▪
OF
THE
CIRcles
of
the
Sphaere
of
Heauen
,
and
of
their
names
,
and
how
they
be
made
.
AStronomers
to
the
end
they
might
shewe
the
motions
of
Heauen
,
and
the
straunge
and
wonderful
conclusions
of
the
Coelestiall
bodies
:
haue
imagined
certaine
Circles
in
the
bodie
of
the
first
Sphaere
or
first
mooueable
,
and
principally
ten
:
whereof
some
be
greater
Circles
of
the
Sphaere
,
so
called
because
the
Center
of
these
Circles
is
also
the
Center
of
Heauen
:
&
euery
such
Circle
diuideth
the
whole
Sphaere
into
two
aequall
parts
.
Of
this
sort
be
sixe
:
the
Aequinoctiall
,
Zodiack
,
Horizon
,
Meridian
,
and
two
Colures
.
Some
bee
lesser
Circles
of
the
Sphaere
so
called
,
because
they
haue
not
the
Center
of
the
world
for
their
Center
,
neither
diuide
the
whole
Sphaere
aequally
.
Of
this
kinde
be
fower
,
the
Tropicke
of
Cancer
,
the
Tropicke
of
Capricorne
,
the
Articke
and
Antarticke
.
The
Aequinoctiall
,
called
the
aequator
or
girdle
of
Heauen
,
is
a
great
Circle
of
the
Sphaere
,
diuiding
the
Sphaere
into
two
aequal
parts
,
and
is
aequally
distant
from
ech
Pole
of
the
worlde
.
And
tooke
his
name
of
the
aequator
,
either
because
it
is
aequally
in
the
middle
of
Heauen
,
as
Euclide
saith
in
his
Opticks
:
or
for
that
the
Sunne
,
comming
to
this
Circle
,
maketh
the
day
and
night
aequall
.
&
it
is
diuided
in
360.
aequall
parts
,
which
parts
are
called
degrees
.
His
Axe
is
the
Axe
of
the
world
,
and
Poles
,
the
Poles
of
the
world
.
The
Zodiack
is
a
great
Circle
of
the
Sphaere
,
which
crosseth
the
Aequinoctiall
in
two
points
,
the
one
being
the
head
of
Aries
,
the
other
of
Libra
,
and
swarneth
from
him
in
all
other
points
,
leaning
toward
ech
Pole
of
the
world
in
the
point
of
his
greatest
swarning
,
23.
degrees
,
30.
minutes
.
This
Zodiack
is
of
breadth
12.
degrees
,
and
of
length
,
that
is
to
say
,
in
compas
360.
degrees
,
and
according
to
his
length
,
is
diuided
into
12.
aequal
parts
,
which
are
called
the
12.
signes
.
Aries
,
Taurus
,
Gemini
,
Cancer
,
Leo
,
Virgo
,
Libra
,
Scorpio
,
Sagittarius
,
Capricornus
,
Aquarius
and
Pisces
.
And
ech
signe
contayneth
of
length
30.
degrees
.
in
the
midle
bredth
of
the
Zodiack
,
we
imagine
a
Circle
to
passe
,
which
we
call
the
Ecliptick
Circle
or
line
:
For
that
that
when
the
Sunne
and
Moone
bee
both
vnder
this
line
in
a
Diameter
:
then
the
Moone
is
Eclipsed
.
Vnder
this
Circle
the
Sunne
mooueth
dayly
(
without
declining
any
waies
)
the
quantity
of
one
degree
very
neere
in
ech
day
.
the
rest
of
the
Planets
are
found
some
times
on
one
side
the
Ecliptick
,
&
some
time
on
the
other
.
This
Zodiack
taketh
his
name
of
a
greeke
word
signifying
a
liuing
creature
:
or
as
the
Latens
will
,
is
called
Signifer
,
for
that
that
it
beareth
the
12.
Signes
.
the
Axe
of
the
Zodiack
and
the
Ecliptick
,
is
all
one
,
being
a
line
diuers
from
the
axe
of
the
world
,
and
the
Poles
bee
two
points
alwayes
so
much
distant
from
the
Poles
of
the
world
:
as
the
greatest
declination
of
the
Ecliptick
commeth
vnto
.
A
Colure
doth
generally
signifie
any
Circle
passing
by
the
Poles
of
the
worlde
,
and
hath
his
name
of
his
vnperfect
shewing
himselfe
in
the
motion
of
heauen
.
But
now
by
the
name
of
Colures
,
we
vnderstand
two
great
Circles
,
the
one
going
from
the
Poles
of
the
worlde
by
the
points
where
the
Aequinoctiall
and
Zodiack
cut
them selues
(
which
be
called
the
Aequinoctiall
points
)
and
is
called
the
Aequinoctiall
Colure
.
The
other
passeth
from
the
Poles
of
the
worlde
,
by
those
points
of
the
Ecliptick
which
swarue
most
of
all
others
from
the
Aequinoctiall
line
(
which
points
are
called
the
Solsticiall
points
)
and
this
is
called
the
Solsticial
Colure
.
And
here
be
you
to
know
that
these
foure
greater
Circles
which
we
haue
defined
:
be
still
the
same
through
the
whole
worlde
,
and
are
sayd
to
be
moueable
Circles
:
for
so
much
as
in
the
motion
of
heauen
,
they
be
also
mooued
.
of
which
,
some
are
moueable
perfectly
:
as
the
Aequinoctiall
and
Zodiack
,
(
for
they
in
the
going
about
of
heauen
,
doe
ascend
by
little
and
little
,
till
the
whole
Circle
haue
gone
oure
the
Horison
)
some
vnperfectly
moueable
,
as
the
two
Colures
,
which
neuer
shewe
the
whole
Circle
in
any
crooked
Sphaere
.
the
other
two
greater
Circles
which
followe
,
be
called
fixed
,
for
that
they
neuer
mooue
by
the
motion
of
heauen
.
But
they
be
changeable
in
euery
Region
.
The
Horizon
is
a
greater
Circle
diuiding
the
halfe
of
the
Heauen
which
we
see
,
from
the
halfe
which
we
see
not
,
and
is
called
in
Latine
Finitor
,
because
it
endeth
our
sight
.
The
Horizon
maketh
fower
principal
points
,
East
,
West
,
North
,
and
South
.
His
Axe
is
a
line
imagined
to
fall
from
the
point
of
heauen
,
which
is
directly
ouer
our
head
where
we
be
,
downe
to
the
ground
like
a
plumme
line
,
and
his
Poles
be
the
endes
of
that
line
,
called
the
Verticall
point
,
and
point
opposite
to
the
Verticall
.
The
Meridian
is
also
a
great
Circle
,
passing
from
the
Poles
of
the
world
by
our
Verticall
point
,
cutting
the
Horizon
in
the
North
and
South
points
his
Axe
is
a
line
going
from
the
East
point
of
the
Horizon
to
the
West
,
and
his
Poles
be
the
same
points
,
and
these
two
Circles
doe
alwayes
chaunge
,
&
are
diuers
in
euery
Region
:
for
so
much
as
the
Verticall
point
of
euery
Region
is
diuers
,
by
the
which
the
Meridian
of
necessitie
must
passe
,
and
is
the
Pole
also
of
the
Horizon
.
▪
HOW
THE
Globe
is
to
be
placed
,
readie
for
his
vse
and
practise
.
THe
placing
of
the
Globe
ought
to
be
such
,
that
the
Horizon
of
the
Globe
may
stand
parallele
or
leuied
to
the
true
Horizon
:
and
the
Meridian
of
the
Globe
stand
in
the
Superficies
of
the
true
Meridian
of
Heauen
,
and
the
Poles
of
the
Globe
and
his
Axe
,
answere
exactly
to
the
Poles
and
Axe
of
Heauen
.
Now
to
the
leuying
of
the
Horizon
:
there
ought
to
bee
at
your
Globe
a
hanging
plummet
.
and
for
the
Meridian
,
a
Needle
touched
of
the
lode
stone
,
and
touching
the
rectifying
of
the
Poles
and
Axe
of
the
Globe
,
the
eleuation
of
the
Pole
of
heauen
is
first
to
be
knowen
.
the
meanes
to
performe
and
accomplish
the
same
,
being
such
as
followe
.
Propositio
.
1.
To
finde
a
Meridian
line
in
any
place
appoynted
.
SEt
vp
on
your
Horizon
or
some
plaine
leuied
boarde
,
a
Gnomon
of
any
reasonable
length
then
,
(
at
such
time
as
the
same
shineth
,
describe
from
the
top
of
your
Gnomon
a
Circle
by
the
tippe
of
his
shadowe
.
and
make
a
marke
in
the
Circle
where
the
shadowe
ended
,
at
your
obseruation
(
which
must
be
before
noone
.
)
Then
marke
in
the
afternoone
at
what
time
the
ende
of
the
shadowe
returneth
into
the
same
Circle
againe
,
and
make
a
marke
at
his
point
of
falling
,
so
shall
ye
haue
a
portion
of
the
sayde
Circle
inclosed
betwixt
the
two
points
:
If
then
ye
diuide
this
portion
into
two
aequal
parts
,
and
drawe
a
line
from
this
middle
point
,
by
the
point
in
which
the
Gnomon
standeth
,
it
shal
be
a
Meridian
line
.
Propositio
.
2.
To
take
the
height
of
any
Starre
.
FRrom
the
point
of
Heauen
,
which
is
directly
ouer
our
heads
(
being
called
the
Verticall
point
,
or
Zenith
:
)
are
imagined
diuers
Circles
to
fall
by
euery
degree
and
minute
of
the
Horizon
:
all
which
Circles
are
called
Verticals
,
&
serue
for
the
height
of
Starres
,
for
so
much
as
the
altitude
of
Sunne
or
starre
is
the
portion
of
the
V●…ticall
Circle
,
inclosed
betwixt
the
Center
of
the
Sunne
or
Starre
(
in
the
time
of
his
obseruation
)
and
the
Horizon
,
which
height
is
thus
found
.
Take
your
Astrolabe
,
and
let
him
hang
freely
by
his
ring
,
then
turne
vp
his
Dioptral
so
long
,
that
ye
see
the
Starre
(
whose
height
yee
seeke
)
thorowe
his
sights
:
for
then
,
howe
many
degrees
and
minutes
are
inclosed
betwixt
the
Dioptrall
and
the
line
of
your
Astrolabe
,
which
is
parallele
to
the
Horizon
:
so
many
hath
that
Starrs
of
height
.
as
the
seauenth
day
of
Ianuarie
.
Anno.
1585.
vnder
the
Meridian
of
Oxford
,
at
9.
of
the
clocke
I
sought
the
height
of
the
Sunne
.
taking
then
my
Astrolabe
,
and
hanging
him
towarde
the
Sunne
,
and
raising
his
Dioptrall
till
I
espyed
the
Sunne
.
I
found
betwixt
the
Dioptral
and
the
line
representing
the
Horizon
seauen
degrees
,
and
16.
minutes
,
so
much
was
the
height
of
the
Sunne
at
that
time
.
Propositio
.
3.
To
take
the
altitude
of
the
Pole
in
in
any
place
or
countrey
.
THe
altitude
of
the
pole
is
the
portion
of
the
Meridian
Circle
inclosed
betwixt
the
Pole
and
the
Horizon
.
and
is
thus
found
.
Find
a
Meridian
line
,
and
drawe
him
in
the
Horizon
by
the
first
proposition
:
then
take
the
height
of
any
fixed
Starre
which
setteth
not
(
and
that
at
the
fore
part
of
the
night
)
at
such
time
as
he
is
pointed
vppon
your
Meridian
line
,
by
the
second
proposition
.
Again
the
next
morning
,
or
any
other
morning
take
the
height
of
the
same
starre
at
such
time
as
hee
is
pointed
with
your
Meridian
line
:
then
subduct
the
lesse
altitude
from
the
greater
,
and
diuide
the
difference
into
two
aequall
partes
.
Lastly
,
adde
halfe
the
difference
to
the
lesse
altitude
,
so
the
whole
number
made
giueth
the
altitude
of
the
Pole
.
As
at
Oxford
I
tooke
the
height
of
a
starre
in
the
fore
part
of
a
night
in
winter
,
being
the
tenth
of
December
.
1584.
at
what
time
he
was
pointed
with
my
Meridian
,
and
found
his
height
.
55.
degrees
.
59.
minutes
.
Againe
the
next
morning
I
tooke
his
height
,
and
found
it
47.
degrees
41.
minutes
.
This
lesse
altitude
I
subourted
from
the
greater
55.
degrees
.
59.
minutes
,
and
the
difference
was
8.
degrees
.
18.
minutes
,
which
being
parted
,
had
4.
for
his
halfe
,
and
9.
minutes
.
This
halfe
added
to
47.
degrees
.
41.
min.
(
the
lesse
altitude
)
giueth
51.
degrees
.
50.
minut
.
for
the
true
eleuation
of
the
Pole
at
Oxford
.
Propositio
.
4.
To
rectifie
the
Globe
perfectly
for
to
be
vsed
.
KNow
first
the
eleuation
of
the
Pole
of
Heauen
,
for
the
place
where
yee
vse
the
Globe
,
by
the
third
proposition
,
then
erect
the
Pole
of
the
Globe
so
many
degrees
aboue
his
Horizon
,
as
the
Pole
of
heauen
is
eleuated
.
Againe
leuell
the
Horizon
of
your
Globe
by
his
hanging
plummet
,
lastly
turne
his
Meridian
to
the
South
by
helpe
of
his
Needle
,
and
put
his
Quadrant
of
altitude
vppon
the
90.
degree
from
his
Horizon
:
for
then
the
Meridian
answereth
to
the
Meridian
of
heauen
.
Axe
to
axe
,
and
Pole
to
Pole
as
is
required
.
But
this
way
of
setting
him
South
,
albeit
it
be
of
antiquitie
:
yet
hath
it
imperfection
by
reason
of
the
variation
of
the
needle
.
but
of
that
ye
shall
heare
more
hereafter
.
Propositio
.
5.
To
finde
the
place
of
the
Sunne
at
any
tyme
.
BY
this
place
,
is
vnderstoode
the
degree
of
the
Ecliptick
line
,
in
which
he
is
,
and
this
place
is
thus
found
.
In
the
Horizon
of
your
Globe
be
set
,
the
windes
,
the
signes
,
and
moneths
with
their
daies
.
find
therfore
the
day
of
your
moneth
in
which
ye
would
haue
the
place
of
the
Sunne
in
the
Horizon
of
the
globe
.
For
looke
what
signe
and
degree
of
signe
is
right
against
the
day
,
the
same
is
the
place
of
the
Sunne
.
As
on
the
twelfth
day
of
December
:
Anno.
1584.
I
sought
the
place
of
the
Sunne
.
this
day
being
had
in
the
Horizon
,
I
found
the
first
degree
of
Capricorne
,
32.
minutes
to
answare
against
it
,
and
therefore
that
was
then
the
place
of
the
Sunne
.
Propositio
.
6.
To
finde
the
declination
of
any
point
of
the
Ecliptick
or
of
the
Sunne
,
at
any
tyme
.
THe
declination
of
any
point
of
the
Ecliptick
,
Sunne
,
or
any
Starre
,
is
the
portion
of
the
Meridian
Circle
,
inclosed
betwixt
the
Aequinoctiall
and
the
say●
point
,
Sunne
,
or
starre
,
and
is
found
thus
.
Turne
the
poynt
whose
Declination
yet
seeke
,
to
the
Meridian
of
the
Globe
,
and
there
see
how
many
degrees
and
minutes
there
be
of
your
Meridian
inclosed
betwixt
the
sayd
poynt
and
the
Aequinoctiall
.
For
so
much
is
the
Declination
.
so
hath
the
Sunne
in
the
5.
of
Aries
2.
degrees
declination
.
And
the
7.
of
Taurus
13.
degrees
.
52.
minutes
.
and
this
declination
is
called
Northren
,
when
the
point
is
of
the
North
side
the
Aequinoctiall
,
and
Southerne
if
of
the
South
side
.
Here
must
ye
also
know
,
that
two
points
of
the
Ecliptick
want
declination
,
and
are
the
two
Aequinoctials
.
Two
haue
greater
declination
then
anyother
,
and
be
the
two
Solstitials
.
of
the
rest
foure
haue
like
declination
.
Propositio
.
7.
To
finde
the
right
ascention
of
the
Sunne
,
or
any
point
of
the
Ecliptick
line
.
THE
right
ascention
of
any
Starre
,
Sunne
,
or
any
point
of
the
Ecliptick
,
is
the
portion
of
the
Aequinoctiall
Circle
from
the
head
of
Aries
,
(
where
the
Aequinoctiall
taketh
his
beginning
)
and
that
point
or
degree
of
the
same
,
which
meeteth
with
the
said
Starre
,
Sunne
,
or
Ecliptick
point
,
vnder
the
Meridian
Circle
in
a
crooked
Sphaere
:
being
numbred
orderly
in
the
Aequinoctiall
,
and
is
thus
found
.
turne
the
Starre
,
Sunne
,
or
any
point
whose
ascention
ye
looke
,
vnder
the
Meridian
of
the
Globe
,
and
see
then
what
portion
of
the
aequator
is
from
the
head
of
Aries
to
that
point
of
the
aequator
which
standeth
then
vnder
the
Meridian
:
for
the
same
portion
,
is
the
right
ascention
of
the
Starre
,
Sun
,
or
point
looked
for
.
So
do
I
finde
the
right
ascention
of
Bootes
a
Starre
,
to
be
209.
degrees
.
1.
minut
.
And
the
right
ascention
of
the
Sunne
when
he
is
in
the
first
of
Taurus
,
to
be
27.
degrees
.
54.
minuts
.
And
the
right
ascention
of
the
first
of
Sagitarie
,
to
be
237.
degrees
.
48.
minuts
.
Propositio
.
8.
To
finde
the
crooked
ascention
of
the
Sunne
,
Starre
,
or
any
point
of
the
Ecliptick
.
THE
crooked
ascention
of
the
Sunne
,
is
that
Ark
of
the
aequator
which
is
inclosed
betwixt
the
beginning
of
the
aequator
,
and
the
point
of
the
same
which
commeth
vp
with
the
Sunne
in
a
crooked
Sphaere
,
&
is
found
thus
.
Take
the
Sunne
Starre
,
or
point
,
whose
crooked
ascention
ye
desire
:
and
put
him
to
the
East
side
of
the
Horizon
till
it
touch
:
Then
marke
what
part
of
the
aequator
is
inclosed
betwixt
the
beginning
of
it
,
and
the
point
now
in
the
Horizon
,
for
so
much
is
the
crooked
ascention
of
the
Sunne
,
Starre
,
or
point
.
Th●…
doe
I
finde
the
crooked
ascention
of
the
Sunne
in
the
first
of
Taurus
,
to
be
the
12.
degrees
.
48.
minuts
.
All
this
being
in
the
Eleuation
52.
degree
.
0.
minut
.
Propositio
.
9.
To
find
the
difference
of
ascention
,
or
increase
of
the
day
.
THE
Sunne
being
in
one
and
the
selfe
same
point
of
the
Ecliptick
(
except
in
the
Aequinoctiall
intersections
)
hath
one
degree
of
the
aequator
that
commeth
vp
with
him
aboue
the
Horizon
in
any
crooked
Sphaere
,
and
an
other
,
(
not
the
same
)
that
commeth
vp
with
him
in
a
right
Sphaere
.
And
therefore
the
portion
of
the
aequator
,
betwixt
the
point
of
the
said
,
that
commeth
vp
with
the
Sunne
in
the
right
Sphaere
:
and
the
point
rising
with
the
same
in
the
crooked
Sphaere
,
is
called
the
difference
of
ascention
.
As
in
a
right
Sphaere
the
Sunne
beeing
in
the
first
of
Taurus
,
there
riseth
with
him
,
the
27.
degree
.
54.
minut
of
the
Aequinoctiall
.
(
Which
point
also
meeteth
him
vnder
the
Meridian
in
a
crooked
Sphaere
:
for
that
the
Meridian
of
any
crooked
Sphaere
,
sheweth
the
same
that
the
Horizon
doth
in
the
right
Sphaere
.
)
but
in
the
crooked
Sphaere
,
where
the
Pole
is
eleuated
52.
degrees
,
there
riseth
with
the
Sunne
the
same
daye
,
the
12.
degree
.
48.
minut
of
the
aequator
.
Subducting
now
the
lesse
from
the
greater
,
the
difference
is
15.
degrees
.
6.
minuts
,
and
is
called
the
difference
of
ascention
.
And
because
the
Artificiall
day
of
the
crooked
Sphaere
,
is
longer
or
shorter
then
the
Aequinoctiall
day
by
twise
this
difference
:
therefore
the
difference
of
ascention
is
called
also
the
increase
of
the
day
.
And
this
difference
is
thus
found
.
Find
the
right
ascention
of
the
Sunne
by
the
7.
proposition
:
and
againe
finde
his
crooked
ascention
by
the
9.
proposition
:
then
subduce
the
lesse
from
the
greater
,
for
the
remaines
is
the
difference
of
ascention
.
Propositio
.
10.
To
finde
the
length
of
the
Artificiall
day
in
any
Region
or
Countrie
.
FInde
out
the
difference
of
ascention
of
the
place
of
the
Sunne
by
the
9.
proposition
,
and
dubble
the
same
then
conuert
is
all
into
howers
and
parts
of
howers
,
allowing
for
one
hower
15.
degrees
,
and
for
a
halfe
7.
degrees
.
30.
minuts
,
&c.
This
time
which
commeth
of
the
difference
of
ascention
adde
to
12.
howers
(
if
the
place
of
the
Sunne
bee
any
degree
betwixt
Aries
and
Libra
:
or
subduct
it
from
12.
if
he
be
betwixt
Libra
and
Aries
,
)
for
the
number
made
or
left
,
is
the
length
of
the
day
.
As
the
Sunne
being
in
the
first
of
Tanrus
,
his
difference
of
ascention
is
15.
degrees
.
6.
minuts
:
this
dubble
and
conuerted
into
time
,
maketh
2.
howers
and
12.
Aequinoctial
minuts
.
And
because
Tanrus
is
a
Northerne
Signe
,
ye
must
ad
this
difference
to
12.
howers
,
so
do
ye
make
14.
howers
and
12.
Aequinoctiall
minuts
,
for
the
length
of
that
whole
day
.
Propositio
.
11.
To
finde
the
hower
of
the
Sunne
rising
,
or
of
his
setting
.
KNowe
the
length
of
the
Artificiall
day
by
the
10.
proposition
:
and
take
halfe
of
the
same
day
,
for
that
sheweth
the
hower
of
Sunne
setting
.
But
if
ye
recken
so
much
from
noone
forward
,
it
giueth
Sunne
rise
.
As
the
Sunne
being
in
the
first
of
Taurus
,
the
day
is
14.
howers
and
12.
minuts
.
The
halfe
is
7.
howers
and
6.
minuts
.
I
say
then
the
Sunne
setteth
after
7.
of
the
clocke
,
6.
minuts
.
Againe
,
thus
much
taken
from
noone
forward
,
sheweth
the
Sunne
to
rise
before
5.
of
the
clocke
,
6.
minuts
.
Propositio
.
12.
An other
way
to
finde
the
same
more
mechanically
.
FInde
the
place
of
the
Sunne
by
the
5.
proposition
,
and
turne
the
saide
place
directly
vnder
the
Meridian
:
them
put
the
Index
of
the
hower
Circle
precisely
on
12.
of
the
clocke
.
Lastly
,
turne
the
saide
place
of
the
Sunne
to
the
East
side
of
the
Horizon
:
for
when
he
is
there
,
then
shall
the
Index
shewe
the
time
of
the
Sunne
rising
.
And
contrariwise
,
putting
the
place
of
the
Sun
to
the
West
,
it
sheweth
his
setting
.
Propositio
.
13.
To
finde
how
farre
the
Sunne
riseth
or
setteth
from
the
true
East
or
West
point
any
day
.
FIrst
finde
the
place
of
the
Sunne
by
the
5.
proposition
:
then
turne
the
same
place
to
the
East
side
of
the
Horizon
til
he
touch
the
same
,
for
then
the
number
of
degrees
in
the
Horizon
,
(
inclosed
betwixt
the
true
East
point
and
the
place
of
the
Sunne
,
)
shewe
how
farr
he
riseth
and
setteth
from
the
true
East
:
And
this
portion
of
the
Horizon
is
called
his
bredth
of
rising
:
and
is
called
Northern
bredth
if
the
Sunne
rise
beyond
the
East
point
toward
the
North
,
&
Southern
if
contrary
.
Likewise
are
ye
to
knowe
,
that
of
the
Ecliptick
two
points
Aries
and
Libra
haue
no
bredth
of
rising
.
Two
points
also
as
Cancer
and
Capricorn
haue
greater
then
any
other
:
and
of
the
rest
fower
points
haue
the
like
.
Propositio
.
14.
To
rectifie
the
Index
of
the
hower
Circle
euery
day
as
he
ought
.
FInde
the
place
of
the
Sunne
euery
day
in
which
ye
vse
the
Index
,
by
the
5.
proposition
,
and
put
the
said
place
vnder
the
Meridian
:
this
being
done
,
them
put
the
Index
on
12.
of
the
clocke
,
for
afterward
in
the
motion
of
the
Globe
he
will
goe
true
as
he
ought
.
Propositio
.
15.
To
finde
the
noone
height
of
the
Sunne
for
any
day
to
come
,
or
gone
in
any
place
whose
eleuation
is
knowen
.
THe
height
of
the
Sunne
,
is
the
portion
of
the
verticall
Circle
inclosed
betwixt
the
Center
of
the
Sunne
and
the
Horizon
.
But
for
as
much
as
at
noone
the
Meridian
,
and
the
Verticall
of
the
Sunne
bee
all
one
Circle
:
therefore
his
noone
height
is
the
portion
of
the
Meridian
betwixt
the
Center
of
the
Sunne
and
the
Horizon
.
this
height
is
thus
to
be
knowen
.
Find
the
place
of
the
Sunne
for
the
day
proposed
,
and
turne
the
same
place
vnder
the
Meridian
,
for
then
the
portion
of
the
Meridian
betwixt
the
sayd
place
and
the
Horizon
is
his
noone
height
.
Thus
found
I
the
height
of
the
Sunne
at
noone
in
Oxford
,
whose
Pole
is
raysed
51.
degrees
.
50.
min.
on
the
2.
day
of
May
to
be
59.
degrees
.
47.
mi.
and
on
the
twelfth
of
Iune
,
to
be
61.
degrees
.
41.
minuts
.
Propositio
.
16.
To
find
the
depression
of
the
Sunne
at
midnight
.
AS
the
Meridian
altitude
is
the
portion
of
the
Meridian
from
the
Center
of
him
,
to
the
Horizon
when
hee
is
aboue
the
earth
:
so
is
his
depression
the
part
of
the
Meridian
betwixt
the
Center
and
the
Horizon
when
he
is
vnder
ground
,
and
may
thus
bee
knowen
.
Finde
the
place
of
the
Sunne
,
and
put
it
to
the
Meridian
vnder
the
Horizon
:
for
then
the
portion
of
the
Meridian
betwixt
it
&
the
Horizon
,
sheweth
his
depression
.
So
find
I
the
depression
of
the
Sunne
,
at
Oxford
(
his
place
being
the
first
of
Taurus
)
to
be
27.
degrees
.
40.
min.
but
his
place
being
the
first
of
Scorpius
,
to
be
50.
degrees
.
0.
min.
Propositio
.
17.
To
find
what
height
the
Sunne
shall
haue
at
any
certaine
hower
of
any
artificiall
day
.
TAke
the
place
of
the
sunne
by
the
5.
proposition
:
&
rectifie
the
Index
by
the
14.
pro.
then
turne
the
Globe
,
till
the
Index
of
the
hower
circle
be
on
the
hower
,
for
whom
ye
desire
the
height
of
the
Sunne
,
and
scopping
the
Globe
there
,
put
the
quadrant
of
altitude
to
the
place
of
the
Sunne
,
for
his
portion
betwixt
the
place
of
th●
Sunne
&
the
Horizon
,
geueth
his
height
.
So
find
I
the
height
of
the
Sunne
at
Oxford
,
at
9.
of
the
clocke
the
7.
day
of
March.
to
be
24.
dedrees
.
25.
min.
and
at
one
of
the
clocke
the
same
day
,
to
be
34.
degrees
.
51.
min.
Propositio
.
18.
By
any
height
of
the
Sunne
geuen
and
his
place
:
to
find
the
hower
of
the
day
.
LEt
it
bee
,
that
either
ye
take
the
height
of
the
Sunne
at
some
time
of
the
day
by
the
second
proposition
:
or
that
yee
haue
some
height
of
him
giuen
by
supposition
,
and
ye
would
knowe
by
it
what
it
is
of
the
clocke
that
day
at
that
time
.
Finde
therefore
the
place
of
the
Sunne
for
that
day
▪
by
the
5.
proposition
&
rectifie
the
Index
by
the
14.
proposition
.
Lastly
put
the
place
of
the
Sunne
to
the
Quadrant
of
Altitude
,
and
mooue
them
both
vp
and
downe
,
till
ye
allowe
him
the
same
height
in
your
Quadrant
,
as
ye
found
or
supposed
him
in
trueth
to
haue
.
For
then
the
Index
of
the
hower
Circle
sheweth
what
was
or
is
of
the
clock
,
as
finding
the
height
of
the
Sunne
before
Noone
on
the
seauenth
of
March
,
at
Oxford
,
to
be
twentie
fower
degrees
.
25.
min.
I
founde
it
to
haue
beene
then
nine
of
the
clocke
.
Propositio
.
19.
By
the
hower
knowen
,
and
the
height
of
the
Sunne
at
that
hower
:
together
with
the
Index
,
rectified
as
he
ought
:
to
find
the
place
of
the
Sunne
at
that
tyme
.
MOoue
your
Globe
till
his
Index
stand
on
the
hower
which
was
knowen
before
.
Then
fixe
the
Globe
for
remoouing
:
Lastly
turne
your
Quadrant
of
altitude
to
the
Ecliptick
line
,
and
looke
what
degree
of
the
Ecliptick
agreeth
in
your
Quadrant
with
the
height
that
was
before
knowen
,
and
that
is
the
place
of
the
Sunne
on
that
day
.
Propositio
.
20.
The
hower
and
place
of
the
Sunne
being
giuen
:
to
find
howe
farre
the
Sunne
is
gone
from
the
true
East
poynt
.
THe
place
of
the
Sunne
being
giuen
by
supposition
:
rectifie
the
Index
by
the
14.
proposition
:
then
turne
the
Globe
till
the
Index
shew
the
hower
giuen
.
This
being
done
,
fixe
the
Globe
that
he
mooue
not
away
,
and
set
the
edge
of
the
Quadrant
of
altitude
to
the
place
of
the
Sunne
:
and
withall
marke
howe
many
degrees
of
the
Horizon
are
inclosed
betwixt
the
true
East
point
,
and
the
edge
of
the
Quadrant
,
at
such
time
as
he
standeth
on
the
place
of
the
sunne
:
for
so
much
is
hee
distaunt
in
the
Horizon
from
true
East
.
Propositio
.
21.
The
distance
of
the
Sunne
being
geuen
,
from
true
East
,
together
with
his
height
at
the
same
time
,
and
the
height
of
the
Pole
for
the
same
region
:
to
finde
the
true
place
of
the
Sunne
,
at
any
time
.
TO
the
ende
wee
make
not
vnnecessarie
repetitions
of
the
first
principles
:
know
this
,
that
in
all
the
propositions
following
,
we
alwayes
suppose
before
the
working
,
the
Globe
rightly
rectifyed
as
is
specified
in
the
beginning
.
For
the
performance
therefore
of
this
practise
:
first
consider
diligently
in
what
quarter
of
the
yere
ye
be
in
▪
that
is
,
whether
it
be
betwixt
the
aequinoctiall
of
March
,
and
height
of
Summer
:
or
betwixt
height
of
Summer
,
and
aequinoctial
of
September
.
Likewise
whether
betwixt
aequinoctial
of
September
and
dept
of
Winter
:
or
betwixt
dept
of
winter
and
aequinoctiall
of
March.
For
then
set
the
edge
of
the
quadrant
of
altitude
at
the
true
distance
of
the
Sunne
from
the
East
:
and
turne
the
Globe
till
that
quarter
of
the
Ecliptick
come
vnder
him
,
which
serueth
for
the
quarter
of
the
yeere
in
which
ye
be
:
and
see
what
degree
of
that
part
of
the
Ecliptick
agreeth
with
the
height
proposed
:
For
that
is
the
place
of
the
Sunne
at
that
time
.
Note
therefore
here
,
that
to
the
Spring
(
which
is
from
the
aequinoctiall
of
March
till
the
height
of
Summer
)
answereth
the
part
of
the
Zodiack
from
Aries
to
Cancer
.
To
summer
which
is
from
the
height
till
the
aequinoctiall
of
September
:
answereth
the
part
from
Cancer
to
Libra
.
The
Autume
is
guided
by
the
quarter
from
Libra
to
Capricorne
:
and
Winter
by
the
signes
from
Capricorne
to
Aries
.
Propositio
.
22.
The
distance
of
the
Sunne
being
geuen
from
true
East
,
and
the
place
of
the
same
:
to
find
the
height
of
the
Sunne
which
he
hath
at
the
same
time
.
PLace
the
quadrant
of
altitude
at
the
true
distance
from
East
,
so
shall
hee
cut
the
place
of
the
Sunne
by
the
21.
proposition
:
and
therefore
the
portion
of
the
Quadrant
betwixt
the
place
of
the
Sunne
,
and
the
Horizon
,
is
his
height
.
Propositio
.
23.
The
distance
of
the
Sunne
from
true
East
being
geuen
,
and
his
place
:
to
find
the
hower
of
the
day
.
FIrst
hauing
his
place
:
rectifie
your
Index
by
the
14.
proposition
:
again
setting
the
Quadrant
of
altitude
in
the
distance
from
true
East
,
reduce
the
place
of
the
sunne
,
till
he
fall
in
the
edge
of
the
Quadrant
,
for
then
the
Index
doth
shewe
the
hower
.
Propositio
.
24.
The
distance
of
the
Sunne
being
geuen
from
true
East
,
and
his
height
,
to
find
the
time
of
his
rising
.
THe
distance
being
giuen
,
find
his
place
by
the
21
proposition
:
and
then
rectifie
the
Index
by
the
14
proposition
:
Lastly
put
the
place
of
the
Sunne
to
the
East
side
of
the
Horizon
:
for
then
the
Index
will
shew
the
Sunne
rising
.
Propositio
.
25.
The
distaunce
of
the
Sunne
being
giuen
from
true
East
,
and
his
height
,
to
finde
his
Declination
.
THE
distaunce
being
giuen
,
his
place
is
found
by
the
21.
proposition
:
&
his
place
being
knowne
,
giueth
his
Declination
by
the
6.
proposition
:
So
may
wee
likewise
by
the
said
distaunce
(
finding
his
place
)
finde
his
right
or
crooked
ascention
,
or
difference
of
ascentions
,
and
length
of
Artificiall
daies
.
Propositio
.
26.
The
declination
of
the
Sunne
being
knowne
:
to
finde
the
place
of
the
Sunne
.
COnsider
first
diligently
in
what
quarter
of
the
yeare
ye
be
in
,
as
was
expressed
before
:
then
take
that
quarter
of
the
Ecliptick
which
answereth
to
your
quarter
of
the
yeare
:
and
mooue
it
still
vnder
the
Meridian
of
your
Globe
,
till
ye
finde
no
more
of
the
Meridian
inclosed
betwixt
the
aequator
and
Ecliptick
,
then
the
declination
that
is
giuen
commeth
vnto
:
for
then
looke
what
degree
of
the
Ecliptick
is
vnder
the
Meridian
,
that
is
the
place
of
the
Sun
.
As
the
declination
of
the
Sunne
in
the
quarter
of
the
yeare
betwixt
the
Aequinoctiall
of
March
,
and
height
of
Summer
was
giuen
to
bee
11.
degrees
.
50.
minuts
.
And
to
this
quarter
of
the
yeere
,
aunswereth
the
quarter
of
the
Ecliptick
from
Aries
to
Cancer
.
Therefore
moouing
the
said
quarter
vnder
the
Meridian
,
I
found
the
first
of
Taurus
to
aunswere
to
this
declination
:
and
therefore
that
was
the
place
of
the
Sunne
.
Propositio
.
27.
The
declination
of
the
Sunne
being
knowne
:
to
finde
the
day
of
the
Moneth
.
BY
the
declination
giuen
,
finde
the
place
of
the
Sunne
by
the
26.
proposition
:
them
take
the
said
place
in
the
Horizon
of
your
Globe
:
for
looke
what
day
aunswereth
against
it
,
that
is
the
day
of
the
Moneth
.
Propositio
.
28.
The
day
of
the
Moneth
being
knowne
,
to
finde
the
length
of
the
Planetarie
hower
.
THE
Artificiall
day
is
from
Sunne
rise
to
Sunne
set
:
and
the
12.
part
of
this
day
,
whether
it
be
longer
or
shorter
then
an
hower
by
the
clocke
,
is
the
Planetarie
hower
:
and
may
thus
be
knowne
.
The
day
being
gi●en
,
finde
the
length
of
that
day
by
the
10.
proposition
:
and
diuide
all
by
12.
The
Quotient
is
the
length
of
a
Planetarie
or
Artificiall
hower
of
that
day
.
As
the
day
being
15.
howers
by
the
clocke
,
I
diuide
it
by
12.
the
Quotient
is
one
hower
and
a
quarter
,
and
so
much
is
a
Planetarie
hower
of
that
day
.
Propositio
.
29.
The
day
of
the
Moneth
being
giuen
:
to
finde
the
dawning
of
the
day
.
BY
the
day
knowne
,
finde
the
place
of
the
Sunne
by
the
5.
proposition
:
and
then
rectifie
your
Index
by
the
14.
proposition
.
Againe
,
take
the
degree
of
the
Ecliptick
which
is
opposite
in
a
Diameter
to
the
place
of
the
Sunne
:
and
mooue
him
toward
the
West
together
with
the
Quadrant
of
Altitude
,
till
ye
haue
18.
degrees
of
height
:
for
then
the
Index
sheweth
the
beginning
of
the
dawning
or
spring
of
the
day
.
Propositio
.
30.
To
finde
the
length
of
the
whole
dawning
.
FInde
the
beginning
of
the
dawning
by
the
29.
proposition
,
and
then
the
Sunne
rise
by
the
11.
or
12.
proposition
:
for
the
difference
of
those
times
is
the
whole
dawning
.
And
thus
farre
haue
I
followed
such
conclusions
,
as
haue
a
more
orderly
cohaerence
:
it
remaineth
now
to
shewe
some
others
,
whose
cohaerence
is
not
so
naturall
.
Propositio
.
31.
An other
way
to
finde
the
length
of
the
Artificiall
day
or
night
.
FInde
the
time
of
the
Sunne
rising
for
your
day
proposed
by
the
12.
proposition
:
then
dubble
all
those
howers
and
partes
of
time
which
be
from
Sunne
rise
till
noone
,
for
it
giueth
the
Artificiall
day
.
Or
if
ye
number
all
the
howers
and
parts
from
Sunne
rise
to
his
setting
,
it
giueth
the
same
.
Propositio
.
32.
To
finde
the
hower
of
the
day
.
PLace
the
Globe
in
the
Sunne
shine
,
and
rectifie
him
to
his
vse
by
the
4.
proposition
,
then
finde
the
place
of
the
Sunne
by
the
5.
proposition
.
Againe
,
rectifie
his
Index
by
the
14.
proposition
.
Lastly
,
〈◊〉
the
needle
or
pinne
directly
vp
in
the
place
of
the
Sunne
:
then
turne
the
Globe
vp
till
the
pinne
cast
no
shadowe
,
for
then
the
Index
sheweth
what
is
then
of
the
clocke
.
Propositio
.
33.
To
finde
the
eleuation
of
the
Pole
,
in
any
place
.
DRawe
in
the
open
ayre
vpon
some
table
that
is
leuell
,
a
Meridian
line
by
the
1.
proposition
,
and
place
the
Globe
so
on
it
,
that
his
Meridian
Circle
hang
directly
●uer
it
:
then
hauing
the
place
of
the
Sunne
,
set
a
pinne
right
vp
in
it
,
and
put
the
said
place
and
pinne
close
to
the
Meridian
circle
.
Lastly
,
lift
vp
the
Pole
and
Meridian
Circle
,
till
the
pinne
cast
no
shadowe
:
for
then
the
degrees
betwixt
the
Pole
and
the
Horizon
,
be
the
true
eleuation
of
that
place
.
But
this
practise
is
to
bee
performed
at
noone
onely
or
height
of
the
day
.
Propositio
34.
An other
way
to
doe
the
same
.
TAke
the
height
of
any
fixed
Starre
(
whom
ye
know
)
by
the
2.
proposition
,
at
such
time
as
he
pointeth
with
the
Meridian
line
:
then
take
the
same
Starre
on
the
Globe
,
and
by
helpe
of
your
Quadrant
or
Meridian
Circle
,
cause
him
to
haue
the
same
Altitude
in
the
Globe
,
and
withall
to
be
vnder
the
Meridian
of
the
Globe
:
for
them
is
the
Pole
at
his
true
Eleuation
.
So
did
I
finde
the
Pole
Starre
(
making
my
obseruation
at
Oxford
,
the
11.
of
December
1584.
)
by
the
plaine
Sphaere
,
to
haue
55.
degrees
▪
59.
minuts
in
Altitude
,
being
then
in
the
Meridian
of
Heauen
:
and
when
I
set
him
at
the
same
in
my
Globe
,
I
found
the
Pole
eleuated
there
51.
degrees
.
50.
minuts
.
And
here
ye
are
to
knowe
,
that
when
soeuer
ye
haue
by
any
way
,
the
eleuation
of
the
Pole
in
any
place
:
if
ye
subduct
the
same
eleuation
from
90.
degrees
,
it
shall
leaue
and
she●…
the
eleuation
of
the
aequator
in
the
sayd
place
.
So
then
the
eleuation
of
the
aequator
at
Oxford
,
is
38.
degrees
.
10.
minuts
.
Propositio
.
35.
An other
way
of
working
the
same
,
with
more
praecisenes
.
FIrst
learne
by
some
good
Ephemeris
the
precise
place
of
the
Sunne
at
noone
in
the
day
of
your
obseruation
:
then
againe
learne
the
exact
declination
of
the
said
place
.
Lastly
,
with
your
〈◊〉
take
the
Meridian
height
of
the
Sunne
that
day
:
And
if
the
declination
bee
Northerne
,
then
subduct
it
from
the
Meridian
Altitude
:
but
if
it
be
Southerne
,
then
ad
it
to
the
Meridian
Altitude
:
so
shall
wee
bring
forth
the
Altitude
of
the
aequator
:
and
this
Altitude
being
subducted
from
90.
degrees
,
leaueth
the
Altitude
of
the
Pole
:
but
if
the
Sunne
in
the
time
of
obseruation
be
in
the
Aequinoctiall
point
,
then
is
the
Meridian
Altitude
,
the
Altitude
also
of
the
aequator
,
and
it
subducted
from
90.
degrees
,
leaueth
the
Altitude
of
the
Pole
.
Propositio
.
36.
To
make
a
Horizontall
Diall
by
the
Globe
.
A
Horizontall
Diall
is
such
a
one
as
is
made
in
a
plaine
Superficies
,
and
lyeth
leuell
with
the
Horizon
.
For
making
whereof
ye
are
to
consider
,
that
from
one
Pole
of
the
Globe
to
the
other
goe
twelue
great
Circles
,
called
hower
Circles
,
and
diuide
the
aequator
into
24.
aequall
parts
:
And
two
of
these
bee
two
Colures
.
Put
therefore
the
Solstitiall
Colure
precisely
vnder
the
Meridian
of
your
Globe
,
(
the
Globe
being
first
perfectly
rectified
)
and
fixe
the
Globe
so
that
he
cannot
mooue
.
Now
marke
how
many
degrees
of
the
Horizon
are
inclosed
betwixt
the
Meridian
and
the
next
hower
Circle
toward
the
East
(
which
for
distinction
sake
I
call
the
second
hower
Circle
)
so
likewise
betwixt
the
first
&
third
,
the
first
&
fourth
,
the
first
and
fifth
,
the
first
and
sixt
,
the
first
and
seuenth
:
(
which
is
he
that
cutteth
in
the
true
East
point
)
and
set
them
all
downe
in
tables
:
then
drawe
on
some
plaine
thing
a
Circle
,
and
diuide
it
into
fower
quarters
,
by
drawing
two
crosse
lines
:
Now
take
the
one
ende
of
any
of
the
two
lines
,
and
terme
it
the
North
point
,
so
shall
his
other
end
be
the
South
point
,
and
the
endes
of
the
other
line
East
and
West
.
Againe
,
diuide
that
quarter
of
this
Circle
which
is
betwixt
the
North
point
and
East
into
90.
aequall
parts
,
and
let
90.
stand
at
the
East
.
So
doe
by
the
quarter
betwixt
North
and
West
.
Lastly
,
recken
from
the
North
point
toward
East
,
so
many
degrées
as
your
tables
shewe
to
haue
〈◊〉
betwixt
the
first
and
second
hower
line
:
and
from
the
point
where
they
ende
,
drawe
a
line
by
the
Center
of
the
saide
Circle
:
and
so
doe
by
all
the
numbers
of
your
tables
:
for
so
shall
ye
haue
your
hower
lines
drawne
for
a
Horizontall
Diall
.
In
whose
Center
must
be
a
stile
erected
,
according
to
the
eleuation
of
your
Pole
.
But
this
I
leaue
obscure
,
as
meaning
to
set
out
an
ample
treatise
of
Dialling
by
it selfe
.
Propositio
.
37.
How
the
Starres
may
be
knowne
by
the
Globe
of
Heauen
.
REctifie
your
Globe
in
the
open
ayre
by
the
4.
proposition
,
them
take
the
height
of
any
knowne
Starre
by
your
Instrument
,
afterward
looke
the
same
Starre
on
the
Globe
,
and
by
helpe
of
your
Quadrant
of
Altitude
put
the
same
Starre
at
his
height
taken
before
,
and
in
the
same
Coast
,
&
then
fixe
the
Globe
.
Now
if
ye
would
knowe
any
other
Starre
of
Heauen
,
then
take
the
same
Starre
his
height
with
your
Instrument
:
lastly
,
turne
your
Quadrant
of
Altitude
toward
the
same
Coast
of
the
Globe
in
which
the
Starre
was
in
:
&
looke
what
Starre
ye
finde
in
that
Coast
,
to
haue
that
Altitude
,
the
same
is
he
whom
ye
seeke
.
The
like
is
to
be
done
by
all
others
.
Propositio
.
38.
To
finde
the
Longitude
of
any
fixed
Starre
.
THE
Longitude
of
a
Starre
,
is
the
portion
of
the
Ecliptick
line
,
taken
from
the
head
of
Aries
,
(
according
to
the
order
of
the
Signes
)
to
the
point
of
the
Ecliptick
,
cut
by
a
Circle
which
passeth
from
the
Pole
of
the
Ecliptick
,
by
the
Center
of
the
sayd
Starre
:
and
is
thus
found
.
Take
the
Globe
from
his
Horizon
,
and
take
of
his
Meridian
Circle
,
and
fixe
the
same
Circle
by
some
meanes
on
the
Poles
of
the
Zodiack
,
then
turne
the
Starre
whose
Longitude
ye
seeke
,
vnder
the
Circle
:
and
recken
all
the
Signes
and
parts
from
the
head
of
Aries
,
to
that
point
of
the
Ecliptick
which
is
vnder
the
Circle
with
the
Starre
:
for
so
much
is
his
Longitude
.
And
the
same
point
of
the
Ecliptick
which
is
so
vnder
the
Circle
,
shal
be
called
the
place
of
that
Starre
.
And
the
Starre
is
sayd
to
bee
vnder
that
Signe
,
of
whom
the
aforesaid
point
is
a
part
.
The
Longitude
may
also
be
taken
,
if
ye
doe
but
fixe
the
Quadrant
of
Altitude
in
the
Pole
of
the
Ecliptick
,
and
stirre
not
at
all
the
Meridian
Circle
.
Propositio
.
39.
To
finde
the
Latitude
of
any
Starre
.
THE
Latitude
of
a
Starre
,
is
the
portion
of
the
Circle
that
passeth
from
the
Poles
of
the
Ecliptick
line
,
by
the
Center
of
any
Starre
,
which
is
inclosed
betwixt
the
Ecliptick
line
and
the
Center
of
the
Starre
,
and
is
found
thus
.
Your
Circle
standing
in
the
Poles
of
the
Zodiack
as
before
:
turne
the
Starr
vnder
the
said
Circle
:
for
then
the
portion
of
that
Circle
betwixt
the
Starre
and
the
Ecliptick
,
is
his
Latitude
.
And
this
Latitude
is
Northern
,
when
the
Starre
is
North
from
the
Ecliptick
:
and
Southerne
of
contrary
.
Propositio
.
40.
To
finde
what
Starres
be
aboue
ground
at
any
time
of
the
day
or
night
.
IF
ye
would
know
it
in
the
day
time
when
the
Sunne
shineth
,
then
take
the
height
of
the
Sunne
by
the
2.
proposition
:
afterward
finde
his
place
by
the
5.
proposition
:
lastly
,
by
help
of
the
Quadrant
of
Altitude
,
set
the
Sunne
at
his
owne
height
&
Coast
,
and
then
all
the
Starres
aboue
the
Horizon
doe
appeare
in
the
Globe
.
Now
if
it
be
in
the
night
,
and
the
Starres
appeare
,
then
take
the
height
of
some
knowne
Starre
,
and
place
the
same
Starr
at
his
due
height
in
the
Globe
,
so
shall
ye
see
the
same
.
Propositio
.
41.
To
doe
the
same
without
Sunne
,
or
appearaunce
of
any
Starre
.
YE
must
knowe
what
it
is
of
the
clocke
at
that
time
when
ye
would
worke
this
conclusion
:
then
rectifie
the
Index
by
the
14.
proposition
:
Lastly
,
turne
the
Globe
till
the
Index
come
on
the
same
hower
as
is
giuen
by
the
clocke
,
for
then
the
Starres
appeare
as
they
should
.
Propositio
.
42.
To
finde
what
Starres
will
passe
directly
ouer
our
heads
in
the
motion
of
the
heauen
.
AFter
that
the
Quadrant
of
Altitudes
is
fixed
in
his
due
place
,
as
is
spoken
of
before
,
so
that
he
now
doe
shewe
the
Zenith
or
Verticall
point
:
then
mooue
about
the
Globe
,
and
marke
what
Starres
passe
vnder
the
Zenith
in
this
motion
,
for
those
bee
such
as
goe
by
our
heads
,
&
are
called
sometimes
Culminant
starres
,
sometimes
Verticall
starres
,
and
haue
their
cheefest
vse
in
Astrologie
.
Propositio
.
43.
To
knowe
with
what
degree
of
the
Ecliptick
any
Starre
rised
,
commeth
to
the
Meridian
:
or
setteth
.
MOue
the
Globe
till
the
Starre
whom
ye
propose
,
ascend
aboue
the
Horizon
,
and
then
marke
the
degrée
of
the
Ecliptick
that
riseth
with
him
.
Againe
mooue
him
to
the
Meridian
,
and
marke
the
degree
of
the
Ecliptick
,
so
doe
by
him
in
the
West
side
of
the
Horizon
,
and
ye
shal
haue
your
intent
.
Propositio
.
44.
To
knowe
the
hower
of
any
Starres
rising
.
REctifie
the
Index
by
the
14.
proposition
,
then
turne
the
Globe
til
the
said
Starre
(
whose
time
of
rising
ye
desire
,
)
touch
the
East
side
of
the
Horizon
:
for
then
the
Index
giueth
his
time
of
rising
.
And
if
ye
turne
him
to
the
Meridian
,
the
Index
will
shewe
his
time
of
comming
the
ther
:
or
if
ye
turne
him
to
the
West
side
of
the
Horizon
,
the
Index
sheweth
his
setting
.
Propositio
.
45.
To
find
in
how
long
time
any
whole
signe
ariseth
.
REctifie
the
Index
by
the
fowerteenth
proposition
:
then
put
the
beginning
of
the
signe
(
whose
time
of
rising
ye
seeke
)
to
the
East
part
of
the
Horizon
:
and
marke
what
the
Index
standeth
on
then
:
againe
,
put
the
last
degree
of
the
sayde
signe
to
the
Horizon
,
and
see
what
the
Index
sheweth
:
for
the
difference
of
the
two
times
by
the
Index
,
is
the
time
in
which
that
signe
riseth
.
Propositio
.
46.
To
find
in
what
coast
any
starre
is
,
and
how
many
degrees
from
the
Meridian
.
FInde
the
Starres
aboue
ground
by
the
40.
proposition
:
then
the
Globe
beeing
fixed
:
put
the
Quadrant
of
altitude
to
any
State
.
Then
shall
the
foote
of
the
Quadrant
shewe
in
the
Horizon
,
how
farre
the
same
Starre
is
from
East
,
West
,
North
or
South
.
But
if
ye
first
rectifie
your
Index
by
the
14.
proposition
:
and
then
finde
the
starres
aboue
by
the
40.
proposition
.
Agayn
at
the
same
time
marke
where
the
Index
standeth
:
lastly
put
any
Starre
vnder
the
Meridian
,
and
againe
note
the
standing
of
the
Index
:
the
difference
of
those
two
times
shewed
by
the
Index
,
is
the
distance
of
that
starre
from
the
Meridian
,
in
the
time
of
your
obseruation
.
Propositio
.
47.
To
find
what
Starres
rise
or
set
any
day
,
Cosmically
,
Achronically
or
Helically
.
SVch
starres
as
bee
neare
to
the
sunne
in
any
day
,
and
ascende
aboue
the
Horizon
a
little
before
the
appearance
of
the
same
:
are
said
to
ryse
helically
,
and
such
Starres
as
set
very
little
after
the
Sunne
,
are
sayd
to
set
helically
.
Againe
such
Starres
as
ascend
together
with
the
Sunne
,
and
such
as
set
at
the
same
time
,
are
sayd
to
rise
and
set
cosmically
.
Lastly
,
such
starres
as
set
together
with
the
Sunne
:
and
such
as
rise
at
the
same
time
:
are
sayde
to
set
and
rise
achronically
,
and
such
may
bee
thus
found
.
Rectifie
the
Index
by
the
14.
proposition
:
and
turne
the
place
of
the
Sunne
to
the
East
side
of
the
Horizon
:
for
the
starres
going
immediatly
before
the
Sunne
,
rise
helically
.
and
those
in
the
Horizon
rise
cosmically
:
and
they
that
are
in
the
Horizon
in
the
west
,
doe
set
cosmically
,
and
such
as
immediatly
rise
after
the
Sunne
,
doe
sette
helically
.
Lastly
turne
the
Sunne
to
the
West
point
of
the
Horizon
,
and
looke
what
starres
touch
the
Horizon
with
him
,
such
set
achronically
:
and
such
as
are
at
the
same
time
rising
in
the
East
,
rise
Achronically
.
Propositio
.
48.
To
knowe
the
hower
of
the
night
,
at
any
time
by
the
Starres
.
REctifie
the
Index
by
the
14.
proposition
,
then
againe
finde
what
starres
bee
aboue
ground
at
the
same
time
,
when
yee
would
know
the
hower
,
by
the
40.
proposition
:
for
then
the
Index
will
shewe
the
hower
.
Propositio
.
49
To
find
the
fower
Cardinall
points
of
heauen
at
any
time
of
day
or
night
.
THe
fower
Cardinall
points
,
bee
the
fower
degrees
of
the
Ecliptick
,
where
of
one
is
in
the
East
rising
:
an
other
is
in
the
South
or
vnder
the
Meridian
,
aboue
at
the
same
time
:
the
third
in
the
West
setting
,
and
the
fourth
vnder
the
Meridian
beneath
ground
,
all
at
one
instant
,
in
the
time
of
any
geniture
,
or
motion
of
any
question
,
and
are
thus
knowen
.
If
yee
seeke
them
in
the
day
(
the
Sunne
shining
)
then
find
the
starres
aboue
ground
by
the
40.
proposition
:
and
with
all
marke
the
degree
of
the
Ecliptick
in
the
East
.
so
likewise
in
the
South
,
West
and
North
,
for
those
be
then
the
Cardinall
points
.
Againe
,
if
it
be
in
the
night
,
then
find
the
starres
aboue
by
the
same
40.
proposition
.
and
the
pointes
shall
likewise
appeare
.
Lastly
,
if
nether
the
Sunne
shine
,
or
starre
:
then
knowe
the
hower
by
the
clock
,
and
afterward
find
the
starres
aboue
ground
at
the
sayd
hower
by
the
41.
proposition
.
so
shall
the
pointes
be
geuen
as
before
.
Propositio
.
50.
To
find
the
bignes
of
the
angle
,
made
betwixt
the
Meridian
Circle
,
and
any
Circle
of
position
.
CIrcles
of
Position
bee
all
such
,
as
are
drawen
from
the
North
point
of
any
Horizon
by
the
Center
of
any
starre
,
and
so
to
go
to
the
South
point
of
the
same
Horizon
,
to
returne
to
the
North
againe
.
And
euery
one
of
these
Circles
doth
make
some
with
the
Meridian
,
and
the
sayd
angle
hath
his
bignes
shewed
,
by
a
portion
of
the
fixed
Verticall
:
so
that
to
find
the
bignes
of
the
angle
made
betwixt
the
Meridian
and
any
Circle
of
position
:
is
to
find
the
portion
of
the
fixed
Vertical
,
inclosed
betwixt
the
Meridian
and
the
said
Circle
of
position
.
that
portion
is
thus
found
.
Put
your
quadrant
of
altitude
,
to
the
true
East
point
,
then
raise
vp
your
Brasse
halfe
Circle
as
high
aboue
the
Horizon
as
yee
please
:
so
that
it
may
nowe
represent
some
circle
of
position
.
for
then
the
degrees
of
the
Quadrant
of
altitude
from
the
Meridian
to
this
circle
:
be
the
bignes
of
the
angle
made
betwixt
the
Meridian
,
and
the
Circle
of
position
.
but
if
your
circle
of
position
fall
on
the
West
side
of
the
Meridian
,
then
put
the
Quadrant
to
the
West
point
;
and
worke
as
before
.
Propositio
.
51.
To
find
the
beginnings
and
endes
of
the
12
howses
of
Heauen
.
COncerning
the
erecting
the
scheme
of
heauen
,
or
as
we
commonly
call
it
the
twelue
howsen
:
though
fower
diuers
waies
haue
bene
receaued
,
touching
the
howsen
,
how
they
ought
to
bee
taken
:
yet
it
is
not
our
entent
to
discourse
of
that
question
,
but
to
shewe
howe
they
ought
to
be
erected
,
according
to
the
most
vsuall
way
,
set
downe
by
Regiomontanus
,
&
called
reasonable
.
Wherefore
first
ye
are
to
knowe
,
that
in
any
Horizon
wheresoeuer
wee
be
,
wee
doe
imagine
sixe
circles
to
be
drawen
from
the
North
point
of
the
Horizon
to
the
South
of
the
same
,
and
diuiding
the
Aequinoctiall
into
12
aequall
partes
,
and
the
12.
spaces
betwixt
these
circles
,
are
called
the
twelue
howses
.
(
&
two
of
the
6.
circles
are
alwaies
the
Meridian
and
Horizon
.
)
in
euery
one
of
these
howsen
is
inclosed
some
portion
of
the
Zodiack
,
and
one
portion
is
greater
than
an
other
.
so
that
to
erect
the
twelue
howsen
,
is
to
find
out
the
portion
of
the
Ecliptick
inclosed
in
ech
space
,
&
to
do
it
,
we
thus
proceede
.
First
find
out
the
fower
Cardinal
points
by
the
49.
proposition
,
for
those
be
the
beginnings
of
4.
howsen
of
the
twelue
:
the
Cardinall
point
vnder
the
Meridian
aboue
ground
,
is
the
beginning
of
the
tenth
howse
.
This
done
,
fixe
the
Globe
,
then
recken
from
the
degree
of
the
aequator
(
being
then
vnder
the
Meridian
)
30.
degrees
toward
the
East
point
,
&
raise
vp
your
brasse
halfe
circle
to
stand
on
the
point
of
the
aequator
on
which
yee
left
.
For
looke
then
what
degre
of
the
Ecliptick
is
cut
then
by
the
brasse
halfe
Circle
:
the
same
is
the
end
of
the
tenth
howse
,
and
beginning
of
the
eleuenth
.
Againe
,
yet
recken
30.
degrees
more
in
the
aequator
toward
the
East
,
and
put
the
brasse
halfe
circle
to
it
,
and
then
take
the
degree
cut
in
the
Ecliptick
,
for
that
is
the
end
of
the
eleuenth
howse
,
and
beginning
of
the
twelfth
.
Againe
the
Cardinall
point
of
the
East
,
is
the
end
of
the
twelfth
howse
,
and
beginning
of
the
first
howse
.
Now
if
in
like
sort
ye
goe
from
the
degree
of
the
aequator
vnder
the
Meridian
,
by
ech
30.
degree
of
the
same
toward
the
West
point
,
and
still
obserue
the
degres
cut
in
the
Ecliptick
:
yee
shall
haue
the
beginnings
and
ends
of
the
ninth
,
eighth
and
seauenth
howse
.
Thus
hauing
erected
sixe
howsen
,
the
degrees
of
the
Zodiack
which
are
opposite
to
these
in
a
Diameter
,
(
one
to
an
other
)
bee
the
beginnings
and
ends
of
the
other
sixe
howsen
,
which
were
to
be
found
.
And
here
must
yee
note
,
that
the
first
howse
beginneth
at
the
East
point
,
and
goeth
vnder
the
ground
toward
the
Meridian
Circle
,
the
second
and
the
third
succeede
.
the
fowerth
,
beginning
at
the
Meridian
vnder
ground
comming
toward
West
,
the
fifth
and
sixth
succeed
,
the
seuenth
beginneth
in
the
West
,
and
goeth
aboue
ground
toward
the
Meridian
,
the
eight
and
ninth
succeed
.
Other
conclusions
lesse
profitable
I
wittingly
auoyded
:
and
the
more
excellent
,
deferred
to
a
more
conuenient
time
.
FINIS
.