THE
FIRST
PART
OF
THE
RVDIMENTS
OF
THE
SPHERE
OF
HEAVEN
,
of
the
Starres
,
of
the
Orbes
of
the
Starres
,
and
the
EARTH
.
SEing
this
litle
Book
of
the
Sphere
dooth
intreat
of
that
part
of
Astronomy
,
which
sheweth
the
diuers
motions
of
the
Celestiall
Orbes
and
starres
,
the
magnitudes
and
distances
of
their
bodies
from
the
Earth
,
with
all
the
diuersities
and
néerenesse
of
appearaunces
in
the
Planets
,
and
fixed
starres
:
therefore
doth
the
Author
write
of
the
Principles
of
the
same
,
in
this
Treatise
of
the
Sphere
,
to
the
great
commodity
of
many
young
Students
in
the
Art
.
For
this
containeth
onely
the
intreating
of
the
Sphere
:
that
is
,
of
a
perfect
and
very
round
body
,
containing
diuers
Circles
,
which
the
learned
doo
also
call
a
Materiall
Sphere
:
of
the
Celestiall
appearances
that
it
describeth
in
the
Instrument
,
named
of
them
the
Materiall
Sphere
.
Now
this
teacheth
fiue
definitions
of
the
same
:
twoe
of
the
Sphere
,
one
of
the
Center
,
one
of
the
Exe
trée
,
and
one
of
the
Poles
of
the
World
.
1.
What
a
Sphere
is
.
EVCLIDE
in
his
eleuenth
Booke
,
thus
defineth
a
Sphere
.
A
Sphere
(
which
in
Latine
is
a
Globe
)
saith
he
,
is
a
sound
Figure
,
made
by
the
turning
of
a
halfe
Circle
,
the
Diameter
of
which
halfe
Circle
continuing
so
long
steddy
,
vntill
it
bée
brought
again
vnto
the
place
,
wher
that
Figure
began
to
be
drawne
.
Or
thus
:
A
Sphere
is
such
a
round
and
sounde
body
,
which
is
described
by
the
drawing
about
of
the
halfe
Circle
.
Theodosius
teacheth
another
definition
of
the
same
:
That
the
Sphere
is
a
certaine
massy
Body
,
or
sound
Figure
,
inclosed
with
an
vpper
face
or
platforme
,
in
whose
middle
is
a
Pricke
,
from
which
all
lines
drawn
from
the
Circumference
or
platforme
are
equally
distant
one
from
the
other
:
and
this
Pricke
,
of
him
named
the
Center
of
the
Sphere
;
and
like
of
the
Globe
.
The
halfe
Sphere
is
contained
in
the
halfe
of
the
Globe
,
and
greatest
Circle
of
the
Sphere
.
The
Exe-trée
of
the
Sphere
is
a
right
line
,
about
which
the
Sphere
fixed
,
doth
the
halfe
Circle
drawne
about
describe
.
There
are
also
two
maner
of
Orbes
,
as
the
Solyde
Orbe
,
and
hollow
Orbe
:
the
Solyde
is
named
the
Globe
or
Sphere
,
which
only
containeth
one
round
vpper
face
,
and
the
same
imbossed
hollow
outward
:
but
the
hollow
Orbe
differeth
,
in
that
the
same
hath
two
vpper
faces
,
the
one
imbossed
outward
,
and
the
other
hollow
within
.
Also
the
Orbes
of
all
the
fixed
starres
,
and
Planets
,
are
like
hollow
,
and
not
Solyde
.
To
the
Sphere
belong
these
differences
,
A
Pricke
,
a
Line
,
Dyametre
,
Parallels
,
an
vpper
face
,
a
Center
,
Exe-trée
,
and
Poles
.
A
Pricke
or
note
is
of
no
bignesse
,
but
the
beginning
of
Magnitudes
,
which
in
the
order
of
nature
goeth
before
them
,
and
not
made
as
a
part
:
in
that
a
Line
is
not
made
of
Prickes
,
nor
Prickes
are
the
partes
of
a
Line
.
For
if
an
infinite
number
of
Prickes
were
heaped
and
ioyned
togither
,
yet
woulde
those
neuer
make
a
Line
:
so
that
a
Line
is
caused
,
through
the
drawing
of
a
Pricke
into
length
.
A
Line
,
is
a
length
without
bredth
and
déepnesse
,
and
ended
with
two
prickes
,
which
cannot
be
comprehended
,
but
by
Imagination
.
A
Dyametre
,
is
any
right
line
drawne
by
the
Center
of
a
Circle
,
and
middle
of
a
Figure
:
whether
the
same
be
plaine
,
Solyde
,
round
,
or
cornered
:
whose
endes
reache
and
come
from
side
to
side
of
the
Circle
about
,
and
deuideth
the
Circle
into
two
equall
partes
or
iust
halfes
.
The
Parallels
are
two
right
Lines
equally
drawne
,
which
extended
on
any
Platforme
vnto
an
infinit
length
,
doo
alwaies
kéepe
one
like
distance
,
and
neither
draw
neerer
,
nor
touch
togither
.
An
vpper
face
,
is
a
length
and
breadth
without
déepenesse
,
made
by
the
drawing
of
a
Line
into
breadth
:
Of
which
,
the
plaine
vpper
face
is
that
,
which
is
expressed
with
those
straight
Lines
which
it
hath
:
that
neither
the
middle
riseth
vppe
,
or
is
raised
at
the
endes
,
nor
the
same
falleth
within
.
The
Sphericall
vpper
face
is
distinguished
,
into
an
imbossed
and
hollow
vpper
face
.
The
imbossed
,
is
the
outward
compasse
about
of
the
Sphere
,
or
bodies
round
:
but
the
hollow
vpper
face
,
is
the
inwarde
compasse
about
in
the
hollow
Orbe
,
or
the
bodies
hollow
.
A
Center
,
is
the
middle
Prick
in
a
Circle
,
from
which
all
right
Lines
drawne
vnto
the
compasse
about
the
same
,
are
equall
betwéene
the
one
and
the
other
.
Also
a
Centre
of
the
Sphere
,
is
a
middle
Pricke
in
the
Sphere
,
from
which
all
right
lines
drawn
vnto
the
imbossed
vpper
face
,
we
agrée
in
length
.
The
Exe
trée
,
is
a
right
line
drawne
by
the
Centre
of
●e
Sphere
,
and
with
both
his
endes
pearcing
vnto
the
●des
of
the
imbossed
vpper
face
,
about
which
the
Sphere
〈◊〉
turned
.
The
Poles
,
are
the
verie
endes
of
the
Exe-trée
,
appeaing
on
each
side
,
about
which
heauen
is
turned
.
Also
the
●oles
of
the
turning
,
are
named
the
endes
and
tops
,
and
named
besides
the
ending
pointes
of
the
Exe-tree
,
drawne
by
the
Centre
of
the
Sphere
:
about
which
the
Shere
and
Circles
of
the
Sphere
are
turned
.
The
Poles
of
the
Sphere
,
and
Circles
described
in
the
Sphere
,
are
pointes
consisting
in
the
vpper
face
of
the
Sphere
,
from
which
all
right
lynes
drawne
vnto
the
compasse
of
the
Circles
are
equall
.
Although
euery
greater
Circle
in
the
Sphere
of
the
worlde
hath
his
Poles
,
yet
is
oftner
mention
made
of
the
Poles
of
the
worlde
,
or
Equinoctiall
of
the
Zodiacke
,
and
Horyzont
.
The
Poles
of
the
world
or
Equinoctiall
,
are
the
two
extreame
poyntes
and
both
endings
of
the
Exe
trée
of
the
world
,
about
which
the
Sphere
is
turned
.
The
one
of
the
Poles
,
which
eleuated
sheweth
to
vs
dwelling
into
the
North
,
and
turneth
alwaies
about
in
our
sight
,
is
named
the
Boreall
and
North
Pole
,
of
the
litle
Beare
neare
to
it
:
which
Pole
is
continualy
séene
and
knowne
by
the
two
starres
neare
to
it
;
of
which
the
one
is
notable
and
cleare
,
of
the
thirde
bignesse
,
standing
at
the
ende
or
top
of
the
tayle
of
the
little
Beare
,
distant
from
the
very
Pole
4.
degrées
,
and
9.
minutes
.
But
the
other
dimmer
,
of
the
fourth
bignesse
,
not
farre
distant
from
the
other
star
afore
,
is
come
nearer
,
and
doeth
scarcely
differ
nowe
50.
minutes
from
the
place
of
the
true
and
very
Pole
.
If
any
will
know
the
Pole
of
the
world
or
Pole
starre
,
let
him
turne
his
face
towarde
the
North
,
the
sky
then
being
cleare
;
leauing
the
East
on
the
right
side
,
and
west
on
the
left
side
,
and
he
shal
see
in
the
little
Beare
seauen
stars
,
placed
like
to
the
forme
of
the
starres
of
the
great
Beare
,
which
are
brighter
.
Of
these
stars
three
doe
fashion
the
tayle
,
and
that
which
is
in
the
top
of
the
tayle
,
is
named
the
Pole
star
,
which
declineth
in
our
time
from
the
Equatour
85
degrées
,
and
5●
▪
minutes
.
So
that
beeing
no
further
off
by
this
declination
from
90
degrees
,
the
distance
of
it
from
the
very
Pole
shall
remaine
and
bee
4.
degrées
,
and
7.
minutes
:
and
this
starre
also
in
processe
of
time
shall
be
ioyned
with
the
Pole
.
The
other
Pole
,
which
through
the
swelling
of
the
earth
,
is
continually
hid
to
vs
of
the
North
,
is
named
the
Meridionall
or
South
Pole
,
right
against
as
it
were
the
North
Pole
.
Beeing
euermore
so
lowe
depressed
,
as
the
North
Pole
raysed
,
in
any
countrey
to
the
North
,
aboue
the
Horizont
.
The
Poles
of
the
Zodiacke
,
are
continually
so
farre
distant
from
the
Poles
of
the
world
,
as
is
the
greatest
declination
of
the
Sun
,
which
in
our
time
is
founde
and
noted
by
obseruations
to
be
of
23.
degrées
,
28.
minutes
,
and
30.
seconds
.
But
the
Borcall
or
North
Pole
of
the
Zodiacke
,
distant
from
the
two
dimme
starres
,
in
the
tryangle
of
the
Dragon
(
being
stars
of
the
sixt
bignesse
)
which
a
right
line
by
imagination
drawne
from
the
third
starre
in
the
tayle
of
the
little
Beare
,
vnto
that
constellation
named
Lyra
,
expresseth
the
same
,
that
it
is
but
a
little
further
distance
then
two
degrées
.
The
Poles
of
the
Horizont
,
are
the
twoe
extreame
pointes
or
ends
of
the
right
lyne
,
drawne
out
of
the
Center
of
the
Earth
,
by
the
top
ouer
our
head
,
vnto
the
opposit
places
of
the
Dyametre
of
the
Merydyan
:
of
which
the
one
,
directly
ouer
our
heade
,
named
the
verticall
poynte
,
and
of
the
Arabians
Zenith
,
the
other
right
against
,
named
of
them
Nadir
.
And
the
Poles
of
each
of
the
greater
Cyrcles
,
doe
differ
from
their
Circles
90.
degrées
,
or
a
quarter
of
an
other
greate
Circle
of
the
Sphere
.
For
by
the
23.
proposition
of
Theodosius
of
the
Sphere
,
a
right
lyne
drawne
from
the
Pole
of
his
Circle
vnto
the
circumference
,
is
equall
to
ech
of
the
foure
quarter
sides
,
descrybed
within
the
same
Circle
,
which
foure
quarter
sides
,
doe
deuide
the
Circle
into
foure
quarters
.
Yet
are
each
greater
Circles
of
a
Sphere
,
equall
betwéene
the
one
and
the
other
.
But
seeing
the
equall
right
lynes
,
doe
take
away
the
equall
compasses
of
the
equall
Circles
,
therefore
should
a
lyne
drawn
from
the
Pole
vnto
the
circumference
of
his
Circle
,
take
away
of
the
greater
Circle
,
one
quarter
of
the
other
Circle
drawne
by
the
Pole
,
euen
like
as
the
sides
of
a
quarter
described
within
the
Circle
.
By
which
appeareth
,
that
the
Poles
of
the
greater
Circles
,
doe
differ
or
be
distant
by
a
quarter
from
their
Circles
,
as
is
aboue
written
.
What
the
World
is
,
and
into
how
many
partes
the
same
is
deuided
,
with
the
motion
of
the
celestiall
Orbes
.
THe
Worlde
after
Orontius
,
is
defined
to
bee
a
perfitte
and
an
entire
composition
of
all
things
:
a
deuine
worke
,
but
finite
,
and
continually
to
be
merueled
at
:
adorned
with
all
kindes
of
formes
and
shapes
of
bodies
that
nature
coulde
make
,
which
in
all
partes
are
procreated
and
appeare
:
and
those
first
created
by
God
(
so
well
in
Earth
as
in
Heauen
)
by
his
onely
wor●
of
nothing
,
to
th'
end
the
same
might
bée
a
proper
mansio●
place
for
man
,
in
which
he
might
dayly
behold
,
and
mak
knowne
.
Aristotle
teacheth
two
definitions
of
the
world
:
the
one
,
that
it
is
an
apt
frame
wrought
,
consisting
both
of
heauen
and
earth
,
and
of
the
celestiall
and
inferiour
bodies
aptly
distributed
,
and
of
other
naturall
thinges
in
them
contayned
.
The
other
definition
is
,
that
the
world
is
a
perfit
body
,
and
most
perfit
rounde
forme
,
contayning
the
ordinance
and
distribution
of
bodies
,
created
by
God
to
tend
vnto
a
purpose
,
which
by
God
,
and
through
God
is
preserued
.
The
parts
or
Regions
of
the
worlde
,
are
two
:
as
the
Ethereall
,
and
Elementary
.
The
Etheriall
region
is
the
higher
and
vpper
parte
of
the
world
,
which
encloseth
the
Elementary
region
,
being
wholy
cleare
and
the
light
perfitte
,
and
contayning
the
Orbes
of
all
the
fixed
starres
and
Planets
,
distinguished
by
a
certaine
order
,
frée
of
all
mixture
and
all
strange
qualities
,
nor
harmed
by
any
alterations
.
In
which
the
celestiall
bodies
are
drawne
about
by
certaine
and
continuall
orders
and
times
of
the
motions
,
that
they
may
so
cause
the
diuersities
of
times
,
dayes
,
yeares
,
and
moneths
:
and
as
well
in
the
Elementary
nature
,
by
his
motion
and
light
,
ingender
,
mixe
,
and
temper
togither
the
first
qualities
,
and
prepare
also
other
effects
.
The
Elementary
region
,
is
the
nether
part
of
the
world
,
which
is
contayned
within
the
hollowe
vpper
face
of
the
Moones
Orbe
and
Sphere
,
in
which
are
all
corruptible
bodies
,
and
thinges
harmed
by
diuerse
alterations
,
except
the
minde
of
man
:
the
causes
of
which
,
are
the
contrary
actions
of
the
first
qualities
.
Also
the
foure
Elements
are
simple
bodies
,
which
into
parts
of
diuers
forms
cannot
be
deuided
:
yet
through
the
mutuall
commixion
of
these
,
are
diuerse
kinds
of
bodies
caused
.
Therefore
,
whatsoeuer
bodies
are
in
the
Elementary
region
,
bee
either
simple
,
myxt
,
or
compound
bodies
:
In
that
the
mixt
bodies
,
are
all
those
which
may
be
deuided
into
parts
of
diuerse
kinds
.
To
these
of
the
foure
Elements
,
the
next
ioyning
within
the
hollow
vpper
face
of
the
Moones
Orbe
,
is
the
most
thinne
Ayre
(
being
the
lightest
of
the
Elements
)
kindled
,
through
the
dayly
moouing
about
of
the
celestiall
circles
:
which
for
this
congruency
with
the
fire
(
named
the
elemental
fire
)
that
is
dayly
drawn
about
by
the
Orbs
compassing
it
,
which
may
appeare
by
the
Comettes
,
and
other
fiery
kindes
,
ingendred
in
the
same
Element
of
a
hot
and
dry
vapoure
,
that
are
likewise
caried
about
.
The
next
within
that
doth
the
ayre
runne
,
being
a
heauier
Element
then
the
fire
,
yet
lighter
then
the
water
:
which
also
is
drawne
about
by
a
like
motion
,
as
may
appeare
by
the
clouds
,
and
other
like
impressions
ingendred
in
the
same
,
but
to
the
nether
region
of
the
same
,
consist
the
laterall
motions
,
as
wée
dayly
sée
by
the
blowing
of
the
windes
.
Farther
,
Vitellio
in
his
tenth
booke
and
60.
chapter
affirmeth
,
that
the
cloudes
are
distant
from
the
vpperface
of
the
earth
25000.
paces
,
or
13.
Germayne
myles
.
But
acording
to
same
writers
,
they
are
vnequally
distant
from
the
earth
:
as
somewhiles
further
off
,
and
somewhiles
néerer
to
the
earth
.
For
when
the
cloudes
are
furthest
distant
from
the
earth
,
they
are
but
772000.
paces
,
and
being
nearest
the
earth
,
are
288000.
paces
distant
.
To
conclude
,
this
Elemente
compasseth
and
encloseth
,
both
the
earth
and
water
by
his
largenesse
.
The
nexte
Element
to
the
Ayre
which
mooueth
,
is
the
water
,
for
the
same
is
mooued
by
a
motion
of
flowing
and
ebbing
which
it
maketh
after
the
motion
of
the
moone
;
in
that
it
floweth
sixe
houres
,
and
ebbeth
so
many
,
vntill
the
moone
by
the
motion
of
the
first
moouer
,
hath
passed
about
all
the
quarters
of
heauen
.
Also
the
water
hath
a
motion
,
and
that
downward
into
the
earth
,
so
that
these
two
ioynt
ly
annexed
make
as
it
were
one
body
.
Yet
the
earth
béeing
the
heauiest
Elemente
,
hath
a
motion
attributed
as
it
were
simply
downwarde
vnto
the
middle
:
notwithstanding
agréed
of
all
men
,
that
the
same
is
immouable
,
and
the
Centre
of
the
world
.
These
foure
:
that
is
,
the
fire
,
ayre
,
water
,
and
earth
,
are
named
to
be
the
foure
Elements
,
and
both
the
simple
,
and
Original
matters
,
of
which
all
mixt
bodies
are
compounded
and
made
.
The
proofe
that
there
is
onely
fowre
Elements
,
is
this
:
that
to
each
Element
the
two
first
qualities
agrée
,
and
the
Combynations
the
like
of
the
foure
qualities
:
as
of
heate
and
dryeth
,
which
consist
in
the
fire
:
of
moysture
and
heat
,
which
rest
in
the
ayre
:
of
coldnesse
and
moysture
,
which
be
in
the
water
:
of
drynesse
&
coldnesse
,
which
is
found
in
the
earth
.
By
these
it
is
euident
,
that
there
are
but
foure
Elements
:
of
which
heate
excéedeth
in
the
fire
,
moysture
in
the
ayre
,
coldnesse
in
the
water
,
and
drynesse
in
the
earth
.
To
conclude
,
it
appeareth
,
that
heat
with
colde
,
and
moysture
with
dryeth
,
cannot
aptly
be
ioyned
.
What
the
Starres
are
,
and
that
,
as
to
the
motion
of
their
Orbes
,
they
are
carried
about
.
THe
Ethereall
region
contayneth
the
Starres
,
which
are
the
thicker
parts
of
their
Orbs
;
perfit
rounde
,
cleare
,
most
pure
and
simple
,
and
frée
of
any
mixture
,
except
the
Moor
which
is
darker
then
the
others
,
yea
variable
and
shadowed
.
And
these
fastened
to
their
Orbes
,
by
which
in
certayne
continuall
and
appoynted
times
and
orders
,
are
drawne
about
,
and
performe
their
returnes
in
the
determinate
spaces
of
times
,
and
those
continually
agréeing
in
themselues
,
that
they
may
so
ingender
the
differences
and
orders
of
times
,
and
in
the
inferiour
nature
prepare
and
cause
the
first
quallities
,
and
other
effects
.
The
Sunne
the
fountaine
of
light
,
doth
not
onely
giue
light
and
make
shine
cleare
the
inferiour
bodies
,
but
the
superiour
also
,
by
the
brightnesse
and
light
of
his
beames
.
But
the
Stars
seeing
with
a
borrowed
light
they
shine
,
which
is
far
weaker
then
the
sunnes
,
therefore
with
that
strange
light
which
they
take
properly
of
the
sun
doe
they
shine
,
although
vnlike
to
the
sun
.
For
into
all
the
starres
,
which
by
nature
are
rounde
about
thynne
,
and
penetrable
,
is
the
sunnes
light
equally
shed
and
pearceth
,
and
so
filleth
all
,
that
they
are
subiect
to
no
times
of
encreasing
and
decreasing
of
light
.
But
the
Moone
,
séeing
it
is
an
vnperfit
body
,
and
that
it
hath
the
partes
some
where
thynne
,
&
somewhere
thicker
and
better
compact
:
therfore
doth
it
not
equally
,
nor
round
about
receiue
the
sunnes
light
.
So
that
the
th
ynner
parts
take
more
of
the
sunnes
light
,
and
of
the
same
doe
clearer
shine
.
But
the
lesser
shadowed
parts
which
also
are
seene
,
appeare
darker
,
as
the
spots
in
the
moone
do
shew
.
That
the
bodies
of
the
starres
are
round
,
doe
the
round
formes
in
the
Eclipses
of
the
sun
and
moone
shew
:
yea
in
what
parts
of
the
world
those
Eclipses
happen
,
doe
the
bodies
also
of
the
starres
at
that
time
appeare
perfit
round
:
Although
the
bodies
of
the
starres
be
knowne
(
by
sundry
reasons
)
to
be
round
as
a
bowl
,
yet
by
their
great
distance
from
the
earth
,
appeare
to
vs
as
playne
or
flat
.
Nor
the
Starres
are
not
moued
by
their
owne
proper
motions
,
but
by
the
Accydentary
,
as
vnto
the
motion
of
the
Orbs
,
to
which
they
hang
,
as
partes
vnto
the
motion
of
the
whole
.
For
to
euery
round
body
doe
two
proper
motions
onely
belong
,
as
a
moning
to
and
fro
,
and
turning
about
.
Therefore
the
Starres
(
séeing
they
be
round
)
are
by
some
proper
and
principall
motion
caried
round
.
But
the
fixed
Stars
are
not
so
moued
rounde
,
in
that
they
turned
about
,
doe
not
altar
the
same
face
or
body
which
they
once
turned
and
shewed
to
vs
:
but
that
the
same
shoulde
of
necessity
happen
like
,
being
turned
round
in
one
place
,
about
their
Exe-trée
,
with
the
others
in
the
same
motion
béeing
in
the
parts
far
distant
,
and
the
others
then
set
and
hidde
vnder
the
earth
.
Nor
are
they
turned
hither
and
thither
,
in
that
they
neuer
change
the
standing
and
place
which
they
haue
in
their
Orbe
,
which
to
those
caried
hither
and
thither
woulde
happen
.
Therefore
,
not
by
a
proper
and
chiefe
motion
are
they
caried
about
,
but
by
an
accidentary
drawing
about
of
their
Orbes
,
which
what
the
same
is
,
shall
after
appeare
.
That
Heauen
is
drawne
round
.
THe
Ethereal
region
,
do
the
Philosophers
also
name
quinta
essentia
,
or
as
it
were
a
fifte
body
,
constituted
aboue
the
foure
Elementes
,
being
incorruptible
&
deuine
,
consisting
of
the
noblest
and
purest
part
of
the
ayre
.
Which
also
is
placed
aboue
the
holow
vpper
face
of
the
moones
Orbe
,
that
reacheth
vnto
the
hollow
vpper
face
of
the
highest
heauen
,
being
most
pure
,
perfitte
rounde
,
continually
caried
about
,
and
bright
appearing
.
This
parte
of
the
world
being
the
Etheriall
region
,
is
named
heauen
,
which
alwaies
drawne
about
by
a
meruelous
swiftnesse
,
is
deuided
into
nine
Orbes
or
Spheres
.
Although
sundry
Astronomers
,
as
Alphonsus
,
Iohannes
de
monte
regio
,
Purbachius
,
and
others
,
haue
added
a
tenth
Sphere
,
through
the
third
contrary
motion
founde
in
the
eighth
Sphere
,
named
of
Thebit
benchore
(
the
first
inuenter
of
the
same
(
Motus
trepidationis
,
or
the
going
and
comming
of
the
eight
Sphere
.
The
first
and
vppermost
Orbe
,
is
named
the
first
moouer
.
The
second
is
that
,
which
is
named
the
ninth
Sphere
or
Christaline
heauen
,
but
of
Ptholomy
,
named
the
firmament
or
Orbe
of
the
fixed
starres
.
And
the
thirde
is
that
,
which
(
of
them
)
named
the
eight
Sphere
,
onely
added
through
that
motion
of
the
trembling
,
or
as
it
were
a
mouing
foorth
and
returne
of
that
eight
Sphere
;
which
properly
is
caused
,
in
the
two
small
Circles
about
the
heades
or
beginnings
of
Aries
and
Libra
:
through
which
diuerse
motion
of
the
eight
Sphere
,
do
the
Equinoctials
and
Solstices
come
and
beginne
sooner
by
certaine
daies
,
and
the
suns
greatest
declination
deminished
(
and
dayly
doeth
)
to
that
in
Ptholomie
and
Hipparcus
time
,
which
then
was
23.
degrées
and
52.
minutes
,
and
30.
seconds
.
And
for
these
haue
Alphonsus
and
sundry
others
,
attributed
diuers
motions
to
the
eight
Sphere
,
adding
a
ninth
and
tenth
Sphere
to
it
.
That
there
are
but
eight
celestiall
Orbs
which
may
be
seene
.
ALthough
Ptholomy
affirmeth
,
that
there
are
nyne
Orbs
equally
distant
,
yet
are
there
but
eight
which
may
perfectly
be
séene
and
decerned
with
the
eie
,
both
in
the
standing
,
variety
of
motions
,
and
differing
in
the
periodes
or
courses
.
Also
they
are
in
such
order
disposed
,
that
no
Orbe
hindereth
the
motion
of
another
néere
to
it
.
As
the
Sphere
of
the
fixed
stars
,
and
the
seauen
Orbs
of
the
Planets
.
And
most
certaine
it
is
,
that
some
of
the
fixed
stars
are
drawn
by
a
swifter
motion
,
and
others
by
a
slower
motion
,
and
that
the
Apogea
or
ascentions
also
of
the
Planets
are
changed
,
after
the
order
of
the
signes
.
The
Orbs
of
the
Planets
thus
containe
and
compasse
one
an
other
,
as
first
the
Sphere
of
Saturne
being
nighest
the
firmament
(
of
which
being
compassed
)
doeth
like
containe
Iupiters
sphere
,
and
Iupiters
,
doth
in
the
same
maner
inclose
Marses
sphere
,
and
Marses
in
like
order
,
the
sunnes
sphere
,
nexte
the
suns
,
doeth
containe
Venus
sphere
,
which
like
doth
compasse
,
Mercuries
sphere
,
and
Mercuries
doeth
containe
the
Moones
sphere
,
being
the
lowest
and
smallest
sphere
.
And
euery
of
these
spheres
,
hath
a
star
a
péece
,
named
eractical
stars
or
planets
:
which
stars
haue
euery
one
their
proper
Orbe
seueral
,
his
motion
seueral
,
and
vnlike
in
time
one
to
another
,
in
that
they
appeare
one
whiles
néere
togither
,
and
another
whiles
are
séene
far
distant
asunder
.
By
which
it
agréeth
,
that
their
equall
motions
,
to
appeare
to
vs
vnequall
,
either
through
the
Poles
of
the
Circles
,
diuers
from
the
Poles
of
the
worlde
about
which
they
bée
turned
,
as
are
the
Poles
of
the
Zodiacke
,
vnder
which
the
eratical
stars
are
continually
drawn
and
moue
;
rather
for
that
the
earth
is
not
the
Center
of
those
Orbes
,
by
which
the
Planets
are
caried
and
moued
about
.
So
that
when
we
consider
those
mouings
by
the
Center
of
the
worlde
,
then
is
caused
,
that
they
séeme
to
vs
as
they
were
encreased
in
a
greater
bignesse
,
when
as
we
beholde
and
sée
them
néere
hand
,
and
that
lesser
in
bignesse
,
when
we
sée
them
placed
far
off
.
Euen
so
in
the
equal
circumferences
of
the
Orbes
,
through
the
diuers
distance
of
sight
,
wée
like
obserue
the
vnequall
motions
,
by
the
equall
times
.
Yet
indéede
neyther
of
these
happeneth
,
but
that
they
are
drawne
aboute
by
vnchangeable
spaces
,
beeing
a
like
distant
,
and
kéeping
one
manner
of
bignesse
.
For
if
this
were
,
then
the
sun
,
or
any
other
star
being
in
the
middle
of
heauen
,
should
séeme
or
appeare
bigger
(
which
it
doth
not
)
then
being
in
the
East
,
or
West
part
.
And
the
contrary
we
sundry
times
sée
,
when
as
the
sun
or
any
other
star
,
appeareth
bigger
in
the
quarters
of
the
East
,
and
West
;
which
is
not
caused
by
reason
of
the
shorter
distance
,
but
for
that
his
beames
in
the
vapors
,
which
doe
thicke
ascend
(
both
in
the
winter
time
,
and
in
raynie
weather
)
that
hang
in
the
ayre
betwéene
our
sight
,
and
the
body
of
the
star
,
are
then
broken
:
which
breaking
of
them
,
doth
cause
the
star
to
appeare
far
bigger
to
the
eie
,
then
in
déede
the
same
is
.
And
that
a
readier
and
easier
knowledge
may
bee
had
(
after
the
mind
of
Ptholomie
)
of
the
first
moouer
,
and
celestial
Orbs
with
the
number
of
the
Circles
and
Elements
inclosed
within
the
first
moouer
,
conceiue
this
figure
here
following
most
aptly
drawn
and
set
out
for
thy
further
instruction
.
This
Figure
declareth
the
number
,
disposition
,
and
order
of
the
celestiall
Spheres
,
about
the
Globe
of
the
Earth
.
That
there
are
two
first
motions
of
the
celestiall
Orbs.
ALthough
the
celestiall
Orbs
are
seuerally
drawne
,
by
proper
and
vnlike
motions
:
yet
be
there
two
first
motions
,
that
are
manifest
,
both
by
obseruation
,
and
iudgement
of
the
eie
.
The
one
is
of
the
first
mouer
,
which
Ptholomy
attributeth
to
the
ninth
Sphere
,
that
is
onely
drawn
about
by
an
equall
swiftnesse
,
from
the
East
into
the
west
,
and
from
thence
againe
into
the
East
,
vppon
the
Poles
of
the
worlde
or
Equatour
,
in
the
space
of
a
naturall
day
or
24.
houres
.
And
this
first
mouer
draweth
with
it
al
the
other
Orbs
,
much
like
a
ship
,
which
being
at
full
saile
,
doth
drawe
and
cary
al
her
men
,
&
other
liuing
things
which
are
in
the
Shippe
.
So
that
by
this
motion
of
the
first
moouer
,
the
neather
Orbes
,
which
the
first
mouer
compasseth
,
are
drawn
once
euery
naturall
day
,
or
in
the
space
of
a
day
and
night
,
about
the
earth
.
Also
this
first
mouer
,
doeth
not
onely
describe
and
measure
a
naturall
day
,
but
causeth
times
,
and
diuersities
of
dayes
and
nights
,
with
the
proper
motion
of
the
sun
;
and
it
dayly
bringeth
vp
stars
to
be
séene
,
and
carieth
vp
to
the
highest
,
and
after
hideth
them
againe
,
vnder
our
Horizont
in
the
west
.
Besides
it
is
the
common
measure
of
al
the
other
motions
.
The
other
motion
is
proper
to
the
eight
Sphere
,
and
to
the
Orbs
of
the
seauen
Planets
,
in
the
which
they
are
contrarily
caried
to
the
first
mouer
,
as
from
the
west
into
the
east
,
in
mouing
vnder
the
Zodiacke
,
and
about
the
Poles
of
the
same
:
and
not
in
Parallels
from
the
Equatour
equally
seperated
;
but
are
drawne
much
slower
,
yea
and
vnlike
.
As
by
a
like
example
;
when
a
ship
by
a
most
swift
course
is
caried
into
the
west
,
yet
may
the
Mariners
and
others
in
the
ship
walke
forwarde
in
the
meane
time
into
the
East
:
Euen
so
is
this
second
motion
of
all
the
other
Spheres
vnder
the
Zodiack
,
vpon
the
Poles
of
the
Eclipticke
.
Also
by
a
swifter
motion
are
they
caried
,
and
sooner
performe
their
courses
,
which
are
néerer
to
the
earth
▪
and
contrariwise
mooue
by
a
slower
pace
,
and
in
longer
t●●e
compasse
and
wander
aboute
the
signes
of
the
Zodiacke
,
which
are
further
distant
from
the
earth
.
Also
in
the
middle
of
their
courses
(
as
it
were
)
each
doe
often
stacke
or
bee
slow
,
and
often
times
stay
as
vnmoueable
,
and
sometimes
are
retrograde
,
after
againe
quicken
their
course
,
and
by
their
swiftnes
recouer
that
lost
of
the
former
tariance
.
So
that
they
neuer
kéepe
one
manner
of
way
,
but
one
whiles
from
the
middle
iourney
of
the
Zodiacke
doe
wander
into
the
North
,
and
another
whiles
into
the
South
.
To
conclude
,
they
be
ascended
high
from
the
earth
,
when
they
are
named
Apogei
,
and
discended
again
vnto
the
earth
,
when
they
are
named
Perigei
.
That
there
are
two
kindes
of
Starres
,
the
fixed
,
and
the
Planets
.
ALL
the
fixed
stars
that
hang
to
the
firmament
(
or
as
Ptholomie
affirmeth
)
to
the
eight
Sphere
,
are
named
fixed
:
not
for
that
they
consist
vnmoueable
,
but
that
they
moue
so
meruellous
slow
,
that
by
iudgement
of
the
eie
they
cannot
be
perceiued
to
mooue
:
yet
the
practitioners
haue
and
do
find
both
by
reason
and
obseruations
,
that
they
alwaies
seperated
by
vnmoueable
spaces
one
from
the
other
,
and
are
caried
in
parallels
as
it
were
in
their
Orbe
.
Ptholomie
,
Aristillus
,
Timochares
,
with
the
obseruations
of
Hipparchus
,
ioyned
vnto
those
which
he
knew
,
noted
that
the
fixed
stars
in
a
hundreth
yéeres
moued
one
degrée
.
But
Copernicus
being
of
later
yeares
(
as
about
the
yeare
of
Christ
1525.
)
that
examined
the
obseruations
of
the
auncient
men
,
and
compared
them
vnto
those
noted
of
him
,
founde
that
not
so
many
as
a
hundreth
yeares
,
but
in
seauentie
and
two
yeares
,
that
the
fixed
had
gone
one
degrée
:
and
that
in
euery
Egiptian
yeare
(
which
containeth
360.
dayes
)
the
fixed
to
haue
moued
50.
seconds
,
and
in
a
day
8.
thirdes
,
and
tenne
fourths
.
And
so
performed
their
whole
course
,
in
twentyfiue
thousand
,
eight
hundreth
,
and
sixtéene
yeares
,
25816.
Of
these
knowne
and
numbred
of
the
ancient
men
,
are
1022.
which
they
haue
deuided
into
sixe
differences
of
magnitudes
;
and
to
these
haue
added
certaine
obscure
,
and
certaine
cloudy
stars
.
The
fixed
stars
of
the
first
bignesse
,
of
which
are
numbred
to
be
fiftéene
,
and
that
both
in
bignesse
and
brightnes
excéede
all
the
other
starres
,
and
in
body
excéede
the
earth
107.
that
is
,
a
hundreth
seauen
times
,
with
a
eleuen
thréescore
fourths
.
The
fixed
stars
of
the
second
bignesse
,
of
which
are
accompted
45.
do
excéede
the
earth
in
greatnes
almost
eighty
seauen
times
.
The
fixed
stars
of
the
third
bignesse
,
of
which
are
numbred
to
be
208.
doe
ouerpasse
or
excéede
the
earth
seauenty
two
times
,
with
a
third
part
almost
.
The
fixed
stars
of
the
fourth
bignesse
,
of
which
are
reckoned
to
be
474.
that
are
fifty
foure
times
greater
then
the
Earth
,
with
a
halfe
or
a
little
more
of
the
earth
.
The
fixed
stars
of
the
fift
bignesse
,
of
which
are
noted
to
bee
216.
that
excéede
by
their
greatnesse
the
earth
31.
times
.
The
fixed
starres
of
the
sixt
bignesse
,
of
which
are
noted
to
be
50.
doe
excéede
the
earth
eightéene
times
,
and
a
little
more
.
The
darke
stars
,
are
accompted
3.
in
number
:
and
the
clowdy
stars
,
are
reckoned
to
be
fiue
.
The
fixed
stars
do
differ
in
brightnesse
,
standing
,
color
,
twinckling
,
and
especially
in
the
configuration
.
Many
of
the
fixed
stars
also
with
the
effects
both
in
the
bignesse
and
brightnesse
,
being
notable
and
néere
together
,
the
ancient
men
that
deuided
them
by
a
certaine
reason
,
haue
gathered
,
digested
,
and
fashioned
them
,
into
forty
and
eight
images
or
similitudes
.
And
vnto
them
through
the
congruence
and
similitude
of
the
noted
formes
or
figures
,
they
gaue
apt
names
:
and
for
the
same
cause
especially
,
that
they
might
the
easier
and
sooner
be
discerned
,
knowne
,
and
noted
by
their
peculiar
names
.
Also
they
deuided
the
stars
,
by
the
standing
into
the
North
and
South
,
and
the
signes
of
the
Zodiacke
.
The
Northerly
stars
that
decline
from
the
Ecclipticke
into
the
North
,
are
twenty
and
one
in
number
.
The
Southerly
,
that
decline
from
the
Ecclipticke
into
the
South
,
are
fiftéene
in
number
.
The
images
that
are
named
the
signes
,
are
twelue
in
number
,
which
consist
in
the
Zodiacke
.
Of
the
celestiall
Images
,
and
of
their
diuers
names
,
being
in
number
,
48.
Of
the
Northerly
.
-
_1
THe
litle
Beare
hath
seuen
stars
,
and
of
those
,
that
star
which
is
in
the
top
of
the
tayle
,
is
named
the
Pole
star
.
-
2
The
great
Beare
,
hath
27
stars
,
8
without
forme
.
-
3
The
Draggon
hath
31.
stars
.
-
4
The
image
named
Cephe
us
,
hath
12
stars
.
-
5
The
image
Bootes
or
Lauceator
,
hath
22.
stars
.
-
6
The
Boreall
or
Northerly
crowne
hath
8.
stars
.
-
7
The
image
kneeling
or
Hercules
,
hath
28.
stars
.
-
8
The
Harpe
or
Griepe
falling
,
hath
10.
among
these
the
brightest
is
that
named
the
Harpe
.
-
9
The
wilde
Swanne
or
Griepe
flying
,
hath
17.
-
10
The
image
Cassiopia
,
hath
13.
stars
.
-
11
The
image
Perseus
carying
the
heade
Algoll
,
hath
26.
stars
:
of
which
,
those
which
are
on
the
lefte
hande
doe
make
the
head
Algoll
or
Gorgons
,
3.
without
forme
.
-
12
The
Cartare
,
hath
14.
starres
,
among
those
,
that
which
standeth
on
the
lefte
shoulder
,
is
the
Goate
:
and
the
other
two
are
named
the
Kids
.
-
13
The
image
Ophiulcus
or
Serpentarius
,
hath
24.
stars
.
-
14
The
Serpent
,
hath
11.
stars
.
-
15
The
figure
named
the
Arrow
,
hath
5.
stars
.
-
16
The
Egle
hath
9.
stars
,
6.
without
forme
.
-
17
The
Dolphin
,
hath
10.
stars
.
-
18
The
deuision
of
the
Horse
,
hath
4.
stars
.
-
19
The
winged
Horse
or
Pegasus
,
hath
20.
stars
.
-
20
The
image
Andromeda
,
hath
23.
stars
.
-
21
The
Tryangle
,
hath
4.
stars
.
The
Summe
of
all
the
Starres
,
are
360
The
12.
Signes
of
the
Zodiacke
.
-
_1
THe
image
named
Aries
hath
13.
stars
.
-
2
The
image
Taurus
hath
23.
of
these
fiue
in
the
fore-head
of
Taurus
,
named
Succulae
or
Hiades
,
and
the
greatest
star
of
Hiades
in
the
Southerly
eie
,
named
Pallilicium
,
and
Pleiades
on
the
back
of
▪
Taurus
,
11.
without
forme
.
-
3
The
images
named
Gemini
,
are
18.
stars
:
of
which
Castor
or
Appollo
goeth
before
,
Pollux
or
Hercules
,
followeth
.
-
4
The
image
Cancer
hath
9.
stars
,
among
these
Presepe
,
and
the
cloudie
star
in
the
Breast
.
-
5
The
image
Leo
hath
27.
stars
:
of
these
,
that
which
is
in
the
heart
of
the
Lion
,
named
Regulus
,
8.
without
forme
;
among
which
is
that
constellation
,
named
Berenices
bush
of
haire
,
betweene
the
tops
or
endes
of
the
Lion
and
great
Beare
.
-
6
The
image
Virgo
hath
26.
stars
:
of
these
,
that
which
is
in
the
right
wing
,
especially
Northerly
,
is
named
Vindenuator
,
but
in
her
left
hand
a
bright
star
,
named
the
ear●
of
corne
,
6.
without
forme
.
-
7
The
image
Libra
,
and
klées
of
the
Scorpion
,
haue
8.
stars
,
and
9.
without
forme
.
-
8
The
image
named
the
Scorpion
,
hath
21.
stars
,
the
midle
star
(
of
the
thrée
stars
)
placed
on
the
Body
,
is
named
the
heart
of
the
Scorpion
,
and
3.
without
forme
.
-
9
The
image
named
Sagitarius
,
hath
31
,
stars
.
-
10
The
image
named
Capricornus
,
hath
28.
stars
.
-
11
The
image
named
Aquarius
,
hath
24.
stars
,
and
3.
without
forme
.
-
12
The
images
named
Pisces
,
haue
34.
stars
.
The
Summe
of
all
the
Starres
,
except
Berenices
bush
,
are
364.
Of
the
Southerly
.
-
_1
THe
image
named
Coetus
,
hath
22.
stars
.
-
2
The
image
named
Orion
,
hath
38.
stars
.
-
3
The
image
named
the
riuer
,
or
Eridanus
,
or
Potamos
,
hath
34.
stars
.
-
4
The
image
named
the
Hare
,
hath
12.
stars
.
-
5
The
image
named
the
Dog
,
hath
18.
stars
,
of
which
that
in
the
mouth
,
is
named
Alhabor
,
12.
without
forme
.
-
6
The
image
named
the
little
Dog
,
or
Caniculare
star
,
hath
2.
stars
;
of
which
the
brightest
is
that
named
Proion
or
the
Dog-starre
.
-
7
The
image
named
the
Ship
,
hath
45.
stars
,
of
which
a
bright
star
going
before
in
temone
.
-
8
The
image
named
the
Water
Serpent
,
hath
25.
stars
and
2.
without
forme
.
-
9
The
image
named
the
Bucket
or
great
Cup
,
hath
7.
starres
.
-
10
The
Rauen
or
Crow
,
hath
7.
stars
.
-
11
The
image
named
Centaurus
,
being
one
halfe
like
a
man
,
and
the
other
halfe
like
a
horse
,
hath
37.
stars
.
-
12
The
Beast
which
the
Centaure
doth
holde
,
being
a
Wolfe
,
hath
19.
stars
.
-
13
The
image
named
the
Aulter
,
hath
7.
stars
.
-
14
The
Southetly
Crowne
,
hath
13.
stars
.
-
15
The
Southerly
fish
,
hath
11.
stars
,
and
6.
without
forme
.
The
Summe
of
all
the
starres
,
are
316.
THe
milkie
way
,
which
Ptholomie
nameth
Galaxian
of
the
white
and
milkie
colour
,
is
a
heape
of
most
small
stars
,
and
dimme
to
sight
;
of
which
is
a
certaine
confused
gathering
together
,
and
abundance
as
it
were
encreased
,
that
no
seuerall
light
is
decerned
:
and
the
same
(
in
the
maner
of
a
girdle
)
compasseth
and
encloseth
heauen
about
.
The
same
also
is
vnequal
,
and
differeth
in
the
standing
,
latitude
,
haunt
of
stars
,
and
in
the
colour
very
much
.
It
is
somewhere
decerned
clefte
,
but
the
parte
going
before
,
is
neither
whole
,
nor
maketh
a
whole
swathe
or
inclosure
about
,
but
lacketh
about
the
swan
and
Aulter
.
And
the
part
folowing
whole
,
being
in
no
place
broken
off
with
a
space
,
and
stretched
thwartly
in
heauen
:
and
from
the
partes
of
the
Zodiacke
Northerly
,
it
passeth
by
Gemini
,
and
Sowtherly
by
Sagitarius
,
and
Capricornus
.
Of
the
Planets
.
THe
Planets
,
named
otherwise
the
erring
and
wandering
starres
;
not
for
that
they
erre
by
a
wandering
and
vncertaine
motion
,
but
in
that
they
are
caried
aboute
by
a
diuers
and
vnlike
motion
.
For
sometimes
they
goe
foreward
,
and
sometimes
retrograde
;
sometimes
are
hidden
and
cleane
out
of
sight
,
after
they
appear
and
shew
themselues
.
Againe
,
they
goe
before
,
and
follow
the
Sun
.
They
are
caried
swift
,
and
their
motions
againe
so
stayed
,
that
they
are
moued
in
a
maner
nothing
at
all
,
but
séeme
as
they
were
stayed
for
a
time
.
From
the
sunnes
way
,
one
while
caried
into
the
South
,
and
another
while
caried
into
the
North
,
and
then
vnto
the
same
way
drawne
backe
againe
:
so
that
their
iourneies
being
passed
and
finished
,
they
steadyly
repeate
their
old
courses
by
the
like
order
.
Of
these
are
seauen
,
and
each
caried
in
their
proper
Orbs
,
and
compasse
about
the
Zodiacke
,
in
vnlike
spaces
of
time
,
SAturne
highest
of
the
Planets
,
and
most
slow
in
course
,
being
cold
and
dry
,
pale
to
a
leady
colour
,
and
perfourmeth
his
course
in
30.
yéeres
,
being
ninty
times
,
with
an
eight
part
greater
then
the
earth
.
And
the
highest
ascention
or
pointe
of
Saturnus
Orbe
(
which
at
this
day
is
in
the
29.
degrée
of
Sagitarius
)
is
from
the
earth
20072.
semidiametres
,
with
a
fourth
part
almost
,
and
15.
minutes
.
But
the
lowest
point
of
Saturns
Orbe
,
is
distant
from
the
earth
,
14378.
with
a
third
part
,
and
20.
minutes
.
IVpiter
being
next
vnto
Saturne
,
temperate
,
and
so
cleare
or
bright
,
that
he
giueth
in
a
maner
a
shadow
(
especially
when
he
is
Perigeus
or
lowest
discended
to
the
earthward
)
and
he
compasseth
about
the
Zodiacke
in
twelue
yeares
.
But
Iupiter
giueth
this
proper
shadowe
,
when
neither
the
lights
bée
aboue
the
earth
,
nor
Venus
néere
to
him
.
Hée
is
greater
then
the
earth
,
by
ninty
fiue
times
,
and
a
half
part
almost
.
And
the
highest
ascention
of
Iupiters
Orbe
,
which
possesseth
the
seauenth
degrée
of
Libra
,
is
from
the
earth
14369.
with
a
fourth
parte
almost
,
and
15.
minutes
,
but
the
lowest
point
of
Iupiters
Orbe
,
is
from
the
earth
distant
8853.
semidiametres
,
with
a
ninth
part
and
45.
minutes
.
MArs
béeing
hot
and
dry
,
and
shining
with
a
fiery
colour
,
doeth
goe
about
the
Zodiacke
,
in
the
space
of
two
yéeres
.
He
is
named
the
fiery
Planet
,
of
his
shining
with
a
fiery
colour
,
or
of
the
effect
which
foloweth
by
him
,
in
that
he
burneth
and
dryeth
vp
.
He
is
one
time
greater
then
the
earth
,
and
a
little
more
then
a
third
parte
.
The
highest
ascention
of
Marses
Orbe
,
that
obtaineth
the
28.
degrée
of
Leo
,
is
now
distant
(
after
Albategnius
)
from
the
earth
8022.
semidiametres
:
but
the
lowest
poynt
from
the
earth
,
is
1176.
semidiametres
.
THe
Sunne
obtaineth
the
middle
place
betwéene
the
Planets
,
wholy
and
throughly
bright
,
being
the
fountaine
and
Author
of
light
:
which
by
his
motion
expresseth
and
deuideth
the
spaces
of
the
Zodiacke
,
and
by
his
going
about
,
haue
the
signes
their
names
.
He
is
greater
then
the
earth
(
after
Ptholomie
)
a
hundreth
thréescore
and
sixe
times
,
with
thrée
eight
parts
.
But
after
Capernicus
,
the
sun
excéedeth
the
earth
,
a
hundreth
thréescore
&
two
times
,
with
eight
parts
lesse
.
The
highest
ascention
or
poynte
of
the
suns
Sphere
,
which
n●w
possesseth
the
seuenth
degrée
of
Cancer
,
is
from
the
earth
distant
1179.
semidiametres
,
but
the
lowest
poynt
of
the
sunnes
Orbe
,
is
from
the
earth
distant
1065.
semidiametres
.
VEnus
next
to
the
Sun
,
being
cold
and
moist
,
white
in
colour
,
clearer
and
brighter
shining
then
Iupiter
,
and
is
caried
about
(
like
the
Sun
)
in
a
yeares
space
,
and
both
goeth
before
and
foloweth
the
sun
;
nor
is
further
distant
in
the
spring
of
the
morning
from
him
,
then
46.
degrées
,
and
47.
minutes
:
but
in
the
euening
,
she
is
seene
digrssed
from
him
,
vnto
47.
degrées
,
and
35
▪
minutes
.
When
she
goeth
in
the
morning
before
the
sun
,
thée
is
named
the
day
star
:
but
when
she
followeth
the
sun
in
the
euening
,
shée
is
then
named
the
euening
star
.
Lesser
shee
is
then
the
earth
,
but
her
true
quantity
is
yet
vnknowne
:
for
that
some
affirme
her
quantity
to
be
the
28.
part
,
and
others
the
37.
part
of
the
earth
.
The
highest
ascention
of
Venus
Sphere
,
that
obtaineth
the
18.
degrée
,
&
20.
minutes
of
Taurus
,
is
from
the
earth
after
Albategnius
1070.
semidiametres
,
but
the
lowest
poynt
,
is
166.
semidiametres
distant
from
the
earth
.
MErcurie
beeing
lower
then
Venus
,
is
variable
and
apte
to
bée
changed
,
bright
,
but
not
white
in
colour
;
and
is
caried
about
the
sunne
like
to
Venus
,
as
one
whiles
mouing
before
,
and
an
other
whiles
following
the
sunne
.
Nor
is
hee
further
distant
in
the
morning
from
him
,
then
29.
degrées
,
and
37.
minutes
,
and
at
the
euening
westwarde
,
27.
degrées
,
and
37.
minutes
.
He
perfourmeth
his
whole
course
,
in
the
space
of
a
yéere
,
as
the
sun
doth
.
Also
he
is
iudged
to
be
the
seauenth
part
of
2●
.
or
22000.
parte
of
the
earth
.
Albategnius
affirmeth
,
the
Star
of
Mercurie
,
to
be
least
of
all
the
starres
,
and
supposeth
or
accounteth
him
to
be
as
one
part
,
of
19000.
parts
of
the
earth
.
The
highest
ascention
of
Mercuries
Sphere
is
from
the
earth
▪
after
Albategnius
)
distant
166.
semidiametres
,
but
the
lowest
point
in
the
same
Orbe
,
is
56.
semidiametres
distant
from
the
earth
.
THe
Moone
being
lowest
of
all
the
Planets
,
doth
compasse
about
the
whole
Zodiack
,
in
27.
dayes
,
7.
hours
43.
minutes
,
and
7.
seconds
.
She
is
lesser
then
the
earth
(
after
the
iudgement
of
Ptholomie
)
by
thrée
hundreth
nine
times
,
and
a
vnity
more
then
eight
parts
.
For
the
triple
proportion
of
the
diametre
of
the
earth
vnto
the
moone
,
by
deuiding
aboue
the
fift
parts
,
is
euen
the
like
,
as
27.
vnto
5.
But
lesser
she
is
then
the
sun
,
by
sixe
thousand
,
fiue
hundreth
,
thirty
and
nine
times
.
Copernicus
(
by
his
obseruations
)
founde
the
earth
greater
then
the
Moone
,
by
forty
thrée
times
:
lesse
then
an
eight
part
:
and
of
this
,
the
sunne
also
is
founde
greater
then
the
moone
,
by
seauen
thousand
parts
,
lacking
thréescore
seconds
.
And
the
greatest
distance
of
the
new
and
full
mòone
from
the
earth
:
after
the
mind
of
Ptholomie
,
is
64.
semidiametres
,
and
10.
scruples
:
but
after
later
obseruations
,
65.
semidiametres
,
and
30.
scruples
.
And
the
lowest
to
the
earth
,
is
55.
semidiametres
,
and
8.
minutes
.
THe
Moone
digressing
from
the
Sun
euery
moneth
,
and
taking
or
receiuing
a
newe
light
as
it
were
,
in
that
she
(
is
changed
,
&
taketh
a
new
light
of
the
sun
)
doeth
after
encrease
by
little
and
litle
,
conceiuing
dayly
a
bigger
forme
and
light
,
vntill
shee
come
in
right
line
against
the
sunne
;
at
what
time
she
shineth
with
full
light
:
after
returning
againe
vnto
the
sun
,
she
waxeth
olde
by
loosing
of
her
light
by
little
and
little
:
and
in
the
contrary
maner
commeth
vnto
the
like
formes
of
light
,
vntil
she
comming
vnder
the
beames
of
the
sun
,
bée
quite
out
of
sight
.
Also
for
that
the
moone
hath
a
body
,
partly
thin
,
partly
thicke
,
solyde
,
and
shadowed
;
therefore
is
she
not
equally
filled
round
about
with
the
beames
of
the
sun
,
but
that
the
same
halfe
of
her
Globe
or
body
,
which
turned
againe
in
heauen
(
that
beholdeth
the
sun
)
is
it
which
shineth
,
and
the
other
halfe
turned
away
from
the
suns
light
,
is
that
which
shineth
not
,
but
remaineth
shadowed
.
That
Heauen
hath
a
round
fourme
and
to
be
carried
circularly
.
FIrst
,
heauen
is
equally
distant
round
about
from
the
earth
,
and
of
this
is
heauen
perfect
rounde
,
after
the
definition
of
the
Sphere
.
Which
reason
is
thus
proued
;
that
if
heauen
shoulde
haue
any
other
forme
then
perfect
round
,
then
of
necessity
must
the
stars
change
their
distances
from
the
earth
,
what
place
vppon
earth
they
shoulde
purchase
,
as
somewhere
more
,
and
somewhere
lesse
they
shoulde
bee
distant
;
and
the
standing
of
them
changed
,
should
also
alter
their
apparant
bignesse
,
in
that
they
should
appeare
greater
being
séene
néere
hande
,
and
lesser
,
being
séene
far
off
.
Yet
neither
of
these
happeneth
,
but
that
they
continually
kéeping
a
sunder
,
are
drawn
about
by
vnchangeable
spaces
,
and
holding
a
like
bignesse
and
distance
,
to
all
places
of
the
earth
.
That
the
stars
about
the
quarters
of
the
East
or
West
,
appeare
sometimes
greater
,
is
not
caused
by
reason
of
the
shorter
distance
,
but
for
that
their
beams
in
the
vapours
,
which
often
times
consist
in
the
ayre
betwéene
the
starres
and
our
eie
,
are
then
broken
;
which
breaking
of
them
,
causeth
the
body
of
the
star
séene
,
to
appeare
much
greater
in
the
eie
,
then
in
déed
it
is
.
That
heauen
is
drawne
circularly
,
is
thus
knowne
;
in
that
wée
alwaies
sée
all
the
Stars
,
from
the
East
into
the
West
,
to
be
drawne
vpward
,
and
that
the
hemisphere
in
our
sight
,
is
carried
continually
in
distant
cyrcles
equidistant
,
neuer
changing
the
standing
or
distance
,
one
from
another
,
neither
in
bignesse
,
as
far
as
the
iudgement
of
the
eie
can
descerne
,
neither
any
whit
lessoned
.
For
they
being
drawue
from
the
neather
place
(
as
from
the
earth
)
are
caried
by
little
and
little
.
And
after
they
be
thus
come
vnto
the
highest
of
their
iourney
(
as
vnto
the
noon-stéede
)
they
decline
again
by
little
and
little
,
till
they
be
brought
down
vnto
the
west
quarter
,
and
there
set
and
hidden
,
vnder
the
earth
:
and
these
places
and
times
,
both
of
the
risings
and
settings
doe
they
repeate
in
certaine
order
.
Therefore
by
these
it
appeareth
,
that
they
are
drawne
and
carried
by
round
.
By
the
second
it
is
euident
,
that
the
Starres
,
which
be
néere
the
Pole
Articke
,
are
neuer
hidden
out
of
our
sight
,
but
are
continually
and
vniformally
drawn
round
about
the
Pole
as
the
Centre
:
in
such
sort
,
that
the
stars
neare
to
it
make
the
lesser
compasses
,
and
the
stars
further
off
,
doe
define
greater
compasses
.
So
that
the
starres
fastened
to
their
proper
Orbs
(
as
aforewritten
)
are
cyrcularly
caried
.
By
which
two
motions
of
the
stars
,
as
well
tending
vnto
the
West
,
as
otherwise
;
it
plainly
appeareth
that
heauen
is
drawn
about
and
caried
round
.
A
manifest
demonstration
appeareth
of
the
former
argument
,
by
this
figure
here
following
.
That
the
Water
and
Earth
are
round
Bodies
,
and
by
a
mutuall
embracing
doe
make
one
Body
,
and
one
hollow
vpperface
.
THat
the
earth
is
round
,
is
thus
proued
.
Wheras
in
euery
vpper
face
,
the
length
and
breadth
is
considered
.
The
length
of
the
vpper
face
of
the
earth
,
is
from
the
West
,
into
the
East
,
or
contrariwise
.
The
bredth
is
from
the
South
,
into
the
North
,
or
contrariwise
.
That
the
earth
also
to
bee
rounde
,
appeareth
after
length
:
in
that
the
Sun
,
Moone
,
and
Stars
,
doe
neither
arise
,
nor
set
at
one
instant
time
alike
,
to
all
persons
dwelling
in
any
parte
of
the
earth
.
But
doe
much
sooner
appeare
and
shine
to
them
dwelling
vnto
the
East
,
and
within
a
whiles
after
they
shewe
to
them
dwelling
in
the
West
.
By
the
second
appeareth
,
that
one
and
the
like
Eclipse
of
the
moone
in
diuers
houres
,
is
séen
both
in
the
East
and
West
.
For
that
which
appeareth
in
the
first
houre
of
the
night
to
them
in
the
West
,
is
séene
to
them
in
the
East
parte
,
in
the
second
,
thirde
,
or
fourth
houre
,
euen
as
they
come
nearer
vnto
the
East
:
which
would
not
be
caused
,
if
the
night
to
both
places
should
happen
and
bée
at
one
moment
,
nor
sooner
woulde
they
appeare
to
them
in
the
East
part
.
Againe
,
there
bée
certaine
stars
,
which
in
their
rising
,
doe
appeare
sooner
to
them
in
the
East
parts
,
then
to
them
in
the
West
,
as
Plinie
writeth
of
Arbelis
(
being
a
towne
in
Asiria
)
where
an
Eclipse
of
the
Moone
was
séene
in
the
second
houre
of
the
night
,
which
in
Sicily
,
was
séene
in
the
first
houre
of
the
night
.
For
the
Assirians
are
more
Easterly
then
the
Sicilians
,
and
therefore
doeth
the
sun
set
sooner
with
them
,
then
with
the
Siciliaus
.
And
when
it
was
also
the
second
houre
of
the
night
in
Assiria
,
the
Sun
first
set
in
Sicilia
,
about
the
first
houre
of
the
night
.
Moreouer
the
Pole
of
the
world
(
acording
to
the
diuersitie
of
places
)
is
eleuated
and
depressed
.
So
that
the
cause
of
the
diuersity
of
this
appearance
,
is
onely
the
swelling
of
the
earth
.
To
be
briefe
,
the
beginnings
and
spaces
of
the
dayes
and
nights
,
and
that
in
diuers
places
of
the
earth
do
vary
,
and
yet
following
in
a
maner
,
one
order
.
But
this
variety
could
not
happen
,
if
the
earth
were
not
Sphericall
,
and
all
about
equally
rounde
,
herein
excluding
both
vallies
,
and
the
toppes
of
hilles
,
which
applied
(
vnto
the
body
of
the
earth
)
cause
no
inequalitie
or
diuersity
at
all
.
For
the
swelling
of
the
earth
causeth
,
that
the
stars
be
not
séene
togither
in
all
countries
,
but
drawne
about
by
little
and
little
,
by
a
certaine
succession
and
order
,
that
they
so
appeare
sooner
to
them
in
the
East
part
,
then
to
them
in
the
West
,
through
the
swelling
as
yet
not
aboue
caried
,
which
swelling
being
high
betwéene
both
,
is
a
let
and
cause
of
the
later
appearing
of
them
to
the
west
:
and
by
that
meanes
also
kéepeth
and
hideth
the
stars
the
longer
from
their
sight
.
So
that
by
these
it
euidently
appeareth
,
that
the
onely
cause
,
is
the
swelling
of
the
earth
.
If
the
earth
were
fashioned
with
a
déepe
hollownesse
,
and
compassed
round
about
with
a
light
inclosure
,
then
should
the
stars
risen
,
be
soonest
séene
to
them
in
the
West
partes
,
and
much
later
appeare
to
them
in
the
East
.
For
that
the
higher
inclosure
to
the
hollownesse
,
as
a
wal
built
about
,
should
be
a
let
and
hinderance
to
the
sight
of
the
beholders
;
in
such
sort
,
that
those
starres
arising
,
it
shoulde
hinder
their
sight
.
If
the
earth
were
formed
with
places
standing
in
sharp
piller
forme
,
or
in
right
line
vp
;
then
should
the
stars
appeare
set
,
and
be
hidden
alike
to
those
places
,
and
no
differences
of
dayes
should
be
caused
,
but
that
they
shoulde
haue
one
like
day
,
and
the
sun
also
appearing
to
that
fide
,
which
they
shewed
:
so
that
whiles
the
Sun
runneth
and
compasseth
about
the
backe
parts
,
they
should
be
without
light
of
the
sun
,
and
should
remaine
al
the
time
in
shadow
and
darknesse
.
And
if
it
should
haue
a
Cubicke
for
me
,
then
should
they
sée
the
sun
sixe
houres
,
and
loose
or
be
without
light
and
sight
of
the
sun
,
other
eightéene
houres
.
If
in
round
piller-wise
,
as
if
the
howndes
were
playne
vnto
both
the
Poles
,
and
the
hollow
partes
should
decline
vnto
the
East
and
West
,
then
should
no
stars
continually
appeare
to
them
dwelling
in
the
hollow
:
but
that
certaine
stars
should
arise
vp
and
set
in
the
West
,
and
other
certain
stars
néere
to
both
the
Poles
,
should
alwaies
be
hid
.
To
conclude
,
if
the
whole
earth
were
framed
with
an
equal
playnesse
throughout
,
then
should
the
stars
appeare
at
one
moment
to
all
countries
;
and
setting
againe
,
should
hide
the
like
out
of
sight
:
and
by
that
meanes
shoulde
the
dayes
begin
and
end
alike
,
and
no
differences
shoulde
bée
obserued
.
To
all
such
arguments
,
seing
experience
onely
doth
repugne
or
contrary
them
:
It
is
therefore
manifest
,
that
the
earth
from
the
West
towarde
the
East
,
riseth
vp
into
an
equall
swelling
.
If
the
earth
also
were
plaine
from
the
East
vnto
the
West
,
then
shoulde
the
starres
arise
so
soone
to
them
in
the
West
,
as
to
those
of
the
East
,
which
is
a
manifest
error
.
Also
,
if
the
earth
wéere
playne
,
from
the
North
vnto
the
South
;
and
like
from
the
South
vnto
the
North
:
then
the
starres
which
were
to
some
of
a
continuall
appearance
,
should
alwaies
séene
the
fame
and
like
,
which
way
or
into
what
quarter
soeuer
a
man
goeth
,
which
also
is
vntrue
.
But
the
cause
which
maketh
the
earth
séene
plaine
,
is
through
the
ouer
great
quantity
,
which
causeth
it
so
to
appeare
to
euery
mans
sight
.
But
that
the
earth
is
round
(
according
to
latitude
)
the
diuers
eleuations
of
the
Pole
and
stars
(
eyther
alwaies
in
sight
,
or
continually
hidden
)
doth
euidently
declare
.
For
from
the
Equatour
,
in
going
forth
easilie
towardes
the
North
,
and
that
the
Pole
Articke
be
higher
raysed
,
and
the
stars
néere
to
the
Pole
raysed
vp
;
then
are
the
Stares
right
against
like
depressed
,
and
as
they
were
out
of
sight
,
and
so
much
the
more
as
they
go
further
from
the
Equatoure
:
nor
the
Northerly
stars
neuer
set
,
but
continually
drawne
about
(
in
sight
)
with
heauen
.
But
the
contrarie
happeneth
,
by
going
from
the
saide
Cyrcle
or
Equatoure
,
vnto
the
contrary
part
.
So
that
there
is
no
greater
cause
of
this
diuersitie
,
than
the
swelling
of
the
earth
,
which
if
the
same
shoulde
bee
plaine
,
the
starres
opposite
or
right
against
(
according
to
latitude
about
the
Poles
)
shoulde
offer
and
appeare
togither
to
all
countries
,
which
the
swelling
of
the
earth
hindreth
to
be
séene
.
An
instrument
,
by
which
the
roundnesse
of
the
Earth
(
according
to
latitude
)
may
be
proued
,
and
all
those
may
easily
be
shewed
which
are
taught
of
the
dayes
Artificiall
.
That
the
Water
hath
a
like
swelling
,
and
runneth
round
.
THis
by
two
reasons
is
prooued
,
the
first
is
most
certaine
,
by
a
mark
or
marks
standing
on
the
sea
banke
,
like
as
a
tower
,
stéeple
,
or
such
like
erected
of
purpose
,
so
that
a
shippe
sayling
into
the
déepe
,
and
carried
so
far
off
,
that
no
more
of
the
sides
or
bottom
can
be
descerned
,
sauing
the
top
of
the
mast
,
which
only
appeareth
to
the
sight
.
Or
thus
,
that
a
marke
stoode
on
the
sea
banke
,
and
a
ship
passing
forth
of
the
hauen
,
sayling
so
far
into
the
sea
,
that
the
eie
of
the
beholder
being
néere
the
foote
of
the
mast
cannot
decerne
the
marke
(
the
ship
in
the
meane
time
staying
or
standing
still
)
so
that
his
eie
being
in
the
top
of
the
mast
,
shall
perfectly
sée
that
marke
:
but
the
others
eie
being
néere
the
foote
of
the
mast
,
shoulde
rather
better
sée
the
marke
,
than
he
which
is
in
the
top
of
the
mast
,
as
may
more
euidently
appeare
,
by
lynes
drawne
from
either
place
vnto
the
mark
:
so
that
the
manifest
cause
of
this
,
appeareth
to
bee
none
other
,
then
the
swelling
of
the
water
.
But
here
are
all
other
impediments
excluded
that
may
otherwise
hinder
;
as
mists
,
foggs
,
and
such
like
vapours
ascending
.
Also
a
like
reason
of
the
impediments
of
this
aboue
written
,
is
,
for
that
the
water
ariseth
into
a
swelling
,
which
hindreth
the
sight
of
the
bottom
or
sides
of
the
ship
(
that
being
in
a
high
place
doeth
not
hinder
the
sight
of
the
same
)
as
the
top
of
the
mast
,
which
either
excéedeth
or
is
equall
with
the
swelling
of
the
water
.
For
men
sayling
on
the
mayne
sea
,
sée
nothing
round
about
but
the
Sky
and
the
Sea
:
but
comming
nearer
the
banks
,
do
by
litle
and
litle
descry
and
sée
,
either
high
hilles
or
cliffes
,
as
if
they
were
rising
forth
of
the
water
.
Also
to
those
that
dwell
on
a
high
ground
,
the
sun
first
ariseth
,
and
last
setteth
.
And
to
this
agréeth
,
that
out
of
the
higher
places
,
both
more
and
further
may
bée
séene
into
the
sea
,
then
in
vallies
or
lower
places
.
By
all
these
therefore
it
is
euident
that
the
vpper
face
of
the
water
swelleth
,
as
by
the
example
following
more
plainly
shall
appeare
:
but
an
other
example
of
the
same
shall
bée
here
rehearsed
,
by
a
similitude
of
one
part
as
the
whole
.
The
similitude
of
which
matter
conceiue
by
this
example
,
that
experience
dayly
teacheth
vs
of
the
drops
of
water
,
which
although
they
bée
small
,
yet
powred
on
drie
wollen
cloth
,
run
into
a
round
or
bunching
forme
;
which
without
doubt
shoulde
not
be
caused
,
if
the
part
folowed
not
the
nature
of
the
whole
of
his
kind
.
Now
the
example
aboue
promised
doeth
here
appeare
,
in
which
by
the
letter
A.
is
the
shippe
ment
to
come
vnto
the
marke
C.
In
which
being
in
the
poynte
A.
that
is
in
the
bothom
of
the
shippe
,
cannot
sée
the
marke
standing
in
C.
through
the
swelling
of
the
water
.
But
he
which
is
in
the
top
of
the
mast
,
as
in
the
poynt
B.
without
all
impediment
may
sée
the
sayde
marke
.
That
the
selfe
same
or
like
to
it
,
may
be
on
land
,
as
from
the
point
D.
none
excepte
hée
bée
foolish
or
starcke
mad
will
affirme
the
like
.
By
the
second
it
is
manifest
that
the
water
by
nature
is
caried
and
runneth
downewarde
,
and
stideth
or
falleth
from
higher
vnto
lower
places
,
so
long
,
vntill
it
hath
filled
and
bee
euen
with
the
earth
,
through
the
staying
of
high
heapes
of
earth
,
hilles
or
such
like
mighty
and
high
banks
inclosing
it
about
that
it
run
no
further
,
nor
make
no
hollownes
in
the
middle
of
the
earth
,
as
a
Center
of
the
earth
.
Which
therfore
gathereth
betwéene
the
empty
places
,
so
long
,
vntill
it
hath
filled
and
be
euen
with
the
earth
;
and
that
the
whole
togither
,
through
the
hollownesse
thus
made
equall
,
doeth
fashion
and
kéepe
a
round
forme
.
So
that
the
earth
,
with
the
sea
,
and
waters
running
about
it
,
do
make
one
round
body
,
and
fill
all
the
whole
vpper
face
:
the
earth
also
gaping
and
open
somewhere
,
receiueth
water
into
those
hollow
places
,
but
a
parte
of
the
earth
appearing
somewhere
aboue
it
,
staying
and
inclo●●ng
it
about
with
strong
inclosures
and
banks
(
wrought
by
diuine
myracle
)
that
the
bare
places
of
the
earth
,
might
be
a
commodious
dwelling
and
féeding
for
all
beastes
,
and
other
liuing
creatures
.
And
that
this
is
true
,
shall
bée
prooued
by
other
two
reasons
.
The
first
,
by
sundry
perygrinations
,
in
which
many
and
most
large
parts
of
the
earth
are
found
toward
all
the
quarters
of
the
worlde
,
which
euidently
witnesseth
,
that
the
earth
is
not
as
Plinie
and
others
writeth
;
which
imagined
that
the
earth
is
compassed
about
with
water
,
and
appearing
so
out
of
the
water
,
like
an
Aple
or
Ball
swimming
aboue
the
water
,
whose
one
halfe
sheweth
out
of
the
water
,
and
the
other
halfe
hid
in
the
water
.
Which
reason
Ptholomie
doeth
not
allowe
,
but
simply
affirmeth
,
that
the
earth
with
the
sea
and
waters
,
make
one
round
body
,
by
filling
of
the
empty
places
,
and
both
to
haue
one
vpper
face
.
Also
Vitruuius
in
his
ninth
booke
writeth
,
that
the
earth
is
placed
in
the
middle
of
the
world
,
and
is
naturally
ioyned
together
with
the
sea
in
the
place
of
the
Center
.
But
what
the
forme
of
the
earth
is
,
aboue
the
waters
,
is
yet
not
throughly
knowne
,
by
reason
of
the
sea
which
runneth
betwéene
it
in
diuers
partes
,
and
breaketh
it
into
sundry
parts
,
like
to
gobbets
or
péeces
.
Ptholomie
affirmeth
the
earth
to
bée
knowne
,
vnto
the
longitude
of
the
halfe
Cyrcle
,
that
is
190.
degrees
,
without
any
running
betwéene
of
the
sea
in
that
space
;
for
that
the
earth
is
wholy
ioyning
together
.
But
into
latitude
,
he
affirmeth
the
space
to
be
much
lesser
,
as
79.
degrées
,
and
of
this
opinion
,
is
both
Strabo
and
Aristotle
.
By
the
second
it
appeareth
,
that
the
water
with
the
earth
,
doeth
equally
make
one
hollow
vpper
face
,
and
the
same
to
be
perfect
round
;
but
whether
is
bigger
,
is
greatly
to
be
doubted
:
although
the
learned
Nouius
,
and
sundry
other
late
writers
,
doe
affirme
the
face
of
the
earth
to
bee
bigger
then
the
water
.
By
the
third
(
which
is
the
Ecclipses
)
In
that
of
necesity
the
earth
must
haue
such
a
forme
with
the
waters
running
in
it
,
as
the
shadowe
of
the
earth
frameth
and
counterfeiteth
in
the
Moones
Ecclipses
;
in
that
the
shadowe
sheweth
and
expresseth
the
forme
of
the
bodie
shadowed
.
But
the
shadow
of
the
earth
to
be
included
round
aboute
with
a
round
vpper
face
,
the
wise
both
sée
&
know
.
Therefore
the
whole
Globe
,
compounded
of
the
earth
and
waters
,
is
comprehended
with
a
round
vpper
face
.
For
it
is
manifest
,
that
the
moone
before
and
after
the
full
,
is
séene
horned
,
and
the
part
shadowed
of
the
whole
cyrcle
,
is
easily
to
be
descerned
from
that
bright
circumference
.
So
that
the
moone
entring
into
shadow
,
or
going
out
of
the
same
,
is
likewise
in
the
same
maner
horned
:
and
the
part
darkned
,
is
alwaies
descerned
from
the
cleare
circumference
of
the
whole
Cyrcle
imbossed
.
Therefore
of
necessity
must
the
beginning
of
the
shadow
,
which
seperateth
the
parte
lighted
,
from
the
shadowed
,
not
bée
fully
straite
,
nor
vnequal
,
nor
vallied
or
winding
,
but
round
:
and
for
that
cause
appeareth
the
vpper
face
of
the
shadowe
not
to
bée
plaine
,
but
round
.
By
these
is
also
manifest
,
as
by
the
first
,
that
there
is
no
difference
betwéene
the
Centre
of
the
earth
,
and
Centre
of
the
water
:
but
that
the
one
,
is
the
Centre
of
both
the
Elements
,
ioyning
togither
into
one
round
body
,
and
tending
vnto
the
one
and
the
same
Centre
of
the
earth
.
For
the
earth
(
séeing
it
is
the
heauier
)
is
opened
,
and
receiueth
the
waters
falling
into
those
places
.
By
the
second
it
is
euidente
,
that
the
place
of
the
water
,
which
ought
to
run
ouer
and
couer
the
whole
earth
,
is
otherwise
chaunged
and
appoynted
by
the
Diuine
will
,
for
the
benefit
of
all
liuing
creatures
.
By
the
thirde
appeareth
,
that
the
opinion
of
certaine
Peripateticans
is
false
;
which
affirmeth
the
water
to
bee
ten
times
greater
then
the
earth
;
and
that
to
one
parte
of
the
earth
,
is
ten
portions
of
the
water
increased
.
But
seauen
times
greater
then
the
earth
it
cannot
be
,
vnlesse
the
earth
rounde
about
were
wasted
and
impayred
,
by
the
Centre
of
the
grauity
(
as
it
were
setling
and
resting
vpon
)
should
yéelde
,
and
giue
place
to
the
waters
,
as
the
heauier
.
Seeing
the
Spheres
are
togither
in
a
triple
reason
of
their
measures
,
then
if
the
earth
were
an
eight
part
,
to
seuen
parts
of
the
water
,
the
diameter
of
it
could
not
be
the
greater
;
as
from
the
Centre
of
the
waters
vnto
the
circumference
of
them
:
that
is
,
by
double
so
much
vnto
the
diameter
of
the
water
,
as
by
this
figure
here
vnder
drawn
appeareth
:
where
this
letter
A.
is
the
Center
both
of
the
earth
and
water
,
B.
the
Centre
both
of
the
magnitude
and
earth
,
G.
A.
D.
the
diametre
of
the
waters
,
A.
B.
D.
the
diameter
of
the
earth
.
If
the
waters
are
seuen
times
bigger
then
the
earth
,
the
diameter
of
them
must
néedes
bée
double
so
much
vnto
the
diameter
of
the
earth
,
as
héere
from
G.
D.
vnto
A.
D.
By
which
example
thus
drawne
,
the
whole
earth
receiueth
the
Center
of
the
waight
,
gyuing
place
to
the
waters
,
and
all
couered
with
waters
;
to
which
generall
experience
gainsayth
and
denieth
,
muchlesse
therefore
can
it
be
greater
ten
times
.
By
which
is
to
be
concluded
,
that
the
water
is
but
litle
in
quantity
,
in
respect
of
the
earth
,
although
it
may
séeme
very
bigge
,
being
vp
to
the
edges
of
the
vpper
face
of
the
earth
.
And
if
the
waters
had
béene
more
bigger
then
the
earth
,
they
had
drowned
or
couered
the
whole
earth
,
euen
of
late
yeares
.
That
the
earth
employeth
the
middle
place
of
the
Worlde
,
and
is
the
Center
of
the
whole
.
A
Ristarchus
Samius
,
which
was
261
yeares
,
before
the
byrth
of
Christ
,
tooke
the
earth
from
the
middle
of
the
world
,
and
placed
it
in
a
peculiar
Orbe
,
included
within
Marses
and
Venus
Sphere
,
and
to
bee
drawne
aboute
by
peculiar
motions
,
about
the
Sunne
;
which
hée
fayned
to
stande
in
the
myddle
of
the
worlde
as
vnmoueable
,
after
the
manner
of
the
fixed
stars
.
The
like
argument
doth
that
learned
Copernicus
,
apply
vnto
his
demonstrations
.
But
ouerpassing
such
reasons
,
least
by
the
newnesse
of
the
arguments
they
may
offend
or
trouble
young
students
in
the
Art
:
wee
therefore
(
by
true
knowledge
of
the
wise
)
doe
attribute
the
middle
seate
of
the
world
to
the
earth
,
and
appoynte
it
the
Center
of
the
whole
,
by
which
the
risings
,
&
settinges
of
the
stars
,
the
Equinoctials
,
the
times
of
the
increasing
and
decreasing
of
the
dayes
,
the
shadowes
,
and
Ecclipses
are
declared
.
The
earth
round
about
is
equally
distant
from
heauen
:
therefore
,
according
to
the
definition
of
the
Center
,
the
earth
is
the
Center
of
the
world
.
That
the
stars
haue
alwaies
one
bignes
,
in
what
place
soeuer
any
shall
beholde
them
:
therefore
are
they
in
an
equall
distance
from
the
earth
.
The
roundnesse
of
the
earthly
globe
,
hath
a
proportion
vnto
the
roundnesse
of
heauen
;
that
is
,
the
certaine
and
proportionall
parts
in
the
earthly
Globe
,
doe
answere
to
certaine
proportionall
partes
of
heauen
:
therefore
is
the
earth
the
Center
of
the
world
.
In
that
siftéene
Germaine
miles
on
earth
,
doe
answere
to
a
degrée
of
the
Meridian
:
and
that
in
euery
houre
doe
fiftéene
degrées
arise
of
the
Equinoctiall
;
which
coulde
not
be
,
if
the
earth
were
not
in
the
middle
of
the
world
.
For
the
vnequall
Arks
,
should
otherwise
appeare
in
the
equal
times
:
and
the
equall
partes
of
the
Meridian
,
shoulde
the
vnequall
spaces
on
earth
answere
:
which
experience
dayly
witnesseth
vnto
the
contrary
.
And
hereof
it
ensueth
,
that
the
earth
stands
in
the
middle
of
the
world
.
In
euery
Artificiall
day
,
doe
sixe
signes
appeare
,
and
sixe
like
set
vnder
the
earth
:
therefore
is
the
earth
in
the
middle
of
the
worlde
,
and
is
also
as
a
pricke
,
to
which
the
halfe
doth
regularly
moue
dayly
.
The
like
is
in
the
opposition
of
the
Sunne
and
Moone
,
when
either
light
is
in
the
Horizont
:
which
could
not
be
,
if
the
earth
should
approch
or
come
néerer
vnto
one
part
,
then
vnto
the
other
.
If
it
were
néerer
to
eyther
of
the
Poles
,
then
could
not
the
vniuersall
Equinoctials
bee
:
for
that
the
one
Arke
alwaies
(
either
in
the
day
and
night
time
)
should
be
greater
then
the
other
.
The
Eccclipses
also
coulde
not
bée
in
the
changes
and
full
moones
:
For
that
there
shoulde
then
bée
vneuen
spaces
from
the
South
vnto
the
North
,
and
from
the
East
vnto
the
West
.
If
the
earth
were
not
as
the
Center
of
the
worlde
,
then
of
necessity
shoulde
these
ensue
,
that
the
earth
shoulde
approch
,
either
néerer
to
the
East
,
or
West
,
or
South
part
:
and
when
any
of
the
starres
(
aswell
the
fixed
as
Planets
)
shall
come
vnto
that
part
,
they
shall
appeare
nearer
to
vs
,
then
being
in
any
other
part
of
heauen
:
and
by
that
aboue
saide
,
they
shall
also
appeare
greater
:
which
is
altogether
vntrue
,
and
we
also
sée
the
contrary
in
that
(
as
aboue
writen
)
they
alwaies
appeare
of
one
greatnesse
,
eyther
being
in
the
East
,
or
in
the
West
.
Also
one
halfe
of
heauen
is
alwaies
aboue
the
earth
,
and
the
other
halfe
vnder
the
earth
:
and
this
is
not
onely
found
and
knowne
in
one
quarter
of
the
earth
,
but
the
like
in
euery
place
(
as
the
Equinoctials
do
witnes
)
then
which
there
can
be
no
more
euident
tryal
.
A
third
reason
may
bée
alleadged
,
if
any
imagined
the
earth
vpon
the
Center
,
to
be
parted
into
two
equal
halfes
,
and
that
the
eie
is
placed
in
the
Center
:
then
shall
the
eie
sée
no
more
then
the
halfe
of
heauen
.
By
which
appeareth
,
that
the
swelling
of
the
earth
,
from
the
Center
vnto
his
compasse
about
,
in
making
a
comparison
vnto
heauen
is
as
in
a
maner
nothing
.
And
it
is
knowne
to
the
learned
in
Astronomie
,
that
any
of
the
fixed
starres
,
is
by
many
times
greater
then
the
earth
:
which
if
any
behold
them
,
they
appeare
as
poynts
in
heauen
.
Now
how
much
lesser
would
the
earth
appear
,
if
a
man
should
behold
it
from
his
place
.
Here
learne
by
this
demonstration
following
,
that
the
earth
standing
without
the
Center
,
in
the
poynt
B.
being
to
the
Meridiane
,
as
is
the
poynte
A.
nearer
;
and
when
a
star
shall
come
vnto
that
poynte
,
then
shall
it
bée
nearer
to
the
earth
,
and
in
the
opposite
poynt
,
as
is
I.
shall
bee
from
the
same
much
further
,
than
in
any
other
place
,
and
shall
euen
there
lesser
appeare
,
which
by
experience
,
is
quite
contrary
.
Further
graunt
that
C.
D.
be
the
thwart
Horrizont
,
yet
the
contrary
,
for
the
second
reason
,
E.
B.
K.
being
the
Equatour
,
which
from
the
said
Horrizont
is
deuided
into
two
vnequall
parts
,
and
by
this
consequent
also
must
the
Zodiacke
bee
deuided
into
two
vnequall
partes
,
from
the
said
Horrizont
:
for
that
those
two
Cyrcles
,
(
as
hereafter
shall
bee
taught
)
doe
crosse
one
another
into
equall
parts
.
Therefore
when
the
sun
,
by
his
proper
motion
,
carried
from
the
East
into
the
West
,
shall
come
vnto
the
crossings
of
the
Equatour
and
Zodiacke
,
and
that
the
greater
part
of
these
Cyrcles
shall
be
vnder
the
earth
,
it
cannot
be
that
the
Equinoctium
or
a
like
day
and
night
,
can
bee
through
out
the
earth
,
no
not
vnder
the
right
Sphere
,
much
lesse
can
it
be
vnder
the
thwart
Sphere
.
IF
this
be
vnpossible
,
it
shall
be
also
as
vnpossible
,
that
sixe
signes
may
alwaies
bee
aboue
the
earth
,
and
the
other
sixe
vnder
the
earth
;
but
rather
that
more
of
the
signes
shall
be
vnder
the
earth
,
and
more
of
them
aboue
:
euen
as
the
earth
is
imagined
to
be
deuided
from
the
Horrizont
aforesaid
,
into
two
equall
parts
;
like
as
when
it
shall
bée
in
the
Center
of
the
whole
,
and
that
from
each
Center
of
the
greater
Cyrcles
,
the
earth
is
deuided
into
two
partes
.
As
all
these
(
to
any
beholding
the
materiall
Sphere
)
are
forthwith
knowne
at
the
first
sight
:
so
by
a
third
reason
is
to
bee
noted
,
that
when
any
imagineth
,
by
the
lyne
E.
F.
that
the
earth
in
the
poynt
G.
standing
as
in
the
Center
of
the
whole
,
is
deuided
by
the
middle
,
as
well
beeing
in
G.
as
H.
for
the
excéeding
distance
from
the
Cyrcumference
,
is
vnpossible
to
sée
alwaies
the
halfe
heauen
.
If
the
Earth
be
not
in
the
middle
of
the
Worlde
,
then
of
necessitie
shall
it
possesse
some
of
these
standings
.
FIrst
,
the
earth
is
placed
without
the
Are
trée
of
the
world
,
yet
in
such
sort
,
that
it
is
equally
distant
from
either
Pole
:
that
is
,
that
the
Equinoctiall
may
be
in
the
plaine
vpper
face
,
as
in
the
letter
D.
appeareth
.
Secondly
,
that
it
is
standing
on
the
Exe-trée
of
the
world
,
yet
without
the
playne
vpper
face
of
the
Equinoctiall
;
that
is
,
that
it
be
néerer
to
eyther
of
the
Poles
,
as
in
the
poynt
B.
or
G.
Thirdly
,
that
it
is
neyther
standing
in
the
Exe-trée
of
the
world
,
nor
in
the
plaine
of
the
Equinoctiall
,
as
in
the
poynts
,
A.
C.
F.
E.
The
first
standing
béeing
graunted
,
these
absurdities
shoulde
then
ensue
,
through
the
diuers
placing
,
in
diuers
and
sundry
places
of
the
playne
Equatoure
.
1
In
the
right
Sphere
,
should
neuer
the
Equinoctium
(
or
a
like
day
and
night
)
be
caused
,
in
that
the
Horrizont
shoulde
neuer
cut
or
part
the
Equinoctiall
into
two
equall
halfes
.
2
In
the
thwart
Sphere
,
shoulde
no
Equinoctiall
Bee
,
and
somewhere
againe
should
the
Equinoctiall
be
,
but
not
in
the
middle
Parallell
,
betwéene
the
two
Tropickes
;
that
is
,
it
should
not
happen
the
sun
being
in
the
Equinoctiall
,
but
in
an
other
lesser
Parallell
Cyrcle
,
being
néerer
to
eyther
Tropicke
poynt
.
3
The
time
from
the
rising
,
vnto
the
Noone
tide
,
shuld
not
be
equall
to
the
time
from
the
Noone
tyde
vnto
the
setting
of
the
sun
.
4
The
magnitudes
and
spaces
betwéen
the
fixed
stars
,
both
in
the
East
and
West
,
shoulde
not
be
séene
equall
or
a
like
.
In
the
second
standing
,
if
that
the
earth
should
bee
placed
on
the
Exe-trée
,
and
not
in
the
myddle
of
the
worlde
,
then
should
these
absurdities
ensue
.
In
euery
Climate
,
the
playne
of
the
Horrizont
shoulde
cut
heauen
into
two
vnequall
halfes
,
except
those
places
hauing
the
right
Sphere
:
yea
,
and
the
Zodiacke
shoulde
be
deuided
into
two
vnequall
Arks
,
so
that
there
should
be
somewhere
more
,
and
somewhere
lesse
then
sixe
signes
of
the
Zodiacke
séene
aboue
the
Horrizont
,
which
is
contrary
to
all
experience
.
2
The
Equinoctiall
shadowes
,
both
of
the
rising
and
setting
of
the
sun
,
shuld
not
agrée
,
in
such
sort
that
they
might
fall
in
right
line
.
Neither
the
shadowe
of
the
rising
of
the
sun
in
the
Solstitial
or
longest
day
,
should
make
or
stretch
in
right
lyne
,
with
the
shadowe
of
the
suns
setting
,
in
the
Brumall
or
shortest
day
,
et
econuerso
In
the
third
standing
,
if
neyther
it
should
be
on
the
Exe-trée
of
the
worlde
standing
,
nor
in
the
plaine
of
the
Equatour
;
then
should
the
same
absurdities
ensue
,
which
are
vttered
in
the
two
former
.
To
conclude
,
wheresoeuer
the
earth
is
generally
placed
without
the
myddle
of
the
world
,
there
is
the
reason
of
the
dayes
equal
increasing
&
decreasing
in
the
thwart
Sphere
confounded
,
and
there
shall
eyther
no
Equinoctials
at
all
bee
caused
,
when
the
sunne
occupieth
the
myddle
way
betwéene
either
Tropicke
.
Nor
the
Moone
alwaies
shadow
the
suns
light
,
although
she
commeth
right
against
the
bodie
of
the
sun
.
And
the
earth
not
standing
in
the
myddle
of
the
world
,
shall
not
shed
or
stretch
his
shadow
to
the
moon
.
So
that
all
these
absurdities
and
vaine
argumentes
doe
grant
,
that
the
earth
cannot
bee
in
any
other
place
,
then
standing
in
the
middle
of
the
world
.
That
the
Earth
abideth
fixed
and
vnmoueable
,
in
the
myddle
of
the
world
.
THat
neyther
the
earth
,
in
right
nor
Cyrculare
motion
is
drawn
about
the
Exe
tree
of
the
world
,
nor
about
any
other
Exe-trée
,
but
to
rest
and
stay
in
the
myddle
of
the
worlde
;
both
holy
scriptures
confirme
,
and
Phisicke
reasons
prooue
.
For
the
Psalme
sayth
,
which
stablished
the
earth
vpon
his
foundation
,
that
it
shall
neuer
bee
moued
.
And
Ecclesiastes
in
the
first
chapter
sayth
:
that
the
earth
standeth
for
euer
,
and
the
sun
both
riseth
,
setteth
,
and
goeth
about
vnto
the
place
where
he
arose
.
Also
that
the
sun
is
drawne
about
,
the
Psalme
doth
manifestly
witnesse
,
where
it
is
saide
:
that
for
the
sun
,
hée
hath
placed
a
Tabernacle
in
them
,
and
he
,
as
a
Bridegroome
going
forth
of
his
chamber
,
doth
reioyce
as
a
Gyant
to
runne
his
course
,
which
goeth
forth
from
the
vttermost
bound
of
heauen
,
and
returneth
about
vnto
the
ende
of
it
againe
.
Also
it
is
knowne
and
numbred
among
myracles
;
that
God
would
haue
the
sun
to
continue
.
The
Phisicke
reasons
are
these
.
THat
of
one
simple
body
,
is
onely
one
simple
motion
.
That
the
earth
is
a
simple
bodie
:
therefore
therevnto
agréeth
but
one
simple
motion
.
But
of
the
simple
motions
,
I
haue
before
taught
,
that
the
one
is
in
right
maner
,
and
the
other
in
Cyrculare
forme
.
That
the
right
motion
séeketh
downwards
vnto
the
myddle
,
whether
being
caried
,
they
settle
and
rest
.
Therefore
is
the
motion
of
the
earth
not
cyrculare
about
.
By
the
second
appeareth
,
that
euerie
graue
or
heauie
matter
by
nature
,
is
thrugh
his
waight
caried
after
a
most
straite
lyne
vnto
the
Center
,
and
both
fetleth
,
stayeth
,
and
resteth
at
the
same
;
where
it
neither
falleth
,
or
is
caried
any
further
.
So
that
all
graue
matters
,
as
the
parts
of
the
earth
,
and
those
which
consist
of
the
earth
,
are
sent
or
caried
by
a
most
straight
leading
vnto
the
earth
,
and
at
his
vpper
face
shall
stay
and
rest
.
And
weare
it
not
that
they
are
staied
through
the
fastnesse
of
the
earth
,
they
should
so
long
be
caried
downwardes
,
vntill
they
came
vnto
the
Center
.
Also
the
earth
through
his
fastnesse
,
receyueth
and
beareth
all
thinges
falling
on
it
.
Therefore
doeth
the
earth
much
more
(
beeing
within
the
Center
)
stay
and
rest
fixed
and
vnmoueable
,
bearing
all
other
heauie
things
falling
on
it
,
séeing
the
earth
is
heauiest
of
all
others
.
By
the
third
it
is
euident
,
that
if
the
earth
shoulde
bee
moued
or
caried
,
it
should
of
necessity
be
either
drawne
in
right
,
or
cyrculare
motion
.
If
it
should
be
caried
in
a
right
maner
(
séeing
it
is
the
heauiest
of
all
others
)
it
shoulde
by
his
swiftnes
moue
and
goe
before
all
other
heauie
things
,
and
shoulde
leaue
behinde
the
liuing
creatures
,
and
other
things
fastned
to
it
,
and
shoulde
also
leaue
them
hanging
behinde
in
the
Ayre
.
If
the
earth
should
be
drawne
about
by
a
cyrculare
motion
,
&
should
in
a
daies
turne
(
at
the
least
)
be
caried
about
the
Exe-trée
,
from
the
West
into
the
East
,
as
either
alone
or
with
the
first
Orbe
:
then
euery
day
,
should
many
most
disordred
things
,
and
contrary
to
experience
happen
.
For
it
shoulde
bée
a
most
spéedy
motion
,
and
swiftnesse
inseperable
,
which
should
draw
cyrcularly
all
the
whole
earthly
body
rounde
about
in
24.
houres
.
And
therefore
that
the
earth
is
caried
with
so
swifte
motion
,
shoulde
not
onely
ouerthrowe
buildinges
,
but
high
hilles
,
and
greatly
shake
and
harme
all
thinges
fastned
and
growing
on
the
earth
:
yea
all
liuing
beasts
,
and
other
creatures
dwelling
on
the
face
of
the
earth
,
shoulde
bee
likewise
shaken
and
harmed
.
Also
the
cloudes
,
foules
,
and
whatsoeuer
liueth
and
hangeth
in
the
Ayre
,
should
bée
caried
and
lefte
behinde
at
the
setting
in
the
West
.
For
by
the
swift
turning
about
of
the
earth
should
all
things
be
ouer
turned
,
and
left
behind
by
a
greate
and
long
space
;
if
by
such
a
swiftnesse
,
the
earth
should
be
turned
about
the
Exe-trée
of
the
world
.
Or
if
by
the
motion
of
the
earth
,
the
ayre
,
and
all
things
hanging
in
the
ayre
,
should
be
drawne
with
a
like
swiftnesse
;
then
should
they
appeare
to
stay
,
or
not
to
be
moued
at
all
.
And
further
,
if
a
stone
or
any
waighty
thing
cast
vpward
shuld
not
light
againe
downe
right
on
the
same
place
:
as
may
be
séene
in
a
shippe
,
at
sayling
.
So
that
to
all
these
,
doeth
euident
experience
deny
,
that
by
no
motion
,
the
earth
is
any
thing
moued
,
dut
continually
stayeth
and
abideth
.
By
the
fourth
it
is
manifest
,
that
in
the
motion
and
turning
about
of
the
Cyrcle
,
the
Center
abideth
vnmoueable
:
which
is
the
earth
,
placed
in
the
myddle
of
the
world
,
and
is
as
the
Center
of
the
worlde
.
Therefore
is
the
Earth
knowne
to
be
vnmoueable
.
That
the
Earth
compared
vnto
Heauen
,
is
as
a
poynt
.
ALthough
to
the
vnskillfull
in
this
Arte
,
the
magnitude
and
largenes
of
the
earth
séemeth
to
be
of
an
excéeding
greatnesse
,
that
no
bond
or
ende
can
be
decerned
with
the
eie
;
nor
any
hauing
trauailed
into
farre
countries
,
could
hytherto
finde
any
bounds
of
the
same
:
yet
the
greatnesse
of
the
earth
compared
vnto
the
mighty
largenesse
of
heauen
is
accompted
but
a
pricke
;
as
the
Geomitricall
rules
declare
.
The
earth
also
is
a
very
small
thing
,
in
respect
of
heauen
:
yea
so
litle
in
comparison
,
as
a
pepper
corne
,
or
seede
of
Colliander
,
vnto
a
Cyrcle
of
a
thowsande
paces
compasse
.
For
if
the
earth
compared
to
the
firmament
,
were
of
any
sensible
greatnesse
,
a
man
shoulde
not
sée
the
halfe
of
heauen
,
nor
the
halfe
Cyrcle
of
the
Equinoctiall
or
Zodiacke
.
And
howe
much
greater
the
earth
shoulde
be
,
by
so
much
the
lesser
should
a
man
sée
the
halfe
of
heauen
.
But
the
contrary
is
knowne
,
in
that
on
any
plaine
of
the
earth
or
vpper
face
of
the
sea
,
a
man
alwaies
séeth
the
halfe
Sphere
of
heauen
,
the
other
halfe
(
in
the
meane
time
)
remayning
hid
:
and
of
this
the
halfe
dyameter
of
the
earth
is
so
small
,
vnto
the
distance
of
the
firmament
,
that
it
may
take
away
nothing
in
a
maner
of
the
halfe
Sphere
,
extant
to
the
eye
.
Besides
these
,
if
the
earth
should
be
imagined
to
be
placed
in
any
of
the
Orbes
of
heauen
,
it
woulde
appeare
but
small
in
respect
of
them
:
for
being
imagined
in
the
Moones
Orb
;
the
earth
should
appeare
thrice
as
great
as
the
moon
is
decerned
from
thence
,
and
somewhat
bigger
.
And
from
the
suns
Orbe
,
the
earth
should
be
decerned
twice
so
large
as
Venus
doth
here
appeare
to
vs
.
And
if
in
Marses
Sphere
you
would
say
that
the
earth
is
equall
to
a
small
star
;
But
from
the
firmament
,
Saturns
Sphere
,
or
Iupiters
(
if
a
man
could
decerne
it
)
the
earth
shoulde
appeare
so
small
,
that
a
man
would
be
abashed
at
the
sight
of
it
.
And
here
an
ignorant
man
,
might
greatly
wonder
,
that
so
small
a
body
,
yea
rather
a
pricke
(
as
it
is
accounted
of
the
learned
)
should
containe
in
it
so
many
Realmes
,
Prouinces
,
Citties
,
Towns
,
Flouds
,
Mountaines
,
Woods
,
Ualleyes
,
Seas
,
Riuers
,
Lakes
,
and
many
other
greate
matters
,
ouer
long
to
be
written
.
That
the
earth
also
is
as
a
Pricke
,
is
declared
by
sundry
reasons
following
.
By
the
first
,
that
round
about
the
earth
,
the
magnituds
and
distances
of
the
stars
,
in
their
times
,
are
decerned
and
séene
euery
where
equall
and
alike
.
By
the
second
,
that
the
Gnomons
or
dyall
shadowes
,
and
the
Centers
of
the
Sphericall
borderes
or
Cyrcles
,
placed
in
any
part
of
the
earth
,
do
somuch
auaile
,
and
kéep
the
considerations
and
guydings
about
of
shadowes
,
so
regularly
,
and
agréeing
to
the
rule
and
matter
,
as
if
those
(
in
very
déede
)
shoulde
bee
placed
in
the
myddle
poynte
of
the
earth
.
By
the
third
,
that
the
Horizont
doeth
euery
where
deuide
the
whole
heauen
into
two
equall
halues
.
For
that
in
euery
moment
,
doe
sixe
signes
of
the
Zodiacke
appeare
aboue
the
Horizont
,
and
in
the
night
time
being
a
fayre
sky
are
they
to
bée
séene
with
the
eye
,
and
so
many
(
at
that
in
.
stant
)
hid
within
the
Horizont
:
so
that
by
a
continuall
drawing
about
of
heauen
doe
sixe
signes
appeare
,
and
as
many
right
against
those
sixe
,
set
vnder
the
earth
.
If
the
magnitude
of
the
earth
shoulde
bée
of
any
light
portion
vnto
heauen
,
then
so
much
of
the
Center
(
the
vpper
face
drawne
aboute
)
shoulde
parte
or
deuide
heauen
into
equall
halfe
Spheres
.
The
other
Spheres
reatching
from
any
part
of
the
vpper
face
,
shoulde
deuide
the
same
into
vnequall
portions
.
Neither
halfe
the
Zodiacke
should
alwaies
appeare
,
but
a
portion
,
much
lesser
than
halfe
the
Zodiack
should
be
séen
aboue
the
earth
,
so
that
the
greater
parte
of
the
earth
,
through
the
folydnesse
excluded
and
hidden
,
should
not
after
be
séene
.
By
the
fourth
,
the
Equinoctiall
shadowes
,
both
of
the
rising
and
setting
of
the
sun
,
doe
make
a
right
line
,
euen
as
if
they
should
be
streached
out
and
lie
on
the
plaine
,
caried
by
the
Center
of
the
earth
.
So
that
all
these
should
not
be
caused
,
if
the
magnitude
of
the
earth
in
respect
of
heauen
,
should
be
of
a
sensible
,
or
of
any
portion
to
it
.
To
conclude
,
Ptholomie
vseth
alwaies
the
body
of
the
earth
for
the
Center
of
the
worlde
,
not
deuiding
the
vpper
face
from
that
which
is
not
in
sight
of
the
earth
.
Certaine
affirme
,
that
one
degrée
of
the
greatest
Cyrcle
in
heauen
contayneth
57051.
common
Germaine
miles
.
Of
which
one
degrée
of
any
earthly
Cyrcle
in
the
vpper
face
of
the
earth
,
doeth
amount
to
15.
Germayne
myles
.
And
that
one
minute
of
the
celestiall
degrée
,
expresseth
,
9509.
Germayne
miles
,
which
(
if
this
bée
true
)
and
certainly
knowne
,
then
is
it
not
vainely
thought
and
gessed
,
that
the
earth
is
as
a
Pricke
,
in
respect
of
heauen
.
To
finde
the
compasse
of
the
Earth
,
and
by
it
the
Dyameter
.
THe
whole
compasse
of
the
earth
,
according
to
Ambrosius
,
Theodosius
,
Macrobius
,
and
Eratostenes
,
doth
contayne
5400.
Germaine
myles
,
and
the
dyameter
of
the
same
,
doth
contayne
1718
4/22.
Germayne
miles
.
But
the
authority
of
Eratostenes
(
after
the
minde
of
Plinie
)
is
more
to
bee
regarded
,
then
the
other
thrée
Philosophers
,
which
prooueth
by
demonstration
and
reasons
,
that
the
compasse
of
the
whole
earth
is
,
252000.
furlongs
.
Yet
Hipparchus
finding
faulte
at
Eratostenes
,
doeth
affirme
the
compasse
of
the
earth
,
to
be
of
277000.
furlongs
.
And
a
furlong
is
here
(
after
the
agréement
of
the
Geometricians
)
of
a
hundreth
,
twenty
,
and
fiue
paces
.
And
this
sentence
is
not
here
mente
,
that
there
is
any
ambiguity
or
vncertainty
in
this
reason
:
but
that
the
one
affirmed
lesser
,
and
the
other
more
furlongs
.
For
after
Eratostenes
,
doe
700.
furlongs
answere
to
one
degrée
:
but
after
Hipparchus
,
774.
furlongs
answere
to
a
degrée
.
So
that
there
is
no
other
diuersity
in
the
matter
,
but
onely
the
number
.
Ptholomie
that
was
after
Eratostenes
,
attributed
seuen
hundred
fifty
furlongs
of
the
earthly
merydiane
,
to
one
degrée
of
the
celestial
meridiane
.
So
that
by
all
these
appeareth
,
that
the
magnitude
of
the
earth
is
as
yet
vnfounde
out
,
through
the
difficultie
of
measuring
.
And
this
whole
compasse
is
not
onely
ment
of
the
earth
,
but
of
the
earth
and
water
ioyntly
togither
,
both
which
are
saide
to
make
one
Sphere
.
Also
Eratostenes
gathereth
the
compasse
of
all
the
earthly
Orbe
,
by
the
proportion
of
the
perticular
,
or
the
degree
of
the
celestiall
Cyrcle
,
vnto
the
like
space
on
earth
.
For
he
affirmeth
,
that
to
one
degrée
of
the
celestiall
Equatour
,
answere
700.
furlongs
,
or
15.
Germayne
myles
,
but
Ptolomie
attributeth
to
a
degrée
,
500.
furlongs
.
Which
is
thus
to
be
vnderstoode
,
that
a
Cyrcle
be
imagined
on
earth
,
directly
vnder
the
Equinoctiall
or
Merydian
lyne
,
deuiding
the
earth
into
twoe
halfes
:
and
that
this
Cyrcle
be
likewise
deuided
into
360.
parts
or
degrées
as
the
celestiall
Cyrcles
are
.
And
ech
of
these
parts
doth
like
vnto
the
celestial
parts
,
containe
700.
furlonges
,
or
15.
Germaine
myles
.
This
nowe
being
tryed
and
found
,
what
the
whole
Summe
eyther
of
the
furlongs
,
or
myles
of
the
whole
cyrcumference
of
the
earth
,
which
contayneth
360.
parts
or
degrées
:
you
shall
easily
finde
and
knowe
the
same
by
this
maner
.
Multiply
the
whole
compasse
of
the
earth
;
that
is
,
the
368.
degrées
,
by
the
700.
furlongs
,
or
fiftéene
Germayne
myles
,
and
the
whole
compasse
shal
either
appeare
to
be
252000.
furlongs
,
or
5400.
Germayne
myles
.
This
whole
compasse
of
the
earth
,
deuide
by
22.
and
the
number
comming
thereof
,
shall
bee
the
22.
part
of
the
compasse
of
it
;
that
is
,
11454
12/22.
furlongs
,
or
254
●0/22.
Germayne
myles
.
And
abate
this
22.
part
,
from
the
whole
Summe
of
the
circumference
,
and
the
number
in
furlongs
shall
remaine
and
be
240545
10/22.
and
in
GErmayne
miles
5154
1●/22.
And
if
any
of
these
sums
be
deuided
a
part
by
3.
it
shal
be
found
in
furlongs
to
be
80181.
a
halfe
,
and
a
third
part
,
or
3/2.
10
/
66.
And
in
Germaine
myles
1718
4/22.
that
is
;
the
dyameter
of
the
earth
,
aswell
in
the
furlonges
,
as
Germayne
miles
.
And
Archimedes
by
sundry
labours
,
and
witty
inuentions
,
and
by
Geometrical
practise
,
hath
found
,
that
the
like
proportion
is
of
the
Circumference
of
the
whole
Cyrcle
vn
to
the
diameter
of
the
same
,
as
is
22.
vnto
7.
that
is
,
the
diameter
thrice
,
with
a
seauenth
part
and
a
halfe
.
But
whensoeuer
any
man
will
(
by
the
cyrcumference
of
the
Cyrcle
)
gather
and
finde
his
diameter
,
worke
the
numbers
thus
,
as
this
example
teacheth
.
First
,
set
down
22.
at
the
left
hand
,
toward
the
right
hand
7.
and
the
cyrcumference
betwéen
those
two
numbers
,
22.
5400.
7.
After
multiply
the
first
by
the
second
,
that
is
,
7.
by
5400.
the
number
increased
,
which
is
,
47800.
deuide
by
the
thirde
,
that
is
,
22.
and
you
shall
finde
in
the
quotient
,
1718
4/22.
Germayne
myles
.
Or
thus
in
furlongs
,
the
number
being
set
downe
alike
22.
252000.
7.
then
multiplie
the
first
by
the
second
,
as
7.
by
25200.
and
the
increase
shall
be
1764000.
after
the
increased
number
:
deuide
by
the
third
,
as
by
22.
and
the
diameter
shall
be
,
80181
18/22.
If
any
couet
to
finde
the
vpper
face
of
the
earth
,
by
the
dyameter
,
and
cyrcumference
known
,
worke
one
into
the
other
,
and
you
shal
haue
that
you
séeke
.
But
if
you
desire
to
knowe
the
thicknesse
of
the
earth
,
then
ioyne
the
superficiall
solydenes
of
the
Sphere
,
vnto
the
sixt
part
of
the
diameter
,
and
you
shall
obtaine
your
desire
.
THE
SECOND
PART
OF
THE
SPHERICALL
Elements
of
the
Celestiall
Circles
,
with
the
vses
of
the
same
Circles
.
What
is
the
Summe
of
this
Second
Part.
WHereas
in
the
first
part
,
were
only
teh
rudiments
of
the
Sphere
handeled
and
taught
(
which
are
also
written
and
contained
in
diuers
Phy●●●e
bookes
)
as
of
the
World
,
and
the
many
parts
thereof
:
that
is
,
of
the
Ethereall
and
Elementarie
Region
:
And
also
of
the
parts
,
motion
and
forme●
of
●he
Etheriall
Region
:
as
Heauen
,
and
the
for●●●e
,
〈◊〉
,
and
quantitie
of
the
Earth
.
Here
in
this
second
parte
shall
fully
bee
●et●●●
th●
and
largely
handled
,
the
manifold
vses
of
the
Cyrcle
,
of
which
the
materiall
Sphere
is
framed
and
made
.
Further
this
second
part
is
deuided
into
thrée
partes
,
the
first
teacheth
the
deuision
of
the
Cyrcles
(
in
that
the
auncient
Astronomers
,
for
a
playner
instruction
,
deuided
heauen
into
sundry
Cyrcles
)
and
of
these
some
in
greater
,
and
other
some
in
lesser
Cyrcles
.
In
the
second
part
,
are
the
definitions
,
descriptions
,
and
vtilities
of
all
the
Cyrcles
taught
.
In
the
third
and
last
part
,
are
the
places
of
the
Zones
,
learnedly
described
,
and
the
vtilities
of
them
.
So
that
this
second
part
doeth
especially
intreate
of
the
Cyrcles
(
séeing
the
principall
poynte
of
the
Sphere
,
is
of
the
celestiall
appearances
)
which
by
reason
of
the
celestiall
Cyrcles
,
or
of
the
first
moouer
are
caused
;
as
may
appeare
of
the
ascentions
and
descentions
of
the
signes
,
by
which
the
whole
knowledge
aswell
of
the
naturall
as
artificiall
day
is
learned
.
Wherefore
in
that
this
instruction
of
the
ascentions
of
the
signes
,
consisteth
in
the
Cyrcles
(
which
the
auncient
Astronomers
imagined
to
bée
in
the
first
mouer
)
therefore
is
this
second
part
of
the
celestiall
Cyrcles
,
aptely
placed
,
and
necessarily
before
taught
.
That
the
Sphere
of
the
worlde
,
is
either
right
,
or
thwart
.
THe
roundnesse
of
the
earth
,
as
is
afore
taught
,
both
altereth
the
standing
of
the
Poles
,
and
the
whole
Sphere
of
the
worlde
,
in
diuers
partes
of
the
earth
.
For
to
them
which
dwell
vnder
the
Equatour
,
either
Pole
falleth
to
the
playnesse
of
the
Horizont
.
But
to
others
dwelling
without
the
Equatoure
,
the
one
Pole
is
raysed
,
and
the
other
depressed
&
hid
:
through
which
diuersitie
of
the
standinges
of
them
,
are
these
differences
caused
;
that
the
risings
and
settings
of
the
signes
are
altered
;
the
spaces
betwéene
the
dayes
and
nights
varied
,
whose
causes
ought
diligently
to
be
sought
.
Therefore
is
the
right
Sphere
,
distinguished
from
the
thwart
Sphere
of
the
worlde
.
In
this
maner
,
as
here
you
may
be
holde
by
these
figures
following
.
That
is
called
the
right
Sphere
,
in
which
either
Pole
resteth
and
standeth
on
the
plaine
of
the
Horizont
and
the
Equatoure
,
which
there
doeth
exactly
possesse
the
middle
place
betwéene
the
Poles
,
and
doeth
with
the
Horrizont
make
a
right
sphericall
angle
:
of
which
it
is
so
named
a
right
Sphere
.
For
they
haue
such
a
standing
vpon
the
Sphere
of
the
worlde
,
as
that
neyther
of
the
Poles
is
eleuated
aboue
the
Horizont
,
to
them
which
dwell
vnder
the
Equatoure
.
The
thwart
,
declined
,
or
bending
Sphere
,
is
that
,
in
which
either
of
the
Poles
of
the
world
eleuated
,
is
séene
aboue
the
Horizont
,
and
the
other
iust
somuch
set
and
hidde
beneath
the
Horizont
:
and
also
that
the
Equatoure
frameth
and
maketh
with
the
Horizont
thwart
and
vnequall
angles
.
And
that
is
called
a
blunte
angle
,
which
séeth
the
Pole
eleuated
:
and
that
a
sharpe
angle
,
declining
vnto
the
contrary
.
They
which
dwell
on
this
side
,
and
beyonde
the
Equatoure
haue
such
a
Sphere
.
But
the
same
forme
and
condicion
of
the
thwart
Sphere
,
is
not
euery
where
;
nor
the
positure
of
it
,
the
same
reason
:
but
that
the
thwartnesse
of
the
Sphere
is
so
much
the
more
increased
,
as
by
how
many
degrées
either
of
the
Poles
are
néere
to
the
earth
:
and
beeing
further
distant
from
the
Equatoure
,
is
raysed
and
caried
higher
,
which
is
the
cause
of
many
obscure
differences
:
which
that
they
may
the
plainer
be
expressed
and
vnderstanded
,
the
skillfull
practisioners
haue
deuided
Cyrcles
in
the
first
mouer
,
by
lynes
drawn
vnto
certaine
stars
or
prickes
from
the
Center
of
the
earth
,
and
drawn
about
either
by
a
continuall
or
dayly
motion
,
by
which
they
imagined
them
to
be
described
.
That
the
Circles
of
the
Sphere
,
be
some
greater
,
some
lesser
,
and
the
number
of
the
Circles
.
HEre
it
is
not
to
be
omitted
,
that
one
Cyrcle
is
greater
then
another
,
by
foure
meanes
.
First
,
by
reason
of
the
magnitude
of
the
celestiall
body
in
which
it
is
imagined
to
be
.
And
of
this
is
the
Equinoctiall
Cyrcle
of
the
first
mouer
,
greater
then
the
Equinoctial
Cyrcle
of
the
eight
spher
,
in
that
the
first
mouer
is
greatest
of
all
the
bodies
.
And
although
the
Equinoctiall
of
the
eight
Sphere
,
doth
deuide
it
into
two
equall
halfes
,
yet
of
the
first
mouer
it
is
named
the
greater
,
for
that
the
same
includeth
all
other
bodies
.
By
the
second
,
it
is
euident
that
the
Equinoctiall
Cyrcle
is
greater
,
by
reason
of
the
appearaunce
,
in
that
the
whole
is
séene
aboue
the
Horizont
.
And
by
the
same
reason
the
Northerly
Cyrcle
(
which
is
named
the
Arcticke
Cyrcle
)
is
the
greater
,
for
that
it
alwaies
appeareth
to
vs
,
aboue
the
Horizont
.
By
the
thirde
,
the
Equinoctiall
is
accompted
greater
then
the
other
,
in
regarde
of
the
influxiue
vertue
:
and
for
this
cause
also
is
the
Zodiacke
called
greater
then
the
others
,
through
his
greater
working
into
these
inferior
bodies
.
For
that
vnder
it
,
the
sun
and
all
other
Planets
are
drawne
.
And
Happarchus
writeth
,
that
this
Cyrcle
is
the
life
of
all
thinges
which
are
in
the
world
,
&c.
In
that
by
the
ascending
of
the
sun
to
vs
,
generation
is
caused
,
and
by
his
falling
or
going
from
vs
,
diminishing
,
that
is
corruption
getteth
the
vpper
hand
.
By
the
fourth
,
is
a
Cyrcle
called
greater
then
the
other
,
insomuch
as
it
is
one
Sphere
,
and
thus
the
equinoctiall
,
is
greatest
of
all
the
Parallel
Cyrcles
,
in
the
first
moouer
:
which
is
euidently
demonstrated
,
by
the
diameter
of
the
Cyrcle
.
Therefore
by
the
definitions
and
reasons
aboue
shewed
,
the
equinoctial
is
the
greater
Cyrcle
,
described
in
the
vpper
face
of
the
first
mouer
,
according
to
each
part
,
or
the
whole
of
it
,
beeing
equally
distant
from
either
Pole
of
the
worlde
.
And
it
is
further
to
bee
considered
,
that
all
the
Cyrcles
of
the
Materiall
Sphere
,
are
imagined
to
bee
in
the
first
mouer
,
which
also
a
materiall
Sphere
doeth
especially
represent
So
that
these
Cyrcles
,
may
also
bee
imagined
in
the
other
Spheres
,
aswell
as
in
the
eight
Sphere
,
&c.
And
although
a
man
may
enter
into
conference
betwéene
these
Cyrcles
and
the
diameter
,
yet
he
shall
be
forced
to
confesse
that
they
be
on
such
wise
vnto
the
sphere
,
as
the
Cyrcle
is
vnto
the
diameter
.
So
that
as
the
diameter
deuideth
the
Cyrcle
into
two
equall
partes
(
in
that
it
passeth
by
the
Center
of
the
same
)
euen
so
doeth
euery
of
the
greatest
Cyrcles
deuide
the
Sphere
into
two
equal
parts
,
because
the
playne
vpper
face
of
it
passeth
by
the
Center
.
And
by
this
it
may
easily
bee
perceyued
,
that
those
which
are
named
the
lesser
Cyrcles
(
of
which
is
a
farre
greater
number
than
is
here
set
down
)
haue
diuers
Centers
from
the
Center
of
the
Sphere
;
and
yet
the
playne
vpper
face
of
them
passeth
not
by
the
Center
of
the
same
Sphere
.
Of
which
ensueth
,
that
they
cannot
deuide
the
sphere
into
two
equall
halfes
:
no
more
then
the
lyne
drawne
without
the
Center
,
into
a
Cyrcle
;
can
deuide
the
same
into
two
equal
halfes
.
And
both
the
greater
and
lesser
of
these
is
mente
,
according
to
the
distance
of
his
Center
,
from
the
Center
of
the
sphere
.
The
inward
Cyrcles
that
be
mouable
,
are
those
,
which
are
descrybed
in
the
first
moouer
,
and
are
drawne
with
it
about
:
as
is
the
equinoctiall
,
the
Zodiacke
,
the
Colures
,
the
Tropickes
,
the
Polare
Cyrcles
,
and
others
descrybed
from
the
poyntes
of
the
first
moouer
.
But
the
outwarde
Cyrcles
,
are
they
that
are
as
immoueable
,
and
not
drawn
about
with
the
first
mouer
,
but
abide
steady
.
The
number
of
which
are
these
:
the
Meridiane
,
the
Horizont
,
the
houre
Cyrcles
,
the
verticiall
Cyrcles
,
and
Cyrcles
of
the
progressions
.
Further
it
is
to
bee
noted
,
that
many
are
the
Celestiall
Cyrcles
(
as
is
aboue
declared
)
whose
vse
partely
vnto
Astronomy
,
and
partly
vnto
Astrologie
,
is
necessary
.
As
the
verticiall
Cyrcles
,
the
Cyrcles
of
the
altitudes
,
the
Cyrcles
of
the
celestiall
houses
.
The
Cyrcles
with
the
which
the
materiall
sphere
is
descrybed
:
and
to
bee
briefe
,
there
are
so
many
celestiall
Cyrcles
,
as
there
may
bée
poynts
ymagined
in
the
first
mouer
.
Yet
are
there
but
onely
ten
Cyrcles
,
which
are
required
vnto
this
sphericall
treatise
;
whose
names
are
the
Equinoctiall
,
the
Zodiacke
,
the
two
Colures
,
the
Meridian
,
the
Horizont
,
the
twoe
Tropickes
,
and
the
twoe
Polare
Cyrcles
.
The
greater
Cyrcles
are
those
,
which
haue
the
same
or
a
like
Center
with
the
earth
,
whose
playn
vpper
face
doth
passe
by
the
Center
of
the
earth
,
so
that
they
deuide
the
sphere
,
into
two
equall
parts
(
and
especially
the
equinoctiall
)
which
for
that
it
is
a
greater
Cyrcle
,
doth
cut
the
spher
into
two
equall
halfes
;
so
that
his
playne
vpper
face
passeth
by
the
Center
of
the
earth
,
according
to
the
definition
of
the
greater
Cyrcles
.
And
by
this
consequent
,
when
the
Sun
is
in
the
equinoctiall
,
he
falleth
into
the
Center
of
the
earth
;
that
is
,
hée
is
in
the
vpper
face
which
passeth
by
the
Center
of
the
earth
.
And
the
sun
is
neuer
in
such
an
vpper
face
,
but
when
he
is
in
the
two
equinoctial
poynts
for
other
wise
,
he
runneth
without
that
vpper
face
.
For
the
greater
Cyrcles
are
a
like
vnto
the
Sphere
,
as
the
diameters
vnto
the
Cyrcle
:
in
that
as
the
diameter
cutteth
the
Cyrcle
in
two
equall
halfes
(
for
that
it
doeth
passe
by
the
Center
of
the
same
)
euen
so
doth
the
greater
Cyrcle
deuide
the
Sphere
into
twoe
equall
halfes
,
in
that
the
playne
vpper
face
of
the
same
,
doth
passe
by
the
Center
of
the
sphere
.
But
the
lesser
Cyrcles
are
those
,
which
haue
diuerse
Centers
,
from
the
Center
of
the
sphere
,
so
that
the
playne
vpper
face
of
them
doeth
not
passe
by
the
Center
of
the
sphere
.
For
how
much
nearer
the
Center
of
the
same
is
to
the
Center
of
the
sphere
,
and
somuch
the
greater
is
that
Cyrcle
,
as
the
Tropicke
.
But
the
further
it
is
from
the
Center
,
euen
so
much
●he
lesser
in
sight
is
the
Cyrcle
,
as
are
the
Polare
circle
.
And
here
none
may
suppose
,
that
either
these
or
other
like
cyrcles
,
to
be
verily
in
the
first
moouer
,
but
only
to
be
vnderstoode
or
imagined
.
For
the
cause
of
deuiding
heauen
into
certaine
spaces
and
regions
,
through
the
helpe
of
which
,
the
courses
of
the
Planets
are
obserued
,
&
brought
vnto
a
rule
.
Further
the
office
of
the
celestiall
cyrcles
;
are
these
.
-
1
That
they
deuide
heauen
,
into
certaine
spaces
,
or
regions
.
-
2
The
courses
of
the
Planetes
,
the
firmament
,
and
first
mouer
,
by
the
helpe
of
these
cyrcles
are
obserued
,
and
brought
vnto
a
rule
.
-
3
They
shew
the
points
of
rising
and
setting
;
the
nearnesse
and
differences
both
of
dayes
and
nights
.
-
4
The
times
and
varieties
of
all
the
celestiall
appearances
,
may
bee
obserued
and
knowne
of
the
cyrcles
by
a
certaine
reason
.
The
sixe
greater
cyrcles
are
numbred
by
names
,
standing
,
and
vse
distinguished
.
As
the
-
Equinoctiall
.
-
Zodiacke
.
-
Colure
of
the
Equinoctials
.
-
Colure
of
the
Solstices
.
-
Meridiane
.
-
Horizont
.
But
there
are
many
others
,
as
the
Cyrcles
defined
or
descrybed
by
the
Poles
of
the
Zodiacke
,
and
Centers
of
the
stars
,
which
are
named
the
cyrcles
of
the
latitudes
.
The
Cyrcles
drawne
by
the
verticial
poynts
of
diuers
places
,
which
may
bee
named
the
cyrcles
of
the
distance
,
or
space
betwéene
places
.
For
that
the
toppes
doe
knit
or
ioyne
together
by
the
nighest
space
of
the
differences
of
places
,
and
doe
shew
the
distance
of
them
.
The
cyrcles
by
the
Centers
of
the
stars
,
and
Poles
of
the
worlde
drawne
,
are
named
the
cyrcles
of
the
declinations
of
the
stars
.
The
sixe
cyrcles
of
the
positions
(
through
which
by
the
thirty
parts
of
the
Equatoure
,
and
the
poynts
,
touched
of
the
Horizont
and
meridian
drawne
ouer
the
Equatoure
)
doth
Regiomontane
part
and
deuide
the
whole
heauen
into
twelue
equall
spaces
,
which
hee
nameth
the
houses
of
heauen
.
The
sixe
greater
cyrcles
(
through
which
by
the
Poles
of
the
Zodiacke
,
and
the
thirty
partes
of
the
same
bended
and
wrythed
)
doeth
Iulius
Firmicus
deuide
the
Zodiacke
into
twelue
equall
parts
,
but
the
Equatoure
into
as
many
vnequall
arks
.
But
that
former
distribution
and
disposing
of
the
Cyrcles
by
Regiomontane
,
both
deuised
and
demonstrated
of
him
,
doth
bring
and
cause
a
reason
of
the
framing
of
the
figures
of
heauen
,
which
they
name
Rationall
:
in
that
the
same
inuented
and
taught
by
principles
and
demonstrations
,
is
declared
by
certaine
reasons
.
The
other
inuented
and
exercised
of
others
,
doth
bring
and
cause
another
reason
of
the
forming
and
erecting
of
the
figures
of
heauen
,
which
of
the
same
they
name
the
equall
maner
;
in
that
it
parteth
or
deuideth
the
Zodiacke
into
equall
arks
.
Many
other
cyrcles
there
are
,
which
for
breuity
be
here
ouerpassed
:
for
that
they
belong
not
vnto
this
determined
treatise
of
the
principles
.
The
lesser
cyrcles
,
although
there
are
in
a
maner
infinite
of
them
,
yet
are
there
foure
only
recited
and
especially
knowne
,
which
also
are
named
Parallelles
.
As
the
-
Tropicke
of
Cancer
.
-
Tropicke
of
Capricorne
.
-
The
Articke
or
Northerly
Circle
.
-
The
Antarticke
.
Of
the
foure
greater
cyrcles
,
afore
written
,
they
both
are
moueable
,
and
are
continually
drawne
about
with
the
first
mouer
and
neuer
changed
.
But
the
two
neather
cyrcles
,
as
the
Meridiane
and
horizont
,
doe
remaine
and
abide
fixed
and
immoueable
,
in
the
going
about
of
heauen
,
and
the
standing
alwaies
changed
on
the
earth
,
towarde
what
quarter
soeuer
they
are
varied
,
as
they
may
be
and
are
in
a
maner
infinite
in
number
.
The
Astronomers
deuide
,
both
the
greater
and
lesser
cyrcles
,
into
360.
degrées
,
which
they
so
named
through
the
suns
passage
or
iourney
in
the
Zodiacke
,
measuring
and
defining
by
his
dayly
course
such
like
partes
and
spaces
.
And
of
these
partes
or
degrées
of
the
greater
cyrcles
,
it
is
found
and
known
,
that
each
degrée
contayneth
in
the
vpper
face
of
the
earth
,
either
62500.
paces
,
or
500.
furlongs
,
or
15.
Germayne
miles
.
But
each
parte
of
the
lesser
cyrcles
,
doe
comprehend
a
lesser
space
by
somuch
,
as
by
howe
much
more
from
the
magnitude
of
the
Parallell
,
which
is
the
middle
and
greatest
,
by
reason
of
the
distance
they
lacke
or
differ
.
And
each
of
the
thrée
hundreth
thréescore
degrées
,
are
also
parted
or
deuided
into
thrée
score
minutes
:
and
each
minute
,
into
thrée
score
seconds
:
and
each
second
into
thrée
score
thirds
:
and
so
forth
from
thirds
vnto
fourthes
:
and
so
vnto
tenths
,
they
distribute
them
.
The
description
,
names
,
and
vtilities
,
of
the
Equinoctiall
.
THe
Equinoctial
,
which
the
Gréeks
name
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
,
is
a
greater
cyrcle
,
placed
in
the
myddle
place
of
the
Sphere
,
betwéene
either
Pole
of
the
worlde
,
and
deuiding
both
by
equall
spaces
moueable
,
and
crossing
the
Zodiacke
in
two
poyntes
,
which
when
the
sun
doth
come
vnto
,
hee
then
causeth
a
like
day
and
night
throughout
the
earth
:
whereof
this
cyrcle
first
purchased
that
name
;
in
that
the
day
is
equall
to
the
night
,
which
happeneth
twice
in
the
yeare
,
as
in
the
beginning
and
entraunce
of
the
sun
,
both
into
Aries
and
Libra
.
And
a
straight
lyne
drawne
out
by
imagination
doeth
describe
this
cyrcle
,
reaching
out
of
the
Center
of
the
earth
by
the
Center
of
the
suns
body
on
a
plaine
or
flat
,
of
the
Equinoctiall
being
vnto
the
first
moouer
,
or
vnto
any
of
the
fixed
stars
to
the
Equatoure
,
fastned
to
the
eight
Sphere
,
as
that
either
of
them
,
which
with
the
thirde
being
somewhat
lower
and
darcker
doe
fashion
the
gyrdle
of
Orione
,
and
that
by
a
dayly
and
continuall
turning
drawne
about
of
the
first
moouer
,
vntill
the
same
bee
returned
vnto
the
place
,
from
whence
it
began
.
And
likewise
the
sun
,
or
any
other
constellation
placed
or
being
in
it
,
doth
in
euery
region
describe
the
halfe
of
the
Parallell
aboue
the
Horizont
,
and
the
other
halfe
,
vnder
the
Horizont
:
which
Ptholomie
nameth
the
cyrcle
of
the
Equatoure
of
the
day
:
and
Alphraganus
,
the
cyrcle
of
the
Equinoctiall
,
and
swathe
or
gyrdle
of
the
first
moouer
,
in
that
it
compasseth
about
the
first
moouer
(
as
Strabo
writeth
)
that
it
parteth
the
Northerly
halfe
Sphere
,
from
the
Southerly
.
For
this
greater
cyrcle
of
the
first
moouer
,
is
the
first
measurer
,
both
of
time
,
and
motion
.
In
that
it
causeth
the
proportionall
cyrcumferences
by
the
spaces
of
times
:
and
whiles
it
is
once
drawne
about
,
a
naturall
day
is
performed
.
And
whiles
the
compasse
also
of
the
whole
,
haue
moued
one
foure
and
twenteth
part
,
an
equall
or
Equinoctiall
houre
hath
passed
:
by
which
it
doth
euidently
appeare
,
that
this
cyrcle
,
belongeth
vnto
the
first
mouer
.
This
Worthy
Circle
hath
diuers
names
.
1
IT
is
named
the
Equinoctiall
,
in
that
it
causeth
a
like
night
,
to
the
artificiall
day
.
2
It
is
by
the
same
reason
named
the
Equatoure
;
for
that
it
maketh
equall
the
night
,
to
the
day
.
3
It
is
named
the
gyrdle
of
the
first
mouer
(
not
vnproperly
)
for
that
as
a
gyrdle
doeth
gyrde
or
deuide
our
body
into
two
equall
halues
;
euen
so
this
cyrcle
deuideth
the
sphere
or
first
mouer
,
by
the
middle
.
4
It
is
named
the
line
of
the
equality
of
the
day
,
or
the
line
of
the
equation
of
the
Orbe
of
the
day
,
or
the
iust
deuision
of
the
day
and
night
.
5
Of
Plinie
it
is
named
the
Center
of
the
earth
,
and
that
not
incongruently
;
séeing
all
the
Parallell
cyrcles
described
from
the
Center
of
the
sun
by
the
motion
of
the
first
mouer
,
haue
their
Centers
from
the
Center
of
the
earth
:
and
that
the
Equatour
onely
,
which
when
the
sun
shall
be
in
the
Equinoctiall
poynt
,
is
then
imagined
to
be
drawne
aboute
with
the
motion
of
the
first
moouer
,
that
hath
the
same
Center
with
the
earth
at
that
time
,
by
which
the
playne
of
the
Equatoure
,
is
then
noted
to
passe
.
So
that
this
is
the
cause
why
Plinie
giueth
that
name
to
it
:
séeing
a
like
day
and
night
is
caused
,
the
sun
then
running
vnder
the
Equatoure
throughout
the
earth
,
as
no
man
of
skill
maketh
doubt
of
.
It
is
named
the
cyrcle
of
the
high
solstice
;
but
this
commeth
to
passe
,
by
reason
of
those
which
dwell
vnder
the
equinoctiall
,
and
haue
foure
solstices
;
as
two
on
hie
,
&
two
below
,
hauing
foure
shadowes
in
the
yeare
:
and
the
sun
passing
twise
a
yeare
by
the
Zenith
,
right
ouer
their
heads
(
as
when
the
sunne
is
in
the
beginning
of
Aries
and
Libra
.
)
And
to
them
also
dwelling
vnder
the
Equinoctial
are
two
summers
and
two
winters
:
and
the
heat
is
mightiest
and
strongest
,
when
the
sun
draweth
from
them
into
the
North
,
or
South
;
yet
doeth
the
sun
alwaies
burne
the
earth
right
vnder
it
,
causing
a
burning
Zone
,
and
not
parteth
far
from
their
heades
.
So
that
their
winters
are
not
perfectly
and
simply
named
winters
,
as
with
vs
which
are
cold
seasons
in
déede
;
but
rather
with
them
is
a
continuall
summer
:
yet
for
that
the
causes
of
heate
with
them
,
are
not
vnformally
,
and
in
a
like
maner
alwaies
,
for
that
the
sun
doth
not
approch
equally
the
Zenith
of
that
parte
,
as
the
same
is
known
to
many
:
whereof
the
heat
to
them
is
not
vnifourme
and
a
like
in
burning
.
But
sometimes
hotter
,
and
sometimes
slacker
and
meaner
of
heate
.
So
that
when
the
sun
is
in
the
Zenith
,
as
in
the
beginnings
of
Aries
and
Libra
,
and
that
they
are
in
their
high
solstices
;
then
is
the
heate
most
vehement
with
them
,
yet
not
without
the
sun
,
this
heate
can
bee
called
mighty
.
But
when
as
the
sun
is
gone
from
their
Zenith
,
which
happeneth
in
the
beginning
of
Cancer
and
Capricorne
,
where
their
low
solstices
are
,
the
heate
is
then
slacker
:
that
is
,
lesser
burning
.
So
that
the
weaker
heate
hapning
in
the
lowe
solstices
,
may
in
a
manner
bée
named
colde
,
in
respecte
of
the
most
burning
heate
,
hapning
in
the
high
solstices
,
yet
it
hath
the
nomination
of
winter
,
although
no
cold
may
bée
felt
.
What
the
offices
or
vtilities
of
the
Equinoctiall
are
.
THe
causes
whie
the
skilfull
practisioners
tooke
and
vsed
the
Equinoctiall
,
with
the
offices
which
they
attributed
to
it
,
and
the
mani
fold
vses
that
it
offereth
,
is
herein
declared
.
1
It
measureth
the
motion
of
the
first
and
vppermost
Orbe
,
and
sheweth
the
same
to
bée
drawne
about
by
a
continuall
and
equall
swiftnesse
.
For
that
in
euery
equall
houre
,
doe
fiftéene
of
the
thrée
hundereth
and
thrée
score
degrées
of
the
same
arise
,
and
so
many
degrées
right
against
,
set
and
are
hidden
vnder
the
Horizont
:
and
that
all
the
thrée
hundreth
and
thrée
score
degrées
,
in
24.
houres
,
are
turned
about
in
the
appoynted
times
,
and
in
their
periods
continually
agréeing
.
And
as
the
Equatour
from
the
Poles
of
the
worlde
(
about
which
the
first
mouer
is
drawne
,
and
is
of
either
side
distant
by
equall
spaces
)
nor
the
Angle
,
which
is
comprehended
&
fashioneth
with
the
Horizont
doth
neuer
change
:
euen
so
(
by
the
same
order
and
like
motion
)
doeth
the
first
heauen
or
moouer
euidently
shew
it selfe
to
be
caried
about
.
For
the
Equinoctiall
measureth
and
determineth
the
motion
of
the
first
mouer
,
in
declaring
his
reuolution
and
yeare
:
which
yeare
of
the
first
moouer
,
is
the
time
of
24.
houres
equall
.
But
by
what
meanes
the
auncient
astronomers
first
found
,
that
the
Equinoctiall
is
drawne
about
in
so
many
houres
:
and
it
is
supposed
they
came
to
the
knowledge
thereof
,
by
the
office
of
some
starre
,
either
in
the
Equinoctiall
,
or
placed
neare
it
,
they
perceiued
the
same
:
as
that
the
Equinoctial
from
some
note
marked
of
them
,
did
returne
to
it
in
such
a
certaine
space
,
as
afore
shewed
.
2
The
diuers
motions
of
the
Zodiack
(
which
hapneth
to
it
through
the
twart
standing
or
lying
▪
)
as
a
cannon
or
rule
,
doth
dyrect
and
point
out
the
beginnings
,
boundes
,
and
time
,
with
the
which
each
parts
or
degrées
of
the
Zodiacke
arise
,
or
doe
set
:
and
with
which
they
touch
these
or
those
quarters
of
the
worlde
.
For
all
the
arckes
of
the
Equatoure
,
are
drawne
by
a
certaine
and
agréeable
motion
continually
.
The
parts
of
the
Zodiacke
drawne
thwartly
,
the
Equatoure
doeth
not
varie
or
is
distant
by
like
spaces
from
the
Poles
of
the
world
,
nor
turned
about
his
,
but
the
same
Poles
of
the
worlde
,
which
doe
differ
by
a
long
space
from
his
,
and
drawn
about
by
a
most
vnlike
motion
and
nothing
at
all
agréeing
in
it selfe
:
For
that
some
parts
or
degrées
are
caried
vp
sooner
or
quicker
,
and
others
appeare
slower
and
later
.
So
that
these
vseth
a
more
space
of
time
in
the
rising
slower
,
and
those
other
passe
vp
by
a
shorter
and
quicker
space
.
But
séeing
that
in
the
Zodiack
the
wandring
stars
or
Planets
,
doe
wander
continually
hither
and
thither
,
and
from
one
side
of
it
to
another
:
and
that
vnto
the
middle
cyrcle
of
it
or
ecclipticke
line
,
the
places
of
all
the
fixed
stars
are
referred
and
applied
:
therefore
cannot
the
times
of
the
rising
or
setting
of
the
starres
,
bée
knowne
and
noted
,
except
they
shoulde
be
guessed
and
attained
,
by
the
next
arks
of
the
equinoctiall
.
It
also
declareth
the
equinoctialles
,
which
are
caused
in
those
proper
dayes
,
in
which
the
sun
hapneth
to
come
into
the
equinoctiall
cyrcle
.
For
these
are
caused
the
sun
being
in
the
first
degrées
of
Aries
and
Libra
,
in
that
the
Zodiacke
and
Equinoctiall
doe
crosse
each
other
in
those
places
;
whereof
Manilius
thus
writeth
.
That
these
signes
Aries
and
Libra
cause
a
right
,
Throughout
the
earth
,
a
like
day
and
night
.
3.
It
defineth
and
measureth
the
spaces
,
both
of
the
naturall
and
artificiall
dayes
.
And
although
the
sun
(
which
drawne
about
with
the
motion
of
the
first
moouer
,
and
in
the
proper
motion
,
caried
forth
in
the
meane
time
by
force
into
the
contrary
,
when
as
hee
causeth
the
times
of
the
daies
and
nightes
,
so
wel
as
the
differences
of
the
natural
daies
)
mooued
,
and
runneth
in
the
Zodiacke
;
yet
of
his
motion
,
the
day
and
night
spaces
cannot
bee
gatherrd
,
through
the
diuersity
and
vnlikenesse
of
the
ascending
or
arising
of
diuers
parts
or
degrées
of
the
Zodiacke
.
But
seeing
the
same
motion
is
of
all
the
partes
of
the
Equatoure
;
therefore
are
the
ascentions
of
the
arcks
of
the
Zodiacke
,
caried
vp
with
the
ascending
of
the
nighest
parts
of
the
Equatour
,
like
arising
.
So
that
both
the
dayes
and
houres
,
by
the
equall
motion
of
these
,
are
not
founde
and
distinguished
by
the
vnlike
and
vnequall
motion
of
them
,
in
that
these
ascentions
can
be
,
of
these
two
cyrcles
.
The
Greekes
by
no
meanes
like
of
the
same
,
in
that
by
a
stedfast
order
,
they
do
mark
the
day
and
night
times
;
therefore
they
parte
and
deuide
them
into
equall
houres
,
which
they
named
times
,
that
from
the
degrées
of
the
Zodiacke
they
might
distinguish
them
.
For
euerie
fiftéene
parts
or
degrées
of
the
Equatour
in
his
motion
and
rising
aboue
the
Horizont
,
doe
make
an
houre
,
and
euery
degrée
foure
minutes
of
an
equall
houre
:
so
that
the
quarters
or
fiftéene
minutes
of
each
degrée
,
doe
produce
and
cause
one
minute
of
an
houre
.
Also
they
obserued
the
ascentions
and
descentions
of
the
signes
in
this
cyrcle
,
for
that
in
any
region
or
countrie
,
a
man
may
knowe
the
length
of
the
artificiall
day
and
night
,
by
hauing
a
sphericall
instrument
,
and
the
sun
placed
in
the
East
Horizont
,
let
the
note
of
the
Equinoctiall
be
moued
,
and
after
the
sun
being
turned
into
the
West
Horizont
,
let
the
note
againe
of
the
Equinoctiall
be
moued
into
the
East
Horizont
.
So
that
the
degrées
of
the
Equinoctiall
numbred
,
marked
with
these
notes
,
do
cause
an
artificiall
day
,
counting
alwaies
fiftéene
degrées
of
the
Equinoctiall
,
for
an
equall
houre
.
To
conclude
the
length
of
the
artificial
day
,
known
by
subtracting
the
same
from
24.
houres
,
the
quantity
of
the
night
remayning
shall
appeare
howe
much
it
is
.
Last
the
sun
being
entred
into
this
cyrcle
,
doth
rise
in
the
iust
East
point
,
and
setteth
full
West
:
but
in
the
highest
of
summer
being
come
to
Cancer
,
he
riseth
Northeast
,
and
setteth
Northwest
:
at
what
time
the
noone-tide
is
highest
.
But
in
the
shortest
time
of
winter
when
the
sun
is
come
to
Capricorne
,
hée
contrariwise
riseth
Southeast
,
and
is
in
the
noonetide
lowest
.
4
It
distinguisheth
the
Equinoctials
and
crosseth
the
Zodiacke
thwartly
wrethed
and
bended
to
it
,
in
two
opposite
points
,
which
when
the
sun
commeth
and
is
in
it
,
he
causeth
like
spaces
of
the
day
and
night
:
and
of
the
same
,
those
entraunces
of
the
sunne
,
are
named
the
Equinoctiall
points
.
And
there
are
two
Equinoctials
caused
in
euery
yeare
:
as
the
one
,
the
sun
entring
the
beginning
of
Aries
,
or
the
spring
poynt
of
the
crossing
of
the
Zodiacke
and
Equinoctiall
,
in
the
beginning
of
the
spring
,
which
the
Latines
name
the
equinoctiall
spring
,
and
the
Gréekes
,
Isemerian
earinén
.
And
the
celestiall
point
of
the
same
equinoctial
,
the
Gréeks
name
the
point
of
our
equinoctiall
spring
.
The
other
equinoctiall
is
caused
,
when
the
sun
hath
his
beginning
of
Libra
,
in
the
entrance
of
haruest
,
called
the
equinoctiall
haruest
.
And
the
celestiall
point
in
which
the
sun
happeneth
,
they
name
the
pointe
of
our
Equinoctiall
haruest
.
These
points
remaine
not
fixed
in
one
place
of
heauen
,
but
in
the
going
before
doe
procéede
or
moue
forwarde
vnder
the
eight
Orbe
,
and
turne
before
the
places
of
the
fixed
stars
.
For
the
point
of
the
equinoctiall
spring
,
that
in
the
first
yeare
of
Olimpias
folowed
the
first
star
of
Aries
of
the
eight
Sphere
,
4.
degrées
,
and
52.
minutes
.
And
in
the
yeare
of
the
death
of
Alexander
,
one
degrée
,
and
58.
minutes
.
The
same
after
the
beginning
of
the
yéeres
of
Iulius
,
Cesar
,
followed
4.
degrées
,
and
50
,
minutes
.
And
in
the
yeare
of
Christes
byrth
,
5.
degrées
and
16.
minutes
.
In
Ptholomies
time
,
6.
degrées
,
and
40.
minutes
,
it
went
before
the
same
star
:
and
in
these
yeares
it
went
before
that
star
,
27.
degrées
,
and
35.
minutes
.
So
that
the
yearely
times
of
the
Equinoctials
are
come
backe
,
from
the
auncient
time
,
and
moue
before
the
marked
dayes
by
a
long
space
:
For
that
the
Equinoctial
spring
which
about
the
beginning
of
the
yeares
of
Olimpias
,
hapned
in
the
first
or
second
of
Aprill
.
In
the
beginning
of
the
yeares
of
Cesar
,
in
the
25.
day
of
March.
In
the
time
of
Christ
our
Sauiors
byrth
,
in
the
23.
or
24.
day
of
March.
In
Ptholomies
time
,
in
the
22.
or
23.
day
of
March
.
But
in
our
time
it
hapneth
,
in
the
11.
or
12.
day
of
March
,
and
in
this
yeare
1570.
it
happeneth
in
the
11.
day
of
March
,
and
in
the
11.
howre
before
noone
,
on
Saturday
.
The
Autumnall
or
haruest
Equinoctiall
,
which
hapned
in
Christ
our
Sauiours
time
,
in
the
23.
or
24.
day
of
september
,
is
brought
backe
and
come
in
this
our
time
,
vnto
the
13.
or
14.
day
of
September
,
and
in
this
yeare
1570.
shall
happen
in
the
13.
day
,
and
in
the
10.
houre
,
and
21.
minutes
after
noone
,
on
Wednesday
.
And
through
this
variation
of
the
fixed
stars
,
and
Equinoctials
,
is
caused
,
that
the
later
practitioners
haue
found
an
other
quantity
of
the
yeare
,
contrary
to
the
auncients
.
For
Hipparchus
and
Ptholomie
,
haue
stablished
in
their
time
the
quantity
of
the
Tropicke
yeare
,
to
bee
of
365.
dayes
,
5.
houres
,
55.
minutes
,
and
12.
seconds
.
The
Alphonsines
,
of
365.
dayes
,
5.
houres
,
55.
minutes
,
and
12.
seconds
,
Albategnius
,
365.
daies
,
5.
houres
,
46.
minutes
and
56.
seconds
.
Cardanus
,
of
365.
daies
,
5.
houres
,
48.
minutes
,
41.
seconds
,
and
47.
thirds
.
And
Thebitius
hath
stablished
the
starrie
yeare
to
be
of
365.
dayes
6
,
houres
,
9.
minutes
,
and
32.
seconds
,
which
is
the
space
of
time
,
in
which
the
sun
returneth
vnto
the
same
fixed
star
.
But
the
Tropicke
yeare
,
is
the
suns
returne
,
after
his
measuring
of
the
whole
Zodiacke
,
vnto
the
Equinoctiall
or
soisticiall
point
.
So
that
by
the
saide
pointes
changed
,
either
in
the
increasing
or
comming
sooner
,
as
hitherto
hath
béene
obserued
,
is
the
quantity
of
the
yeare
,
found
to
be
in
diuerse
and
sundry
wise
of
the
practisioners
.
By
it
also
is
learned
and
knowne
which
stars
and
images
celestial
,
are
toward
the
North
or
South
from
it
.
And
by
it
is
the
starrieskie
deuided
into
two
equall
halfes
,
of
which
the
one
halfe
is
toward
the
North
,
and
the
other
towarde
the
South
.
So
that
the
denomination
,
so
well
of
the
Planets
,
as
fixed
stars
,
are
there
by
learned
;
whether
they
bee
Southerly
,
or
the
Northerly
.
An other
authour
writeth
thus
of
it
;
that
it
deuideth
heauen
into
two
parts
,
of
which
the
one
is
named
Northerly
,
of
the
seauen
stars
in
the
great
Beare
;
the
other
Southerly
,
in
that
the
sun
about
the
South
,
séemeth
alwaies
to
abide
with
vs
in
that
quarter
.
And
if
the
same
may
be
knowne
,
which
stars
are
named
Northerly
,
and
which
Southerly
:
and
when
the
Planets
are
named
Northerly
,
and
when
Southerly
.
So
that
by
this
reason
,
all
the
stars
and
images
from
it
,
tending
toward
the
North
,
to
be
Northerly
:
and
from
it
tending
toward
the
South
,
to
be
Southerly
.
The
Northerly
images
,
in
respect
of
the
Equinoctiall
,
are
these
.
THe
Bull
named
in
latine
Taurus
,
is
adorned
with
33.
stars
,
although
an
other
writer
mentioneth
but
of
32.
Of
these
,
5.
are
in
the
face
,
and
about
the
eies
,
and
in
the
places
where
the
hornes
are
described
to
be
,
are
one
star
a
piece
,
which
make
seauen
in
number
;
named
Hyades
in
Gréeke
,
and
Succullae
in
Latine
,
in
that
they
stand
like
to
the
letter
Y.
These
in
the
10.
11.
and
12
▪
degrées
of
Taurus
,
hauing
their
latitude
Southerly
:
of
which
4.
are
of
the
third
bignesse
,
and
one
brighter
then
the
rest
in
the
Southerly
eie
,
named
properly
Aldebaran
,
of
the
first
bignes
,
and
of
the
nature
of
Marse
.
The
seauen
stars
on
the
back
of
this
signe
,
named
Pleiades
,
and
in
Latine
Virgiliae
,
but
in
English
the
clustring
stars
;
in
that
they
stande
so
neare
togither
that
they
can
scarcely
be
numbred
:
yet
these
more
regarded
then
any
of
the
others
,
in
that
at
the
appearance
of
them
,
Summer
is
signified
;
and
at
the
setting
of
them
,
(
which
is
sixe
moneths
after
)
winter
is
then
in
entrance
,
like
which
is
not
shewed
in
the
other
signes
.
And
in
our
time
,
they
are
in
the
22.
and
23.
degrée
of
Taurus
,
the
sun
ioyneth
with
them
euery
yeare
,
in
the
thirde
and
fourth
day
of
May
.
So
that
after
those
daies
,
through
the
suns
departing
from
them
,
they
are
knowne
to
arise
Heliace
before
the
sun
,
and
then
is
summer
entred
:
which
in
our
time
hapneth
about
the
7.
8.
9.
or
10.
day
of
may
.
And
when
the
sun
is
come
(
by
his
course
)
vnto
the
22.
and
23.
degrée
of
Scorpio
,
which
hapneth
in
our
time
,
in
the
5.
and
6.
day
of
Nouember
,
then
is
the
sunne
directly
against
Pleiades
:
and
the
sun
then
arising
in
the
morning
,
they
doe
set
:
and
aboute
these
daies
,
(
as
in
the
5.
6.
7.
8.
9.
and
10.
day
of
Nouember
)
winter
is
entred
.
These
as
Ptholomie
writeth
,
are
of
the
nature
of
Mars
and
the
Moone
:
but
all
the
others
,
being
some
of
the
third
and
fourth
,
and
some
of
the
fist
bignesse
,
are
of
the
nature
of
Saturne
,
and
a
litle
of
Mercurie
.
THe
signe
Gemini
is
placed
in
heauen
,
as
that
betwéen
them
and
Taurus
,
is
that
constellation
Orion
standing
Their
headed
deuideb
from
the
rest
of
the
body
,
yet
imbracing
one
the
other
by
bodies
,
and
doe
dyrectly
set
with
the
féete
,
and
arise
together
bended
,
as
they
were
lying
.
Of
which
those
two
be
the
notablest
,
that
stand
in
the
heads
:
and
that
clear
star
in
the
head
which
goeth
before
(
named
Castor
,
and
of
some
Appollo
)
hauing
besides
in
eyther
shoulder
a
cleare
starre
,
in
the
right
elbowe
one
,
in
either
knée
one
,
and
in
either
foote
one
star
.
And
the
other
which
followeth
,
beeing
next
to
Cancer
,
hath
in
the
heade
a
star
named
Pollux
,
of
others
Hercules
,
on
the
left
shoulder
one
,
in
the
right
another
,
and
in
the
other
partes
sundry
other
stars
,
to
the
number
of
18.
knowne
in
both
.
There
is
an
other
star
standing
without
the
forme
of
Gemini
,
going
before
the
foote
of
Gemini
,
and
following
after
,
called
Propus
:
and
is
in
our
time
,
in
the
24.
degrée
of
Gemini
.
Of
which
two
are
of
the
second
bignesse
,
as
those
in
the
heads
,
but
the
others
are
of
the
thirde
,
fourth
,
and
fifte
bignesse
.
And
are
all
of
the
nature
of
Saturne
,
sauing
the
head
going
before
is
of
the
nature
of
Mercurie
:
and
that
in
the
heade
following
,
of
the
nature
of
Mars
.
THe
signe
Leo
looking
vnto
the
West
,
is
placed
on
the
body
of
Hydra
,
and
not
in
the
head
,
by
which
Cancer
is
nigh
vnto
the
halfe
of
it
,
hauing
the
middle
deuided
by
the
summer
cyrcle
,
in
such
sort
,
that
vnder
that
Orbe
hée
hath
the
fore
féet
placed
,
setting
and
rising
with
the
head
.
Also
he
hath
in
the
head
thrée
stars
,
in
the
nape
of
the
neck
two
,
in
the
breast
one
,
in
the
space
betwéene
the
shoulders
vnder
the
necke
or
behiude
the
necke
thrée
,
in
the
middle
of
the
taile
one
,
in
the
ende
of
the
taile
another
,
and
in
the
belly
one
cleare
or
bright
star
(
named
the
hart
of
the
Lion
)
which
also
is
called
aroyal
star
,
in
that
it
is
more
about
the
Zodiack
then
the
other
great
fixed
stars
;
and
for
this
cause
called
a
star
of
the
first
bignesse
,
although
in
truth
,
it
is
but
a
star
of
the
second
bignesse
,
being
of
the
nature
of
Iupiter
and
Mars
.
All
the
stars
which
this
signe
hath
(
as
Ptolomie
writeth
)
are
27.
Of
which
many
are
of
a
greate
brightnesse
,
as
the
two
in
the
nape
of
the
necke
,
of
the
second
bignesse
:
that
on
the
heart
,
of
the
first
bignesse
,
another
on
the
backe
,
of
the
second
bignesse
:
another
in
the
end
of
the
taile
,
of
the
first
bignesse
:
and
all
the
rest
,
of
the
third
,
fourth
,
and
fift
bignesse
.
THe
image
named
the
Carter
or
dri●●●
of
the
Car
,
Ptolomie
doeth
decke
with
14.
staires
,
being
all
nowe
in
Gemini
,
and
of
the
1.
2.
3.
4.
5.
and
6.
bignesse
,
of
the
nature
of
Mars
and
Mercurie
.
Also
this
image
named
the
Carter
,
hath
a
cleare
starre
,
named
the
Goate
standing
on
his
left
shoulder
,
being
a
starre
of
the
first
bignesse
,
and
in
our
time
in
the
15.
degrée
of
Gemini
:
borowing
nature
of
Mars
and
Mercurie
.
And
that
image
or
constellation
named
the
Kiddes
,
(
beeing
two
small
stars
,
standing
on
the
left
hand
of
the
Carter
)
are
in
our
time
,
in
the
12.
degrée
of
Gemini
,
of
the
fourth
bignesse
,
and
of
the
nature
of
Mars
,
and
Mercurie
.
THe
image
named
Perseus
,
hath
26.
stars
which
forme
two
perticuler
images
:
of
which
that
which
is
séene
on
his
left
side
,
is
named
Gorgon
,
or
the
head
Algoll
.
And
hereof
it
commeth
that
they
are
called
the
Gorgon
stars
.
The
other
séene
on
his
right
side
,
the
ancient
astronomers
name
the
Cyrcle
o●
sithe
.
Also
Ptholomie
in
the
description
of
Perseus
,
attributeth
to
the
heade
of
Algoll
(
that
is
Medusa
)
as
to
a
perticular
image
,
foure
starres
.
And
the
brighter
stars
of
them
(
being
in
the
heade
of
Algoll
is
the
12.
star
)
is
in
our
time
,
in
the
●9
degrée
,
and
twenty
minutes
of
Taurus
.
The
following
star
(
being
of
the
fourth
bignesse
)
is
in
our
time
in
the
18.
degrée
of
Taurus
.
And
Ptholomie
writeth
,
that
the
head
of
Algoll
beeing
of
the
second
bignesse
,
is
of
the
nature
of
Saturne
and
Iupiter
:
and
that
on
the
right
side
of
Perscus
,
of
the
second
bignesse
,
is
of
the
nature
of
Saturne
and
Iupiter
,
and
is
in
our
time
in
24.
and
28.
minutes
of
Taurus
.
ON
the
head
of
Aries
(
not
far
from
the
féete
of
Andromed●
)
standeth
a
figure
,
which
the
Gréekes
(
for
the
likenesse
of
the
letter
Delta
)
●a●e
Deltoton
;
and
the
Latines
,
for
the
similitude
of
the
fourme
called
a
Tryangle
.
This
figur●
hath
〈◊〉
equall
sides
,
but
the
third
not
so
perfect
fashioned
,
yet
easily
to
bee
knowne
;
for
that
it
shineth
brighter
then
many
other
starres
about
it
:
To
which
the
starres
of
Aries
are
a
litle
Southerly
.
And
to
it
Ptholomie
attributeth
foure
stars
,
although
all
other
authors
affirme
onely
thrée
stars
,
except
Alphonsus
,
which
in
our
time
are
in
Taurus
,
being
of
the
thirde
and
fourth
bignesse
,
and
altogether
of
the
nature
of
Mercurie
.
THe
image
of
Andromeda
(
placed
in
heauen
with
the
armes
stretched
abroad
,
and
each
hand
bound
)
Ptholomie
declareth
it
to
haue
23.
stars
,
of
the
thirde
,
fourth
,
and
fift
bignesse
,
and
in
our
time
are
in
Aries
and
Taurus
,
whose
nature
resembleth
Venus
.
This
Cassiopia
is
figured
like
to
a
woman
sitting
in
a
chayre
,
with
the
handes
lifted
vp
after
a
wayling
maner
;
and
in
the
turning
of
the
world
about
,
she
is
drawne
with
the
head
alwaies
vpward
.
Ptholomie
doeth
number
13.
stars
in
that
image
,
of
the
3.
4.
5.
and
sixe
bignesse
,
which
in
our
time
,
are
in
the
signes
Aries
and
Taurus
,
and
of
the
nature
of
Saturne
and
Venus
.
Among
the
Astrologians
onely
Ptholomie
and
Alphonsus
doe
place
twoe
horses
in
heauen
:
or
(
as
I
may
more
rightly
speake
)
the
two
partes
of
horses
:
of
which
the
one
is
called
the
fore
horse
,
or
head
of
the
horse
,
to
which
Ptholomie
attributeth
foure
darke
stars
,
which
in
our
time
are
in
Aquarius
.
The
other
figure
named
of
the
Arabians
,
Alpheratz
,
in
English
the
second
horse
,
the
halfe
horse
winged
,
or
Pegasus
,
whose
fore
parte
is
described
vnto
the
nauell
:
and
of
this
,
doth
the
greater
number
of
authors
write
.
Ptholomie
decketh
this
image
with
20.
stars
,
being
of
the
2.
3.
4.
and
5.
bignesse
,
which
in
our
time
are
in
Aquaries
,
Pisces
,
and
Aries
,
altogither
hauing
the
qualitie
or
nature
of
Iupiter
and
Mars
.
THe
celestiall
image
of
that
fish
named
the
Dolphine
,
the
ancient
men
placed
in
heauen
among
the
starre●
(
not
far
from
that
constellation
named
the
Eagle
.
)
And
many
of
the
ancient
astronomers
,
attributed
but
9.
stars
,
to
this
Dolphin
,
which
are
of
the
thirde
,
fourth
,
and
sixte
magnitude
,
and
in
our
time
be
in
Aquarius
,
retaining
the
nature
of
Saturne
and
Mars
.
THe
figure
named
the
celestiall
Arrow
,
placed
in
heauen
without
a
bowe
,
to
which
the
Swanne
flyeth
,
is
neare
to
the
North.
To
this
Arrow
doth
Ptholomie
atribute
fiue
stars
,
which
in
our
time
are
about
the
end
of
Capricornus
,
being
of
the
fourth
,
fift
,
and
sixt
greatnesse
,
and
hauing
the
qualitie
of
Mars
,
and
a
litle
of
Venus
.
The
figure
named
the
Eagle
(
whereon
Aquarius
séemeth
to
fly
)
which
many
affirme
to
be
Ganimedes
,
Ptholomie
doth
deck
with
nine
stars
,
of
the
second
,
third
,
fourth
,
and
fifte
bignesse
,
that
in
his
time
were
in
Sagitarius
and
Capricornus
,
and
in
our
time
are
in
Capricornus
,
which
folow
the
qualities
of
Mars
and
Iupiter
.
Many
auncient
authours
vsed
for
the
celestiall
Harpe
,
the
Griepe
falling
,
which
for
that
there
is
so
litle
thereof
mentioned
,
shall
here
bee
ouerpassed
.
But
Ptholomie
giueth
to
this
celestiall
Harpe
,
10.
stars
,
being
all
of
the
first
third
,
and
fourth
magnitude
,
and
in
his
time
were
in
Sagitarius
(
except
the
fift
and
sixte
starre
)
which
then
were
in
Capricornus
,
and
haue
the
qualities
of
Venus
and
Mercurie
.
The
image
Hercules
(
named
of
Aratus
and
sundry
others
Eugonasis
)
is
thus
placed
in
heauen
,
it
maketh
the
Dragon
appeare
to
haue
his
heade
vpright
,
and
Hercules
with
the
right
foote
,
the
knée
beeing
bended
or
bowed
,
séemeth
with
the
left
foote
to
thrust
down
the
right
side
of
his
head
,
and
in
his
right
hand
holding
vp
a
greate
naile
as
it
were
to
stricke
,
and
couered
on
the
lefte
side
with
a
Lions
skin
,
séemeth
earnestly
to
fight
and
●●ea
the
same
vnarmed
.
This
image
doeth
Ptholomie
describe
with
29.
stars
,
and
others
onely
28
:
which
in
our
time
are
all
in
Libra
,
Scorpio
,
and
Sagitarius
,
and
of
the
quality
of
Mercurie
.
Where
Aratos
,
Ptholomie
and
Alphonsus
write
of
two
manner
of
Crownes
(
as
the
Northerly
,
and
Sowtherly
)
therefore
shall
first
bee
shewed
of
the
Northerly
Crowne
,
and
after
of
the
Sowtherly
in
their
proper
place
.
This
bright
constellation
named
the
Northerly
Crowne
,
doeth
Ptholomie
declare
to
haue
8.
stars
,
which
in
his
time
were
all
in
Virgo
,
and
at
this
day
are
in
Scorpio
.
And
in
the
same
constellation
is
a
bright
star
,
of
the
second
bignesse
,
by
the
name
of
the
whole
image
:
of
the
Arabians
named
Alpheta
of
Virgill
,
Geor.
Guofia
.
The
image
named
the
Swan
,
the
Fowle
,
the
Hen
,
and
the
Griepe
flying
,
doeth
Ptholomie
decke
with
17.
stars
,
of
the
seconde
,
thirde
,
fourth
,
and
fift
bignesse
,
and
in
his
time
were
in
Capricornus
&
Aquarius
,
but
in
our
time
are
in
Capricornus
,
Aquarius
,
and
Pisces
,
and
bee
all
of
the
nature
of
Venus
and
Mercurie
.
The
image
named
Arctipholax
,
or
Bootes
,
which
in
English
may
bee
named
the
Heardman
,
or
rather
the
kéeper
of
the
wagon
,
in
that
he
séemeth
to
follow
the
wagon
:
that
is
the
Northerly
stars
.
And
Plinie
writing
of
Boots
,
(
which
he
otherwise
nameth
Arcturus
)
doth
affirme
,
that
this
constellation
in
a
manner
neuer
riseth
,
but
a
stormy
haile
ensueth
.
Also
Arcturus
is
a
bright
star
not
in
fashion
of
the
first
bignesse
,
standing
betwéene
the
legs
of
Bootes
,
as
Ptholomie
writeth
:
but
Hyginus
,
Rufus
,
and
others
,
doe
place
that
star
in
the
gyrdle
of
Bootes
.
This
Bootes
,
(
after
Ptholomie
)
hath
22.
stars
,
which
in
his
time
were
in
Virgo
and
Libra
,
and
in
our
time
are
onely
foure
of
the
first
in
Virgo
and
all
the
others
in
Libra
.
But
as
touching
the
natures
of
them
,
Ptholomie
doth
onely
write
hf
Arcturus
,
which
hee
affirmeth
to
haue
the
nature
of
Iupiter
and
Mars
.
The
image
named
Cepheus
,
Ptholomie
affirmeth
to
haue
twelue
stars
,
of
the
third
,
fourth
,
and
fift
magnitude
beeing
in
his
time
in
Pisces
and
Aries
:
and
in
our
time
in
Pisces
,
Aries
,
and
Taurus
,
and
following
the
nature
of
Iupiter
and
Saturne
.
The
image
named
the
celestiall
Dragon
,
that
other
ancient
men
name
the
Serpent
,
hath
(
after
Ptholomie
)
13.
starres
placed
ouer
all
:
which
in
his
time
were
in
Libra
,
Scorpio
,
Sagitarius
,
Capricornus
,
Aquarius
,
Pisces
,
Aries
,
Taurus
,
Gemini
,
Cancer
,
Leo
,
and
Virgo
,
and
in
our
time
are
in
these
;
Scorpio
Sagitarius
,
Capricornus
,
Aquarius
,
Pisces
,
Aries
,
Taurus
,
Geminini
,
Cancer
,
Leo
,
Virgo
,
and
Libra
:
being
of
the
3.
4.
5.
and
6
,
bignesse
.
Those
that
shine
brightest
are
eight
,
and
of
the
thirde
greatnesse
,
as
that
third
star
,
which
is
on
the
eye
;
the
fift
star
which
is
on
the
heade
called
Rastaben
;
the
24.
and
25.
declining
vnto
the
North
,
the
29.
which
standeth
beyonde
the
furthest
winding
,
the
30.
which
is
nere
the
end
of
the
taile
,
and
the
31.
which
is
at
the
very
end
.
And
these
brighter
shining
stars
are
of
the
nature
of
Saturne
and
Mars
.
The
image
named
the
greater
celestiall
Beare
,
and
of
many
(
for
the
fourme
of
the
Starres
standing
together
)
Charles-Waine
.
All
the
seauen
stars
,
of
which
two
bée
alike
,
and
are
séene
in
one
place
,
called
of
the
auncient
the
two
Oxen
,
in
that
they
séeme
equally
to
moue
,
as
yoaked
Oxen.
The
other
5.
starres
they
imagined
to
fashion
the
wagon
and
the
signe
or
image
next
to
it
,
to
bée
Bootes
,
or
in
English
the
wagon
driuer
,
which
seauen
stars
(
being
the
greater
Beare
)
are
drawne
once
about
the
Pole
of
the
worlde
in
24.
houres
,
and
neuer
set
out
of
sight
:
For
one
while
it
carieth
three
vnto
the
highest
,
and
the
other
foure
vnto
to
the
lowest
:
and
an
other
while
it
draweth
the
four
vnto
the
highest
,
and
bringeth
the
thrée
to
the
lowest
.
This
constellation
named
the
greater
Beare
,
doeth
Ptholomie
declare
to
haue
27.
stars
,
which
in
his
time
were
in
Gemini
,
Cancer
,
and
Leo
,
and
in
our
time
in
Cancer
,
Leo
,
and
Virgo
,
hauing
all
the
qualitie
of
Mars
.
But
here
I
ouerpasse
all
the
stars
of
that
constellation
,
and
onely
take
those
which
form
the
wagon
(
being
7.
in
number
)
of
which
foure
in
the
order
of
the
stars
of
the
greater
Beare
,
beeing
the
16.
17.
18.
and
19.
that
goe
before
the
wagon
,
or
the
whéeles
of
the
same
.
The
16.
17.
and
19.
are
of
the
second
greatnesse
,
but
the
18
,
is
of
the
third
bignesse
.
The
25.
is
of
the
second
signe
(
named
Alioth
)
that
is
before
the
beame
which
containeth
the
yoake
.
The
26.
and
27.
that
stand
in
steade
of
the
places
of
the
two
Oxen.
All
these
are
described
,
in
a
maner
after
the
minde
of
Hyginius
,
but
Cesar
the
Germaine
attributeth
the
three
stars
of
the
taile
,
to
the
beame
of
the
wagon
,
and
the
other
Starres
to
the
whéeles
of
the
wagon
.
The
figure
named
Cynosura
,
the
litle
Beare
,
or
lesser
wagon
,
did
the
men
of
Syria
more
diligently
regarde
,
supposing
to
saile
the
truer
and
surer
by
it
:
and
of
this
thought
through
their
first
finding
of
the
same
(
to
haue
it
called
after
them
,
Phenicen
.
This
litle
Beare
after
Ptholomie
,
called
the
Northerly
stars
,
or
lesser
wagon
(
as
aboue
said
)
hath
seauen
stars
,
which
in
Ptholomies
time
were
in
Gemini
and
Cancer
,
and
in
our
time
are
in
Cancer
and
Leo.
Of
these
the
first
star
,
which
is
on
the
ende
of
the
tayle
,
is
named
the
Pole
star
,
about
which
the
first
moouer
is
supposed
to
be
drawne
,
and
is
of
the
third
bignesse
.
The
two
following
stars
in
the
taile
,
and
the
two
fore
whéele
stars
,
are
of
the
fourth
bignesse
,
and
the
two
hinder
whéele
stars
following
,
are
of
the
second
greatnesse
,
and
these
starres
haue
the
quality
of
Saturne
,
and
a
litle
of
Venus
,
as
Ptholomie
in
primo
Quadri
,
writeth
.
The
Southerly
images
,
in
respect
of
the
Equinoctiall
,
are
these
.
The
signe
Libra
is
a
part
of
Scorpio
,
which
through
the
magnitude
of
the
members
is
deuided
into
two
signes
,
of
which
the
figure
of
the
one
they
called
Libra
.
And
that
part
was
rightly
named
Libra
,
in
that
when
the
sun
is
entred
the
beginning
of
that
signe
,
the
day
and
night
is
deuided
a
like
as
by
an
equall
ballance
.
For
the
Equinoctiall
haruest
like
hapneth
,
at
the
entrance
of
the
sun
into
Aries
as
the
Equinoctiall
spring
doeth
.
This
signe
hath
eight
stars
(
which
are
in
forme
)
of
which
one
in
the
Southerly
ballance
and
another
in
the
Northerly
ballance
,
and
of
the
second
greatnesse
.
But
the
others
which
either
do
follow
or
mooue
before
either
ballance
,
are
of
the
fourth
and
fifte
bignesse
.
Nine
others
there
are
which
bee
not
in
forme
,
placed
within
and
without
the
ballances
.
Being
all
of
the
nature
of
Mars
and
Mercurie
.
The
fore
part
of
Scorpius
is
so
hidden
of
the
Equinoctial
cyrcle
,
that
it
appeareth
to
stay
or
hold
the
same
vp
.
It
setteth
with
the
heade
inclined
,
and
ariseth
right
vp
.
The
signe
Scorpio
hath
in
those
(
which
are
called
the
Klées
)
in
each
of
them
two
stars
,
of
which
the
fore
stars
are
the
clearer
,
and
haue
the
quallity
of
Mars
,
and
a
parte
of
Saturne
.
It
hath
also
in
the
foreheade
thrée
stars
,
of
which
the
middle
stars
is
the
clearest
,
and
of
the
thirde
bignesse
.
In
the
space
betwéene
the
shoulders
vnder
the
necke
,
thrée
stars
.
In
the
belly
two
.
In
the
toppe
of
the
taile
fiue
,
with
the
which
he
is
spposed
to
strike
,
two
stars
.
In
the
whole
the
signe
hath
24.
stars
.
That
one
star
which
is
named
Antares
(
or
the
heart
of
the
Scorpion
)
is
of
the
second
greatnes
and
of
the
nature
of
Iupiter
and
Mars
.
And
many
stars
(
especially
those
which
are
placed
on
the
body
)
are
of
the
3.
greatnesse
,
and
haue
the
quality
of
Iupiter
and
Mars
.
The
stars
by
the
forehead
,
of
the
nature
of
Mars
,
and
parte
of
Saturne
.
The
stars
on
the
legges
and
feet
,
are
of
the
fourth
and
fift
bignesse
,
and
haue
the
qualitie
of
Iupiter
,
Saturne
,
Mars
,
Mercurie
,
and
part
of
Venus
.
THe
signe
Sagitarius
looketh
vnto
the
West
,
and
is
figured
with
the
body
of
a
Centaure
,
as
it
were
shooting
arowes
,
beginning
from
the
féete
,
vnto
the
shoulders
.
It
is
so
placed
in
the
winter
cyrcle
,
that
his
heade
onely
may
séeme
to
appeare
without
the
same
Cyrcle
:
whose
halfe
Bow
is
deuided
by
the
milky
cyrcle
.
And
before
his
feete
standeth
the
Crowne
decked
with
certaine
stars
:
he
seteth
headlong
,
and
ariseth
straight
vp
.
This
signe
hath
in
the
head
two
stars
,
of
the
fourth
bignes
,
of
the
nature
of
Mars
and
the
Sun
.
In
the
right
elbow
one
,
and
in
the
forehead
one
.
In
the
belly
one
,
in
the
left
shoulder
one
,
of
the
third
bignesse
,
and
quality
of
Iupiter
and
Saturne
.
The
stars
of
either
side
the
roote
of
the
tayle
,
of
the
fift
bignesse
,
and
of
the
nature
of
Venus
,
and
parte
Saturne
.
In
the
fore
knée
,
one
star
&c.
This
signe
in
the
whole
,
hath
31.
stars
.
Of
which
those
on
the
Bowe
,
on
the
North
,
South
,
and
middle
part
,
are
of
the
third
bignesse
,
and
of
the
nature
of
Iupiter
and
Mars
.
And
two
on
the
left
foote
,
of
the
second
bignesse
,
the
one
on
the
right
ankle
,
of
the
thyrd
bignesse
:
and
that
star
in
the
right
elbow
,
of
the
fourth
bignesse
,
and
hauing
the
quality
of
Iupiter
and
Saturne
al
the
others
are
of
the
fourth
or
fift
magnitude
.
THe
signe
Capricornus
looketh
vnto
the
West
,
and
is
wholy
figured
in
the
Zodiacke
cyrcle
.
The
taile
with
the
whole
body
,
is
deuided
by
halfe
(
of
the
Winter
cyrcle
)
and
reacheth
to
the
left
hand
of
Aquarius
,
hée
setteth
headlong
,
and
ariseth
right
vp
:
hee
hath
a
star
on
the
nose
,
and
another
going
before
the
two
stars
in
the
mouth
,
another
following
them
,
and
another
Southerly
of
the
thrée
in
the
mouth
:
all
of
the
sixt
bignesse
,
and
of
the
nature
of
Saturn
,
and
part
Mars
,
and
Venus
.
A
star
going
before
the
three
,
vnder
the
right
eye
of
the
fift
bignesse
,
and
of
the
nature
of
Mars
and
Mercurie
.
The
Southerly
of
the
thrée
following
behinde
the
horne
,
of
the
third
bignesse
;
the
Northerly
of
the
thrée
behind
the
horne
,
of
the
third
bignesse
.
The
Northerlier
,
and
Southerlier
of
the
stars
in
the
necke
,
of
the
fift
and
sixt
bignesse
.
In
the
neck
betwéene
the
shoulders
seauen
,
on
the
breast
two
,
on
the
belly
and
body
seauen
of
the
fifte
bignesse
,
and
of
the
nature
of
Mars
and
Mercurie
.
The
stars
on
the
taile
,
of
the
third
,
fourth
,
and
fift
bignes
,
and
of
the
nature
of
Saturne
and
Iupiter
.
In
the
whole
hée
hath
28.
stars
knowne
,
of
which
the
two
on
the
hornes
are
of
the
third
bignesse
,
but
all
the
others
be
of
the
fourth
,
fift
,
and
sixt
bignesse
.
The
auncient
astronomers
as
Aratus
,
Hyginus
,
and
others
,
do
assigne
thrée
images
in
one
constellation
:
as
the
Hydra
or
monstrous
serpent
,
on
whose
taile
they
describe
the
Rauen
to
sit
,
&
almost
in
the
middle
of
the
same
figure
,
they
affirme
the
cuppe
to
stand
.
It
is
a
signe
in
the
South
part
,
hauing
the
heade
declining
vnto
Cancer
:
the
halfe
of
whose
winding
body
is
placed
vnder
Leo
,
but
he
reacheth
the
taile
vnto
the
Centaure
,
on
which
the
Rauen
doeth
sit
.
To
this
Hydra
or
water
serpent
,
doeth
Ptholomie
giue
25.
stars
,
being
of
the
second
,
third
,
fourth
,
fift
,
&
sixt
bignesse
,
his
beginning
in
Ptholomies
time
was
in
the
fourtéene
de
grée
of
Cancer
,
but
the
end
almost
in
the
fourtéene
degrée
of
Libra
:
and
in
our
time
the
beginning
is
in
the
4.
degrée
of
Leo
,
and
the
end
in
the
third
degrée
of
Scorpius
,
beeing
of
the
nature
of
Saturne
and
Venus
.
The
great
water
Cup
or
pitcher
,
doth
Ptholomie
decke
with
seauen
stars
,
being
of
the
fourth
bignes
,
which
in
his
time
were
in
Leo
and
Virgo
,
and
in
our
time
in
Virgo
,
and
of
the
quality
of
Venus
,
and
a
litle
of
Mercurie
.
The
Rauen
(
after
Ptholomie
)
hath
seauen
stars
,
being
of
the
third
,
fourth
,
and
fift
bignesse
,
which
in
Ptholomies
time
were
all
in
Virgo
,
&
in
our
time
are
in
Libra
,
hauing
the
quality
of
Saturne
and
Mars
.
The
cellestiall
figure
named
the
Aulter
,
doeth
Aratus
place
in
heauen
,
vnder
that
beast
called
the
Woolfe
,
neare
to
the
South
,
and
standing
vnder
the
taile
of
Scorpius
.
To
this
figure
doth
Ptholomie
assigne
seauen
stars
,
that
in
his
time
were
in
Scorpio
,
of
the
fourth
and
fift
magnitude
:
but
in
our
time
are
in
Sagitarius
,
and
haue
the
quality
of
Venus
,
and
a
litle
of
Mercurie
.
The
image
named
the
Centaur
,
is
thus
described
of
Aratus
,
that
the
parts
of
this
image
likned
to
the
man
,
do
ly
within
the
signe
Scorpius
;
but
the
hinder
halfe
likened
to
the
Horse
,
lyeth
or
standeth
vnder
the
Klees
.
And
is
likened
to
one
hauing
his
right
hande
continually
open
,
towarde
the
round
aulter
.
And
as
one
offering
sacrifice
on
the
aulter
,
which
sacrifice
the
monster
holding
in
his
right
hande
to
offer
on
the
aulter
,
they
call
a
wilde
beast
.
In
that
monster
or
Centaur
named
of
Hyginus
,
Chiron
,
doth
Ptholomie
number
37.
starres
,
of
the
first
,
second
,
third
,
fourth
,
and
fift
magnitude
,
which
in
his
time
were
all
in
Libra
,
but
in
our
time
in
Libra
and
Scorpio
.
The
starres
standing
fashioned
in
the
forme
of
a
man
,
haue
the
quality
of
Venus
and
Mars
,
and
those
which
represent
the
forme
of
a
horse
,
are
of
the
nature
of
Iupiter
and
Venus
.
The
image
named
the
celestiall
Wolfe
,
doeth
the
Centaur
séeme
to
hold
:
yet
it
is
a
seuerall
constellation
from
the
other
.
To
which
Ptholomie
doth
assigne
19.
stars
,
being
of
the
thirde
,
fourth
,
and
fift
magnitude
,
that
in
his
time
were
in
Libra
and
Scorpio
,
and
in
our
time
are
all
in
Scorpio
.
The
celestial
figure
named
the
Riuer
streached
from
Orion
,
doe
some
name
Eridanus
,
which
otherwise
Padus
,
some
Gyon
or
Nylus
,
and
some
Oceanus
.
To
this
Riuer
Eridanus
,
that
commeth
from
the
left
foote
of
Orion
,
doeth
Ptholomie
giue
34.
starres
,
of
the
first
,
thirde
,
fourth
,
and
fifte
bignesse
:
that
in
his
time
were
in
Aries
and
Taurus
,
and
in
our
time
in
Aries
,
Taurus
,
and
Gemini
.
The
last
star
of
the
34.
in
the
rowe
(
of
the
first
magnitude
)
hath
the
quality
of
Iupiter
,
and
all
the
others
,
are
of
the
nature
of
Saturne
.
The
long
Ship
(
named
Argo
)
not
the
whole
forme
of
it
is
described
or
seene
among
the
stars
(
in
that
it
is
deuided
from
the
fore
part
vnto
the
mast
)
that
may
signifie
to
men
litle
to
dispayre
,
although
the
Shippe
happen
to
breake
.
Aratus
writeth
,
that
the
fore
halfe
of
Argo
,
is
turned
about
right
with
the
taile
of
the
great
Dogge
.
But
in
a
contrary
order
mooued
,
in
that
the
fore
halfe
is
séene
,
and
the
other
halfe
hid
;
much
like
a
ship
rising
with
the
swelling
of
the
Sea
,
whose
fore
halfe
is
séene
,
and
the
other
halfe
hid
,
through
that
hinder
parte
darkned
or
hidde
,
and
without
stars
.
To
the
ship
Argo
doth
Ptholomie
ascribe
45.
stars
of
the
1.
2.
3.
4.
and
5.
magnituds
.
The
greater
of
these
in
order
44.
of
the
first
bignesse
,
is
that
star
(
named
of
the
Arabians
Rubail
,
of
the
Latines
Canopus
)
which
standeth
at
the
end
of
the
Rother
stéerer
of
the
shippe
,
that
in
Ptholomies
time
was
in
the
17.
degrée
,
and
10.
minutes
of
Gemini
,
hauing
the
Southerly
latitude
75.
degrées
,
and
the
declination
Southerly
51.
degrées
,
and
41.
minutes
.
And
in
our
time
is
almost
in
the
7.
degrée
of
Cancer
,
hauing
his
latitude
Southerly
75.
degrees
,
and
declination
of
51.
degrées
,
and
34.
minutes
.
All
the
other
stars
are
of
the
quality
of
Saturne
and
Iupiter
,
and
were
by
Ptholomies
time
,
vnto
our
time
in
Gemini
,
Cancer
,
Leo
,
and
Virgo
.
The
celestiall
Hare
placed
vnder
the
féete
of
Orion
,
is
as
hee
were
running
before
the
houndes
of
Orion
,
being
fained
to
be
a
hunter
.
To
this
celestiall
figure
doth
Ptholomie
assigne
12.
stars
,
of
the
thirde
,
fourth
,
and
fift
magnitude
,
that
in
his
time
were
in
Taurus
and
Gemini
,
and
in
our
time
are
all
in
Gemini
,
and
haue
the
quality
of
Saturne
and
Mercurie
.
The
image
named
Ingula
,
and
also
Orion
,
lieth
thwart
vnder
to
the
section
of
Taurus
,
and
hath
starres
standing
and
shining
before
the
féete
of
Tautus
;
named
Orion
of
the
worde
Vrina
:
that
is
,
of
the
floude
of
waters
.
For
in
the
winter
time
(
when
this
image
or
constellation
ariseth
)
he
troubleth
both
the
Sea
and
Land
,
with
showers
of
raine
,
and
tempests
.
The
Romanes
also
name
him
Ingula
,
for
that
he
appeareth
armed
,
as
girded
with
a
sword
,
whose
shape
is
terrible
and
most
cleare
to
be
séen
in
the
shining
of
the
stars
.
For
if
it
shineth
bright
and
cleare
,
then
doth
it
portend
fayre
weather
to
follow
,
if
it
appeare
dimme
,
then
doth
it
threaten
a
tempest
to
ensue
.
The
head
of
this
signe
is
drawn
by
thrée
stars
,
of
which
the
two
cleare
stars
,
are
called
the
shoulders
,
betwéene
which
stars
the
necke
is
imagined
to
be
,
ane
thereof
named
Ingular
.
Plinie
doth
often
make
mention
of
Orion
,
as
of
his
rising
and
setting
whole
,
and
in
some
places
of
part
,
as
his
gyrdle
,
or
sword
.
Also
he
doth
number
Orion
among
the
fearefull
stars
,
causing
tempests
.
To
this
Orion
doth
Ptholomie
assigne
31.
stars
,
which
whiles
hee
liued
,
were
all
in
Taurus
and
Gemini
,
of
the
1.
2.
3.
4.
5.
and
6.
magnitude
,
and
one
cloudy
.
The
second
star
is
of
the
first
bignesse
,
and
the
thirde
is
,
of
the
sedond
bignesse
,
in
the
order
of
the
stars
of
Orion
,
which
are
in
the
shoulders
,
and
haue
the
quality
of
Mars
,
and
Mercurie
.
The
constellation
named
the
Zone
or
gyrdle
of
Orion
,
hath
thrée
stars
shining
very
bright
,
of
the
second
greatnesse
,
in
the
order
of
the
stars
of
Orion
,
beeing
the
26.
27.
and
28.
That
figure
named
his
sworde
hath
6.
stars
of
the
third
and
fourth
bignesse
,
decked
in
the
order
29.
30.
31.
32.
33.
and
34.
The
figure
named
the
Clubbe
that
Orion
bare
in
his
right
hand
,
when
he
fought
with
the
dreadfull
Bull
,
that
possesseth
foure
stars
,
of
the
fifte
and
sixt
bignesse
.
In
the
order
9.
10.
11.
and
12.
of
these
the
9.
and
10.
are
in
the
right
hand
.
Further
the
other
stars
,
either
of
the
first
or
second
bignesse
,
as
the
26
,
27.
and
28.
bee
of
the
nature
of
Iupiter
and
Saturne
.
But
the
other
stars
which
are
in
the
3.
4.
5.
and
6.
and
the
cloudy
star
,
do
imitate
the
quality
of
Saturne
,
the
35.
which
is
on
his
left
foote
,
is
of
the
Arabians
named
Rigel
,
of
the
first
bignesse
,
and
referred
to
the
nature
of
Iupiter
;
but
the
others
vnto
the
quality
of
Iupiter
and
Saturne
.
The
auncient
astronomers
placed
two
Dogges
in
heauen
,
as
they
were
following
the
Hare
running
:
of
which
the
one
they
named
Procion
,
and
the
other
the
Dag
.
The
image
named
Proceon
(
in
English
the
fore-Dogge
)
hath
no
other
name
with
the
Romanes
,
than
the
Caniculer
:
that
is
,
the
lesser
Dog
▪
And
of
Tully
(
in
fragmentis
Arati
)
hée
is
named
the
fore-Dog
.
But
the
other
doeth
Aratus
place
vnder
the
hinder
féete
of
the
fore-Dog
.
To
this
fore-Dog
doth
Ptholomie
attribute
onely
two
stars
,
others
do
number
thrée
,
that
in
Ptholomies
time
were
in
Gemini
,
and
in
our
time
are
in
Cancer
.
Of
which
the
fore
star
which
is
in
the
addition
of
the
same
,
doth
possesse
the
magnitude
.
The
scond
star
,
which
standeth
on
the
legge
shining
bright
,
is
Procion
;
of
the
first
bignesse
,
al
are
of
the
nature
of
Mercutie
,
and
a
litle
of
Mars
.
The
other
Dogge
being
the
greater
,
is
named
of
the
Arabians
Alhabor
,
which
properly
is
named
the
greater
dog
.
And
this
vnderstand
,
that
the
same
starre
is
brightest
shining
,
which
standeth
on
the
mouth
or
tung
of
the
Dogge
,
being
of
the
first
bignesse
,
and
named
by
authors
the
dog
,
in
the
name
of
the
whole
image
.
The
star
named
Syrius
or
the
Dog
,
is
placed
in
the
middle
Center
of
heauen
,
vnto
which
when
the
sun
shall
come
,
the
heate
is
then
doubled
,
and
mens
bodies
affected
with
faintnesse
.
Also
they
suppose
that
star
to
be
called
Syrius
,
though
the
brightnesse
of
his
fiery
shining
.
The
Latins
name
him
,
the
Caniculer
or
Dog-star
.
Of
which
the
Caniculer
or
Dog
daies
were
named
:
in
that
whiles
the
sun
runneth
in
that
part
,
it
is
dangerous
,
and
this
through
the
quality
of
the
season
then
being
,
that
disposeth
the
time
to
health
or
sicknesses
.
And
hercos
it
is
,
that
whiles
for
a
time
it
ariseth
,
the
season
is
not
alwaies
contagious
.
Ptholomie
nameth
that
Starre
which
is
on
the
mouth
of
the
Dog
;
and
assigneth
him
to
be
of
the
first
bignesse
,
most
cleare
and
bright
in
shining
.
And
to
that
star
which
standeth
or
is
placed
on
the
head
,
he
giueth
a
small
quantity
:
that
is
,
to
be
a
star
of
the
fift
bignes
.
Auicen
thus
writing
of
the
Dog-daies
,
willeth
men
to
beware
,
and
learne
the
time
in
which
the
greater
Dog
ariseth
,
and
the
season
in
which
the
snow
lieth
stil
on
the
high
hilles
or
mountaines
,
and
the
frosty
or
sharpe
colde
time
,
for
then
is
no
apt
time
of
ministring
medicine
.
But
a
medicine
may
safely
bee
druncke
,
or
otherwise
giuen
,
in
the
spring
and
haruest
time
.
Hippocrates
beeing
of
the
same
minde
,
affirmeth
that
in
the
Dog-daies
,
and
before
them
no
purgation
may
safely
be
ministred
.
The
beginning
of
the
Dog-daies
varieth
,
according
to
the
diuersity
of
Regions
,
Climates
,
and
Latitudes
.
In
our
time
the
Dogge-dayes
begin
at
the
suns
entrance
into
the
10.
11.
and
12.
degrée
of
Leo.
That
which
aboue
was
said
,
that
the
star
Syrius
is
in
the
middle
Center
of
heauen
,
is
ment
that
the
star
is
in
a
celestiall
cyrcle
,
as
the
Solsticiall
colure
,
whose
Center
is
the
Center
of
heauen
,
in
which
that
cyrcle
is
described
.
This
vnderstand
,
that
the
sunne
is
then
ioyned
with
the
star
Syrius
,
when
they
both
arise
together
in
the
Horizont
aboue
the
earth
,
and
setteth
Heliace
West
with
the
sun
,
though
it
cannot
be
séene
rise
in
the
morning
,
for
the
bright
beames
of
the
sun
:
but
after
the
suns
dayly
mouing
from
it
,
the
star
beginneth
to
arise
and
be
seene
in
the
morning
before
the
sun
.
To
a
man
of
knowledge
this
is
not
strange
,
that
the
Dog-star
ariseth
once
euery
naturall
day
:
yet
the
words
of
Auicen
are
thus
ment
,
that
in
what
time
the
Dog-star
ascendeth
with
the
sun
,
and
this
at
the
Horizontall
méeting
and
ioyning
together
of
them
in
the
morning
:
which
pestilent
Caniculare
time
do
the
phisicians
determine
to
be
of
40.
daies
long
.
But
the
malice
of
that
season
is
many
times
ouercome
&
changed
through
the
strong
beames
of
the
Planets
hapning
in
this
time
:
as
of
Iupiter
,
Venus
,
and
sometimes
of
Saturne
.
Ptholomie
doth
assigne
to
this
constellation
named
the
Dog-star
,
18.
stars
,
of
the
first
,
3.
4.
and
5.
magnitude
,
that
in
his
time
were
all
in
Gemini
,
and
in
our
time
in
Cancer
(
except
the
17.
star
)
which
is
in
the
end
of
Gemini
.
And
that
which
is
brightest
shining
in
the
Dogs
mouth
,
is
named
Alhabor
,
hauing
the
quality
of
Iupiter
,
and
a
litle
of
Mars
,
and
al
the
others
applied
to
Venus
.
Hyginus
writing
of
this
image
,
named
the
Southerly
Crown
(
which
of
many
is
named
Vraniscus
)
as
if
the
same
appeared
fashioned
hollow
from
heauen
.
The
same
doth
he
thus
describe
,
that
before
the
fore
féete
of
Sagitarius
,
are
a
fewe
stars
,
fashioned
into
a
roundnesse
,
which
forme
his
Crowne
,
that
many
haue
imagined
as
cast
from
him
in
bondage
maner
.
And
many
meane
by
this
Greeke
word
Ouraniseos
,
the
Palat
,
in
that
this
crowne
appeareth
fashioned
like
to
the
Palate
,
which
is
a
hollownesse
aboue
the
toung
.
To
this
celestiall
Crowne
,
fashioned
like
a
litle
Palate
,
doth
Ptholomie
assigne
13.
starres
,
of
the
fourth
,
fift
,
and
sixt
magnitude
,
that
in
his
time
were
all
in
Sagitarius
,
and
in
our
time
are
in
Sagitarius
and
Capricornus
,
of
the
nature
of
Saturne
and
Mars
.
This
image
do
some
name
the
monstrous
Fish
,
the
terible
fish
,
the
monstrous
sea
beast
,
and
sea
Lion
or
Beare
.
This
huge
fish
named
the
celestiall
Whale
,
is
placed
vnder
Aries
,
and
both
the
fishes
,
lying
a
litle
aboue
the
starry
Riuer
in
the
Region
of
heauen
.
Ptholomie
doth
assigne
to
this
celestiall
Whale
22.
stars
,
of
the
third
,
fourth
,
and
fift
bignesse
,
that
in
his
time
were
all
placed
in
Pisces
and
Aries
,
and
at
this
day
are
in
Pisces
,
Aries
,
and
Taurus
,
and
most
of
them
are
of
the
nature
of
Saturne
and
Venus
,
and
some
onely
of
Saturne
.
This
Meridiane
fish
(
named
the
Southern
or
Southerly
fish
)
and
greate
,
whose
Aliances
are
the
fishes
named
,
which
are
placed
in
the
cyrcle
of
the
Zodiacke
.
This
signe
or
image
is
placed
in
the
South
parte
,
and
séemeth
(
as
it
were
)
with
the
mouth
to
drincke
of
the
water
comming
from
the
signe
Aquarius
.
Ptholomie
doth
number
and
giue
to
this
Southerly
fish
,
11.
stars
,
being
of
the
first
,
fourth
,
and
fift
magnitude
,
that
in
his
time
were
all
in
Capricornus
and
Aquarius
,
and
in
our
time
are
all
in
Aquarius
.
The
brghter
starre
in
his
mouth
,
hath
the
quality
of
Venus
and
Mercurie
.
But
those
stars
placed
on
the
body
of
the
same
,
are
agréeable
and
a
like
to
the
nature
of
Saturne
.
These
hitherto
for
the
images
placed
on
the
North
and
South
side
of
the
Equatoure
.
5
By
the
fift
,
is
the
declination
of
the
parts
of
the
Ecclipticke
from
the
Equatoure
,
as
at
the
bound
from
which
it
is
knowne
,
and
both
the
declinations
of
the
stars
,
and
the
latitudes
of
places
learned
.
The
declinations
of
the
stars
are
called
the
distances
of
them
from
the
Equatour
,
toward
either
of
the
Poles
of
the
worlde
.
The
latitudes
of
places
,
the
spaces
from
the
Equatoure
vnto
the
highest
of
them
raised
in
the
Meridiane
,
as
by
the
toppes
gathered
and
learned
,
in
the
standing
right
ouer
.
Also
by
the
Equatoure
doe
we
learne
the
declinations
of
the
Planets
,
aswel
Northerly
,
as
Southerly
moued
,
as
more
euidently
doth
appeare
,
in
the
solyde
Sphere
or
Globe
.
So
that
by
the
declination
of
the
stars
knowne
,
a
man
may
easily
place
them
in
proper
instrumentes
,
by
which
greate
vtility
ariseth
.
And
it
is
the
measure
of
time
,
in
that
the
length
of
the
naturall
day
is
knowne
thereby
.
6
By
the
sixt
is
learned
,
that
in
the
same
Cyrcle
(
as
by
the
subiect
)
is
both
the
length
of
the
whole
earth
,
and
perticular
places
standing
in
diuers
parts
of
the
earth
,
considered
and
measured
.
For
according
to
the
exact
doctrine
of
the
sphericall
tryangles
,
the
longitude
or
length
of
places
,
and
the
difference
of
longitudes
is
alwaies
the
Equinoctiall
Arke
,
and
not
any
Parallell
.
By
it
also
the
declination
of
any
degrée
of
the
Zodiacke
is
knowne
,
which
being
had
in
any
day
at
noone
(
the
sun
then
shining
cleare
forth
)
the
Northerly
latitude
or
eleuation
of
the
Pole
of
any
Towne
,
may
artificially
be
knowne
.
It
is
besides
the
measure
of
time
,
in
that
a
naturall
day
is
perfourmed
by
one
whole
returne
of
the
Equinoctiall
,
with
an
adition
or
inerease
to
that
parte
of
the
Ecclipticke
,
which
the
sun
in
the
meane
whiles
accomplisheth
by
his
proper
motion
,
against
the
motion
of
the
first
mouer
.
7
By
the
seuenth
,
it
much
auaileth
and
helpeth
the
doctrine
of
astrology
,
in
that
by
the
guide
and
leading
of
the
same
,
are
the
beginnings
of
the
twelue
houses
of
heauen
found
,
when
astrologiall
figures
are
erected
and
fashioned
to
prognosticate
or
iudge
by
:
which
can
neuer
so
perfectly
be
searched
and
found
without
the
Equatoure
,
and
this
through
the
vnlike
motion
and
ascention
of
the
parts
or
signes
of
the
Zodiacke
.
By
it
also
are
all
Townes
according
to
their
longitude
and
latitude
,
easily
placed
and
found
in
the
earthly
Globe
:
so
that
by
it
a
man
may
readily
know
which
Townes
are
Northerly
,
and
which
Southerly
.
It
hath
besides
a
most
great
vse
in
Geography
,
vnto
finding
the
distances
of
places
,
and
vnto
placing
of
Cities
in
the
earthly
globe
,
in
hauing
the
true
longitude
and
latitude
of
them
.
8
The
eight
instruction
,
that
by
it
a
man
may
attaine
the
knowledge
of
all
the
celestiall
Parallell
cyrcles
,
and
the
earthly
Zones
lying
vnder
them
.
As
by
this
example
,
the
Parallel
streached
along
by
Rodes
,
cannot
otherwise
be
knowne
,
but
by
his
distance
from
the
Equinoctial
as
by
his
principall
&
fore
noted
Parallell
:
which
a
man
may
learne
and
know
to
bée
from
the
Equatoure
,
toward
the
North
36.
degrées
.
The
same
knowledge
may
aptly
be
had
,
of
all
the
other
Parallell
cyrcles
rightly
knowne
,
so
that
none
(
otherwise
)
can
bee
prompt
and
saillfull
in
Geographicall
matters
.
Cleonedes
affirmeth
(
prima
Meteor
)
that
it
afterwards
behoueth
to
know
how
to
discribe
each
turning
about
of
the
fixed
stars
with
the
first
mouer
,
about
his
Center
cyrcle
,
as
that
all
the
Parallell
cyrcles
are
knowne
.
Séeing
among
those
cyrcles
,
the
Equinoctiall
is
greatest
,
and
those
Parallell
cyrcles
least
which
are
drawne
about
the
Poles
of
the
worlde
:
euen
the
like
are
those
the
greater
cyrcles
according
to
proportion
from
them
,
which
are
described
vnto
the
Equinoctiall
.
9
The
niuth
sheweth
,
that
no
description
of
the
earth
,
(
although
in
platefourme
)
can
bee
expressed
,
neither
by
straight
nor
crooked
lines
,
without
the
knowledge
of
the
Equatoure
.
10
By
the
tenth
appeareth
,
what
commodity
of
the
same
hath
and
serueth
in
the
iudging
of
genitures
,
is
here
by
silence
ouerpassed
,
séeing
with
breuity
it
cannot
bée
vttered
.
The
description
,
names
,
and
offices
of
the
Zodiacke
,
and
Ecclipticke
line
,
or
way
of
the
Sunne
.
AFter
the
ancient
Astronomers
had
deuided
heauen
into
twoe
equall
halfes
by
the
Equinoctiall
,
and
diligently
obserued
and
noted
the
thwart
drawing
and
standing
of
the
Zodiacke
,
and
a
like
forme
of
a
larger
Zone
,
the
diuers
courses
,
motions
,
and
wandrings
,
both
of
the
sun
,
moone
,
and
other
Planets
which
being
drawne
about
with
the
first
moouer
,
kept
no
equall
spaces
in
them selues
agréeing
to
the
first
moouer
,
nor
a
like
distaunt
in
their
motions
from
the
Equatoure
:
but
that
whiles
they
were
dayly
drawn
by
a
contrary
motion
of
the
first
moouer
into
the
East
,
they
in
the
meane
time
wandered
one
whiles
into
the
North
,
and
anotherwhiles
into
the
South
,
vnto
a
certaine
elongation
and
distiance
,
and
so
returned
vnto
that
cyrcle
.
They
abserued
also
that
the
Planets
kept
alwaies
one
maner
of
iourney
and
way
,
and
that
way
cutting
or
cressing
heauen
and
the
Equinoctiall
by
a
thwart
manner
,
the
same
of
these
,
they
named
the
Zodiacke
.
This
cyrcle
of
the
12
signes
,
commonly
called
the
Zodiacke
(
which
also
is
a
greater
cyrcle
,
and
thwart
lying
)
hauing
a
latitude
moueable
vnto
the
motion
of
the
sphere
to
which
it
fasteneth
,
and
euery
where
is
a
like
,
vnder
which
the
Planettes
by
a
continuall
motion
are
drawne
and
run
.
This
cyrcle
also
doe
the
Latines
name
thwart
,
through
the
thwart
standing
of
it
:
for
the
Equatour
doth
compasse
the
sphere
of
the
worlde
,
by
the
iust
middle
space
betwéen
either
Pole
:
but
the
Zodiacke
is
thwartly
drawn
both
to
the
sphere
of
the
worlde
,
and
to
the
Equatoure
:
so
that
in
some
partes
it
is
nearer
to
the
Poles
of
the
same
,
and
in
some
parts
further
distance
from
it
.
It
is
crossed
also
of
the
Equatoure
into
two
eqnall
halfe
cyrcles
;
of
which
the
one
is
called
the
Boreall
or
Northerly
halfe
cyrcle
,
and
the
other
the
Meridionall
or
Southerly
halfe
cyrcle
:
therefore
by
the
continuall
turning
of
heauen
drawne
about
,
vnto
any
right
and
thwart
Horizont
,
inclined
according
to
the
thwart
Angles
,
it
doeth
both
chaunge
and
varie
those
Angles
by
the
continuall
motion
and
turning
about
.
For
to
certaine
Arks
it
figureth
and
formeth
righter
,
and
to
certaine
others
thwarter
Angels
,
through
that
diuers
inclination
vnto
the
Horizont
,
which
ensueth
after
the
standing
of
it
.
And
the
diuersitie
of
the
inclination
of
it
vnto
the
Horizont
,
doth
also
cause
a
varietie
in
the
motion
.
For
those
doe
slower
arise
,
which
make
right
Angles
with
the
Horizont
,
and
those
are
sooner
drawne
vp
and
appeare
,
which
doe
cause
thwart
Angles
.
In
the
thwart
Sphere
,
(
with
that
thwartnesse
of
the
Sphere
and
the
Angles
,
which
the
Horizont
and
Zodiack
performe
)
is
the
thwartnesse
encreased
.
What
the
names
are
of
this
Circle
.
_1
THis
Cyrcle
is
named
the
Zodiacke
,
of
this
Gréeke
worde
zoes
;
that
is
in
English
Life
:
in
that
it
is
the
path
,
or
the
comming
and
going
of
the
sun
,
which
is
called
the
author
of
life
,
&
causer
of
generations
(
as
Aristotle
writeth
.
)
Or
of
the
Gréeke
name
zódion
,
which
in
English
is
the
figures
of
Beastes
,
with
the
which
this
cyrcle
is
imagined
to
be
formed
by
the
concourse
of
stars
.
2
This
Cyrcle
is
named
thwart
or
bowing
,
in
that
it
crosseth
thwartly
the
Equinoctiall
and
first
moouer
,
and
doth
appeare
thwart
in
respect
of
the
Poles
of
the
worlde
,
from
which
it
is
not
equally
distant
.
Or
for
that
it
maketh
not
right
but
thwart
Angles
,
with
the
Equinoctiall
,
and
Colures
,
or
Tropickes
.
Or
for
that
it
doeth
not
regularly
ascend
and
discend
according
to
his
partes
(
like
as
the
Equinoctiall
doth
)
but
that
certaine
parts
or
signes
of
the
same
doe
righter
and
slower
;
and
certaine
thwarter
and
swifter
arise
in
either
Sphere
.
But
the
Zodiacke
is
not
named
thwart
(
compared
vnto
the
proper
Poles
)
séeing
from
them
it
is
equidistant
according
to
each
parte
;
as
the
Equinoctiall
from
the
Poles
of
the
world
.
Yet
compared
vnto
the
Poles
of
the
world
(
in
that
the
one
halfe
of
it
declineth
vnto
the
North
,
and
the
other
vnto
the
South
)
and
séeing
vpon
these
it
is
thwartly
drawne
by
the
dayly
motion
,
vnto
the
mouing
of
the
Orbe
in
which
it
is
:
In
this
respect
,
is
the
circle
named
thwart
.
3
This
Cyrcle
is
also
called
Signifere
,
of
the
12.
signes
caried
in
it
,
with
the
which
the
Zodiacke
is
described
.
Or
for
that
this
Cyrcle
is
deuided
into
twelue
equall
partes
,
(
which
are
called
signes
)
and
each
hauing
a
name
of
some
proper
beast
:
or
for
the
disposing
of
stars
being
in
the
signe
,
or
for
some
property
common
to
the
beast
and
signe
(
which
Ptholomie
nameth
the
Orbe
of
the
signes
)
Plinie
,
Capella
,
and
sundry
Poets
doe
name
Signifere
:
but
Aristotle
nameth
a
thwart
cyrcle
,
in
that
it
doth
thwartly
crosse
the
Equatour
,
as
witnesseth
Proclus
.
What
is
the
cause
of
the
thwartnesse
of
the
Zodiacke
.
1
THere
are
two
causes
,
why
the
Zodiacke
is
thwart
:
the
one
is
,
that
the
neather
Spheres
vpon
the
other
Exe-trée
,
and
Poles
,
may
bee
caried
contrary
to
the
motion
of
the
first
mouer
.
2
The
other
is
,
that
there
may
be
diuersities
of
times
,
and
varieties
of
qualities
and
tempearances
:
that
the
sun
also
may
wander
and
goe
about
diuers
partes
of
the
earth
,
running
in
the
thwart
cyrcle
;
wherof
Aristotle
writeth
,
that
it
is
necessary
,
that
the
proper
motion
in
the
Zodiacke
is
vnlike
to
the
motion
of
the
first
mouer
,
that
it
may
therby
cause
the
variety
of
cresent
or
growing
things
.
For
if
there
were
onely
one
motion
,
there
should
no
varietie
of
growing
things
be
caused
.
3
A
like
reason
to
this
,
that
of
the
same
,
one
parte
of
it
doeth
drawe
nigh
to
the
top
and
highest
ouer
our
heades
,
and
the
other
,
that
it
is
remoued
and
distant
from
vs
,
doth
cause
most
commonly
the
diuersitie
in
effectes
,
which
vnto
the
life
of
things
is
requisite
.
As
for
example
,
when
the
sun
is
in
the
Northerly
halfe
of
this
cyrcle
,
and
neare
the
Zenith
and
highest
ouer
our
heades
,
hee
doeth
cause
a
strong
and
mighty
heat
on
all
things
of
the
earth
▪
as
by
tryall
we
finde
and
sée
in
the
summer
.
If
therefore
the
Zodiacke
were
not
thwart
,
but
shoulde
equally
approach
or
drawe
nigh
according
to
all
the
parts
of
it
,
then
should
the
sun
be
alwaies
a
like
neare
vs
.
And
when
in
a
short
time
of
summer
he
should
cause
such
a
heat
,
that
his
heat
vndoubtedly
should
be
so
mighty
,
that
nothing
shoulde
growe
or
bee
increased
,
but
that
those
thinges
already
growne
vp
and
dryed
shoulde
bee
consumed
and
burnt
vp
:
wherefore
the
Zodiack
is
thwartly
placed
,
that
the
sun
mouing
into
the
further
halfe
,
his
heat
may
thereby
bee
slaked
and
weakened
,
in
which
he
being
caried
departeth
from
our
Zenith
,
and
cold
then
taken
place
,
as
apeareth
in
the
winter
.
And
if
the
sun
should
continually
run
in
the
South
parte
of
the
Zodiack
,
then
through
extremity
of
cold
should
all
things
be
destroyed
in
the
North
part
.
And
as
neither
heate
nor
cold
is
continuall
,
but
successiuely
,
as
those
which
bée
engendred
and
caused
by
heate
,
and
consumed
by
colde
.
So
that
the
sun
procureth
(
by
comming
nigh
,
and
going
from
vs
)
in
the
Zodiacke
,
that
it
behoueth
the
Zodiacke
to
bée
thwart
.
Also
a
diuersity
of
the
Planets
in
the
Zodiacke
.
To
conclude
,
we
sée
that
by
the
comming
of
the
sun
to
vs
,
generation
is
caused
,
&
by
his
departure
from
vs
,
thinges
wither
and
dry
.
This
cyrcle
called
the
Zodiack
(
acording
to
longitude
)
is
deuided
into
twelue
parts
or
signes
,
and
neither
more
nor
fewer
.
And
according
to
latitude
or
breadth
,
into
12.
degrées
.
This
cyrcle
deuided
into
twelue
signes
,
in
that
of
the
auncients
it
hath
béene
noted
,
that
in
euery
reuolution
of
the
sun
,
the
moon
is
twelue
time
changed
and
new
,
and
so
many
times
hath
hee
full
light
.
And
that
so
many
changes
and
full
moones
doe
happen
within
the
compasse
of
one
yeare
:
by
which
it
pleased
them
to
deuide
the
Zodiacke
into
so
many
parts
,
according
to
length
.
But
the
diuision
of
the
breadth
,
hath
another
cause
;
that
is
,
of
the
other
Planets
,
(
except
the
sun
)
diuersly
wandring
from
the
same
cyrcle
.
To
be
briefe
,
this
whole
cyrcle
is
deuided
into
360.
degrées
,
for
the
commodity
of
this
number
;
in
that
the
dayes
of
the
yeare
exceede
this
number
by
certayne
partes
:
for
the
common
yeare
hath
365.
dayes
,
and
6.
houres
.
There
is
a
latitude
atributed
to
the
Zodiack
,
by
which
it
differeth
from
the
other
cyrcles
,
in
that
they
are
descrybed
with
one
simple
compasse
,
that
it
might
by
the
larger
space
,
containe
the
wandring
of
the
Planettes
,
on
either
side
the
Ecclipticke
line
,
least
they
should
excéed
the
bonds
.
Yet
the
sun
kéepeth
one
maner
of
way
and
iourney
continually
in
the
middle
of
the
Zodiacke
,
and
neuer
declineth
from
it
,
neither
vnto
the
right
nor
lefte
side
,
but
still
kéeping
his
proper
places
immoueable
;
both
in
the
rising
and
setting
in
either
quarter
,
and
is
all
alike
in
the
winter
and
summer
seasons
.
The
declinations
also
of
the
sun
,
do
shew
and
appeare
to
be
equal
,
being
on
either
side
the
Equator
.
So
these
doe
witnesse
,
that
the
sun
continually
〈◊〉
his
yéerly
motion
,
describeth
and
kéepeth
vnder
that
line
named
the
Ecclipticke
.
But
the
other
Planets
doe
neither
kéepe
continually
the
suns
way
,
nor
is
drawne
in
a
right
path
like
him
,
but
digressing
on
either
side
the
suns
way
,
doe
wander
the
Zodiacke
by
a
crooked
or
bending
course
;
as
one
whiles
moued
into
the
North
,
and
an
otherwhiles
into
the
South
:
and
from
thence
returning
vnto
the
sunnes
way
,
as
the
like
knowledge
may
be
had
and
descerned
by
the
eie
.
For
this
cause
,
the
learned
practisioners
described
the
suns
course
in
the
middle
place
of
the
Zodiacke
,
and
imagined
from
it
a
latitude
to
bée
attributed
to
the
Zodiacke
,
which
the
auncient
astronomers
determined
to
bee
of
eyther
side
6.
degrées
.
But
the
late
writers
haue
encreased
the
same
,
by
adding
twoe
degrées
to
either
side
,
through
the
digressions
of
Mars
and
Venus
from
the
sunnes
way
;
which
hath
béene
obserued
and
noted
to
digresse
and
decline
litle
lesse
then
eight
degrées
.
So
that
the
latitude
of
the
whole
Zodiacke
(
in
our
time
)
is
concluded
and
agréed
to
bee
of
16.
degrées
,
and
the
latitude
is
reached
on
either
side
,
from
the
middle
space
of
the
suns
cyrcle
towarde
the
Poles
of
the
Zodiacke
,
eight
degrées
.
The
beginning
of
the
longitude
of
the
Zodiacke
(
although
in
the
compasse
of
the
circle
,
neither
the
beginning
nor
end
can
be
assigned
)
which
bendeth
or
is
drawne
perfectly
round
into
it selfe
;
and
both
closeth
and
containeth
it selfe
:
yet
the
practisioners
haue
assigned
by
the
principall
and
most
auncient
doctrine
of
the
godly
fathers
,
,
to
bee
in
the
poiut
of
the
Equinoctiall
spring
,
which
is
by
the
suns
comming
vnto
the
Equinoctiall
poynte
:
or
truer
by
the
change
of
the
moone
that
followeth
nexte
the
Equinoctiall
spring
,
is
not
to
be
doubted
that
the
yeare
then
begun
.
So
that
they
began
to
recken
the
Zodiacke
from
that
pointe
,
where
the
motions
and
workings
of
the
sun
(
the
authour
and
shewer
of
the
yearely
space
ensued
)
which
after
the
day
and
night
being
alike
,
the
day
encreaseth
,
and
hée
ascending
to
vs
ward
,
doth
after
abate
the
cold
on
the
earth
,
and
both
slaketh
and
melteth
the
frostes
and
yce
,
and
the
hidden
vertues
againe
of
the
earth
,
hee
then
beginneth
to
loose
,
open
,
chearish
,
and
stirre
vp
by
his
liuely
heate
,
and
both
looseth
and
sheadeth
forth
the
dew
moysture
inclosed
;
and
draweth
vppe
and
procureth
young
plants
to
spring
,
through
his
comfortable
warmth
dayly
shewed
vpon
the
earth
.
They
deuided
the
whole
Zodiacke
according
to
length
into
twelue
equall
partes
(
which
they
named
signes
)
through
the
moone
as
guide
and
ruler
of
the
same
:
which
passing
yearely
by
the
Zodiack
13.
times
,
to
the
suns
slower
going
twelue
times
;
&
conioyned
with
him
in
twelue
places
of
heauen
.
Those
signes
the
ancient
Gréeks
name
zòdia
,
either
by
the
figures
of
creatures
,
(
which
the
fixed
stars
in
their
standing
shewe
and
expresse
)
or
by
some
naturall
agréement
,
they
so
assigned
names
to
them
.
Or
els
they
appointed
the
names
of
beasts
to
the
signes
,
through
the
congruent
nature
betwixt
Starres
and
beastes
.
Also
through
the
effects
which
the
sun
hath
in
those
places
.
Besides
these
,
the
auncient
astronomers
described
the
other
starres
without
the
Zodiacke
by
images
,
that
placed
into
images
,
they
might
be
the
commodiouser
taught
and
expressed
in
heauen
to
the
vnderstanding
of
yong
students
,
and
that
their
rising
and
setting
might
also
bee
the
more
readily
demonstrated
.
Ptholomie
named
those
Dodekatemòria
,
that
is
,
the
twelue
parts
.
The
Latines
called
them
signes
,
and
constellations
.
Also
they
named
those
partes
signes
,
for
that
in
those
twelue
parts
,
all
the
seasons
of
the
yeare
are
noted
.
Again
they
named
the
parts
of
the
signes
degrées
,
of
the
dayly
iourney
of
the
sun
in
the
Zodiack
,
for
that
in
iourneying
by
litle
and
litle
,
he
passeth
through
the
whole
Zodiacke
.
They
also
deuided
each
signe
into
30.
parts
or
degrées
,
through
the
suns
dayly
iourneys
gained
of
the
first
mouer
,
which
in
thirty
dayes
they
declare
by
experience
,
to
haue
measured
and
gone
almost
a
twelfe
part
of
the
Zodiacke
.
Or
for
that
the
space
from
one
coniunction
vnto
an
other
is
of
30.
dayes
,
which
space
(
of
all
writers
)
is
named
a
moneth
.
Or
else
in
that
the
sunne
by
the
same
number
of
daies
,
hath
measured
almost
this
Arke
or
space
of
the
Zodiacke
.
Whereof
they
named
the
selfe
same
,
the
thirty
part
of
a
signe
,
through
the
suns
motion
euery
24.
houres
,
which
the
later
Latines
call
degrées
,
and
the
Gréeks
Merè
,
that
the
ancient
call
parts
.
But
the
tenne
partes
or
degrées
of
euery
signe
,
the
Gréekes
name
Dekatas
,
and
the
Latines
Faces
;
of
which
each
signe
doth
conteyne
thrée
.
The
names
and
characters
of
the
signes
of
the
Zodiacke
,
are
these
♈
Aries
,
♉
Taurus
,
♊
Gemini
,
♋
Cancer
,
♌
Leo
,
♍
Virgo
.
These
in
that
they
make
the
halfe
cyrcle
of
the
Zodiacke
,
declining
into
the
North
from
the
Equatoure
,
therefore
doe
they
name
them
,
the
Boreall
and
Northerly
signes
.
The
names
and
Characters
of
the
other
signes
of
the
Zodiacke
,
are
these
.
Libra
♎
,
Scorpio
♏
,
Sagitarius
♐
,
Capricornus
♑
,
Aquarius
♒
,
Pisces
♓
.
These
in
that
they
possesse
the
opposite
place
,
and
the
halfe
cyrcle
reaching
into
the
South
of
the
Zodiacke
:
therefore
do
they
name
them
,
the
Meridionall
and
Southerly
signes
.
The
sunne
also
iourneyeth
by
these
signes
(
as
from
the
West
into
the
East
)
by
a
contrary
order
to
the
first
moouer
,
as
this
figure
plainly
demonstrateth
:
beginning
neuerthelesse
at
Aries
,
and
from
Aries
,
passing
into
Taurus
,
and
from
Taurus
into
Gemini
,
and
so
to
the
ende
of
the
signes
.
They
deuided
each
signe
,
into
30.
degrées
of
length
,
in
that
the
whole
Zodiacke
(
like
as
the
other
greater
or
lesser
cyrcle
)
containeth
363.
parts
,
or
degrées
.
And
as
the
Zodiacke
hath
in
length
12.
signes
,
euen
so
it
is
requisite
the
same
should
be
so
many
degrées
broad
(
as
Capella
writeth
.
And
as
a
degrée
is
in
the
signe
the
thirtieth
parte
or
length
,
the
compasse
of
the
whole
Zodiacke
should
be
the
like
in
breadth
.
Although
Mars
and
Venus
do
sometimes
digresse
from
those
bonds
,
yet
that
excesse
is
litle
,
and
very
seldome
:
and
there
can
bee
no
other
reason
of
the
same
,
then
that
such
a
latitude
is
permitted
or
assigned
to
the
Zodiacke
.
To
this
demaund
,
why
there
are
onely
twelue
signes
,
and
no
more
,
doeth
Albumaser
answere
:
affirming
,
that
the
first
obseruers
of
the
stars
,
noted
48.
images
in
the
8.
heauen
,
placed
and
decked
with
the
stars
,
that
represent
sundry
formes
,
and
called
by
them
,
for
the
form
,
standing
,
or
nature
of
the
stars
,
of
which
they
appointed
12.
for
the
sunnes
way
:
and
therefore
so
many
,
are
the
signes
of
the
Zodiacke
.
But
here
may
bée
demanded
,
where
the
Circumference
of
the
Zodiacke
is
,
to
which
is
thus
answered
that
all
the
circumferences
of
the
cyrcles
imagined
are
in
that
hollow
of
the
first
heauen
,
and
likewise
the
signes
are
conceiued
there
to
bee
.
And
where
the
signes
with
the
images
of
the
eight
sphere
are
moueable
,
and
the
starres
in
them
seperated
after
a
time
.
Yet
the
number
and
names
,
both
of
the
signes
and
images
remaine
.
So
that
it
is
not
materiall
,
if
that
the
starrie
Aries
seperate
from
the
first
Aries
of
the
zodiacke
,
and
the
other
signes
the
like
from
one
another
,
by
a
most
slowe
course
are
caried
,
and
seperated
.
The
auncient
men
deuided
the
partes
or
degrées
of
the
signes
into
lesser
portions
,
for
the
better
attaining
the
precise
point
in
the
suns
place
.
So
that
they
appointed
to
ech
degrée
60.
minutes
,
to
each
minute
60.
seconds
,
to
each
second
,
60.
thirdes
,
&c.
For
the
infinite
commodity
of
the
numbers
in
calculating
,
by
reason
of
multiplication
and
diuision
.
They
also
deuided
the
signes
after
two
condicions
,
as
in
the
standing
,
and
qualities
.
In
the
standing
,
they
distinguished
them
into
principall
,
fixed
,
and
common
signes
.
The
principall
and
moueable
signes
,
are
those
which
nighest
succeede
the
foure
principal
points
of
the
zodiacke
:
of
which
two
possesse
the
Equinoctiall
points
of
the
whole
cyrcle
(
as
Aries
and
Libra
)
.
The
other
twoe
nighest
to
the
Solstitiall
points
,
are
named
the
Tropickes
(
as
Cancer
and
Capricornus
.
)
The
firme
or
fixed
signes
,
next
to
the
principall
,
are
Taurus
,
Leo
,
Virgo
,
and
Aquarius
.
The
common
,
or
meane
(
or
of
two
bodies
,
being
the
other
foure
)
which
placed
(
as
in
the
middle
betwéen
the
principall
and
fixed
signes
)
doe
so
obtaine
a
common
nature
of
both
,
as
Gemini
,
Virgo
,
Sagitarius
,
and
Pisces
.
In
the
qualities
,
they
assigned
them
into
foure
Trients
,
which
the
Latines
name
Tryangles
,
and
thrée
cornered
the
common
writers
nameth
Triangularites
,
or
Tripli
'
cities
.
The
first
trient
containeth
Aries
,
Leo
,
and
Sagitarius
,
which
are
by
the
space
of
foure
signes
inclusiuely
distant
,
or
of
120.
degrées
:
that
are
hot
and
dry
,
fiery
,
cholericke
,
and
masculine
.
The
second
Tyient
comprehended
Taurus
,
Virgo
,
and
Capricornus
;
which
beeing
distaunt
by
the
like
space
,
are
colde
,
and
drie
,
earthly
,
melancholicke
,
and
feminine
.
The
third
Trient
hath
Libra
,
Gemini
,
and
Aquarius
,
which
beeing
distaunt
by
the
space
of
foure
signes
,
are
hot
and
moyst
,
sanguine
,
aereall
,
and
masculine
.
The
fourth
Trigon
or
Trient
,
doeth
containe
Cancer
,
Scorpio
,
and
Pisces
,
which
are
distant
by
the
space
of
foure
signes
,
and
are
in
quality
colde
and
moyst
,
waterie
,
flegmaticke
,
and
feminine
.
All
which
signes
,
are
agréeing
to
the
foure
Elements
,
in
their
qualities
.
Of
the
Ecclipticke
line
,
or
way
of
the
Sunne
.
HEre
it
is
diligently
to
be
considered
and
noted
,
that
it
behoueth
not
onely
to
know
and
vnderstand
the
places
of
the
Planets
in
the
Zodiacke
(
according
to
the
longitude
of
the
same
)
but
also
to
learne
and
finde
their
places
(
according
to
latitude
)
wheather
they
be
in
that
part
of
the
zodiack
which
bendeth
or
declineth
into
the
North
,
or
in
that
parte
which
leaneth
into
the
South
:
which
the
better
to
vnderstand
and
know
,
the
ancient
astronomers
imagined
a
certaine
line
,
going
rounde
about
the
zodiacke
,
and
deuiding
the
same
after
length
by
the
middle
,
in
such
sorte
,
that
it
parteth
and
leaueth
eight
degrées
toward
the
North
,
&
as
many
toward
the
South
.
So
that
this
line
is
a
greater
cyrcle
,
deuiding
the
latitude
of
the
zodiacke
into
twoe
equall
halfes
,
and
hath
sundrie
names
:
as
the
suns
way
,
the
suns
●yr●uite
,
the
suns
iourney
,
the
suns
place
,
the
suns
cyrcle
,
the
Ecclipticke
line
,
and
the
Ecclipticke
place
.
This
line
named
the
suns
way
,
in
that
the
sun
kéepeth
alwaies
the
middle
vnder
this
line
,
not
digressing
to
the
one
side
nor
other
:
but
describeth
the
same
in
his
yearely
motion
.
But
the
other
Planets
doe
wander
one
whiles
vnder
it
,
and
an
other
whiles
on
either
●oe
,
which
if
a
Planet
tendeth
in
that
part
of
the
latitude
which
is
vnto
the
North
,
wandring
there
,
hee
is
then
named
to
haue
a
latitude
Northerly
,
as
to
vs
dwelling
Northward
:
but
if
on
the
other
side
they
haue
a
latitude
Southerly
,
then
are
they
named
discending
and
running
lowe
,
And
by
the
like
reason
,
the
same
line
is
named
the
suns
iourney
.
Also
of
Cleomedes
,
called
the
suns
cyrcle
,
in
that
vnder
the
same
the
sun
continually
runneth
.
And
he
alone
being
drawne
by
the
middle
of
the
zodiacke
,
neuer
wandreth
into
the
North
nor
South
parte
from
that
line
(
as
we
haue
afore
written
)
but
continually
iourneyeth
about
by
the
middle
of
it
.
So
that
of
the
same
,
it
is
called
the
suns
cyrcle
.
It
is
named
the
suns
place
,
in
that
vnder
this
cyrcle
the
sun
continually
abideth
.
To
conclude
,
it
is
named
by
the
vsuall
name
the
Ecclipticke
line
.
For
that
no
Ecclipse
or
abating
of
the
suns
or
moones
light
hapneth
,
but
when
the
sun
and
moone
are
linally
vnder
that
line
(
or
néere
come
vnto
the
moone
)
as
in
the
same
degrée
right
against
.
For
in
the
same
degrée
,
at
the
chaunge
,
is
the
moone
come
right
betwéene
our
sight
,
and
the
suns
body
;
thereby
abating
his
light
.
But
the
Ecclipse
of
the
moone
hapneth
at
the
full
,
when
as
the
sun
is
right
against
the
moone
;
&
that
the
shadowe
of
the
earth
falleth
betwéen
both
,
whereby
the
moons
light
is
darkned
.
So
that
the
moones
Ecclipse
is
none
other
,
then
the
falling
of
the
earths
shadowe
betwéene
the
sun
and
moone
.
The
measure
of
the
large
space
of
either
side
,
occupied
by
the
Planets
,
limited
and
included
by
twoe
lynes
,
and
the
third
drawne
or
described
by
the
middle
,
is
named
the
Ecclipticke
line
,
and
suns
place
.
The
Eccliptick
line
is
a
greater
cyrcle
consisting
in
the
middle
of
the
Zodiacke
,
and
deuiding
it
into
twoe
equall
compasses
,
defined
to
be
eight
degrées
in
breadth
on
either
side
,
which
the
sunne
maketh
by
a
yearely
motion
,
going
thwartly
in
one
continuall
way
,
is
deuided
by
the
foure
principall
points
;
as
the
two
Equinoctials
,
and
the
Solstices
,
into
foure
quarters
.
For
as
the
whole
Zodiacke
,
euen
so
the
Eccliptick
to
the
Equatour
,
resting
as
it
were
in
two
onely
points
,
but
in
the
rest
of
the
cyrcle
it
bendeth
●●om
either
point
toward
the
opposite
Poles
of
the
worlde
declined
by
the
one
halfe
cyrcle
into
the
North
,
and
by
the
other
halfe
into
the
South
.
The
pointes
that
touch
,
are
the
Equinoctiall
(
as
wee
haue
aboue
written
)
but
the
other
two
,
furthest
distaunt
from
the
Equatoure
(
which
are
as
markes
or
boundes
for
the
suns
departure
)
that
when
he
commeth
to
the
one
,
hée
is
carried
no
further
,
but
stayeth
there
,
and
from
thence
drawne
vnto
the
contrary
bound
:
through
which
turning
backe
of
the
sunne
,
they
are
named
the
Tropickes
of
the
Gréeks
,
and
of
the
Latines
;
the
solsticiall
points
.
Not
for
that
the
sun
beeing
carried
vnto
them
,
stayeth
and
remaineth
any
space
,
but
neuer
resteth
,
nor
leaueth
of
his
courses
:
séeing
within
certaine
daies
the
Meridiane
or
Noone
shadowes
are
varied
,
the
day
&
night
spaces
either
lengthened
and
increased
,
or
decreased
and
shortned
notably
;
as
the
like
is
yearely
séene
.
Of
these
,
that
which
in
the
Northerly
halfe
cyrcle
is
furthest
distant
from
the
Equatoure
(
named
the
pointe
of
the
summer
solstice
)
the
other
standing
or
being
right
against
that
,
the
point
of
the
winter
solstice
.
These
points
change
their
places
two
maner
of
waies
,
as
well
according
to
length
of
the
zodiacke
by
créeping
further
in
the
fore
going
,
as
in
going
to
and
comming
short
vnto
the
Equatoure
.
First
that
the
Equinoctiall
pointes
,
doe
ouer
go
the
places
of
the
fixed
stars
,
against
the
order
and
course
of
the
signes
;
and
therefore
doe
the
daies
of
the
solstices
begin
and
goe
before
.
For
the
summer
solstice
about
the
beginning
of
Olimpias
the
first
day
of
Iuly
,
which
began
the
yeare
with
the
Gréeks
at
the
morning
rising
of
that
constellation
Syrius
,
being
notably
knowne
to
many
:
but
in
the
yeare
of
Christes
birth
,
it
hapned
in
the
24.
day
of
Iune
,
And
in
the
yeare
1570.
it
hapneth
in
the
12.
day
of
Iune
,
about
11.
of
the
clocke
before
Noone
.
The
winter
solstice
in
the
first
beginning
of
Olympias
,
hapned
the
first
day
of
Ianuary
,
or
there
about
.
In
the
year
of
Christs
byrth
it
hapned
the
15.
day
of
Decmber
(
in
which
day
at
the
houre
of
12.
in
the
night
,
they
affirme
our
sauiour
to
bee
borne
.
The
same
winter
solstice
hapneth
in
the
same
yeare
1570.
on
the
12.
day
of
December
,
aboute
2.
of
the
clocke
at
after
Noone
.
In
the
second
then
happen
vnto
the
Equatoure
by
the
Ecclipticke
(
as
it
were
winding
)
and
remoued
againe
in
the
same
departing
.
For
the
obseruations
of
many
times
doe
witnesse
,
that
the
arcke
of
the
Colure
of
the
Solstices
reached
to
these
points
and
Equatoure
(
which
they
name
the
suns
greatest
thwartnesse
or
declination
)
is
deminished
by
litle
&
litle
.
For
before
Ptholomies
time
by
forty
yéeres
Aristarchus
,
Samius
,
founde
the
same
to
bee
of
23.
degrées
,
52.
minutes
,
and
20.
seconds
.
And
Ptholomie
noted
,
that
he
found
it
to
be
iust
asmuch
.
Mahometes
Aratensir
which
was
after
Ptholomie
749.
yeares
,
found
this
declination
to
be
of
23.
degrées
,
and
35.
minutes
.
Arzahell
the
Spaniard
that
was
190.
yeares
after
Albategnius
,
found
it
to
bée
of
23.
degrées
,
and
34.
minutes
.
Prophatius
Iudius
which
was
230.
yeares
after
Arzahell
founde
this
declination
to
bée
of
23.
degrées
,
and
●2
.
minutes
.
Dominicus
Maria
being
in
the
yeare
of
Christ
1491.
found
this
declination
to
be
of
23.
degrées
,
and
29.
minutes
.
Vueruerus
being
in
the
yeare
of
Christ
1514.
found
this
declination
to
be
of
23.
degrées
,
and
28.
minutes
,
and
30.
seconds
.
Copernicus
being
a
later
writer
,
as
in
the
year
of
Christ
1525.
found
this
declination
to
be
of
23.
degrées
,
28.
minutes
,
and
2.
fifts
of
a
minute
.
Of
these
(
but
by
many
notes
considered
)
that
the
equalities
haue
decreased
by
the
regulare
motion
,
and
yet
shal
decrease
,
vntill
an
extreame
tearme
of
diminishing
ensueth
,
which
hee
affirmeth
to
bée
of
23.
degrées
,
and
28.
minutes
:
the
same
Copernicus
after
gathered
shal
againe
increase
;
and
that
the
greatest
thwartnesse
which
may
bee
caused
on
the
sun
or
Ecclipticke
line
,
is
23.
degrées
,
and
52.
minutes
:
&
the
least
declination
to
bee
of
23.
degrées
,
and
28.
minutes
.
So
that
the
stablished
the
difference
of
the
greatest
and
least
to
be
of
24
,
minutes
.
But
hee
defineth
the
periode
motion
of
the
increasing
or
diminishing
to
be
in
1717.
yeares
:
and
that
so
many
yeares
,
the
motion
of
the
decrease
and
increase
shall
be
,
and
that
the
whole
restitution
also
of
the
thwartnesse
,
to
be
in
3434.
yeares
.
So
that
as
the
thwartnesse
failing
or
diminishing
;
euen
so
the
points
of
the
greatest
declination
(
which
are
named
the
solstices
)
are
yearely
drawne
and
moued
néerer
vnto
the
Equatoure
by
6.
minutes
,
27.
seconds
,
24.
thirdes
,
and
9.
fourthes
:
but
dayly
by
one
second
,
two
thirds
,
and
so
many
fourthes
,
caried
neare
vnto
it
.
And
the
thwartnesse
increasing
,
may
by
the
like
order
and
condicion
,
and
in
the
same
motion
be
againe
abated
.
As
the
Equinoctiall
points
deuide
the
Ecclipticke
lyne
into
a
Northerly
and
Southerly
halfe
cyrcle
,
euen
so
the
solstitiall
pointes
parte
the
same
into
a
halfe
cyrcle
(
ascending
and
descending
)
as
to
vs
.
The
ascending
beginneth
from
the
beginning
of
Capricornus
,
and
endeth
at
the
last
pointe
of
Gemini
,
and
containeth
Capricornus
,
Aquarius
,
Pisces
,
Aries
Taurus
,
and
Gemini
.
And
the
descending
from
the
beginning
of
Cancer
,
reacheth
vnto
the
end
of
Sagitarius
,
and
comprehendeth
Cancer
,
Leo
,
Virgo
,
Libra
,
Scorpio
,
and
Sagitarius
.
So
that
the
sun
in
that
halfe
cyrcle
,
ascendeth
from
the
Southerly
region
vnto
vs
,
in
that
from
vs
it
is
digressed
into
the
South
,
and
of
the
same
they
receiued
those
names
.
What
the
latitude
of
a
Planet
is
,
after
two
definitions
.
FIrst
,
that
the
arke
of
the
great
cyrcle
is
crossed
betwéene
the
Ecclipticke
,
and
true
place
of
the
Planet
,
(
and
that
is
named
the
latitude
of
the
Planet
)
for
that
according
to
the
same
,
the
Planet
into
latitude
,
that
is
,
into
the
South
or
North
,
swarueth
from
the
Eccliptick
line
:
whereof
the
Planets
are
named
to
haue
a
latitude
,
one
whiles
into
the
North
,
and
another
whiles
into
the
South
.
But
the
degrée
expressed
and
shewed
by
that
great
cyrcle
in
the
Eccliptick
,
is
called
the
degrée
of
the
longitude
of
the
star
or
planet
,
which
according
to
longitude
from
the
beginning
of
Aries
vnto
that
place
,
is
the
Planet
moued
.
The
other
instructeth
,
and
by
demonstration
sheweth
,
that
from
this
line
the
other
fiue
Planettes
wander
,
one
whiles
into
the
North
,
&
another
whiles
into
the
South
beeing
not
equally
caried
.
This
wandring
from
the
saide
line
,
is
named
the
latitude
of
the
Planets
,
and
is
the
arke
of
the
great
cyrcle
,
passing
by
the
Poles
of
the
Zodiacke
and
true
place
of
the
Planet
,
comprehended
betwéene
the
Ecclipticke
,
and
Center
of
the
star
.
According
to
this
distance
,
he
is
named
a
Planetary
star
(
what
star
soeuer
the
same
be
)
that
to
latitude
from
the
eclipticke
,
is
carried
either
Northerly
or
southerly
.
So
that
it
cannot
be
saide
that
a
planet
is
without
the
Zodiacke
,
séeing
the
auncient
obseruers
of
the
stars
(
being
moued
)
did
attribute
to
this
cyrcle
a
latitude
.
As
may
be
(
the
Ecclipticke
line
)
noted
with
A.
and
B.
and
the
letter
C.
the
Pole
of
the
Northerly
Ecclipticke
,
by
which
the
Cyrcle
noted
with
C.
G.
D.
and
Q.
is
ment
,
béeing
the
shewer
of
the
Latitudes
,
and
when
a
star
shall
be
in
the
point
G.
he
shal
then
be
without
or
haue
no
latitude
,
but
if
in
the
letter
E.
he
shal
then
haue
a
latitude
Northerly
,
whose
quantity
,
the
arke
G.
E.
sheweth
.
If
so
be
a
star
shall
be
in
the
point
D.
then
shall
it
be
Meridional
,
vnto
the
quantity
of
the
arke
G.
D.
and
L.
D.
K.
the
letters
M.
E.
N.
are
the
Parallelles
drawne
about
the
saide
latitudes
,
on
either
side
.
So
that
this
demonstration
euidently
sheweth
,
what
the
latitude
of
a
star
is
;
that
is
,
when
such
a
latitude
is
attributed
to
the
Zodiack
.
What
the
longitude
of
a
Starre
is
,
and
where
he
beginneth
.
THe
longitude
of
a
star
,
is
the
arke
of
the
Zodiacke
or
ecclipticke
line
,
from
the
beginning
of
Aries
,
reckned
euen
vnto
that
point
of
the
eccliptickes
,
which
is
touched
by
the
great
cyrcle
,
drawne
by
the
Poles
of
the
Zodiack
,
and
true
place
and
degrée
of
the
longitude
of
the
stars
.
As
may
be
conceiued
in
the
figure
aboue
,
where
the
pointe
A.
representeth
the
beginning
of
Aries
,
the
letters
A.
G.
the
longitude
of
the
star
,
if
the
same
shall
bee
in
the
Ecclipticke
,
the
letters
C.
G.
D.
the
cyrcle
ending
the
longitudes
.
The
difference
betwéene
a
declination
and
latitude
:
is
this
,
that
a
latitude
is
the
distance
of
a
star
or
Planet
from
the
eccliptick
,
toward
either
of
the
Poles
:
which
distance
is
measured
in
the
greate
cyrcle
drawne
by
the
body
of
a
star
,
and
Poles
of
the
Zodiacke
.
But
the
declination
is
a
distance
from
the
Equinoctial
,
when
as
the
sun
is
caried
by
a
continual
and
dayly
course
in
the
vpper
face
of
the
Ecclipticke
,
and
hath
no
latitude
,
but
a
declination
onely
:
yet
the
other
sixe
Planets
,
haue
a
latitude
and
declination
.
The
declination
of
Planets
,
is
the
distance
of
them
(
or
a
degrée
of
the
eccliptick
)
from
the
equinoctiall
.
And
this
measured
by
the
cyrcle
drawne
by
the
body
of
a
starre
,
or
degrée
of
the
ecclipticke
,
and
by
the
Poles
of
the
worlde
.
The
Planets
also
are
said
to
ascend
and
descend
,
by
reason
of
the
thwartnesse
and
bending
of
the
Zodiacke
:
for
the
sun
doeth
ascend
in
the
Northerly
signes
,
but
hee
descendeth
in
the
Southerly
.
In
the
like
maner
doe
all
the
other
Planets
,
as
well
by
the
reason
of
the
ascention
,
as
also
of
the
place
.
For
planets
beeing
in
Northerly
signes
,
haue
the
arke
of
ascention
greater
than
in
the
Southerly
.
Besides
,
this
part
of
the
world
which
declineth
into
the
North
,
is
supposed
and
iudged
as
to
vs
,
to
be
raised
higher
,
by
reason
of
the
Horizont
.
Further
the
definition
of
a
signe
shall
here
bee
declared
,
that
the
same
is
ment
sundry
wayes
:
one
whiles
to
bee
a
circumference
,
an
other
whiles
an
vpper
face
:
and
sometime
to
be
a
solyde
body
.
The
Zodiacke
(
as
I
haue
afore
declared
)
is
one
whiles
a
line
all
circumference
(
which
is
named
the
Ecclipticke
line
)
an
other
whiles
a
swathe
,
of
eight
degrées
in
breadth
of
either
side
:
Sometimes
the
zodiacke
is
called
the
plain
vpper
face
of
that
Ecclipticke
:
and
in
an
other
place
the
same
called
a
solyde
body
,
which
of
the
saide
swathe
,
and
by
the
two
imagined
vpper
faces
is
crossed
;
of
which
the
tops
or
highest
places
ouer
the
head
are
ioyned
togither
in
the
Center
of
the
earth
,
and
the
féete
are
those
Parallels
of
the
Ecclipticke
ending
the
swathe
,
which
may
worthily
be
called
a
solide
zodiacke
.
Further
a
signe
in
the
fifte
maner
,
is
a
portion
of
the
sphericall
vpper
face
(
inclosed
betwéene
two
halfe
cyrcles
)
ended
at
the
Poles
of
the
ecclipticke
.
To
conclude
,
a
signe
in
the
sixt
maner
is
mente
a
solyde
deuider
of
the
Sphere
,
contained
in
the
saide
halfe
Cyrcles
and
Sphericall
vpper
face
,
which
is
a
signe
vnderstood
in
the
fift
maner
.
These
diuers
diuisions
serueth
(
as
they
write
)
vnto
that
end
,
whereby
all
things
might
be
inclosed
within
the
signes
.
For
if
signes
be
described
in
the
first
maner
,
then
on
such
wise
those
stars
onely
,
and
those
points
are
said
to
be
in
the
signes
,
whatsoeuer
shall
be
in
that
cyrcumference
of
the
ecclipticke
.
And
in
the
first
signification
also
is
ment
to
be
vnder
the
ecclipticke
,
which
agréeth
onely
to
the
sun
,
as
at
this
day
the
sun
is
(
beeing
the
23.
day
of
August
)
in
the
9.
degrée
,
and
9.
minutes
,
of
Virgo
at
Noone
,
which
is
ment
to
be
vnder
that
part
of
the
eccliptick
,
that
is
named
the
9.
degrée
of
Virgo
.
If
in
the
second
maner
planets
shall
be
in
signes
,
which
doe
not
excéed
sixe
degrées
of
latitude
;
or
thus
in
the
second
signification
,
to
be
vnder
the
zodiacke
is
monte
,
that
here
a
signe
is
expressed
,
inclosed
within
a
square
pinnacle
portion
.
This
signification
agréeth
to
the
other
planets
(
except
the
sun
)
which
decline
from
the
ecclipticke
,
as
Mars
in
this
yeare
1599.
is
in
the
15.
degrée
of
Virgo
,
which
is
vnder
that
parte
of
the
zodiacke
,
that
is
saide
to
be
the
15.
of
Virgo
.
Also
he
hath
a
latitude
Northerly
of
two
degrées
,
and
28.
minutes
.
If
in
the
thirde
maner
,
the
sun
or
any
starre
shall
bee
in
signes
(
placed
in
the
plain
of
the
eccliptick
,
or
in
the
third
signification
to
be
in
a
signe
)
signifieth
to
be
referred
vnto
any
signe
of
the
zodiacke
.
For
the
whole
heauen
is
deuided
into
twelue
Regions
(
in
cyrcles
passing
by
the
beginnings
of
the
signes
,
and
Poles
of
the
Zodiacke
)
of
which
Regions
each
is
named
a
signe
.
And
this
signification
agréeth
to
the
stars
,
standing
without
the
zodiacke
:
as
the
Northerly
Crowne
,
which
in
our
time
is
in
Scorpio
,
and
referred
vnto
the
signe
of
the
zodiacke
that
is
called
Scorpio
;
in
that
it
is
betwéene
those
twoe
halfe
cyrcles
which
passe
by
the
beginning
and
end
of
Scorpio
.
If
in
the
fourth
maner
,
the
planets
and
stars
also
,
not
further
distant
then
sixe
degrées
from
the
ecclipticke
.
Or
in
the
fourth
signification
,
is
ment
or
referred
vnto
any
of
the
twelue
Regions
of
heauen
;
into
which
,
heauen
by
those
sixe
Cyrcles
which
passe
by
the
beginninges
of
the
signes
and
Poles
of
the
zodiacke
(
as
is
afore
written
)
is
deuided
.
This
signification
agréeth
to
those
which
are
in
the
ayre
,
(
as
be
the
Comets
.
)
As
if
I
wrote
that
a
Comet
were
in
Leo
,
here
I
meane
the
sixe
cyrcles
passing
by
the
Poles
of
the
zodiacke
,
and
beginnings
of
the
signes
,
deuiding
both
heauen
and
the
whole
neather
Region
of
the
worlde
into
twelue
equall
partes
.
So
that
a
Comet
is
saide
to
bee
in
Leo
,
séeing
it
is
in
that
twelfe
parte
which
the
twoe
halfe
cyrcles
describe
,
running
or
stretching
by
the
beginning
and
end
of
Leo.
If
in
the
fift
maner
,
all
the
stars
and
points
ment
in
the
vpper
face
of
the
sphere
,
be
included
in
signes
.
If
in
the
sixt
maner
,
then
whatsoeuer
is
in
the
world
(
whether
the
same
be
in
the
Ethereall
,
or
Elementarie
region
)
is
accounted
to
be
included
within
a
signe
.
Here
conceiue
,
where
the
cyrcumferences
of
the
cyrcles
are
ment
.
And
first
imagine
the
circumference
of
the
Zodiacke
,
and
all
the
other
cyrcles
(
as
I
haue
afore
written
)
to
be
in
the
hollow
vpper
face
of
the
first
mouer
,
and
runneth
as
it
were
in
the
first
(
after
the
second
condicion
of
motions
)
and
demonstrateth
alike
distaunce
and
continuing
of
the
cyrcles
without
impediment
.
Although
the
Horizont
,
the
Meridiane
,
the
Uerticiall
,
and
other
cyrcles
(
in
respect
of
the
habitation
or
dwelling
place
)
remaine
immoueable
in
that
vpper
face
of
the
first
moouer
:
yet
doeth
it
nothing
hinder
(
although
heauen
or
the
first
mouer
be
drawne
about
)
that
such
cyrcles
be
imagined
to
bee
immoueable
.
For
there
is
nothing
more
agréeable
,
then
to
imagine
cyrcles
fixed
,
and
those
abiding
in
any
vpper
face
of
the
earth
.
So
that
it
is
necessary
,
that
the
Zodiacke
,
the
Equatoure
,
and
the
other
cyrcles
be
described
moueable
in
the
hollow
face
of
the
first
mouer
,
as
the
bound
and
inclosure
of
the
whole
worlde
.
The
Horizont
and
Meridiane
,
and
the
others
,
placed
immoueable
in
that
hollowe
and
fixed
vpper
face
,
in
which
the
whole
earth
is
placed
,
by
this
meanes
the
fixed
cyrcles
shoulde
stay
in
the
fixed
vpper
face
,
and
the
mouable
cyrcles
shuld
be
drawne
about
with
the
moueable
.
As
in
a
materiall
instrument
,
and
solide
sphere
a
man
may
sée
,
in
which
the
zodiacke
,
the
Equatoure
,
and
other
moueable
cyrcles
,
are
drawne
about
vpon
the
Exe-trée
,
betwéene
the
two
Cyrcles
remaining
steady
,
of
which
the
one
representeth
the
Horizont
,
the
other
the
Meridian
.
Whether
the
same
may
be
described
in
the
hollowe
,
or
in
the
imbossing
of
the
first
moouer
of
the
saide
cyrcumference
,
it
is
little
or
nothing
regarded
:
yet
consider
this
,
that
all
men
may
behold
and
sée
within
the
heauen
or
first
mouer
,
the
hollowe
vpper
face
of
his
inclosure
,
to
describe
and
imagine
the
cyrcles
in
the
same
.
The
Cyrcles
placed
without
the
materiall
instrument
,
must
of
necessity
force
a
man
to
describe
the
cyrcumferences
of
the
Cyrcles
in
that
outwarde
face
of
the
Instrument
.
To
conclude
,
the
Zodiacke
is
ment
and
described
according
to
his
diffinition
(
being
a
greater
Cyrcle
)
whose
cyrcumference
in
the
hollowe
of
the
first
moouer
described
into
signes
,
degrées
,
and
minutes
,
(
as
was
afore
writen
)
is
deuided
.
And
séeing
that
Cyrcle
described
by
the
suns
yearely
motion
,
is
imagined
straight
drawne
and
defined
or
determined
from
the
Center
of
the
suns
course
by
the
Center
of
the
sun
,
which
with
the
sun
is
drawne
by
a
perfect
reuolution
toward
the
East
.
For
this
line
in
that
motion
cutting
the
hollowe
vpper
face
of
the
first
mouer
,
doeth
describe
the
cyrcumference
of
the
Zdiacke
.
So
that
if
the
plaine
vpper
face
of
the
suns
course
bée
extended
,
vntill
it
cutteth
the
foresaide
hollowe
vpper
face
,
which
common
section
or
cutting
shall
be
the
selfe
same
cyrcumference
of
the
Zodiacke
,
vnto
which
the
place
of
the
force
and
vertue
of
any
star
is
applied
.
Therefore
by
the
same
meanes
that
vertue
of
the
moone
,
or
any
of
the
planets
,
drawne
in
the
same
hollowe
of
the
vpper
heauen
,
shall
be
like
the
same
described
.
cording
to
the
diuers
eleuation
of
the
Pole
,
whereof
the
Colures
are
called
vnperfect
cyrcles
.
There
are
two
maner
of
Colures
,
as
the
Colure
of
the
solstices
,
and
Colure
of
the
equinoctials
.
These
two
greater
cyrcles
are
drawne
by
the
Poles
of
the
world
:
of
which
the
one
goeth
by
the
Poles
of
the
Zodiacke
,
and
the
other
by
the
sections
of
the
Zodiacke
and
Equatoure
.
That
which
passeth
by
the
Poles
of
the
equatour
and
Zodiack
,
doth
deuide
in
two
parts
each
halfe
cyrcle
,
as
well
of
the
equatour
,
as
the
Zodiacke
.
Therefore
the
one
condicion
of
the
Colures
goeth
by
the
solsticiall
pointes
of
the
Zodiacke
(
which
are
the
beginnings
of
Cancer
and
Capricorn
,
and
the
furthest
pointes
from
the
equatour
)
whereof
it
is
named
the
solsticiall
Colure
.
The
other
is
named
the
equinoctiall
Colure
,
séeing
it
entreth
by
the
saide
equinoctiall
sections
,
which
are
the
beginnings
of
Aries
and
Libra
;
that
is
,
the
equinoctiall
points
.
So
that
these
Colures
deuide
aswell
the
equinoctiall
as
the
Zodiacke
into
foure
quarters
,
in
that
they
goe
by
the
foure
principall
poyntes
of
them
.
The
Colures
generally
are
called
al
the
greater
cyrcles
drawne
by
the
Poles
of
the
world
,
which
take
their
name
thereof
,
insomuch
as
they
neuer
are
descerned
or
séene
whole
in
the
turning
about
of
the
worlde
,
as
the
other
cyrcles
,
but
vnperfect
and
lacking
.
For
both
the
arks
right
against
one
another
about
the
Poles
,
in
the
thwart
sphere
are
not
séene
both
at
once
.
For
they
are
either
continually
in
sight
to
vs
,
and
neuer
drawne
away
or
hid
like
vnto
those
which
be
neare
to
the
eleuated
Pole
.
Or
else
they
neuer
appeare
in
sight
to
vs
,
but
are
continually
hid
from
vs
,
as
those
which
be
the
opposites
.
But
the
reaching
of
the
Colures
fastneth
in
the
two
circles
,
extended
and
passing
by
the
foure
principall
pointes
of
the
ecclipticke
,
as
the
equinoctials
and
solsticials
,
which
touching
one
another
in
the
Poles
of
the
world
,
do
in
their
cyrcumferences
make
right
angles
,
and
part
the
Zodiack
and
equatoure
into
foure
equall
quarters
.
The
Colure
of
the
equinoctials
,
resting
in
the
equinoctiall
points
.
The
other
containing
the
solstiticiall
pointes
,
is
called
the
Colure
of
the
solstices
▪
The
Colure
of
the
equinoctials
is
a
greater
cyrcle
,
moueable
,
and
euery
where
alike
:
drawne
by
the
Poles
of
the
worlde
or
equatour
,
and
the
equinoctial
points
,
as
the
beginnings
of
Aries
and
Libra
,
making
with
the
equatour
right
sphericall
angles
,
with
the
Zodiack
thwart
angles
.
For
oftentimes
the
greatest
cyrcles
(
by
a
mutual
touching
togither
)
doe
make
right
angles
in
the
sphere
,
as
they
cut
in
two
parts
or
into
equall
halfe
cyrcles
,
and
by
the
Poles
one
another
:
and
contrariwaise
when
they
cutte
one
another
by
the
Poles
,
then
doe
they
forme
and
make
right
angles
with
their
cyrcumferences
,
and
part
one
the
other
into
equall
parts
(
as
writeth
Theodosius
in
his
first
Booke
de
Sphera
,
and
in
propositi
,
18.
19.
20.
and
21.
)
Or
thus
,
the
Colure
of
the
equinoctials
(
which
is
named
the
equinoctiall
Colure
)
is
a
greater
Cyrcle
passing
by
the
poles
of
the
world
,
and
the
first
pointes
of
Aries
&
Libra
;
where
the
two
Equinoctiall
points
are
said
to
be
:
in
that
the
sunne
causeth
a
like
day
and
night
in
euery
place
;
or
for
that
these
pointes
are
in
the
Equator
,
wherof
it
is
called
the
Colure
distinguishing
the
equinoctials
:
so
that
the
two
Colures
crosse
one
another
on
the
Poles
of
the
world
,
at
right
spericall
Angles
.
It
is
called
the
Colure
of
the
equinoctials
,
for
that
it
passeth
by
the
equinoctiall
pointes
,
as
by
the
beginnings
of
Aries
&
Libra
(
which
they
call
the
Equinoctial
pointes
)
for
that
when
the
sunne
hapneth
into
either
of
them
,
the
day
and
night
is
of
equall
length
throughout
the
Earth
;
which
commeth
to
passe
twise
in
the
yeare
(
as
in
the
Spring
and
Haruest
)
whereof
the
one
is
called
the
Equinoctiall
spring
(
and
at
this
day
is
about
the
eleuenth
of
March
)
which
is
the
day
before
Gregory
:
the
other
,
the
Haruest
Spring
,
and
hapneth
in
our
time
the
14.
of
September
,
that
is
,
thrée
daies
afore
Lambert
,
whereof
ariseth
this
auncient
verse
:
Lampert
,
Gregori
,
nox
est
aequata
diei
.
The
Colure
of
the
Solstices
is
a
greater
circle
,
moueable
,
and
euery
where
alike
drawn
by
the
solsticiall
points
or
the
beginnings
of
Cancer
&
Capricornus
,
and
the
Poles
of
the
Zodiacke
and
Equatoure
,
making
right
sphericall
angles
with
both
,
for
of
both
is
the
Poles
comprehended
.
And
according
to
Theodosius
propo
.
lib.
2.
de
Spera
,
that
by
any
twoe
cyrcles
crossing
one
the
other
(
when
a
thirde
deuideth
the
parts
of
both
equally
and
in
two
partes
)
the
same
is
the
greater
cyrcle
,
and
passeth
by
the
poles
of
both
.
But
that
which
passeth
by
the
Poles
of
the
other
Cyrcle
,
doth
part
it
in
two
parts
,
and
at
right
angles
.
Here
may
be
demanded
,
why
the
other
twoe
are
called
the
solsticiall
pointes
,
séeing
the
Sunne
stayeth
no
where
.
Which
is
thus
answered
,
that
the
sun
digressing
from
either
equinoctiall
poynt
by
his
proper
motion
,
doeth
dayly
depart
from
the
equinoctiall
cyrcle
,
till
hée
come
vnto
the
solstitiall
point
,
where
he
is
furthest
distant
from
the
equatoure
.
But
immediately
after
hee
beginneth
to
returne
and
come
againe
vnto
the
equatour
,
till
he
come
vnto
the
other
equinoctiall
pointe
.
So
that
the
pointe
of
the
suns
furthest
distance
(
which
is
the
beginning
of
Cancer
or
Capricornus
)
and
of
the
same
called
the
solstice
,
in
that
the
sun
stayeth
there
:
that
is
,
ceaseth
from
his
further
going
or
departure
,
and
beginneth
againe
to
come
to
the
Equatoure
.
For
the
sun
after
his
comming
vnto
that
point
departeth
,
and
commeth
againe
to
the
equatour
:
so
that
the
end
,
the
departure
,
and
beginning
of
his
comming
,
is
the
solstice
.
Therefore
not
for
that
the
sun
stayeth
there
,
are
they
called
the
solstices
,
although
about
those
pointes
of
the
going
and
comming
of
the
sun
,
it
is
so
small
,
that
for
foure
,
sire
,
or
more
daies
after
,
he
séemeth
in
iudgement
as
it
were
to
stay
in
one
declination
:
and
therefore
for
that
cause
may
be
named
the
solstitials
.
These
of
sundrie
(
as
of
Campanus
)
are
also
called
Tropicke
points
,
through
the
suns
returning
.
And
these
may
be
called
Uerticiall
or
Cardinal
cyrcles
(
séeing
they
goe
by
those
tops
of
the
world
)
and
expresse
or
shewe
the
foure
quarters
of
the
Zodiacke
.
Moreouer
séeing
certaine
parts
of
these
cyrcles
being
neare
the
pole
are
hid
,
and
the
other
right
against
them
nothing
at
all
discerned
at
any
time
:
therefore
is
it
that
they
are
called
in
Greeke
Kolouroi
,
which
is
in
English
,
maimed
and
vnperfect
,
as
Proclus
,
Diadochus
,
Mocrobius
and
Capella
,
write
.
But
this
agréeth
not
in
the
right
Horizont
,
séeing
there
is
no
part
of
heauen
,
which
doeth
alwaies
remaine
there
hid
.
But
in
the
description
of
the
astrolobie
,
howe
large
soeuer
the
same
bee
,
yet
onely
these
cyrcles
appeare
continually
vnperfect
.
Yet
further
,
the
Colure
of
the
solstices
,
or
the
cyrcle
distinguishing
the
solstices
,
which
also
is
called
the
solstitiall
cyrcle
,
is
a
greater
cyrcle
drawne
and
passing
by
the
poles
of
the
world
,
and
Zodiacke
,
and
the
greatest
declinations
of
the
same
:
and
by
the
beginnings
of
Cancer
and
Capricornus
.
It
is
called
the
Colure
of
the
solstices
,
in
that
it
passeth
by
the
solsticiall
pointes
(
as
by
the
beginnings
of
Cancer
and
Capricornus
)
which
are
named
the
solsticiall
pointes
;
for
that
in
them
the
solstice
is
caused
:
that
is
,
the
suns
comming
vnto
those
pointes
,
departeth
not
further
from
the
Equinoctiall
,
but
commeth
)
againe
vnto
the
Equinoctiall
,
which
is
caused
twice
in
the
yeare
,
as
in
summer
and
winter
:
whereof
the
one
is
called
the
summer
solstice
(
which
in
our
time
hapneth
the
12.
of
Iune
or
thereabout
)
beeing
the
nexte
day
after
S.
Barnabe
the
Apostle
,
where
the
longest
day
is
holden
to
bée
.
The
other
the
winter
solstice
,
which
in
our
time
hapneth
about
the
11.
or
12.
day
of
December
(
being
a
day
or
two
before
Lucie
)
where
the
day
is
accompted
shortest
:
whereof
is
this
auncient
verse
extant
.
Vitus
est
Lucia
,
dant
tibi
solstitia
bina
.
Of
the
former
also
ensueth
,
that
there
is
certaine
fixed
and
moueable
Colures
.
For
there
is
a
fixed
Colure
of
the
equi●octiale
,
which
passeth
by
the
poles
of
the
world
,
and
section
of
the
equatoure
and
Ecclipticke
of
the
first
mouer
.
The
fixed
Colure
of
the
solstices
doth
cut
this
at
right
angles
in
the
poles
of
the
world
,
and
passeth
by
the
middle
of
the
suns
greatest
declination
.
Séeing
neither
the
equinoctials
nor
solstices
,
are
caused
according
to
the
true
meaning
of
the
astronomers
(
as
afore
may
appeare
)
both
in
these
points
,
aswell
as
in
others
:
Therefore
a
man
must
conceiue
,
that
the
Colures
be
moueable
:
of
which
the
one
goeth
by
the
true
equinoctiall
;
that
is
,
by
the
section
of
the
suns
way
,
and
equatour
,
and
by
the
Poles
of
the
worlde
,
and
the
other
of
the
solstices
,
passeth
by
the
suns
greatest
declination
.
These
hitherto
written
,
may
more
plainer
appeare
,
by
this
demonstration
here
following
.
In
this
figure
,
are
the
cyrcles
,
and
parts
of
the
cyrcles
noted
with
their
names
.
In
which
the
letter
F.
expresseth
the
true
and
moueable
equinoctiall
.
The
letter
E.
is
a
note
of
the
fixed
Equinoctiall
.
The
letter
D.
pointeth
out
the
head
of
Aries
,
of
the
eight
sphere
.
The
letter
C.
the
center
of
the
eight
Sphere
.
The
letter
A.
of
the
ninth
and
tenth
sphere
.
The
letters
K.
N.
represent
the
suns
greatest
declination
truely
.
The
letters
R.
M.
the
suns
middle
declination
greatest
.
How
much
the
Equinoctials
are
distant
one
from
another
,
the
former
large
instruction
of
the
equinoctials
,
may
easily
shew
at
any
time
,
vnto
which
a
man
must
alwaies
resorte
.
The
suns
greatest
declination
,
is
the
arke
of
the
Colure
of
the
solstices
,
contained
betwéene
the
equatoure
and
eyther
Tropicke
:
this
of
sundry
practisioners
is
diuersly
noted
.
For
Ptholomie
founde
the
same
in
his
time
to
bee
of
23.
degrées
,
51.
minutes
,
and
20.
seconds
:
of
which
the
whole
cyrcle
is
noted
to
bée
360.
degrées
,
but
after
Alnieon
,
of
23.
degrées
,
and
33.
minutes
.
But
the
later
practisioners
haue
founde
the
same
to
bee
23.
degrées
,
and
30.
minutes
.
Purbachius
hath
found
the
same
to
be
of
23.
and
21.
minutes
:
which
variation
of
the
suns
greatest
declination
is
,
through
the
comming
and
going
of
the
eight
Sphere
,
(
which
is
named
the
trembling
motion
.
)
But
this
is
demonstrated
and
taught
more
at
large
in
the
Theoricks
.
If
any
desire
to
obserue
the
suns
greatest
declination
,
let
him
take
the
altitude
of
the
sunne
about
the
winter
solstice
,
in
the
shortest
day
at
Noone
:
which
altitude
beeing
kept
a
parte
,
worke
the
like
,
the
sun
being
about
the
summer
solstice
,
and
the
suns
greatest
altitude
at
Noone
found
by
the
rule
of
the
astrolobie
;
looke
that
in
the
bordure
of
the
same
,
and
take
the
middle
of
that
arke
,
which
is
betwéene
the
suns
least
and
greatest
eleuation
at
Noone
,
which
possesseth
the
myddle
,
and
shall
bee
the
Suns
greatest
declination
.
The
knowledge
of
the
suns
declinations
,
with
the
other
stars
,
is
very
profitable
;
in
that
by
the
same
,
and
the
perfection
of
the
eleuation
of
the
pole
,
the
true
place
of
the
sun
(
if
the
same
be
vnknowne
)
may
bee
knowne
,
the
suns
greatest
declination
presupposed
,
after
this
maner
as
followeth
.
Marcke
and
consider
diligently
(
the
sun
being
in
the
Noonestead
cyrcle
)
caried
vp
from
the
Horizont
:
which
founde
,
if
the
sun
run
in
the
Northerly
signes
,
abate
from
the
saide
eleuation
the
complement
of
the
eleuation
of
th●
Pole
.
If
the
sun
bee
caried
in
the
Southerly
signes
,
then
worke
contrary
;
for
that
which
remaineth
,
shall
bee
the
suns
particular
declination
.
As
by
a
like
example
vse
this
.
The
sun
beeing
imagined
to
bee
eleuated
aboue
the
Horizont
63.
degrées
.
21.
minutes
,
and
4.
seconds
,
the
eleuation
of
the
Pole
is
41.
degrées
,
and
30.
minutes
,
and
the
comple●●nt
of
the
same
altitude
of
the
Pole
to
bée
48.
degrées
,
and
30.
minutes
;
with
the
which
subtract
the
suns
altitude
at
Noone
,
and
the
remaurer
shall
be
the
suns
declination
,
which
is
14.
degrées
,
51.
minutes
,
&
4.
seconds
.
being
the
distance
of
the
sun
from
the
beginning
of
Aries
,
abated
for
the
suns
running
in
the
Northerly
signes
,
at
the
time
of
the
obseruation
before
the
summer
solstice
.
What
the
offices
or
vtilities
of
the
Colures
are
.
_1
SHe
common
offices
in
generall
of
the
Colures
are
,
to
shewe
the
foure
principall
points
of
the
zodiacke
,
in
which
through
the
suns
motion
the
greatest
chaunges
and
alterations
of
time
is
caused
.
2
They
serue
to
demonstrat
the
solstices
and
equinoctialles
,
and
to
deuide
the
Zodiacke
into
foure
equall
partes
,
to
which
the
foure
seasons
of
the
yeare
doe
answere
.
3.
The
vse
of
the
one
is
to
expresse
and
make
manifest
the
pointes
of
the
equinoctials
,
and
the
other
to
shewe
the
points
of
the
solstices
.
4
They
both
cut
the
Zodiacke
and
equatour
,
into
two
equall
halfe
Cyrcles
,
and
both
deuide
either
Cyrcle
into
foure
equall
quarters
.
5
But
the
Colure
of
the
solsticis
offereth
many
other
vses
:
for
in
the
same
is
the
sunnes
greatest
declination
or
thwartnesse
measured
and
numbred
,
in
that
the
sunnes
greatest
declination
,
is
the
Arke
of
the
Colure
of
the
colsticis
(
inclosed
betwéene
the
beginning
of
Cancer
and
the
Equatour
)
which
arcke
is
either
increased
or
diminished
,
according
to
the
winding
in
and
out
of
the
eclipticke
vnto
the
Equatour
,
as
is
afore
mentioned
.
6.
They
serue
to
distinguish
the
Equinectiall
,
the
Zodiacke
,
and
all
heauen
into
foure
equall
partes
:
the
vse
of
which
matter
shall
appeare
in
the
place
of
the
ascentions
of
the
signes
.
7
Each
Colure
besides
,
hath
his
priuate
office
or
vtilities
:
as
the
Colure
of
the
solstices
,
which
hath
foure
offices
.
The
first
demonstrateth
the
solsticiall
pointes
.
The
second
containeth
and
measureth
,
the
suns
greatest
declination
.
The
third
,
that
it
stayeth
vp
the
poles
of
the
Zodiack
,
and
sheweth
their
distance
from
the
poles
of
world
.
The
fourth
,
that
it
deuideth
the
Zodiack
into
two
halfes
,
as
into
the
ascending
and
descending
.
Also
the
same
in
the
thwart
Sphere
,
doeth
seperate
the
signes
rightly
arising
,
from
the
signes
thwartly
rising
.
8
The
Colure
of
the
equinoctials
hath
twoe
offices
.
The
first
,
that
it
demonstrateth
the
Equinoctiall
pointes
.
The
second
,
that
it
deuideth
the
Zodiacke
into
two
halfs
;
as
into
the
Northerly
and
Southerly
halfe
,
9
To
conclude
,
the
Colure
of
the
solstices
doeth
often
supply
and
is
vsed
in
the
stead
of
the
Meridiane
,
when
as
in
euery
dayly
reuolution
of
the
first
mouer
,
it
doth
twice
enter
into
the
place
of
the
meridiane
,
or
is
twice
ioyned
in
the
plaine
of
the
same
.
The
descriptions
,
names
,
and
offices
of
the
Meridiane
Circles
,
and
Horizont
.
THe
foure
greater
cyrcles
which
we
haue
already
described
,
that
with
the
motion
of
the
sphere
are
drawn
about
,
and
euery
where
are
alike
,
which
the
other
twoe
Cyrcles
are
contrary
;
as
the
meridiane
and
Horizont
,
that
are
not
turned
in
the
drawing
about
of
the
Sphere
,
but
remaine
as
immoueable
and
fixed
;
neither
are
they
alike
in
all
places
,
but
are
continually
changed
,
standing
or
placed
on
the
earth
.
In
that
all
places
haue
their
proper
meridians
,
and
Horizonts
.
For
both
by
a
mutuall
touching
and
ioyning
together
doe
make
right
angles
,
and
they
continually
deuide
the
whole
heauen
into
foure
equall
parts
,
and
make
the
foure
angles
and
quarters
of
heauen
,
vnto
which
by
a
continuall
turning
aboute
of
heauen
,
both
the
one
and
the
other
stars
(
as
it
were
by
an
orderly
succession
drawne
)
worke
and
send
forth
their
vertues
more
effectuous
,
and
excercise
their
qualities
in
the
Elements
,
then
in
any
other
places
:
especially
the
sun
being
drawne
vnto
those
bonds
,
for
hée
both
beginneth
and
endeth
the
dayes
and
nightes
,
and
distinguisheth
them
equally
,
as
it
were
in
the
middle
parcels
of
time
.
The
sun
also
come
vnto
the
meridian
,
doeth
then
more
heat
,
dry
vp
and
consume
vapors
.
The
Meridiane
of
any
place
,
is
a
greater
cyrcle
,
which
goeth
or
reacheth
by
the
poles
of
the
worlde
and
height
of
any
place
:
and
for
that
it
passeth
by
the
poles
of
the
equatour
,
Parallels
,
and
the
Horizont
,
through
the
same
doth
it
make
right
angles
with
them
.
And
of
this
it
deuideth
all
the
arks
of
the
Parallels
as
well
in
sight
as
not
in
sight
into
two
equall
halfes
.
This
circle
hath
sundry
names
,
for
Varro
nameth
it
the
Meridian
or
midday
cyrcle
of
the
noonestéed
,
in
that
when
the
sun
is
in
the
meridian
,
or
any
other
star
aboue
the
earth
,
then
hath
it
performed
halfe
the
day
arke
,
and
is
then
at
the
bounde
of
the
Noone
time
.
But
the
other
halfe
of
the
night
is
caused
,
at
the
instant
point
of
midnight
,
the
halfe
then
reaching
from
East
and
West
.
So
that
of
the
same
(
this
cyrcle
of
all
writers
in
this
science
)
named
the
meridiane
,
but
of
Ptholomie
the
cyrcle
of
midday
and
middle
heauen
,
by
the
same
reason
.
The
astrologians
call
this
cyrcle
the
royall
Cuspe
,
the
regall
quarter
,
the
beginning
of
the
tenth
house
,
and
the
middle
of
heauen
:
in
that
this
place
is
principall
,
and
of
worthier
dignity
then
the
other
quarters
,
of
which
shall
further
be
written
in
his
proper
place
.
Further
it
behoueth
by
the
addition
(
31.
Primi
Theodosij
)
that
the
Equat●ure
and
Horizont
,
in
the
contrary
maner
,
to
passe
by
the
poles
of
the
meridian
:
&
of
the
same
that
those
poles
is
none
otherwise
placed
,
than
in
the
common
sections
of
the
equatour
and
Horizont
.
By
which
sections
,
&
by
those
poles
of
the
Horizont
,
is
a
certaine
thirde
cyrcle
greater
drawne
,
which
Iohannes
(
a
Regio
monte
)
nameth
the
verticial
circle
:
so
that
by
the
foresaid
Corolary
or
addition
ensueth
,
that
of
these
thrée
cyrcles
of
each
Exe-trée
and
Pole
,
are
they
in
that
common
section
of
the
other
two
cyrcles
.
Like
as
of
the
Equinoctiall
,
and
two
colures
by
right
may
be
concluded
.
So
that
a
triple
deuision
is
caused
by
the
thrée
cyrcles
,
which
appeareth
on
this
wise
:
that
as
the
meridian
tendeth
by
our
top
and
height
from
the
South
into
the
North
;
euen
so
by
the
same
top
it
behoueth
the
other
cyrcle
to
be
drawne
and
passe
from
the
east
into
the
west
that
both
cutting
one
the
other
at
right
angle
,
shoulde
expresse
the
foure
foresaide
quarters
of
the
world
.
As
the
Horizont
distinguisheth
the
vpper
halfe
sphere
,
from
the
neather
,
and
the
meridiane
from
the
East
to
the
West
;
euen
so
it
falleth
out
,
that
the
thirde
cyrcle
,
as
that
verticiall
,
shoulde
seperate
the
Northerly
from
the
Southerly
halfe
sphere
.
To
these
,
while
any
standeth
vpright
toward
the
Welt
,
on
such
maner
,
that
the
middle
of
his
body
is
in
the
common
Center
of
thrée
cyrcles
;
then
doth
the
Horizont
deuide
his
vpper
halfe
from
the
neather
,
and
the
Meridiane
,
the
fore
part
from
the
hinder
;
and
the
verticall
cyrcle
the
right
part
from
the
left
.
The
thrée
common
sections
of
these
cyrcles
,
are
their
Exe-trées
(
as
is
afore
written
)
doe
indicate
or
shewe
the
foure
principall
points
of
heauen
(
which
are
the
fixe
poles
of
the
cyrcles
)
placed
in
the
sections
of
the
cyrcumferences
,
as
the
highest
or
lowest
point
(
which
are
the
poles
of
the
Horizont
)
the
point
also
most
Easterly
and
Westerly
,
which
are
the
Poles
of
the
Meridiane
:
to
conclude
,
the
pointe
most
Northerly
and
Southerly
,
which
are
the
Poles
of
the
verticiall
cyrcle
.
Those
people
that
séeme
to
haue
their
féete
against
ours
(
in
respect
of
the
roundnesse
of
the
earth
)
that
they
dwell
as
it
were
vnder
vs
haue
alike
horizont
agréeable
to
ours
,
alike
meridian
,
and
alike
verticial
circle
.
But
of
these
two
,
the
halfe
cyrcles
which
be
extant
to
vs
are
hid
or
as
it
were
vnder
them
.
Contrariwise
,
those
which
be
hid
to
vs
,
are
to
them
extaunt
.
The
pointe
also
highest
to
vs
,
is
lowest
to
them
:
contrariwise
the
lowest
to
vs
,
is
highest
to
them
.
The
figure
afore
placed
,
doth
plainer
expresse
that
afore
taught
:
where
the
letters
A.
B.
C.
D.
represent
the
Meridiane
,
the
letters
B.
E.
D.
F.
the
Horizont
:
the
letters
F.
A.
E.
C.
the
vertical
cyrcle
:
the
letter
G.
the
center
of
the
cyrcles
and
world
:
the
letters
A.
C.
the
Exe-trée
of
the
Horizont
,
the
letters
B.
D.
the
Exe-trée
of
the
verticiall
cyrcle
:
the
letters
E.
F.
the
Exe-trée
of
the
Meridian
.
To
conclude
,
the
point
that
to
vs
is
most
Easterly
,
is
to
them
most
Westerly
,
et
è
contrario
.
For
the
pointe
most
Northerly
and
Southerly
,
doe
not
change
the
surname
,
except
you
list
to
change
or
alter
the
names
,
like
as
of
the
Poles
of
the
worlde
.
For
that
which
is
to
vs
apparant
,
is
to
them
hid
:
and
contrariwise
to
vs
hidde
,
to
them
manifest
.
Here
may
be
demaunded
whether
that
point
of
heauen
most
Northerly
,
be
not
the
Northerly
Pole
of
the
world
,
and
that
point
most
Southerly
,
the
Southerly
Pole
of
the
world
.
To
which
is
thus
answered
,
that
if
regard
be
had
vnto
the
Equatoure
and
right
Horizont
,
which
passeth
by
the
Poles
of
the
world
,
and
hath
the
equatour
for
the
verticiall
,
or
in
stéede
of
the
verticiall
cyrcle
.
But
wee
which
haue
not
the
Poles
of
the
world
in
the
Horizont
(
in
whose
cyrcumference
these
foure
principall
pointes
of
the
East
,
West
,
North
,
and
South
,
are
accustomed
to
be
noted
)
are
forced
to
call
that
Northerly
section
of
the
Meridiane
and
Horizont
,
the
most
Northerly
point
,
and
that
section
right
against
the
most
Southerly
point
.
For
in
euery
place
there
are
two
sections
which
the
meridiane
and
verticiall
cyrcle
doe
make
with
the
Horizont
,
which
are
two
right
sections
in
the
plaine
of
that
Horizont
(
cutting
at
right
angles
one
an
other
in
the
Center
)
that
expresse
and
shew
those
foure
quarters
of
the
worlde
,
from
which
the
principall
windes
blowe
;
as
East
,
West
,
North
,
and
South
.
So
that
the
foresaid
right
sections
doe
part
the
Horizont
,
and
cyrcumference
of
the
same
into
foure
quarters
.
The
foure
principall
windes
(
of
the
common
sorte
)
are
thus
called
,
that
which
bloweth
from
the
East
,
the
Leuant
winde
,
and
that
right
against
it
the
Ponent
:
that
from
the
North
,
Transmontanus
,
and
that
right
against
it
the
Mer●dional
.
These
foure
of
later
yeares
,
they
haue
deuided
into
32.
windes
,
after
the
noted
lines
and
pointes
drawne
in
the
Saylers
carde
,
and
other
Mappes
euery
where
to
be
séene
.
Also
the
Saylers
compasse
doth
expresse
so
many
windes
,
directed
by
the
adamant
or
lodestone
,
which
howe
the
same
doeth
direct
and
shewe
the
windes
,
needeth
not
here
be
shewed
,
séeing
the
same
is
sufficiently
known
to
euery
sayler
,
which
by
the
guide
of
their
compasse
,
direct
their
course
in
clowdy
weather
(
either
by
day
or
night
)
in
marking
diligently
the
points
of
the
compasse
,
how
they
coast
.
To
returne
vnto
the
matter
of
the
Meridiane
:
the
diuersitie
of
Meridianes
is
no
otherwise
caused
,
then
the
swelling
of
the
earth
,
as
in
the
first
part
I
haue
sufficiently
written
:
the
cause
of
which
is
,
that
one
like
parte
of
heauen
cannot
be
the
top
or
height
of
euery
place
.
Therefore
one
meridiane
cannot
serue
all
places
,
but
that
in
all
places
a
proper
Meridiane
is
caused
ouer
the
head
.
The
meridiane
also
is
that
which
when
the
sun
commeth
vnto
the
highest
ouer
vs
,
foresheweth
by
his
working
and
heat
the
midday
.
This
meridiane
is
a
greater
cyrcle
,
passing
by
the
poles
of
the
world
and
Zenith
,
or
a
direct
pointe
ouer
the
head
,
abiding
immoueable
at
the
motion
of
the
sphere
.
This
cyrcle
is
differing
to
euery
Citty
and
people
,
by
reason
of
the
East
and
West
,
and
is
a
proper
meridiane
caused
ouer
the
heade
.
For
this
is
manifest
,
that
at
the
chaunging
of
the
verticiall
point
,
there
is
caused
an
other
Meridian
,
through
the
swelling
and
roundnesse
of
the
earth
.
Also
a
man
may
of
one
meridian
line
,
describe
many
(
as
writeth
Iohannes
a
regio
monte
)
for
in
that
instant
of
the
Noonetide
,
by
letting
downe
right
a
plum
line
,
the
shadowe
of
the
line
causeth
a
newe
Meridiane
line
on
the
platforme
.
Therefore
these
with
the
verticiall
line
in
the
the
Center
to
the
Horizont
(
crossing
one
an
other
at
right
angles
)
doe
indicate
the
foure
quarters
of
the
worlde
:
as
the
meridian
line
,
the
North
and
South
,
the
verticial
line
,
the
East
and
West
.
The
Horizont
formeth
the
quarters
of
the
east
and
west
:
of
which
the
one
is
called
the
East
rising
,
or
easterly
quarter
or
end
:
the
other
called
the
West
setting
,
and
quarter
of
the
West
.
The
Meridiane
defineth
the
boundes
of
the
lowest
and
highest
of
heauen
,
and
the
quarters
or
middle
motions
of
the
day
and
night
time
:
of
which
,
that
consisting
the
vpper
halfe
Sphere
,
is
named
the
highest
place
and
middle
of
heauen
,
the
other
which
containeth
the
lowest
place
right
against
it
,
called
the
bothom
or
lowest
of
heauen
.
The
Meridiane
is
a
greater
cyrcle
,
immoueable
,
not
one
and
the
same
euery
where
,
but
to
euery
place
peculiar
and
proper
,
drawne
by
the
top
of
the
place
and
Poles
of
the
worlde
(
vnto
which
the
sun
carried
by
the
motion
of
the
first
moouer
)
doeth
in
the
day
time
cause
high
Noone
,
and
in
the
night
time
drawne
right
against
it
causeth
midnight
.
If
this
cyrcle
were
moueable
like
others
,
then
at
the
motion
of
the
sphere
woulde
it
departe
from
our
Zenith
,
and
so
loose
the
name
of
the
Meridiane
:
neither
woulde
it
deuide
in
proper
place
vnder
it
,
the
artificial
day
into
two
equall
parts
;
séeing
by
that
motion
,
the
Meridiane
should
approach
néerer
to
one
part
of
the
Horizont
,
then
to
the
other
part
.
Nor
should
it
stay
the
Horizont
at
right
angles
,
of
which
it
is
numbred
and
accompted
amongest
the
outwarde
cyrcles
of
the
sphere
.
The
like
affirmeth
Proclus
,
writing
that
the
Meridiane
is
none
of
those
cyrcles
which
is
noted
and
decked
with
starres
.
For
the
cyrcles
of
the
sphere
are
distinguished
by
starres
,
whereby
those
cyrcles
may
more
easily
be
knowne
in
heauen
.
The
meridianes
are
changed
by
the
continuall
chaunging
of
place
in
the
swelling
or
imbossing
of
the
earth
(
according
to
longitude
.
)
For
by
going
continually
right
forth
toward
the
East
and
West
,
it
doeth
purchase
newe
Meridianes
:
as
by
going
thrée
miles
forth
,
then
is
an
other
pointe
of
heauen
,
differing
from
the
first
ouer
a
mans
heade
and
gone
further
by
foure
minutes
of
a
degrée
.
Proclus
affirmeth
,
that
300.
furlongs
cause
no
sensible
alterations
to
happen
of
the
Meridian
:
and
this
is
ment
of
those
which
are
placed
vnder
diuers
Meridianes
,
and
Parallelles
.
For
those
which
are
placed
vnder
one
Parallell
and
diuers
Meridianes
,
perceiue
and
sée
no
alteration
at
all
.
Hee
which
goeth
strait
from
the
North
into
the
South
,
or
they
which
directly
iourney
toward
either
of
the
Poles
of
the
worlde
,
doe
continually
trauaile
vnder
one
Meridiane
.
In
that
all
Merdianes
doe
go
from
one
Pole
to
another
,
therefore
no
iourney
causeth
by
this
meanes
an
other
meridiane
.
There
are
as
many
meridians
in
number
,
as
there
bée
differences
of
verticiall
points
(
right
ouer
diuers
parts
of
the
earth
)
in
going
toward
the
East
and
West
.
The
halfe
of
the
equinoctiall
hath
180.
degrées
,
whereof
the
Cosmographers
doe
assigne
and
distinguish
so
many
meridians
,
in
such
sorte
,
that
each
Meridiane
doeth
passe
by
the
twoe
opposite
degrées
of
that
Equinoctiall
,
and
Poles
of
the
world
.
The
longitude
of
a
place
is
the
arcke
of
the
equinoctiall
cyrcle
,
or
of
any
Parallell
contained
betwéene
two
Meridianes
,
of
which
the
one
lyeth
ouer
the
fortunate
Iles
,
and
the
other
streacheth
ouer
the
top
of
the
proper
place
noted
,
where
the
same
distance
of
place
is
gathered
from
the
fortunate
Iles
at
the
equinectiall
,
or
at
the
Parallell
of
the
place
.
The
fortunate
Iles
are
situated
and
lying
in
the
sea
,
called
Oceanus
Libicus
beyond
Mauritania
(
betwéene
the
Equatoure
and
the
tropicke
of
Cancer
)
which
in
our
time
is
called
the
Iles
of
Canarie
,
and
lie
further
into
the
North
from
the
equatour
,
then
Ptholomie
noted
or
acounted
them
.
But
the
latitude
,
they
accompted
to
bee
a
space
of
the
earth
lying
betwéene
either
pole
,
accompted
in
the
Meridiane
drawne
by
the
poles
of
the
worlde
,
or
a
whole
tract
of
the
earth
knowne
and
streached
beyonde
,
and
on
this
side
the
equatoure
,
toward
either
Pole
of
the
worlde
.
They
stablished
the
beginning
of
the
latitude
in
the
equinoctiall
(
as
in
the
middle
cyrcle
exquisitely
betweene
either
pole
)
and
common
bound
to
both
the
Southerly
and
Northerly
places
,
So
that
the
latitude
of
a
place
,
is
the
arke
of
the
meridiane
,
betwéene
the
equinoctiall
and
Parallell
drawne
by
the
top
of
the
place
:
or
it
is
the
distance
of
a
place
from
the
equinoctiall
.
This
alwaies
is
accounted
in
that
meridian
,
which
hangeth
directly
ouer
the
top
of
the
place
,
and
to
one
degrée
of
the
same
,
doe
500.
surlongs
,
or
15.
Germaine
miles
answere
.
The
arks
of
the
latitudes
doe
not
differ
from
the
eleuations
of
the
pole
,
but
in
the
standing
onely
.
For
the
eleuation
of
the
pole
is
the
arke
of
the
meridian
,
from
the
Horizont
vnto
the
Pole
,
raysed
on
high
from
the
plaine
of
the
Horizont
.
The
latitude
of
a
place
,
is
the
arke
of
the
same
meridian
,
placed
betweene
the
equinoctiall
and
verticiall
point
.
To
conclude
,
the
latitude
of
a
place
,
and
eleuation
of
the
pole
do
not
differ
in
the
magnitude
or
largenes
,
but
in
standing
onely
.
By
the
former
figure
appeareth
,
that
the
Arke
of
the
longitude
of
places
or
citties
known
,
is
forthwith
offered
at
the
first
sight
:
as
the
arke
E.
P.
or
P.
O.
or
O.
N.
&c.
And
séeing
the
equatour
(
being
in
compasse
about
360.
degrées
)
doeth
wholy
ascend
in
24.
houres
aboue
the
Horizont
regularly
:
of
this
it
commeth
to
passe
(
whiles
in
ech
houre
15.
degrées
of
the
equatour
doe
ascend
)
that
through
the
longitude
of
cities
,
it
is
easily
knowne
the
hourely
distance
of
one
place
vnto
an
other
,
séeing
the
sun
commeth
later
to
the
meridian
to
them
which
are
nearer
to
the
East
then
to
them
in
the
West
,
whereof
if
a
citty
shall
be
situated
in
L.
and
an
other
in
K.
the
arke
L.
K.
shall
be
of
30.
degrées
:
then
shall
the
sun
come
sooner
vnto
the
Easterlier
meridian
K.
by
two
houres
,
then
vnto
the
Westerly
.
But
if
one
citty
shall
bee
in
P.
and
the
other
in
Z.
then
(
in
latitude
onely
)
shall
they
differ
,
and
shall
be
vnder
one
meridian
;
which
is
declared
in
the
last
part
of
the
description
of
the
meridian
.
What
the
offices
and
vtilities
of
the
Meridiane
are
.
1
THe
vtilities
and
vses
of
this
circle
are
many
,
of
which
the
first
is
,
that
it
distinguisheth
the
dayes
and
nightes
into
vnequal
spaces
:
it
determineth
the
forenoone
time
or
morning
,
and
the
after
noone
or
euening
time
of
the
artificiall
day
:
the
like
of
the
night
into
houres
(
which
are
before
night
)
and
those
which
follow
vnto
morning
.
Many
of
the
astronomers
accompt
their
beginning
of
the
naturall
day
from
this
cyrcle
.
It
doth
besides
represent
(
without
the
equin●●tiall
)
the
Horizont
of
the
right
sphere
,
and
in
euery
habitude
of
the
sphere
it
doeth
represent
the
right
Horizont
,
and
sheweth
the
points
of
the
midday
,
and
midnight
.
2
This
cyrcle
in
the
thwart
sphere
giueth
and
suprlyeth
the
office
of
the
right
Horizont
:
for
to
euery
thwart
Horizont
it
leaueth
or
stayeth
at
right
angles
.
So
that
the
astronomer
maketh
or
accompteth
not
his
day
,
from
the
rising
or
setting
of
the
sun
through
the
thwartnesse
of
the
Horizont
,
which
causeth
the
variety
&
notable
difference
of
the
inclination
of
the
Zodiacke
,
vnto
the
horizont
of
the
angles
,
and
largenesse
of
the
rising
.
But
they
begin
to
accompt
from
noone
or
midnight
(
the
sun
then
occupying
the
Meridian
)
through
the
Sunne
,
which
congruence
all
the
meridianes
haue
with
the
right
horizont
.
And
that
a
lesser
variety
of
the
inclination
of
the
Zodiacke
hapneth
vnto
the
meridiane
and
angles
,
which
it
maketh
with
the
meridiane
.
Also
in
this
cyrcle
is
the
Zenith
or
direct
point
noted
,
from
which
the
distances
of
the
stars
,
and
Parallel
cyrcles
are
gathered
.
4
In
the
meridianes
(
as
in
the
subiect
)
the
distances
of
the
stars
from
the
equatoure
,
the
latitudes
of
places
,
and
the
eleuations
of
the
Pole
are
accompted
.
For
the
studious
and
skillfull
practisioners
,
obserue
the
latitudes
of
places
and
the
eleuations
of
the
pole
,
not
to
differ
in
the
quantity
,
but
in
the
standing
onely
.
For
the
eleuation
of
the
pole
,
is
the
arke
of
the
meridiane
from
the
horizont
,
raised
vnto
the
pole
.
The
latitude
of
the
place
,
is
the
arke
of
the
same
meridian
,
contained
betwéen
the
equatour
and
verticiall
point
:
so
that
it
is
manifest
that
these
arks
differing
in
the
standing
,
doe
agrée
in
magnitude
,
whose
verticiall
points
,
one
meridiane
containeth
,
but
not
one
Parallell
,
by
an
equall
space
from
the
west
)
be
vnequall
distant
from
the
equatour
,
and
are
then
said
to
differ
in
the
latitude
only
.
Contrariwise
,
to
whose
tops
one
and
the
same
Parallell
,
and
not
one
meridian
,
but
each
place
proper
;
those
by
like
spaces
from
the
equatour
,
be
distant
by
vnlike
spaces
from
the
fortunate
Iles
,
and
are
said
to
differ
in
the
longitude
onely
.
So
that
in
both
they
are
saide
to
differ
;
to
whome
the
Parallell
only
serueth
,
and
they
to
whome
the
proper
meridiane
serueth
:
for
they
haue
their
spaces
vnequall
to
either
bound
.
Therfore
the
difference
of
latitude
is
the
arke
of
the
meridiane
,
contained
betwéene
the
Parallelles
of
the
two
places
,
distant
from
the
equatour
.
The
quantity
of
the
same
is
thus
knowne
;
if
from
the
halfe
Equatour
toward
either
pole
of
the
places
standing
,
the
lesser
latitude
of
the
nearer
,
bee
abated
from
the
greater
latitude
more
further
off
:
if
from
the
halfe
equatour
the
places
be
deuided
vnder
(
that
the
one
half
leaneth
into
the
North
and
the
other
into
the
South
)
by
the
latitudes
of
both
ioyned
,
whether
one
or
both
ly
vnder
one
meridian
or
diuers
meridians
.
For
it
forceth
not
in
the
meridian
of
both
,
that
the
latitudes
bee
ioyned
togither
,
séeing
all
meridians
are
alike
in
the
sphere
.
The
difference
of
the
longitude
,
is
the
arke
of
the
equinoctiall
or
Parallell
,
inclosed
betwéene
the
meridianes
of
the
twoe
places
,
distaunt
from
the
fortunate
Iles
,
and
in
themselues
:
by
which
the
longitude
of
one
place
excéedeth
the
longitude
of
another
.
The
same
longitude
is
the
arcke
of
the
equinoctial
,
séeing
the
places
be
vnder
the
equatour
.
For
in
the
only
longitude
the
places
,
the
common
Parallelles
,
and
tops
of
both
bended
,
doe
differ
:
in
that
the
Parallelles
(
from
the
equatour
)
toward
the
opposite
quarters
of
the
equall
Parallelles
(
as
places
to
which
they
be
right
ouer
)
doe
likewise
differ
.
The
meridians
(
as
is
afore
declared
)
are
the
greatest
cyrcles
of
the
sphere
of
the
worlde
,
bended
by
the
verticiall
points
of
all
places
,
but
drawn
to
the
equatoure
(
as
by
the
Poles
)
of
which
they
passe
vnto
right
angles
,
and
by
a
mutuall
consent
,
make
angles
in
the
Poles
of
the
world
,
which
the
arks
of
the
equatour
being
placed
betwéene
those
meridians
,
are
measured
,
that
by
so
much
as
a
quarter
of
the
cyrcle
they
bee
distant
from
them
:
euen
so
the
equatoure
from
his
Poles
,
is
on
either
part
distant
by
a
quarter
of
the
greatest
cyrcle
.
Those
arks
doe
containe
the
difference
of
longitude
,
by
which
one
of
the
meridianes
is
further
distant
into
the
East
then
the
other
;
so
that
the
angles
vnto
the
Poles
betwéene
the
meridianes
,
are
rightly
named
the
angles
of
the
difference
of
longitude
;
and
by
the
arks
of
the
equatour
,
those
also
come
into
knowledge
:
for
there
is
a
mutuall
relation
betweene
the
angles
and
arkes
each
one
of
them
towards
another
,
which
doe
measure
the
angles
.
The
latitude
of
places
,
is
the
distance
of
the
verticiall
points
from
the
equatour
,
gathered
in
the
meridian
.
If
then
from
the
whole
quarters
of
the
meridians
(
which
to
the
equatoure
and
Pole
of
the
world
,
toward
which
the
places
decline
the
equall
arkes
bee
stretched
to
the
latitudes
,
then
the
seates
of
the
places
giuen
,
or
the
verticiall
points
of
them
shall
be
found
.
And
the
other
arks
from
these
points
vnto
the
Pole
(
which
by
a
mutuall
section
doe
make
an
angle
)
the
complements
of
the
latitudes
,
be
known
by
the
degrées
abated
from
90.
in
the
degrées
of
the
latitudes
.
Further
by
the
suns
meridian
had
and
found
,
you
may
easily
conceiue
the
eleuation
of
the
pole
,
and
habitude
of
the
sphere
.
For
the
whole
quarter
is
,
of
90.
degrées
.
Séeing
the
suns
meridian
altitude
in
the
equinoctiall
,
must
be
subtracted
from
90.
degrées
,
the
rest
shew
the
eleuation
of
the
Pole
.
As
for
example
,
the
suns
meridian
altitude
of
Viteberge
in
Germanie
,
in
the
time
of
the
equinoctiall
,
is
of
38.
degrées
,
and
10.
minutes
,
the
rest
of
the
degrées
of
the
quarter
shall
appeare
to
bee
51.
degrées
,
and
50.
minutes
,
which
eleuation
of
the
pole
neer
agréeth
to
London
.
So
that
by
so
many
degrées
,
is
the
Pole
there
eleuated
aboue
the
Horizont
.
And
as
the
quadrant
is
from
the
pole
vnto
the
equinoctial
:
euen
so
is
the
quadrant
from
the
Zenith
vnto
the
Horizont
.
If
therefore
in
the
time
of
the
Equinoctiall
,
the
distance
of
the
Horizont
vnto
the
suns
altitude
be
of
38.
degrées
,
and
10.
minutes
;
which
is
not
the
halfe
part
of
the
quarter
,
the
same
yet
being
subtracted
from
the
whole
quarter
,
doeth
shew
that
the
rest
shall
bee
more
then
halfe
part
of
the
quarter
:
that
is
,
51.
degrées
,
and
51.
minutes
.
For
those
spaces
which
are
from
the
pole
vnto
the
Equinoctiall
,
and
from
the
Zenith
vnto
the
Horizont
,
are
alike
:
what
the
distance
of
the
Zenith
is
from
the
equinoctiall
,
the
same
likewise
is
the
Horizont
vnto
the
Pole
;
that
is
,
the
latitude
of
the
place
,
is
equall
to
the
eleuation
of
the
pole
.
To
declare
that
the
latitude
of
a
place
is
equall
to
the
eleuation
of
the
pole
,
these
foure
propositions
are
to
be
conceiued
.
First
,
the
quarters
of
one
and
the
same
cyrcle
,
any
where
taken
,
are
equall
one
to
the
other
.
Secondly
,
the
poles
by
the
quarter
;
that
is
,
90.
degrées
bee
distant
from
their
cyrcle
.
Thirdly
,
the
Zenith
is
the
pole
of
the
Horizont
.
Fourthly
and
last
,
the
equals
abated
from
the
equals
the
equals
still
remaine
.
So
that
two
quarters
of
the
meridian
taken
(
as
that
which
is
from
the
equinoctiall
vnto
the
pole
,
and
that
which
is
from
the
Zenith
vnto
the
Horizont
)
which
séeing
they
are
quarters
of
one
and
the
same
cyrcle
,
therefore
are
they
likewise
equall
one
to
the
other
;
that
is
,
either
containeth
90.
degrées
,
when
from
these
two
quarters
the
common
arke
is
abated
;
which
is
betwéene
the
Zenith
and
Pole
of
the
worlde
:
and
the
rest
of
the
equals
remaine
(
as
the
arke
which
is
from
the
equinoctiall
vnto
the
Zenith
)
and
called
the
latitude
of
the
place
;
and
the
arke
(
which
is
from
the
Pole
of
the
world
vnto
the
Horizont
)
also
called
the
eleuation
of
the
Pole
,
as
may
be
vnderstanded
of
the
former
Viteberge
,
that
is
of
51.
degrées
,
and
50.
minutes
.
Yet
that
you
may
easilier
finde
and
knowe
the
eleuation
of
the
Pole
of
your
City
or
Towne
,
you
must
first
obtaine
and
haue
the
suns
meridian
altitude
;
which
workemanly
may
be
had
and
obserued
by
the
shadow
.
As
when
the
suns
altitude
in
the
time
of
the
equinoctiall
is
precisely
of
45.
degrees
,
the
shadowe
then
is
like
to
the
Gnomone
,
which
is
at
Venice
(
as
Plinie
writeth
)
also
of
Milaine
and
Lions
:
for
the
sun
to
them
is
in
the
time
of
the
equinoctial
,
in
the
middle
of
the
quarter
.
But
when
the
suns
altitude
excéedeth
45.
degrées
,
then
is
the
shadow
caused
lesser
,
as
of
Rome
,
where
the
sunnes
meridian
altitude
in
the
equinoctiall
is
of
42.
degrées
,
and
10.
minutes
:
so
that
the
shadowe
is
there
shorter
.
Also
Plinie
writeth
of
Rome
,
that
the
ninth
part
of
the
Gnomon
in
the
equinoctiall
,
doth
lack
of
the
noone
shadow
.
But
when
the
suns
altitude
is
lesser
then
45.
degrées
,
the
shadow
of
the
Gnomon
is
caused
longer
.
The
like
is
with
vs
through
all
winter
and
the
time
of
the
equinoctiall
:
for
we
sée
the
shadowes
of
mens
bodies
to
be
longer
,
for
that
the
suns
altitude
in
that
time
is
neuer
45.
degrées
.
For
how
much
the
shadow
is
longer
then
the
halfe
part
of
the
quarter
,
so
much
the
lesser
is
the
suns
altitude
then
45.
degrées
.
As
of
Viteberge
in
the
10.
day
of
September
,
the
suns
meridian
altitude
is
then
of
39.
degrees
,
and
21.
minutes
:
but
when
the
sun
is
further
distant
by
the
45
degrée
of
the
quarter
(
or
by
the
halfe
of
the
quarter
)
then
ensueth
,
that
the
shadow
is
so
much
longer
then
the
Gnomon
,
or
45
,
degrées
.
For
the
Noone
shadow
in
the
10.
day
of
September
is
the
like
vnto
the
Gnomon
,
as
the
50.
degrées
,
and
39.
minutes
,
are
vnto
45.
degrées
.
Heere
you
sée
how
by
the
meridian
shadowe
,
you
may
finde
the
suns
altitude
;
which
obtained
,
you
shall
easily
find
the
altitude
or
eleuation
of
the
Pole
(
especially
in
the
time
of
the
equinoctiall
.
)
For
the
suns
altitude
then
from
the
whole
quarter
;
that
is
,
from
90.
degrées
,
must
be
subtracted
,
and
the
eleuation
of
the
pole
shall
remaine
and
appeare
to
be
,
as
is
aboue
taught
.
Seeing
it
is
somewhat
harde
to
finde
the
height
of
the
Pole
vnto
any
day
prescribed
,
&
that
the
same
may
more
easily
and
surer
be
attained
and
founde
,
you
shall
vse
this
table
here
following
:
by
the
helpe
of
which
you
may
without
great
labour
,
finde
and
know
the
eleuation
of
the
pole
.
For
to
procéede
and
worke
by
this
manner
,
seeke
first
the
suns
meridian
altitude
at
the
day
offered
,
either
by
an
astrolaby
or
quadrant
;
but
rather
by
the
instrument
named
the
quadrant
,
in
whose
bordure
are
90.
degrées
drown
or
written
,
expressed
by
reason
of
the
Gnomon
and
shadowe
vpwarde
.
After
séeke
the
degrée
of
the
Ecclipticke
by
the
Ephemerides
,
which
the
sun
obtaineth
at
noone
of
the
day
offered
:
next
by
the
table
folowing
,
take
the
declination
of
the
degrée
founde
(
by
meane
of
the
equinoctiall
)
if
the
sun
then
shall
bee
in
Northerly
signes
,
abate
or
subtract
from
the
suns
altitude
afore
found
:
but
if
in
Southerly
signes
,
then
adde
vnto
the
suns
altitude
.
The
produce
or
rest
is
the
eleuation
of
the
equinoctiall
,
which
abstracted
or
abated
from
the
whole
quarter
;
that
is
,
from
90.
degrées
,
leaueth
&
sheweth
the
eleuation
of
the
pole
,
as
in
the
10.
day
of
September
,
the
suns
altitude
in
the
twelfe
houre
(
or
at
noone
)
is
of
39.
degrées
,
and
21.
minutes
.
To
finde
this
eleuation
of
the
pole
,
I
enter
the
table
following
,
where
I
finde
and
sée
the
27.
degrée
of
Virgo
,
to
haue
the
declination
of
one
degrée
,
and
11.
minutes
:
which
degrée
and
minutes
(
séeing
they
are
in
the
Northerly
part
of
the
worlde
)
are
to
be
subtracted
from
the
suns
altitude
that
day
,
and
the
degrées
which
remaine
are
38.
and
10.
minutes
.
The
altitude
of
the
equinoctial
that
day
,
which
subtracted
or
abated
from
the
whole
quarter
;
that
is
,
from
90.
degrées
,
the
eleuation
of
the
pole
which
remaineth
,
is
51.
degrées
,
and
50.
minutes
.
This
Table
of
the
Suns
declinations
,
containeth
the
number
of
the
degrees
of
the
Zodiacke
,
increasing
in
descending
on
the
left
hand
,
and
increasing
by
ascending
on
the
right
hand
,
with
the
Signes
decently
placed
:
the
Arks
or
roots
of
the
declinations
follow
those
numbers
:
which
rootes
are
no
other
then
the
arkes
of
the
circle
of
the
Latitude
:
that
is
,
the
circle
passing
by
the
Poles
of
the
Ecliptike
,
included
betweene
the
Ecliptike
and
Equatour
.
The
generall
Table
of
the
Declinations
.
|
♈
♎
Arkes
.
|
♉
♏
Arkes
.
|
♊
♐
Arkes
.
|
|
G
|
●r
.
|
m̄
|
●r
.
|
m̄
|
●r
.
|
m̄
|
G
|
0
|
0
|
0
|
12
|
16
|
20
|
38
|
30
|
1
|
0
|
26
|
12
|
37
|
20
|
40
|
29
|
2
|
0
|
12
|
12
|
37
|
21
|
0
|
28
|
3
|
1
|
18
|
12
|
58
|
21
|
11
|
27
|
4
|
1
|
44
|
12
|
58
|
21
|
21
|
26
|
5
|
2
|
10
|
13
|
19
|
21
|
31
|
25
|
6
|
2
|
36
|
13
|
40
|
21
|
40
|
24
|
7
|
3
|
2
|
14
|
0
|
21
|
49
|
23
|
8
|
3
|
28
|
14
|
20
|
21
|
58
|
22
|
9
|
3
|
53
|
14
|
40
|
22
|
6
|
21
|
10
|
4
|
19
|
14
|
50
|
22
|
14
|
20
|
11
|
4
|
45
|
15
|
18
|
22
|
21
|
19
|
12
|
5
|
10
|
15
|
37
|
22
|
28
|
18
|
13
|
5
|
25
|
15
|
55
|
22
|
35
|
17
|
14
|
6
|
0
|
16
|
●
|
22
|
41
|
16
|
15
|
6
|
25
|
17
|
31
|
22
|
47
|
15
|
16
|
6
|
50
|
17
|
48
|
23
|
52
|
14
|
17
|
7
|
15
|
17
|
5
|
23
|
57
|
13
|
18
|
7
|
39
|
17
|
22
|
23
|
2
|
12
|
19
|
8
|
3
|
18
|
●8
|
23
|
7
|
11
|
20
|
8
|
27
|
18
|
54
|
23
|
11
|
10
|
21
|
8
|
●●
|
18
|
0
|
23
|
15
|
9
|
22
|
9
|
15
|
18
|
25
|
23
|
18
|
8
|
23
|
9
|
39
|
19
|
40
|
23
|
21
|
7
|
24
|
10
|
2
|
10
|
55
|
23
|
23
|
6
|
25
|
10
|
25
|
19
|
9
|
23
|
25
|
5
|
26
|
10
|
48
|
19
|
23
|
23
|
27
|
4
|
27
|
11
|
10
|
20
|
36
|
23
|
28
|
3
|
28
|
11
|
32
|
20
|
49
|
23
|
29
|
2
|
29
|
11
|
54
|
20
|
36
|
23
|
30
|
1
|
30
|
12
|
16
|
20
|
30
|
23
|
30
|
0
|
Ecli●
|
♏
|
♓
|
♌
|
♒
|
♋
|
♉
|
Ecli●
|
THe
meridianes
with
the
Horizont
,
in
any
right
or
thwart
,
&
in
the
other
foure
greater
cyrcles
,
doe
distinguish
all
heauen
into
twelue
spaces
,
which
they
call
the
houses
of
heauen
.
Of
these
foure
,
which
occupy
the
angles
of
heauen
,
are
called
the
quarters
:
the
foure
nexte
to
these
,
are
named
the
succedents
:
the
last
(
included
by
the
succedentes
and
angles
)
are
named
the
declining
houses
,
and
the
cadent
from
the
angles
.
The
meridian
also
hath
a
most
great
vse
in
Cosmographie
:
for
by
it
the
describers
of
the
world
measure
the
longitudes
and
latitudes
of
places
and
cities
:
which
beeing
knowne
,
the
distance
of
cities
may
easily
be
found
.
That
you
may
vnderstand
what
the
longitude
and
latitude
of
a
place
is
,
it
behoueth
you
to
know
the
distinction
of
the
earth
after
the
Geographers
,
which
is
on
this
wise
,
The
Geographers
doe
assigne
or
imagine
two
points
on
the
earth
,
right
vnder
the
poles
of
the
world
:
after
that
they
deuise
a
cyrcle
equally
distant
on
either
side
from
these
these
two
points
(
right
vnder
the
equinoctiall
)
which
deuideth
the
whole
Globe
of
the
earth
and
water
into
twoe
equall
halfes
.
This
cyrcle
thus
described
on
earth
,
they
distribute
into
360.
parts
or
degrées
,
in
procéeding
from
the
West
into
the
East
,
by
each
degrées
of
this
cyrcle
;
and
by
the
points
right
vnder
the
poles
,
they
imagine
and
draw
180.
cyrcles
;
which
,
for
that
they
are
vnder
the
celestiall
meridians
,
they
also
call
meridians
,
and
those
they
deuide
into
thrée
hundred
&
thréescore
parts
or
degrées
;
by
which
parts
they
imagine
and
draw
the
Parallell
or
equidistant
cyrcles
to
the
equinoctiall
,
procéeding
from
the
equinoctiall
on
either
side
,
towardes
the
pointes
in
the
poles
lying
vnder
these
Parallels
,
&
although
they
bee
not
of
the
same
bignesse
or
largenesse
(
for
how
much
nearer
the
poles
they
are
,
so
much
the
narrower
and
strayter
they
run
togither
.
Contrariwise
,
how
farre
of
they
bee
from
the
Poles
,
and
nearer
to
the
Equinoctiall
,
so
much
the
wider
and
larger
they
runne
)
yet
doe
they
deuide
as
the
Equinoctiall
,
or
any
other
greate
cyrcle
,
into
thrée
hundreth
and
thrée
score
partes
or
degrées
.
Howe
this
deuision
of
the
earth
beeing
learned
and
vnderstoode
,
a
man
may
the
more
easily
conceiue
what
the
longitude
and
latitude
of
places
is
.
The
longitude
of
a
place
(
as
I
haue
afore
written
)
is
the
arke
of
the
equinoctiall
cyrcle
,
or
Parallell
,
passing
by
the
Zenith
of
the
place
which
is
sought
after
,
included
betweene
the
two
meridians
;
as
betwéene
the
first
meridian
(
which
by
the
Zenith
of
the
Iles
of
Canarie
(
and
further
off
)
is
imagined
to
bee
drawne
,
and
the
Meridian
of
the
place
offered
:
that
is
,
the
longitude
of
any
place
,
is
the
distance
thereof
from
that
westerly
point
,
from
which
the
beginning
of
longitudes
is
accounted
toward
the
East
.
They
began
to
account
the
longitude
from
the
west
,
through
the
proper
motions
of
the
Planets
,
which
are
caried
vnto
the
contrary
quarter
from
the
West
:
or
rather
for
the
Moone
,
at
whose
Ecclipses
it
is
well
knowne
that
it
more
auaileth
,
then
the
true
finding
out
the
longitudes
of
places
,
or
as
some
rather
thinke
likelier
,
that
the
places
which
ende
and
stand
furthest
Westward
inhabited
,
haue
bene
sures
and
perfecter
found
.
For
through
the
nearenesse
and
opportunity
of
the
iourneyes
(
which
they
in
auncient
time
were
mooued
to
f●aua●le
and
saile
●●●●
)
as
the
twoe
Iles
(
named
Gades
)
which
lie
by
the
furthest
parts
of
Spaine
beyond
Granade
,
and
since
through
the
passage
by
West
Occean
,
men
of
later
yeares
haue
sailed
about
the
furthest
partes
without
stop
or
impediment
.
But
vnto
the
Eastward
,
they
were
stopped
of
their
course
by
a
great
distance
through
the
difficulty
and
perill
of
the
iourney
.
And
since
beyond
the
halfe
circle
almost
thréescore
degrées
,
men
haue
sailed
to
Scythia
besides
Imaus
(
which
nowe
is
named
the
great
Tartaria
)
that
reacheth
bordering
to
the
vpper
India
,
where
the
most
large
kingdome
of
Cathagia
vnder
the
parallell
of
Thracia
flourisheth
,
where
Bebeid
Cham
was
gouernour
.
And
that
is
the
part
of
Tartaria
,
which
beginneth
from
the
riuer
Tanais
,
so
that
the
largenesse
of
Schithia
Asiatica
(
from
the
West
to
the
East
)
doeth
almost
take
vp
84.
whole
degrées
.
America
in
the
sea
Atlanticus
,
is
of
such
greatnesse
,
that
the
same
is
supposed
to
be
a
fourth
part
of
the
world
inhabited
:
the
middle
or
halfe
of
it
hath
the
longitude
of
330.
degrées
,
and
the
latitude
of
tenne
degrées
Southward
.
The
sea
Altanticus
hath
many
large
Ilands
in
it
;
among
which
,
the
most
notable
are
Spagnolla
,
Cuba
,
Parias
(
otherwise
Chersouesus
)
by
the
straight
that
reacheth
vpward
into
the
north
.
The
middle
of
the
same
hath
the
longitude
of
285.
degrées
:
the
latitude
Northerly
44.
degrées
.
For
from
11.
vnto
50.
almost
,
it
reacheih
vnto
.
America
streacheth
far
into
the
South
,
beyond
the
tropick
of
Capricorne
,
although
his
bounde
or
furthest
part
Southerly
bee
not
yet
founde
or
knowne
.
To
the
auncient
it
was
no
further
knowne
Southward
,
then
17.
degrées
beyond
the
Equinoctiall
:
and
the
furthest
knowne
to
them
Northwarde
,
excéeded
not
thrée
score
and
thrée
degrées
,
which
(
as
Ptholomie
witnesseth
)
was
vnto
the
Iland
Thylen
.
So
that
the
whole
latitude
found
by
them
,
appeareth
to
be
80.
degrées
,
both
of
the
one
and
the
other
side
of
the
equinoctial
:
and
on
earth
the
same
containeth
40.
thousand
furlongs
,
to
which
50.
hundred
paces
answere
,
but
Germaine
miles
two
hundreth
thousand
agrée
.
Also
the
Iland
Thilen
or
Thulen
,
standeth
beyond
Scotland
,
and
the
Iles
Hebrides
and
Orchades
,
that
be
into
the
North
and
East
,
which
is
distant
from
the
furthest
bound
of
Scotland
,
but
thrée
dayes
sayling
,
if
prosperous
windes
bée
their
helpe
.
At
this
day
men
haue
found
beyond
Thylen
(
but
somwhat
into
the
East
(
and
most
large
bounds
stretched
and
found
beyond
the
articke
or
Northerly
cyrcle
,
&
these
are
whole
without
breaking
of
any
sea
betwéene
;
and
containe
Suetia
,
Norway
,
Iseland
,
Grunland
and
Lapeland
.
The
kingdome
of
Suetia
appeareth
most
large
,
and
containeth
sundry
nations
and
people
;
among
which
,
they
are
of
most
account
,
the
East
and
West
Gutland
people
,
inhabiting
neare
to
Norway
.
And
vnder
the
King
of
Suetia
are
the
Lapeland
people
,
(
as
the
Finelapons
and
Dikilapons
)
where
are
a
wild
and
fierce
people
,
dwelling
almost
vnder
the
pole
articke
(
especially
the
Lapeland
people
)
to
whome
the
sun
neuer
setteth
in
the
summer
for
40.
dayes
space
.
Aboue
these
inhabit
a
people
of
a
cubite
long
or
high
,
hauing
small
and
crooked
bodies
(
named
of
some
Pigmalions
)
that
liue
vnder
a
very
darke
and
bitter
cold
ayre
or
sky
.
And
aboue
Scania
(
néere
to
the
West
boundes
of
Suetia
)
doeth
Norway
stretch
into
the
North
,
whose
vttermost
limit
extendeth
vnto
the
71.
degrée
almost
of
the
Northerly
latitude
.
Aboue
this
is
the
country
named
Iseland
,
by
reason
of
the
frozen
waters
and
sea
:
where
throughout
the
yeare
it
so
bitterly
fréezeth
,
that
through
the
ycie
seas
there
thicke
frozen
,
it
permitteth
no
ships
to
come
vnto
them
,
except
in
the
thrée
hottest
months
of
the
yeare
.
It
aboundeth
with
brimstone
,
and
burneth
in
many
places
through
the
sulphure
&
brimstone
veines
.
Plinie
writeth
,
that
the
Occean
sea
in
North
is
very
large
,
which
in
these
our
dayes
is
well
knowne
.
This
also
was
learned
of
certaine
skillfull
sailers
(
which
inhabited
and
very
much
had
traualed
this
coast
)
that
they
knew
not
the
limits
or
bounds
of
this
sea
toward
the
North
,
but
supposed
that
this
sea
did
compasse
the
whole
earth
.
By
this
sea
dwell
many
and
mighty
people
;
as
the
Danes
,
the
Swedens
,
Norwaies
,
Gotelandes
,
Finelands
,
Russians
,
and
Pruchenians
:
and
vnder
the
pole
artick
the
Laplands
.
The
reason
why
in
these
places
such
force
of
moysture
aboundeth
,
is
for
that
a
dayly
and
continuall
cold
of
these
places
gathereth
and
thickneth
the
ayre
,
and
by
a
continual
working
resolueth
into
water
.
For
when
the
ayre
is
not
throughly
purged
by
the
suns
beames
,
then
the
weaknes
of
them
,
and
far
distance
of
the
sun
from
these
places
,
must
of
necessity
bee
continually
thicke
and
darke
,
which
afterwardes
yéeldeth
and
giueth
plentifull
floodes
by
deawes
and
raines
.
Albert
mag.
in
his
booke
de
natura
loci
,
and
8.
chapter
,
assigneth
a
witty
and
laudable
reason
,
why
the
Northerly
be
inhabitable
.
The
cause
he
setteth
downe
,
in
that
sundry
skillfull
Mariners
affirme
(
that
haue
many
times
sailed
into
the
Northerly
partes
of
the
Ocean
sea
)
that
in
those
places
is
a
continuall
darknesse
,
which
when
men
sawe
they
returned
for
feare
,
supposing
(
nay
rather
doubting
)
that
none
coulde
saile
any
further
in
that
quarter
of
the
worlde
,
through
the
darknesse
,
and
thicke
mist
,
which
hindreth
the
direction
of
their
iourney
.
So
that
the
nature
of
those
places
cannot
bee
sufficiently
knowne
to
vs
,
séeing
no
man
(
as
the
learned
report
)
hath
attempted
thither
,
through
extremitie
of
colde
their
bearing
sway
.
And
for
that
excéeding
cold
is
a
mortifying
quality
,
therefore
a
man
may
coniecture
,
that
few
liuing
creatures
and
beasts
can
there
liue
&c.
Yet
the
part
of
the
Northerly
Occean
(
vnto
the
Easterly
side
)
is
sufficiently
knowne
to
many
trauailers
.
Although
the
vttermost
boundes
of
the
earth
are
not
wholy
knowne
,
yet
the
nearest
aprroaching
to
them
shall
here
bee
applied
,
as
the
longitude
of
the
earth
distaunt
betwéene
Peru
(
the
Realme
of
America
)
and
Cathaya
,
to
expresse
315.
degrées
:
or
if
any
minde
to
accompt
the
longitude
from
the
fortunate
Iles
,
they
may
by
a
whole
cyrcle
containe
them
,
euen
as
the
whole
Orbe
about
in
a
maner
doth
partly
giue
place
to
the
water
,
and
are
partly
dwellings
for
men
,
beasts
,
and
other
liuing
creatures
;
although
some
places
of
the
earth
bee
more
inhabited
then
others
.
But
as
touching
the
latitude
;
if
towarde
the
North
in
the
country
of
Lapous
,
&
the
south
(
toward
the
vtmost
coast
of
America
shal
end
)
seing
the
vtmost
distance
of
the
earth
hath
very
litle
béene
noted
,
of
this
shall
small
errour
be
caused
.
If
two
places
offered
or
giuen
be
placed
vnder
the
Equatour
,
of
which
the
space
is
sought
,
then
the
arke
of
the
difference
of
latitude
,
is
the
same
with
the
arke
of
the
distance
,
neither
doth
the
verticiall
cyrcle
differ
from
the
Equatour
.
For
the
equatour
of
either
place
doeth
containe
the
verticiall
points
,
as
may
appeare
in
this
tryangle
,
noted
with
A.
B.
C.
Of
which
,
if
15.
germain
miles
be
wrought
into
parts
of
the
difference
of
longitude
,
and
any
scruples
after
remaine
,
deuide
those
by
4.
For
(
by
so
many
minutes
of
a
degrée
,
doth
a
Germain
mile
answere
)
that
the
distance
shall
make
.
As
Ptholomie
writeth
,
of
the
places
vnder
the
Equatour
.
The
high
lande
or
mountaine
of
the
Satyres
,
in
the
country
of
Syna
,
whose
longitude
is
of
175
degrées
,
and
no
minutes
,
nor
hath
any
latitude
.
Myrica
an
Ile
of
Ethiope
vnder
Aegipt
,
whose
longitude
is
of
85.
degrées
,
the
angle
of
the
difference
of
longitude
betwéene
the
meridians
of
these
places
,
is
straight
or
right
,
and
containeth
a
whole
quarter
or
60.
degrées
.
The
like
are
these
places
standing
vnder
the
equatour
.
Colipolis
a
citty
of
India
beyond
the
riuer
Ganges
,
which
hath
the
longitude
194.
degrées
,
and
20.
minutes
,
&
Essina
the
greate
Mart-towne
of
Aethiope
vnder
Aegipt
,
whose
longitude
is
of
70.
degrées
,
and
3.
minutes
.
The
angle
of
the
difference
of
longitude
(
which
the
meridians
of
these
compasse
)
is
blunte
,
and
containeth
94.
degrées
,
and
17.
minutes
.
Againe
the
same
or
the
like
meridians
containe
and
make
a
sharpe
angle
of
43
degrées
,
as
of
the
citty
Nubarta
of
Taprobane
,
which
at
this
day
is
Sumatra
,
and
Colipolis
of
Inde
beyond
or
aboue
Ganges
:
for
it
is
distant
from
the
west
122.
degrées
,
and
20.
minutes
,
and
this
containeth
164.
degrées
,
and
20.
minutes
.
If
two
places
be
giuen
,
the
one
standing
vnder
the
Equatour
,
and
the
other
distant
toward
any
other
quarter
from
it
.
The
first
,
that
the
angle
of
the
difference
of
longitude
is
straight
to
these
here
placed
.
In
that
if
two
places
giuen
the
one
shall
be
vnder
the
equatoure
,
but
the
other
distant
from
the
same
toward
some
quarter
,
them
must
the
angle
of
the
difference
of
longitude
bee
considered
.
If
the
same
shal
be
right
,
then
shal
the
distance
of
either
place
be
the
quadrant
of
the
greatest
cyrcle
.
As
in
this
tryangle
A.
B.
C.
where
the
letter
A.
representeth
the
Pole
of
the
equatour
and
the
places
giuen
,
that
the
one
be
standing
in
the
point
B.
vnder
the
equatour
,
and
the
arke
A.
B.
be
the
quadrant
:
and
that
the
other
consisteth
in
the
letter
C.
the
angle
then
of
the
difference
of
longitude
,
being
C.
A.
B.
is
right
.
By
Regio
a
montano
de
trangulis
appeareth
,
that
C.
B.
the
ark
of
the
distance
of
places
which
reacheth
out
right
,
is
a
quarter
of
the
greatest
cyrcle
.
Wherefore
if
the
degrées
bee
multiplied
by
15.
and
the
minutes
deuided
by
4.
the
distance
then
shal
be
knowne
.
As
for
example
,
Nubarta
of
Taprobone
hath
the
longitude
121.
degrées
,
and
20.
minutes
,
but
no
latitude
:
the
city
Pyse
of
the
Tuscanes
in
Italie
,
hath
the
longitude
31.
degrées
,
and
20.
minutes
almost
,
the
latitude
of
42.
degrées
,
and
11.
minutes
:
then
the
angle
of
the
difference
of
longitude
is
right
,
for
the
difference
is
of
90.
degrées
,
or
a
whole
quadrant
.
These
then
multiplied
by
15.
do
procreate
or
bring
forth
the
distance
to
be
of
13
▪
50.
Germaine
miles
.
Essina
a
Mart-towne
or
principal
●itty
of
Aethiope
vnder
the
gouernment
of
Aegipt
,
hath
the
longitude
of
70.
degrées
,
and
3.
minutes
,
but
it
hath
no
latitude
.
The
I
le
of
Tyrus
hath
the
longitude
of
67.
degrées
,
and
no
minutes
the
latitude
of
33.
degrées
,
and
20.
minutes
.
The
difference
of
longitude
,
betweene
the
one
and
the
other
,
is
of
3.
degrées
,
and
3.
minutes
.
The
complement
of
the
difference
of
longitude
,
is
of
86.
degrées
,
and
57.
minutes
,
of
the
latitude
of
the
place
not
standing
vnder
the
equatour
,
the
complement
is
56.
degrées
,
and
40.
minutes
.
The
royall
citty
Colipolis
of
Inde
(
aboue
the
riuer
Ganges
)
hath
the
longitude
of
164.
degrées
,
and
20.
minutes
,
but
no
latitude
knowne
.
The
longitude
of
Tyrus
is
of
67.
degrées
,
and
no
minutes
,
the
latitude
hath
33
degrées
,
&
20.
minutes
.
The
difference
of
longitude
greater
then
the
quadrant
,
is
of
97.
degrées
,
and
20.
minutes
.
The
quadrant
being
abated
,
there
remaineth
7.
degrées
,
and
20.
minutes
.
The
complement
of
the
latitude
of
Tyrus
,
is
of
56.
degrées
,
and
40.
minutes
.
If
of
two
places
giuen
,
either
standeth
without
the
Equatoure
toward
some
one
of
the
opposite
quarters
;
and
the
other
vnder
the
equatoure
:
then
is
the
reason
of
the
standing
considered
,
and
the
angle
of
the
difference
of
longitude
.
For
the
one
differeth
either
by
like
spaces
from
each
bound
,
and
is
nearer
to
the
Pole
,
the
other
to
the
Equatoure
.
The
same
appeareth
by
the
compared
latitudes
,
which
like
toppes
of
either
place
containe
the
same
Parallel
,
the
vnlike
being
distant
,
and
the
Parallell
by
a
space
seperated
,
toward
each
place
,
doe
argue
peculiar
and
proper
tops
.
But
the
angle
of
the
difference
of
longitude
,
either
it
is
right
,
blunt
,
or
sharpe
.
This
of
the
placing
and
diuersitie
of
the
angles
,
doeth
much
varie
or
alter
the
reason
&
methode
of
the
searching
of
these
.
If
two
places
giuen
haue
equall
arks
of
the
latitudes
,
and
from
the
middle
or
halfe
of
the
equatoure
bee
alike
distant
,
and
how
much
so
euer
the
angle
of
the
difference
of
longitude
be
,
as
here
vnder
the
difference
of
longitude
is
in
the
first
,
of
the
example
taught
:
yet
are
the
arkes
of
the
latitudes
agréeing
and
equally
founde
,
so
that
in
this
example
appeareth
no
difference
,
but
in
the
only
longitudes
of
the
places
offered
.
As
for
example
.
The
longitude
of
Danske
is
of
39.
degrées
,
and
twoe
scruples
or
minutes
:
the
latitude
of
the
same
hath
54
,
degrées
,
and
48.
minutes
.
The
longitude
of
Lubecke
is
of
28.
degrées
,
and
20.
scruples
,
the
latitude
hath
54.
degrées
,
and
48.
scruples
.
The
difference
of
longitude
consisteth
,
of
10.
degrées
,
and
42.
minutes
.
The
halfe
difference
is
,
of
5.
degrées
,
and
21.
scruples
.
The
distance
on
earth
,
betwéene
Danske
and
Lubecke
,
is
of
92
Germaine
miles
,
and
a
halfe
.
The
great
citie
Alexandria
vnder
the
Turke
(
after
Ptolomie
)
hath
the
longitude
of
122.
degrées
,
the
latitude
of
the
same
,
is
of
41.
degrées
.
That
famous
Toletum
or
Toledo
of
Spaine
,
hath
a
longitude
to
the
same
,
of
10.
degrées
,
the
latitude
of
the
same
is
,
of
41.
degrees
.
The
difference
of
longitude
betwéene
the
one
and
the
other
,
is
of
102.
degrées
.
The
halfe
difference
,
hath
51.
degrées
.
The
complement
of
the
equall
latitudes
of
either
,
is
of
49.
degrées
.
The
whole
distance
betwéen
both
appeareth
to
containe
1077.
Germaine
miles
and
a
halfe
.
If
of
two
places
giuen
,
the
one
bee
further
distant
from
the
equatour
then
the
other
,
and
the
greatnesse
of
the
complements
of
either
latitude
differing
(
as
that
the
arkes
of
the
latitudes
be
vnequall
)
so
that
the
diuersity
of
the
angle
included
with
the
arks
of
the
complements
,
shal
varie
the
methode
or
reason
of
the
search
,
for
that
the
one
giueth
and
formeth
a
right
angle
,
another
a
sharpe
,
another
a
blunt
angle
:
yet
to
these
,
the
angle
of
the
difference
of
longitude
is
right
.
The
example
of
two
places
differing
alike
(
both
in
the
longitude
and
latitude
)
here
appeareth
.
The
citty
Tacola
(
which
at
this
day
is
called
Malchaia
or
Magna
)
a
place
of
much
resort
of
Marchants
.
This
from
the
West
hath
the
longitude
of
160.
degrées
,
and
30.
minutes
,
of
latitude
from
the
equatour
,
it
is
4.
degrées
,
and
15.
scruples
distant
.
The
other
city
and
place
in
the
countrey
of
Pontus
(
named
Trapezus
)
being
a
head
city
of
Cappadocia
and
was
the
auncient
seat
of
the
Emperours
.
This
hath
the
longitude
of
70.
degrées
,
and
30.
minutes
,
and
the
latitude
of
the
same
is
of
43.
degrées
,
and
5.
scruples
.
The
difference
of
longitude
betwéene
the
one
and
the
other
,
is
of
90.
degrées
.
The
arke
of
distance
betwéene
both
places
is
of
87.
degrées
,
and
6.
minutes
:
to
which
1306.
&
a
halfe
Germaine
miles
answere
.
If
the
vnequall
arkes
of
the
latitudes
,
and
angle
of
the
difference
of
longitude
be
lesser
then
the
right
,
it
causeth
a
diuers
reason
of
the
search
,
by
which
the
arke
of
the
complement
of
the
greater
latitude
doth
varie
thrée
waies
,
as
it
is
greater
or
lesser
,
and
as
with
the
arke
by
the
second
in
quisition
surely
knowne
,
and
beeing
ioyned
,
forme
either
more
or
lesse
a
quarter
of
the
cyrcle
.
Or
thus
,
that
the
angle
which
the
vnequall
complements
of
the
vnequall
latitudes
include
,
be
sharpe
;
that
is
,
and
if
the
arks
of
the
latitudes
of
either
place
be
vnequall
,
and
the
difference
of
longitude
bee
lesser
then
the
quadrant
.
As
in
this
example
more
plainer
appeareth
,
of
twoe
places
beeing
of
sundry
longitudes
.
That
worthie
citty
Trapezus
of
Cappadocia
,
whose
longitude
is
of
70.
degrées
,
and
30.
minutes
,
the
latitude
43.
degrées
,
and
5.
minutes
.
The
longitude
of
that
well
knowne
city
of
Rome
,
hath
39.
degrées
,
and
8.
scruples
,
the
latitude
41.
degrées
,
and
8.
minutes
.
The
difference
of
longitude
,
betwéene
the
one
and
the
other
,
is
of
33.
degrées
,
and
22.
minutes
.
Another
example
not
vnlike
the
former
,
and
not
much
varying
from
the
former
:
as
the
longitude
of
Ierusalem
,
which
is
of
66.
degrées
,
and
no
minutes
,
the
latitude
,
of
31.
degrées
,
and
40.
scruples
.
The
longitude
of
Viteberge
,
being
of
30.
degrées
,
and
30.
minutes
,
the
latitude
51.
degrées
,
and
50.
scruples
.
The
difference
betwéene
the
one
and
the
other
of
longitude
is
of
35.
degrées
,
and
50.
scruples
.
If
in
places
vnequally
distant
from
the
equatoure
,
the
angle
of
the
difference
of
longitude
shal
be
blunt
,
by
which
the
difference
of
longitude
shall
appeare
greater
than
the
quadrant
.
Or
thus
,
that
the
angle
of
the
difference
of
longitude
be
blunt
,
séeing
the
places
are
further
distant
then
a
whole
quarter
,
and
thereby
causeth
a
diuers
reason
and
way
of
serch
from
the
former
;
which
semblably
the
diuers
quantity
of
the
complement
of
the
greater
latitude
doeth
thrée
manner
of
waies
varie
,
as
in
the
same
arke
(
which
perfectly
knowne
by
the
second
)
is
either
greater
or
lesser
.
The
example
of
this
appeareth
of
these
two
places
:
the
noble
city
Antiochia
in
Syria
,
which
was
after
caled
Seleucia
,
hath
the
longitude
of
106.
degrées
,
and
no
minutes
,
the
latitude
is
of
40.
degrées
,
and
40.
scruples
,
The
other
of
Toletum
,
whose
longitude
is
of
7.
degrées
,
and
4.
scruples
,
the
latitude
hath
37.
degrées
,
and
50.
minutes
.
The
difference
of
longitude
is
of
98.
degrées
,
and
56.
scruples
,
which
deducted
from
the
halfe
cyrcle
(
or
180.
degrées
)
the
difference
that
remaineth
vnto
the
halfe
cyrcle
,
is
of
81.
degrées
,
and
4.
minutes
.
The
like
example
not
much
varying
from
the
former
of
these
two
places
:
as
the
noble
city
of
Portugale
named
Lysebone
,
whose
longitude
is
of
4.
degrées
,
and
18.
scruples
,
the
latitude
hath
39.
degrées
,
and
38.
scruples
.
The
other
named
Calecute
(
although
the
latitude
differeth
)
hath
the
longitude
of
112.
degrées
,
and
no
minutes
,
the
latitude
is
of
5.
degrées
,
and
no
minutes
.
The
difference
of
longitude
,
containeth
107.
degrées
.
and
42.
scruples
more
then
the
quadrant
.
The
same
deducted
from
the
halfe
cyrcle
,
doth
expresse
the
difference
remaining
vnto
the
halfe
cyrcle
to
bee
of
72.
degrées
,
and
18.
minutes
.
The
complement
of
the
greater
latitude
,
is
of
50.
degrées
,
and
22.
scruples
.
The
complement
of
the
lesser
latitude
,
is
of
85.
degrées
,
and
no
scruples
.
Another
example
of
two
places
distant
from
the
Equatour
,
of
which
the
one
is
distant
from
the
middle
of
the
Equatour
into
the
North
,
and
the
other
into
the
South
,
as
this
example
further
instructeth
;
the
one
beeing
the
Ile
of
Thilen
(
which
in
Ptholomies
●●me
was
the
vttermost
bond
of
the
earth
knowne
,
Northward
)
that
hath
the
longitude
of
33.
degrées
,
the
latitude
Northerly
,
of
63.
degrees
.
The
other
called
the
Ile
of
S.
Thomas
,
hath
the
longitude
of
27
degrées
,
and
20.
minutes
,
the
latitude
Southerly
,
of
16.
degrées
.
The
difference
of
longitude
,
is
of
5●
degrées
,
●nd
40.
minutes
.
The
complement
of
the
latitude
Northerly
,
is
of
26.
degrées
.
A
third
example
of
the
difference
of
other
two
places
,
as
Bas●a
of
Taprobane
,
which
Ptholomie
affirmeth
to
bee
in
longitude
126.
degrées
,
and
in
latitude
toward
the
South
6.
degrées
,
and
30.
scruples
.
The
other
named
Stocholma
,
in
the
Realme
of
Suecia
,
hath
the
longitude
of
42.
degrées
,
and
38.
scruples
,
and
the
latitude
of
60.
degrées
,
&
30.
scruples
.
The
complement
of
the
latitude
Boreal
,
is
29.
degrées
,
and
30.
minutes
.
The
common
way
of
measuring
of
places
,
with
their
spaces
,
by
the
rules
of
longitudes
and
latitudes
.
HEre
before
I
haue
somewhat
written
of
sundry
habitable
places
on
the
earth
,
whose
sundry
points
differ
betwéene
the
one
and
the
other
;
either
in
the
onely
longitude
,
or
in
the
onely
latitude
,
or
in
the
longitude
and
latitude
both
together
.
Those
places
which
do
differ
in
the
onely
longitude
,
be
distant
by
equal
spaces
from
the
equatoure
,
toward
either
of
the
Poles
of
the
worlde
:
the
verticiall
pointes
of
those
places
ended
by
the
same
Parallell
ioyning
next
the
same
space
betwéene
:
yet
each
haue
their
owne
proper
meridians
,
being
not
distant
by
a
like
space
from
the
Westerly
bounde
.
The
distance
of
these
is
alwaies
gathered
and
noted
in
the
same
Parallel
,
which
commonly
belongeth
to
either
place
standing
or
hanging
right
ouer
the
tops
of
them
.
Those
places
which
doe
differ
in
the
onely
latitude
,
are
standing
●●der
the
same
meridiane
,
but
they
haue
diuers
Parallels
▪
●●d
each
proper
;
and
those
continually
distant
vnequally
,
either
towarde
one
pole
from
the
middle
of
the
Equatour
(
if
either
place
declineth
vnto
one
and
the
same
quarter
)
or
otherwise
from
the
middle
of
the
equatoure
seuered
and
distant
into
the
contrary
quarters
,
by
equall
or
vnequall
spaces
.
If
that
one
of
the
places
looke
into
the
South
,
and
the
other
into
the
North
,
the
distance
of
these
is
alwaies
accompted
in
the
common
meridian
.
Those
places
which
do
differ
both
in
the
longitude
and
latitude
togither
,
or
both
decline
towarde
one
Pole
of
the
world
,
or
seperated
and
distant
from
the
midst
of
the
equatoure
towarde
the
opposite
Poles
(
as
the
one
looking
into
the
North
,
and
the
other
into
the
south
)
or
els
by
equal
Parallels
distant
from
the
equatour
;
of
which
two
onely
are
in
the
Sphere
.
If
they
bee
reduced
and
applied
vnto
one
great
cyrcle
(
per
3.
secundi
Theodosij
)
or
els
bee
vnder
by
vnequall
Parallels
,
and
by
an
vnequall
space
.
The
difference
of
the
longitude
of
those
(
which
either
bee
towarde
them
,
or
toward
the
Poles
equally
distant
)
is
alway
gathered
in
the
middle
Parallell
betwéen
either
of
the
bonds
by
arithmeticall
proportion
,
as
afore
taught
.
But
in
those
places
which
haue
equall
Parallels
,
and
equally
dastant
vnto
the
opposite
quarters
,
the
difference
of
longitude
is
imagined
&
noted
in
eith●●
of
the
equall
Parallels
.
Therefore
the
arke
hath
the
distance
of
the
places
standing
,
by
the
next
space
drawne
ouerthwart
by
the
pointes
of
those
places
,
which
with
the
arks
of
the
difference
of
either
(
both
of
the
longitude
and
latitude
)
doth
forme
and
make
a
sphericall
tryangle
right
cornered
,
alwaies
in
the
vpper
face
of
the
Globe
.
If
that
two
meridianes
méete
and
ende
at
the
poles
of
the
worlde
,
and
beeing
cut
by
the
ouerthwart
cyrcumferences
of
the
Parallels
,
doe
make
with
the
included
arkes
of
them
right
cornered
tryangles
,
through
the
foure
right
lesser
angles
:
but
the
angles
beeing
not
right
,
the
arke
of
the
distance
of
the
places
doth
deuide
them
into
two
right
cornered
tryangles
.
One
of
those
tryangles
is
vsed
in
the
common
accompt
for
the
right
cornered
;
because
in
places
not
farre
distant
from
the
equatoure
,
the
angles
contained
betwéene
the
mutuall
sections
of
the
meridians
and
Parallelles
,
doe
not
so
much
varie
from
the
right
angles
:
but
in
places
far
distant
from
the
equatour
,
they
varie
very
much
.
Now
the
rules
for
the
diuers
standing
of
places
shall
be
taught
in
an
easie
and
common
maner
.
If
places
doe
differ
in
the
onely
longitude
.
TO
the
searching
and
knowing
of
this
,
like
as
in
the
former
,
are
the
longitudes
and
latitudes
of
places
giuen
required
;
by
which
they
being
founde
(
séeing
in
the
latitude
there
is
no
diuersity
)
the
difference
of
longitude
is
onely
to
be
considered
,
by
deducting
the
lesser
longitude
out
of
the
greater
,
and
then
howemany
miles
by
proportion
of
the
Parallell
,
vnder
which
the
places
stand
or
lie
to
the
equatoure
,
answere
to
one
degrée
of
the
same
.
The
same
doth
that
rule
(
set
forth
in
the
fourme
of
a
table
here
following
)
declare
,
beeing
drawne
and
made
vnto
this
vse
by
the
learned
;
in
which
,
the
miles
that
answere
to
one
degrée
of
each
Parallell
,
are
there
founde
and
noted
vnto
one
degrée
of
the
distance
of
the
Parallell
from
the
equatour
.
If
to
the
whole
degrées
of
the
distance
of
the
Parallels
doe
minutes
depend
,
then
from
the
difference
of
the
two
next
numbers
to
one
degrée
,
may
the
proportionall
part
be
deducted
or
drawne
:
which
from
the
number
of
the
miles
expressed
vnto
a
whole
degrée
is
abated
,
that
the
Parallels
succéeding
,
may
be
litle
&
litle
be
caused
to
streach
&
appeare
narower
.
To
be
briefe
,
the
miles
with
the
scruples
or
quarters
(
if
any
bee
adioyned
)
let
them
bee
reduced
into
the
whole
arke
of
the
difference
of
longitude
,
which
then
shall
manifestly
shewe
and
expresse
,
the
measured
space
by
the
Germaine
miles
.
Ptholomie
when
he
had
learned
the
longitudes
and
latitudes
of
certaine
notable
places
,
he
could
extract
and
gather
by
them
the
other
vnknowne
places
,
by
the
distances
truly
learned
from
trauailers
.
For
by
the
longitudes
and
latitudes
knowne
of
two
cyrcles
,
and
the
distance
also
of
them
from
any
third
place
,
there
is
then
offered
and
giuen
to
know
,
as
well
the
longitude
,
as
the
latitude
of
the
third
place
.
Further
,
in
any
two
places
lying
and
being
in
the
vpper
face
of
the
earth
,
are
fiue
notes
commonly
learned
.
The
distance
of
them
,
conuerted
into
degrées
:
the
latitude
of
the
one
,
and
the
latitude
of
the
other
:
the
difference
of
longitudes
:
the
angle
vnder
the
circumferencial
distance
:
and
the
meridians
contained
by
the
other
.
Of
the
which
fiue
,
if
thrée
onely
be
knowne
,
it
is
certaine
that
the
other
two
may
easily
come
to
knowledge
by
the
practise
and
skil
of
the
sphericall
tryangles
.
An
example
of
these
former
words
(
as
touching
the
difference
of
longitude
of
two
places
)
the
latitudes
beeing
alike
.
As
the
city
Byzantium
nowe
called
Constantinople
,
whose
longitude
is
55.
degrées
,
and
no
minutes
,
the
latitude
hath
43.
degrées
,
and
5.
minutes
.
The
other
city
Trapezus
hath
the
longitude
of
70.
degrées
,
and
50.
minutes
,
the
latitude
of
43.
degrées
,
and
5.
minutes
.
The
difference
of
longitude
is
of
15.
degrées
,
and
50.
minutes
to
one
degrée
of
the
common
Parallell
,
and
to
each
place
,
doe
10.
Germaine
miles
with
29/30.
answere
or
agrée
.
These
now
brought
into
the
difference
of
longitude
,
doe
cause
&
make
174.
Germaine
miles
almost
.
The
like
example
to
the
former
,
is
Arbela
of
Assiria
,
which
hath
the
longitude
of
80
and
no
minutes
,
the
latitude
of
37.
and
15.
minutes
.
The
other
Athens
,
whose
longitude
is
of
52.
degrées
,
and
15.
minutes
,
the
latitude
37.
degrées
,
and
15.
minutes
.
The
difference
is
of
27.
degrées
,
and
45.
minutes
.
Other
briefe
examples
.
|
Lon.
|
Lati.
|
Areca
in
Comagena
being
a
part
of
Syria
.
|
70.
10.
|
37.
15.
|
Megara
the
country
of
Euclide
.
|
52.
0.
|
37.
15.
|
The
difference
is
of
18.
10.
|
Lon.
|
Lat.
|
Philippi
a
city
in
Thracia
or
country
of
Alexandria
.
|
50.
45.
|
41.
50.
|
The
royall
city
of
Roome
.
|
36.
20.
|
41.
50.
|
The
difference
is
of
14.
25.
longitude
.
Lipsia
,
|
29.
58.
|
51.
24.
|
The
difference
of
long
.
is
9.
degr.
&
42.
min.
The
difference
of
long
.
is
6.
degrées
,
&
4.
min.
|
Antwarpe
,
|
20.
16.
|
51.
28.
|
Vratislauia
,
|
34.
34
|
51.
10.
|
Erphordia
,
|
28.
30.
|
51.
10.
|
If
places
doe
differ
in
the
onely
latitude
,
or
that
both
be
placed
toward
one
pole
,
or
either
distant
from
the
middle
of
the
equatour
,
so
that
in
the
onele
latitude
the
places
differ
,
when
the
longitudes
be
like
,
the
standing
of
the
places
is
to
bee
considered
towarde
either
Pole
,
whether
either
place
declineth
toward
one
Pole
,
or
that
the
one
be
Southerly
,
and
the
other
Northerly
.
If
they
decline
vnto
one
place
and
quarter
,
then
deduct
the
lesser
latitude
,
out
of
the
more
,
and
the
difference
of
latitude
shall
appeare
.
If
eyther
be
distant
from
the
middle
of
the
equatoure
,
the
latitudes
ioyned
doe
shew
the
difference
.
The
degrées
,
of
the
difference
wrought
by
15.
and
the
scruples
deuided
by
4.
shall
offer
&
giue
the
estimate
distance
in
Germaine
miles
.
As
in
this
example
,
the
city
of
Noriberge
hath
28.
degrées
,
and
20.
minutes
of
longitude
,
the
latitude
is
of
49.
degrées
,
and
24.
minutes
.
The
other
is
Mylayne
,
whose
longitude
is
of
28.
degrées
,
and
20.
minutes
,
the
latitude
hath
45.
degrées
,
and
6.
minutes
.
The
difference
of
latitude
,
is
of
4.
degrées
,
and
18.
minutes
:
the
space
betwéene
,
is
64.
miles
and
a
halfe
.
Like
examples
are
these
.
Trapezus
,
|
70.
15.
|
43.
5.
|
The
difference
of
latit
.
is
5.
degrees
,
&
45.
min.
The
difference
of
latit
.
is
6.
degrées
,
&
44.
min.
|
Antioch
,
|
70.
15.
|
37.
20.
|
Padua
,
|
31.
50.
|
51.
0.
|
Budissina
,
|
31.
50.
|
44.
16.
|
If
two
differ
together
in
the
longitude
and
latitude
,
and
that
either
declineth
towarde
one
Pole
,
then
in
either
toward
the
places
differing
,
as
in
the
longitude
and
latitude
are
the
differences
of
the
spaces
from
either
bounde
of
the
latitude
and
longitude
gathered
.
The
halfe
difference
of
the
latitude
added
to
the
lesser
altitude
shall
shew
the
Parallell
in
which
the
difference
of
longitude
is
accompted
.
With
that
Parallell
by
this
rule
are
the
miles
gathered
and
knowne
,
which
answere
or
agrée
to
one
degrée
.
These
founde
,
reduce
into
the
whole
difference
of
the
longitude
,
and
that
which
procéedeth
(
agréeably
)
of
the
same
;
that
is
,
multiplied
in
it selfe
or
arising
of
the
multiplication
kéepe
.
After
the
degrées
of
the
difference
of
longitude
reduce
into
15.
and
the
minutes
annexed
(
if
any
such
be
)
distribute
or
deuide
by
foure
,
that
which
ariseth
of
either
working
,
reduce
ioyntly
one
to
the
other
,
and
adde
to
the
number
kept
afore
.
For
of
the
whole
gathered
may
the
square
roote
be
attained
,
which
sheweth
the
distaunce
of
places
.
As
by
a
like
example
,
the
city
of
Witeberge
hath
the
longitude
of
30.
degrees
,
and
30.
minutes
:
the
latitude
of
51.
degrées
,
and
50.
minutes
.
The
other
being
Ierusalem
hath
66.
degrées
of
longitude
,
and
no
minutes
:
the
latitude
is
of
31.
degrées
,
and
55.
minutes
.
The
difference
of
longitude
is
of
35.
degrées
,
and
30.
minutes
:
the
difference
of
latitude
is
of
19.
degrées
,
and
55.
minutes
.
The
middle
Parallel
in
which
the
difference
of
longitude
is
accompted
,
doth
differ
or
is
distant
from
the
equatour
41
degrées
,
and
52.
minutes
:
to
one
degrée
of
the
same
doe
11.
miles
,
and
10.
scruples
of
a
Germaine
mile
answere
,
which
reduced
into
the
difference
of
longitude
,
doe
procreate
or
bring
foorth
396.
Germaine
miles
:
these
wrought
together
make
156816.
The
degrées
of
the
difference
of
latitude
beeing
wrought
by
15.
&
the
scruples
deuided
by
foure
,
doe
make
266.
Germaine
miles
;
which
multiplied
one
in
the
other
,
do
performe
and
make
89401.
Either
of
these
square
numbers
ioyned
,
and
the
roote
extracted
,
the
distance
shall
appeare
to
be
4●5
.
miles
.
The
finding
of
the
distances
of
places
or
citties
,
in
a
more
easier
maner
.
THat
you
may
knowe
howe
by
the
longitudes
and
latitudes
of
twoe
places
or
citties
,
the
distaunce
of
them
may
be
found
:
thus
do
,
when
two
cities
be
offered
(
whose
largenesse
is
to
you
vnknowne
)
sée●
the
longitude
and
latitude
of
both
by
the
Cosmographie
of
Apian
,
or
Pto
lomies
Geography
;
which
being
found
,
write
downe
the
longitude
of
the
one
vnder
the
longitude
of
the
other
,
and
the
latitude
of
the
one
vnder
the
latitude
of
the
other
(
as
the
former
examples
shew
)
in
such
sort
,
that
the
degrées
of
the
other
,
and
likwise
the
minutes
vnder
the
minutes
.
After
séeke
the
difference
as
well
of
the
longitudes
and
latitudes
,
in
this
maner
:
subtract
the
lesser
longitude
from
the
greater
,
the
remainer
is
called
the
difference
of
the
longitudes
.
After
deduct
the
lesser
latitude
out
of
the
more
,
and
the
difference
of
the
latitudes
shall
remaine
.
By
the
differences
of
the
longitudes
and
latitudes
,
shall
the
distance
of
cities
giuen
be
gathered
.
But
in
that
there
is
thrée
maner
difference
of
places
,
as
that
there
be
certaine
places
which
differ
in
the
onely
latitude
;
that
is
,
vnder
one
meridiane
,
and
yet
lie
vnder
diuers
Parallels
:
and
certaine
that
differ
in
the
onely
longitude
;
that
is
,
vnder
one
Parallell
:
yet
are
diuers
meridians
:
and
certaine
that
do
differ
both
in
the
longitude
and
latitude
;
that
is
,
they
lie
vnder
diuers
meridians
,
and
Parallels
,
thrée
rules
also
of
the
searching
of
distances
,
betwéene
two
places
,
are
taught
of
the
Geographers
.
The
first
rule
.
WHen
two
cities
hauing
one
longitude
are
offered
(
but
hauing
sundry
latitudes
)
deducte
the
lesser
out
of
the
more
:
the
rest
of
degrées
,
in
that
they
be
the
degrées
of
the
great
cyrcle
,
multiply
by
15.
(
for
that
15.
Germaine
miles
answere
to
one
degrée
of
the
great
cyrcle
)
and
then
shall
you
haue
the
distance
of
the
cities
.
But
if
minutes
depend
to
the
degrées
of
difference
,
them
deuide
them
by
foure
,
the
quotient
adde
to
the
fore
number
of
the
miles
.
For
séeing
one
degrée
or
60.
minutes
do
make
15.
Germaine
miles
;
it
ensueth
,
that
foure
minutes
make
one
Germaine
mile
,
&c.
An
Example
.
MAdeburge
and
Egra
agrée
only
in
longitude
;
that
is
,
they
bee
equally
distant
from
the
West
or
from
the
meridian
,
which
is
drawne
or
stretched
by
the
fortunate
Iles.
For
the
longitude
of
either
towne
is
of
29.
degrées
,
the
latitude
of
Madeburge
is
of
52.
and
20.
minutes
:
the
latitude
of
Egra
is
of
50.
degrées
,
and
5.
minutes
:
therefore
is
Egra
more
Southerly
then
Madeburge
.
The
difference
of
the
latitudes
,
is
2.
degrées
,
&
15.
minutes
;
that
is
,
33.
Germaine
miles
,
stith
a
halfe
&
a
quarter
of
a
Germain
mile
.
Another
.
TThe
longitude
of
Trydent
is
of
30.
degrées
,
and
30.
minutes
.
The
longitude
of
Viteberge
is
asmuch
.
The
latitude
of
Trydent
is
of
45.
degrées
,
&
14.
minutes
.
The
latitude
of
Viteberge
is
of
51.
degrées
,
and
50.
minutes
.
These
now
differ
in
the
onely
latitude
,
which
difference
of
the
latitude
is
of
6.
degrees
,
and
36.
minutes
;
that
is
,
99.
Germaine
miles
.
So
much
is
the
distance
almost
between
Trydent
and
Viteberge
.
Another
.
THe
longitude
of
Thunis
is
of
●6
.
degrées
,
and
50.
minutes
:
the
longitude
of
Salerne
in
a
maner
the
same
.
The
latitude
of
Thunis
is
of
32.
degrées
,
and
30.
minutes
.
The
latitude
of
Salerne
is
of
40.
degrées
,
and
30.
minutes
.
The
difference
of
latitude
is
of
▪
〈◊〉
degrees
,
&
〈◊〉
minutes
,
that
is
,
120.
miles
.
And
somuch
is
the
distance
betwéene
Thunis
and
Salerne
.
Another
.
THe
City
of
Yorke
,
and
the
Towne
of
Barwicke
,
agrée
in
longitude
,
for
the
longitude
of
either
place
,
is
of
17.
degrées
,
and
no
minutes
.
But
they
differ
in
latitude
,
in
that
the
latitude
of
Yorke
is
of
54.
degrées
,
&
no
minutes
,
the
latitude
of
Barwicke
,
is
of
56.
degrées
,
&
50.
minutes
.
The
difference
of
the
latitude
is
of
2.
degrées
,
and
50.
minutes
:
that
is
,
210.
English
miles
.
So
much
in
a
manner
is
the
distaunce
,
betwéene
the
City
of
Yorke
,
and
Barwicke
.
Another
.
THe
City
of
London
and
Northampton
,
in
a
maner
is
of
like
longitude
.
For
the
longitude
of
London
is
of
16.
degrées
,
and
30.
minutes
approued
.
But
they
differ
in
latitude
,
in
that
London
hath
the
latitude
of
51.
degrées
and
34.
minutes
,
the
latitude
of
Northampton
is
of
52.
degrées
,
and
50.
minutes
.
The
difference
of
the
latitude
,
is
of
1.
degrée
,
and
16.
minutes
;
that
is
,
7●
.
English
miles
.
So
much
in
a
maner
is
the
distance
betwéene
London
and
Northampton
.
Another
.
THis
example
differeth
both
in
the
longitude
and
latitude
somewhat
.
For
the
longitude
of
Colchester
,
is
18.
degrées
,
and
30.
minutes
,
the
longitude
of
Oxeforde
hath
15.
degrées
,
and
no
minutes
.
The
difference
of
longitude
betwéene
the
one
and
the
other
,
is
of
3.
degrees
,
38
minutes
,
that
is
,
109.
English
miles
.
The
latitude
of
Colchester
hath
51.
degrees
,
and
59.
minutes
.
The
difference
of
latitude
,
is
no
degrées
,
and
16.
minutes
.
So
that
16.
English
miles
,
is
the
distaunce
betwéene
the
one
and
the
other
,
after
their
standing
Northward
.
Another
.
CYgnea
and
Ratisbone
,
agrée
in
longitude
,
for
either
is
of
29.
degrées
,
and
51.
minutes
:
but
they
differ
in
latitude
,
in
that
the
latitude
of
Cygnea
hath
50.
degrées
,
and
46.
minutes
,
the
latitude
of
Ratisbone
,
of
48.
degrées
,
and
56.
minutes
.
The
difference
of
latitude
betwéene
the
one
and
the
other
,
is
1.
degrée
,
and
50.
minutes
,
which
make
27.
and
a
halfe
Germaine
miles
.
The
second
rule
.
BEfore
the
second
rule
be
here
taught
,
it
behoueth
that
you
know
howe
many
Germaine
miles
aunswere
to
each
degrée
of
the
parallel
(
passing
by
the
Zenith
of
Cities
offered
.
)
Here
conceiue
that
not
as
in
the
former
rule
,
to
euery
degrée
of
each
parallell
,
but
to
each
degrées
onely
of
the
parallell
Cyrcle
,
which
streacheth
and
is
vnder
the
Equinoctiall
,
and
as
principall
of
all
the
parallels
,
deuideth
the
whole
earth
into
twoe
equall
halues
,
to
which
are
15.
Germaine
miles
attributed
,
as
to
a
degrée
of
it
.
Where
the
other
cyrcles
(
as
afore
written
)
be
not
of
the
same
bignesse
,
but
how
much
nearer
they
be
to
the
poles
,
so
much
the
lesser
they
are
:
and
how
furder
of
they
be
from
the
●n●●s
,
so
much
the
greater
they
are
.
Whereof
it
is
manife●e
mile
▪
aswell
the
greater
as
the
lesse
Cyrcle
of
the
parallels
,
●●tes
,
stributed
or
deuided
into
360.
degrées
,
and
that
those
degrées
(
according
to
the
distance
of
those
parallels
from
the
poles
)
be
greater
or
lesser
.
For
the
same
cause
shall
you
here
finde
in
the
table
following
,
how
many
Germaine
miles
answere
in
each
eleuations
,
to
the
degrées
of
the
parallels
.
A
Table
,
containing
the
degrees
of
the
differences
of
each
Paralels
,
from
the
Equator
vnto
the
proper
Pole
,
by
whole
degrees
of
the
Latitudes
conuerted
into
Myles
.
Degrees
.
|
Myles
.
|
Scruples
.
|
Degrees
.
|
Myles
.
|
Scruples
.
|
Degrees
.
|
Myles
.
|
Scruples
.
|
Degrees
.
|
Myles
.
|
Scruples
.
|
Degrees
.
|
Myles
.
|
Scruples
.
|
1
|
14
|
59
|
19
|
14
|
11
|
37
|
11
|
59
|
55
|
8
|
30
|
73
|
4
|
23
|
2
|
14
|
59
|
20
|
14
|
6
|
38
|
11
|
49
|
56
|
8
|
23
|
74
|
4
|
8
|
3
|
14
|
58
|
21
|
14
|
0
|
39
|
11
|
39
|
57
|
8
|
10
|
75
|
3
|
53
|
4
|
14
|
58
|
22
|
13
|
54
|
40
|
11
|
29
|
58
|
7
|
57
|
76
|
3
|
38
|
5
|
14
|
56
|
23
|
13
|
48
|
41
|
11
|
19
|
59
|
7
|
43
|
77
|
3
|
22
|
6
|
14
|
55
|
24
|
13
|
42
|
42
|
11
|
9
|
60
|
7
|
30
|
78
|
3
|
7
|
7
|
14
|
53
|
25
|
13
|
36
|
43
|
10
|
58
|
61
|
7
|
16
|
79
|
2
|
52
|
8
|
14
|
51
|
26
|
13
|
29
|
44
|
10
|
47
|
62
|
7
|
2
|
80
|
2
|
36
|
9
|
14
|
48
|
27
|
13
|
22
|
45
|
10
|
36
|
63
|
6
|
48
|
81
|
2
|
21
|
10
|
14
|
46
|
28
|
13
|
15
|
46
|
10
|
25
|
64
|
6
|
34
|
82
|
2
|
5
|
11
|
14
|
43
|
29
|
13
|
7
|
47
|
10
|
14
|
65
|
6
|
20
|
83
|
1
|
50
|
12
|
14
|
●●
|
●0
|
12
|
59
|
48
|
10
|
2
|
66
|
6
|
6
|
84
|
1
|
34
|
13
|
●●
|
●●
|
31
|
12
|
51
|
40
|
9
|
50
|
67
|
5
|
52
|
85
|
1
|
18
|
14
|
●4
|
33
|
32
|
12
|
43
|
50
|
9
|
38
|
68
|
5
|
37
|
86
|
1
|
3
|
15
|
14
|
29
|
33
|
12
|
35
|
51
|
9
|
26
|
69
|
5
|
23
|
87
|
0
|
47
|
16
|
14
|
25
|
34
|
12
|
26
|
52
|
9
|
●4
|
70
|
5
|
8
|
88
|
0
|
31
|
17
|
14
|
21
|
35
|
12
|
17
|
53
|
9
|
12
|
71
|
4
|
53
|
89
|
0
|
16
|
18
|
14
|
26
|
36
|
12
|
8
|
54
|
8
|
49
|
72
|
4
|
38
|
90
|
0
|
0
|
An
Example
for
the
vse
of
this
Table
.
LVneburgum
and
Stetinum
,
haue
the
eleuation
of
the
Pole
precisely
of
54.
degrées
,
to
knowe
howe
many
Germaine
miles
aunswere
to
one
degree
of
the
Parallell
,
passing
by
the
Zenith
of
either
Citty
,
enter
your
Table
,
and
there
diligently
looking
,
you
shall
finde
by
the
degrée
of
that
latitude
54.
noted
eight
miles
,
and
49.
scruples
of
a
mile
.
For
so
many
miles
in
that
Parallell
answere
to
a
degrée
;
that
is
,
eight
,
a
halfe
,
and
the
third
parte
almost
of
a
Germaine
mile
.
And
this
is
easily
found
,
if
the
eleuation
doth
onely
consist
in
whole
degrées
.
For
in
each
eleuation
are
certaine
miles
,
and
the
scruples
of
a
mile
,
answering
to
each
degrée
assigned
.
But
if
the
place
or
city
haue
minutes
depending
to
the
latitude
as
Viteberge
whose
latitude
is
of
51.
degrées
,
and
50.
minutes
:
then
séeke
in
this
table
how
many
miles
and
scruples
of
a
mile
,
are
atributed
to
the
whole
degrées
,
and
you
shal
finde
by
the
degrée
of
the
latitude
of
51.
noted
9.
miles
and
26.
scruples
of
a
Germaine
mile
.
After
séeke
the
miles
and
minutes
that
nexte
ioyne
to
the
eleuation
following
,
being
52.
and
you
shal
find
right
against
9.
miles
,
and
14.
scruples
of
a
mile
:
which
so
set
down
or
placed
,
that
the
miles
bee
vnder
the
miles
,
and
the
minutes
vnder
the
minutes
,
after
this
maner
.
miles
|
minutes
|
9.
|
26.
|
9.
|
14.
|
Subtract
the
lesser
number
out
of
the
more
and
vpper
written
,
and
there
will
remaine
12.
minutes
,
of
this
rest
;
that
is
,
of
the
12.
minutes
,
séeke
the
number
proportional
,
according
to
the
proportion
of
one
degrée
or
60.
minutes
,
vnto
the
minutes
depending
to
the
latitude
offered
,
as
of
the
latitude
of
Viteberge
to
the
whole
degrées
,
do
50.
scruples
depend
.
Of
which
so
place
the
numbers
by
the
Rule
of
thrée
,
working
and
saying
on
this
wise
,
that
if
one
degrée
or
60.
minutes
of
the
degrée
doe
giue
28.
minutes
of
a
mile
,
how
many
scruples
of
a
Germaine
mile
,
doe
12.
minutes
of
a
degrée
giue
.
To
know
this
,
multiply
the
first
by
the
second
,
that
is
,
12.
by
50.
&
the
increase
shal
be
600.
this
product
diuide
by
the
thirde
number
which
is
60.
and
the
part
proportional
shal
be
10.
This
proportional
part
found
,
substract
out
of
the
miles
,
and
minutes
of
the
former
eleuation
;
that
is
,
from
the
9.
miles
,
and
26.
minutes
:
deduct
the
10.
and
there
will
remaine
9.
miles
,
and
16.
scruples
,
precisely
answering
to
one
degree
of
the
Parallell
passing
by
Viteberge
.
Here
the
second
rule
followeth
,
which
is
easie
to
conceiue
,
if
you
worke
according
to
the
former
taught
.
The
second
Rule
.
IF
two
Citties
be
offered
,
which
differ
in
the
only
longitude
,
first
séeke
by
the
instruction
aboue
taught
,
the
miles
,
and
minutes
of
a
mile
answering
to
one
degrée
of
the
Parallel
,
passing
by
the
Zenith
of
those
Citties
.
After
,
séeke
the
difference
of
longitudes
in
the
degrées
and
minutes
:
then
multiply
the
difference
of
longitudes
,
with
the
miles
and
scruples
of
the
miles
,
and
the
distance
shall
appeare
of
the
Cities
giuen
.
An
Example
.
VIteberge
and
Westphalia
agrée
in
latitude
:
that
is
,
they
be
both
standing
vnder
one
Parallell
.
For
the
latitude
of
Viteberge
is
51.
degrées
,
and
50.
scruples
,
and
excéedeth
the
latitude
of
Westphalia
by
certaine
minutes
,
which
here
we
passe
,
but
they
differ
in
longitude
,
in
that
Westphalia
lies
more
to
the
West
.
The
longitude
of
Vite
berge
is
30.
degrées
,
and
30.
scruples
:
the
longitudes
of
Westphalia
is
24.
deg.
&
no
min.
To
find
the
distance
,
see
how
many
miles
answere
to
one
degrée
of
longitude
in
the
parallel
,
passing
by
the
Zenith
of
the
Citties
giuen
.
Before
was
taught
,
that
in
the
Parallel
of
Viteberge
9.
miles
and
16.
scruples
do
answere
to
one
degree
:
wherefore
seek
the
difference
of
longitudes
of
the
two
Cities
,
and
deduct
the
lesser
number
out
of
the
more
;
that
is
,
let
the
24.
degrées
and
no
minutes
bee
deducted
from
the
30.
degrées
,
&
30.
scruples
,
&
the
difference
resting
,
shall
be
of
6.
degrées
,
and
30.
scruples
.
Last
,
multiply
the
6.
miles
and
16.
scruples
,
with
the
difference
of
longitude
;
that
is
,
with
6.
degrées
,
and
30.
minutes
,
and
you
shall
haue
the
distance
of
the
twoe
Cities
.
But
here
obserue
and
note
diligently
in
the
multiplication
of
the
degrées
,
miles
,
and
minutes
,
what
procéedeth
and
commeth
of
the
same
.
For
the
miles
multiplied
by
the
degrées
,
doe
bring
foorth
the
miles
:
and
the
miles
multiplied
by
the
minutes
of
the
degrées
,
doe
bring
forth
the
scruples
of
the
miles
.
The
minutes
of
the
miles
multiplied
by
the
degrées
,
doe
produce
or
bring
foorth
the
minutes
of
the
miles
.
And
last
,
the
minutes
of
the
miles
multiplied
by
the
minutes
of
the
degrees
,
doe
produce
the
seconds
of
the
miles
.
But
that
this
may
the
readier
be
conceiued
,
vse
this
example
,
the
former
Westphalia
and
Viteberge
:
where
the
9
miles
and
16.
scruples
,
are
to
bee
multiplied
by
the
6.
degrees
,
&
30.
minutes
on
this
wise
.
Multiply
the
9.
whole
miles
,
by
the
6.
whole
degrees
,
thus
:
as
sixe
time
6.
bringeth
out
54.
miles
.
Multiply
after
that
,
the
whole
miles
by
the
minutes
of
the
degrees
;
thus
,
that
9.
times
30.
doe
make
270.
minutes
of
miles
.
After
multiply
the
minutes
of
the
miles
by
the
whole
degrees
,
and
by
the
minutes
of
the
degrees
:
as
the
16.
minutes
of
the
miles
multiplied
by
the
6.
degrees
,
doe
make
99.
minutes
of
miles
.
After
this
the
16.
minutes
of
the
miles
multiplied
by
30.
minutes
of
the
degrees
,
doe
make
480.
secondes
of
miles
;
which
minutes
and
seconds
gather
into
whole
miles
,
in
this
maner
.
First
deuide
the
480.
seconds
by
60.
and
the
quotient
shall
be
8.
minutes
.
(
For
that
one
minute
containeth
60.
seconds
,
as
one
degrée
doth
containe
60.
minutes
.
These
8.
minutes
,
adde
to
the
minutes
procéeded
of
the
former
or
vpper
working
;
that
is
,
the
270.
and
the
96.
&
you
shall
haue
374.
scruples
of
miles
,
which
deuided
by
60.
the
quotient
will
be
6.
whole
miles
,
and
14.
scruples
;
that
is
,
almost
the
fourth
part
of
a
Germaine
mile
.
These
miles
gathered
of
the
seconds
and
minutes
of
the
miles
,
adde
to
the
54.
miles
gathered
afore
by
the
multiplication
of
the
degrées
and
miles
,
and
you
shall
haue
the
true
distaunce
betwéene
Viteberge
and
the
Monasterie
of
Vestphalia
;
that
is
,
60.
Germaine
miles
,
and
almost
a
quarter
.
This
maner
of
working
in
searching
the
distance
of
places
(
which
differ
in
the
onely
longitude
)
obserue
in
the
other
examples
following
:
in
which
you
shal
finde
their
distance
,
by
hauing
their
longitudes
and
latitudes
.
Here
folowing
shall
be
sundrie
examples
,
in
which
the
young
students
and
practisers
may
excercise
them
according
to
rule
.
An
Example
.
COleine
and
Marburge
do
differ
in
the
only
longitude
:
for
the
longitude
of
Coleyne
is
of
23.
degrées
,
and
28.
scruples
,
the
longitude
of
Margburge
hath
25.
degrées
,
and
45.
minutes
.
The
latitude
of
either
(
which
agrée
)
is
of
51.
degrees
,
and
no
minutes
.
The
difference
of
longitudes
is
of
2.
degrées
,
and
17.
minutes
.
The
miles
answering
to
one
degrée
(
drawn
in
that
Parallell
by
the
Zenith
of
the
Cities
giuen
)
are
9.
miles
,
and
26.
scruples
,
as
may
appeare
in
the
former
table
.
But
séeing
no
minutes
depend
to
the
latitude
,
the
9.
miles
,
and
26.
minutes
are
to
bee
multiplied
by
the
difference
of
the
longitudes
:
that
is
,
the
2.
degrées
,
and
17.
minutes
,
in
this
manner
:
saying
twice
9.
doe
make
18.
miles
,
twice
29.
are
52.
minutes
of
miles
,
nine
times
28.
doe
make
152.
minutes
of
miles
,
and
seauentéene
times
26.
are
442.
secondes
of
miles
:
which
secondes
and
minutes
deuided
by
60.
doe
make
thrée
miles
,
32.
minutes
and
22.
seconds
.
These
added
vnto
the
18.
miles
,
declare
the
distance
of
Coleyne
and
Margburge
,
to
bee
of
21.
Germaine
miles
,
and
a
halfe
.
Another
.
THe
longitude
of
Franckeforde
is
of
25.
degrées
,
and
38.
minutes
.
Hasforde
is
of
longitude
37.
degrées
,
and
52.
scruples
.
The
latitude
of
either
,
is
of
50.
degrees
,
and
12.
minutes
.
Nowe
they
differ
in
the
onely
longitude
,
for
that
the
difference
of
the
longitudes
is
,
of
2.
degrées
,
and
14.
scruples
;
that
is
,
Franckeforde
by
twoe
degrées
,
and
14.
minutes
,
is
more
towarde
the
West
,
than
Hasforde
.
The
miles
according
to
latitude
50.
are
9.
and
38.
minutes
,
and
the
miles
according
to
the
latitude
following
,
as
51.
are
9.
and
26.
minutes
.
The
difference
of
these
twoe
manner
of
miles
and
minutes
,
is
12.
minutes
:
the
parte
proportionall
subtracted
,
is
twoe
.
The
miles
answering
to
one
degree
,
in
the
Parallell
drawne
by
the
Zenith
of
Franckeforde
and
Hasphorde
,
are
9.
and
36.
minutes
.
Nowe
as
aboue
these
miles
and
minutes
(
with
the
difference
of
the
longitude
)
that
is
,
twoe
degrées
,
and
fouretéene
minutes
multiplied
,
you
shal
haue
the
distance
in
Germaine
miles
;
that
is
,
twenty
and
two
,
and
almost
a
halfe
.
Another
.
The
longitude
of
Gawnt
(
the
natiue
towne
of
Charles
the
first
Emperour
)
of
19.
degrées
,
and
8.
minutes
.
The
longitude
of
Lipsia
of
29.
degrées
,
and
28.
minutes
.
The
latitude
of
either
is
of
51.
degrées
,
and
24.
minutes
.
The
difference
of
longitudes
is
of
10.
degrées
,
and
50.
minutes
.
The
miles
according
to
the
eleuation
51.
are
9.
and
26
,
minutes
:
the
miles
ensuing
the
eleuation
assigned
,
are
9.
and
14.
minutes
.
The
difference
of
these
two
manner
of
miles
and
minutes
,
is
12
minutes
:
the
part
proportional
subtracted
,
is
4.
minutes
.
The
miles
answering
to
one
degrée
in
the
Parallell
(
to
Gaunt
or
Lipsia
)
are
9.
and
22.
minutes
.
These
miles
and
minutes
multiplied
with
the
difference
of
the
longitudes
,
do
offer
and
shew
the
distance
betwéen
Gawnt
and
Lipsia
;
that
is
,
101.
Germaine
miles
,
and
almost
a
halfe
.
Another
.
THe
longitude
of
Straseborow
is
of
24.
degrées
,
and
30.
minutes
,
the
longitude
of
Landunum
of
Bauier
is
of
30.
degrées
,
and
25.
minutes
.
The
latitude
of
either
is
of
48.
degrées
,
and
45.
minutes
.
The
difference
of
longitude
,
is
5.
degrées
,
and
55.
minutes
,
&c.
Another
.
THe
longitude
of
Direpsa
is
of
130.
degrées
,
and
no
minutes
;
the
longitude
of
Danaba
of
104.
degrées
,
and
no
minutes
neither
.
The
latitude
of
either
is
of
45.
degrées
,
and
no
minutes
.
The
difference
of
longitude
,
is
26.
degrées
,
and
no
minutes
.
An
easier
working
.
IF
this
curi●sity
in
obseruing
minutes
trouble
you
,
you
may
then
with
lesser
paine
and
errour
leaue
them
,
especially
in
places
beeing
not
far
distant
a
sunder
,
where
the
minutes
omitted
doe
litle
force
or
hinder
,
howe
neare
soeuer
you
finde
the
true
distance
.
And
by
this
meanes
the
second
rule
,
is
of
no
difficulty
:
for
that
euery
painefull
labor
doth
especially
consist
in
the
multiplying
of
the
diffeence
of
longitudes
,
with
the
whole
miles
offered
by
the
former
Table
,
acording
to
the
degrée
of
latitude
,
of
the
Cities
giuen
.
An
Example
.
AMsterdame
and
Brandenburge
(
which
as
vnto
whole
degrées
appartaineth
)
agree
in
latitude
:
for
the
latitude
of
either
place
in
whole
degrées
,
is
52.
degrees
.
But
they
differ
in
longitude
,
in
that
the
longitude
of
Amsterdame
is
21.
degrees
,
and
4.
minutes
,
the
longitude
of
Bradenburge
of
30.
degrees
,
and
35.
minutes
.
They
differ
in
longitude
9.
degrees
;
that
is
,
Amsterdame
is
nearer
to
the
West
then
Bradenburge
by
9.
degrees
,
as
the
former
table
teacheth
in
the
Parallell
of
the
latitude
52.
which
containeth
9.
miles
.
Now
by
so
many
miles
is
Bradenburge
distant
from
Amsterdame
.
Another
.
NOrdlinga
and
Nicostadium
,
agree
in
latitude
,
for
the
eleuation
of
the
Pole
,
or
latitude
of
either
is
of
48.
degrees
.
But
they
agree
not
in
longitude
,
in
that
the
longitude
of
Nordlinga
is
of
27.
degrees
,
and
54.
minutes
,
the
longitude
of
Nicostadium
of
29.
degrees
,
&
32.
minutes
:
so
that
they
differ
2.
degrees
,
which
make
20.
Germaine
miles
,
as
may
appeare
by
the
fourmer
table
,
where
10.
miles
are
assigned
to
the
latitude
48.
Now
you
shall
vnderstand
that
the
distance
of
Nordlinga
and
Nicostadium
,
is
of
20.
Germaine
miles
almost
.
Another
.
THe
longitude
of
the
City
of
Venice
is
of
32.
degrées
,
and
30.
minutes
,
the
longitude
,
of
Spoletum
is
of
36.
degrées
,
and
30.
minutes
.
The
latitude
of
either
,
is
of
44.
degrées
.
The
difference
of
the
longitude
is
of
4.
degrées
.
And
10.
miles
doe
answere
to
one
degrée
in
the
Parallel
of
the
latitude
44.
The
miles
being
multiplied
by
the
difference
of
the
longitudes
;
that
is
,
by
foure
degrées
,
doe
declare
the
distaunce
of
Venice
and
Spol●tum
,
to
bee
of
forty
miles
.
If
of
two
places
,
the
one
being
Southerly
,
and
the
other
Northerly
.
IF
of
twoe
places
giuen
,
the
one
hath
a
latitude
Northerly
,
and
the
other
a
latitude
Southerly
:
séek
the
difference
of
either
space
of
the
longitude
;
after
subtract
the
lesser
longitude
out
of
the
greater
(
but
of
the
latitude
Northerly
and
Southerly
)
according
to
the
latitudes
ioyned
of
either
place
.
In
the
second
place
the
standing
must
bee
cosidered
,
whether
they
be
scituated
vnder
equall
Parallelles
,
and
both
distaunt
by
a
like
space
from
the
Equatoure
,
or
else
otherwise
seperated
by
vnequall
Parallelles
,
and
by
an
vnlike
space
.
For
if
the
Paralles
of
the
places
giuen
shall
bee
equall
,
then
must
the
difference
of
longitude
be
accompted
in
either
alike
:
but
if
vnequall
(
and
that
both
shall
bee
distant
by
an
vnlike
space
)
then
the
halfe
of
the
greater
latitude
applied
to
the
lesser
latitude
,
shall
demonstrate
and
shewe
the
Parallell
apte
and
méete
to
this
instruction
:
with
the
same
Parallell
are
the
degrées
answering
to
each
degree
,
declared
by
the
former
rule
,
and
the
other
is
taught
&
shewed
,
as
in
the
precedent
place
is
declared
.
Meroe
a
Region
of
Aethiopia
vnder
Aegypt
,
hath
the
longitude
of
91.
degrées
,
and
30.
minutes
,
the
latitude
of
16.
degrées
Northerly
.
The
I
le
of
S.
Thomas
in
the
bordure
of
Aphrica
hath
the
longitude
of
27.
degrées
,
and
20.
minutes
,
the
latitude
Southerly
is
16.
degrées
.
The
difference
of
longitude
is
34.
degrées
,
and
10.
scruples
.
The
difference
of
latitude
which
the
conioyned
latitudes
do
make
)
is
of
32.
degrées
.
And
séeing
both
by
an
equall
space
bee
distant
toward
the
opposite
poles
from
the
equatour
,
it
therefore
forceth
not
,
that
the
difference
of
longitude
bee
gathered
in
either
Parallell
Northerly
or
Southerly
,
in
that
they
be
equall
.
For
to
one
degrée
of
the
Parallell
(
which
is
of
16.
degrées
,
distant
from
the
equatour
)
doe
14.
miles
,
and
25.
scruples
,
answere
or
agrée
:
which
reduced
into
the
difference
of
longitude
,
doe
bring
forth
492.
Germaine
miles
;
which
multiplied
togither
,
doe
bring
forth
241064.
The
difference
of
latitude
wrought
or
multiplied
by
15.
doe
bring
foorth
480.
Germaine
miles
,
which
againe
wrought
togither
do
cause
230400.
And
by
either
quadrant
conioyned
,
the
square
roote
drawne
out
of
the
same
,
doth
then
declare
and
shew
the
distance
to
be
of
686.
Germaine
miles
.
The
I
le
of
Thylen
hath
the
longitude
of
33.
degrées
,
the
latitude
is
.
of
63.
degrées
Northerly
.
The
I
le
of
S.
Thomas
hath
the
longitude
of
27.
degrées
,
and
20.
scruples
,
,
the
latitude
Southerly
,
of
16.
degrées
.
The
difference
of
longitude
,
hath
5.
degrées
,
and
40.
scruples
,
the
difference
of
latitude
,
is
of
79.
degrées
.
The
halfe
difference
of
the
greater
latitude
,
applied
to
the
Southerly
latitude
,
bringeth
foorth
that
the
Parallell
is
distaunt
from
the
equatoure
47.
degrées
,
and
30.
scruples
:
in
which
the
difference
of
longitude
,
must
be
accompted
.
And
to
one
degrée
of
it
in
the
rule
,
doe
10.
Germaine
miles
,
and
7.
scruples
answere
;
which
wrought
into
the
difference
of
longitude
,
do
bring
forth
57.
Germain
miles
almost
.
Those
multiplied
,
doe
make
the
increase
to
be
3239.
By
the
difference
also
of
the
latitude
,
those
multiplied
,
doe
bring
forth
1404225.
Of
the
quadrants
ioyned
,
the
roote
hath
1189.
Germaine
miles
almost
;
that
is
,
the
distances
sought
of
the
places
.
That
the
studious
and
diligent
practioners
may
easter
perceiue
and
perfecter
vnderstand
these
differences
of
the
standing
of
places
,
let
them
often
accustome
themselues
therein
,
that
when
the
longitudes
and
latitudes
of
sundry
places
be
offered
,
they
then
consider
whether
they
differ
in
the
onely
longitude
,
or
latitude
only
,
or
in
both
,
and
what
the
latitude
is
of
either
,
and
into
which
parte
from
the
Equatour
:
and
besides
that
,
they
learne
to
expresse
the
standing
of
them
by
proper
lines
drawne
,
and
the
places
noted
.
If
the
numbers
of
the
latitudes
be
alike
,
and
the
numbers
of
the
longitudes
be
vnlike
,
then
doe
the
places
onely
differ
in
the
longitude
.
Therfore
by
two
meridians
found
and
defined
,
lying
crosse
to
them
in
one
Parallel
,
imagine
and
set
the
place
of
the
greater
longitude
in
the
pointe
of
the
crossing
further
off
,
that
the
other
in
the
nearer
may
be
placed
vnto
the
West
.
For
the
place
alwaies
(
whose
longitude
is
lesser
then
the
other
)
is
nearer
founde
to
the
West
,
and
the
other
is
further
distant
into
the
East
.
The
arke
also
of
the
Parallell
included
betwéene
either
meridian
,
doth
demonstrate
the
difference
of
longitude
.
If
the
numbers
of
the
longitudes
shall
be
alike
,
and
the
numbers
of
the
latitudes
vnlike
,
then
is
the
diuersity
of
the
places
in
the
onely
latitude
.
Therefore
two
Parallels
drawn
crosse
,
of
which
the
one
being
higher
and
the
other
lower
and
crossing
them
by
one
meridian
,
they
doe
set
the
place
of
the
greater
latitude
in
the
vppermost
point
of
the
crossing
,
and
the
other
in
the
lowest
point
.
If
the
latitudes
be
alike
,
as
the
one
Southerly
,
and
the
other
Northerly
:
then
the
middle
arcke
of
the
Merydian
being
betwéene
,
is
equally
crossed
by
the
Parallels
of
the
places
drawne
thwartly
by
the
Arke
of
the
Equatour
,
in
such
sort
,
that
the
Equatour
is
by
an
equall
space
distant
from
either
.
If
both
the
numbers
of
the
longitudes
and
latitudes
shall
be
vnequall
,
and
either
place
distant
into
the
North
from
the
Equatour
,
therefore
in
both
is
there
a
diuersity
.
Therefore
two
Meridians
being
imagined
,
the
one
Orientall
dextre
,
and
the
other
Occidentall
synistre
,
and
that
by
so
marry
Parallels
drawne
thwartly
,
which
crosse
the
Meridians
,
the
one
Southerly
,
the
other
Northerly
:
and
that
the
place
whose
greater
longitude
is
touched
in
the
lowest
and
furthest
point
,
and
the
other
to
be
noted
right
against
;
that
is
,
in
the
vpper
and
neerest
point
.
Or
thus
contrariwise
:
If
one
place
shall
exceed
the
other
,
both
in
longitude
and
latitude
,
and
be
further
standing
in
the
higher
pointe
of
the
crossing
,
and
thereby
more
farther
distant
,
and
the
other
noted
to
stand
right
against
,
and
the
seates
also
of
the
places
vnequally
touch
,
which
declareth
and
containeth
the
nighest
distance
of
such
places
.
In
the
same
maner
is
the
standing
of
places
descending
vnto
diuers
partes
from
the
Equatour
expressed
;
being
obserued
in
such
order
,
that
if
the
places
of
either
be
alike
distaunte
from
the
Equatour
,
the
Equatour
then
is
exquisitly
standing
in
the
middle
of
both
:
but
if
the
places
happen
to
bée
vnequall
,
then
is
the
Equatour
by
an
vnequall
distance
,
placed
farther
off
.
A
third
rule
.
IF
twoe
Citties
offered
doe
differ
both
in
the
longitude
and
latitude
,
séeke
first
the
difference
aswell
of
the
longitude
,
as
latitude
.
After
halfe
of
the
difference
of
latitudes
adde
vnto
the
lesser
latitude
,
and
with
the
produce
enter
the
table
which
in
the
former
examples
hath
bene
taught
and
practised
:
searching
there
the
miles
and
minutes
aunswering
properly
to
one
degrée
.
The
miles
and
minutes
found
,
multiply
with
the
degrées
of
the
difference
of
longitude
,
and
the
produce
multiply
in
it selfe
,
and
you
shall
obtaine
and
haue
the
first
quadrate
.
Thirdly
,
multiply
the
difference
of
latitude
by
the
15.
Germaine
miles
,
and
this
produce
also
multiply
in
it selfe
,
and
you
shall
haue
the
second
quadrate
.
Last
,
ioyne
or
adde
togither
these
tw●●
quadrate
numbers
(
and
of
that
produced
or
encreased
)
search
out
the
quadrate
roote
.
The
quadrate
or
square
root●
,
is
the
distance
of
Cities
offered
.
An
Example
of
the
third
rule
.
Wischegarda
and
Verona
,
do
differ
both
in
the
longitude
and
latitude
,
in
that
the
longitude
of
Vuischegarda
is
of
41.
degrées
,
and
17.
minutes
,
the
latitude
is
of
52.
degrées
,
and
4.
minutes
.
The
longitude
of
Verona
hath
31.
degrées
,
&
18.
minutes
,
the
latitude
is
of
44.
degrées
,
and
49.
minutes
.
The
difference
of
the
longitudes
is
of
9.
degrées
and
59.
minutes
.
The
difference
of
the
latitudes
is
of
7.
degrées
and
15.
minutes
.
The
halfe
of
the
difference
of
the
latitudes
,
is
3.
degrées
,
&
37.
minutes
,
which
halfe
added
to
the
lesser
latitude
;
that
is
,
to
Verona
,
which
is
of
44.
degrées
,
add
49.
minutes
,
doeth
then
produce
or
bring
forth
48.
degrées
,
&
26.
minutes
.
This
produce
or
increase
is
named
the
middle
latitude
,
in
that
it
is
distant
by
equal
degrées
and
minutes
from
either
latitude
of
Vuischegarda
and
Verona
;
that
is
,
it
excéedeth
the
latitude
of
Verona
by
3.
degrées
,
and
37.
minutes
,
and
Verona
doeth
excéede
Vuischegarda
by
so
many
degrées
,
and
minutes
.
With
this
product
or
middle
latitude
;
that
is
,
with
48.
degrées
,
&
26.
minutes
.
I
enter
the
former
table
,
and
according
to
the
instruction
afore
taught
in
the
second
rule
,
I
finde
in
the
parallell
which
is
drawne
by
the
middle
latitude
,
to
answer
to
one
degrée
right
against
10.
Germain
wiles
,
and
2.
minutes
.
It
was
also
taught
in
the
second
rule
,
that
if
minutes
depended
to
the
latitude
,
that
those
should
be
sought
in
the
former
table
,
and
by
the
next
eleuation
folowing
,
the
proportionall
part
to
be
sought
.
As
in
this
example
.
The
latitude
52.
are
9.
miles
,
and
14.
scruples
noted
,
and
in
that
3.
degrées
,
and
37.
scruples
depende
to
a
middle
latitude
,
I
séeke
in
the
table
how
many
miles
and
scruples
are
noted
next
to
the
latitude
folowing
,
55.
and
there
I
finde
8.
miles
,
and
36.
scruples
.
The
difference
betwéen
the
miles
and
scruples
of
the
eleuations
of
52.
and
55.
is
1.
degrée
,
&
22.
minutes
.
By
the
proportion
of
this
difference
,
is
the
proportionall
part
gathered
and
founde
,
according
to
the
maner
afore
taught
in
the
second
rule
.
Another
example
of
this
third
rule
for
thy
further
instructing
of
Viteberge
and
Lipsia
,
which
differ
in
the
longitude
and
latitude
:
for
the
longitude
of
Viteberge
is
of
30.
degrées
,
and
30.
minutes
,
the
latitude
hath
51.
degrees
,
and
50.
minutes
.
The
longitude
of
Lipsia
is
of
29.
degrées
,
and
58.
minutes
,
the
latitude
hath
51.
degrées
,
and
24.
minutes
.
The
difference
of
the
longitudes
is
of
thirty
twoe
minutes
,
the
difference
of
the
latitudes
is
of
twenty
sixe
minutes
.
The
halfe
of
the
difference
of
the
latitudes
is
of
thirtéene
minutes
,
which
halfe
added
to
the
lesser
latitude
(
as
to
Lipsia
)
which
is
of
51.
degrées
,
and
24.
minutes
,
doth
produce
●1.
degrees
,
and
37.
minutes
.
The
product
is
caled
the
middle
latitude
,
in
that
by
equal
minuts
it
is
distant
from
either
latitude
of
Viteberge
and
Lipsia
;
that
is
,
it
excéedeth
the
latitude
of
Lipsia
,
13.
minutes
,
and
by
so
many
minuts
is
it
excéeded
of
Viteberge
.
With
this
product
or
middle
latitude
;
that
is
51.
degrées
and
37.
minutes
,
I
enter
the
former
Table
,
and
by
the
Instruction
afore
vttered
in
the
second
rule
,
I
find
in
the
Parallel
which
is
drawne
by
the
middle
latitude
,
that
9.
miles
,
and
19.
scruples
doe
answere
there
to
one
degrée
.
And
in
the
second
rule
afore
is
taught
,
that
if
minutes
depende
to
the
latitude
,
which
is
sought
in
the
former
Lable
,
then
by
the
next
eleuation
must
the
part
proportional
be
sought
.
As
in
this
example
to
the
latitude
,
51.
degrées
,
are
9.
miles
and
26.
scruples
noted
.
And
in
that
37.
minutes
depend
to
the
middle
latitude
,
I
therefore
séeke
in
the
table
how
many
miles
and
scruples
are
assigned
to
the
latitude
next
following
;
that
is
,
52.
degrées
:
right
against
which
I
finde
noted
9.
miles
,
and
14.
scruples
.
The
difference
betwéene
the
miles
and
scruples
of
the
eleuations
of
51.
and
52.
is
of
12.
minutes
:
so
that
by
the
proportion
of
this
difference
vnto
the
whole
degrée
,
or
60.
minutes
,
is
the
proportionall
parte
drawne
or
gathered
,
according
to
the
manner
afore
taught
in
the
second
rule
.
As
thus
,
that
as
69.
minutes
yeelde
12
,
euen
so
doe
37.
giue
7.
minutes
,
which
is
the
parte
proportionall
.
The
same
minutes
subtracted
from
the
miles
and
scruples
assigned
to
the
latitude
51.
that
is
,
from
the
9.
miles
,
and
26.
scruples
,
there
remaine
9.
miles
,
and
19.
scruples
.
And
so
many
miles
and
scruples
in
the
Parallel
of
the
middle
latitude
doth
answere
vnto
one
degree
.
Which
being
founde
and
knowne
,
these
nine
miles
and
the
scruples
,
with
the
differences
of
longitude
,
which
is
of
thirty
two
minutes
,
I
then
multiply
,
and
they
shew
and
bring
forth
298.
minutes
:
which
multiplied
againe
in
it selfe
,
do
bring
forth
the
first
quadrate
to
be
88804.
minutes
.
And
this
is
the
first
parte
of
the
working
of
these
.
Nowe
followeth
the
other
part
.
I
multiply
first
the
difference
of
latitude
,
as
the
26.
minutes
by
15.
Germaine
miles
,
and
they
bring
forth
390.
minutes
,
which
multiplied
againe
in
it selfe
doe
yéelde
151200.
minutes
,
as
the
second
quadrant
is
.
Now
these
two
numbers
quadrate
added
,
doe
bring
forth
and
make
240904.
minutes
,
of
which
the
quadrate
or
square
roote
is
of
494.
minutes
of
miles
.
These
for
that
they
are
the
minutes
of
miles
,
ought
to
be
deuided
by
60.
and
then
they
bring
foorth
8.
whole
miles
,
and
14.
scruples
;
that
is
,
a
fourth
part
almost
of
a
Germaiue
mile
.
So
that
somuch
is
the
distance
,
betwéene
Viteberge
and
Lipsia
.
Another
.
THe
longitude
of
Buda
is
of
37.
degrées
,
and
44.
minutes
,
the
latitude
hath
47.
degrées
,
and
no
minutes
.
The
longitude
of
Aquisgranum
is
of
22.
degrées
,
and
24.
minutes
,
the
latitude
hath
51.
degrées
,
and
6.
minutes
.
The
difference
of
the
longitudes
,
is
of
15.
degrées
,
and
20.
minutes
.
The
difference
of
the
latitudes
is
of
4.
degrées
,
and
6.
minutes
.
The
halfe
of
the
difference
of
the
latitudes
,
is
of
2.
degrées
,
and
3.
minutes
.
The
middle
latitude
is
of
the
degrées
,
and
thrée
minutes
:
here
(
in
that
3.
minutes
doe
onely
depend
to
the
middle
latitude
)
are
omitted
,
séeing
the
leauing
of
them
bring
or
cause
small
error
.
Then
must
you
take
the
miles
assigned
to
the
latitude
49.
that
are
9.
miles
,
and
50.
scruples
,
which
with
the
difference
of
the
longitude
;
that
is
,
15.
degrees
,
and
20.
minutes
are
to
be
multiplied
,
and
they
shall
bring
forth
150.
miles
,
and
46.
scruples
:
which
miles
containe
as
a
quadrate
;
that
is
,
one
parte
in
it selfe
with
the
minutes
,
that
may
bee
multiplied
and
resolued
also
into
minutes
in
the
multiplication
by
60.
it
shall
then
bring
foorth
9000.
minutes
▪
to
these
adde
the
46.
minutes
,
and
the
number
then
shall
be
of
9046.
minutes
.
These
minutes
againe
multiplied
in
it selfe
doe
bring
forth
and
offer
the
first
quadrate
,
that
is
81830116.
The
difference
of
the
latitude
,
as
the
4.
degrées
,
and
6.
minutes
,
multiplied
by
15.
doth
produce
or
bring
forth
61.
miles
and
30.
scruples
:
which
as
they
may
bee
wrought
and
multiplied
againe
in
themselues
,
they
may
bee
resolued
into
minutes
,
and
you
shall
haue
3660.
minutes
.
These
further
wrought
in
themselues
doe
bring
forth
and
shew
the
second
quadrate
,
which
containeth
13395600.
The
two
quadrate
numbers
also
conioyned
,
doe
make
95225716.
minutes
.
The
roote
of
this
;
that
is
,
9758.
deuided
by
60.
declareth
the
space
betweene
Buda
and
Aquisgranum
,
to
be
162.
Germain
miles
and
a
halfe
.
Another
.
THe
longitude
of
Roome
is
of
36.
degrées
,
and
20.
minutes
,
the
latitude
hath
41.
degrees
,
&
50.
minutes
.
The
longitude
of
Ierusalem
hath
66.
degrées
,
and
no
minutes
,
the
latitude
is
of
31.
degrées
,
and
40
minutes
.
The
difference
of
the
longitudes
is
of
29.
degrées
,
and
40.
minutes
.
The
difference
of
the
latitudes
is
of
10.
degrées
,
and
10.
minutes
.
The
halfe
of
the
difference
of
the
latitudes
,
is
of
5.
degrées
,
and
5.
minutes
.
The
middle
latitude
,
is
of
36.
degrees
,
and
45.
minutes
.
The
miles
answering
to
one
degrée
in
the
Parallel
of
the
latitude
nexte
following
,
are
11.
and
59.
minutes
.
These
subtracted
from
the
miles
and
minutes
of
the
former
eleuation
,
there
doe
9.
minutes
remaine
.
These
thus
founde
and
knowne
séeke
the
proportional
part
to
bee
subtracted
,
in
saying
,
if
one
degrée
or
60.
minutes
in
this
Parallel
doe
yéeld
9.
minutes
of
a
Germaine
mile
,
howe
many
minutes
of
a
mile
doe
45.
minutes
yéelde
or
make
,
which
depende
to
the
degrées
of
the
middle
latitude
.
To
know
this
,
multiply
45.
by
9.
and
the
product
deuide
by
60.
then
will
9.
minutes
remaine
in
the
quotient
.
The
part
proportionall
must
also
bee
subtracted
,
which
deducted
from
the
miles
and
minutes
assigned
to
the
latitude
36
,
as
from
the
12.
miles
,
and
8.
minutes
,
doe
12.
miles
,
and
2.
minutes
remaine
.
By
which
appeareth
,
that
so
many
miles
and
minutes
,
do
answere
to
one
degrée
in
the
Parallell
of
the
middle
latitude
.
This
now
is
as
a
preparation
and
entrance
,
vnto
the
second
working
.
To
haue
therefore
the
distance
of
the
fore saide
citties
,
multiply
first
the
12.
miles
,
and
minutes
,
with
the
difference
of
the
longitudes
29.
degrees
,
and
40.
minutes
,
and
they
shall
bring
foorth
356.
Germaine
miles
,
and
●9
.
minutes
,
which
356.
miles
,
that
may
bee
wrought
togither
with
the
minutes
59
,
are
to
be
resolued
into
minutes
,
the
same
is
performed
,
if
they
bee
multiplied
by
60.
To
the
same
product
being
21369.
adde
the
59.
minutes
,
and
they
make
21419.
These
minutes
againe
multiplied
in
themselues
,
do
offer
the
first
quadrate
,
that
is
,
458773561.
Thus
you
haue
the
vnderstanding
and
knowledge
of
the
working
of
the
first
place
.
After
this
multiply
the
10.
degrées
of
the
difference
of
the
latitude
by
15.
and
you
shall
readily
haue
the
miles
150.
to
which
ad
for
the
10.
minutes
depending
,
2
miles
,
and
a
halfe
of
a
Germaine
mile
,
and
you
shall
haue
in
this
second
part
of
the
working
152.
miles
,
and
a
halfe
or
30.
scruples
of
a
Germaine
mile
.
Which
miles
,
as
they
may
with
the
minutes
bee
multiplied
togither
in
themselues
,
so
are
they
to
bee
resolued
by
that
60.
multiplied
into
minutes
,
which
then
bring
foorth
9120.
to
which
adde
the
halfe
or
30.
miles
,
and
you
shall
then
haue
the
whole
to
be
9150.
minutes
:
which
againe
multiplied
in
themselues
doe
make
the
later
quadrate
to
be
8372●500
.
Nowe
vnto
the
last
,
conioyne
these
two
quadrates
,
and
the
whole
summe
shall
bee
542496061.
minutes
.
The
roote
of
this
number
;
that
is
,
23299.
séeing
it
representeth
the
minutes
of
miles
,
deuided
by
50.
doth
then
shew
the
space
which
is
betwéene
Icrusalem
and
Roome
,
in
Germaine
miles
,
to
be
388.
with
a
third
part
almost
of
a
mile
.
Another
.
THe
longitude
of
Hamburge
is
of
37.
degrées
only
,
the
latitude
hath
45.
degrées
,
and
24.
minutes
.
The
longitude
of
Magdeburge
hath
29.
degrées
,
and
38.
minutes
the
latitude
is
of
52.
degrées
,
and
20.
minutes
.
The
difference
of
the
longitudes
is
of
2.
degrées
,
and
38.
minutes
.
The
difference
of
the
latitudes
is
of
2.
degrées
,
and
4.
minutes
.
The
halfe
of
the
difference
of
the
latitudes
,
is
one
degrée
,
and
2.
minutes
.
The
middle
latitude
is
of
53.
degrées
,
and
22.
minutes
.
The
miles
assigned
to
the
eleuation
53.
are
9.
and
2.
minutes
.
The
miles
assigned
to
the
degrées
of
the
eleuation
following
,
beeing
54.
are
8.
and
49.
minutes
.
The
difference
now
of
these
two
manner
of
miles
and
minutes
,
hath
13.
minutes
.
The
proportionall
parte
subtracted
is
of
4.
minutes
;
which
minutes
,
let
foure
be
deducted
out
of
the
9.
miles
,
and
2.
minutes
assigned
to
the
eleuation
53.
there
will
then
remaine
8.
miles
,
and
58.
minutes
.
Therefore
so
many
miles
and
minutes
,
doe
answere
to
one
degrée
in
the
Parallel
of
the
middle
latitude
.
These
miles
and
minutes
now
found
,
multiplied
with
the
difference
of
the
longitudes
,
doe
bring
foorth
23.
miles
,
and
36.
scruples
.
And
these
23.
miles
,
wrought
togither
with
the
minutes
;
that
is
,
multipled
in
it selfe
,
and
that
resolued
into
minutes
,
to
the
producte
also
adde
the
minutes
36.
and
the
whole
then
shall
appeare
1416.
minutes
.
This
number
againe
wrought
into
it selfe
,
doth
offer
the
first
quadrate
,
which
is
2005056
,
minutes
.
After
multiply
the
difference
of
the
latitudes
,
by
15.
miles
,
and
the
increase
shall
be
31.
miles
.
These
miles
againe
resolued
doe
yéeld
or
giue
1860.
minutes
,
which
multiplied
againe
in
themselues
,
doe
offer
the
later
quadrante
,
which
containeth
3459600.
minutes
.
The
whole
summe
,
that
is
,
the
numbers
increased
of
these
two
quadrats
,
are
5464656.
The
roote
of
the
minutes
,
which
is
of
2337.
minutes
,
deuided
by
60.
doth
declare
the
distance
which
is
betwéene
Hamburge
and
Magdeburge
,
to
bee
39.
Germaine
miles
almost
.
An
easier
working
.
and
lesse
curious
.
THis
great
labour
perhaps
after
the
kind
,
may
feare
some
from
the
practise
of
these
,
and
the
rather
in
that
this
curious
or
diligent
multiplication
of
the
minutes
,
néedeth
not
in
all
or
at
all
times
,
especially
if
the
space
of
the
two
cities
doeth
not
containe
many
miles
,
or
that
the
cities
offered
be
but
alitle
space
distant
one
from
the
other
.
For
where
the
distance
is
great
,
as
of
Viteberge
&
Frankforde
,
Noriberge
and
Roome
&c.
The
minutes
then
neglected
,
do
cause
great
errour
.
But
if
the
space
be
small
betwéene
the
cities
giuen
,
without
the
acompt
also
of
the
minutes
(
for
that
seldome
in
the
onely
minutes
,
as
are
the
neare
places
togither
,
doe
they
onely
differ
)
the
distaunce
then
by
the
onely
degrées
&
miles
whole
,
cannot
be
found
.
But
if
any
be
minded
not
so
curiously
to
search
the
distances
of
places
,
then
let
him
or
them
omit
the
minutes
depending
aswell
to
the
degrées
of
the
longitudes
and
latitudes
,
as
the
miles
,
and
according
to
the
instruction
of
the
third
rule
,
the
minutes
beeing
neglected
or
omitted
,
you
shall
then
finde
without
any
difficulty
the
distance
of
places
giuen
.
An
Example
.
THe
longitude
of
Franckeforde
is
of
25.
degrées
,
the
latitude
is
of
53.
degrees
.
The
longitude
of
Viteberge
,
is
of
30.
degrees
,
the
latitude
hath
51
,
degrees
.
The
difference
of
the
longitudes
,
is
of
5.
degrees
.
The
difference
of
the
latitudes
,
is
1.
degree
.
The
halfe
of
the
difference
of
the
latitudes
in
whole
degrées
is
nothing
,
wherefore
the
middle
latitude
,
is
the
like
nothing
.
The
miles
assigned
to
the
lesser
latitude
,
as
to
the
51.
degrées
,
are
9
,
multiply
nowe
these
9.
miles
with
the
difference
of
the
longitudes
,
with
5.
degrées
,
and
the
increase
shall
be
46.
which
multiplied
in
it selfe
,
doe
offer
the
first
quadrate
;
that
is
,
2025.
After
multiply
the
difference
of
the
latitudes
,
that
is
,
one
degrée
with
15.
miles
,
which
15
miles
multiplied
againe
in
it selfe
,
do
produce
or
bring
forth
225.
which
is
the
later
quadrate
.
These
two
quadrates
conioyne
,
and
of
the
increase
séek
the
root
,
which
then
declareth
the
distance
betwéene
Franckforde
and
Viteberge
,
to
bee
of
Germaine
miles
about
74.
Another
.
THe
longitude
of
Brunsweeke
is
of
28.
degrees
,
the
latitude
of
52.
degrees
.
The
longitude
of
Viteberge
is
30.
degrees
,
the
latitude
of
51.
degrees
.
The
difference
of
the
longitudes
,
is
of
2.
degrees
.
The
difference
of
the
latitudes
,
is
1.
degrée
.
The
miles
assigned
to
the
lesser
latitude
,
are
9.
The
difference
of
the
longitude
multiplied
by
9.
miles
,
doeth
produce
18.
miles
,
which
multiplied
againe
in
it selfe
doe
produce
324.
that
is
the
first
quadrate
.
The
difference
of
the
latitude
,
being
one
degrée
doth
make
&
containe
15.
miles
,
which
also
wrought
againe
in
themselues
doe
offer
the
later
quadrate
,
which
containeth
225.
Now
of
these
two
quadrates
conioyned
,
the
roote
is
of
23.
which
number
is
almost
the
distance
of
Viteberge
,
in
germaine
miles
,
from
Brunsweeke
.
Another
.
THe
longitude
of
Danske
hath
39.
degrées
,
the
latitude
of
62.
degrées
.
The
longitude
of
Noriberge
,
hath
28.
degrées
,
the
latitude
is
of
49.
degrées
.
The
difference
of
the
longitudes
is
of
11.
degrées
.
The
difference
of
the
latitudes
,
is
of
5.
degrées
.
The
middle
latitude
,
is
of
51.
degrées
.
The
miles
answering
to
one
degrée
in
latitude
,
are
9.
The
difference
of
the
longitudes
,
that
is
multiplied
with
the
9.
doth
yéeld
99.
miles
,
which
againe
multiplied
in
themselues
,
do
produce
the
first
quadrate
which
containeth
9801.
The
difference
of
the
latitudes
(
being
5.
degrées
)
multiplied
by
the
15.
doeth
then
produce
75.
miles
,
which
wrought
againe
in
themselues
do
offer
the
later
quadrate
which
containeth
5625.
The
increase
now
of
the
two
quadrates
,
comprehendeth
15426.
The
root
containeth
124.
And
so
many
are
the
miles
almost
,
betwéene
Danske
and
Noriberge
.
Another
.
THe
longitude
of
Ierusalem
hath
66.
degrées
,
the
latitude
is
of
31.
degrées
.
The
longitude
of
Nazareth
hath
67.
degrées
,
the
latitude
is
of
32.
degrées
.
The
difference
of
the
longitudes
is
1.
degrée
.
The
difference
of
the
latitudes
,
is
the
like
one
degree
.
The
miles
assigned
to
1.
degree
in
the
Parallel
of
the
lesser
latitude
,
are
12.
The
first
quadrate
doth
containe
144.
The
miles
answering
to
one
degree
of
the
difference
of
the
latitude
,
are
15.
The
later
quadrate
,
comprehendeth
225.
The
increase
of
the
quadrates
,
containeth
369.
The
root
containeth
16.
miles
.
Now
the
distance
in
a
maner
is
so
much
,
betweene
Ierusalem
and
Nazareth
.
And
thus
by
other
examples
,
may
young
practisioners
excercise
,
without
labour
,
tediousnes
,
and
paine
,
to
finde
the
spaces
of
places
giuen
,
by
the
degrees
of
the
longitudes
,
and
latitudes
.
A
demonstration
of
the
third
rule
.
THe
demonstration
of
this
working
or
instruction
,
is
taken
out
of
the
last
proposition
of
the
first
book
of
Euclide
,
where
hee
doeth
teach
and
demonstrate
,
that
in
the
tryangle
right
cornered
,
the
quadrate
which
by
the
line
or
side
drawne
and
stretching
to
,
maketh
a
right
angle
,
that
is
equall
in
the
two
squares
,
which
are
caused
by
the
sides
containing
the
right
angle
.
Which
that
you
may
easier
conceaue
and
vnderstand
,
in
the
page
going
before
is
placed
an
apte
figure
to
this
matter
,
by
which
,
a
reason
not
onely
of
the
third
,
but
also
of
the
rules
of
the
first
&
second
may
be
practised
and
declared
.
Also
there
is
repeated
those
thinges
,
which
afore
were
declared
of
the
Theoricke
of
the
longitudes
and
latitudes
,
that
the
yonger
practisers
may
the
readier
and
easier
conceaue
the
rules
hereafter
taught
.
The
line
E.
F.
doeth
represent
the
Equinoctiall
on
earth
,
lying
vnder
the
celestial
Equinoctial
cyrcle
.
The
line
B.
C.
doth
represent
the
Parallell
;
that
is
,
the
cyrcle
equ●ich
●unt
to
the
Equinoctiall
cyrcle
,
drawne
ouer
the
head
or
Zenith
of
the
city
C.
The
line
A.
D.
doth
represent
the
Parallel
,
yea
equidistant
to
that
Equinoctiall
,
drawne
by
the
Zenith
of
the
cities
,
A.
and
D.
The
line
A.
B.
E.
doeth
represent
the
meridian
,
of
the
proper
city
or
place
A.
The
line
D.
CF.
doth
represent
the
meridian
,
of
the
cities
C.
and
D.
The
declaration
of
the
first
rule
.
THe
two
Cities
C.
and
D.
agrée
in
longitude
,
in
that
they
are
vnder
one
meridian
;
that
is
,
they
bee
distant
by
like
spaces
from
the
West
.
But
they
haue
not
alike
latitude
,
for
that
the
City
C.
is
nearer
to
the
Equinoctiall
than
the
City
D.
by
thrée
degrées
.
To
haue
therefore
the
distance
,
or
that
space
betwéene
,
you
shall
easily
finde
the
same
by
the
degrées
of
the
meridian
.
The
declaration
of
the
second
rule
.
THe
two
Cities
A.
and
D.
agrée
in
the
latitude
,
or
they
haue
one
like
eleuation
of
the
Pole
,
in
that
they
are
vnder
one
Parallel
,
and
the
Zenith
of
both
is
by
fiue
degrées
distant
from
the
Equinoctiall
.
But
the
longitude
of
them
is
not
alike
;
that
is
,
they
be
not
equally
distant
from
the
West
:
for
the
city
A.
is
more
Westerly
then
the
citty
D.
by
foure
degrées
.
So
that
the
distance
is
to
bee
gathered
and
learned
by
those
degrées
betwéene
,
in
that
Parallell
.
The
declaration
of
the
third
rule
.
THe
two
Cities
A.
an●
●
.
be
distant
by
vnlike
spaces
,
aswell
from
the
〈◊〉
from
the
Equinoctiall
.
For
they
be
vnder
diuers
meridians
and
Parallels
.
The
city
A.
is
nearer
to
the
West
than
the
city
C.
by
foure
degrées
,
and
it
is
further
distant
from
the
Equinoctiall
than
C
,
by
thrée
degrées
.
Wherefore
by
those
degrées
in
which
it
is
nearer
to
the
West
and
furthest
distaunt
from
the
Equinoctiall
,
must
the
distance
of
the
two
cities
A.
and
C.
be
sought
.
For
that
the
space
betwéene
the
meridiane
A.
B.
passing
by
the
Zenith
of
the
City
A.
and
meridiane
C.
D.
stretching
by
the
Zenith
of
the
city
C.
containeth
foure
degrées
:
yet
those
degrées
are
not
in
the
great
cyrcle
,
in
that
those
two
Parallels
doe
not
deuide
the
earth
into
two
iust
halues
,
but
into
vnequall
halues
:
so
that
of
necessity
it
must
follow
,
that
the
degrées
of
diuers
Parallels
haue
vnequall
spaces
.
Wherfore
in
the
third
rule
are
not
the
miles
answering
to
the
degrées
of
the
lesser
eleuation
taken
,
except
the
difference
of
the
latitudes
bee
small
:
nor
the
miles
taken
,
answering
to
the
degrées
of
the
greater
eleuation
:
but
the
miles
are
taken
answering
to
the
degrées
of
the
middle
latitude
:
for
that
it
lacketh
in
one
part
,
may
be
restored
in
the
other
.
Of
the
same
may
the
distance
in
miles
be
sought
,
according
to
the
longitude
.
After
this
,
in
that
the
space
betwéene
the
Parallel
A.
C.
passing
by
the
Zenith
of
the
city
A.
and
the
parallel
B.
C.
reaching
by
the
zenith
of
the
city
C.
containeth
thrée
degrées
,
and
these
are
the
degrées
of
the
meridian
;
that
is
,
of
the
great
Cyrcle
,
where
to
one
degrée
doe
alwaies
and
euery
where
fiftéene
Germaine
miles
answere
.
So
that
the
distance
of
those
Cities
are
easily
found
,
according
to
their
latitude
.
And
in
the
same
by
that
multiplication
of
the
miles
and
degrées
,
the
adding
of
the
product
,
by
the
increase
and
extraction
of
the
root
,
that
the
distance
of
the
Cities
may
necessarily
and
surely
be
gathered
,
is
thus
demonstrated
.
That
in
euery
tryangle
right
cornered
,
the
square
which
is
made
by
the
side
,
is
drawne
against
a
right
angle
,
and
is
equall
to
the
two
squares
which
are
made
by
the
sides
containing
a
right
angle
.
As
the
quadrate
which
is
made
by
the
drawing
of
the
line
A.
C.
into
it selfe
,
that
is
equall
to
the
squares
,
which
are
caused
by
the
drawing
of
the
line
A.
B.
into
it selfe
,
and
B.
C.
into
it selfe
:
which
by
Arithmeticall
practise
may
more
readier
and
better
bee
vnderstood
of
yoong
students
and
practisioners
in
this
maner
.
First
the
side
A.
B.
containeth
thrée
spaces
,
which
multiplied
,
doe
bring
forthus
.
The
line
B.
C.
comprehendeth
4.
distances
,
which
multiplied
,
doe
produce
or
bring
for
16.
which
two
squares
conioyned
,
doe
make
25
:
&
the
square
which
procéedeth
of
the
5.
multiplied
(
which
the
line
A.
C.
containeth
)
doe
they
equate
.
Euen
so
in
the
instruction
of
finding
the
distances
of
places
according
to
the
third
rule
,
the
difference
of
the
longitudes
is
represented
by
the
line
B.
C.
but
the
difference
of
the
latitudes
by
the
line
A.
B.
Therefore
as
by
the
quantities
knowne
of
the
lines
A.
B.
and
B
C.
is
the
quantitie
of
the
line
A
C.
attained
.
Also
by
the
differences
of
the
longitudes
and
the
latitudes
of
places
knowne
,
and
those
afore
taught
being
multiplied
and
increased
,
the
distance
of
them
is
easily
knowne
,
which
by
the
line
A
C.
is
represented
.
And
in
the
Triangle
and
quadrate
,
is
the
side
(
but
in
the
number
)
named
the
roote
.
These
hitherto
,
for
the
knowledge
of
finding
the
distances
of
places
shall
suffice
.
The
definition
,
appellations
,
diuision
,
and
offices
or
vtilities
of
the
Horizont
.
THe
Horizont
called
the
ender
and
Cyrcle
of
the
halfe
Sphere
,
is
the
edge
betwéene
the
light
part
,
that
standeth
for
the
same
wee
sée
,
and
the
darke
halfe
that
wee
cannot
sée
of
the
skie
.
The
Horizont
(
as
Proclus
writeth
)
is
a
greater
cyrcle
,
immoueable
or
fixed
,
not
one
and
the
same
euery
where
,
but
to
each
place
proper
from
the
verticiall
point
,
and
round
about
equally
distant
,
and
deuiding
the
whole
sphere
of
the
world
into
two
equall
halfe
spheres
;
of
which
,
the
one
halfe
appeareth
in
sight
to
vs
,
and
the
other
halfe
hid
vnder
the
earth
.
The
description
of
the
Horizont
doth
Macrobius
teach
;
where
he
writeth
,
that
the
Horizont
is
after
two
condicions
:
the
one
,
extendeth
on
euery
side
vnto
the
firmament
and
serueth
peculiarly
as
it
were
for
the
deuision
of
heauen
,
in
deuiding
iustly
the
skie
into
two
halues
:
of
which
the
one
appeareth
in
sight
to
vs
aboue
the
proper
Horizont
and
the
other
hid
vnder
that
Horizont
from
vs
.
Which
Horizont
hath
his
name
of
the
skie
,
and
of
the
same
called
the
celestiall
Horizont
:
whose
diameter
(
after
Macrobius
)
is
as
large
as
the
diameter
of
the
eight
sphere
,
which
(
as
he
affirmeth
)
is
the
furthest
and
highest
parte
of
the
skie
,
that
men
can
readily
sée
and
discerne
with
the
eie
.
But
the
earthly
Horizont
,
in
that
the
same
serueth
for
the
sightes
onely
of
the
earth
and
water
,
and
not
stretching
vnto
the
firmament
;
nor
that
his
halfe
diameter
(
as
Macrobius
writeth
)
doeth
excéede
180.
furlongs
,
which
containeth
22.
miles
,
and
½
.
So
that
the
whole
diameter
after
his
account
,
is
but
45.
miles
in
length
.
Which
if
any
man
stand
vpon
an
euen
or
plaine
ground
(
orels
on
the
sea
)
may
see
round
about
him
22.
miles
&
a
halfe
euery
waies
.
Which
rounde
compasse
of
the
whole
Horizont
(
after
Macrobius
)
doth
containe
141.
miles
,
and
3/7.
parts
.
A
comparison
,
that
as
the
meridian
is
an
immoueable
cyrcle
,
euen
so
is
the
Horizone
:
for
if
the
same
were
moueable
,
it
woulde
not
crosse
the
meridian
at
right
angles
:
and
vnto
these
should
be
imagined
,
that
if
it
were
moueable
,
in
each
day
the
same
would
mooue
with
the
meridian
cyrcle
.
The
appellations
and
diuers
names
of
the
Horizont
.
1
THis
circle
is
called
the
Horizon
,
as
it
were
the
cyrcle
deuiding
the
halfe
spheres
,
or
of
the
greek
worde
Orizomai
,
which
in
English
signifieth
to
define
,
determine
,
and
set
out
,
in
that
the
same
defineth
the
parte
of
the
worlde
séene
.
Or
of
Oros
or
Orion
,
that
is
the
bound
or
ender
.
2
It
is
named
also
the
gyrdle
,
or
the
cyrcle
of
rising
.
3
Macrobius
calleth
the
Horizone
that
bounde
of
heauen
that
is
séene
aboue
the
earth
(
lib.
1.
cap.
15.
)
In
that
it
is
the
end
or
bound
seperating
the
neather
halfe
Sphere
from
the
vpper
.
And
of
him
also
called
the
edge
of
the
halfe
sphere
.
And
Alfragnus
called
it
the
cyrcle
of
the
halfe
sphere
.
4
The
Horizone
also
is
so
defined
of
his
office
,
in
that
his
office
is
to
deuide
that
part
of
the
worlde
in
sight
,
from
that
hidde
vnder
the
earth
.
Whereof
it
is
not
vnworthily
called
the
ender
,
séeing
it
permitteth
nor
suffereth
any
to
sée
but
the
halfe
sphere
at
one
time
,
and
therefore
is
called
of
some
,
the
cyrcle
of
the
half
sphere
,
as
afore
taught
.
This
cyrcle
is
alwaies
vnderstood
to
be
described
by
the
verticiall
point
,
in
that
as
the
verticall
point
is
changed
,
euen
so
likewise
is
the
Horizone
.
The
Horizone
is
deuided
after
twoe
sortes
;
first
into
a
right
and
thwart
:
secondly
,
into
a
sensible
and
rationall
Horizone
.
The
Horizone
of
the
right
sphere
is
called
right
or
right
cornered
,
aboue
which
neither
of
the
Poles
of
the
worlde
is
eleuated
,
which
they
haue
whose
Zenith
is
vnder
the
Equinoctial
,
or
dwell
vnder
the
Equinoctiall
.
Their
Horizone
is
the
cyrcle
drawne
by
the
Poles
of
the
worlde
,
which
deuideth
aswell
the
meridian
as
the
Equatoure
at
right
angle
,
through
which
rightnesse
it
obtaineth
that
name
,
that
it
is
called
the
right
Horizone
.
The
sensible
Horizone
is
a
space
of
the
earth
defined
by
a
compasse
rounde
about
,
which
the
sight
of
the
eie
attayneth
and
comprehendeth
in
a
plaine
and
euen
field
.
Or
thus
,
the
sensible
Horizone
is
that
which
the
eie
●●●fectly
séeth
,
and
describeth
according
to
the
●ounde
of
●ight
,
and
called
of
some
the
artificiall
Horizon
,
and
that
fo
,
the
s●●●
cause
,
that
which
is
contained
by
sight
,
is
by
a
certaine
similitude
agreeing
with
the
artificiall
day
.
And
as
the
artificiall
day
is
so
named
,
for
that
artificers
doe
especially
worke
in
it
,
euen
so
the
like
is
the
horizone
named
artificiall
,
in
that
towers
,
foretresses
,
and
castles
in
time
past
,
were
built
like
the
horizone
.
The
diameter
of
this
horizone
(
after
Macrobius
)
which
nearer
agréeth
to
a
truth
(
then
either
Proclus
or
Albertus
)
as
afore
was
taught
,
is
of
36.
furlongs
,
to
which
almost
foure
Germaine
miles
answere
,
and
22.
English
miles
:
and
so
far
on
a
plain
and
euen
ground
not
hindred
by
hils
or
thicke
mists
,
may
a
man
fully
sée
.
And
in
the
same
space
the
imbossed
rounds
of
the
earth
,
being
without
hils
,
is
increased
,
and
groweth
to
250.
féele
,
or
125.
cubits
:
so
that
this
horizone
is
not
sodainly
changed
,
nor
in
a
short
space
.
Therefore
of
necessity
must
ensue
,
that
those
which
are
distaunt
by
a
lesser
space
then
360.
furlongs
,
to
sée
alwaies
some
part
of
the
earth
common
to
both
.
But
those
which
are
distant
by
many
spaces
,
doe
comprehend
diuers
compasses
by
sight
of
the
eie
and
diuers
horizones
.
The
rationall
horizone
is
that
which
afore
was
described
,
that
the
same
is
a
greater
cyrcle
,
lying
by
the
edge
of
the
earth
,
and
reaching
round
about
vnto
the
skie
,
and
deuiding
the
celestiall
Orbs
into
two
equall
halfe
Spheres
,
as
the
one
halfe
in
sight
,
and
the
other
hid
to
vs
.
Although
the
plain
vpper
face
of
the
horizone
passeth
not
by
the
center
of
the
earth
,
yet
by
the
edge
of
the
same
,
through
which
we
sée
and
obserue
the
celestiall
bodies
,
that
rise
aboue
and
set
vnder
it
:
so
that
they
euidently
shew
,
that
the
same
deuideth
heauen
into
two
equall
halfe
spheres
,
as
aboue
remembred
.
For
in
euery
moment
,
doe
sixe
signes
of
the
Zodiacke
appeare
aboue
the
earth
,
as
in
the
night
to
the
eie
may
be
numbred
and
noted
,
that
sixe
signes
set
vnder
the
earth
,
and
be
gone
out
of
sight
.
This
is
also
called
rationall
,
séeing
the
eie
cannot
descerne
vnto
the
highest
heauen
,
nor
aptly
frame
this
diuision
of
heauen
into
two
equall
halues
:
yet
the
mind
by
examining
,
gathereth
and
concludeth
,
as
by
a
perseuerance
passing
before
,
and
in
the
shewing
of
the
starres
that
rise
and
set
,
and
in
considering
the
tarriances
of
them
in
either
halfe
sphere
.
This
besides
is
called
the
artificiall
horizone
,
in
that
by
the
benefite
of
the
astronomicall
art
,
it
was
inuented
.
Or
thus
not
much
agréeing
to
the
former
,
the
rationall
horizone
(
which
of
some
is
named
natural
)
and
according
to
the
mind
of
Ptholomie
,
Cleomedes
,
and
Proclus
,
belongeth
vnto
the
Sphere
of
the
fixed
stars
,
and
reacheth
euen
vnto
the
same
Sphere
,
and
deuideth
heauen
into
equall
halfe
Spheres
,
the
one
halfe
appearing
aboue
the
same
circle
,
and
the
other
halfe
not
appearing
,
hid
vnder
it
.
Such
a
maner
of
imagining
is
not
in
vaine
,
nor
without
cause
determined
and
deuised
,
séeing
that
men
in
the
night
and
in
a
cleare
season
,
standing
on
an
euen
grounde
,
may
sée
stars
arise
vnto
sight
in
the
East
,
which
a
litle
before
appeared
not
to
the
sight
:
and
those
after
drawne
by
the
first
moouer
vnto
the
West
horizone
,
that
began
to
go
downe
be
set
,
and
doe
not
after
appeare
.
By
which
they
concluded
that
there
is
a
cyrcle
in
heauen
,
deuiding
and
ending
matters
in
sight
from
those
not
séen
.
So
that
they
nothing
doubted
to
call
this
cyrcle
the
rationall
horizon
(
which
togither
with
the
vpper
face
by
the
center
of
the
earth
stretched
round
about
vnto
heauen
)
and
by
the
foure
quarters
of
the
world
,
as
East
,
West
,
North
,
and
South
,
deuided
things
séene
,
from
those
not
séene
.
And
a
great
helpe
it
giueth
vnto
this
imagination
that
the
earth
is
perfect
round
and
imbossed
,
in
that
of
a
Globe
through
his
imbossing
can
be
séene
but
the
halfe
at
a
time
.
This
also
yéeldeth
a
helpe
to
reason
,
by
the
appearances
in
the
celestiall
bodies
,
although
our
sight
cannot
attaine
vnto
the
starrie
sky
,
nor
fully
descerne
heauen
,
although
a
man
earnestly
looke
vp
and
behold
it
:
yet
doe
we
sée
stars
,
whose
light
extend
vnto
our
eie
.
As
by
this
example
may
euidently
appeare
,
of
that
royall
star
named
the
heart
of
the
Lion
,
which
in
our
time
is
in
the
22.
degrée
almost
of
Leo.
And
the
star
standing
on
the
left
buttocke
of
Aquarius
in
the
22.
degrée
almost
of
the
same
signe●
that
is
diametraly
or
right
against
one
the
other
situated
.
Which
doe
on
this
wise
,
that
as
the
one
appeareth
aboue
the
horizone
,
the
other
is
hidden
vnder
it
,
et
e
contra
.
So
that
as
the
one
riseth
,
the
other
setteth
,
and
on
this
manner
doe
they
continually
.
Of
which
reason
it
is
concluded
,
that
a
certaine
cyrcle
deuideth
heauen
into
twoe
equall
halues
,
and
do
part
(
as
afore
taught
)
the
things
séene
,
from
those
not
séene
.
Although
the
tariance
be
but
small
,
in
that
this
star
appeareth
a
very
smal
while
aboue
the
earth
,
through
the
same
,
that
this
star
of
Aquarius
is
Southerly
from
the
ecclipticke
line
,
it
greatly
forceth
not
.
The
like
examples
may
be
applied
of
the
superiour
planets
,
when
they
be
situated
or
appeare
opposite
in
heauen
,
as
they
also
may
be
euidently
seen
,
in
the
opposition
of
the
sun
and
moone
,
when
they
bee
séene
neare
to
the
East
and
West
horizone
,
and
where
the
moone
is
neare
the
suns
way
.
The
diameter
of
the
rationall
horizone
,
although
the
same
cannot
be
found
nor
comprehended
,
through
his
excéeding
distaunce
by
exteriour
sence
and
iudgement
:
yet
reason
it selfe
iudgeth
,
that
the
same
may
extend
vnto
the
starry
sky
,
whose
sight
from
that
not
séene
it
doth
describe
and
the
same
is
of
32655932.
Germaine
miles
,
and
20.
minutes
,
which
distance
by
the
outward
senses
,
is
iudged
as
infinite
.
The
Pole
of
the
rational
horizon
,
is
the
verticall
point
.
for
it
is
distant
by
a
quarter
of
the
greatest
cyrcle
,
that
is
,
90.
degrées
,
from
the
compasse
round
about
of
the
horizon
,
yet
not
to
all
places
serueth
one
horizon
,
for
that
as
a
man
changeth
place
and
country
,
euen
so
ariseth
a
newe
horizon
,
whether
so
euer
he
trauaileth
.
And
new
horizons
also
appeare
and
happen
,
if
a
man
either
trauaile
toward
either
of
the
poles
of
the
worlde
,
or
in
right
line
toward
the
East
and
West
,
and
the
like
vnto
diuers
quarters
,
as
into
the
North
,
the
East
,
or
West
,
or
contrariwise
iourneying
by
the
opposite
course
,
the
Horizones
vary
and
change
.
And
if
the
places
bee
either
situated
partly
toward
the
East
or
West
,
and
partly
toward
the
South
or
North
,
the
horizones
there
decline
and
varie
them
partly
toward
the
East
or
West
,
and
partly
toward
the
south
or
North
:
which
hapneth
,
by
reason
that
the
City
is
not
vnder
one
Parallell
.
And
Cities
or
countries
situated
vnder
one
meridiane
doe
vary
their
horizons
directly
;
either
toward
the
South
or
North.
There
be
as
many
horizons
,
as
there
be
meridians
.
And
for
so
much
as
that
of
all
places
cannot
bee
one
manner
of
Zenith
,
therefore
cannot
one
Meridiane
serue
for
all
places
.
And
séeing
the
Pole
of
the
Horizone
is
the
Zenith
of
it
,
which
is
in
the
Meridiane
,
and
that
to
each
place
belongeth
a
proper
Zenith
,
and
a
proper
Meridian
,
it
followeth
that
to
each
place
belongeth
a
proper
Horizone
.
Toward
the
Poles
by
the
chaunging
of
places
are
the
horizons
chaunged
,
and
the
diuers
eleuations
of
the
Pole
by
a
certaine
occasion
caused
:
also
they
euidently
declare
a
like
alteration
to
bee
caused
in
the
respect
of
the
opposite
quarters
of
the
East
and
West
,
and
doe
procure
and
cause
diuers
beginnings
of
the
daies
and
nights
,
insomuch
that
the
starres
generally
appearing
and
seene
,
doe
by
order
of
times
and
in
sundry
places
,
arise
and
set
in
the
West
and
hide
them
vnder
the
Horizon
.
For
the
same
maner
of
Ecclipse
,
which
is
seene
at
Arbela
(
after
Plinie
)
in
the
fifte
houre
of
the
night
,
to
them
of
Carthage
it
appeareth
in
the
second
houre
:
so
that
the
sun
sooner
setteth
to
them
of
Arbela
by
thrée
houres
,
then
to
them
of
Carthage
.
Therefore
the
horizon
of
Arbela
is
much
further
distant
into
the
East
then
the
horizon
of
Carthage
.
The
same
rationall
horizon
(
as
it
were
on
the
plainesse
of
the
earth
)
drawne
and
streached
vnto
the
sky
,
doeth
the
meridian
extend
to
it
downward
,
and
deuide
the
same
into
twoe
halfe
cyrcles
:
of
which
the
one
declineth
vnto
the
East
,
and
therof
called
the
East
quarter
,
and
the
other
vnto
the
West
,
and
of
that
named
the
West
quarter
.
And
the
diuers
places
of
the
suns
rising
and
setting
,
doe
sundry
wise
deuide
either
halfe
cyrcle
.
For
the
Equinoctiall
rising
,
and
the
Equinoctiall
setting
,
(
which
are
points
of
the
horizon
,
that
the
sun
in
the
equatoure
placed
,
by
rising
and
setting
passeth
)
doe
parte
and
deuide
either
halfe
cyrcle
into
equall
quarters
.
And
with
these
points
do
the
Poles
of
the
meridian
ioyne
.
And
either
quarters
do
the
other
two
(
as
the
rising
and
setting
)
deuide
into
two
vnequall
arks
.
For
of
the
twoe
Northerly
quarters
,
the
same
which
tendeth
and
looketh
vnto
the
East
,
is
the
solsticial
rising
,
and
the
other
the
solsticiall
setting
.
But
of
the
twoe
Southerly
,
the
Easterly
doth
the
winter
rising
deuide
,
and
the
Westerly
doeth
the
winter
setting
part
.
But
by
what
space
these
risings
and
settings
may
differ
and
be
distant
from
the
former
middle
in
euery
horizon
,
and
in
the
largenesse
of
rising
doth
Ptholomie
instruct
in
that
eleuation
of
40.
degrées
,
and
fiftéene
scruples
.
Of
the
shadowes
which
the
sun
arising
and
setting
in
these
points
of
the
horizon
causeth
,
is
worthie
to
bee
considered
and
noted
,
in
that
the
Equinoctial
shadowes
(
which
through
the
sunnes
rising
and
setting
in
the
Equinoctiall
pointes
are
caused
)
doe
fall
and
extend
in
straight
maner
.
But
the
other
shadowes
not
in
the
same
condicion
or
not
in
straight
line
doe
fall
,
but
that
the
solsticiall
shadowes
in
the
rising
,
with
the
winter
shadowes
in
the
setting
,
and
contrariwise
the
winter
shadowes
in
the
rising
,
with
the
Solsticiall
in
the
setting
doe
fourme
and
make
right
shadowes
.
The
offices
or
vtilities
of
the
Horizon
.
_1
THis
circle
(
like
as
al
the
others
)
so
that
nothing
in
heauen
is
friuolous
and
of
a
vaine
imagination
hath
many
vtilities
.
First
it
deuideth
the
whole
heauen
into
two
equall
halfe
spheres
.
2
It
declareth
which
starres
be
of
continual
appearance
,
and
which
continually
hid
vnder
the
horizon
:
which
doe
set
,
and
which
doe
arise
aboue
the
horizon
.
So
that
it
appeareth
,
that
the
stars
consist
in
a
triple
defference
,
as
that
certaine
do
arise
and
set
,
certaine
neuer
appeare
aboue
the
horizone
,
and
certaine
continue
and
be
alwaies
aboue
the
horizon
.
3
The
horizon
therefore
is
caused
of
the
habitude
,
as
well
of
the
right
,
as
the
thwart
sphere
.
4
The
rising
and
setting
of
the
stars
are
applied
vnto
the
horizon
,
by
which
settings
and
risings
,
the
discriptions
of
times
are
chaunged
,
and
it
also
declareth
the
degrée
of
the
Zodiacke
,
with
the
which
each
starre
riseth
and
setteth
.
5
The
horizone
sheweth
the
rising
and
setting
of
the
signes
of
the
Zodiacke
,
the
exaltations
,
or
eleuations
of
the
pole
and
the
equatoure
,
the
latitudes
of
places
,
to
the
largenesse
of
rising
,
which
is
the
arke
of
the
horizon
to
the
stars
or
points
of
the
ecclipticke
and
equatour
,
arising
togither
,
included
with
the
beginnings
of
the
twelue
houses
of
heauen
.
6
By
the
office
of
the
horizone
,
at
any
time
wee
may
learne
and
knowe
the
quantity
of
the
artificiall
day
and
night
:
and
likewise
procureth
or
sheweth
the
iust
cause
of
the
inequalitie
of
the
artificiall
daies
,
it
doeth
also
declare
the
rising
and
setting
of
the
sun
.
For
as
the
horizons
,
according
to
the
eleuation
or
depression
of
the
pole
,
are
varied
:
euen
so
are
the
verticiall
daies
in
themselues
caused
vnequall
,
yea
in
those
points
of
the
Zodiacke
.
7
By
the
benifit
of
the
horizon
(
the
sun
shining
)
we
attaine
and
come
each
day
vnto
the
knowledge
of
the
vnequall
houre
of
the
day
.
8
It
sheweth
to
vs
the
elongation
of
the
stars
from
the
rising
and
setting
,
which
the
astronomers
call
the
largenesse
of
the
rising
and
setting
,
or
the
Zenith
of
the
rising
and
setting
.
9
By
this
cyrcle
we
learne
how
much
the
rising
aswell
of
the
stars
,
as
the
other
points
of
heauen
,
is
distant
from
the
true
and
the
Equinoctiall
rising
:
that
is
,
in
the
same
are
the
latitudes
of
the
stars
accompted
from
the
equinoctiall
,
and
also
their
risings
and
settings
.
10
It
manifesteth
the
degrée
of
the
Zodiack
,
with
the
which
the
purposed
star
riseth
and
setteth
.
11
It
iudicateth
the
stars
,
or
the
celestial
images
that
be
continually
in
sight
,
or
alwaies
hid
.
12
It
maketh
manifest
the
risings
and
settings
of
the
signes
of
the
Zodiacke
.
It
doth
likewise
make
distinction
,
betwéene
the
Sun
and
Moones
Ecclipses
,
séene
as
well
aboue
the
horizon
,
as
not
in
sight
.
13
It
helpeth
and
furthereth
much
vnto
the
finding
of
the
latitude
of
a
purposed
place
,
whereof
(
through
the
benifite
of
this
cyrcle
and
the
meridian
)
may
the
distaunces
of
places
be
certainly
found
.
Of
the
verticall
Circles
.
BEsides
the
former
cyrcles
at
large
mentioned
,
are
there
other
cyrcles
which
shall
here
bee
vttered
and
taught
,
as
in
an
apte
place
agréeing
to
that
aforesaide
,
which
be●
these
:
the
verticall
cyrcles
;
the
cyrcles
of
the
positions
,
and
of
the
12.
houses
.
Of
these
in
order
shal
here
bee
written
(
as
the
necessary
matter
offereth
)
séeing
a
speciall
part
of
astronomie
dependeth
of
them
,
and
the
whole
composition
of
the
celestial
instruments
séemeth
likewise
one
of
them
.
First
the
verticals
,
be
cyrcles
which
from
the
top
of
any
place
giuen
,
are
drawne
vnto
each
part
of
the
horizon
,
and
deuide
the
vpper
halfe
Sphere
in
sight
into
so
many
partes
,
as
the
Horizone
is
deuided
;
and
all
concurre
and
méete
aboue
in
each
verticall
pointe
or
Pole
of
the
Horizon
.
To
the
number
of
these
,
is
the
meridian
adioyned
.
These
cyrcles
,
are
likewise
vnderstoode
and
noted
immouable
,
as
the
meridian
and
Horizone
;
that
is
,
they
are
not
drawne
about
with
the
first
mouer
,
as
the
Zodiacke
,
the
Equatoure
,
the
Colures
,
and
the
other
cyrcles
in●ixed
to
the
first
mouer
.
The
Circles
of
the
Altitude
.
THe
Cyrcles
of
the
altitudes
be●
those
,
which
are
equidistantly
described
about
the
toppe
of
places
.
As
the
verticall
cyrcles
doe
deuide
each
of
these
cyrcles
into
360.
degrées
,
euen
so
doe
these
deuide
a
quarter
of
each
verticall
cyrcle
into
90.
degrées
.
So
that
none
of
the
altitude
cyrcles
is
greater
then
the
horizone
,
nor
lesser
than
that
which
is
imagined
and
vnderstoode
to
be
described
about
the
verticiall
pointe
.
The
especiall
office
of
these
cyrcles
is
,
that
aswell
the
altitudes
of
the
fixed
stars
as
the
Planets
,
may
bee
measured
and
knowne
,
as
the
fixed
stars
aboue
the
horizone
:
by
which
altitude
or
eleuation
,
the
times
;
that
is
,
the
houres
are
knowne
,
and
the
places
of
the
starres
,
as
may
appeare
in
tables
made
for
that
onely
purpose
.
Séeing
then
it
cannot
be
(
and
that
through
the
roundnesse
of
heauen
)
but
that
any
star
giuen
or
supposed
vnto
the
motion
of
the
whole
,
is
imagined
by
his
altitude
to
be
distinguished
in
some
Parallel
:
therefore
is
the
altitude
of
the
star
or
of
any
other
celestiall
point
,
the
arke
of
the
verticiall
cyrcle
,
drawne
by
the
Center
of
the
star
,
contained
betwéene
the
horizon
and
the
star
giuen
,
which
(
as
afore
written
)
is
distinguished
of
the
said
parallell
.
The
méeting
and
ioyning
togither
of
these
cyrcles
with
the
verticals
,
is
not
moued
,
but
at
the
motion
of
the
verticall
point
;
which
is
none
other
,
then
the
pole
of
the
horizon
,
from
which
all
the
parallels
of
the
altitudes
,
are
imagined
to
be
described
by
equall
distaunces
.
But
this
(
in
mine
opinion
)
is
not
to
bee
ouerpassed
;
that
is
,
that
any
star
,
when
it
shall
be
equally
distant
from
the
meridian
,
either
hath
or
may
haue
the
same
altitude
from
the
horizon
,
as
to
the
eie
is
offered
in
this
figure
folowing
.
Where
a
b
d
c.
is
the
Meridian
:
b
e
c.
the
greatest
halfe
of
the
Paralels
of
the
horizon
:
f
g.
the
least
:
b.
the
North
,
and
c.
the
South
:
a.
the
point
of
the
top
:
o.
or
q.
the
place
of
the
starre
giuen
,
by
which
a
o
k.
or
a
q
n
,
the
verticall
Circle
passeth
,
and
the
like
doth
the
Parallell
p
l
k.
The
Arke
k
o.
or
n
q.
is
affirmed
to
be
the
altitude
or
eleuation
of
the
starre
from
the
horizon
,
that
endeth
at
the
parallell
p
o
l
r.
and
p
o.
is
the
distance
of
the
starre
from
the
noonestead
a
p
d
c.
Now
when
the
starre
(
by
the
motion
of
the
principall
)
is
drawne
vnto
the
point
q.
in
which
when
the
same
shal
be
,
it
will
be
equally
distant
from
the
Meridian
Circle
:
wherefore
through
the
equal
distance
of
the
parallels
,
of
which
they
be
named
,
shall
the
Arke
o
k.
bee
equall
to
the
Arke
n
q.
Of
this
procéedeth
and
is
caused
that
in
the
howers
equidistant
from
the
noonestead
,
as
is
the
seauenth
houre
before
noone
,
and
the
fifte
houre
after
noone
:
likewise
the
eight
and
the
fourth
,
the
ninth
and
the
thirde
,
the
tenth
and
second
,
and
so
of
the
rest
.
The
sunne
obtaineth
equal
eleuations
aboue
the
horizon
.
This
much
auaileth
in
the
composition
or
making
of
dials
,
and
giueth
great
light
and
breuity
to
the
same
practise
,
as
may
appeare
elsewhere
:
but
the
verticall
Circles
in
the
solyde
Spheres
and
Globes
,
by
one
quarter
of
the
Circle
,
depending
of
the
verticall
point
vnto
the
horizon
(
diuided
into
90.
degrées
)
is
declared
.
The
houre
Circles
.
IN
that
the
whole
worke
of
dialles
dependeth
vpon
the
knowledge
of
the
houre
cyrcles
;
it
is
therefore
requisite
and
necessarie
to
entreate
fully
of
the
cyrcles
distinguishers
of
the
houres
,
or
at
the
least
vtter
a
brief
instruction
of
this
.
First
you
shall
vnderstande
,
that
the
Equatoure
onely
,
which
(
as
afore
taught
)
the
sunne
beeing
either
in
the
beginning
of
Aries
or
Libra
,
is
regularly
moued
,
aswel
in
the
right
,
as
thwart
Horizone
;
and
thereof
is
alwaies
the
one
halfe
aboue
the
horizon
,
&
the
other
halfe
hid
vnder
the
Horizon
.
Through
this
his
equall
motion
or
regulare
motions
,
is
it
iudged
worthy
and
laudable
:
séeing
by
it
the
equall
houres
(
as
well
by
day
as
night
)
are
attained
and
had
.
And
this
conceaue
,
that
there
are
twelue
greater
cyrcles
vnderstoode
,
which
crosse
the
Equatoure
at
right
angles
,
and
passe
by
both
the
poles
of
the
first
mouer
,
from
which
the
said
equatour
,
is
distinguished
into
24.
equall
parts
,
which
are
called
the
distances
or
spaces
of
the
houres
,
in
that
each
be
distant
from
other
by
15.
degrées
.
For
they
deuide
the
verticall
,
the
Zodiacke
,
and
the
horizone
into
24.
partes
,
but
vnequally
:
at
which
Poles
the
nearer
partes
to
them
are
narower
then
those
which
be
and
draw
nearer
to
the
equatour
.
And
that
these
may
clearer
and
perfecter
be
vnderstoode
,
imagine
your selfe
to
bée
vnder
the
equatoure
;
that
is
,
in
the
right
Sphere
:
in
such
a
standing
shall
the
halfe
meridian
Cyrcle
bee
the
line
of
the
twelfe
houre
,
and
the
halfe
horizontal
circle
,
the
line
of
the
sixt
houre
before
noon
:
and
the
other
halfe
of
it
,
the
line
of
the
sixt
houre
at
after
noone
.
By
which
imagination
firmely
conceiued
,
may
a
man
imagine
betwéen
the
halfe
horizontall
cyrcle
,
and
the
halfe
meridian
cyrcle
,
to
be
other
fiue
halfe
cyrcles
firme
and
immoueable
,
which
are
not
mooued
but
as
the
verticall
point
is
moued
,
being
distant
each
from
other
by
an
equall
distance
,
as
by
15.
degrées
of
the
equatour
.
The
first
after
the
horizon
,
is
applied
to
the
seuenth
houre
,
&
so
forth
of
the
rest
.
And
in
like
maner
betwéen
the
meridian
halfe
cyrcle
,
and
the
occidentall
horizone
are
other
fiue
cyrcles
vnderstoode
(
according
to
the
fourmer
deuision
)
and
that
which
followeth
the
meridian
,
shall
be
applied
to
the
first
houre
,
that
which
next
foloweth
to
the
second
houre
,
and
so
forth
of
the
others
.
Besides
,
imagine
the
sun
to
ascend
from
the
horizon
,
and
when
he
shall
be
come
vnto
the
first
halfe
cyrcle
from
the
horizon
,
then
shall
he
shed
a
shadowe
furthest
westward
,
and
being
drawne
vp
vnto
the
second
,
shal
make
a
shorter
shadow
,
and
the
shadow
shal
alwaies
(
vntill
the
sun
bee
come
vnto
the
halfe
noonestéede
cyrcle
,
where
he
sheddeth
or
sendeth
a
shadow
)
plum
down
right
to
the
earth
:
but
descending
from
the
Noonstéede
vnto
the
West
,
the
Sunne
causeth
then
the
like
shadowes
contrarie
.
Further
conceiue
,
that
the
Exe-trée
of
the
worlde
,
in
whose
poles
(
as
is
afore
taught
)
all
the
houre
cyrcles
méet
together
in
one
,
doeth
performe
&
expresse
the
same
,
which
the
foresaid
cyrcles
taught
:
as
by
the
sun
dials
the
like
is
readily
vnderstood
and
knowne
.
The
Circles
deuiding
the
twelue
houses
of
Heauen
.
NOw
resteth
to
entreate
of
the
cyrcles
distinguishers
of
the
houses
,
and
the
cyrcle
of
the
positions
:
but
first
I
will
write
of
the
distinguishers
of
the
houses
.
As
there
are
sixe
cyrcles
that
are
imagined
of
the
astronomers
,
by
which
heauen
is
deuided
into
twelue
parts
;
among
which
are
the
Horizone
and
meridian
,
whereby
the
whole
is
deuided
into
foure
equall
parts
:
and
those
twelue
parts
,
are
(
of
the
astronomers
)
called
mansions
or
houses
.
But
as
touching
the
constitution
and
forming
of
the
celestial
houses
,
there
are
sundry
old
and
late
opinions
,
but
whether
opinion
is
the
worthier
,
or
to
be
the
rather
allowed
,
is
not
here
mente
to
bee
stoode
vpon
,
nor
aptely
belongeth
to
the
matter
I
entreat
of
,
so
well
as
in
the
proper
place
is
agréeing
:
yet
certaine
,
and
especially
the
auncient
,
which
were
Campanus
,
a
singular
mathematician
and
astronmer
,
deuided
the
houses
by
the
fiue
cyrcles
of
heauen
,
méeting
an●
ioyning
at
the
Poles
of
the
world
;
from
which
they
deuided
the
whole
heauen
(
togither
with
the
meridiane
)
into
twelue
equal
houses
.
But
for
a
better
and
readier
instruction
,
they
formed
and
drewe
them
in
this
maner
.
After
the
foure
principall
quarters
or
angles
of
heauen
were
drawne
,
and
that
the
right
ascention
of
the
middle
of
heauen
was
had
,
then
were
the
partes
of
the
Zodiacke
diligently
considered
(
that
occupy
as
well
the
Easterly
as
the
Westerly
Horizone
)
and
then
were
the
right
ascentions
sought
of
those
partes
:
which
being
done
,
the
constitution
and
making
of
the
two
houses
in
the
Easterly
part
of
heauen
,
was
the
right
ascention
of
the
mid
heauen
,
deducted
from
the
right
ascention
of
the
Horizone
:
and
the
remayner
,
was
distributed
into
thrée
equall
parts
.
In
the
bound
of
the
first
part
(
in
accompting
from
the
Noonstéed
toward
the
East
)
was
there
imagined
a
cyrcle
for
the
beginning
of
the
eleuenth
house
:
but
in
the
bound
of
the
second
parte
(
from
the
Noonestéede
)
was
the
beginning
of
the
twelfe
house
placed
.
After
in
the
bounde
of
the
third
parte
,
from
the
Noonstéed
,
was
the
beginning
of
the
first
house
drawn
:
and
the
like
was
wrought
and
done
in
searching
for
the
2.
Westerly
houses
,
as
the
ninth
and
the
eight
house
.
For
they
deducted
and
subtracted
the
right
ascention
of
the
west
part
,
from
the
right
ascention
of
the
mid
heauen
or
noonestead
,
and
the
remainer
or
rest
(
as
afore
taught
)
was
distributed
into
thrée
equall
parts
.
After
that
in
the
ende
of
the
first
portion
(
from
the
noonstead
towardes
the
West
)
the
auncients
constituted
or
placed
the
bound
of
the
ninth
house
,
with
the
circle
comming
from
the
poles
of
the
world
:
and
in
the
bound
of
the
second
portion
,
was
the
beginning
of
the
eight
house
formed
.
These
attained
,
the
degrées
and
partes
of
the
degrées
of
the
Zodiack
answering
to
ech
arkes
of
the
Equatoure
,
were
sought
in
the
Tables
of
the
right
sphere
:
but
the
houses
standing
vnder
,
were
defined
and
made
like
to
their
opposites
.
And
séeing
this
maner
of
forming
the
houses
is
vnperfect
,
therefore
shal
here
no
further
be
taught
of
the
same
.
In
which
a
e.
is
the
verticall
circle
,
crossing
a
d
e
c.
at
right
angles
:
f
g
b.
the
equatour
:
d
g
c.
the
horison
,
d.
and
c.
be
the
points
in
which
the
distinguishers
of
the
houses
concurre
and
méet
;
which
also
do
make
equall
distinctions
in
the
verticall
circle
,
and
thereby
be
the
houses
noted
and
diuided
.
But
the
later
Astronomers
,
moued
by
the
authority
of
the
incomparable
Mathematician
Regiomontanus
,
inur̄ted
and
deuised
another
order
of
the
houses
,
more
agréeing
to
reason
than
the
former
.
For
they
deuided
the
quarters
of
the
equatour
,
comprehended
betweene
the
horison
and
noonstead
,
into
thrée
equall
spaces
,
and
by
each
section
they
imagined
great
circles
,
ioyning
in
the
sections
of
the
Meridian
and
horison
,
as
the
former
,
Although
all
these
are
plainer
and
more
euidently
taught
and
known
in
the
materiall
Sphere
,
yet
we
thought
good
to
speak
somwhat
(
as
our
possibility
serueth
)
in
plaine
forme
.
Wherefore
grant
that
a
f
c.
is
the
Meridian
,
a.
the
Top
,
n.
the
Northerly
pole
:
k.
the
Southerly
pole
,
b.
and
c.
the
points
of
the
sections
of
the
horison
and
Meridian
,
where
the
distinguishers
of
the
houses
concurre
and
méet
,
which
also
are
imagined
by
the
equall
distinctions
of
the
equatour
e
i
l.
as
to
the
eie
sufficiently
appeareth
,
that
b
i
c.
is
the
horison
circle
,
d.
the
easterly
point
or
rising
of
the
equatour
,
from
which
the
first
house
taketh
his
beginning
.
The
Circle
of
position
.
AL
these
Circles
being
set
down
,
the
Astronomers
notwithstanding
do
write
of
another
Circle
,
whose
vse
and
office
serueth
to
great
purpose
,
for
the
Art
of
directing
&
searching
other
more
secret
matters
in
Astronomy
,
and
is
thereof
called
the
circle
of
Position
,
which
passeth
at
al
times
by
the
former
sections
of
the
meridian
and
Horizone
,
and
by
the
Center
of
the
star
,
or
of
any
other
purposed
point
in
heauen
,
like
to
the
soresaid
cyrcles
,
whether
that
star
be
aboue
the
earth
,
or
vnder
the
earth
.
That
this
may
clearly
appeare
,
marke
and
consider
this
figure
here
expressed
,
where
the
letter
c.
representeth
the
top
pointe
,
d.
the
Northerly
Pole
,
e.
the
opposite
pole
,
a
g
b
f.
the
cyrcle
of
the
position
passing
by
the
sections
of
the
horizon
and
meridian
,
b
c
d
e.
the
meridian
a
b.
the
Horizone
,
g
f.
the
Centers
of
the
stars
(
of
which
the
one
is
in
g.
aboue
the
earth
,
and
the
other
vnder
the
earth
in
the
point
f.
)
And
many
other
cyrcles
besides
all
these
,
which
hetherto
haue
bene
described
,
may
bee
inuented
and
imagined
in
the
sphere
,
for
the
necessity
of
the
workings
.
The
difinitions
,
names
,
and
offices
of
the
foure
lesser
Circles
.
THe
Parallels
are
lesser
cyrcles
,
which
from
either
of
the
greater
circles
drawn
thwartly
on
the
sphere
,
doe
equally
difand
bee
distant
from
the
Equatoure
or
Zodiacke
toward
their
poles
:
so
that
they
doe
not
deuide
the
Sphere
into
equall
halfe
Spheres
,
but
into
vnequall
portions
.
For
séeing
the
sphere
from
the
middle
streacheth
or
draweth
by
litle
and
litle
straighter
and
narower
toward
the
furthest
and
highest
toppes
:
euen
so
must
the
parallels
which
are
distant
from
the
middle
and
greatest
,
and
that
by
equall
spaces
on
each
side
agréeing
,
drawe
of
necessity
narrower
,
and
so
much
the
narower
,
as
they
nearer
approach
vnto
the
poles
.
As
writeth
Theodosius
in
the
sixte
proposition
of
his
first
Booke
of
the
sphere
.
And
the
same
Author
in
the
14.
proposition
of
his
first
Book
of
the
sphere
,
and
in
the
sixt
,
of
his
second
Booke
writeth
,
that
all
the
parallels
haue
the
same
poles
agréeing
with
the
greater
cyrcles
vnto
which
the
parallels
are
.
And
certaine
of
the
Paralels
are
applied
vnto
the
plain
of
the
Equatoure
,
others
vnto
the
plaine
of
the
eccliptick
.
These
doe
as
well
the
fixed
starres
,
as
the
planets
placed
without
the
ecclipticke
,
and
drawne
about
the
Exe-trée
stretched
b●
the
poles
of
the
ecclipticke
and
Center
of
the
worlde
discribe
:
yet
do
all
their
centers
consist
in
the
Exe-trée
of
the
Zodiack
,
and
the
middle
cyrcle
of
them
,
and
the
greatest
is
the
ecclipticke
.
These
also
doe
the
same
stars
,
and
the
verticiall
or
toppe
points
of
each
places
,
or
any
other
applied
vnto
the
plaine
of
the
equatour
,
drawne
as
it
were
by
the
first
mouer
about
the
Exetrée
and
poles
of
the
world
define
.
And
the
Centers
of
these
be
in
the
Exe-trée
of
the
worlde
or
equatoure
,
but
the
middle
and
greatest
of
these
,
is
the
equatour
.
It
is
manifest
by
that
afore
taught
,
that
the
sun
in
euery
day
doth
gaine
toward
the
East
(
against
the
dayly
motion
)
one
degrée
of
the
Zodiack
:
and
of
this
hapneth
,
that
he
in
each
day
through
the
thwartnesse
of
the
Zodiack
describeth
a
certaine
newe
cyrcle
in
heauen
,
and
in
the
nexte
day
another
,
and
so
forth
by
order
,
as
the
like
may
be
compared
by
a
small
corde
,
winded
close
about
a
Nun
or
top
,
beginning
from
the
foote
vpward
,
euen
so
the
sun
beginning
to
turne
againe
at
the
first
degrée
of
Capricorne
,
doth
euery
day
after
change
a
new
Parallel
,
vntill
hée
become
backe
vnto
the
first
degrée
of
Cancer
,
and
by
and
by
after
returned
from
Cancer
,
he
in
the
like
order
goeth
vnto
the
Capricorne
:
so
that
in
the
next
day
following
,
the
Sun
riseth
not
with
the
same
Parallel
aboue
the
Horizone
that
hee
did
in
the
morning
before
,
nor
shall
not
run
the
nexte
morrow
in
that
Parallel
that
he
did
in
this
day
.
And
each
of
these
Parallelles
(
euen
as
the
greater
cyrcles
)
containe
360.
degrées
,
which
bée
so
much
lesser
,
then
the
degrées
of
the
greater
cyrcles
,
and
occupy
or
comprehend
somuch
the
lesser
space
in
heauen
,
as
answereth
to
the
vpper
face
of
the
earth
,
as
by
how
much
the
more
from
the
compasse
and
largenesse
of
the
greatest
cyrcle
they
lacke
,
by
reason
of
the
distance
.
And
although
they
yéeld
and
be
lesse
in
the
quantity
,
yet
vnto
the
degrées
of
the
greatest
cyrcles
be
they
agréeable
and
like
,
as
(
writeth
Theodosius
)
in
the
14.
proposition
of
his
second
booke
of
the
sphere
.
These
lesser
cyrcles
,
do
offer
and
teach
sundry
vtilities
.
First
the
Parallels
,
of
which
on
this
side
and
beyond
the
Equatour
,
are
182
,
that
the
sun
yearly
by
his
dayly
motion
describeth
:
and
doe
expresse
the
causes
of
the
continuall
equallity
of
the
daies
in
the
right
Sphere
,
and
of
the
vnequalnesse
in
the
thwart
or
bowing
sphere
,
and
where
the
day
spaces
are
encreased
and
lengthened
,
there
the
night
spaces
be
lessened
and
decreased
:
and
being
otherwise
they
shew
the
contrary
.
In
the
second
,
the
Parallels
(
which
the
verticial
points
forme
)
when
they
expresse
the
boundes
of
the
latitudes
of
places
,
then
are
they
standing
vnder
,
by
which
their
longitudes
or
distances
from
the
West
are
accompted
.
In
the
third
,
the
Parallels
(
which
either
the
Planets
or
the
fixed
stars
describe
)
referred
vnto
the
Equatour
,
do
expresse
the
boundes
of
their
drawings
or
motions
from
the
equatour
.
The
others
or
rest
,
which
applied
vnto
the
ecclipticke
described
,
doe
shew
the
bounds
of
the
latitudes
▪
and
that
for
how
long
time
they
tarry
aboue
the
earth
,
or
otherwise
hid
within
the
earth
,
and
vnder
the
Horizone
,
doth
either
shew
.
In
the
fourth
,
the
greatest
and
chiefest
vtilities
of
the
Parallels
are
,
that
which
on
the
habitable
earth
the
practisioners
seuer
by
such
distances
,
as
by
how
much
the
greatest
artificiall
daies
are
by
a
quarter
of
an
houre
longer
increased
and
extended
.
For
they
distinguish
the
habitable
earth
(
and
that
by
obseruation
)
into
certain
necessary
spaces
,
and
doe
iudicate
the
regular
increasings
of
the
daies
,
and
what
is
common
to
each
dwelling
vnder
those
parallels
,
in
asmuch
as
the
quantities
,
the
increasings
and
deminishings
of
the
dayes
and
nightes
,
the
risings
and
settings
of
the
stars
,
the
Noonstéede
shadowes
,
and
the
nature
of
the
Winter
and
Summer
but
those
which
are
contrary
,
as
that
there
is
a
difference
&
diuersity
of
the
dwelling
places
being
vnder
diuers
Parallelles
,
they
indéede
bee
necessary
vnto
the
distribution
and
description
of
the
clymate
.
Although
the
number
of
these
cyrcles
bee
so
infinite
,
as
is
the
infinite
variety
of
the
stars
and
verticall
points
:
yet
are
there
foure
vsually
rehearsed
in
these
Elements
or
introduction
,
that
be
especially
noted
and
described
by
peculiar
names
:
and
for
the
same
cause
(
as
séemeth
to
mée
)
in
that
they
deuide
the
whole
Globe
of
heauen
and
earth
into
fiue
Zones
,
and
these
applied
vnto
the
plaine
or
flat
of
the
equatour
.
The
tropicke
of
Cancer
,
or
summer
tropicke
.
The
tropicke
of
Capricorne
,
or
winter
tropicke
.
The
articke
or
Northerly
Pole
.
The
antarticke
,
or
Southerly
Pole
.
Which
Circles
are
called
the
Tropickes
.
THe
Sun
(
according
to
the
former
words
)
through
the
motion
of
the
first
mouer
is
in
24
houres
,
drawn
once
about
:
and
for
that
hee
is
caried
in
the
thwart
Cyrcle
,
and
in
the
same
by
his
proper
motion
changeth
dayly
vnto
other
places
of
the
Zodiacke
,
it
must
néeds
ensue
,
that
he
describeth
in
each
day
a
new
parallel
.
And
those
doeth
the
sun
repeat
in
the
partes
of
the
Zodiack
,
which
be
equidistant
from
the
solsticiall
points
;
in
such
wise
,
that
they
be
in
the
whole
182.
cyrcles
.
And
these
do
they
call
the
cyrcles
of
the
natural
daies
,
of
which
the
vttermost
and
furthest
that
include
the
suns
way
,
are
named
the
Tropicks
,
which
is
(
in
English
)
the
sun
bounds
,
in
that
the
sunne
neuer
passeth
them
,
neither
toward
the
North
nor
toward
the
South
:
but
after
his
touching
of
each
,
he
returneth
againe
.
The
one
of
these
called
the
tropicke
of
Cancer
,
and
the
other
the
tropicke
of
Capricorne
.
Why
these
are
called
the
Tropickes
.
THey
are
named
the
Tropicks
,
of
the
Gréeke
word
Tropikoi
,
which
is
in
English
,
the
turnings
againe
;
in
that
when
the
Sun
is
digressed
from
the
Equatoure
and
come
vnto
those
,
hee
turneth
backe
againe
.
Also
the
Tropicke
cyrcles
touch
the
Zodiack
,
at
the
beginnings
of
Cancer
and
Capricorne
,
of
which
the
one
is
called
the
Tropicke
of
Cancer
,
and
the
other
of
Capricorne
,
the
one
being
Northerly
,
and
the
other
Southerly
.
And
as
to
our
dwelling
,
the
one
is
called
the
summer
Circle
,
and
the
other
the
Winter
.
So
that
when
the
sun
toucheth
any
of
these
,
he
turneth
againe
,
and
is
carried
toward
the
other
.
As
by
this
example
further
appeareth
,
where
all
that
season
and
time
(
from
the
twelfth
day
of
December
vnto
the
eleuenth
day
of
Iune
)
a
manne
may
perceiue
the
Sunne
euery
day
arising
higher
and
higher
:
and
when
he
is
at
the
highest
ouer
our
heades
,
that
day
doth
he
by
his
course
describe
the
summer
Tropicke
:
from
which
againe
turning
,
the
sunne
euery
day
after
draweth
lower
and
lower
from
our
verticall
pointe
,
vntill
he
be
come
againe
vnto
the
lowest
.
In
which
twelfe
day
of
December
(
not
going
any
further
toward
the
South
,
but
being
come
vnto
the
beginning
of
Capricorne
)
he
describeth
the
winter
Tropicke
.
The
Tropicke
of
Cancer
is
a
lesser
Circle
,
which
the
sunne
describeth
at
the
entring
into
the
beginning
therof
,
and
is
drawne
by
the
daily
motion
,
whose
plaine
or
flat
passeth
not
by
the
center
of
the
earth
:
and
it
is
one
of
the
naturall
Circles
which
is
outermost
,
described
of
the
sun
toward
the
North
,
and
drawne
by
the
beginning
of
Cancer
.
And
it
hath
also
his
name
of
the
standing
,
in
that
the
same
is
the
bound
of
the
sunnes
iourney
or
course
toward
the
North
,
and
the
nighest
comming
vnto
vs
:
vnto
which
being
brought
,
he
turneth
backe
,
and
directeth
his
course
into
the
South
;
of
which
that
place
is
called
Trope
.
It
is
continually
distant
from
the
Equatour
,
by
the
quantity
of
the
suns
greatest
declination
,
which
at
this
day
is
of
23.
degrées
,
28.
minutes
,
and
two
fifts
almost
:
and
it
encloseth
also
the
suns
way
,
and
doth
besides
,
with
the
other
3.
Parallels
,
deuide
the
Zones
of
heauen
and
earth
.
Further
,
this
is
named
the
cyrcle
of
the
summer
solstice
,
by
the
same
reason
,
in
that
it
is
drawne
by
the
pointe
of
the
summer
solstice
.
And
the
Northerly
Tropicke
in
that
it
is
the
Northerly
part
of
the
world
.
And
the
summer
cyrcle
,
for
that
the
Sun
in
the
summer
falleth
into
this
cyrcle
.
Also
this
cyrcle
in
all
the
Northerly
tract
is
on
this
wise
,
that
the
greater
part
or
portion
is
aboue
the
Horizone
,
and
the
lesser
part
(
as
to
vs
)
vnder
the
Horizon
:
so
that
the
sunne
runing
in
that
cyrcle
,
causeth
the
longest
day
of
summer
.
And
whiles
the
sun
describeth
these
cyrcles
,
the
dayes
bee
longer
then
the
nightes
.
For
the
longest
day
increaseth
from
minute
to
minute
,
from
houre
to
houre
,
and
from
the
latitude
of
one
degrée
,
vnto
the
latitude
of
66.
degrées
,
and
30.
minutes
.
In
which
the
day
artificial
is
of
24.
houres
,
and
is
thereof
called
a
whole
day
.
For
in
the
latitudes
following
,
and
beyonde
,
hee
increaseth
into
many
whole
daies
.
A
like
definition
hath
Proelus
,
where
hee
writeth
that
the
summer
Tropicke
,
is
the
furthest
cyrcle
Northwarde
that
the
sun
describeth
:
into
which
when
the
sun
is
come
,
he
then
maketh
his
summer
turne
,
and
causeth
also
at
that
time
the
longest
day
and
shortest
night
of
the
yeare
:
from
which
turning
backe
,
he
goeth
againe
toward
the
contrary
coast
of
the
world
:
so
that
of
the
same
Proclus
it
is
called
a
Tropicke
(
which
is
in
English
)
a
returning
cyrcle
.
For
it
is
euident
to
all
men
,
that
after
the
sunne
beginneth
to
turne
,
he
may
in
short
time
after
,
or
at
the
least
within
5.
dayes
,
but
especially
at
Noone
in
euery
wéeke
,
be
well
perceiued
to
discend
and
go
lower
and
lower
,
vntil
he
become
vnto
the
Tropicke
of
Capricorne
or
the
winter
cyrcle
:
where
he
turneth
againe
,
as
you
may
plainly
learne
and
vnderstand
by
the
former
description
of
that
cyrcle
.
The
Tropicke
of
Capricorne
is
a
lesser
cyrcle
,
and
one
of
the
naturall
cyrcles
,
which
is
by
the
like
space
distaunt
from
the
Equatoure
into
the
South
,
and
described
of
the
sun
in
the
beginning
of
Capricorne
,
as
being
vttermost
toward
the
South
(
which
is
the
bound
of
the
suns
greatest
departure
from
vs
,
and
of
his
longest
digression
vnto
the
South
)
that
he
defineth
and
maketh
.
This
cyrcle
also
is
called
the
winter
Solstice
,
and
winter
Tropicke
;
in
that
when
the
sun
commeth
into
this
cyrcle
,
it
is
presently
winter
:
that
is
,
the
shortest
day
of
the
yeare
.
Also
the
less●●
portion
of
this
cyrcle
is
to
vs
aboue
the
horizone
,
and
the
greater
beneath
or
vnder
the
Horizon
.
Besides
the
suns
iourney
endeth
at
the
south
,
and
crosseth
or
deuideth
both
the
burning
and
temperate
Southerly
Zone
.
The
Brumall
or
winter
tropicke
(
as
writeth
Proclus
)
that
is
furthest
toward
the
South
,
of
all
those
which
the
sunne
describeth
by
his
drawing
about
of
the
first
moouer
:
into
which
when
the
sunne
falleth
,
he
causeth
his
winterly
returne
:
so
that
the
longest
night
of
the
yeare
and
shortest
day
,
is
at
that
time
procured
.
From
which
he
goeth
no
further
toward
the
South
,
but
returneth
vnto
the
contrary
quarter
of
the
world
:
and
hereof
this
Circle
is
called
a
Tropicke
,
or
circle
of
returne
.
Now
these
thrée
are
principally
noted
:
the
equatour
,
and
the
two
Tropickes
,
for
the
course
of
the
sunne
.
That
the
instructions
of
the
two
Tropicks
afore
spoken
of
,
may
more
perfectly
be
vnderstoode
,
conceiue
this
Figure
heere
demonstrated
:
In
which
a
h
b
e.
is
the
meridian
,
a
d
b.
the
right
Horizone
d.
the
Center
of
the
principall
a.
the
Northerly
Pole
,
b.
the
Southerly
Pole
,
g
d
c.
the
cyrcle
of
the
Zodiacke
,
h
d
e.
the
Equatour
,
which
here
is
ment
to
bée
abatingly
described
,
when
the
sun
shall
bee
in
the
center
of
the
earth
,
or
in
the
true
section
of
the
Equatoure
and
Zodiacke
,
as
in
the
letter
d.
from
which
point
when
the
sun
returnes
toward
the
Northerly
pole
a.
vnder
the
cyrcle
g
d
c.
he
then
describeth
in
each
day
by
the
motion
of
the
first
mouer
each
Parallels
,
vntill
he
be
come
in
the
Meridiane
vnto
the
point
g
,
from
which
hee
can
not
further
ascend
toward
our
Zenith
in
the
meridian
.
Of
which
in
the
same
day
,
the
sun
describeth
g
f.
the
parallell
to
the
equatour
,
which
is
called
the
Tropicke
of
Cancer
,
in
that
the
sun
beginneth
from
this
place
to
approach
or
draw
nearer
to
the
Equatoure
;
vnto
which
when
the
sun
shall
come
,
hee
then
descendeth
vnto
the
neather
halfe
sphere
,
in
the
halfe
cyrcle
d
c.
Hee
being
come
againe
vnto
the
point
c
,
doth
from
his
center
by
the
motion
of
the
principall
or
first
mouer
in
the
Poles
of
the
world
,
describe
the
Parallell
c
i.
that
is
,
the
tropicke
of
Capricorne
.
The
Polare
cyrcles
,
are
two
of
the
lesser
cyrcles
neare
to
the
Poles
of
the
world
,
being
alike
equall
distant
to
the
equatour
which
vpon
the
Poles
of
the
equatour
described
are
drawne
by
the
Poles
of
the
Zodiacke
.
And
these
are
named
the
Polare
Cyrcles
,
in
that
they
bee
neare
to
the
Poles
:
of
which
,
that
neare
to
the
Pole
articke
,
is
called
the
arcticke
cyrcle
,
of
the
greater
or
lesser
Beare
drawne
in
it
,
or
for
that
this
cyrcle
is
described
about
the
pole
articke
:
the
other
that
is
right
against
▪
is
named
the
antarticke
Cyrcle
,
in
that
it
is
drawne
aboute
the
Antarticke
Pole
.
Or
thus
,
the
arcticke
is
a
lesser
cyrcle
,
which
the
Northerly
pole
of
the
Zodiacke
is
so
far
distant
from
the
Pole
articke
of
the
world
,
as
is
the
suns
greatest
declination
:
or
as
Proclus
writeth
,
that
the
fore
foote
of
the
greater
Beare
by
the
dayly
motion
formeth
.
The
same
cyrcle
(
after
the
minde
of
the
learned
)
is
distant
from
the
equatour
66.
degrées
,
and
30.
minutes
almost
.
To
whome
this
altitude
is
higher
by
23.
degrées
,
and
almost
29.
minutes
.
To
those
parts
of
the
earth
is
the
pole
arcticke
extaunt
in
sight
,
and
continually
appeareth
.
It
also
secludeth
and
parteth
the
vntemperate
Northerly
Zone
,
from
the
next
temperate
Zone
:
where
the
Solsticiall
Tropicke
is
made
the
Northerly
cyrcle
,
and
in
that
place
vnder
this
altitude
of
the
pole
66.
degrées
,
and
31.
minutes
:
there
all
the
stars
and
images
contained
from
the
solsticiall
Tropicke
vnto
the
Pole
are
seene
:
as
both
the
Beares
,
the
Dragon
,
Cepheus
,
Cassiopia
,
Perseus
,
Auriga
or
the
Carter
,
whole
Bootes
(
except
from
the
knées
downeward
)
the
crowne
Hercules
(
except
the
head
and
right
arme
)
the
Harpe
,
the
Swan
,
the
great
Horse
Andromeda
(
except
the
left
Cubit
)
the
halfe
of
the
Northerly
Fish
almost
,
Deltoton
,
a
part
of
the
backe
of
Taurus
,
the
necke
and
Northerly
Horne
,
a
great
parte
of
Gemini
,
and
the
head
and
necke
of
Leo.
And
not
vnlike
to
the
former
,
doth
Proclus
describe
them
:
where
hee
writeth
,
that
the
Northerly
cyrcle
is
the
same
,
which
of
al
those
that
to
vs
continually
be
séen
or
appeare
,
is
for
trueth
the
greatest
;
and
that
also
toucheth
the
Horizone
at
one
onely
point
,
being
wholy
described
aboue
the
earth
.
And
the
stars
that
are
inclosed
within
this
cyrcle
,
do
neither
rise
nor
set
,
but
are
continually
séen
all
the
night
drawn
about
the
Pole
.
The
South
or
antarticke
cyrcle
,
is
thus
defined
of
him
,
that
the
same
is
equal
and
equidistant
to
the
Northerly
or
articke
cyrcle
,
and
toucheth
the
Horizon
at
one
point
.
The
whole
of
this
cyrcle
is
hidden
vnder
our
Horizone
,
so
that
all
the
stars
placed
and
drawn
in
it
,
abide
euer
out
of
sight
to
vs
.
The
like
description
that
the
antarticke
Parallel
is
a
lesser
Cyrcle
,
which
the
Southerly
Pole
of
the
Zodiacke
draweth
about
as
it
were
by
the
dayly
motion
,
doeth
describe
about
the
Southerly
toppe
of
the
world
,
and
is
by
a
like
space
distaunt
from
the
Equatoure
and
the
antarticke
pole
of
the
world
,
as
the
articke
is
from
his
opposite
.
And
doth
seperate
or
deuide
the
vntemperate
Southerly
Zone
from
the
next
temperate
Zone
.
Further
it
is
manifest
,
that
the
distance
of
the
Poles
of
the
ecclipticke
from
the
poles
of
the
world
,
doe
agrée
with
the
greatest
bowing
or
declination
of
the
ecclipticke
or
the
sun
:
In
that
the
poles
from
their
cyrcles
,
bee
alwaies
distant
a
quarter
of
the
cyrcle
,
and
the
colure
of
the
solstices
,
is
here
taken
for
that
which
comprehendeth
either
Pole
.
And
when
the
quarters
standing
betwéene
the
poles
,
and
the
cyrcles
of
the
poles
,
be
in
themselues
,
or
betwéene
one
the
other
equall
,
as
the
arke
of
the
same
cyrcle
,
then
the
middle
arke
common
to
both
,
which
(
as
exempted
)
goeth
betwéene
the
poles
of
the
world
and
the
ecclipticke
,
and
so
parteth
and
leaueth
them
equall
.
For
the
one
halfe
of
the
other
equall
arks
,
is
from
the
poles
of
the
ecclipticke
vnto
the
poles
of
the
world
,
and
the
other
,
is
from
the
furthest
point
of
the
ecclipticke
vnto
the
equatour
.
By
which
it
appeareth
,
that
so
much
is
the
distance
of
the
poles
of
the
Ecclipticke
from
the
poles
of
the
worlde
,
as
is
the
suns
greatest
declination
,
being
23.
degrées
,
and
28.
minutes
,
and
two
fiftes
almost
.
Or
thus
,
that
the
pole
of
the
Zodiacke
is
far
distant
from
the
pole
of
the
world
,
as
is
the
greatest
declination
af
the
sun
from
the
Equinoctiall
cyrcle
:
and
by
the
equidistance
also
on
each
side
of
the
arctick
cyrcle
from
the
Pole
of
the
world
,
that
that
part
of
the
Colure
comprehended
betwéene
the
first
point
of
Cancer
and
the
articke
cyrcle
,
is
almost
double
so
much
vnto
the
greatest
declination
of
the
sun
.
And
if
cyrcumspectly
you
consider
the
maner
of
the
motions
,
you
shall
readily
perceiue
that
those
cyrcles
which
euer
more
be
of
like
largenesse
,
increase
and
decrease
togither
with
the
twoe
Tropicke
cyrcles
,
according
to
the
increase
or
decrease
of
the
suns
declination
.
As
appeareth
by
the
letter
n.
in
the
foresaid
figure
,
that
representeth
the
Northerly
pole
of
the
ecclipticke
or
Zodiack
,
moued
from
the
letter
n.
into
o.
by
the
motion
of
the
first
moouer
,
and
returning
againe
into
the
point
n
,
shall
be
moued
the
cyrcle
describing
n
o.
being
distant
from
the
Northerly
pole
a.
asmuch
as
is
the
suns
greatest
declination
h
g.
as
hereafter
by
demonstration
shall
plainer
appeare
.
And
this
cyrcle
named
the
arcticke
,
in
that
it
is
described
by
the
arcticke
of
the
Zodiacke
.
The
like
is
described
from
the
point
r.
being
the
pole
antarcticke
,
by
the
motion
from
r.
vnto
s.
and
returning
againe
vnto
r.
so
that
the
antarcticke
cyrcle
r
s.
is
equall
to
his
opposite
,
and
equidistaunt
to
the
Equatoure
.
This
probation
,
that
the
distaunce
of
the
Poles
of
the
worlde
and
Zodiacke
,
is
equall
to
the
suns
greatest
declination
,
doth
require
before
hand
,
these
thrée
propositions
.
The
first
that
the
quarters
of
each
cyrcle
any
where
taken
be
in
themselues
or
betwéene
one
another
equall
.
The
second
,
that
the
poles
by
a
quarter
;
that
is
,
by
90.
degrées
,
be
distant
from
their
proper
cyrcle
.
The
third
,
that
the
equals
deducted
from
their
equalles
,
then
doe
the
equalles
rest
.
As
for
example
,
if
you
borowe
two
fourthes
in
one
and
the
same
Colure
cyrcle
,
that
is
the
Solsticiall
of
the
same
parte
,
where
it
passeth
by
the
beginning
of
Capricorne
,
and
is
the
like
from
the
pole
of
the
worlde
vnto
the
Equinoctiall
,
and
that
other
,
is
that
which
is
from
the
Pole
of
the
Zodiack
vnto
the
Zodiacke
or
ecclipticke
:
and
of
this
I
thus
reason
,
that
when
the
equals
be
deducted
or
abated
from
the
equals
,
the
remainer
shall
be
equall
.
Therefore
are
the
foresaid
quarters
equal
,
in
that
they
be
in
the
same
cyrcle
,
and
that
from
either
is
the
equall
or
common
arke
deducted
;
that
is
,
the
same
which
is
contained
betweene
the
Equinoctiall
and
the
pole
of
the
Zodiacke
,
which
arke
doeth
containe
66.
degrées
,
and
31.
minutes
almost
.
So
that
the
arks
,
resting
or
remaining
of
these
quarters
be
equall
;
that
is
,
the
distance
of
the
poles
of
the
Zodiack
,
and
the
Equinoctiall
,
is
equal
to
the
suns
greatest
declination
.
For
if
66.
degrées
,
and
31.
minutes
bee
deducted
from
either
quarter
,
the
remainer
then
shal
be
23
degrées
,
and
31
minutes
:
which
is
the
distance
betwéen
the
foresaid
poles
and
the
greatest
declination
of
the
sun
.
This
other
example
demonstrateth
,
that
the
suns
greatest
declination
and
the
distance
of
the
poles
of
the
zodiack
or
ecclipticke
from
the
poles
of
the
world
,
is
equall
and
of
like
largenes
,
and
that
what
soeuer
hapneth
to
the
distances
of
the
said
Poles
.
For
as
this
increaseth
or
decreaseth
,
the
like
doth
that
decrease
or
increase
.
Of
this
it
is
manifest
,
that
the
two
foresaide
articke
cyrcles
,
is
nowe
in
our
time
lesser
through
the
decreasing
of
the
suns
greatest
declination
,
and
that
the
Tropickes
are
greater
then
they
were
in
Ptholomies
time
.
The
offices
or
vtilities
of
the
foure
lesser
Cyrcles
.
1
THe
office
of
the
Solsticiall
Tropicke
:
(
after
the
Gréekes
)
is
to
define
the
longest
summer
day
:
and
the
winter
Tropicke
,
to
determine
the
shortest
winter
day
and
longest
night
.
For
Proclus
to
finde
the
longest
day
,
did
deuide
the
summer
solstice
into
8.
equall
partes
:
of
which
so
deuided
,
he
affirmed
thrée
parts
to
be
continually
hidde
vnder
the
horizon
,
and
fiue
aboue
.
The
truth
of
which
is
known
,
if
the
Sphere
bee
rectified
for
the
latitude
of
41.
degrées
,
where
by
this
diuision
the
longest
day
containeth
15
hours
and
the
night
but
9.
houres
.
2
Many
and
notable
offices
doe
the
Tropicke
cyrcles
offer
,
as
well
vnto
the
composition
of
dialles
,
as
vnto
the
preparing
many
other
Instruments
in
Astronomie
.
3
They
declare
the
places
of
the
Ecclipticke
,
in
which
the
suns
solstices
are
caused
:
whereof
the
longest
or
shortest
daies
by
them
are
knowne
.
Or
thus
,
they
declare
in
euery
standing
of
the
sphere
,
the
longest
and
shortest
day
,
with
their
quantity
.
4
They
include
the
Suns
way
,
in
that
they
bee
as
the
bounds
including
the
Region
in
heauen
,
in
which
the
sun
is
continually
moued
.
5
They
declare
the
suns
greatest
declination
,
as
afore
hath
bene
often
taught
.
6
They
seperate
in
heauen
,
the
burning
Zone
,
from
the
two
temperate
Zones
.
But
of
the
Polare
cyrcles
,
these
be
the
chiefest
and
especialest
vtilities
.
1
They
iudicate
or
shewe
the
Poles
▪
of
the
Zodiacke
,
and
howe
farre
they
bee
distaunt
from
the
Poles
of
the
world
.
2
They
inclose
those
stars
which
euer
appeare
aboue
our
Horizone
,
and
those
in
like
maner
right
against
being
alwaies
hid
vnto
vs
.
But
for
that
euery
seueral
Climate
(
hath
disagréeing
from
other
Climates
these
cyrcles
)
their
distance
therefore
cannot
bee
certaine
from
the
other
Parallel
cyrcles
,
sauing
for
one
Region
certaine
,
as
neither
their
quantities
,
nor
their
order
.
For
in
that
place
,
where
the
altitude
of
the
pole
is
lesser
then
66.
degrées
and
a
half
,
these
cyrcles
there
are
lesser
then
the
Tropicks
,
and
in
order
are
betwéene
them
and
the
poles
,
and
is
from
the
pole
continually
distant
by
so
many
degrées
,
as
the
pole
in
that
country
is
raised
aboue
the
Horizon
.
So
that
in
the
same
place
,
the
Pole
raised
more
then
66.
degrées
and
a
halfe
.
The
Tropicke
then
is
aboue
the
horizone
,
as
the
like
may
be
vnderstoode
by
that
place
called
Wardehouse
.
So
that
in
the
same
Climate
,
the
arcticke
cyrcle
is
greater
then
the
Tropicke
of
Cancer
,
as
witnesseth
the
learned
Stoeflerus
,
Iustingensis
.
3
They
distinguish
(
after
the
mind
of
the
Gréeks
)
the
cold
Zones
,
from
the
temperate
.
Which
Ferio
denieth
,
affirming
that
the
arctick
and
antarcticke
cyrcles
,
kéeping
no
vniformitie
to
all
countries
and
béeing
vncertaine
and
variable
boundes
,
can
limit
any
certaine
place
.
For
the
temperate
Zones
are
places
certaine
,
the
arcticke
and
antarcticke
cyrcles
bee
changeable
limits
,
therefore
cannot
they
be
as
bounds
of
the
temperate
Zones
:
yet
dooth
hee
better
allowe
and
agrée
vnto
that
,
that
the
Tropickes
bee
bounds
of
the
temperate
zones
.
So
that
changeable
limits
(
by
this
argument
)
cannot
be
appointed
as
bounds
to
vnchangeable
places
.
4
They
deuide
togither
with
the
Tropicks
,
all
heauen
into
fiue
parts
or
Regions
,
which
they
call
zones
.
The
descriptions
,
names
,
qualities
,
and
vtilities
of
the
Zones
.
THe
foure
lesser
cyrcles
called
Parallels
(
that
were
afore
described
,
doe
deuide
the
whole
heauen
towarde
the
Poles
into
fiue
spaces
:
which
that
heauen
might
bee
compassed
aboute
with
these
larger
swathes
,
the
astronomers
of
the
same
called
them
Zones
,
or
otherwise
of
the
Latines
Gerdils
.
The
Cosmographers
by
the
same
imagination
applied
,
doe
also
dispose
and
distribute
the
whole
Globe
of
the
earth
into
fiue
roomes
or
spaces
,
lying
directly
vnder
,
and
agréeable
in
proportion
to
them
in
heauen
.
Wherefore
a
zone
(
after
the
minde
of
the
Gréekes
)
is
a
portion
,
tract
,
or
space
of
heauen
,
or
earth
,
betwéene
the
two
Parallels
or
lesser
cyrcles
,
being
nighest
equidistant
,
or
contained
betwéene
the
roome
equidistaunt
and
Pole
of
the
world
,
and
gyrdeth
or
compasseth
as
it
were
the
heauen
or
earth
.
Or
thus
,
a
zone
is
a
space
of
earth
like
to
the
two
Parallels
or
lesser
cyrcles
aboue
,
which
the
astronomers
imagine
to
run
on
the
vpper
face
of
the
sphere
.
And
as
the
whole
portion
included
by
the
two
Tropicks
called
the
burning
zone
,
doth
compasse
heauen
as
a
gyrdle
:
euen
so
imagine
the
roome
of
the
earth
,
lying
right
vnder
the
Tropicks
.
The
zones
haue
sundry
names
,
for
of
the
Gréekes
they
be
called
zóne
,
and
of
the
Latines
by
a
borowed
word
Zona
,
as
may
appeare
by
Iulius
Firmicus
,
Macrobius
,
Virgilius
,
Ouide
,
and
other
Latines
.
That
heauen
or
earth
is
imagined
to
bee
gyrded
about
with
these
.
Martianus
nameth
them
swathes
,
Tully
and
Macrobius
nameth
them
by
the
like
reason
gyrdles
.
Ouide
nameth
them
plagues
;
that
is
,
roomes
or
spaces
.
And
how
many
zones
they
bee
,
may
easily
appeare
,
in
that
the
astrologians
,
Geographers
,
Phisitions
and
Poets
,
do
deuide
as
well
the
heauen
as
earth
into
siue
roomes
or
spaces
,
by
the
foure
Parallels
or
lesser
cyrcles
:
of
which
there
bee
two
maner
of
zones
:
the
celestiall
and
the
earthlie
.
The
celestiall
,
are
the
cause
of
the
earthly
,
in
that
the
earthly
lie
directly
vnder
them
.
And
of
the
zones
,
the
celestiall
bee
they
which
the
astronomers
by
imagination
describe
and
distribute
in
the
hollow
of
heauen
:
the
earthly
,
be
they
which
lie
perpendicularly
vnder
.
And
both
also
be
temperate
,
and
vntemperate
zones
.
The
celestiall
zones
,
in
that
they
haue
nothing
of
the
elementary
qualities
,
therefore
doe
they
not
by
heat
burne
and
scorch
,
nor
by
cold
make
stiffe
:
nor
cause
a
temperate
mixture
of
qualities
or
temperatnesse
,
yet
are
they
noted
and
descerned
by
the
names
of
the
qualities
;
as
the
earthly
zones
,
which
being
the
author
of
the
sun
,
and
fountaine
both
of
light
and
heate
,
and
running
continually
in
the
middle
zone
of
heauen
is
diuersly
felt
,
according
to
the
maner
of
the
distance
.
Or
thus
,
there
are
no
qualities
formally
attributed
to
the
celestiall
zones
,
but
to
them
onely
vertually
,
which
is
on
this
wise
to
be
vnderstoode
,
as
that
the
celestiall
zones
of
themselues
be
neither
cold
,
hot
,
nor
temperate
,
but
are
so
called
through
the
suns
declination
from
the
equatour
,
as
well
into
the
North
,
as
into
the
South
quarter
of
the
world
:
In
the
which
declination
,
is
the
like
matter
felte
,
as
well
in
the
suns
right
sending
downe
of
beames
,
as
in
the
thwart
proiection
of
them
on
the
vpper
face
of
the
earth
,
which
diuersly
changeth
the
heat
〈◊〉
.
The
scorching
or
vntemperate
middle
Zone
(
which
through
the
heat
and
burning
beames
,
the
sun
there
causeth
,
when
he
is
ouer
the
head
or
in
the
Noonestéed
place
)
is
contained
betwéene
the
boundes
of
the
sunnes
iourney
which
the
two
Tropicks
make
,
and
includeth
47.
degrées
of
heauen
.
For
the
two
Tropicks
are
on
either
side
the
equatoure
,
so
that
it
vseth
the
middle
roome
in
the
burning
zone
,
from
which
the
sun
towarde
the
North
and
South
,
neuer
declineth
aboue
23.
degrées
,
and
29.
minutes
.
By
which
appeareth
,
that
it
is
there
as
hot
in
the
middle
of
winter
,
as
it
is
in
Spaine
in
the
middle
of
summer
:
and
therefore
not
disagréeing
to
that
which
the
auncient
Cosmographers
wrote
,
that
the
countries
lying
vnder
this
space
,
or
rather
vnder
the
equatour
,
is
vnhabited
through
the
burning
heate
:
and
of
them
for
this
cause
,
named
the
burning
or
scorching
zone
.
But
of
later
yeares
it
is
found
contrary
,
in
that
at
Molucca
,
Good-hope
,
Calicute
,
and
Samatra
,
rich
drugges
,
and
other
fine
spices
haue
beene
there
gotten
by
the
Spantards
and
Portingals
,
and
yéerly
haunted
by
them
,
as
at
this
day
the
same
is
throughly
known
to
many
:
which
also
confesse
that
the
places
vnder
the
Equinoctiall
,
and
the
rich
City
Calecute
,
being
by
the
sea
coast
of
Inde
,
standing
betwéene
the
equatour
and
our
Tropicke
of
Cancer
,
and
vnto
the
other
Tropicke
South
vnder
the
Burning
zone
,
that
the
places
is
habitable
and
peopled
,
although
very
cumbersome
with
extremity
of
heat
.
Also
that
space
on
earth
containeth
685.
Germaine
miles
,
or
23500.
furlongs
.
Ptholomie
and
Auicen
affirme
,
that
the
places
betwéen
the
equatour
and
summer
Tropicke
is
habitable
,
and
that
many
Cities
bee
there
,
although
the
sunne
in
those
places
through
his
direct
beames
(
and
especially
vnder
the
equatour
)
doth
by
the
ouer
much
heat
and
continual
heat
,
burn
and
mightily
scorch
.
The
like
doe
sundry
others
affirme
,
which
write
,
that
those
places
is
conuenient
for
the
life
of
creatures
,
in
that
vnder
the
equatour
there
bee
many
waters
,
which
although
resolued
and
run
through
the
heate
,
yet
doe
they
breath
and
send
vpward
colde
vapors
,
which
the
sun
continually
maintaineth
in
drawing
vp
through
his
vehement
heat
,
and
sending
down
mighty
showers
of
raine
:
which
vapors
in
the
night
(
through
the
suns
furthest
distance
vnder
the
earth
,
and
especially
at
midnight
)
cause
a
mighty
cold
and
chilling
ayre
:
which
the
sun
after
his
rising
,
vntill
he
be
somewhat
ascended
aboue
the
earth
cannot
sodainly
ouercome
and
put
away
that
cold
impression
of
the
ayre
.
So
that
the
people
there
inhabiting
,
bee
monstrous
of
forme
,
and
haue
rude
wits
,
wondrous
wild
and
terible
conditions
,
like
to
wilde
and
furious
beasts
.
The
countries
which
lie
vnder
the
Southerly
Parallels
,
as
those
which
are
described
by
the
Equinoctiall
line
,
vnto
the
summer
Tropicke
,
where
the
sun
is
drawne
and
runneth
ouer
the
tops
of
them
:
there
through
the
aboundance
of
vapors
,
rayne
,
and
night
colde
,
is
the
suns
heate
repressed
,
mitigated
,
and
dulled
;
so
that
the
heades
of
the
Ethiopians
or
Moores
be
litle
,
hauing
but
litle
and
withered
braines
,
their
bodies
short
,
hauing
thicke
crisped
haire
on
their
heades
,
grosse
and
dull
of
senses
,
blacke
scorched
or
burned
bodies
,
withred
or
wrinckled
faces
,
crooked
of
stature
,
being
in
a
maner
hot
by
nature
,
and
cruell
condicions
,
through
the
mightinesse
of
heat
in
those
places
.
And
the
constitution
also
of
the
ayre
is
there
such
,
that
al
liuing
and
cresent
things
on
that
earth
,
are
found
and
known
to
agrée
with
them
.
Further
it
is
to
be
noted
and
vnderstood
,
that
any
there
trauailing
from
the
Northerly
places
,
the
further
they
goe
towarde
the
South
,
somuch
the
stronger
heat
or
burning
they
shal
be
annoyed
with
.
The
two
temperate
zones
be
next
adioining
to
the
burning
zone
,
the
one
on
the
Northerly
,
and
the
other
on
the
Southerly
side
of
it
.
And
the
beginnings
of
either
bee
the
hotter
,
the
ends
colder
,
the
middle
of
them
exquisitly
temperate
:
in
the
other
parts
doth
the
heat
either
so
much
the
more
excéede
,
or
the
bitter
colde
ouercommeth
and
ruleth
,
as
howe
much
the
nearer
they
approach
or
come
vnto
the
burning
Zone
,
or
otherwise
vnto
either
of
the
extreame
Zones
,
which
continually
cause
a
bitter
and
an
extreame
colde
.
The
cause
of
this
diuersity
,
is
through
the
suns
beames
,
for
the
sun
continually
moouing
in
the
middle
iourney
of
heauen
(
described
betwéene
the
two
Tropicks
)
and
digressing
or
going
beyond
the
prefixed
bounds
of
nature
,
doeth
not
shew
his
beames
vnto
diuers
parts
of
the
earth
in
one
manner
,
but
vnto
the
places
right
vnder
,
and
in
the
burning
zone
the
tractes
or
countries
contained
vnder
them
,
doth
he
send
downe
right
beames
,
which
stretcheth
to
the
vpper
face
of
the
earth
at
right
angles
.
And
vnto
the
countries
of
either
temperate
zone
,
doeth
the
sun
send
downe
thwart
or
slope
beames
.
And
vnto
the
places
vnder
either
cold
zone
,
doth
he
streach
long
beames
on
the
plaine
of
the
earth
,
euen
the
like
as
being
neare
to
the
Horizone
,
which
neither
reach
vnto
the
vpper
face
of
the
earth
,
nor
cause
angles
,
but
kéep
an
equall
distance
vnto
it
,
do
streach
forth
infinitely
.
But
those
beames
of
the
sun
doe
neither
giue
light
,
nor
heat
,
but
turne
backeward
:
in
that
the
property
of
the
reflexion
which
of
the
beame
against
a
solider
resistance
,
prohibiting
or
letting
the
penetration
,
is
a
certaine
repercussion
and
reuerberation
)
that
increaseth
and
doubleth
the
force
of
the
direct
beame
,
and
by
the
reflexed
beame
to
it
adioyned
,
or
at
the
least
by
his
vertue
applied
and
communicated
.
Séeing
this
reflexion
is
the
especiallest
cause
of
the
heat
and
that
the
angles
of
the
reflexions
falling
doe
continually
make
or
be
equal
in
the
angles
:
for
that
cause
do
they
much
vnlike
increase
the
force
of
the
directe
beames
,
and
their
effectes
doe
notably
varie
.
So
that
in
the
burning
zone
,
the
reflexion
stretcheth
vnto
right
angles
,
séeing
the
straight
or
right
beames
are
caried
&
led
into
themselues
,
in
such
sort
that
as
direct
and
re●lexen
,
they
méete
and
bee
mixed
,
and
in
this
,
doubling
as
it
were
the
vertue
and
force
of
the
direct
beames
,
is
on
such
wise
increased
,
that
it
kindleth
,
burneth
,
and
consumeth
.
And
in
either
temperate
zone
,
is
the
reflexion
caused
at
right
angles
in
that
the
sun
beames
doe
thwartly
reach
to
the
vpper
face
of
the
earth
,
and
are
turned
and
extended
backward
vnto
thwart
angles
,
which
how
much
the
néerer
and
liker
they
bee
to
the
right
,
so
much
the
nearer
doe
they
ioyne
either
beames
togither
:
by
which
they
procéed
and
come
into
the
nearer
parts
of
the
burning
zone
.
But
so
much
the
blunter
as
they
streach
,
so
much
the
longer
do
they
seperate
either
beames
,
as
howe
much
the
more
they
are
extended
vnto
the
extreame
or
outmost
bounds
.
And
for
this
cause
doe
they
more
heat
then
the
fore
parts
of
the
temperate
zone
,
whose
heate
is
a
litle
gentler
or
milder
then
the
heate
of
the
burning
zone
,
and
the
beames
a
litle
further
of
:
whose
colde
notwithstanding
differeth
somewhat
from
the
extreame
or
outmost
vntemperate
zones
.
And
those
which
streach
and
fall
into
the
middle
region
of
either
temperate
zone
,
doe
cause
a
meane
betwéene
the
right
and
very
sharp
angles
,
and
yet
not
directly
matched
or
ioyned
,
nor
doe
they
by
so
neare
a
space
communicate
their
vertue
,
as
in
the
beginning
of
it
▪
neither
by
so
large
a
distance
as
in
the
end
,
but
in
the
middle
in
a
maner
:
So
that
they
cause
and
increase
a
temperate
heate
in
the
same
zone
.
But
in
the
extreame
or
colde
Zones
,
is
no
reflexion
of
beames
caused
,
for
those
beames
equally
distant
from
the
earth
are
streached
forth
infinitely
:
and
for
that
cause
doe
those
neither
giue
light
nor
moue
or
procure
heat
,
neither
doe
those
zones
at
any
time
warme
,
either
perfectly
cleare
,
or
appeare
bright
:
but
that
they
continually
be
foggy
,
misty
,
darke
,
and
bitter
or
extreame
cold
,
through
the
continuall
mists
,
which
more
and
more
increase
,
especially
toward
the
northerly
pole
.
And
yet
many
affirme
,
a
reasonable
dwelling
in
those
places
,
yea
and
vnder
the
Northerly
pole
,
but
far
colder
and
bitterer
dwelling
,
through
the
far
being
from
the
way
of
the
sun
,
and
beholding
of
the
comfortabler
starres
.
For
the
Sunne
through
his
ouer
far
distance
,
cannot
by
his
presence
aboue
the
earth
comfort
and
heate
.
This
now
is
the
perfect
cause
of
the
diuers
and
vniuersall
coustitutions
of
the
ayre
and
chiefe
qualities
in
each
zones
:
so
that
of
the
particular
constitutions
be
other
causes
.
But
to
returne
vnto
the
temperate
Zones
,
the
latitude
of
either
temperate
Zone
is
of
43.
degrées
almost
,
of
Germaine
miles
645.
and
of
furlongs
21500.
So
that
the
Boreallor
Northerly
zone
beginning
from
the
Tropick
of
Cancer
,
endeth
at
the
arcticke
cyrcle
,
or
at
the
degrée
of
latitude
66.
and
31.
minutes
.
And
the
Southerly
from
the
Tropicke
of
Capricorne
,
is
extended
or
reacheth
vnto
the
antarcticke
cyrcle
,
or
the
degrée
of
the
Southerly
latitude
66.
and
32.
minutes
.
The
vntemperate
cold
zones
that
reach
from
either
temperate
vnto
the
poles
of
the
worlde
,
doe
mooue
continuall
cold
and
frosts
.
So
that
the
beames
of
the
sun
,
although
they
pearse
and
enter
through
,
yet
seeing
they
extende
not
backward
,
nor
through
the
reflexion
or
streaching
backeward
be
strengthned
and
sharpned
,
therefore
can
they
not
so
heate
,
that
by
the
thawing
they
dissolue
the
earth
and
yse
,
nor
put
away
or
voyde
the
mist.
Now
the
vntemperate
Northerly
zone
,
beginning
from
the
66.
degrée
and
31.
minutes
of
the
Northerly
latitude
,
endeth
at
the
Pole
arcticke
:
and
the
vntemperate
southerly
zone
,
begun
from
the
same
bounde
of
the
Southerly
latitude
,
extendeth
and
endeth
at
the
pole
antarcticke
.
Those
people
which
dwell
vnder
the
burning
zone
,
bee
named
of
the
Gréekes
Amphiskioi
Amphiscij
,
in
that
the
Noone
shadowes
,
at
diuers
times
of
the
yeare
,
goe
or
be
cast
to
them
twoe
waies
,
as
toward
the
South
or
North.
And
twise
also
in
the
year
runneth
the
sun
right
ouer
their
heades
(
as
is
demonstrated
in
the
second
Theorme
of
Euclide
)
so
that
at
Noone
it
commeth
to
passe
,
that
they
haue
almost
no
shadow
:
for
the
sun
being
direct
or
in
right
line
ouer
their
heades
at
Noone
,
hee
then
sendeth
downe
right
Beames
,
which
are
cast
or
streached
to
the
plaine
of
the
earth
at
right
angles
:
so
that
their
shadowe
falleth
and
is
right
vnder
the
feete
,
and
not
on
any
side
of
them
.
So
that
the
sun
in
any
other
time
of
the
yeare
beeing
without
the
verticall
pointes
,
the
shadowes
at
Noone
are
one
whiles
cast
into
the
South
,
and
another
whiles
into
the
North
vnto
them
:
euen
as
the
sun
digressing
from
their
toppes
or
Noonstéed
is
either
caried
into
the
North
,
or
otherwise
declineth
into
the
South
.
This
sorte
of
people
which
bee
vnder
either
temperate
zone
,
are
called
of
the
Gréeke
Cosmographers
Eteroskioi
,
Heteroscij
,
in
that
they
haue
a
single
shadowe
.
For
with
them
the
Nooneshadowes
continually
run
or
goe
toward
one
quarter
onely
.
So
that
to
them
dwelling
Northward
the
Noon
shadow
streacheth
towarth
the
arcticke
or
Northerly
quarter
.
By
which
it
appeareth
that
the
sun
neuer
ascendeth
ouer
their
heades
,
but
continually
casteth
or
streacheth
his
beames
thwartly
into
those
contries
,
which
alwaies
forme
their
thwart
angles
with
the
plaine
of
the
earth
,
or
els
fall
a-slope
vpon
the
earth
.
Those
people
which
possesse
,
and
dwel
vnder
either
vntemperate
or
cold
zones
,
are
named
of
the
Gréeke
writers
Periskioi
,
Periscij
:
for
that
their
shadowes
in
one
artificiall
day
are
caried
and
run
rounde
,
as
it
were
about
them
on
the
plaine
of
the
earth
:
so
that
the
sun
vnto
those
places
casteth
or
sendeth
not
straight
,
thwart
,
or
sloape
,
but
long
beames
running
on
the
horizone
,
which
as
they
streach
along
infinitly
;
euen
so
the
shadowes
going
and
lying
on
the
flat
of
the
earth
,
and
extended
along
,
doe
increase
infinitly
.
And
these
zones
also
vnder
the
poles
,
extend
to
that
proper
place
,
where
the
Tropicke
cyrcles
,
and
the
Arctick
cyrcles
be
all
one
.
Strabo
likewise
writeth
,
that
the
colde
zone
reacheth
to
that
place
,
where
the
Tropick
is
the
arcticke
cyrcle
;
that
is
,
where
this
first
Zone
endeth
,
and
the
temperate
beginneth
:
the
Pole
beeing
66.
degrées
,
and
a
halfe
aboue
the
horizon
:
so
that
this
pole
must
be
from
the
toppe
of
their
heads
in
that
place
23.
degrées
,
and
a
halfe
.
Further
,
these
people
that
haue
their
shadowes
running
rounde
about
them
,
dwell
within
the
Polare
cyrcles
:
In
that
all
people
whose
Zenith
is
within
23.
degrees
and
a
halfe
of
any
of
both
the
Poles
,
haue
their
shadowes
compassing
aboute
them
,
but
those
people
(
as
afore
written
)
dwelling
nearer
vnder
the
Pole
,
the
longer
is
their
day
,
and
by
that
reason
doe
the
shadowes
run
the
oftner
about
them
.
For
where
the
day
is
of
24.
houres
long
,
the
shadow
doth
run
but
once
about
,
yet
where
the
day
is
of
halfe
a
yeare
long
,
the
shadowes
doe
run
183.
times
about
.
Here
conceiue
that
there
be
fiue
zones
on
earth
,
answering
to
the
fiue
celestiall
zones
,
both
in
the
heat
,
temperatnesse
,
and
cold
:
which
for
a
plainer
vnderstanding
,
vse
this
figure
here
following
demonstrated
.
Where
the
Orb
or
cyrcle
described
on
the
plaine
of
the
earth
,
is
distributed
by
the
two
vnknown
diameters
into
foure
equall
partes
:
as
to
the
outward
points
of
the
one
diameter
,
note
the
letters
a
b.
To
the
points
of
the
other
diameter
,
adde
the
letters
c
d.
The
letter
c.
the
Northerly
Pole
,
and
the
letter
d.
representing
the
Southerly
pole
.
The
arke
of
the
Orbe
a
c.
deuide
after
the
common
maner
into
90.
parts
or
degrées
,
the
number
(
as
the
vse
is
)
noted
by
5.
10.
15.
20.
25.
&c.
And
beginning
to
recken
at
the
letter
a.
in
ascending
by
the
number
5.
vnto
the
letter
c.
beeing
the
Northerly
pole
.
Againe
set
one
foote
of
the
compasse
vnchaunged
on
the
letter
c.
representing
the
Northerly
Pole
,
and
with
the
other
opened
,
make
a
point
of
the
one
side
,
and
after
on
the
other
side
,
in
drawing
a
line
besides
from
point
to
pointe
,
and
the
ends
of
that
line
note
with
the
letters
●
k.
that
declare
the
arcticke
cyrcle
.
And
likewise
set
one
foote
of
the
compasse
on
the
note
d.
iudicating
the
Southerly
pole
,
and
after
the
marking
with
points
on
either
side
,
draw
a
right
line
;
at
the
endes
of
which
,
note
these
letters
l
m.
that
represent
the
antarcticke
cyrcle
.
These
so
finished
,
you
shall
then
sée
on
that
plaine
or
flat
the
fiue
earthly
zones
rightly
described
.
For
the
space
here
represented
of
the
earth
by
the
Tropicke
lines
e
f.
and
g
h.
included
,
doth
demonstrate
the
burning
zone
.
In
that
the
suns
heat
by
his
direct
beams
ouer
it
,
doth
continually
strongly
heat
and
burne
that
space
of
the
earth
:
wherefore
you
may
rightly
draw
a
straight
line
from
the
letter
g.
vnto
f.
representing
the
suns
iourney
.
And
the
space
of
the
earth
included
of
the
line
i
k.
the
articke
cyrcle
,
and
the
arke
answering
to
the
Northerly
line
i
k
,
doth
iudiacate
the
cold
and
frozen
zone
Northerly
.
And
that
other
Region
or
space
contained
right
against
,
representing
the
antarcticke
cyrcle
,
doth
demonstrate
the
colde
Southerly
zone
.
And
the
tract
or
space
of
the
earth
included
within
the
lines
i
k.
and
E
F.
doth
iudicate
our
temperate
zone
Northward
,
and
that
reasonably
habitable
:
and
the
other
portion
of
the
earth
contained
within
the
lines
g
h.
and
l
m.
doth
manifestly
shew
the
temperate
southerly
zone
.
Where
Ptholomie
and
other
auncient
Cosmographers
write
,
that
the
burning
zone
is
vnhabited
,
or
as
a
desart
,
Aristotle
,
Plinie
,
and
Iohn
de
sacro
bosco
(
in
his
treatise
of
the
Sphere
)
write
the
contrary
:
Besides
these
,
it
is
well
knowne
at
this
day
,
yea
by
experience
vnderstood
of
those
that
haue
yearely
gone
and
come
from
the
countries
lying
vnder
that
zone
;
that
is
,
betwéene
the
two
Tropicks
to
be
inhabited
.
Further
this
burnt
zone
is
inhabited
and
well
replenished
with
people
that
there
dwell
,
as
the
same
is
throughly
known
to
many
that
haue
passed
to
and
frothe
Indies
:
so
that
it
may
euidently
appeare
,
that
the
heate
there
is
not
extreame
,
nor
so
distemperate
,
séeing
the
time
of
the
heate
that
they
suffer
,
continueth
not
long
,
nor
the
heat
sharply
worketh
or
causeth
his
vttermost
effect
.
For
the
sun
but
a
small
time
tarieth
aboue
the
Horizone
in
the
burnt
Region
or
Zone
(
as
certain
astronomers
write
)
as
the
space
of
twelue
houres
onely
:
so
that
the
heat
there
is
much
qualified
and
suppressed
,
through
the
colde
rising
in
the
night
time
;
whereof
it
is
manifest
,
that
he
causeth
not
his
extreame
hotnesse
there
,
although
hee
streacheth
his
beames
perpendicularly
on
the
earth
.
Therefore
may
many
maruaile
,
that
sundry
ancient
men
affirme
these
parts
to
be
vnhabitable
,
séeing
they
knew
of
Arabia
,
Foelix
,
Aethiopia
,
Taprobana
,
and
diuers
other
contries
lying
vnder
the
burnt
zone
:
yea
besides
these
,
are
Guinea
,
Calicute
,
Muluca
and
Gatigara
,
well
knowne
to
lie
or
bee
vnder
the
burning
Zone
:
and
many
of
the
people
in
those
countries
liue
long
:
and
the
same
Region
also
is
inhabited
and
replenished
well
with
people
.
A
like
affirmation
hath
Albertus
and
Auicen
(
as
afore
written
)
that
the
middle
zone
is
habitable
,
for
they
agrée
contrary
to
the
old
writers
,
that
in
the
same
Region
of
the
world
,
which
the
auncient
Cosmographers
named
to
bee
the
burnt
Zone
,
that
it
is
a
far
temperater
dwelling
,
than
vnder
the
Tropicks
it
can
bee
in
any
wise
.
And
that
people
dwell
vnder
the
Tropickes
,
the
ancient
neuer
doubted
.
Wherfore
if
so
resonable
dwelling
be
vnder
the
Tropicks
,
it
cannot
be
otherwise
(
as
affirmeth
Petrus
de
apono
)
that
vnder
the
Equatoure
,
(
notwithstanding
the
sunnes
sharpe
heate
)
but
that
men
may
dwell
there
for
all
the
vntemperatnesse
of
heate
.
To
bee
briefe
,
al
the
writers
of
later
yeares
agrée
,
that
the
middle
zone
is
not
onely
habitable
,
but
found
and
known
by
many
reasons
,
and
by
experience
,
that
the
same
is
most
temperate
,
and
the
earth
vnder
it
rich
,
both
of
golde
and
rich
drugges
,
and
reasonable
well
furnished
of
all
things
néedfull
for
mans
life
.
So
that
in
the
same
middle
Region
of
the
earth
vnder
the
Equatour
,
it
appeareth
,
that
through
the
coldnesse
of
the
night
,
it
doth
there
temper
sufficiently
the
burning
heat
of
the
day
.
Besides
these
,
after
the
mind
of
Hiero.
Cardane
,
in
that
Saturne
,
Mercurie
,
and
the
moon
(
which
properly
are
cold
and
moyst
planets
)
haue
a
great
force
in
the
Regions
vnder
this
zone
,
but
especially
the
moon
,
that
worketh
her
most
force
there
in
the
night
time
,
more
then
the
other
twoe
:
and
of
this
cause
more
temperatnesse
in
the
day
time
.
Besides
these
,
it
is
well
known
that
those
people
haue
two
summers
,
and
two
winters
in
the
yeare
.
For
in
the
yeare
of
our
Lord
1530.
at
the
will
and
charge
of
Charles
the
fift
Emperor
,
a
parte
of
America
westward
was
discouered
,
where
Peru
among
the
rest
,
was
found
richest
both
of
Gold
and
other
rich
things
and
costly
drugges
,
which
is
situated
in
longitude
,
of
290.
degrées
from
the
West
toward
the
East
,
and
is
distant
5.
degrées
from
the
Equatoure
toward
the
South
.
But
what
substance
of
Gold
and
other
rich
things
hath
yearely
bene
brought
from
this
yle
,
néedeth
not
here
any
further
rehersall
.
And
the
like
is
to
be
considered
and
noted
of
the
other
two
zones
,
contained
betwéene
the
Polare
cyrcles
,
and
Poles
of
the
worlde
.
Although
Albertus
Mag.
denieth
,
a
commodious
dwelling
for
men
in
those
places
,
and
confirmeth
the
same
by
probable
reasons
,
yet
experience
reclaimeth
and
denieth
those
opinions
of
his
,
and
other
ancient
writers
.
In
that
it
is
well
knowne
that
Gothland
,
Norway
,
Russia
,
Lapeland
,
Groueland
,
and
diuers
other
countries
towarde
the
North
pole
,
is
inhabited
and
well
peopled
.
And
Galeottus
Naruiensis
proueth
,
that
men
dwell
vnder
the
North
pole
,
affirming
the
same
not
to
bee
true
,
that
the
cause
of
the
cold
there
is
onely
the
far
distaunce
of
the
sun
,
as
not
of
the
heate
by
nearenesse
of
his
comming
.
In
that
the
sun
by
reason
of
the
signe
in
which
he
is
,
either
increaseth
or
diminisheth
them
with
vs
.
Besides
he
affirmeth
,
that
the
colde
is
not
so
dispersed
rounde
about
,
as
that
it
compasseth
rounde
after
the
forme
of
a
cyrcle
,
nor
that
the
heate
in
like
sort
doeth
run
round
about
the
whole
body
of
the
earth
.
Further
Cardane
writeth
,
that
vnder
the
poles
,
there
is
no
such
coldnes
as
some
suppose
,
in
that
the
Moone
,
Venus
,
and
Mars
▪
haue
the
greatest
latitudes
,
in
respect
of
the
sun
,
and
the
others
besides
.
For
the
moon
hath
fiue
degrées
to
the
North
,
Venus
and
Mars
excéed
vnto
eight
degrées
Northward
,
but
Saturne
which
is
the
author
of
cold
,
scarcely
performeth
thrée
degrées
Northward
.
Besides
these
,
the
Moone
more
auaileth
Northward
and
Southward
neare
to
the
poles
,
then
the
sunne
,
in
that
she
nearer
approacheth
those
parts
.
For
the
Moone
(
as
aboue
said
)
hath
fiue
degrées
of
latitude
:
as
well
to
the
North
,
as
South
:
so
that
when
she
shall
be
in
the
first
degrée
of
Cancer
,
with
her
greatest
latitude
Northward
;
that
is
,
in
the
head
of
the
Dragon
,
she
shal
then
be
néerer
by
fiue
degrées
to
the
Northerly
pole
,
then
the
sunne
.
And
in
like
maner
,
when
she
shal
be
in
the
taile
of
the
Dragon
(
at
the
entrance
and
beginning
of
Capricorne
)
she
shall
bee
nearer
the
pole
antarcticke
by
fiue
degrées
than
the
sun
.
Although
in
the
winter
the
moone
should
be
in
the
beginning
of
Capricorn
with
the
Southerly
latitude
of
foure
or
fiue
degrées
,
yet
may
she
worke
and
cause
more
in
the
change
of
weather
,
and
shall
cause
more
in
Scotland
than
the
sun
,
in
that
her
power
and
vertue
there
is
such
.
But
in
Brasilia
and
vnder
the
antarcticke
pole
for
two
causes
,
the
one
,
in
that
shee
is
there
of
such
power
,
and
the
other
for
that
in
her
working
she
is
nearer
.
What
the
longitudes
and
latitudes
of
the
celestiall
Zones
are
.
THe
longitude
of
Zones
beginneth
from
the
West
,
and
is
extended
by
the
Noonestéede
into
the
East
,
and
from
the
East
againe
by
the
midnight
pointe
into
the
West
.
The
motions
of
the
sun
in
the
zodiacke
,
and
Poles
of
the
zodiacke
,
doe
describe
the
latitude
of
the
zones
.
For
the
suns
motion
or
the
zodiacke
do
describe
the
burnt
zone
,
séeing
the
sun
on
the
one
parte
of
the
zodiacke
goeth
toward
the
North
vnto
the
elongation
of
23.
degrées
,
28.
minutes
,
and
being
by
his
dayly
motion
in
the
beginning
of
Cancer
,
doth
describe
the
Tropick
of
Cancer
,
which
is
the
bound
of
the
two
zones
,
the
burnt
zone
,
and
Northerly
temperate
Zone
.
And
on
the
other
part
of
the
zodiacke
doeth
the
sun
goe
into
the
South
vnto
the
same
elongation
,
and
being
in
the
beginning
of
Capricorne
,
doth
likewise
describe
the
Tropicke
of
Capricorne
,
which
is
the
bounde
of
the
other
twoe
zones
:
in
that
it
distinguisheth
the
burnt
from
the
southerly
temporate
zone
.
And
the
space
also
included
in
these
two
cyrcles
,
vsing
the
middle
place
,
is
called
the
burnt
zone
,
and
thus
the
burnt
zone
,
doth
imploy
46.
degrées
,
and
57.
minutes
.
The
Poles
of
the
Zodiacke
(
which
are
dayly
about
the
Poles
of
the
worlde
)
from
which
they
differ
23.
degrées
,
and
28.
minutes
,
and
are
drawn
by
the
motion
of
the
first
mouer
,
doe
describe
two
cyrcles
in
the
diuers
parts
of
heauen
as
the
Polare
cyrcles
,
which
also
be
the
bounds
of
the
zones
,
that
distinguish
the
twoe
temperate
from
the
colde
zones
.
So
that
the
latitude
of
either
colde
zone
,
vnto
the
poles
of
the
world
,
is
of
23.
degrées
,
and
28.
minutes
.
The
other
degrées
of
the
semicyrcle
are
atributed
to
the
temperate
zones
;
so
that
either
zone
containeth
43.
degrées
,
and
3.
minutes
.
What
is
the
Longitude
and
Latitude
of
the
earthly
Zones
.
THe
longitude
of
the
earthly
zones
,
is
like
to
the
longitude
of
the
celestiall
,
as
from
the
West
by
the
noon
stéed
into
the
East
,
and
from
thence
by
the
midnight
pointe
againe
into
the
West
.
And
the
latitude
of
them
is
like
to
the
latitude
of
the
celestial
zones
:
for
as
the
maner
of
the
latitude
of
the
celestiall
burnt
Zone
is
vnto
the
whole
cyrcumference
;
euen
so
is
the
maner
of
the
earthly
burnt
zone
,
vnto
the
compasse
about
of
the
earthly
Globe
;
that
is
,
as
47.
degrées
is
vnto
360.
and
so
likewise
conceiue
of
the
others
.
And
that
this
may
plainer
appeare
,
vse
the
figure
following
,
in
which
a
l
h
e.
is
the
meridian
,
or
Colure
of
the
solstices
,
e
x
l.
the
Equatoure
,
a
x
h.
the
meridian
,
s
u
p.
the
earthly
Globe
,
s
n.
the
earthly
Tropicke
of
Cancer
,
k
o.
the
Tropicke
of
Capricorne
t
u.
and
q
p.
the
arcticke
cyrcles
.
To
these
answere
f
r
o
k
b
b.
and
d
s
m
c
c.
also
c
ff
b
a
g
e
e
i.
the
celestiall
cyrcles
.
And
what
the
proportion
f
d.
is
,
vnto
the
whole
compasse
d
a
k
g
f
the
same
is
(
as
aboue
written
)
the
proportion
r
s.
vnto
the
whole
cyrcumference
of
the
earthly
Globe
:
and
on
this
wise
conceiue
of
the
other
cyrcles
.
The
letters
f
d.
bee
the
latitude
of
the
celestiall
burnt
zone
,
and
r
s.
of
the
earthly
,
d
c.
and
f
g.
be
the
latitudes
of
the
temperate
zones
in
heauen
,
and
s
t
a
c
r
q.
of
them
on
earth
.
The
twoe
outwarde
zones
,
to
these
here
drawne
,
bee
by
themselues
noted
,
as
well
in
heauen
,
as
on
earth
.
Now
that
wee
haue
declared
with
the
fiue
cyrcles
,
the
latitudes
either
of
the
celestiall
or
terestriall
zones
are
defined
,
it
shall
therefore
be
necessary
to
write
here
of
the
latitudes
of
the
earthly
zones
in
miles
.
And
that
you
may
readily
find
the
latitude
in
miles
,
multiply
the
degrées
by
15.
(
in
that
so
many
Germaine
miles
,
answere
to
one
degrée
of
the
great
cyrcle
in
heauen
)
as
the
43.
degrées
of
the
burnt
zone
,
being
the
suns
greatest
declination
,
multiplied
by
the
15.
miles
,
doe
produce
705.
Germain
miles
,
which
is
the
latitude
of
the
burning
zone
.
The
latitude
of
either
temperate
zones
,
containeth
646.
Germain
miles
almost
.
And
from
either
Tropicke
,
vnto
the
pointes
right
vnder
the
poles
,
doeth
the
space
or
distaunce
containe
352.
Germaine
miles
.
Where
is
the
beginning
and
end
of
euerie
Zone
,
according
to
latitude
,
and
which
places
are
in
which
Zones
.
THe
middle
of
the
burning
zone
is
vnder
the
Equinoctiall
line
,
where
either
pole
is
in
the
Horizon
.
And
both
be
his
bounds
(
where
the
eleuation
of
the
pole
,
aswell
Southerly
as
Northerly
is
)
of
13.
degrées
,
and
28.
minutes
.
For
either
temperate
zone
doeth
there
begin
,
and
streacheth
vnto
the
same
place
,
where
the
eleuation
of
the
pole
is
,
of
66.
degrées
,
and
30.
minutes
:
which
place
,
is
the
beginning
of
the
cold
zones
.
By
these
nowe
may
a
man
easily
conceiue
,
which
places
are
in
which
zone
:
for
if
the
eleuation
of
the
Pole
Northerly
,
be
lesser
then
23.
degrées
,
and
28.
minutes
,
this
place
then
is
in
the
burning
zone
,
as
the
inner
Libia
,
Aethiopia
,
a
part
of
Arabia
Felix
,
and
India
.
But
if
the
eleuation
containeth
precisely
so
many
degrées
and
minutes
,
the
place
then
is
in
the
bounde
of
the
burnt
and
temperate
zone
;
as
is
Siene
a
city
of
Aegypt
.
Further
if
the
eleuation
of
the
Northerly
Pole
bee
greater
then
23.
degrées
,
and
28.
minutes
,
yet
lesser
then
66.
degrées
,
and
30.
minutes
,
this
place
then
is
in
the
temperate
zone
,
as
Greece
,
Italy
,
Spaine
,
Germanie
,
France
,
England
&c.
But
if
the
latitude
be
precisely
of
66
degrées
,
and
30.
minutes
,
the
place
is
in
the
bound
of
the
temperate
and
cold
zone
,
as
is
almost
Lagenla●us
of
Suetia
.
Last
,
if
the
eleuation
of
the
pole
excéedeth
66.
degrées
,
and
30.
minutes
,
the
place
is
in
the
cold
zone
beyond
which
degrées
hath
Nicolaus
Douis
a
Germaine
added
a
table
of
Noreway
,
Gothland
,
Iseland
,
Greenland
,
Fineland
,
and
Lapeland
&c.
How
the
Zones
and
Climats
doe
differ
.
THe
Zone
is
a
space
or
roome
of
the
earth
,
from
the
West
into
the
East
,
and
from
thence
by
the
midnight
pointe
againe
into
the
West
.
But
the
Clymate
is
a
space
of
the
earth
,
whose
beginning
is
constituted
in
the
west
and
ende
in
the
East
.
A
Zone
also
is
the
space
of
earth
,
betwéene
two
cyrcles
equidistant
,
but
a
Climate
is
the
only
space
or
roome
of
the
habitable
earth
,
contained
betwéene
two
lines
equidistant
.
What
the
qualities
of
the
Zones
are
.
TO
the
celestiall
Zones
are
qualities
attributed
,
not
formally
,
but
onely
vertually
;
that
is
,
the
celestial
zones
are
neither
cold
,
hot
,
nor
temperate
,
but
of
this
named
colde
,
burning
,
and
temperate
,
through
the
sunne
,
which
one
whiles
comming
into
this
,
and
another
whiles
declining
into
that
parte
of
the
worlde
,
do●th
send
downe
his
beames
to
the
earth
in
sundry
maner
:
as
one
whiles
plum
downe
right
,
when
the
sun
runneth
vnder
the
equinoctiall
,
and
another
whiles
by
a
thwart
maner
,
as
in
the
thwart
sphere
:
which
beames
(
besides
how
right
angles
they
make
on
earth
)
so
much
the
greater
heate
they
cause
,
and
how
thwarter
angles
they
make
,
somuch
the
weaker
heat
they
procure
.
So
that
vnder
the
Equinoctiall
the
beames
most
rightly
and
downe
right
falling
,
doe
make
right
angles
on
the
vpper
face
of
the
earth
,
which
through
the
same
causeth
a
most
great
heat
.
Also
the
beames
faling
toward
either
poles
,
doe
cause
thwarter
angles
,
and
they
make
the
angles
more
vneuen
or
thwarter
,
and
therof
the
same
heat
is
the
lesser
.
And
in
the
temperate
zone
(
especially
in
the
summer
)
the
beames
doe
make
almost
angles
falling
vnto
a
rightnes
,
but
in
the
winter
vnto
a
thwartnes
;
so
that
in
the
same
Region
is
a
commodious
dwelling
.
But
in
the
colde
zones
the
angles
are
caused
vnlike
or
vneuen
,
&
thwartest
or
slopest
,
as
in
the
burnt
Zone
they
are
rightest
and
most
downward
:
in
somuch
that
the
cold
zones
euen
(
as
the
burnt
)
are
commodious
to
dwel
vnder
.
For
the
beames
falling
and
reflexed
,
how
much
néerer
they
fal
and
be
togither
,
somuch
the
stronger
and
mightier
they
moue
and
cause
the
heat
:
as
we
dayly
sée
that
the
sun
in
the
noonstéed
being
(
as
in
the
summer
)
to
cast
or
streach
downe
almost
perpendicular
or
down
right
beames
:
which
beames
also
are
almost
reflected
into
themselues
,
of
which
the
greatest
heat
of
the
day
then
is
caused
.
And
contrariwise
,
the
sun
being
in
the
East
or
west
,
where
the
beames
streaching
downward
and
reflexed
,
are
scatred
and
run
abroade
;
the
effects
be
lesser
,
and
the
heat
much
abated
and
féebled
.
Euen
so
the
beames
in
the
burnt
zone
bee
perpendicular
or
plum
downright
,
which
reflexed
into
themselues
do
cause
a
most
great
heat
.
In
the
temperate
zone
doe
the
beames
bylitle
and
litle
fall
sloper
and
sloper
,
of
which
they
cause
there
a
temperate
heat
.
But
in
the
cold
zones
the
beames
furthest
decline
or
fall
slopest
,
through
which
they
procure
no
effect
,
&
of
the
consequent
cause
there
a
very
weake
heat
.
What
the
vtilities
of
the
Zones
be
.
_1
THe
auncient
considerers
of
the
stars
,
haue
thus
instituted
the
distribution
of
the
zones
for
two
causes
.
The
one
is
,
that
by
this
reason
they
might
shewe
to
vs
which
places
of
the
earth
be
reasonably
habitable
,
&
most
commodious
to
dwell
vnder
.
2
The
other
is
(
as
wee
learne
by
experience
)
that
the
wits
of
men
,
and
nature
of
places
by
them
appeare
and
are
knowne
,
in
that
the
ayre
compassing
vs
,
is
a
certaine
cause
of
the
temperatnes
.
For
the
maners
and
condicions
of
men
(
as
writeth
Galen
)
doe
for
the
most
parte
ensue
the
temperaments
of
the
bodies
:
yea
the
nature
of
trées
,
plants
,
hearbs
,
and
beasts
do
like
ensue
the
temperament
of
ayre
.
Of
which
that
we
might
bee
the
surer
and
certainer
of
the
natures
of
the
foresaid
matter
,
it
pleased
the
ancient
to
deuide
them
into
fiue
zones
.
Of
which
(
it
is
wel
known
)
that
the
bodies
of
men
or
people
dwelling
vnder
the
burning
zone
(
as
the
Moores
)
be
shorter
of
stature
,
than
those
people
dwelling
vnder
the
temperate
zones
,
wilder
,
and
crueler
.
Also
they
bee
crafty
and
subtill
of
nature
,
hauing
besides
wrinkled
faces
,
thick
crisped
heare
on
the
head
,
and
blacke
scorched
bodies
,
and
crooked
of
stature
.
Also
all
liuing
and
cresent
things
,
are
found
to
agrée
according
to
the
quality
of
the
ayre
in
that
Region
.
Further
the
people
dwelling
vnder
the
Northerly
Parallels
or
Polare
cyrcles
(
where
the
places
bound
of
colde
and
moysture
)
be
white
of
body
,
hauing
long
heare
on
the
head
,
tall
and
comely
of
stature
and
personage
,
cold
of
qualitie
,
yet
in
maners
or
condicions
wilde
and
cruell
,
through
the
force
of
the
cold
in
those
places
,
and
agréeing
with
these
is
the
greatnes
of
the
winter
,
and
the
greatnesse
of
fierce
and
cruel
beasts
,
and
other
liuing
things
there
bréeding
,
with
a
furious
people
inhabiting
,
called
generally
the
Scythians
.
Last
,
those
dwelling
vnder
the
temperate
zones
,
be
a
gentler
and
ciuiler
people
beeing
some
tawnie
(
especially
toward
the
South
)
and
others
toward
the
North
reasonable
white
of
skin
and
bodie
,
being
meane
of
stature
,
and
temperate
in
nature
and
quality
,
and
of
the
same
like
in
condicions
and
behauiuor
,
&c.
And
thus
much
,
for
the
second
part
of
this
Treatise
.
FINIS
.