The
true
motion
it selfe
of
the
Planet
is
an
arch
of
the
Eclipticke
,
comprehended
betwixt
the
true
Vernall
Equinox
and
the
line
of
the
true
motion
.
As
in
the
foresaid
figure
the
arch
D
S
is
called
the
true
motion
of
the
Planet
.
28.
The
equacion
of
the
Argument
,
which
Copernicus
calleth
the
Parallax
of
the
orbe
,
and
others
call
the
same
the
Prosthapheresis
of
the
Epicicle
,
is
an
arch
of
the
Eclipticke
,
comprehended
betwixt
the
line
of
the
true
motion
of
the
Epicicle
,
and
the
line
of
the
true
motion
of
the
Planet
,
as
in
the
former
figure
the
arch
S
L
is
the
equacion
of
the
argument
.
This
equacion
is
found
by
helpe
of
the
coequated
Anomalia
of
Commutation
,
in
such
order
as
is
shewed
in
the
34
Precept
,
and
in
the
19
Cannon
in
the
Colume
,
whose
title
is
Paralaxis
Orbis
.
The
greatest
equacion
that
Saturne
can
haue
,
when
the
Epicicle
is
in
the
Auge
of
his
Excentrique
,
and
the
Planet
is
distant
from
the
Auge
of
the
Epicicle
96
degrees
,
is
5
degrees
,
i/55
ii/33
But
the
greatest
equacion
belonging
to
him
when
the
Epicicle
is
in
the
opposit
Auge
of
the
Excentrique
,
and
the
Planet
is
distant
from
the
Auge
of
the
Epicicle
almost
97
degrees
,
is
6
degrees
,
i/38
ii/38
29.
The
excesse
of
the
equacion
of
the
Argument
,
which
the
Alphonsines
call
the
diuersitie
of
the
diameter
,
is
an
arch
of
the
Eclipticke
,
whereby
the
equacion
of
the
Epicicle
being
in
the
opposit
Auge
of
the
Excentrique
,
exceedeth
the
said
equacion
,
when
the
Epicicle
is
in
the
Auge
of
his
Excentrique
.
As
you
shall
more
plainely
perceiue
by
this
figure
following
.
30.
The
proportionall
minutes
are
the
60
parts
of
the
excesse
,
by
helpe
whereof
the
equacions
of
the
Epicicle
,
being
not
in
the
Auge
,
nor
in
the
opposit
Auge
of
the
Excentrique
are
equated
or
corrected
.
As
in
the
former
figure
the
arch
P
L
,
which
is
the
excesse
,
is
supposed
to
be
deuided
into
60
equall
parts
,
by
helpe
of
which
diuision
the
proportionall
minutes
are
found
in
what
place
of
the
Excentrique
soeuer
the
epicicle
is
placed
.
As
suppose
the
true
place
thereof
to
be
in
the
point
F
,
in
which
situation
of
the
Epicicle
,
the
arch
O
L
is
the
equacion
of
the
Argument
,
which
equacion
is
greater
than
it
was
when
the
Epicicle
was
in
the
point
E
,
and
the
difference
betwixt
these
two
equacions
is
the
arch
I
L.
Now
if
you
suppose
the
arch
P
L
to
bee
deuided
into
60
equall
parts
,
looke
how
many
of
those
parts
the
arch
I
L
doth
containe
,
so
many
proportionall
minutes
are
belonging
to
the
equacion
of
the
argument
of
the
Epicicle
,
when
the
place
of
the
said
Epicicle
is
in
the
point
F.
The
finding
of
these
proportionall
minutes
is
taught
in
the
34
Precept
,
and
are
set
downe
in
the
19
Cannon
in
the
Colume
,
whose
title
is
Scrupula
Proportionalia
.
31.
The
absolute
equacion
is
an
arch
of
the
Eclipticke
,
which
is
compounded
of
the
equacion
of
the
Argument
,
and
the
excesse
answerable
vnto
the
proportionall
minutes
.
And
this
absolute
equacion
is
either
added
or
subtracted
vnto
the
true
mouing
of
the
Epicicle
,
and
the
summe
of
such
addition
or
the
remainer
of
the
subtraction
will
shew
the
true
distance
of
the
Planet
from
the
first
starre
of
the
Rams
horne
:
whereunto
if
you
adde
the
true
Precession
of
the
Equinox
,
the
summe
of
that
addition
will
shew
the
true
longitude
of
the
Planet
.
CHAP.
VI.
Of
the
sixt
Heauen
,
or
the
Heauen
of
Iupiter
.
THe
sixt
Heauen
,
which
is
of
Iupiter
,
consisteth
of
like
orbes
as
doth
the
Heauen
of
Saturne
,
&
therfore
the
demonstrations
belonging
to
this
Heauen
,
doe
not
differ
from
those
which
were
set
downe
in
the
heauen
of
Saturne
,
but
only
in
the
time
of
their
motions
&
in
the
quantitie
of
some
arches
:
for
the
deferents
of
the
Auge
and
opposit
Auge
in
the
heauen
of
Iupiter
doe
make
their
reuolution
in
109756
Aegyptian
yeares
.
And
the
Excentrique
of
this
Heauen
maketh
his
reuolution
in
11
Aegyptian
years
,
318
daies
,
and
one
houre
almost
.
And
the
excentricitie
of
the
Excentrique
of
Iupiter
is
2
degrees
,
i/45
and
the
excentricitie
of
the
circle
Equant
is
5
degrees
,
i/30
The
Epicicle
of
this
Heauen
maketh
his
reuolution
in
398
dayes
,
21
houres
,
i/13
ii/15
iii●●°
and
the
daily
motion
thereof
is
i/54
ii/9
iii/4
The
greatest
equacion
of
the
centre
which
belongeth
vnto
Iupiter
,
is
5
degrees
,
i/13
ii/59
and
that
is
when
the
centre
of
the
Epicicle
is
distant
from
the
true
Auge
of
the
Excentrique
93
degrees
,
whether
it
be
according
or
contrarie
to
the
succession
of
the
signes
.
And
the
greatest
equacion
of
the
Argument
,
when
the
centre
of
the
Epicicle
is
in
the
Auge
of
the
Excentrique
,
is
10
degrees
,
i/30
ii/9
and
then
the
distance
of
the
Planet
from
the
true
Auge
of
his
Epicicle
,
is
100
degrees
,
i30
almost
.
And
the
greatest
equacion
of
the
said
Argument
,
when
the
Epicicle
is
in
the
opposit
Auge
of
the
Excentrique
,
is
11
degrees
,
i/31
ii/2
&
then
the
Planet
is
distant
from
the
true
Auge
of
the
Epicicle
102
degrees
almost
.
The
equall
or
meane
moouing
of
Iupiters
longitude
from
the
first
starre
of
the
Rams
horne
,
is
daily
i/4
ii/59
iii/8
and
the
yearely
motion
thereof
is
30
degrees
,
i/19
ii/4
iii/6
&
maketh
one
entire
reuolution
in
11
Aegyptian
years
,
214
dayes
,
21
houres
,
i/16
ii/24
The
rest
of
the
lines
and
arches
belonging
to
this
Planet
,
are
defined
in
the
former
fift
Chapter
:
and
the
finding
of
all
such
things
as
are
needfull
for
that
purpose
are
set
downe
in
the
said
fift
Chapter
,
differing
nothing
from
the
manner
which
was
therein
shewed
,
except
it
bee
in
the
number
of
the
Cannon
,
which
for
Saturne
was
the
19
,
and
for
this
Planet
it
is
the
20
Cannon
.
CHAP.
VII
.
Of
the
fift
Heauen
,
or
Heauen
of
Mars
.
THe
fift
Heauen
belonging
to
Mars
,
hath
like
number
of
orbes
,
as
hath
the
Heauen
of
Saturne
,
and
the
said
orbes
are
placed
euen
as
they
were
in
Saturne
.
And
therefore
I
shall
not
need
to
make
any
perticular
relation
of
the
orbes
or
lines
of
this
sphere
,
but
to
referre
you
to
the
fift
Chapter
,
shewing
only
here
the
difference
of
the
motions
.
The
deferents
of
the
Auge
in
the
Heauen
of
Mars
doe
make
their
reuolution
in
45088
Aegyptian
yeares
,
so
as
their
daily
motion
is
iii/4
iiii/43
and
their
yearely
motion
is
ii/28
iii/44
iiii/37
The
Excentrique
of
this
Heauen
maketh
his
reuolution
in
one
yeare
,
and
322
daies
almost
,
so
as
his
daily
motion
is
i/31
ii/26
iii/26
iiii/15
and
the
yearely
motion
therof
is
191
degrees
,
i/15
ii/49
iii/44
iiii/3
The
Epicicle
of
this
Heauen
maketh
his
reuolution
in
2
yeares
,
49
dayes
,
19
houres
,
i/43
and
the
daily
motion
thereof
is
i/27
ii/41
iii/40
and
his
yearely
motion
is
168
degrees
,
i/2
ii/30
iii/42
The
greatest
equacion
of
the
centre
belonging
vnto
Mars
,
is
11
degrees
,
i/5
ii/59
and
that
is
when
the
centre
of
his
Epicicle
is
distant
from
the
true
Auge
of
the
Excentrique
95
degrees
and
i/30
be
it
according
or
contrarie
to
the
succession
of
the
signes
.
The
greatest
equacion
of
the
argument
,
when
the
centre
of
the
Epicicle
is
in
the
Auge
of
the
Excentrique
,
is
36
degrees
,
i/54
ii/18
and
then
the
distance
of
the
Planet
from
the
true
Auge
of
his
epicicle
is
127
degrees
almost
.
And
the
greatest
equacion
of
the
Argument
,
when
the
centre
of
the
Epicicle
is
in
the
opposit
Auge
of
his
Excentrique
,
is
46
degrees
,
i/38
ii/4
and
that
is
when
the
Planet
is
distant
from
the
Auge
of
the
Epicicle
137
deg.
The
meane
mouing
of
the
longitude
of
Mars
is
euery
day
i/31
ii/26
iii/31
and
the
yearely
motion
thereof
is
191
i/16
ii/18
iii/29
and
maketh
one
entire
reuolution
in
one
yeare
,
321
dayes
,
23
houres
,
i/32
All
other
lines
and
arches
belonging
to
Mars
are
defined
in
the
fift
Chapter
:
and
the
Cannon
seruing
for
the
finding
of
them
and
their
places
,
is
the
21
Cannon
in
number
.
CHAP.
VIII
.
Of
the
fourth
Heauen
,
or
Heauen
of
the
Sunne
.
THe
next
Heauen
vnder
that
of
Mars
,
is
the
Heauen
of
the
Sunne
,
and
hath
his
proper
and
peculiar
motion
from
West
to
East
.
This
Heauen
consisteth
of
fiue
orbes
:
wherof
two
are
called
the
deferents
of
the
meane
Auge
of
the
Suns
Excentrique
,
the
other
two
orbes
are
called
the
deferents
of
the
true
Auge
of
his
Excentrique
,
or
the
orbes
of
the
Anomalia
of
the
true
Auge
and
of
the
excentricitie
of
the
Sunne
.
The
fift
Orbe
is
called
the
deferent
of
the
body
of
the
Sunne
.
All
which
you
may
euidently
see
in
the
figure
following
.
¶
The
first
figure
belonging
to
the
Theorique
of
the
Sunne
.
IN
which
figure
,
the
outermost
broad
circle
,
in
which
are
set
the
caracters
of
the
12
signes
,
signifieth
the
Eclipticke
of
the
eight
Heauen
,
the
centre
whereof
is
marked
with
the
letter
A
,
which
signifieth
the
centre
of
the
world
.
Next
vnto
this
Eclipticke
is
one
of
the
deferents
of
the
meane
Auge
signified
by
the
outermost
blacke
orbe
,
the
centre
of
whose
convex
superficies
is
the
point
A
,
and
the
centre
of
his
concaue
superficies
is
the
point
B
,
the
other
deferent
of
the
said
meane
Auge
is
the
lesser
broad
blacke
circle
,
the
centre
of
whose
convex
superficies
is
the
point
B
,
and
the
centre
of
his
concaue
superficies
is
the
point
A.
And
betwixt
the
blacke
orbes
are
two
shaddowed
orbes
,
which
are
the
deferents
of
the
Sunnes
Excentrique
:
and
the
convex
superficies
of
the
outermost
of
these
two
shaddowed
orbes
,
as
also
the
concaue
superficies
of
the
lower
of
them
haue
for
their
centre
the
point
B
,
and
the
concaue
superficies
of
the
higher
and
convex
superficies
of
the
lower
haue
the
point
C
for
their
centre
.
Betwixt
which
two
orbes
is
the
Excentrique
of
the
Sunne
,
which
Excentrique
is
signified
by
the
broad
white
circle
:
in
the
middle
of
which
white
circle
is
drawne
a
circle
,
in
which
the
centre
of
the
Sunne
is
continually
moued
:
and
the
centre
of
the
Excentrique
is
marked
with
the
letter
C
,
which
point
is
called
the
moouable
centre
of
the
Excentrique
,
by
whose
motion
is
described
the
little
circle
in
the
middle
of
the
figure
,
the
centre
of
which
circle
is
the
point
B.
1.
The
deferents
of
the
meane
Auge
of
the
Sunne
are
two
orbes
of
vnequall
thicknesse
,
being
in
some
respect
concentricall
with
the
Eclipticke
,
and
in
another
respect
excentricall
:
for
the
convex
superficies
of
the
higher
,
and
the
concaue
superficies
of
the
lower
haue
for
their
centre
the
centre
of
the
world
,
marked
with
A
:
but
the
concaue
superficies
of
the
higher
,
and
convex
superficies
of
the
lower
haue
a
centre
differing
from
the
centre
of
the
world
:
and
these
two
orbes
haue
their
proper
and
peculiar
motion
from
West
to
East
vpon
the
axes
and
poles
of
the
true
Eclipticke
,
and
their
Diurnall
motion
is
iii●°
iiii/12
and
their
yearely
motion
is
ii/25
iii/33
iiii/12
and
do
make
one
entire
reuolution
in
50717
Aegyptian
yeares
:
and
these
two
orbes
doe
only
serue
to
carry
the
meane
Auge
of
the
Excentrique
.
2.
The
meane
Auge
of
the
Excentrique
is
that
point
in
the
deferent
of
the
Excentrique
,
which
is
furthest
distant
from
the
centre
of
the
world
.
As
for
example
,
the
point
G
in
the
former
figure
signifieth
the
meane
Auge
of
the
Excentrique
.
3.
And
this
point
is
alwaies
determined
in
the
Zodiake
by
a
right
line
,
drawne
from
the
centre
of
the
world
through
the
centre
of
the
little
circle
,
marked
with
B
,
vnto
the
Eclipticke
line
,
and
the
line
so
drawne
,
is
called
the
line
of
the
meane
Auge
,
as
the
line
A
B
G
,
which
is
called
the
line
of
the
meane
Auge
.
4.
But
the
motion
of
the
meane
Auge
is
an
arch
of
the
Eclipticke
,
beginning
at
the
first
starre
of
the
Rams
horne
,
and
ending
at
the
line
of
the
meane
Auge
,
as
in
the
said
figure
the
arch
*
G
is
the
motion
of
the
meane
Auge
:
but
if
the
said
arch
begin
at
the
Aequinoctiall
,
whether
the
same
be
meane
or
true
,
then
is
the
said
motion
called
the
motion
of
the
mean
Equinox
,
extending
from
the
mean
Equinox
or
from
the
true
Equinox
vnto
the
foresaid
line
of
the
meane
Auge
,
the
finding
of
euery
of
which
motions
is
shewed
in
the
16
Precept
.
5.
The
deferents
of
the
Excentrique
,
which
sometimes
are
called
the
orbes
of
the
Anomalia
of
the
excentricitie
,
are
the
two
shaddowed
orbes
which
do
carry
the
orbe
Excentrique
.
And
these
two
orbes
haue
their
proper
motion
also
from
East
to
West
,
making
their
reuolution
once
in
3434
Aegyptian
yeares
,
and
10
dayes
,
and
their
daily
motion
is
ii/1
iii/2
iiii/2
and
their
yearly
motion
is
i/6
ii/17
iii/24
iiii/9
And
those
deferents
are
moued
vpon
the
centre
of
the
little
circle
(
which
centre
is
marked
with
the
letter
B
,
and
is
distant
from
the
centre
of
the
world
2
degrees
,
i/1
such
degrees
as
the
length
of
the
semidiameter
of
the
Excentrique
containeth
60
degrees
)
and
their
proper
axletree
is
paralell
vnto
the
axletree
of
the
Eclipticke
,
and
passeth
through
the
centre
of
the
said
little
circle
,
as
the
next
figure
following
sheweth
.
And
the
,
motion
of
these
orbes
doth
begin
at
the
line
of
the
mean
Auge
before
defined
in
the
third
definition
of
this
chapter
.
And
it
is
called
the
Anomalia
or
Argument
of
the
Auge
,
and
of
the
excentricitie
of
the
Sunne
.
By
the
motion
of
which
Orbes
the
centre
of
the
Excentrique
is
imagined
to
describe
a
little
circle
aboue
the
centre
of
the
world
,
whereby
the
excentricitie
of
the
Sunne
changeth
euery
day
.
6.
The
excentricitie
of
the
Sunne
is
the
distance
betwixt
the
centre
of
the
world
and
the
centre
of
the
Suns
Excentrique
:
and
this
is
threefold
,
greatest
,
least
,
or
meane
.
7.
The
greatest
excentricitie
of
the
Sunne
is
when
the
centre
of
the
Excentrique
is
in
the
Auge
of
the
little
circle
,
viz.
in
the
point
C
,
and
the
quantitie
of
this
greatest
excentricitie
,
is
2
degrees
,
i/3
ii/7
such
like
degrees
as
the
semidiameter
of
the
Excentrique
containeth
60
degrees
,
or
the
quantitie
of
the
said
greatest
excentricitie
is
41700
,
when
the
semidiameter
of
the
Excentrique
is
1000000.
8.
The
least
excentricitie
is
when
the
centre
of
the
Excentrique
is
in
the
opposit
Auge
of
the
little
circle
,
and
then
the
distance
betwixt
the
centre
of
the
earth
and
the
centre
of
the
Excentrique
,
is
1
degree
,
i/55
ii/53
supposing
the
semidiameter
of
the
Excentrique
to
be
deuided
into
60
equall
parts
,
but
if
the
said
semidiameter
be
deuided
into
1000000
,
then
the
said
least
excentricitie
will
be
32190.
9.
The
meane
excentricitie
is
when
the
centre
of
the
Excentrique
is
in
the
middle
distance
betwixt
the
Auge
and
opposit
Auge
of
the
little
circle
,
and
then
the
said
excentricitie
is
0
degrees
,
i34
.
ii14
.
such
parts
as
the
semidiameter
of
the
Excentrique
containeth
60.
But
if
the
said
semidiameter
bee
supposed
to
bee
deuided
into
1000000
parts
,
then
the
said
mean
excentricitie
is
9510.
And
the
semidiameter
of
that
little
circle
containeth
0
degrees
,
i/17
.
ii/7
10.
The
Anomalia
of
the
Auge
and
excentricitie
,
which
is
also
called
the
centre
of
the
Sunne
,
is
an
arch
in
the
concaue
superficies
of
the
outermost
deferent
of
the
meane
Auge
,
which
arch
is
comprehended
betwixt
the
line
of
the
meane
Auge
,
and
a
right
line
drawn
from
the
centre
of
the
little
circle
through
the
mouable
centre
of
the
Excentrique
vnto
the
concave
supe●ficies
of
the
said
outermost
orbe
.
Or
thus
,
the
centre
of
the
Sun
is
an
arch
of
the
little
circle
,
beginning
at
the
Auge
of
said
little
circle
,
and
ending
at
the
mouable
centre
of
the
Excentrique
.
As
for
example
.
¶
The
second
figure
belonging
to
the
Theorique
of
the
Sunne
.
In
this
figure
suppose
the
point
A
to
be
the
centre
of
the
world
,
and
B
the
centre
of
the
concave
superficies
of
the
outermost
of
the
two
deferents
of
the
meane
Auge
,
and
C
the
centre
of
the
Excentrique
,
whose
place
was
sometimes
in
the
point
P
,
but
now
is
gone
from
thence
vnto
C
,
so
is
A
G
the
line
of
the
meane
Auge
,
and
A
P
is
the
greatest
excentricitie
,
and
A
O
the
least
excentricitie
,
and
P
O
is
the
difference
betwixt
the
greatest
and
least
excentricitie
,
the
halfe
whereof
is
B
O
,
and
A
B
is
the
quantitie
of
the
meane
excentricitie
,
and
the
place
of
the
centre
of
the
Excentrique
is
in
the
point
C
,
and
the
arch
G
F
is
the
Anomalia
or
Argument
of
the
Auge
and
of
the
excentricitie
in
the
concaue
superficies
of
the
highest
deferent
of
the
meane
Auge
,
and
the
arch
P
C
of
the
little
circle
is
the
Anomalia
of
the
Auge
and
excentricitie
:
and
the
right
line
B
C
F
is
the
line
which
sheweth
the
meane
Auge
of
the
orbes
of
the
Anomalia
of
the
Auge
,
in
respect
of
their
centre
.
11.
The
meane
Auge
of
the
orbes
of
the
Anomalia
of
the
excentricitie
,
is
that
point
in
the
concave
superficies
of
the
highest
deferent
of
the
Excentrique
,
which
is
furthest
distant
from
the
centre
of
the
little
circle
,
and
is
pointed
out
by
a
right
line
drawne
from
the
centre
of
the
said
little
circle
,
through
the
mouable
centre
of
the
Excentrique
.
As
in
this
second
figure
,
in
which
the
point
B
is
the
centre
of
the
little
circle
,
and
C
is
the
centre
of
the
Excentrique
,
through
which
point
C
if
you
draw
a
right
line
from
A
vnto
the
concauitie
of
the
highest
deferent
of
the
Excentrique
,
as
vnto
the
point
E
,
the
said
point
E
is
the
mean
Auge
of
the
orbes
of
the
Anomalia
of
the
excentricitie
.
Now
if
you
adde
the
daily
mouing
of
this
meane
Auge
,
which
is
ii/1
iii/2
iiii/2
(
as
was
said
in
the
fift
definition
of
this
Chapter
)
vnto
the
daily
moouing
of
the
meane
Auge
of
the
excentricitie
,
which
is
iii/4
iiii/12
(
as
was
said
in
the
first
definition
of
this
Chapter
)
the
summe
of
that
addition
will
be
ii/1
iii/6
iiii/14
and
this
is
the
daily
distance
betwixt
the
two
meane
Auges
,
viz.
that
of
the
excentricitie
,
and
this
of
the
orbes
of
the
Anomalia
of
the
excentricitie
.
12.
The
orbe
Excentrique
is
an
orbe
in
the
Theorique
of
the
Sunne
,
in
which
the
body
of
the
Sunne
is
continually
caried
about
.
This
orbe
is
placed
betwixt
the
two
orbes
,
which
are
the
deferents
of
the
Excentrique
,
and
mooueth
from
West
to
East
vpon
his
owne
moouable
centre
(
which
centre
is
mouable
,
by
reason
of
the
moouing
of
the
two
orbes
,
which
are
the
deferents
of
the
Excentrique
)
and
the
axletree
which
is
also
mouable
according
to
the
motion
of
the
centre
of
the
Excentrique
in
the
circumference
of
the
said
litle
circle
.
And
the
daily
motion
of
this
orbe
from
the
meane
Auge
of
the
orbes
of
the
Anomalia
of
the
excentricitie
is
i/59
ii/9
iii●3·
iiii/24
and
maketh
his
entire
reuolution
in
365
dayes
,
3
houres
,
i/36
ii/25
which
motion
is
reckoned
from
the
meane
Auge
of
the
orbes
of
the
Anomalia
of
the
excentricitie
.
For
the
Sunne
returneth
to
the
said
point
or
meane
Auge
in
365
dayes
,
3
houres
,
i/36
ii/2
13.
The
line
of
the
true
place
of
the
Sunne
is
a
right
line
drawne
from
the
centre
of
the
world
through
the
centre
of
the
Sunne
vnto
the
Eclipticke
:
and
the
point
in
the
Eclipticke
in
which
the
said
line
endeth
,
is
the
true
place
of
the
Sunne
.
As
in
the
former
second
figure
,
suppose
the
centre
of
the
Sunne
to
be
in
the
point
M
of
the
Excentrique
,
and
hauing
drawne
a
line
from
A
to
M
,
and
so
forth
vnto
the
Eclipticke
in
the
point
R
,
the
said
line
A
R
is
called
the
line
of
the
true
place
of
the
Sunne
,
and
the
point
R
is
said
to
be
the
true
place
of
the
Sunne
in
the
Eclipticke
.
14.
The
yearely
Anomalia
of
the
Sunne
,
which
is
also
called
the
meane
Argument
of
the
Sunne
,
is
an
arch
of
the
Excentrique
,
which
is
comprehended
betwixt
the
line
of
the
meane
Auge
of
the
Excentrique
,
and
the
line
of
the
true
place
of
the
Sunne
.
As
in
the
foresaid
second
figure
the
arch
L
M
is
called
the
yearely
Anomalia
of
the
Sunne
.
Or
thus
,
The
yearely
Anomalia
of
the
Sunne
is
the
excesse
or
difference
,
whereby
the
daily
motion
of
the
Sun
from
the
mean
Auge
of
the
orbes
of
the
Anomalia
of
the
excentricitie
,
exceedeth
the
daily
distance
betwixt
the
meane
Auge
of
the
Excentrique
,
and
the
meane
Auge
of
the
orbes
of
the
Anomalia
:
and
this
Anomalia
is
found
by
subtracting
the
daily
distance
of
the
said
two
Auges
,
which
is
ii/1
iii/6
iiii/14
(
as
was
shewed
in
the
11
definition
of
this
Chapter
)
out
of
i/59
ii/9
iii/13
iiii/24
which
is
the
daily
motion
of
the
Excentrique
from
the
meane
Auge
of
the
orbes
of
the
Anomalia
of
the
excentricitie
(
as
was
shewed
before
in
the
12
definition
:
)
the
remainer
of
which
subtraction
will
be
i/59
ii/8
iii/7
iiii/10
And
although
that
this
Anomalia
doth
belong
properly
vnto
the
Excentrique
:
yet
notwithstanding
the
said
Anomalia
is
also
supposed
to
be
in
the
Eclipticke
,
by
imagining
a
line
to
bee
drawne
from
the
centre
of
the
world
vnto
the
Eclipticke
,
in
such
order
as
that
the
said
line
may
be
paralell
vnto
another
line
which
is
drawne
from
the
centre
of
the
Excentrique
vnto
the
place
or
centre
of
the
Sun
:
and
the
line
so
drawn
,
may
be
called
the
line
of
the
Imaginarie
motion
of
the
Sun
.
As
in
the
foresaid
second
figure
let
a
right
line
be
drawn
from
C
to
M
,
then
vnto
the
same
line
draw
another
paralell
right
line
from
the
centre
A
,
and
produce
the
same
vnto
the
Eclipticke
in
the
point
N
;
so
shall
the
arch
of
the
Eclipticke
,
which
is
comprehended
betwixt
the
points
E
and
N
,
bee
the
yearely
Anomalia
or
meane
Argument
of
the
Sunne
in
the
Zodiake
.
The
finding
of
which
Anomalia
for
any
time
appointed
,
is
taught
in
the
8
Precept
,
by
helpe
of
the
13
and
14
Cannons
in
that
Collum
,
whose
title
is
Anomalia
annua
Solis
.
15.
The
true
Auge
of
the
Excentrique
is
that
point
in
the
Excentrique
which
is
furthest
distant
from
the
centre
of
the
world
.
And
this
true
Auge
is
pointed
or
shewed
by
a
right
line
drawne
from
the
centre
of
the
world
through
the
moouable
centre
of
the
Excentrique
vnto
the
Eclipticke
,
and
the
point
in
the
Eclipticke
,
in
which
the
said
right
line
doth
end
,
is
the
place
of
the
true
Auge
of
the
Excentrique
in
the
Eclipticke
:
and
the
said
right
line
is
called
the
line
of
the
true
Auge
of
the
Excentrique
:
as
in
the
foresaid
second
figure
the
point
A
signifying
the
centre
of
the
world
,
and
the
point
C
the
centre
of
the
Excentrique
,
in
the
superficies
of
which
Excentrique
the
point
D
is
furthest
distant
from
the
centre
A
,
and
therefore
the
point
D
is
the
true
Auge
of
the
Excentrique
:
and
the
right
line
A
C
D
is
called
the
line
of
the
true
Auge
of
the
Excentrique
:
and
the
point
K
in
the
Eclipticke
,
in
which
the
said
line
endeth
,
is
the
place
of
the
true
Auge
in
the
Eclipticke
,
the
finding
whereof
is
taught
in
the
16
Precept
.
16.
The
motion
of
the
true
Auge
of
the
Excentrique
is
an
arch
of
the
Eclipticke
,
beginning
at
some
principall
point
in
the
Eclipticke
,
and
ending
at
the
line
of
the
true
Auge
of
the
Excentrique
:
which
principall
point
if
it
be
the
first
starre
of
the
Rams
horne
,
then
is
the
said
motion
called
the
moouing
of
the
true
Auge
from
the
first
starre
of
Aries
:
and
if
the
said
motion
or
arch
doth
begin
at
the
true
Equinox
,
then
is
the
said
motion
called
the
moouing
of
the
true
Auge
from
the
true
Equinox
.
17.
The
equacion
of
the
centre
is
an
arch
of
the
Eclipticke
,
which
is
comprehended
betwixt
the
meane
Auge
of
the
outer
blacke
orbes
,
and
the
true
Auge
of
the
Excentrique
,
as
in
the
foresaid
second
figure
of
this
Chapter
,
the
arch
K
G
in
the
Eclipticke
is
called
the
equacion
of
the
centre
:
and
this
equacion
neuer
exceedeth
7
degrees
,
i/23
ii/36
the
manner
of
the
finding
of
which
equacion
is
shewed
in
the
15
Precept
,
by
helpe
of
the
17
Cannon
in
that
Colume
,
whose
title
is
Centri
.
18.
The
true
Argument
of
the
Sunne
,
which
is
also
called
the
equated
yearely
Anomalia
,
is
an
arch
of
the
Ecliptick
,
which
is
contained
betwixt
the
line
of
the
true
Auge
of
the
Excentrique
,
and
the
line
of
the
Imaginarie
motion
of
the
Sunne
.
As
in
the
foresaid
second
figure
the
line
A
K
is
the
line
of
the
true
Auge
of
the
Excentrique
,
and
the
place
of
the
said
true
Auge
in
the
Eclipticke
is
the
point
K.
Likewise
the
line
A
N
is
the
line
of
the
Imaginarie
motion
of
the
Sunne
.
Now
the
arch
of
the
Eclipticke
,
which
is
contained
betwixt
the
2
points
K
and
N
,
is
called
the
true
Argument
or
equated
Argument
of
the
Sunne
.
For
the
difference
betwixt
the
mean
and
true
Arguments
of
the
Sunne
,
is
also
the
difference
which
is
betwixt
the
meane
and
true
Auge
of
the
Excentrique
,
which
difference
is
called
the
equacion
of
the
centre
before
defined
in
the
17
definition
of
this
Chapter
.
The
manner
of
equating
the
Argument
,
is
taught
in
the
15
Precept
.
19.
The
equall
simple
mouing
of
the
Sunne
is
an
arch
of
the
Ecliptick
,
beginning
at
the
first
starre
of
the
Rams
horne
,
and
ending
at
the
line
of
the
Imaginarie
motion
(
which
line
we
call
hereafter
the
line
of
the
meane
moouing
of
the
Sunne
)
as
in
the
foresaid
second
figure
of
this
Chapter
,
the
arch
*
N
is
the
equall
simple
moouing
of
the
Sunne
:
The
quantitie
of
which
simple
moouing
is
i/59
ii/8
iii/1
iiii/22
euery
day
,
and
according
to
this
motion
the
Sunne
maketh
one
entire
reuolution
in
365
dayes
,
6
houres
,
i/9
ii/39
20.
The
equall
compound
mouing
of
the
Sunne
is
an
arch
of
the
Eclipticke
,
beginning
at
the
meane
vernall
Equinox
,
and
ending
at
the
line
of
the
meane
moouing
of
the
Sunne
.
Whereby
it
appeareth
,
that
if
the
meane
Precession
of
the
Equinox
be
added
vnto
the
equall
simple
motion
of
the
Sunne
,
the
summe
of
that
addition
will
be
the
compound
motion
of
the
Sun
.
And
the
daily
compound
motion
is
i●●°
ii/8
iii/19
iiii/13
whereby
the
Sunne
according
to
the
equall
compound
motion
maketh
his
reuolution
in
365
dayes
,
5
houres
,
i/49
ii/16
The
manner
of
finding
of
these
two
equall
motions
of
the
Sun
,
that
is
to
say
,
the
simple
and
compound
moouing
,
is
taught
in
the
8
Precept
,
by
helpe
of
the
13
and
14
Cannons
.
21.
The
true
motion
of
the
Sunne
is
an
arch
of
the
Eclipticke
,
beginning
at
the
first
star
of
the
Rams
horne
,
and
ending
at
the
true
place
of
the
Sunne
:
and
then
is
the
said
true
motion
called
the
true
mouing
of
the
Sun
vnder
the
8
sphere
.
But
sometimes
the
said
arch
of
true
motion
is
supposed
to
begin
at
the
true
Vernall
Equinox
,
and
then
it
is
called
the
true
motion
of
the
Sunne
vnder
the
first
mouable
.
22.
The
proportionall
minutes
are
the
60
parts
wherby
the
equacions
of
the
Argument
doe
encrease
or
decrease
,
according
as
the
excentricitie
of
the
Sun
encreaseth
or
decreaseth
.
The
finding
of
which
proportionall
minutes
is
taught
in
the
fifteenth
Precept
,
and
are
set
downe
in
the
seuenteenth
Cannon
in
the
Collum
,
whose
title
is
Scrupula
Proportionalia
.
23.
The
equacion
of
the
Argument
or
yearely
Prosthapheresis
is
an
arch
of
the
Eclipticke
,
which
is
comprehended
betwixt
the
line
of
the
meane
moouing
and
the
line
of
the
true
mouing
of
the
Sun
.
And
this
equacion
of
the
Argument
is
nothing
,
when
the
Sunne
is
either
in
the
Auge
or
in
the
opposit
Auge
of
the
Excentrique
,
and
is
alwaies
greatest
in
the
meane
longitudes
of
the
Sunne
:
which
meane
longitudes
are
pointed
out
in
the
circumference
of
the
Excentrique
,
by
a
right
line
drawne
perpendicularly
vpon
the
line
of
the
true
Auge
through
the
centre
of
the
world
.
As
in
the
foresaid
second
figure
of
this
Chapter
,
the
line
A
D
is
the
line
of
the
true
Auge
of
the
Excentrique
,
which
another
line
crosseth
with
right
angles
in
the
point
A
,
which
perpendicular
line
is
the
line
T
V
,
and
beeing
produced
vnto
the
Excentrique
,
sheweth
the
points
T
and
V
to
be
the
points
of
meane
longitudes
.
And
the
greatest
equacion
of
the
Argument
that
can
be
,
which
is
when
the
centre
of
the
Excentrique
is
in
the
Auge
of
the
little
circle
,
is
two
degrees
,
i/23
ii/24
and
that
is
when
the
Sun
is
distant
from
the
true
Auge
or
from
the
Auge
of
the
Excentrique
93
degrees
.
But
when
the
centre
of
the
Excentrique
is
in
the
opposit
Auge
of
the
said
little
circle
,
then
is
the
greatest
equacion
of
the
Argument
no
more
but
1
degree
,
i/50
ii/41
and
that
is
when
the
distance
of
the
Sunne
from
the
true
Auge
,
is
92
degrees
.
And
this
equacion
is
called
in
the
tables
,
The
equacion
of
the
orbe
:
the
finding
whereof
is
taught
in
the
15
Precept
,
by
helpe
of
the
17
Cannon
,
in
the
Collum
whose
title
is
Orbis
.
24.
The
true
argument
of
the
Sunne
,
is
the
distance
of
the
Sunne
from
the
true
Auge
of
his
Excentrique
.
25.
The
excesse
or
diuersitie
of
the
diameter
,
is
an
arch
of
the
Eclipticke
,
whereby
the
equacion
of
the
argument
(
the
centre
of
the
Excentrique
being
in
the
Auge
of
the
little
circle
)
exceedeth
the
equacion
of
the
argument
,
when
the
centre
of
the
Excentrique
is
in
the
opposit
Auge
of
the
little
circle
.
The
true
argument
of
the
Sunne
being
of
one selfe
quantitie
in
each
position
of
the
centre
of
the
Excentrique
in
the
circumference
of
the
little
circle
.
For
the
equacions
of
the
argument
doe
decrease
continually
,
so
long
as
the
centre
of
the
Excentrique
is
descending
from
the
Auge
of
the
little
circle
,
vntill
it
come
to
the
opposit
Auge
of
the
said
litle
circle
,
and
from
thence
do
begin
againe
to
encrease
,
vntill
the
centre
of
the
Excentrique
returneth
again
vnto
the
Auge
of
the
little
circle
.
The
finding
of
which
Excesse
is
taught
in
the
15
Precept
,
and
is
set
downe
in
the
17
Cannon
in
that
Colume
,
whose
title
is
Excessus
.
26.
The
coequated
and
true
equacion
,
which
is
otherwise
called
the
absolute
equacion
of
the
orbe
,
is
an
arch
compounded
of
the
true
equacion
of
the
argument
,
and
of
the
excesse
,
proportionable
vnto
the
proportionall
minutes
.
CHAP.
IX
.
Of
the
third
Heauen
,
or
Heauen
of
Venus
.
THe
next
Heauen
vnder
that
of
the
Sunne
,
is
the
Heauen
of
Venus
,
which
hath
his
proper
mouing
from
West
to
East
.
This
Heauen
hath
foure
orbes
,
as
the
Heauen
of
the
three
higher
Planets
haue
,
that
is
to
say
,
two
,
which
are
called
the
deferents
of
the
two
Auges
,
then
the
Orbe
Excentrique
,
or
the
deferent
of
the
Epicicle
,
and
the
Epicicle
it selfe
,
in
the
circumference
whereof
the
Planet
is
alwayes
carried
.
And
because
I
haue
defined
the
said
orbes
in
the
fift
Chapter
,
I
thinke
them
needlesse
to
be
here
againe
repeated
:
and
therefore
I
referre
you
to
that
Chapter
:
For
the
Orbes
of
Venus
doe
not
differ
from
the
Orbes
of
Saturne
in
shape
and
position
,
but
onely
in
the
quantitie
of
their
motions
.
The
deferents
of
the
Auge
and
opposit
Auge
in
the
Heauen
of
Venus
do
continue
without
any
motion
,
and
the
place
of
her
Auge
,
which
is
in
the
Eclipticke
of
the
eight
Heauen
,
is
alwaies
48
degrees
,
i/21
reckoning
from
the
first
starre
of
the
Rams
horne
:
and
the
opposit
Auge
is
alwaies
3
Sex
.
48
degrees
,
i/21
from
the
first
starre
of
the
Rams
horne
,
accounting
the
said
distance
according
to
the
succession
of
the
signes
.
The
Excentrique
of
Venus
mooueth
according
to
the
succession
of
the
signes
vpon
his
proper
centre
,
which
is
differing
from
the
centre
of
the
world
,
and
the
poles
and
axletree
of
this
Orbe
are
moouable
,
sometimes
approching
neare
vnto
the
poles
of
the
Eclipticke
,
and
at
other
times
are
further
off
.
Howbeit
this
Excentrique
maketh
one
entire
reuolution
,
beginning
at
the
first
starre
of
the
Rams
horn
in
365
dayes
,
6
houres
,
i/9
ii/39
so
as
the
moouing
of
this
orbe
is
equall
vnto
the
simple
equall
mouing
of
the
Sunne
,
before
defined
in
the
19
definition
of
the
8
Chapter
.
And
therefore
the
line
of
the
meane
moouing
of
the
centre
of
Venus
her
Epicicle
,
is
alwaies
in
the
same
place
of
the
Zodiake
,
in
which
the
line
of
the
meane
mouing
of
the
Sunne
is
:
so
as
in
seeking
for
the
meane
mouing
of
Venus
her
longitude
,
you
are
to
find
the
simple
equall
mouing
of
the
Sunne
in
such
order
as
the
eight
Precept
teacheth
:
from
which
if
you
subtract
48
degrees
,
i/21
the
remainer
will
shew
the
meane
Anomalia
of
the
Excentrique
,
or
meane
centre
,
before
defined
in
the
13
definition
of
the
7
Chapter
.
Which
if
you
subtract
out
of
the
true
motion
of
the
longitude
of
the
Epicicle
(
which
is
defined
in
the
17
definition
of
the
7
Chapter
)
the
remainer
will
be
the
true
centre
or
the
equated
Anomalia
of
the
Excentrique
,
which
is
defined
in
the
16
definition
of
the
7
Chapter
.
The
Epicicle
of
Venus
hath
also
his
proper
motion
in
the
Excentrique
,
whereby
it
swarueth
from
the
plane
of
the
Excentrique
.
The
semidiameter
of
the
Epicicle
is
43
degrees
,
i/10
such
like
degrees
,
as
the
semidiameter
of
the
Excentrique
containeth
60
degrees
.
And
because
that
the
line
of
the
meane
moouing
of
her
centre
is
all
one
with
the
line
of
the
meane
moouing
of
the
Sunne
,
it
may
easily
appeare
,
that
the
starre
or
Planet
will
be
twice
conjoined
with
the
Sunne
in
one
reuolution
of
her
Epicicle
,
that
is
to
say
,
once
in
the
Auge
,
and
once
in
the
opposit
Auge
of
the
Epicicle
.
But
if
she
be
neither
in
the
Auge
nor
in
the
opposit
Auge
of
the
Epicicle
,
then
in
her
ascending
from
the
opposit
Auge
of
her
Epicicle
vnto
the
Auge
thereof
she
goeth
before
the
Sunne
,
and
is
our
morning
star
,
called
of
the
Latines
Lucifer
.
But
in
descending
from
the
Auge
of
her
Epicicle
vnto
the
opposit
Auge
therof
,
she
goeth
after
the
Sunne
,
and
is
our
euening
star
,
called
of
the
Latines
Hesperus
.
The
daily
mouing
of
the
Anomalia
of
Commutation
(
which
was
defined
in
the
23
definition
of
the
7
chapter
)
is
i/16
ii/59
iii/28
and
the
yearely
motion
thereof
is
3
Sex
.
45
degrees
,
i/1
ii/45
iii/21
and
maketh
one
entire
reuolution
in
one
yeare
218
dayes
,
21
houres
,
15
minutes
.
The
greatest
equacion
of
her
Epicicle
is
45
degrees
,
i/10
ii/20
if
the
centre
of
the
Epicicle
be
in
the
Auge
of
her
Excentrique
,
and
that
the
Planet
bee
distant
from
the
Auge
of
the
Epicicle
any
way
2
Sex
.
15
degrees
,
i/5
but
if
the
centre
of
the
Epicicle
be
in
the
opposit
Auge
of
the
Excentrique
,
and
that
the
Planet
be
distant
2
Sex
.
17
degrees
from
the
Auge
of
the
Epicicle
,
then
is
the
greatest
equacion
of
the
argument
of
Venus
46
degrees
,
i/51
ii/29
What
other
points
,
lines
,
and
arches
are
needfull
to
be
known
for
the
calculating
of
her
motion
at
any
time
,
are
set
downe
before
in
the
7
Chapter
,
vnto
which
I
referre
you
,
onely
the
finding
of
the
equacions
belonging
vnto
this
Planet
,
must
be
sought
for
in
the
22
Cannon
,
in
such
order
as
is
taught
in
the
34
Precept
.
And
thus
I
end
with
Venus
.
CHAP.
X.
Of
the
second
Heauen
,
or
Heauen
of
Mercurie
.
NExt
vnder
the
Heauen
of
Venus
is
the
Heauen
of
Mercurie
,
which
consisteth
of
six
orbes
,
that
is
to
say
,
2
deferents
of
the
Auge
of
the
circle
Equant
,
two
deferents
of
the
Auge
of
the
Anomalia
of
the
Excentrique
,
the
fift
orbe
is
the
Excentrique
,
and
the
sixt
is
the
Epicicle
.
The
fiue
first
orbes
are
in
all
respects
like
vnto
the
fiue
orbes
of
the
Sun
,
whereof
wee
spake
in
the
8
Chapter
.
And
the
sixt
orbe
,
which
is
the
Epicicle
,
is
like
vnto
the
Epicicle
in
the
other
Planets
whereof
we
spake
in
the
fift
Chapter
.
Notwithstanding
I
think
it
not
amisse
for
your
better
vnderstanding
to
set
downe
the
said
orbes
in
this
figure
here
next
following
.
¶
The
first
figure
belonging
to
the
Theorique
of
Mercurie
.
IN
this
figure
the
two
outermost
circles
,
in
which
are
set
the
caracters
of
the
twelue
signes
,
doe
signifie
the
two
Ecliptickes
,
one
of
the
first
mouable
,
the
other
the
Eclipticke
of
the
eight
Heauen
.
The
two
broad
&
black
circles
doe
signifie
the
two
deferents
of
the
Auge
of
the
circle
Equant
,
and
the
two
shaddowed
circles
do
signifie
the
deferents
of
the
Auge
of
the
Excentrique
,
and
betwixt
them
is
a
broad
white
circle
,
which
representeth
the
Excentrique
:
in
the
middest
whereof
is
the
circumference
of
a
circle
,
which
the
centre
of
the
Epicicle
is
imagined
to
describe
.
And
another
circumference
is
also
drawn
in
the
said
Excentrique
,
which
cutteth
the
former
circumference
in
the
two
points
I
and
G
,
and
this
circumference
signifieth
the
circle
Equant
.
Againe
,
in
the
Excentrique
is
another
litle
circle
,
representing
the
Epicicle
,
the
centre
whereof
is
the
point
H
,
and
in
the
circumference
thereof
is
a
little
starre
,
which
signifieth
the
Planet
of
Mercurie
.
The
point
in
the
middle
of
●●is
Figure
,
which
is
marked
with
the
letter
A
,
signifieth
the
centre
of
the
world
,
and
C
is
the
centre
of
the
Excentrique
,
and
B
is
the
centre
of
a
litle
circle
,
in
the
circumference
whereof
the
centre
C
alwaies
moueth
about
the
centre
B
,
and
D
is
the
centre
of
the
circle
Equant
.
The
motion
of
the
two
deferents
of
the
Auge
of
the
Equant
is
like
vnto
the
motion
of
the
deferents
of
the
meane
Auge
of
the
Sun
,
for
it
is
equall
and
regular
vpon
the
centre
of
the
world
according
to
the
succession
of
the
signs
,
that
is
to
say
,
from
West
to
East
vpon
their
own
proper
poles
,
which
are
equally
distant
from
the
poles
of
the
Eclipticke
:
and
the
daily
motion
of
these
orbes
is
iii/9
iiii/31
and
their
yearely
motion
is
ii/57
iii/50
iiii/38
and
so
do
make
one
entire
reuolution
in
22700
Aegyptian
yeares
.
The
excentricitie
,
that
is
to
say
,
the
distance
of
the
centre
of
the
circle
Equant
from
the
centre
of
the
world
,
is
3
degrees
,
such
degrees
as
the
semidiameter
of
the
said
circle
Equant
containeth
60
degrees
.
The
line
A
B
N
signifieth
the
line
of
the
Auge
of
the
circle
Equant
:
and
this
line
is
drawne
through
the
centre
of
the
world
,
and
also
through
the
centre
of
the
little
circle
,
marked
with
B
,
euen
as
the
line
of
the
meane
Auge
of
the
Sunne
is
wont
to
be
drawne
,
as
was
said
in
the
third
definition
of
the
eight
Chapter
.
And
the
place
of
the
Auge
of
the
said
circle
Equant
is
marked
with
the
letter
N
,
like
as
the
point
M
is
the
place
of
the
opposit
Auge
of
the
said
circle
Equant
.
And
the
arch
of
the
eight
Eclipticke
,
marked
with
the
first
starre
of
the
Rams
horne
,
and
with
the
letters
M
N
,
is
the
motion
of
the
Auge
of
the
Equant
vnder
the
eight
sphere
.
But
the
arch
D
M
N
is
the
motion
of
the
said
Auge
vnder
the
first
mouable
or
from
the
true
Equinoctiall
point
,
marked
in
the
said
Eclipticke
of
the
first
mouable
with
the
letter
D.
The
deferents
of
the
Excentrique
doe
moue
regularly
about
the
centre
of
the
little
circle
,
contrarie
to
the
succession
of
the
signes
,
as
the
orbes
of
the
Anomalia
of
the
Auge
of
the
Sunne
doe
mooue
namely
vpon
their
proper
poles
and
axletree
,
and
do
make
their
reuolution
in
365
dayes
,
6
houres
,
i/33
ii/8
and
their
daily
motion
is
i/59
ii/8
iii●°
iiii/52
And
the
centre
of
the
little
circle
is
distant
from
the
centre
of
the
world
6
degrees
,
and
from
the
centre
of
the
Equant
3
degrees
,
such
degrees
I
mean
as
the
semidiameter
of
the
Equant
containeth
60
degrees
.
By
meanes
of
which
motion
,
the
excentricitie
of
the
Planet
changeth
euery
day
,
and
is
greatest
when
the
centre
of
the
Excentrique
is
in
the
Auge
of
the
little
circle
,
and
the
said
excentricitie
is
least
when
the
centre
of
the
said
Excentrique
is
in
the
opposit
Auge
of
the
said
little
circle
,
and
the
said
excentricitie
is
meane
when
the
centre
of
the
centre
of
the
Excentrique
is
in
the
middle
point
betwixt
the
Auge
and
opposit
Auge
of
the
said
little
circle
.
All
which
things
were
shewed
in
the
7
,
8
,
and
9
definitions
of
the
8
Chapter
.
The
Excentrique
hath
his
proper
motion
vpon
his
owne
poles
,
which
are
also
moouable
,
and
the
motion
thereof
is
according
to
the
succession
of
the
signs
,
which
motion
although
it
be
irregular
and
vnequall
in
respect
of
the
centre
of
the
world
,
yet
is
the
same
regular
and
equall
in
respect
of
the
centre
of
the
circle
Equant
:
and
the
daily
motion
is
i/59
ii/8
iii/1
iiii/52
and
maketh
one
entire
reuolution
in
365
dayes
,
6
houres
,
i/33
ii/8
And
this
motion
is
found
by
subtracting
the
daily
motion
of
the
deferents
of
the
Auge
of
the
Equant
(
which
is
iii/9
iiii/31
)
out
of
the
daily
motion
of
the
longitude
of
Mercurie
,
which
is
i/59
ii/8
iii/11
iiii/22
for
so
the
remainer
wil
be
i/59
ii/8
iii/1
iiii/52
which
summe
is
the
daily
motion
of
the
Excentrique
,
counting
from
the
line
of
the
Auge
of
the
Equant
.
And
you
haue
to
note
,
that
the
motion
of
the
longitude
of
Mercurie
is
equall
vnto
the
simple
equall
mouing
of
the
Sunne
,
so
as
when
you
are
to
find
out
the
equall
longitude
of
Mercurie
,
you
haue
to
seek
in
the
Prutenical
tables
the
equal
simple
mouing
of
the
Sunne
for
the
time
giuen
:
and
as
for
the
moouing
of
the
Anomalia
of
the
Excentrique
,
you
are
taught
how
to
find
the
same
at
any
time
by
the
8
Precept
,
by
helpe
of
the
13
and
14
Cannons
,
in
the
Collum
,
whose
title
is
Apogei
Mercurij
.
As
for
the
true
Auge
of
the
Excentrique
,
the
same
is
found
as
was
shewed
,
in
the
15
definition
of
the
8
Chap.
The
Epicicle
of
Mercurie
hath
his
proper
motion
vpon
his
mouable
axletree
,
and
the
daily
motion
therof
is
3
degrees
,
i/6
ii/24
iii/14
iiii/5
v/36·
and
maketh
one
entire
reuolution
in
115
dayes
,
21
houres
,
i/3
ii/26
iii/54
and
the
semidiameter
of
the
Epicicle
is
22
degrees
,
i/30
such
degrees
as
the
semidiameter
of
the
Excentrique
containeth
60
,
like
as
was
said
before
of
Venus
:
For
since
the
motion
of
his
longitude
is
alwaies
equall
vnto
the
equall
simple
mouing
of
the
Sunne
,
it
cannot
be
but
that
this
Planet
must
be
alwaies
neare
vnto
the
Sunne
;
sometimes
going
before
the
same
,
and
then
it
may
be
seene
in
the
morning
before
the
Sunne
riseth
;
and
sometimes
it
followeth
the
Sun
,
and
then
it
may
be
seene
in
the
euening
.
Lastly
,
the
greatest
equacion
of
the
Argument
of
Mercurie
,
when
the
centre
of
his
Epicicle
is
in
the
Auge
of
his
Excentrique
(
the
Planet
being
then
distant
from
the
Auge
of
the
Epicicle
109
degrees
)
is
19
degrees
,
i/3
ii/6
But
if
he
be
distant
114
degrees
from
the
Auge
of
his
Epicicle
,
and
that
the
centre
of
the
Epicicle
be
in
the
opposit
Auge
of
the
Excentrique
,
then
is
the
greatest
equacion
of
his
argument
23
degrees
,
i●1·
ii/35
Now
,
as
for
the
points
,
lines
,
and
arches
belonging
to
the
calculating
of
the
Motions
of
Mercurie
,
because
they
doe
not
differ
from
those
which
we
haue
shewed
in
the
5
Chapter
,
I
therefore
referre
you
to
that
Chapter
:
and
as
for
the
particular
equacions
,
you
shal
find
them
set
down
in
the
23
Cannon
of
the
Prutenicall
Tables
.
CHAP.
XI
.
Of
the
first
Heauen
,
or
Heauen
of
the
Moone
.
THe
last
or
lowest
Heauen
is
the
Heauen
of
the
Moone
,
and
it
consisteth
of
foure
orbes
,
whereof
the
first
is
called
the
orbe
or
circle
of
Nodes
,
or
the
deferent
of
the
head
and
taile
of
the
Dragon
.
The
next
orbe
is
called
the
deferent
of
the
Epicicles
.
The
third
orbe
is
called
the
first
Epicicle
.
And
the
fourth
is
the
second
Epicicle
.
All
which
orbes
are
set
down
in
this
figure
following
.
¶
The
first
figure
belonging
to
the
Theorique
of
the
Moone
.
You
shall
find
the
two
Epicicles
of
the
Moone
more
plainely
set
downe
in
the
third
figure
here
following
.
IN
the
former
figure
,
the
two
outermost
circles
do
signifie
the
two
Eclipticks
,
as
in
the
Heauen
of
Mercurie
.
Next
vnto
them
is
another
white
circle
,
in
which
are
set
the
caracters
of
the
head
and
taile
of
the
Dragon
,
signifying
the
deferent
of
the
Nodes
,
and
in
the
middle
thereof
is
the
circumference
of
a
circle
,
in
which
the
two
Nodes
doe
continually
moue
.
Next
vnto
that
is
a
great
broad
and
blacke
orbe
,
signifying
the
deferent
of
the
Epicicles
:
in
which
orbe
is
a
shadowed
circle
,
which
representeth
the
first
Epicicle
,
whose
centre
is
marked
with
the
letter
E
:
and
vpon
the
perpendicular
line
C
B
are
placed
two
other
little
circles
,
one
aboue
,
and
another
beneath
the
centre
E
,
both
whose
centres
are
marked
with
the
letter
F
,
and
these
two
little
circles
beeing
white
within
,
doe
signifie
the
second
Epicicles
.
And
in
the
circumference
of
either
of
them
is
set
the
caracter
of
the
Moone
.
The
point
A
signifieth
the
centre
of
the
world
,
the
point
B
signifieth
the
Auge
of
the
first
Epicicle
,
and
the
point
C
is
the
opposit
Auge
of
the
said
first
Epicicle
.
1.
The
deferent
of
the
Nodes
is
an
orbe
in
the
Theorique
of
the
Moone
,
in
which
the
Nodes
doe
continually
moue
,
marked
in
the
former
figure
with
the
head
and
taile
of
the
Dragon
,
describing
the
middle
circle
of
the
said
orbe
.
This
orbe
is
concentricall
,
that
is
,
hath
one selfe
centre
with
the
Zodiake
:
and
the
motion
of
this
orbe
is
regular
and
equall
in
respect
of
the
centre
of
the
earth
,
vpon
the
axletree
and
poles
of
the
Zodiake
,
contrarie
to
the
succession
of
the
signes
,
and
the
daily
motion
thereof
is
i/3
ii/10
iii/47
and
in
one
yeare
mooueth
19
degrees
,
i/10
ii/3
iii/44
and
so
maketh
one
entire
reuolution
in
18
Aegyptian
yeares
,
223
dayes
,
6
houres
,
i/12
and
by
the
violence
or
strength
of
his
motion
,
he
carrieth
the
other
orbes
round
about
with
him
.
2.
The
deferent
of
the
Epicicles
is
the
foresaid
blacke
Orbe
in
the
Theorique
of
the
Moone
,
in
which
the
Epicicles
of
the
Moone
are
carried
continually
about
.
And
this
blacke
orbe
hath
his
owne
proper
motion
,
which
is
according
to
the
succession
of
the
signes
,
and
is
regular
in
respect
of
the
centre
of
the
world
,
marked
with
the
letter
A
,
and
mooueth
vpon
his
owne
axletree
,
which
cutteth
the
axletree
of
the
Eclipticke
in
the
point
A
,
the
centre
of
the
world
,
and
the
poles
thereof
are
alwayes
no
more
but
fiue
degrees
from
the
Eclipticke
:
whereby
it
happeneth
,
that
the
plane
of
this
Orbe
cutteth
the
plane
of
the
Eclipticke
in
two
points
,
which
are
called
the
Nodes
,
or
the
head
and
taile
of
the
Dragon
.
For
the
vnderstanding
whereof
I
haue
set
downe
this
other
figure
next
following
.
¶
The
second
figure
belonging
to
the
Theorique
of
the
Moone
.
IN
which
figure
the
circle
F
C
E
K
signifieth
the
plane
of
the
Eclipticke
,
and
the
centre
thereof
is
marked
with
the
point
A
:
and
the
circle
F
B
E
I
signifieth
the
plane
of
the
deferent
of
the
Epicicle
,
in
the
circumference
whereof
is
the
centre
of
the
first
Epicicle
,
marked
with
the
letter
L
;
and
in
the
circumference
thereof
is
the
centre
of
the
second
Epicicle
,
marked
with
the
letter
M
,
and
in
the
circumference
thereof
is
the
character
of
the
Moone
:
and
the
centre
of
the
deferent
of
the
Epicicle
,
is
the
same
which
the
Eclipticke
hath
,
that
is
to
say
,
the
centre
A
;
and
this
circle
crosseth
the
Eclipticke
in
two
opposit
points
,
that
is
to
say
,
in
the
point
F
and
E
,
called
the
Nodes
,
the
one
of
which
is
called
the
head
of
the
Dragon
,
marked
with
this
caracter
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
,
and
the
other
is
called
the
taile
of
the
Dragon
,
marked
with
this
caracter
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
.
Vnto
either
of
which
two
Nodes
when
the
Moon
commeth
,
then
she
is
in
the
Eclipticke
,
and
in
her
moouing
from
either
of
the
said
two
Nodes
shee
goeth
further
and
further
from
the
Eclipticke
,
vntill
she
come
to
one
of
the
2
limits
of
her
latitude
either
North
or
South
.
3.
Whereof
her
North
limit
is
marked
in
this
figure
with
the
letter
B
,
and
her
South
limit
with
the
letter
l
,
either
of
which
limits
is
neuer
more
distant
from
the
Ecliptick
than
fiue
degrees
,
but
from
the
Nodes
each
limit
is
distant
90
degrees
.
4.
And
hereby
you
may
gather
,
that
the
two
Nodes
are
nothing
els
but
two
points
,
in
which
the
plane
of
the
deferent
of
the
Epicicles
dooth
crosse
the
plane
of
the
Eclipticke
.
And
the
one
of
these
Nodes
is
called
the
ascending
Node
or
head
of
the
Dragon
,
and
the
other
is
called
the
descending
Node
or
the
taile
of
the
Dragon
.
5.
The
head
of
the
Dragon
is
that
Node
,
vnto
which
when
the
Moon
commeth
,
she
beginneth
to
go
Northward
from
the
Eclipticke
:
and
that
Node
is
marked
with
this
caracter
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
.
6.
The
taile
of
the
Dragon
is
that
Node
,
vnto
which
when
the
Moone
commeth
,
she
beginneth
to
go
Southward
from
the
Ecliptick
,
which
Node
is
marked
with
this
caracter
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
.
7.
The
line
of
the
mean
or
true
mouing
of
the
Nodes
is
a
line
drawne
from
the
centre
of
the
world
vnto
any
of
the
said
Nodes
:
as
in
the
former
figure
the
line
A
F
signifieth
the
line
of
the
mouing
of
the
head
of
the
Dragon
,
and
the
line
A
E
signifieth
the
line
of
the
mouing
of
the
taile
of
the
Dragon
.
8.
The
meane
mouing
of
the
Nodes
is
an
arch
of
the
Eclipticke
,
beginning
at
the
first
star
of
the
Rams
home
or
at
the
first
true
Vernall
Equinox
,
and
endeth
at
the
line
of
the
mouing
of
the
Node
,
so
as
the
said
arch
bee
reckoned
contrarie
to
the
succession
of
the
signes
.
9.
The
true
moouing
of
the
Nodes
is
an
arch
of
the
Eclipticke
,
beginning
at
the
first
starre
of
the
Rams
horn
,
if
the
same
be
reckoned
in
the
Eclipticke
of
the
eight
Heauen
,
or
at
the
true
Vernall
Equinox
,
if
the
same
bee
reckoned
in
the
Eclipticke
of
the
first
mouable
,
and
ending
at
the
line
of
the
mouing
of
the
Node
,
so
as
the
said
arch
be
numbered
according
to
the
succession
of
the
signes
.
10.
The
line
of
the
meane
mouing
of
the
Moone
is
a
line
drawne
from
the
centre
of
the
world
through
the
centre
of
the
first
Epicicle
,
and
so
forth
vnto
the
Eclipticke
.
As
for
example
,
in
the
first
figure
the
right
line
A
E
B
is
the
line
of
the
meane
mouing
of
the
Moone
.
11.
The
place
of
the
centre
of
the
first
Epicicle
in
the
Eclipticke
,
is
that
point
in
which
the
line
of
the
meane
mouing
of
the
Moone
falleth
in
the
Eclipticke
.
As
in
the
said
first
figure
the
point
B
in
the
Eclipticke
is
the
place
of
the
centre
of
the
first
Epicicle
.
12.
The
meane
simple
moouing
of
the
Moones
longitude
,
is
an
arch
of
the
Eclipticke
,
beginning
at
the
first
starre
of
the
Rams
horne
,
and
ending
at
the
place
of
the
centre
of
the
first
Epicicle
.
As
in
the
said
first
figure
the
arch
*
H
K
is
called
the
mean
,
equall
,
or
simple
mouing
of
the
Moones
longitude
:
and
the
daily
mouing
of
this
simple
longitude
is
13
degrees
,
i/10
ii/34
iii/53
and
according
vnto
this
motion
the
Moone
maketh
her
reuolution
in
27
dayes
,
7
houres
,
i/43
ii/7
for
in
this
time
shee
returneth
vnto
the
first
starre
of
the
Rams
horne
,
and
this
is
called
the
Periodicall
moneth
.
As
in
the
first
figure
the
arch
*
H
K
is
the
equall
simple
mouing
of
the
longitude
of
the
Moone
.
13.
But
if
the
said
motion
dooth
begin
at
the
meane
place
of
the
Sunne
,
that
is
,
at
the
line
of
the
meane
mouing
of
the
Sunne
,
then
is
it
called
the
equall
or
meane
longitude
of
the
Moone
from
the
Sunne
,
and
then
the
daily
motion
is
12
degrees
i/11
ii/26
iii/41
and
according
vnto
this
,
the
Moone
maketh
her
reuolution
in
29
dayes
,
12
houres
,
i/44
ii/3
and
the
time
of
this
reuolution
is
called
the
Synodicall
moneth
.
So
as
if
you
subtract
the
equall
simple
moouing
of
the
Sunne
out
of
the
equall
simple
moouing
of
the
Moones
longitude
,
the
remainer
will
shew
the
meane
longitude
of
the
Moone
from
the
Sunne
.
As
in
the
said
first
figure
suppose
the
arch
*
H
to
be
the
equall
simple
mouing
of
the
Sunne
,
and
the
arch
*
H
K
to
be
the
equall
simple
moouing
of
the
Moones
longitude
.
Now
if
you
subtract
*
H
out
of
*
H
K
,
the
remainer
will
be
H
K
,
and
that
is
the
meane
longitude
of
the
Moone
from
the
Sunne
.
And
the
finding
of
this
at
any
time
giuen
,
is
taught
in
the
8
Precept
,
by
helpe
of
the
13
and
14
Cannons
,
in
the
Collume
whose
title
is
Longitudo
media
à
Sole
.
14.
And
againe
,
sometimes
the
meane
moouing
of
the
centre
of
the
first
Epicicle
or
of
the
Moone
,
is
accounted
to
begin
at
the
North
limit
,
and
then
is
it
called
by
Ptolomey
and
Copernicus
the
mean
motion
of
the
latitude
of
the
Moone
;
because
that
after
the
same
be
corrected
,
it
sheweth
the
true
latitude
of
the
Moon
:
&
the
finding
of
this
motion
at
any
time
is
to
be
found
in
such
order
as
is
shewed
in
the
8
Precept
,
by
help
of
the
13
and
14
Cannons
in
the
Colume
,
whose
title
is
Latitudinis
Lunae
.
15.
But
Alphonsus
and
his
followers
make
the
beginning
of
the
said
motion
to
be
at
the
head
of
the
Dragon
,
and
is
called
by
them
the
Argument
of
the
latitude
of
the
Moone
,
and
the
daily
motion
of
the
Moons
latitude
is
13
degrees
,
i/1
ii/45
iii●9·
and
according
vnto
this
motion
she
maketh
her
reuolution
in
27
dayes
,
5
houres
,
i/5
ii/36
And
the
Argument
of
the
Moones
latitude
is
to
be
sound
at
any
time
giuen
,
by
adding
of
90
degrees
vnto
the
mean
motion
of
her
latitude
:
the
manner
of
the
finding
whereof
was
shewed
in
the
14
definition
of
this
Chapter
.
16.
And
you
haue
to
note
,
that
according
to
the
motion
of
the
deferent
of
the
Epicicle
,
the
centre
of
the
Epicicle
is
imagined
to
describe
a
circle
in
the
middle
of
the
said
deferent
:
which
circle
is
called
the
circle
of
the
mouing
of
the
centre
;
and
this
circle
is
signified
in
the
first
figure
by
the
white
circle
in
the
middle
of
the
blacke
deferent
of
the
Epicicle
,
described
by
the
centre
of
the
first
Epicicle
.
17.
The
first
Epicicle
is
an
orbe
in
the
Theorique
of
the
Moone
,
which
continually
carieth
about
the
second
Epicicle
of
the
Moone
.
This
orbe
hath
his
owne
proper
motion
about
his
owne
poles
and
axletree
,
which
axletree
is
perpendicular
vnto
the
plane
of
the
deferent
of
the
Epicicle
,
and
is
paralell
vnto
the
said
axletree
of
the
said
deferent
:
wherby
it
commeth
to
passe
,
that
the
plane
of
this
first
Epicicle
is
alwaies
in
the
plane
of
his
deferent
.
And
the
motion
of
this
Epicicle
is
contrary
to
the
succession
of
the
signes
,
and
the
daily
motion
thereof
is
13
degrees
,
i/3
ii/53
iii/56
and
maketh
one
entire
reuolution
in
27
dayes
and
13
houres
almost
:
and
the
semidiameter
of
this
Epicicle
is
6
degrees
,
i/35
whereof
the
semidiameter
of
the
mouing
of
his
centre
containeth
60.
18.
The
Auge
of
the
first
Epicicle
is
a
point
in
the
superficies
thereof
,
which
is
furthest
distant
from
the
centre
of
the
earth
.
And
the
opposit
Auge
is
that
point
which
is
nearest
vnto
the
centre
of
the
earth
.
And
the
Auge
and
opposit
Auge
is
determined
by
a
right
line
drawne
from
the
centre
of
the
earth
vnto
the
circumference
of
the
said
first
Epicicle
,
through
the
centre
of
the
same
.
As
in
the
first
figure
the
point
B
is
the
Auge
of
the
first
Epicicle
,
and
the
point
C
the
opposit
Auge
thereof
.
19.
The
meane
Anomalia
of
the
Epicicle
,
which
is
otherwise
called
the
meane
Argument
,
is
an
arch
of
the
first
Epicicle
,
containing
the
distance
betwixt
the
centre
of
the
second
Epicicle
,
and
the
Auge
of
the
first
Epicicle
.
And
this
is
determined
by
a
right
line
drawne
from
the
centre
of
the
first
Epicicle
vnto
the
centre
of
the
second
Epicicle
,
as
this
figure
next
following
sheweth
.
¶
The
third
figure
belonging
to
the
Theorique
of
the
Moone
.
IN
which
figure
,
the
outermost
circle
representeth
the
Eclipticke
,
and
the
lesser
circle
within
that
is
a
circle
which
the
centre
of
the
first
Epicicle
is
imagined
to
describe
.
The
semidiameter
whereof
is
the
line
A
E
,
and
the
point
E
signifieth
the
centre
of
the
first
Epicicle
,
whose
semidiameter
is
the
line
E
B
,
and
the
point
B
is
the
Auge
,
and
the
point
C
the
opposit
Auge
thereof
:
the
point
F
signifieth
the
centre
of
the
second
Epicicle
,
and
the
arch
B
F
is
the
meane
Anomalia
of
the
Moon
:
and
this
is
called
Anomalia
motus
in
the
Prutenicall
tables
,
the
finding
whereof
is
taught
in
the
8
Precept
by
helpe
of
the
13
and
14
Cannons
,
in
the
Colume
,
whose
title
is
Anomalia
Lunae
.
20.
The
first
Epicicle
is
imagined
to
be
deuided
into
two
parts
,
whereof
the
one
part
is
called
the
higher
or
vpper
part
,
and
the
other
is
called
the
lower
part
of
the
Epicicle
.
And
these
two
parts
are
shewed
by
two
right
lines
,
drawne
from
the
centre
of
the
world
,
marked
with
A
,
so
as
they
touch
the
said
first
Epicicle
on
both
sides
.
As
in
this
present
figure
the
two
lines
,
A
L
and
A
M
are
drawne
from
the
centre
A
,
and
doe
touch
the
first
Epicicle
in
the
points
L
and
M
:
and
that
part
of
the
Epicicle
,
which
is
aboue
the
points
L
and
M
,
marked
with
the
letters
L
B
F
M
,
is
the
higher
part
,
but
the
other
part
,
viz.
L
C
M
,
is
the
lower
part
of
the
Epicicle
.
21.
And
the
two
points
L
and
M
are
the
Touch-points
of
the
first
Epicicle
.
22.
The
second
Epicicle
is
an
Orbe
in
the
Theorique
of
the
Moone
,
in
the
circumference
whereof
the
bodie
of
the
Moone
is
alwaies
carried
about
.
The
plane
of
this
Epicicle
is
alwaies
in
the
plane
of
the
first
,
and
the
axletree
thereof
is
perpendicular
vnto
the
plane
of
the
first
Epicicle
,
and
therfore
the
axletrees
of
the
two
Epicicles
and
of
the
deferent
of
the
first
Epicicle
,
are
paralels
one
to
another
.
And
the
mouing
of
this
second
Epicicle
is
contrarie
vnto
the
moouing
of
the
first
Epicicle
:
and
the
motion
hereof
beginneth
at
the
Auge
of
the
second
Epicicle
.
23.
The
Auge
of
the
second
Epicicle
is
that
point
in
the
circumference
of
the
said
second
Epicicle
,
which
is
nearest
vnto
the
centre
of
the
first
Epicicle
:
and
the
opposit
Auge
thereof
is
furthest
from
the
centre
of
the
said
Epicicle
:
for
these
Auges
haue
respect
to
the
centre
of
the
first
Epicicle
,
and
not
to
the
centre
of
the
earth
.
24.
The
Anomalia
of
the
Excentrique
,
which
some
call
the
centre
of
the
Moone
,
is
an
arch
of
the
second
Epicicle
,
beginning
at
the
Auge
of
the
said
second
Epicicle
,
and
ending
at
the
body
of
the
Moone
.
As
in
the
third
figure
of
this
Chapter
the
point
R
signifieth
the
Auge
of
the
second
Epicicle
,
and
the
place
of
the
Moon
is
signified
by
her
proper
caracter
in
the
circumference
thereof
,
and
the
arch
of
the
said
little
circle
,
contained
betwixt
R
and
the
caracter
of
the
Moone
,
is
called
the
Anomalia
of
the
Excentrique
,
or
centre
of
the
Moone
.
And
this
Anomalia
is
called
in
the
Prutenicall
Tables
Longitudo
Duplicata
,
or
the
double
longitude
of
the
Moone
from
the
Sunne
:
and
the
simple
longitude
was
defined
before
in
the
13
definition
of
this
Chapter
.
And
it
is
called
the
doubled
longitude
,
because
that
the
motion
of
the
Moone
in
the
second
Epicicle
is
double
vnto
the
motion
of
the
centre
of
the
first
Epicicle
,
from
the
line
of
the
meane
moouing
of
the
Sunne
.
For
according
vnto
this
motion
the
Moone
maketh
her
reuolution
in
14
dayes
,
18
houres
,
i/22
ii/1
and
her
daily
motion
is
24
degrees
,
i/22
ii/53
iii/23
and
is
found
in
the
Prutenicall
tables
,
by
doubling
the
meane
longitude
of
the
Moone
from
the
Sunne
.
25.
The
line
of
the
true
Anomalia
of
the
Moone
is
a
right
line
drawne
from
the
centre
of
the
first
Epicicle
vnto
the
body
of
the
Moone
.
As
in
the
third
figure
of
this
Chapter
the
right
line
E
G
,
and
the
caracter
of
the
Moone
is
called
the
line
of
the
true
Anomalia
,
because
it
is
drawne
from
the
centre
of
the
first
Epicicle
,
which
is
marked
with
the
letter
E
,
vnto
the
body
of
the
Moone
,
marked
with
the
caracter
of
the
Moone
.
26.
The
true
Anomalia
of
the
Moone
,
which
the
Alphonsines
doe
call
the
true
Argument
,
is
an
arch
of
the
first
Epicicle
,
contained
betwixt
the
Auge
of
the
said
first
Epicicle
,
and
the
line
of
the
true
Anomalia
.
As
in
the
said
third
figure
the
arch
B
G
is
called
the
true
or
equated
Anomalia
,
or
the
true
Argument
of
the
Moone
.
27.
The
equacion
of
the
centre
,
which
in
the
Prutenicall
tables
is
called
the
equacion
of
the
second
Epicicle
,
is
an
arch
of
the
first
Epicicle
,
whereby
the
true
and
meane
Anomalias
do
differ
the
one
from
the
other
.
As
in
the
said
third
figure
the
arch
B
G
is
the
true
Argument
of
Moone
,
and
the
arch
B
F
is
the
mean
Anomalia
or
Argument
of
the
Moone
,
or
of
the
Epicicle
,
defined
in
the
19
definition
of
this
Chapter
:
the
difference
betwixt
these
two
arches
,
is
the
little
arch
G
F
,
and
this
difference
,
is
called
the
Prosthapheresis
of
the
centre
.
The
finding
whereof
by
the
Prutenicall
tables
,
is
taught
in
the
24
Precept
,
by
helpe
of
the
18
Cannon
,
in
that
Collum
whose
title
is
Secundi
Epicycli
.
And
this
equacion
is
to
be
added
or
subtracted
from
the
mean
Anomalia
,
as
is
shewed
in
the
said
24
Precept
,
to
the
end
that
the
true
Argument
or
Anomalia
may
bee
had
.
And
the
greatest
equacion
that
can
be
,
is
12
degrees
,
i/26
ii/57
which
then
happeneth
,
when
the
Moone
is
in
either
of
the
Touch-points
of
the
second
Epicicle
:
which
Touch-points
are
determined
by
two
right
lines
drawne
from
the
centre
of
the
first
Epicicle
:
and
touching
the
circumference
of
the
second
Epicicle
,
on
each
side
thereof
.
28.
The
line
of
the
true
motion
of
the
Moon
is
a
right
line
drawn
from
the
centre
of
the
world
,
throgh
the
body
of
the
Moon
vnto
the
Ecliptick
,
&
the
point
in
the
Eclipticke
,
where
that
line
endeth
,
is
the
true
place
of
the
Moone
:
as
in
the
third
figure
the
line
A
G
T
signifieth
the
line
of
her
true
mouing
,
and
the
point
T
is
the
true
place
of
the
Moone
.
29.
The
true
or
apparent
motion
of
the
Moone
is
an
arch
of
the
Eclipticke
,
beginning
at
some
knowne
place
of
the
Eclipticke
,
and
ending
a●
the
true
place
of
the
Moone
:
which
arch
dooth
begin
either
at
the
first
starre
of
the
Rams
horne
,
or
at
the
Vernall
Equinox
,
either
meane
or
true
,
or
els
at
the
line
of
the
meane
place
of
the
Sunne
.
As
in
the
said
third
figure
the
arch
*
T
is
the
apparent
or
true
moouing
of
the
Moone
from
the
first
starre
of
the
Rams
horne
.
30.
The
equacion
of
the
first
Epicicle
is
an
arch
of
the
Eclipticke
,
contained
betwixt
the
line
of
the
meane
mouing
of
the
Moone
,
and
the
line
of
her
true
mouing
.
As
for
example
,
in
the
third
figure
of
this
Chapter
the
line
A
V
is
the
line
of
the
meane
mouing
of
the
Moon
,
and
the
line
A
T
is
the
line
of
her
true
mouing
,
and
the
arch
of
the
Eclipticke
,
contained
betwixt
these
two
lines
,
that
is
to
say
,
the
arch
T
V
,
is
called
the
equacion
of
the
first
Epicicle
,
or
the
equacion
of
the
Argument
.
And
the
finding
of
this
equacion
at
any
time
giuen
,
is
taught
in
the
24
Precept
,
by
helpe
of
the
18
Cannon
,
in
the
Collum
,
whose
title
is
Primi
Epicycli
.
But
because
this
equacion
doth
varie
,
and
is
sometimes
greater
and
sometimes
lesser
,
therefore
the
absolute
and
perfect
equacion
is
to
be
found
by
the
proportionall
minutes
,
and
the
excesse
,
which
were
defined
before
in
the
29
definition
of
the
fift
Chapter
,
and
therefore
I
need
not
here
again
to
define
the
same
,
but
onely
to
tell
you
,
that
the
proportionall
minutes
are
to
be
found
in
the
18
Cannon
,
in
the
Collum
,
whose
title
is
Scrupula
Proportionalia
:
and
the
excesse
is
to
be
found
in
the
said
18
Cannon
,
in
the
Colume
,
whose
title
is
Excessus
.
Here
endeth
my
Extract
of
Maginus
his
Theoriques
:
And
if
this
my
labour
shall
content
you
,
then
looke
shortly
for
the
vse
of
the
Prutenicall
Tables
.