THE
FYRST
TREATISE
OF
THE
CASTLE
OF
KNOWLEDGE
.
whiche
is
an
induction
to
the
necessary
partes
of
the
Sphere
,
as
well
celestiall
as
materiall
.
SCHOLAR
.
The
desire
of
knowledge
.
THE
TIME
SEMETH
longe
(
bee
it
neuer
so
shorte
in
deed
)
to
hym
that
desirously
looketh
for
any
thing
:
for
as
the
obtaining
of
it
bringeth
great
pleasure
,
namelye
the
thinge
it selfe
being
profitable
,
so
the
wante
therof
causeth
displeasure
and
continuall
grief
tyll
the
desire
be
eyther
fully
satisfied
,
other
partly
(
at
the
least
)
accomplished
.
Maister
.
And
sometimes
we
see
,
that
when
the
desire
is
partly
perfourmed
,
and
the
pleasantnes
of
the
same
ones
tasted
of
,
the
desire
therby
nothinge
asswageth
,
but
contrarye
ways
greatly
increaseth
:
and
the
more
it
getteth
,
the
more
it
desireth
.
so
that
in
this
point
may
knowledge
well
be
compared
to
couetousnes
:
for
as
the
couetous
mynd
with
gettyng
is
neuer
satisfied
,
so
knowledge
by
knowing
doth
couet
styll
more
:
And
as
it
increaseth
,
so
doth
it
still
learne
the
vilenes
of
Ignorance
,
and
profite
of
Sciences
,
and
therfore
can
not
rest
from
searching
more
knowledge
,
as
long
as
it
spyeth
any
spot
of
ignorance
.
Schollar
.
This
oftentymes
as
I
haue
considered
,
maketh
me
to
muse
what
mynd
is
in
them
,
which
care
for
no
knowledge
,
nor
esteeme
any
science
.
The
grosenes
of
ignorance
.
Maister
.
This
is
the
greatest
pointe
of
all
ignorance
,
not
to
know
the
grossenes
of
ignorance
,
and
not
to
vnderstand
the
benefite
of
knowledge
,
and
with
this
faulte
are
a
greate
numbre
spotted
.
The
nexte
is
their
faulte
,
whiche
perceaue
sufficientlye
what
vilenes
is
in
ignorance
,
and
what
profite
in
knowledge
,
and
yet
of
a
certaine
negligence
partelye
,
and
partlye
for
other
pleasures
,
they
omytte
to
trauayle
anye
whitte
for
knowledge
,
and
contente
them selues
wyth
wilfull
ignoraunce
:
but
as
these
men
do
trouble
the
good
state
of
the
worlde
,
so
the
talke
of
them
wyll
hynder
the
talke
of
the
worldes
knowledge
,
whiche
is
the
thinge
that
you
so
muche
longe
after
:
and
therefore
beste
it
is
,
that
wee
let
them
lye
still
tomblinge
in
the
dyche
of
ignoraunce
,
and
that
wee
trauaile
forward
towarde
the
Castle
of
knowledge
.
But
first
let
me
heare
what
is
your
chief
desire
.
Schollar
.
The
occasion
of
this
booke
.
Syth
my
laste
talke
with
you
aboute
the
knowledge
of
the
worlde
and
the
partes
of
it
,
I
haue
readd
dyuers
bookes
that
intreate
of
that
matter
,
as
namelye
Proclus
sphere
,
Ioannes
de
Sacro
bosco
,
Orontius
cosmographye
,
and
diuers
other
,
whose
woordes
in
manye
thinges
I
remembre
,
but
of
the
matter
I
haue
sondry
doubtes
,
and
therefore
desire
muche
your
healpe
therein
.
For
althoughe
I
haue
consulted
with
diuers
men
therein
,
yet
me
thynketh
they
tell
me
but
the
same
woordes
in
lyke
sorte
as
I
readde
theym
before
,
or
lyttle
other
wayes
altered
,
but
lyghte
of
vnderstandynge
,
I
haue
gotten
lyttle
yet
.
Master
.
Then
proue
againe
,
peraduenture
your
chaunce
may
be
better
:
that
whiche
at
the
fyrste
semeth
harde
,
maye
at
lengthe
become
easy
:
for
Vse
maketh
masterye
,
all
men
confesse
.
And
,
The
best
thynges
are
not
moste
easiest
to
attayne
.
begynne
in
that
ordre
as
youre
Authors
doo
.
Scholar
.
The
diuersitye
of
writers
.
Theyr
ordres
bee
as
dyuers
as
theyr
names
be
,
so
that
I
knowe
not
whose
ordre
is
best
.
For
Proclus
in
treatinge
of
the
Sphere
,
defineth
firste
the
Axe
tree
of
the
worlde
,
before
hee
had
shewed
other
what
the
worlde
is
,
or
what
hee
calleth
a
Sphere
,
or
what
neede
the
worlde
hathe
of
anie
Axe
tree
.
Therfore
I
tourned
to
Ioannes
de
Sacro
bosco
our
contry
man
,
whiche
beginneth
firste
with
the
definition
of
a
sphere
,
but
nothinge
lyke
to
that
sphere
,
whiche
I
before
had
bought
,
as
an
apt
instrument
to
learne
by
.
Then
see
I
Orontius
disagree
from
them
bothe
:
and
generallie
,
eueryeone
from
other
,
so
that
I
know
not
wher
to
beginne
.
Master
.
As
touchynge
those
writers
,
I
will
saye
no
more
nowe
,
but
although
eueryeone
of
them
haue
some
thinges
that
exactlie
scanned
may
be
misliked
,
yet
he
that
hath
doone
worste
,
is
woorthie
of
thankes
,
for
his
studious
paines
in
furtheringe
of
knowledge
.
And
seyng
you
doubte
of
their
ordre
,
lette
the
thinge
it selfe
minister
ordre
.
What
is
it
that
you
desire
to
knowe
?
Scholar
.
I
see
in
the
heauen
meruailous
motions
,
and
in
the
reste
of
the
worlde
straunge
transmutations
,
and
therfore
desire
muche
to
know
what
the
worlde
is
,
The
argument
of
this
booke
.
and
what
are
the
principall
partes
of
it
,
and
also
how
all
these
straung
sightes
doo
come
.
Maister
.
Then
is
the
worlde
the
thinge
that
you
woulde
knowe
first
,
syth
all
these
other
thinges
are
incident
to
it
.
What
doo
your
authors
call
the
Worlde
?
Scholar
.
what
the
worlde
is
.
Orontius
defineth
the
worlde
to
be
the
perfect
and
entiere
composition
of
all
thinges
:
a
diuine
worke
,
infinite
and
wonderfull
,
adorned
with
all
kindes
and
formes
of
bodies
,
that
nature
coulde
make
.
Master
.
This
definition
doth
muche
agree
with
those
that
bee
writen
by
aunciente
authors
,
and
namely
Aristotle
whiche
defineth
it
thus
.
{αβγδ}
.
Mundus
est
compages
ex
coelo
&
terra
,
&
reliquis
in
ijsdem
contentis
naturis
.
The
worlde
is
an
apte
frame
of
heauen
and
earthe
,
and
all
other
naturall
thinges
contained
in
them
.
The
like
wordes
hath
Cleomedes
and
others
.
So
that
the
worlde
is
that
entiere
body
,
whiche
containeth
all
thinges
that
euer
God
made
,
and
man
can
see
,
nothinge
excepted
but
God
himself
only
,
whiche
is
not
comprehensible
by
any
worldly
meanes
.
This
worke
is
so
pure
and
wonderfull
in
beauty
,
that
it
beareth
the
name
of
cleannes
,
wherof
the
worlde
is
named
.
bothe
in
Greke
and
Latine
,
that
is
〈◇〉
in
Greeke
,
and
Mundus
in
Latine
.
and
thereto
alludeth
Sibyll
in
her
verses
,
speakinge
of
the
dissolution
of
the
worlde
,
saying
:
{αβγδ}
.
Erit
mundus
immundus
,
pereuntibus
hominibus
.
The
worlde
(
saith
she
)
shal
be
vnclean
,
or
leese
his
beuty
,
when
all
men
shal
perish
.
Schollar
.
And
so
dooth
that
sentence
leese
his
beautye
by
the
translation
,
for
there
canne
bee
no
suche
allusion
of
woordes
in
the
englyshe
of
that
sentence
,
as
there
is
in
the
other
tongues
.
Master
.
You
say
truthe
,
except
a
man
wold
rather
allude
at
the
woordes
,
then
expresse
the
sentence
,
for
so
might
it
be
translated
thus
:
It
shall
bee
an
vnworldlye
worlde
,
when
all
men
shall
perishe
:
But
here
the
sense
is
loste
:
for
this
name
Worlde
,
Diuers
significations
of
that
worde
worlde
.
hath
not
the
like
deriuation
of
cleannes
in
englysh
,
as
the
Latine
and
Greeke
names
haue
in
their
tongues
:
nother
can
I
well
tell
wherof
this
englyshe
name
is
deriued
,
although
I
remembre
som
other
significations
of
this
worde
,
as
firste
it
is
vsed
in
Scripture
for
a
name
of
long
continuance
of
tyme
,
when
we
say
:
Worlde
without
ende
.
and
,
thorough
worlde
of
worldes
:
whiche
signifieth
for
euer
.
Also
this
name
dooth
signifye
sometymes
a
greate
wonder
,
as
when
wee
saye
:
It
is
a
worlde
to
see
the
crafte
that
some
menne
vse
vnder
colour
of
simplicitye
.
Nowe
if
anye
man
wyll
contende
,
that
this
worde
Worlde
dooth
principallye
betoken
a
wonder
,
and
that
the
worlde
for
the
wonderfull
shape
of
it
,
tooke
that
name
,
as
the
chieffe
wonder
of
all
wonders
,
I
will
not
greatelye
repine
,
but
then
muste
I
needes
wonder
,
to
see
the
chieffe
worldely
men
to
wonder
so
lyttle
at
this
wonderfull
wonder
,
and
to
bend
all
theyr
studye
to
the
centre
of
the
worlde
,
I
meane
the
Earthe
,
whiche
in
comparison
to
the
whole
worlde
is
not
onlye
a
parte
without
all
notable
quantitye
,
but
also
leaste
adourned
with
meruailous
woorkes
,
and
moste
subiecte
to
all
frayle
transmutation
and
chaunge
,
styll
replenished
with
continuall
corruption
.
And
yet
on
it
only
doth
the
greatest
numbre
set
all
their
studye
.
For
it
they
sustaine
greate
trauaile
and
toyle
:
for
yt
they
chide
,
quarrell
and
fyghte
:
to
gette
it
they
venter
lyfe
and
lymme
,
and
when
they
thynke
moste
assuredlye
that
they
haue
gotten
the
Earthe
,
then
in
deede
the
earthe
hathe
gotten
them
,
and
moste
commonlye
then
doothe
the
earthe
consume
them
,
when
they
thinke
theym selues
fulle
maisters
of
yt
.
Schollar
.
By
these
mennes
trauaile
(
I
thynke
)
it
came
to
passe
,
that
the
earthe
doothe
vsurpe
the
name
of
the
Worlde
,
as
thoughe
it
were
all
,
and
that
besides
it
were
nothinge
.
Master
.
Thereof
commeth
that
common
Prouerbe
of
a
couetous
manne
:
All
the
worlde
is
to
lyttle
for
him
.
where
he
in
deede
seeketh
nothynge
but
the
earthe
,
The
smalenes
of
the
earthe
to
the
whole
worlde
.
whiche
earthe
in
comparison
to
the
whole
worlde
beareth
no
greater
vewe
,
then
a
mustarde
corne
on
Malborne
hylles
,
or
a
droppe
of
water
in
the
Occean
sea
.
for
of
all
the
partes
of
the
worlde
,
the
earthe
is
the
leaste
,
and
that
withoute
comparison
,
as
hereafter
I
shall
not
onlye
tell
you
,
but
also
prooue
it
by
inuincible
reason
.
And
therefore
to
proceede
in
oure
matter
,
I
thynke
it
beste
not
onlye
to
make
discourse
lyghtlye
of
the
principall
partes
of
the
worlde
,
but
to
dooe
it
in
suche
a
brief
sorte
,
as
the
mynde
maye
conceaue
it
soonest
,
The
best
ordre
in
teachinge
.
and
the
memorye
also
retaine
it
longest
:
and
therefore
will
I
omytte
all
proofes
,
tyll
we
haue
ones
generally
drawen
the
ymage
of
the
whole
worlde
,
so
shall
not
your
memory
be
troubled
with
sundrye
thinges
at
ones
,
as
in
learnyng
a
science
whiche
seemeth
sumthing
straunge
,
and
in
conceauyng
the
reasons
of
it
,
whiche
in
declaring
,
seeme
much
more
straunge
.
Scholar
.
In
deed
I
haue
felt
the
discommoditie
of
suche
hasty
desires
:
for
where
I
haue
sought
reason
,
before
I
vnderstoode
,
whereto
that
reason
tended
,
I
haue
troubled
my
mynde
,
and
hyndred
my
knowledge
.
wherefore
it
may
please
you
in
your
ordre
to
procede
.
Master
.
I
haue
all
ready
sayd
,
that
of
all
the
partes
of
the
worlde
the
Earthe
is
the
leaste
:
The
ordre
of
the
elementes
.
wherby
you
may
conceaue
,
that
within
it
is
nothyng
:
for
so
should
that
(
what
so
euer
it
were
)
be
lesser
then
the
earthe
.
but
without
the
earthe
,
dooth
the
Waterlye
,
whiche
couereth
a
greate
parte
of
the
same
:
about
them
bothe
,
dooth
the
Ayer
run
,
and
occupieth
(
as
we
maye
easilye
consider
)
muche
more
roome
,
then
bothe
the
sea
and
the
londe
:
aboue
the
ayer
,
and
rounde
about
it
,
(
after
the
agreement
of
moste
wise
men
)
dooth
the
Fyer
occupye
his
place
.
And
these
foure
,
that
is
,
earth
,
water
ayer
and
fyer
,
are
named
the
foure
elementes
,
that
is
to
say
,
the
fyrste
,
symple
and
originall
matters
,
whereof
all
myxt
and
compounde
bodies
be
made
,
All
thinges
compounde
ar
made
of
the
foure
elementes
.
and
into
whiche
all
shall
tourne
againe
.
Scholar
.
Oftentimes
haue
I
heard
it
,
that
bothe
man
and
beastes
are
made
of
earthe
,
and
into
earthe
shall
retourne
againe
:
but
I
thought
not
that
they
had
been
made
of
water
,
and
muche
lesse
of
ayer
or
fyer
.
Master
.
Of
earthe
only
,
nothinge
is
made
but
earthe
:
for
an
herbe
or
tree
can
not
growe
(
as
all
men
confesse
)
excepte
it
be
helped
and
nourished
with
ayer
conuenient
,
and
due
wateringe
,
and
also
haue
the
heat
of
the
Son
,
and
generally
,
syth
all
thynge
is
maintained
by
his
lyke
,
and
is
destroyed
by
his
contrarye
,
than
if
man
can
not
be
maintained
without
fyer
,
ayer
and
water
,
it
must
needes
appeare
,
that
he
is
made
of
them
,
as
well
as
of
earthe
,
and
so
likewaies
all
other
thinges
that
be
compounde
.
Scholar
.
This
talke
delyteth
me
meruailously
,
so
that
I
can
not
bee
wearye
of
it
,
as
longe
as
it
shall
please
you
to
continue
it
.
Maister
.
This
talke
is
not
for
this
place
,
partly
for
that
it
is
more
physicall
then
astronomicall
:
and
partly
bicause
I
determined
in
this
firste
parte
,
to
omitt
the
causes
and
reasons
of
all
thinges
,
and
brieflie
to
declare
the
partes
of
the
worlde
,
whereof
these
foure
elementes
,
beinge
vncompounde
of
them selfe
,
that
is
simple
and
vnmixt
,
are
accompted
as
one
parte
of
the
worlde
,
The
elementes
are
simple
.
The
elementes
do
alter
dailye
in
their
parts
The
skye
.
The
ordre
of
the
spheres
.
The
seuen
Planetes
.
whiche
therfore
is
called
the
Elementarie
parte
,
and
bicause
those
elementes
do
dailye
in
crease
and
decrease
in
some
partes
of
them
(
though
not
in
all
partes
at
ones
)
and
are
subiecte
to
continuall
corruption
,
thei
are
distinct
from
the
rest
of
the
worlde
,
which
hath
no
suche
alteration
nor
corruption
,
whiche
parte
is
aboue
all
the
foure
elementes
,
and
compasseth
them
about
,
and
is
called
the
Skie
,
or
Welkin
,
&
also
the
Heauens
:
this
part
hath
in
it
diuers
lesser
or
special
parts
,
named
commonly
Spheres
:
as
the
sphere
of
the
Moone
which
is
lowest
,
and
nexte
vnto
the
elementes
:
then
aboue
it
,
the
sphere
of
Mercury
:
and
nexte
to
it
the
sphere
of
Venus
:
then
foloweth
the
Sonne
,
with
his
sphere
:
and
then
Mars
in
his
ordre
:
aboue
him
,
is
Iupiter
:
and
aboue
him
,
is
Saturne
.
These
seuen
,
are
named
the
seuen
Planetes
,
euery
one
hauinge
his
sphere
by
himselfe
seuerallie
,
and
his
motion
also
seuerall
,
and
vnlike
in
time
to
anie
other
.
But
aboue
these
seuen
planetes
,
is
there
an
other
heauen
or
skie
,
whiche
commonly
is
named
the
Firmament
,
and
hath
in
it
an
infinite
numbre
of
starres
,
wherof
it
is
called
the
Starrye
skie
.
and
bicause
it
is
the
eighte
in
ordre
of
the
heauens
or
sphers
,
it
is
named
also
the
Eight
sphere
.
This
heauen
is
manifest
inough
to
all
mennes
eies
,
so
that
no
man
needeth
to
doubte
of
it
,
for
it
is
that
skie
,
wherein
are
all
those
starres
that
we
see
,
except
the
fiue
lesser
planets
,
whiche
I
dyd
name
before
,
that
is
Saturnus
,
Iupiter
,
Mars
,
Venus
and
Mercurye
.
Schollar
.
The
Sonne
and
Moone
also
must
bee
excepte
oute
of
that
numbre
,
for
they
haue
their
spheres
by
them selues
,
as
well
as
the
other
Planetes
.
Master
.
Truthe
it
is
.
but
bicause
no
man
dooth
accompte
them
as
starres
,
therefore
they
neede
none
exception
,
where
mention
is
made
of
starres
onlye
,
where
as
the
other
fiue
smaller
Planets
(
which
I
named
before
)
ar
so
like
to
other
starres
,
that
no
manne
,
but
suche
as
are
of
good
experience
in
Astronomy
,
can
discerne
them
from
the
other
starres
,
Howe
the
Planets
are
knowen
from
other
starres
.
although
manye
men
doo
make
a
difference
of
them
by
twinkelinge
,
affirming
that
the
Fixed
starres
doo
twinkle
,
and
not
the
Planetes
,
with
other
differences
difficult
to
obserue
,
and
scarse
certeine
in
distinction
.
But
this
is
their
moste
certaine
difference
,
that
all
those
starres
,
whiche
be
in
the
firmament
,
do
stande
and
continue
in
one
forme
of
distaunce
eche
from
other
,
and
chaunge
not
their
places
in
their
spere
,
and
therefore
be
they
called
Fixed
starres
:
for
althoughe
thei
go
rounde
aboute
the
worlde
in
24.
houres
,
that
is
euerye
day
ones
,
yet
they
keepe
their
places
in
their
sphere
,
and
tourne
onlye
with
their
sphere
:
or
(
as
Aratus
sayth
)
thei
be
drawen
with
their
heauen
,
wher
as
the
seuen
Planetes
are
not
only
carried
round
about
the
earthe
with
the
like
motion
of
heauen
euery
day
,
but
they
do
moue
of
them selues
,
and
doo
chaunge
their
places
in
their
owne
spheres
,
and
for
that
cause
are
they
called
Planetes
,
that
is
to
say
,
Wanderynge
starres
.
Scholar
.
Oftentimes
haue
I
hearde
this
,
but
yet
can
I
not
tell
howe
to
perceaue
it
.
Maister
.
That
shall
be
referred
to
the
fourth
treatise
,
wher
I
wyll
shewe
you
the
proofe
of
all
that
you
shall
thinke
doubtfull
.
Scholar
.
Yet
I
beseche
you
lette
me
knowe
this
,
Whye
are
those
heauens
called
Spheres
?
for
(
in
my
phantasye
)
they
are
nothinge
like
that
instrument
of
sundrye
cirkles
,
whiche
is
commonly
called
the
Sphere
,
syth
neither
can
I
se
in
them
suche
cyrkles
as
are
in
that
materiall
sphere
:
nother
is
there
in
the
materiall
sphere
anye
suche
representation
of
suche
dyuers
heauens
,
nother
of
suche
varietie
of
starres
.
Maister
.
This
doubte
was
moued
before
nowe
,
by
Ioachim
Ringelbergh
,
in
a
treatise
that
he
wrote
of
the
Sphere
,
but
it
shall
be
answered
easily
by
your selfe
,
after
a
lyttle
declaration
of
the
celestiall
spheres
.
And
for
that
cause
,
I
wyll
omitte
it
tyll
anone
,
and
will
firste
declare
certaine
other
accidentes
of
the
heauens
,
and
of
the
other
partes
of
the
worlde
.
Hitherto
you
haue
hearde
onlye
the
names
of
the
partes
of
the
worlde
,
and
of
their
situation
,
howe
they
be
placed
in
ordre
.
Nowe
for
the
forme
and
shape
of
them
,
you
shall
vnderstande
,
that
the
whole
worlde
is
rounde
exactlye
as
anye
ball
or
globe
,
The
forme
of
the
world
and
his
partes
.
and
so
are
all
the
principall
partes
of
it
,
euerye
sphere
seuerallye
and
ioyntlye
,
as
well
of
the
Planetes
,
as
of
the
Fixed
starres
,
and
so
are
all
the
foure
Elementes
.
depiction of the planetary spheres.
And
they
are
aptely
placed
togither
,
not
as
a
numbre
of
rounde
balles
in
a
nette
,
but
euery
sphere
includeth
other
,
as
they
be
in
ordre
of
greatnes
,
beginning
at
the
eightesphere
or
firmamente
,
and
so
descending
to
the
laste
and
lowest
sphere
,
is
the
Sphere
of
the
Mone
:
vnder
which
the
foure
elementes
succede
:
first
the
fier
,
then
the
ayer
:
nexte
foloweth
the
water
:
which
with
the
earth
ioyntlie
annexed
,
maketh
as
it
were
,
one
sphere
only
.
Scholar
.
This
I
do
well
vnderstande
in
wordes
,
and
the
easier
by
this
picture
,
whiche
I
finde
in
euerie
booke
of
the
Sphere
,
but
that
I
see
there
more
spheres
,
then
you
speake
of
:
for
in
some
bookes
mention
is
made
of
nyne
spheres
:
and
in
other
are
ten
spheres
named
,
where
you
sette
foorthe
but
eighte
.
Master
.
The
cause
of
this
diuersitie
will
I
in
the
fourthe
treatise
declare
:
in
the
meane
season
,
I
thinke
it
best
to
tell
you
of
no
mo
spheres
,
then
are
perceptible
by
sighte
,
for
so
manye
are
we
certaine
of
.
And
therefore
vnderstande
you
thus
,
that
as
the
eihhte
sphere
is
the
greatest
,
and
hath
none
other
without
him
that
maye
be
seene
,
so
the
earthe
is
the
leaste
,
The
earthe
is
the
centre
of
the
worlde
.
and
hathe
none
other
within
hym
,
but
it
standeth
in
the
middle
and
in
the
centre
of
the
whole
worlde
,
and
of
euery
one
of
these
spheres
,
and
therfore
it
is
called
the
Centre
of
the
worlde
:
so
that
although
the
earthe
in
it selfe
haue
a
greate
and
notable
quantity
,
The
earthe
hath
no
quantity
in
respecte
to
the
world
.
yet
in
comparison
to
the
firmament
,
it
is
to
bee
esteemed
but
as
a
centre
or
little
pricke
,
yea
in
deed
muche
lesse
than
any
notable
starre
that
you
see
,
&
if
I
shall
speak
boldly
that
which
I
intend
herafter
to
proue
certainly
,
the
earthe
is
lesser
then
the
leaste
starre
in
the
firmament
whiche
is
commonly
seen
,
but
yet
is
it
greater
thē
Venus
or
Mercury
,
yea
greater
then
the
Moone
.
Schollar
.
This
affirmation
seemeth
to
me
impossible
,
or
at
the
least
contrary
to
sence
:
for
the
Mone
seemeth
bygger
muche
then
any
starre
,
yea
somwhat
bigger
then
the
Sonne
.
Master
.
Content
your selfe
to
credite
me
,
tyll
tyme
serue
for
the
proof
of
my
woordes
,
and
in
the
meane
season
,
to
procede
as
I
began
.
You
must
thinke
,
that
the
earth
and
the
water
annexed
togither
in
one
globe
,
are
of
no
notable
quantitye
,
in
comparison
to
the
firmament
,
and
that
it
stan
deth
as
the
centre
of
the
worlde
,
The
earthe
hath
no
motion
.
and
hath
no
motion
out
of
his
place
,
nother
yet
circular
mouyng
about
his
owne
centre
,
but
resteth
(
as
we
may
say
)
quiete
without
all
such
mouyng
,
Lyke
wayes
must
you
thinke
of
the
other
elementes
,
whiche
of
their
owne
nature
haue
none
other
motion
then
a
stone
or
a
lyghte
fether
,
so
that
they
may
be
accompted
all
four
to
be
without
naturall
motion
.
Scholar
.
Yet
in
the
water
and
in
the
ayer
we
see
euerye
day
notable
mouynge
.
and
sometime
I
haue
hearde
of
mouynge
of
the
earthe
,
by
earthquakes
:
and
as
for
the
fyer
that
we
see
,
it
alwaies
moueth
and
fly
ckereth
in
burninge
.
Master
.
And
so
you
haue
seene
a
stone
moue
swiftelye
,
when
it
fell
from
anye
hyghe
place
.
but
these
motions
haue
an
ende
quicklye
,
excepte
they
be
continued
with
violence
,
as
hereafter
I
will
sufficientlye
declare
.
But
as
the
stone
although
it
wyll
moue
in
fallinge
,
yet
in
his
place
lyeth
quiete
without
motion
:
so
the
earthe
of
it selfe
,
and
the
other
elementes
muste
be
accompted
quyete
by
nature
,
and
without
motion
.
The
motions
of
the
heauens
.
¶
The
heauens
contrarye
wayes
haue
suche
a
naturall
motion
that
neuer
resteth
nyghte
nor
daye
,
nother
can
be
staied
by
any
violence
.
This
motion
wee
se
in
the
heauens
daylye
by
their
mouinge
from
the
easte
to
the
weste
,
and
from
the
weste
to
the
easte
againe
,
aboute
the
earthe
,
ones
euerye
24.
howers
,
and
therfore
is
thys
motion
named
the
Daily
motion
,
for
it
is
the
measure
of
a
Naturall
day
,
A
Daye
.
commonly
accompted
.
and
this
motion
is
lykewayes
called
of
aunciente
writers
the
motion
of
the
First
firmament
,
accordynge
to
whiche
motion
you
see
the
Sonne
in
the
daye
tyme
,
and
the
starres
in
the
nyghte
tyme
,
and
the
Moone
both
in
the
day
and
the
nyghte
,
to
passe
from
the
easte
into
the
southe
,
and
so
into
the
weste
,
and
at
the
ende
of
24.
houres
to
come
againe
into
the
easte
:
wherby
you
may
easily
vnderstand
,
that
this
motion
is
common
to
all
the
spheres
of
heauen
.
Scholar
.
This
maye
all
men
see
,
that
can
see
any
thing
.
yet
haue
I
heard
of
some
so
grossely
witted
,
that
they
doubted
which
way
the
Son
and
the
Moone
dyd
come
into
the
cast
agayne
,
as
though
they
did
not
thinke
that
the
skye
dydde
moue
about
the
earthe
.
Master
.
Suche
grosse
ignorance
happened
somrymes
to
famous
men
,
for
lacke
of
due
consideration
of
that
,
whiche
all
men
maye
see
,
as
I
will
in
place
conueniente
more
largelye
note
.
Schollar
.
Yet
one
doubte
I
haue
,
of
whiche
I
wolde
gladly
be
rydde
,
and
that
is
of
the
Moone
:
for
as
you
saye
,
and
by
syghte
wee
perceaue
,
all
the
starres
with
the
Sonne
and
Moone
go
round
about
the
earth
in
24.
houres
,
A
diuers
motion
in
the
Mone
.
saue
that
the
Moone
is
slacker
then
all
the
rest
,
for
she
is
euerye
daye
later
in
rysynge
by
an
hower
,
then
she
was
the
daye
before
:
but
howe
that
cometh
to
passe
,
I
doo
not
vnderstande
.
Ma.
This
doubt
is
well
moued
,
and
in
good
tyme
,
for
by
it
will
I
take
occasion
to
instruct
you
not
only
in
the
true
knowledge
of
it
,
but
also
of
other
sondrye
motions
in
all
the
heauens
:
for
in
euery
one
of
them
dooth
there
appeare
a
lyke
motion
,
contrarye
to
the
dailye
mouinge
of
the
Firmament
,
whiche
in
the
Moone
is
moste
swiftest
,
and
therefore
may
be
perceaued
daylye
of
all
men
:
but
in
the
Sonne
it
is
not
so
swifte
,
and
therfore
not
so
easilye
perceaued
:
yet
all
men
see
a
greate
alteration
in
the
mouynge
of
the
Sonne
in
one
yeare
:
A
scuerall
mouing
in
the
Sonne
.
for
somtimes
he
is
hygher
and
nearer
ouer
our
headdes
,
and
sometime
farther
from
our
headdes
,
and
lower
in
the
southe
:
yea
sometime
he
shineth
with
vs
almoste
18.
howers
,
(
as
in
the
middle
of
the
Sommer
)
and
in
the
middle
of
Winter
hee
shineth
but
6.
houres
or
lyttle
more
:
this
euerye
childe
dooth
see
,
althoughe
they
knowe
not
the
reason
thereof
.
Scholar
.
Yet
the
reason
of
that
is
easy
inough
to
be
conceaued
,
for
when
the
daye
is
at
the
longest
,
the
Sonne
muste
needes
shine
the
more
tyme
,
and
so
must
it
needes
shine
the
lesser
tyme
,
when
the
day
is
at
the
shortest
:
this
reason
I
haue
hearde
many
men
declare
.
Master
.
That
may
well
be
called
a
crabbed
reason
,
for
it
goeth
backward
lyke
a
crabbe
.
The
day
maketh
not
the
son
to
shyne
,
but
the
Sonne
shynynge
maketh
the
daye
.
And
so
the
lengthe
of
the
daye
maketh
not
the
Sonne
to
shine
longe
,
nother
the
shortenes
of
the
day
causeth
not
the
Son
to
shyne
the
lesser
tyme
,
but
contrarye
waies
the
longe
shyninge
of
the
Sonne
maketh
the
longe
daye
,
and
the
shorte
shyning
of
the
sonne
maketh
the
lesser
daye
:
els
answere
me
,
what
maketh
the
dayes
longe
or
shorte
?
Schollar
.
I
haue
heard
wise
men
say
,
that
Sommer
maketh
the
longe
dayes
,
and
Wynter
maketh
the
longe
nyghtes
.
Master
.
They
myghte
haue
sayde
more
wiselyc
,
that
long
dayes
make
sommer
,
and
shorte
dayes
make
winter
.
Schollar
.
Why
all
that
seemeth
one
thing
to
me
.
Maister
.
Is
it
all
one
to
say
.
God
made
the
earth
.
and
the
carthe
made
God
▪
Couetousnes
ouer
cometh
all
men
.
and
all
men
ouercome
couetousnes
.
Schollar
.
No
not
so
,
for
heere
the
effecte
is
tourned
to
bee
the
cause
,
and
the
agente
is
made
the
paciente
.
Master
.
So
is
it
to
saye
,
Sommer
maketh
longe
dayes
,
where
you
shoulde
saye
:
Longe
dayes
make
sommer
.
Schollar
.
I
perceaue
it
nowe
,
but
I
was
so
blynded
with
the
volgare
erroure
,
that
if
you
hadde
demaunded
of
me
farther
what
dydde
make
the
Sommer
,
I
hadde
beene
lyke
to
haue
aunswered
,
that
greene
leaues
doo
make
Sommer
:
and
the
sooner
by
remembraunce
of
an
olde
sayinge
:
that
a
yeare
shoulde
come
,
in
whiche
the
Sommer
shoulde
not
bee
knowen
,
but
by
the
greene
leaues
.
Master
.
Yet
this
sayinge
dooth
not
importe
that
greene
leaues
do
make
sommer
,
but
they
betoken
sommer
:
so
are
they
the
signe
and
not
the
cause
of
sommer
.
Schollar
.
So
I
perceaue
nowe
that
the
longe
shinynge
of
the
Sonne
doth
make
the
dayes
longe
.
But
nowe
can
I
not
tell
what
causeth
the
Sonne
to
shine
longer
one
tyme
of
the
yeare
,
then
an
other
.
Master
.
That
is
it
that
draue
wise
menne
to
searche
,
and
marke
the
motions
of
the
Sonne
,
whereby
at
lengthe
they
founde
,
that
the
Sonne
hathe
an
other
course
,
contrarye
to
the
daylye
motion
of
the
skye
.
And
as
the
Moone
doth
accomply
she
her
propre
course
(
whiche
is
from
the
west
into
the
easte
,
contrarye
to
the
daylye
motion
)
euerye
moneth
in
the
yeare
,
A
yeare
.
so
the
Sonne
dothe
ende
his
course
,
in
his
propre
motion
,
but
ones
in
the
yeare
.
And
to
expresse
it
aptlye
,
I
muste
saye
,
that
the
true
terme
of
a
yeare
is
nothynge
els
,
but
the
verye
tyme
of
the
course
of
the
Sonne
from
a
certaine
pointe
in
heauen
,
tyll
his
retourne
to
the
same
pointe
againe
.
A
moneth
.
And
a
Moneth
is
the
iuste
time
of
the
propre
course
of
the
Moone
,
from
chaunge
to
chaunge
:
and
euerye
quarter
of
the
Moone
maketh
a
Weeke
.
A
weeke
.
of
whiche
I
will
speake
more
in
the
nexte
treatise
,
with
the
declaration
of
the
diuersitye
for
the
begynninge
of
Monethes
and
Yeares
.
But
nowe
to
contynewe
oure
principall
matter
the
more
ordrelye
,
I
woulde
haue
you
repeate
the
chieffe
articles
of
our
talke
hitherto
.
Schollar
.
This
is
the
summe
of
all
your
doctrine
hytherto
.
The
fyrste
repetition
.
1.
That
the
worlde
is
that
entiere
body
,
which
containeth
in
it
all
the
heauens
and
the
elements
,
with
all
that
in
them
is
.
2.
The
partes
of
the
world
ar
two
especial
,
the
heauens
whiche
are
eighte
in
numbre
,
and
the
elemenents
whiche
are
.iiij.
in
kinde
.
3.
The
ordre
and
situation
of
all
these
partes
,
as
well
elementes
as
heauenly
spheres
,
beginning
at
the
highest
,
and
proceding
to
the
lowest
,
is
this
.
the
Firmanent
,
Saturne
,
Iupiter
,
Mars
,
the
Sonne
,
Venus
,
Mercury
,
and
the
Moone
.
THE
FOVRE
ELEMENTES
.
Fyer
,
Ayer
,
Water
,
and
Earthe
.
and
euer
the
hygher
incloseth
all
that
is
vnder
it
.
4
The
worlde
and
all
his
principall
partes
are
rounde
in
fourme
and
shape
,
as
a
globe
or
ball
.
5.
The
earthe
is
in
the
middle
of
the
worlde
,
as
the
centre
of
it
:
&
beareth
no
vewe
of
quantitye
in
comparison
to
the
worlde
.
6.
The
earthe
hathe
no
motion
of
it selfe
,
no
more
then
a
stone
,
but
resteth
quietly
:
and
so
the
other
elementes
do
,
except
they
be
forceably
moued
.
7.
The
heauens
do
moue
continually
from
the
easte
to
the
west
,
and
that
motion
is
called
,
The
dayly
motion
:
and
is
the
measure
of
the
Common
day
.
8.
The
Mone
hath
a
seuerall
motion
from
the
west
toward
the
easte
,
contrarye
to
that
mouyng
of
the
dailye
course
,
and
that
motion
is
the
iust
measure
of
a
moneth
,
and
euery
quarter
dooth
make
a
weeke
.
9.
The
Son
also
hath
a
peculier
motion
from
the
west
toward
the
easte
,
whiche
he
accomplisheth
in
a
yeare
,
and
of
that
course
the
yeare
taketh
his
measure
and
quantitye
.
Now
then
it
may
please
you
to
procede
to
farther
explication
of
the
apparaunces
which
are
noted
in
the
heauens
,
and
to
shew
the
manner
of
their
motions
.
Master
.
To
the
intent
that
you
may
vnderstand
all
thinges
the
more
easilye
,
A
materiall
sphere
.
I
thinke
it
good
to
describe
vnto
you
a
Materiall
sphere
,
whiche
shall
containe
in
it
suche
notable
cyrcles
only
,
as
haue
speciall
vse
in
the
declaration
of
the
heauenly
motions
,
and
suche
as
reason
shall
driue
a
man
to
appointe
,
as
certaine
boundes
of
the
motions
in
the
heauens
:
yea
suche
I
saye
,
as
your selfe
shall
by
interrogatories
be
constrayned
to
confesse
needfull
to
that
knowledg
which
you
desire
.
Schollar
.
If
nothinge
bee
placed
in
that
sphere
but
that
which
must
needes
be
had
,
then
can
I
not
accompt
any
part
of
it
superfluous
.
And
againe
,
if
it
serue
sufficiently
to
instructe
me
in
that
I
desyre
to
knowe
,
I
canne
not
iustlye
blame
it
in
anye
pointe
as
insufficiente
,
so
muste
it
needes
be
a
perfect
instrument
,
voyde
of
defaulte
,
and
without
superfluitye
.
Master
.
So
shall
it
be
,
for
so
muche
as
this
parte
of
knowledge
requireth
.
Now
then
to
begin
.
ye
doo
beleue
that
the
worlde
is
rounde
.
Schollar
.
Yea
for
soothe
.
Master
.
The
makig
of
a
Globe
.
Then
must
that
instrument
also
be
round
,
which
shall
aptelye
expresse
the
forme
of
the
worlde
.
Schol
.
Truth
it
is
.
Mast
.
Can
there
be
any
thinge
more
round
then
a
circle
?
Schollar
.
No
trulye
.
Maister
.
And
dooth
not
twoo
halfe
cyrcles
make
a
whole
circle
?
Schollar
.
It
can
not
be
denayed
.
Master
.
Then
take
halfe
a
circle
,
and
fasten
it
on
an
axtre
or
on
any
diameter
,
and
then
tourne
it
rounde
about
,
fyrste
lettyng
the
halfe
cyrcle
hang
downward
vnder
the
diameter
Geometrical diagram.
as
heere
you
se
it
Geometrical diagram.
figured
,
in
the
halfe
cirkle
A
B
,
C.
then
tourne
the
half
cyrcle
right
vp
ouer
the
diameter
,
as
here
also
is
represented
in
the
halfe
cyrcle
A
,
D
,
C.
do
not
these
two
positions
make
a
whole
cyrcle
?
Scholar
.
Yes
surely
.
Master
.
Then
set
the
halfe
circle
so
,
that
the
diameter
may
stande
styll
firmelye
fixed
,
and
the
halfe
cyrcle
maye
tourne
rounde
about
.
Do
not
you
imagin
nowe
that
euery
dyuers
position
of
this
halfe
cyrcle
with
the
contrary
place
against
it
,
dooth
make
a
whole
cyrcle
.
Schollar
.
Yes
verelye
.
Master
.
And
bycause
there
is
no
place
round
aboute
that
diameter
,
within
the
reache
of
that
halfe
circle
,
but
that
half
circle
hathe
passed
it
,
there
can
no
voyde
place
be
assigned
but
it
is
occupied
and
fylled
with
halfe
a
cyrcle
,
and
euerye
halfe
cyrcle
with
his
contrarye
dooth
make
a
whole
cyrcle
,
so
doth
this
whole
reuolution
of
the
halfe
circle
make
a
iust
cyrcular
bodye
.
Here
is
the
lyke
fourme
of
that
worke
.
diagram expressing the form of a sphere.
Schollar
.
So
it
appeareth
trulye
.
Maister
.
A
Sphere
is
defined
.
This
circular
body
is
named
a
sphere
,
as
it
may
appeare
by
the
description
that
Euclide
maketh
of
a
sphere
:
whiche
is
this
in
greeke
,
as
him selfe
wrote
it
,
in
his
eleuenth
booke
of
Geometrye
.
{αβγδ}
Whiche
into
Latine
may
well
be
translated
thus
.
Sphaera
est
figura
comprehensa
ex
circumductu
semicirculi
,
donec
eò
redeat
,
vnde
moueri
incoepit
,
manente
interim
immota
semicirculi
eius
diametro
.
And
thus
it
soundeth
in
englishe
.
A
Sphere
is
a
sound
figure
,
made
by
the
tournynge
of
half
a
circle
,
tyll
it
ende
where
it
began
to
be
moued
,
the
diameter
of
that
halfe
circle
continuyng
steddye
all
the
meane
whyle
.
This
description
dooeh
Ioannes
de
Sacro
bosco
expounde
thus
:
that
a
sphere
is
a
rounde
and
sound
body
made
by
the
tournynge
of
halfe
a
circle
.
Schollar
.
So
that
a
sphere
is
nothinge
els
but
a
rounde
and
massye
bodye
closed
with
one
plat
forme
,
whiche
you
in
your
Pathwaye
doo
call
a
Globe
.
Master
.
The
centre
of
a
Globe
or
Sphere
.
You
take
it
ryghte
.
But
nowe
must
you
marke
,
that
as
a
circle
is
made
about
his
centre
,
so
a
globe
also
hath
his
centre
,
as
you
may
easilye
vnderstande
,
from
which
center
all
the
lynes
that
may
be
drawen
to
the
plat
forme
,
or
vtter
parte
of
the
globe
,
are
all
equall
togither
,
accordyng
to
Theodosius
definition
,
whiche
saythe
thus
:
A
sphere
is
a
massye
bodye
,
inclosed
with
one
plat
forme
,
and
in
the
middle
of
it
there
is
a
pricke
,
from
which
all
lynes
drawen
to
the
sayde
plat
forme
,
are
equall
eche
to
other
,
and
that
pricke
is
the
centre
of
the
globe
and
so
sayth
Euclide
also
.
{αβγδ}
.
Idem
centrum
sphaerae
est
,
quod
&
semicirculi
.
The
centre
of
a
globe
is
the
same
centre
that
a
semicircle
hath
,
by
whiche
the
globe
was
made
.
Schollar
.
It
muste
needes
bee
so
:
and
lykewaies
the
diameter
of
them
bothe
muste
needes
be
all
one
,
as
I
thynke
.
Maister
.
You
saye
not
muche
amysse
.
Yet
must
you
put
a
difference
in
a
globe
,
A
Diameter
and
an
Axe
tree
differ
.
betwene
a
Diameter
and
an
Axe
tre
.
For
euery
right
lyne
that
passeth
from
side
to
syde
in
a
globe
,
and
toucheth
the
centre
,
is
aptely
called
a
diameter
.
so
that
as
ther
may
be
many
diameters
in
a
cyrkle
,
so
may
ther
be
as
many
also
in
a
Globe
:
But
of
all
that
multitude
,
one
only
is
called
the
Axe
tree
,
and
that
is
it
on
whiche
the
globe
tourneth
.
This
difference
did
Ioannes
de
Sacro
bosco
ouerpasse
not
ignorantly
,
but
negligently
,
or
els
wittingly
:
but
so
dyd
not
Euclide
,
whiche
defineth
them
bothe
thus
.
An
axe
tre
{αβγδ}
.
Axis
Sphaerae
est
,
recta
illa
stabilis
linea
,
circa
quam
semicirculus
rotatur
.
diagram showing a sphere on an axis.
The
Axe
tree
(
saith
he
)
is
that
righte
lyne
whiche
moueth
not
,
but
the
halfe
cirkle
moueth
aboute
it
.
These
wordes
haue
respect
not
only
to
the
makynge
of
a
Globe
or
Sphere
,
but
also
to
the
vse
of
it
.
But
now
the
diameter
is
defined
by
him
thus
:
{αβγδ}
.
A
diameter
Dimetiens
vero
Sphaerae
est
recta
quae{qu}
linea
per
centrum
acta
,
&
vtrinque
desinens
in
sphaerae
superficie
:
Geometrical diagram.
The
diameter
of
a
Sphere
,
is
anye
ryghte
lyne
that
is
drawen
by
the
centre
,
and
ended
in
the
plat
forme
of
the
sphere
.
Schollar
.
This
difference
muste
needes
seeme
reasonable
,
syth
there
maye
be
so
many
diameters
drawen
as
a
man
lysteth
,
but
Axe
trees
there
can
be
but
one
in
one
globe
.
Maister
.
When
a
globe
tourneth
rounde
,
are
there
anye
mo
poyntes
then
twoo
in
that
globe
,
on
whiche
it
doothe
tourne
?
Schollar
.
By
proof
it
appeareth
,
that
all
partes
of
the
globe
moue
,
excepte
the
two
endes
of
that
Axe
tree
,
wheron
it
mooueth
,
and
they
mooue
not
out
of
their
place
.
Master
.
Poles
of
a
Sphere
.
Those
twoo
pointes
are
named
the
poles
in
a
sphere
,
wherby
also
you
may
vnderstande
,
that
there
can
be
but
two
poles
in
one
sphere
:
marke
this
well
,
for
it
will
serue
your
turne
in
place
conueniente
.
Nowe
applye
all
these
to
the
worlde
,
whiche
in
his
whole
substaunce
is
rounde
,
and
therefore
aptelye
maye
bee
called
a
sphere
:
yow
see
it
tourne
aboute
rounde
,
and
therefore
must
it
haue
twoo
poles
,
on
whiche
it
tourneth
so
.
Also
bicause
it
is
rounde
,
it
muste
haue
a
centre
(
whiche
I
dyd
affirme
before
to
bee
the
earthe
)
and
by
this
centre
,
we
may
imagine
a
right
line
to
run
from
the
one
pole
to
the
other
,
whiche
righte
lyne
muste
be
called
the
Axe
tre
of
the
worlde
.
Schollar
.
For
the
centre
of
the
worlde
,
it
muste
needes
be
somthinge
:
for
I
perceaue
a
globe
can
not
be
,
but
it
must
necessarily
haue
a
middle
pricke
or
centre
,
no
more
then
a
lyne
maye
be
made
whiche
hath
no
myddell
,
or
a
circle
that
hathe
no
centre
:
whiche
bothe
appeare
vnpossible
.
Also
for
the
pooles
,
they
appeare
needefull
,
or
rather
of
necessity
to
folowe
the
mouinges
of
heauen
.
For
in
all
rounde
thinges
that
mooue
roundly
,
there
be
suche
two
pointes
that
seeme
not
to
moue
:
but
why
there
shoulde
be
any
axe
tree
requyred
in
the
worlde
,
I
see
no
reason
:
for
if
the
myghtye
power
of
God
dyd
not
staye
the
worlde
,
there
coulde
bee
no
Axe
tree
able
to
beare
it
.
Master
.
Your
imagination
in
this
pointe
is
to
grosse
.
I
sayde
not
that
the
Axe
tre
was
made
to
stay
the
worlde
,
but
that
it
passeth
as
a
lyne
only
from
the
one
pole
to
the
other
:
and
is
not
without
greate
and
profitable
vse
,
bothe
in
doctrine
,
and
also
in
practise
,
for
placynge
of
instruments
,
as
you
shall
know
better
hereafter
.
But
nowe
heare
howe
Proclus
dooth
applye
these
to
the
worlde
.
{αβγδ}
.
Whiche
wordes
our
worthye
contrye
man
D.
Linaker
,
translateth
thus
.
Axis
mundi
vocatur
dimetiens
ipsius
,
circa
quam
voluitur
.
Axis
extrema
,
poli
mundi
(
seu
vertices
)
sunt
nominati
:
horum
alter
Septentrionalis
,
alter
Austrinus
dicitur
.
The
Axe
tree
of
the
worlde
,
is
named
the
Diameter
of
it
,
aboute
whiche
it
tourneth
.
The
north
and
southe
Poles
.
and
the
endes
of
that
Axe
tree
,
are
called
the
Poles
of
the
world
.
of
whiche
poles
one
is
named
the
Northe
pole
,
and
the
other
the
South
pole
.
The
North
pole
is
alwaies
seene
of
vs
where
as
we
dwell
,
and
the
Southe
pole
is
neuer
seene
in
this
oure
contrye
,
but
is
euer
more
vnder
our
Horizonte
,
and
that
as
lowe
,
as
the
Northe
pole
is
highe
aboue
our
Horizonte
.
Schollar
.
I
haue
beene
taughte
to
knowe
the
Northe
pole
,
and
I
haue
marked
it
oftentimes
,
wherby
I
perceaued
a
great
numbre
of
starres
to
moue
aboute
it
,
and
were
sometymes
higher
then
it
,
and
sometymes
lower
then
it
:
nowe
on
the
easte
syde
of
it
,
and
nowe
on
the
west
syde
:
but
that
pole
starre
seemed
not
to
sturre
oute
of
his
place
at
anye
tyme
:
whereby
I
gather
,
that
he
is
neuer
oute
of
sighte
to
vs
,
when
the
starres
appeare
,
and
that
is
all
the
nyghte
.
but
what
becommeth
of
him
in
the
daye
tyme
,
I
can
not
tell
.
Master
.
I
wyll
cleere
you
of
all
suche
doubtes
before
I
leaue
you
:
The
Horizonte
.
but
in
the
meane
tyme
I
meruaile
you
founde
no
doubte
at
the
name
of
the
Horizonte
.
Schollar
.
That
name
I
learned
to
signifye
that
cyrcle
,
whiche
goeth
along
by
the
edge
of
the
ground
,
and
parteth
that
parte
of
the
worlde
whiche
we
see
,
from
that
part
which
we
se
not
:
&
when
the
Son
riseth
,
then
is
he
in
our
horizonte
,
&
so
is
he
,
when
he
is
goyng
downe
as
lowe
as
we
can
see
him
.
Master
.
This
is
not
greatlye
amisse
.
the
lyke
expressynge
Here
the
Horizonte
is
represented
by
the
lyne
A.
C.
Geometrical diagram.
of
it
dooth
Hyginius
vse
in
his
fyrste
booke
,
and
in
the
.iiij.
also
of
his
astronomye
:
but
Proclus
in
his
Sphere
,
dooth
define
it
thus
.
{αβγδ}
.
Horizon
vero
circulus
est
,
qui
conspectam
mundi
partem
ab
inconspecta
dirimit
:
itaque
in
duas
partes
vniuersam
Sphaeram
secat
,
vt
alterum
hemisphaerium
supra
terram
,
alterum
sub
terra
relinquat
.
The
Horizonte
is
a
cyrcle
whiche
parteth
that
parte
of
the
worlde
that
wee
see
,
from
that
whiche
wee
see
not
:
and
it
deuideth
the
whole
And
here
the
Horizonte
is
the
edge
betwene
the
lyght
parte
(
whiche
standeth
for
that
whiche
wee
see
)
and
the
darke
part
whiche
dooth
signifie
that
whiche
wee
can
not
see
of
the
skye
.
Geometrical diagram.
sphere
of
the
world
into
twoo
equall
partes
,
in
suche
sorte
,
that
half
of
that
sphere
is
euer
abooue
the
grounde
,
&
halfe
alwaies
vnder
the
earthe
.
This
cyrcle
you
perceaue
to
be
necessary
in
the
materiall
sphere
,
seynge
it
hath
so
greate
vse
in
the
heauenly
motions
,
that
by
it
we
iudge
the
risynges
and
settings
of
the
Sonne
and
the
Moone
and
all
other
starres
.
what
say
you
then
for
the
noone
steede
of
the
day
,
from
whiche
you
recken
all
your
houres
,
as
it
appeareth
both
by
the
clockes
and
dyals
?
for
as
the
clocke
striketh
one
nexte
after
noone
,
The
meridian
circle
and
so
in
creaseth
forward
in
the
numbre
of
houres
,
so
likewaies
are
your
howers
marked
in
the
dialles
.
Schollar
.
I
thinke
it
very
meete
to
haue
the
south
pointe
well
knowen
,
as
well
for
this
,
as
for
standynge
dialles
,
and
for
knowledge
of
the
tyme
of
the
nyght
by
the
moone
,
and
by
other
starres
.
Maister
.
Then
muste
there
be
a
circle
appointed
for
that
vse
,
whiche
is
called
therfore
the
Meridiane
circle
,
and
may
be
named
well
the
Noone
steede
cyrcle
.
The
Nonesteed
circle
This
circle
is
thus
defined
by
Proclus
.
{αβγδ}
.
Meridianus
circulus
est
,
qui
per
mundi
polos
&
punctum
,
quod
nobis
supra
verticem
eminet
,
ducitur
.
in
quem
cum
solincidit
,
medios
dies
,
mediasque
noctes
efficit
.
The
Meridian
is
a
cyrcle
drawen
by
the
poles
of
the
world
,
&
the
point
right
ouer
our
heads
.
in
which
circle
when
the
Son
is
,
he
maketh
the
myddle
of
the
day
,
&
the
middle
of
the
nyghte
.
Nowe
farther
to
procede
to
other
partes
needfull
in
the
sphere
.
you
do
se
,
that
twise
The
Meridiane
cyrcle
here
is
resembled
to
the
circle
,
A
,
B
,
C
,
D.
Geometrical diagram.
in
the
year
the
daies
&
nights
ar
equall
,
&
the
Son
riseth
in
the
iust
east
,
&
goeth
doune
in
the
full
west
,
wher
as
in
the
sommer
the
Son
riseth
northeast
,
and
setteth
northweste
:
&
at
nonetide
is
very
high
ouer
our
heds
:
but
in
the
winter
,
contrary
ways
the
son
riseth
south
east
,
&
setteth
southwest
:
&
at
nonetide
is
very
low
.
thynk
you
not
that
these
thre
boundes
of
the
course
of
the
Son
would
be
well
noted
,
and
haue
their
peculiar
circles
,
for
distinction
of
those
tymes
?
Schollar
.
I
thynke
nothinge
more
needefull
then
that
.
Master
.
These
thre
circles
(
with
two
other
that
I
will
next
speake
of
)
are
named
the
fiue
Paralelles
:
and
the
middle
circle
of
those
,
is
named
the
Equinoctiall
,
bicause
that
when
the
Sonne
is
vnder
it
,
the
dayes
and
nyghtes
are
equall
in
all
the
worlde
,
except
only
twoo
places
.
This
circle
is
thus
defined
by
Proclus
.
The
Equinoctial
circle
{αβγδ}
.
Aequator
,
circulus
is
est
,
qui
maximus
aequidistatium
circulorum
statuitur
,
ita
nimirum
ab
Horizonte
dissectus
,
vt
alter
eius
semicircultie
supra
terram
,
alter
sub
terra
condatur
:
in
hoc
sol
duplex
aequinoctium
,
vernum
autumnaleque
facit
.
The
equinoctiall
circle
is
the
greatest
of
the
fiue
Parallele
circles
,
and
is
deuided
so
equallye
into
two
partes
,
by
the
Horizonte
,
that
the
one
halfe
of
it
is
aboue
grounde
,
and
the
other
is
vnder
the
horizonte
:
and
when
the
Sonne
is
in
this
circle
,
he
maketh
the
daies
equall
with
the
nightes
,
ones
in
the
Springe
tyme
,
and
againe
in
the
Haruest
.
This
equinoctiall
circle
and
the
other
seuen
that
folowe
,
to
be
declared
,
doo
moue
all
as
the
skye
moueth
.
but
the
Horizonte
and
the
Meridian
doo
not
moue
with
the
heauen
,
but
stand
stedye
,
and
keepe
their
places
.
Schollar
.
That
seemeth
reasonable
,
els
coulde
not
men
knowe
the
risyng
,
setting
,
and
noonesteed
of
the
Sonne
.
but
howe
shall
I
knowe
this
equinoctiall
circle
in
heauen
,
seynge
I
can
not
see
any
suche
circle
there
?
Master
.
Howe
to
knowe
the
place
of
the
circle
equinoctial
Marke
the
course
of
the
Sonne
aboute
the
eleuenth
daye
of
Marche
,
or
els
about
the
fourtenth
daye
of
Septembre
,
and
so
may
you
best
vnderstande
the
place
of
this
circle
,
for
at
those
two
tymes
the
Sonne
runneth
directly
vnder
the
equinoctiall
circle
,
and
dothe
(
as
it
were
)
describe
it
by
his
motion
,
in
four
and
twenty-howers
.
And
if
you
lyste
do
marke
the
rysinge
of
the
sonne
that
daye
,
you
maye
know
the
precise
pointe
of
the
easte
,
and
at
nyghte
he
setteth
in
the
iuste
poynt
of
the
weste
.
Schollar
.
I
woulde
I
knewe
as
good
markes
of
the
other
cyrcles
.
Master
.
So
wyll
I
geue
you
in
their
conuenient
places
and
times
good
orders
to
know
them
al
:
and
first
I
must
tel
you
,
that
these
other
two
cyrcles
,
which
I
named
before
(
with
the
equinoctiall
)
are
called
the
twoo
Tropike
cyrcles
after
the
greeke
deriuation
,
The
knowledg
of
the
ij
.
tropikes
and
maye
be
called
in
englyshe
the
Sonne
boundes
,
bycause
the
Sonne
doth
neuer
passe
them
,
nother
towardes
the
northe
,
nor
yet
toward
the
southe
:
but
when
he
toucheth
any
one
of
them
,
he
doth
tourn
his
course
toward
the
other
.
as
for
example
:
All
the
tyme
from
the
myddle
of
December
vntill
the
eleuenth
daye
of
Iune
,
you
maye
perceaue
the
Sonne
to
ryse
higher
Examples
of
those
circles
and
other
that
foloweth
.
diagram of the circles of latitude on the celestial sphere.
-
A
,
C.
the
Horizonte
.
-
**
The
poles
of
the
worlde
.
-
G
,
H.
The
Equinoctiall
circle
.
-
B
,
F
,
one
tropike
,
and
-
E
,
D.
the
other
tropike
.
-
A
,
The
Sommer
tropike
.
I
,
the
artike
circle
,
-
C
,
K.
the
antartike
circle
.
and
hygher
,
and
that
daye
hee
is
at
the
hyghest
that
hee
canne
go
towardes
our
heads
,
and
then
dooth
hee
by
his
course
describe
that
Sommer
tropike
,
after
whiche
daye
hee
draweth
agayne
lower
and
lower
euerye
daye
,
tyll
the
twelfte
daye
of
December
,
for
then
he
is
at
the
lowest
,
and
that
daye
he
doth
describe
the
Winter
tropike
.
Nowe
marke
howe
Proclus
defineth
them
.
The
winter
tropik
{αβγδ}
,
Linacer
nimium
coactè
commune
no
men
utrique
tropico
ae
stiuo
vni
tribuit
,
Plimum
importunè
secutus
.
*
Solstitialis
autem
circulus
is
est
,
qui
omnium
,
qui
à
sole
describuntur
maximè
septemtrionalis
habetur
.
in
quem
quum
se
sol
receperit
,
aestiuam
ceciprocationem
peragit
,
longissimusque
totius
anni
dies
,
breuissimaque
noxerit
.
post
hancautem
reciprocationem
,
nequaquam
vltra
versus
septemtriones
solem
progredi
,
quin
potius
ad
diuer
sa
mundi
regredi
cernas
.
vnde
&
Tropico
graecenomen
.
The
Sommer
tropike
is
the
moste
northerlye
circle
of
all
thē
that
the
Sonne
describeth
:
in
the
which
when
the
Sonne
is
,
he
maketh
his
Sommer
turne
,
at
which
time
is
the
longest
day
of
al
the
year
,
and
the
shortest
night
:
for
after
this
Sommer
turne
,
you
se
the
Sonne
go
no
more
toward
the
north
,
but
turneth
to
the
contrary
coaste
of
the
worlde
,
and
therof
is
that
circle
named
(
in
greeke
)
a
Tropike
:
that
is
to
saye
,
a
Returninge
circle
,
or
a
circle
of
Returne
.
The
Sonne
aftter
he
beginneth
to
turne
,
maye
be
perceaued
euery
day
,
or
at
the
least
euery
weeke
,
and
chiefly
at
nonetide
to
waxe
lower
&
lower
,
vntill
he
come
to
the
Winter
tropike
,
and
there
he
turneth
againe
,
as
by
the
definition
of
that
tropike
you
may
vnderstande
.
The
winter
tropik
.
{αβγδ}
.
Brumalis
circulus
is
est
,
qui
omnium
circulorum
qui
à
Sole
circumactu
mundi
describuntur
,
maximè
ad
austrum
pertinet
:
in
quo
sol
brumalem
reciprocationem
facit
,
maximaque
totius
anni
nox
,
minimusque
dies
efficitur
.
post
hanc
metam
nequaquam
vltra
progreditur
*
sol
,
Intellige
versus
austrum
quod
&
graecè
additur
.
sed
ad
alteras
mundi
partes
reuertitur
:
vnde
tropicus
hic
quoque
,
quasi
versilis
,
appellatur
.
The
winter
tropike
,
sayth
Proclus
,
is
the
moste
southerlye
circle
of
all
them
that
the
Sonne
doth
describe
,
by
the
reuolution
of
the
worlde
,
in
whiche
when
the
Sonne
is
,
hee
maketh
his
Winterly
tourne
,
and
then
is
the
longest
nyghte
in
all
the
year
,
and
the
shortest
day
,
for
after
this
Winter
turn
,
the
Sonne
is
not
seene
to
go
any
farther
towarde
the
south
,
but
tournith
to
the
contrarye
coastes
of
the
worlde
,
and
thereof
is
this
cyrcle
also
named
a
Tropike
or
cyrcle
of
Retourne
.
And
thus
haue
we
the
three
circles
that
are
principallye
noted
for
the
course
of
the
Sonne
.
The
southe
and
northe
circles
.
Nowe
are
there
other
twoo
whiche
be
Paralleles
with
these
thre
,
whereof
the
one
is
more
southerlye
(
to
vs
)
then
is
the
Winter
tropike
,
and
the
other
is
more
northerly
,
thē
is
the
Sommer
tropik
,
whiche
whether
they
be
needfull
or
not
,
their
vse
maye
declare
.
I
remembre
,
that
you
sayd
,
you
had
oftentymes
beholden
the
Northe
pole
,
where
you
myghte
see
manye
starres
about
it
,
that
neuer
go
vnder
our
Horizont
.
do
you
not
thinke
it
good
that
all
those
starres
were
inclosed
in
a
circle
to
be
discerued
from
al
other
,
which
rise
somtime
aboue
the
Horizont
,
and
somtime
againe
do
set
vnder
the
same
?
Schollar
.
Yes
verilye
,
it
were
pleasaunt
to
know
.
Mast
.
And
profitable
also
,
as
you
shal
hereafter
perceaue
.
Now
contrary
waies
,
The
vse
of
the
Arctik
and
Antarctik
circles
there
are
other
starres
,
that
are
neuer
seene
of
vs
in
this
cuntrye
,
and
yet
muche
mention
is
made
of
them
in
writers
,
were
it
not
good
that
their
bounde
were
marked
,
that
all
other
maye
be
knowen
from
them
?
Schollar
.
Els
myghte
men
often
looke
for
suche
starres
as
they
reade
of
,
and
shulde
loose
their
labour
,
for
they
shall
not
see
them
.
Master
.
And
yet
are
there
goodlye
bryghte
and
notable
starres
,
whiche
are
not
seene
here
,
but
in
southe
Spaine
,
in
Barbary
,
in
Guinea
and
Calecut
,
and
many
other
cuntries
,
they
appeare
fayre
and
pleasaunt
to
beholde
.
Scholar
.
I
pray
you
,
what
call
you
those
cyrcles
that
incloseth
those
starres
?
Master
.
They
are
named
after
the
coaste
of
the
worlde
where
they
bee
.
So
that
the
circle
whiche
incloseth
all
those
starres
that
be
about
the
Northe
pole
,
is
named
the
Arctyke
circle
or
Northe
circle
:
and
the
contrary
circle
in
the
south
,
is
called
the
Antartike
circle
by
the
greeke
composition
,
as
you
woulde
say
,
Contrary
or
against
the
Arctike
circle
:
and
it
may
well
be
called
the
South
circle
.
But
nowe
heare
howe
Proclus
defineth
them
.
The
Arctik
circle
.
{αβγδ}
.
Septentrionalis
circulus
est
is
,
qui
omnium
quos
perpetuo
cernimus
,
planè
maximus
est
,
quique
Horizontem
solo
puncto
contingit
,
totus
supra
terram
interceptus
.
intra
hunc
quaecunque
clauduntur
astra
,
nec
ortum
nec
occasum
norunt
,
sed
circa
polum
uerti
tota
nocte
cernuntur
.
The
Arctike
cirle
is
the
greattest
of
all
those
circles
whiche
do
alwaies
appear
,
and
toucheth
the
Horizonte
in
one
only
pointe
,
and
is
all
togither
aboue
the
earthe
,
and
all
the
starres
that
bee
within
this
circle
nother
rise
nother
sette
,
but
are
seene
to
runne
rounde
about
the
Pole
all
the
nyghte
.
Thus
haue
you
the
fourth
parallele
,
Nowe
resteth
the
fyfte
whiche
is
described
thus
of
Proclus
.
The
Antarctik
circle
.
{αβγδ}
.
Antarcticus
vero
circulus
aequalis
&
aequidistans
Septentrionali
circulo
est
,
&
Horizontavno
puncto
contingens
.
totus
praeterea
sub
terris
mersus
,
intra
quem
sita
astra
semper
nobis
occulta
manent
.
The
Antartike
circle
is
equall
and
equidistant
to
the
Arctike
circle
,
and
toucheth
the
Horizonte
in
one
only
point
,
and
is
all
vnder
grounde
,
and
all
the
starres
that
be
in
it
,
are
euer
more
out
of
our
sighte
.
These
are
al
the
Paralleles
which
are
wont
to
be
set
forthe
in
the
materiall
sphere
,
and
that
agreeably
of
all
men
,
saue
that
touchinge
the
two
laste
circles
there
is
a
difference
,
of
which
I
will
instruct
you
at
large
in
the
next
part
of
our
talke
,
and
omitting
it
for
this
time
,
will
go
forward
to
other
thre
circles
whiche
yet
remaine
,
The
zodiake
.
and
are
needfull
to
oure
sphere
.
Bycause
oure
chieffe
consideration
consisteth
aboute
marking
of
the
motions
of
the
Sonne
,
the
Moone
and
the
other
planetes
,
howe
they
chaunge
their
places
in
the
skye
,
and
therfore
make
diuers
apparaunces
to
vs
that
beholde
them
,
and
mark
their
courses
,
and
yet
all
they
haue
(
as
it
were
)
one
common
path
or
waye
,
from
whiche
they
swarue
not
,
but
kepe
them selues
still
within
the
limites
of
it
:
how
think
you
is
not
that
path
of
theirs
well
to
be
marked
,
and
worthy
to
haue
a
notable
name
?
Schollar
.
Mary
that
is
the
principall
pointe
(
as
I
take
it
)
of
all
the
reste
:
for
without
knowledge
of
that
,
nothing
els
can
be
knowen
.
Master
.
That
common
path
of
the
Planets
,
wherin
all
thei
haue
their
course
,
is
called
of
Astronomers
the
Zodiake
:
whiche
is
,
The
.xij.
signes
.
as
you
maye
englishe
it
,
the
Circle
of
the
Signes
:
whiche
signes
are
the
greatest
and
notablest
partes
of
that
circle
,
and
were
inuented
for
the
more
exacte
distinction
of
the
motion
of
the
Planetes
monethlye
.
For
as
there
bee
but
twelue
monethes
in
the
yeare
,
so
there
are
twelue
partes
of
the
Zodiake
distincte
by
seuerall
names
,
and
correspondent
to
euery
moneth
,
althoughe
they
varye
something
now
from
their
first
application
,
wherof
hereafter
I
will
instructe
you
sufficiently
.
and
now
will
touch
them
briefly
as
this
place
doth
require
.
Their
order
in
the
zodiak
and
their
names
ar
these
that
folow
,
in
greek
and
latin
,
which
maye
bee
englished
as
I
haue
vnder
written
,
and
are
often
tymes
mentioned
of
our
english
Poetes
.
{αβγδ}
.
|
{αβγδ}
.
|
{αβγδ}
.
|
{αβγδ}
.
|
{αβγδ}
.
|
{αβγδ}
.
|
Aries
.
|
Taurus
.
|
Gemini
.
|
Cancer
.
|
Leo
.
|
Virgo
.
|
the
Ramme
.
|
the
Bull
.
|
the
Twinnes
.
|
the
Crabbe
.
|
the
Lyon
.
|
the
Virgin
.
|
♈
|
♉
|
♊
|
♋
|
♌
|
♍
|
{αβγδ}
.
|
{αβγδ}
.
|
{αβγδ}
.
|
{αβγδ}
.
|
{αβγδ}
.
|
{αβγδ}
.
|
Libra
.
|
Scorpius
.
|
Sagittarius
.
|
Capricornus
.
|
Aquarius
.
|
Pisces
.
|
the
Balance
.
|
the
Scorpion
.
|
the
Archer
.
|
the
Goate
.
|
the
waterman
.
|
the
Fishes
.
|
♎
|
♏
|
♐
|
♑
|
♒
|
♓
|
And
bicause
that
their
names
alwaies
can
not
bee
placed
in
small
instrumentes
,
there
ar
certain
figures
deuised
for
their
names
,
whiche
I
haue
also
sette
vnder
their
names
,
that
you
maye
the
better
knowe
them
.
The
degrees
of
the
signes
.
These
Signes
are
all
of
one
lengthe
,
eche
beynge
the
iuste
twelfte
parte
of
the
Zodiake
.
And
for
exacter
knowledg
of
the
motion
of
the
planettes
euerye
daye
,
eche
Signe
is
deuyded
into
thyrtye
equall
partes
,
which
are
called
Degrees
,
so
that
in
the
whole
circuite
of
the
zodiake
there
must
bee
360
degrees
,
whiche
agree
almost
with
the
dayes
of
the
yeare
.
Scholar
.
And
therby
I
gather
,
that
as
the
Son
doth
moue
throughout
all
the
zodiake
in
a
yeare
,
so
euerye
moneth
he
moueth
,
he
runneth
one
signe
,
&
euery
daye
nere
one
degree
.
Master
.
You
gether
well
,
but
this
muste
you
marke
also
,
that
by
this
same
nombre
of
degrees
all
the
cyrcles
in
the
sphere
are
deuided
,
so
that
of
euery
circle
greate
or
lesse
,
what
a
degree
is
in
measure
.
a
degree
is
the
360
parte
and
not
anye
measure
certaine
,
as
a
foote
,
a
yarde
,
a
myle
,
or
suche
lyke
.
Schollar
.
I
vnderstande
you
thus
:
as
a
quarter
is
no
measure
certaine
,
but
sometyme
is
referred
to
one
thinge
,
and
sometime
to
an
other
,
and
yet
still
it
betokeneth
the
fourth
parte
of
that
whervnto
it
is
referred
,
for
when
we
say
:
a
year
and
a
quarter
:
an
houre
and
a
quarter
:
a
yard
and
a
quarter
:
a
quarter
of
a
foote
:
in
all
these
sayings
,
the
quarters
differ
.
so
when
wee
saye
:
a
quarter
of
corne
:
a
quarter
of
clothe
:
a
quarter
of
pepper
:
a
quarter
of
allame
:
by
the
accustumed
measures
all
men
vnderstande
our
meanynge
,
and
yet
these
quarters
differ
,
and
be
in
common
meaning
,
a
quarter
of
a
weye
,
or
eight
bushels
,
a
quarter
of
a
yarde
,
a
quarter
of
a
pounde
,
a
quarter
of
a
hundreth
.
Master
.
So
is
a
degree
the
thirteth
parte
of
a
signe
,
and
a
signe
the
twelfte
parte
of
any
circle
.
howe
be
it
,
commonlye
&
chiefly
the
name
of
Signes
,
is
attributed
to
the
Zodiak
.
(
whiche
many
doo
call
the
Thwarte
circle
)
This
Zodiake
is
thus
described
of
Proclus
.
The
zodiake
.
{αβγδ}
.
Obliquus
circulus
is
est
,
qui
duodecim
signa
continet
,
ex
tribus
aequidistantibus
circulis
constans
:
quorum
duo
latitudinem
signiferi
determinant
,
vnus
per
media
signa
ductus
vocatur
.
hic
adeo
duos
pares
&
aequidistantes
circulos
attingit
,
Solstitialem
in
prima
Cancri
parte
,
Brumalem
in
Capricorni
principio
.
Latitudo
Signiferi
continet
partes
duodecim
.
Dictus
estautē
hic
circulus
Obliquus
,
quod
aequidistantes
(
ad
inaequales
angulos
)
intersecet
.
The
thwarte
cyrcle
(
or
zodiake
)
is
the
cyrcle
of
the
twelue
signes
,
and
is
made
of
thre
circles
,
wherof
two
are
the
boundes
of
his
bredthe
,
and
the
thyrd
is
called
the
Middle
signe
circle
,
(
bicause
it
goeth
by
the
middle
of
the
signes
in
the
zodiake
)
and
it
toucheth
two
equal
This
whole
circle
representeth
the
zodiake
,
and
the
myddle
circle
signifieth
the
ecliptike
lyne
.
diagram of the zodiac.
circles
of
the
parallels
:
that
is
to
say
,
the
Sommer
tropike
in
the
firste
point
of
the
Crabbe
called
Cancer
,
and
also
the
Wynter
tropike
in
the
firste
degre
of
the
Goate
,
called
Capricorne
.
The
breadth
of
the
zodiake
,
containeth
twelue
degrees
.
This
zodiak
is
called
a
Thwart
circle
,
bycause
it
crosseth
the
parallele
circles
,
goynge
ouerthwarte
them
.
By
these
wordes
of
Proclus
you
may
vnderstande
,
that
the
zodiake
dooth
not
go
directly
betwene
the
two
poles
of
the
worlde
,
as
all
the
fiue
paralleles
doo
,
but
is
drawen
crosse
the
sphere
,
so
that
his
middle
(
in
breadthe
)
doth
touche
the
two
tropikes
,
and
that
middle
line
is
called
of
latin
writers
the
Ecliptike
lyne
,
The
Ecliptike
line
.
bicause
there
can
be
no
eclipse
of
Sonne
or
Moone
,
onles
the
Moone
be
vnder
that
lyne
:
as
hereafter
I
wyll
declare
in
place
conuenient
.
But
touching
this
zodiake
(
of
which
wee
spake
laste
)
I
sayde
it
was
diuided
into
twelue
signes
,
according
to
the
twelue
monethes
of
the
year
.
And
bicause
euery
quarter
of
the
yeare
maye
bee
the
more
exactlye
knowen
a
sonder
,
this
zodiake
is
parted
into
foure
partes
principall
,
euery
part
(
as
it
must
needes
folow
)
containing
thre
signes
.
Schollar
.
This
is
a
very
apte
agreement
of
arte
vnto
nature
:
for
as
the
whole
zodiake
agreeth
with
the
whole
year
,
so
for
the
foure
quarters
of
the
one
,
there
is
foure
quarters
in
the
other
:
and
for
the
twelue
monthes
of
the
yeare
,
twelue
signes
in
the
zodiake
:
and
for
the
thirtye
dayes
of
the
moneth
,
thirtye
degrees
in
euerye
signe
.
But
I
praye
you
syr
,
dooth
the
beginninge
of
these
signes
answere
to
the
beginning
of
our
yeare
?
Master
.
The
yeare
when
it
be
ginneth
.
The
beginning
of
the
yeare
is
diuers
in
dyuers
nations
,
as
I
will
shewe
you
an
other
tyme
,
with
the
reason
why
we
begin
our
yeare
in
Ianuary
:
but
for
this
tyme
it
shal
be
sufficient
,
to
declare
the
agreement
of
our
yeare
with
the
Astronomers
yeare
.
The
Astronomers
beginne
the
twelue
signes
of
the
zodiake
at
Aries
,
and
lykewaise
do
they
begin
the
yeare
that
daye
and
hower
,
that
the
Sonne
entreth
into
that
signe
of
Aries
,
whiche
is
nowe
at
the
eleuenth
daye
of
Marche
:
The
spring
of
the
year
and
from
thence
they
recken
the
Springe
of
the
yeare
thre
monethes
,
whyle
the
Sonne
is
in
the
fyrste
three
signes
.
Then
at
the
eleuenth
day
of
Iune
;
they
accompte
the
ende
of
the
springe
,
and
the
beginning
of
Sommer
,
bicause
then
the
Sonne
entreth
into
Cancer
,
The
Sommer
whiche
is
the
fourthe
signe
.
and
while
the
Sonne
passeth
other
thre
signes
,
(
which
maketh
the
seconde
quarter
of
the
zodiake
)
they
accompte
the
second
quarter
of
the
yeare
,
which
we
call
Sommer
,
&
that
endureth
till
the
14
day
of
September
,
at
which
time
the
Son
entreth
into
Libra
,
wher
the
third
quarter
of
the
zodiak
doth
begin
,
&
so
with
it
beginneth
Haruest
,
which
is
the
third
quarter
of
the
year
,
Haruest
.
and
continueth
till
the
twelft
day
of
December
,
and
then
doth
the
Son
entre
into
Capricorn
.
winter
.
&
Winter
beginneth
,
being
the
4
and
last
quarter
,
which
continueth
tyll
the
eleuenth
daye
of
Marche
,
where
the
olde
yeare
endeth
,
and
a
newe
yeare
beginneth
.
Scho
.
These
4.
signes
,
Aries
,
Cancer
,
Libra
&
Capricorn
,
seeme
to
haue
a
certain
prerogatiue
,
that
they
begin
the
4.
quarters
of
the
year
,
therfore
thei
wold
be
well
noted
in
the
zodiake
.
Master
.
You
say
well
,
and
yet
thei
haue
other
notable
qualities
,
for
in
the
beginning
of
Aries
and
Libra
,
the
son
maketh
the
daies
equall
with
the
nights
.
&
these
2.
points
ar
named
the
equinoctial
points
.
In
the
first
part
of
Cancer
,
the
day
is
at
the
longest
,
and
beginneth
to
shorten
by
the
descending
of
the
son
from
our
heds
,
&
when
the
son
doth
enter
into
Capricorn
,
the
day
is
at
the
shortest
,
&
then
the
son
beginneth
to
returne
to
vs
again
,
&
the
day
doth
thē
begin
to
increase
.
and
these
2.
points
ar
called
the
ij
.
Tropike
points
:
The
Colures
.
Wherfore
as
these
4.
points
are
notable
,
so
are
ther
ij
.
circles
appointed
for
their
lymites
,
the
one
going
by
the
beginning
of
Aries
&
Libra
,
and
the
other
by
the
beginning
of
Cancer
and
Capricorn
.
these
ij
.
circles
ar
called
Colures
,
Tropike
Colure
.
wherof
the
one
only
which
passeth
by
Cancer
and
Capricorn
,
is
described
of
the
grekes
,
the
reason
thereof
I
will
shewe
you
in
the
fourthe
treatise
.
But
this
fyrste
colure
,
whiche
is
called
the
Tropike
colure
,
is
thus
described
by
Proclus
.
{αβγδ}
λ
.
significat
.
30.
quae
semissis
est
circuli
maximi
diuisi
in
60.
partes
,
quod
Procl{us}
facit
.
Vt
perperam
quidā
α
.
hic
p
λ
.
substituerint
.
Sunt
&
per
polos
ducti
circuli
quos
nonnulli
Coluros
vocant
:
ijs
accidit
,
vt
in
ambitus
suos
mundi
polos
recipiant
.
Coluri
autem
dicti
sunt
,
quod
partes
aliquas
in
se
minimè
conspectas
habent
.
reliqui
enim
circuli
in
mundi
circumactu
integri
cernuntur
,
sed
colurorū
partes
quae
piam
quae
videlicet
ab
Antarctico
legendum
,
contra
exemplarium
omnium
consensum
.
Arctico
sub
Horizonte
latent
,
cerni
non
possunt
.
Signantur
autem
hi
circuli
per
tropica
puncta
,
diuiduntque
per
duas
ad
modum
aptè
Linacer
transtulit
loco
λ
.
literae
,
{per}
semissim
hic
significare
,
suprà
admonui
.
duas
aequas
partes
circulum
qui
per
media
signiferi
ducitur
.
diagram of the colures circles on the celestial sphere.
The
circles
that
go
by
the
poles
are
those
,
whiche
some
men
call
Colures
:
thei
haue
the
poles
of
the
worlde
in
their
circumference
.
And
ar
named
Colures
in
greek
,
that
is
trunked
circles
,
bycause
some
partes
of
them
come
not
into
oure
sighte
.
for
the
other
circles
by
the
turning
of
the
world
are
all
seene
,
but
some
parts
of
the
Colures
are
not
seene
,
that
is
,
those
partes
whiche
are
in
the
Antartike
circle
,
and
remaine
vnder
our
Horizonte
.
The
Equinoctiall
colure
.
These
cyrcles
are
deawen
by
the
two
tropike
pointes
of
the
eclipte
circle
,
and
so
deuide
it
into
two
equall
partes
.
The
Equinoctiall
colure
goeth
by
the
poles
of
the
sphere
,
and
by
the
.ij.
equinoctiall
pointes
of
the
Zodiake
,
in
Aries
and
Libra
.
Thus
haue
you
nowe
all
the
cyrcles
needfull
for
a
materiall
sphere
.
let
me
heare
howe
you
doo
remembre
their
names
.
Schollar
.
If
I
shoulde
not
remembre
theim
,
I
dydde
but
leese
my
laboure
,
A
good
lesson
.
and
occasion
you
to
spend
your
tyme
in
vaine
:
for
I
know
that
in
this
science
and
in
all
other
,
he
that
coueteth
to
runne
styll
forwarde
,
and
remembreth
not
that
,
that
is
gone
before
,
shall
neuer
attaine
that
whiche
remaineth
behynde
,
but
while
he
deliteth
to
muche
to
see
the
end
,
he
deceaueth
him selfe
of
the
frutefull
ende
of
knowledge
.
muche
lyke
a
man
that
is
delited
in
hearing
a
cunning
song
of
musyke
,
but
when
it
is
done
,
doth
remembre
nothing
of
it
,
so
is
his
profite
and
pleasure
bothe
ended
,
when
the
song
is
ended
.
Therfore
(
if
it
please
you
)
I
will
repeate
the
chieffe
pointes
that
I
haue
learned
sythe
my
former
repetition
.
Maister
.
Doo
so
then
.
Schollar
.
This
it
is
as
I
remmembre
,
-
The
second
repetition
.
1
Fyrst
you
taught
me
what
a
sphere
is
,
and
howe
it
is
made
,
also
what
is
his
Centre
,
his
Axetree
,
his
Diameter
,
and
his
Poles
,
and
what
the
Poles
are
named
.
-
2
Nexte
you
declared
two
circles
,
that
is
the
Horizonte
,
and
the
Meridiane
circle
,
whiche
(
I
perceaue
)
stand
styll
,
and
tourne
not
with
the
worlde
,
but
keepe
their
places
.
-
3
Then
did
you
describe
fiue
parallele
circles
,
the
Equinoctiall
,
the
twoo
Tropikes
:
the
Sommer
tropike
,
and
the
winter
tropike
,
and
then
the
other
two
Paralleles
,
that
is
,
the
Northe
circle
,
and
the
Southe
.
-
4
After
that
,
you
shewed
me
what
the
Zodiake
was
,
and
the
twelue
Signes
that
be
in
him
,
and
of
their
diuision
.
-
5
And
laste
of
all
,
you
described
the
twoo
Colures
,
whiche
diuide
the
Zodiake
into
foure
equall
and
principall
partes
,
accordynge
to
the
four
tymes
of
the
yeare
.
Maister
.
This
good
remembraunce
declared
your
good
will
to
knowledge
,
whiche
I
shall
with
as
good
a
will
healpe
to
further
.
Now
you
looke
(
I
think
)
to
be
instructed
in
the
vse
of
all
these
thinges
,
and
to
vnderstand
therby
the
celestiall
motions
,
and
the
diuers
appearances
that
therby
doo
ensue
:
how
be
it
,
bycause
that
a
materiall
instrument
is
a
great
helpe
for
them
that
begin
to
trauaile
in
this
arte
,
and
dothe
as
an
image
represent
to
the
eies
those
thinges
,
which
by
only
hearing
,
were
very
hard
to
conceaue
,
besides
many
other
commodities
,
whiche
shall
be
vttered
in
their
place
,
I
think
it
moste
conuenient
order
,
fyrst
to
teache
you
the
manner
howe
to
make
suche
a
materiall
sphere
,
as
may
serue
both
to
learne
by
,
and
also
to
worke
by
,
in
practising
the
obseruations
needefull
to
this
arte
.
THE
THIRDE
TREATISE
,
WHERIN
IS
BRIEFLY
TAVGHT
the
vse
of
the
Sphere
,
for
certaine
conclusions
of
daily
appearaunces
and
other
lyke
matters
.
MASTER
.
NOW
YOV
LOOKE
TO
HEARE
SOMwhat
of
the
vse
of
the
Sphere
,
as
you
shall
do
anon
:
And
for
an
induction
thervnto
,
you
must
diligentlye
knowe
the
plages
of
the
world
,
The
plages
of
the
worlde
.
amongest
whiche
there
are
four
principall
,
that
is
,
the
Easte
,
the
Weste
,
the
Northe
and
the
Southe
:
and
betwene
these
are
there
other
diuers
,
which
are
sufficiently
set
forth
in
the
Horizont
of
the
Globe
,
as
muche
as
shall
at
this
time
bee
needefull
.
You
must
knowe
also
,
The
Paralleles
in
the
earthe
.
that
euery
one
of
the
Paralleles
in
the
heauen
hath
a
lyke
circle
in
the
earthe
proportionably
drawen
,
and
answeringe
to
those
that
are
in
heauen
,
in
iuste
rate
of
distance
.
So
is
ther
fyrst
an
equinoctiall
in
the
earthe
exactlye
drawen
vnder
that
Equinoctiall
in
heauen
,
The
earthly
equinoctiall
.
and
it
diuideth
the
whole
earthe
into
twoo
equall
partes
,
betwene
the
southe
and
the
northe
,
so
that
it
poynteth
precisely
the
myddle
of
the
earthe
,
in
that
respecte
:
The
middle
of
the
earth
and
all
the
partes
of
the
earthe
from
that
earthly
Equinoctiall
toward
the
north
,
is
called
the
Northe
parte
of
the
earthe
:
and
of
the
world
lykewayes
all
that
is
beyond
that
cyrcle
towardes
the
south
,
The
northe
part
of
the
earthe
.
The
southe
parts
of
the
earthe
.
is
called
the
Southe
partes
of
the
earthe
.
Schollar
.
Yet
wee
doo
call
that
parte
only
Northe
,
that
is
northe
from
vs
:
and
that
wee
call
Southe
,
that
is
southe
from
vs.
Master
.
You
muste
consider
that
there
is
two
formes
of
speakinge
in
suche
talke
,
the
one
vulgare
,
and
commonly
vsed
,
as
well
of
the
vnlearned
as
of
the
learned
,
and
that
maketh
not
the
comparison
to
the
whole
world
,
which
few
men
doth
know
,
but
it
regardeth
principally
their
owne
cuntry
,
which
they
do
best
know
.
The
other
talk
is
general
in
forme
of
speakinge
,
bycause
it
hathe
respecte
to
the
whole
earthe
,
and
yet
is
it
not
generall
in
knowledge
,
for
fewe
men
canne
aptlye
skyll
of
it
:
so
that
bothe
are
true
in
their
due
vse
,
but
the
one
is
lesse
knowen
then
the
other
.
Schollar
.
So
I
perceaue
then
,
that
although
in
common
talke
we
do
call
Spaine
southe
,
and
likewaies
other
cuntries
,
yet
is
not
that
true
in
comparison
to
the
partes
of
the
whole
worlde
,
but
in
comparison
to
vs
,
for
our
common
talke
hath
chiefe
relation
in
suche
thinges
to
our
owne
cuntrye
.
But
I
pray
you
then
,
where
is
the
myddle
of
the
earthe
,
from
whiche
we
must
make
our
accompt
,
and
vnto
whiche
we
muste
haue
regarde
in
all
suche
generall
talke
?
Master
.
That
wyll
I
tell
you
anone
,
but
firste
we
muste
ende
that
matter
that
we
beganne
withall
,
touchynge
the
Paralleles
on
the
earthe
,
whereof
I
haue
named
yet
onlye
An
example
of
the
Paralleles
in
earth
agreably
to
the
Paralleles
in
the
skye
.
diagram representing the parallel circles in relation to the celestial sphere.
the
Equinoctial
,
but
nowe
must
you
imagin
other
2.
parallels
next
vnto
it
,
the
one
toward
the
Southe
,
&
the
other
towarde
the
north
,
The
Tropikes
on
the
earthe
.
which
maye
answer
to
the
2.
Tropiks
.
And
for
a
general
knowledge
fyrst
,
vnderstand
this
,
that
al
nations
ouer
whose
heds
the
son
doth
run
directly
,
when
he
is
in
the
hyest
point
toward
the
north
that
is
in
the
beginning
of
Cancer
,
wher
he
describeth
the
tropik
of
Cancer
in
the
skie
,
al
those
people
I
saye
dwell
iust
in
the
course
of
the
like
tropike
in
earth
:
And
contrary
waies
,
all
those
people
ouer
whose
heddes
the
Son
passeth
directly
,
when
he
is
in
the
Winter
tropike
,
they
dwell
in
the
course
of
that
south
Tropike
in
earthe
,
and
haue
the
sonne
right
ouer
their
heddes
that
daye
that
he
entreth
into
the
firste
degree
of
Capricorne
.
Schollar
.
By
these
examples
I
can
imagine
the
southe
and
north
circles
in
the
earth
to
be
vnder
the
Antarctike
and
Arctike
circles
in
heauen
,
The
other
Parallele
.
and
so
two
Polare
circles
in
earthe
vnder
the
two
Pole
circles
in
heauen
.
Then
are
there
seuen
Paralleles
in
earthe
,
answering
to
seuen
other
in
the
skye
.
Mast
.
That
is
sufficient
.
howbeit
for
this
time
I
will
omit
the
circles
Arctike
&
Antarctike
,
bicause
in
mine
opinion
,
they
make
no
Zone
in
earth
,
though
all
the
Grekes
in
apperance
do
say
the
contrary
,
but
I
will
bringe
inuincible
reason
for
my
purpose
,
when
we
come
to
the
scanning
of
repugnant
sentences
,
especially
when
I
do
disagree
with
the
grekes
,
which
are
the
fathers
of
witte
.
but
in
this
pointe
of
the
fiue
Zones
,
I
like
much
better
our
own
cuntry
man
Iohn
de
Sacro
bosco
as
I
will
now
only
affirme
,
Ioan
.
de
S.
Bosco
zonarum
restaurator
&
in
the
fourth
treatise
wil
proue
it
substantially
.
Therefore
to
continew
our
matter
as
we
began
:
there
are
made
by
these
v.
paralleles
,
v.
large
roomes
in
the
heauen
,
and
other
v.
in
the
earthe
,
The
fyue
zones
.
agreable
to
them
in
heauen
,
whiche
spaces
are
called
Zones
.
Scholl
.
Example
of
the
zones
.
By
your
fauour
,
ther
are
sixe
Zones
,
if
euery
space
betwene
the
Paralleles
be
accompted
for
one
zone
,
and
that
doth
not
only
the
accompt
of
thē
by
memorye
declare
vnto
me
,
but
also
the
sighte
of
them
in
this
figure
,
which
is
commonly
named
the
figure
of
the
Zones
.
Master
.
Nother
doth
the
accompte
deceaue
you
,
nother
yet
the
sight
of
the
figure
,
but
wante
of
knowledge
of
their
naturall
qualities
,
whiche
therefore
I
will
tell
you
by
and
by
,
though
these
parallele
circles
do
sufficiently
distincte
them
,
as
their
notable
boundes
,
The
qualities
of
the
fiue
zones
.
yet
by
the
qualities
bee
they
distincte
also
.
for
as
reason
doth
leade
you
,
all
the
space
betwene
the
2.
Tropikes
,
diagram classifying the climates between the circles of latitude, illustrated by the four winds at the corners.
MERIDIES
.
A
ZONA
FRIGIDA
.
B
ZONA
TEMPERATA
AVS
.
C
ZONA
TORRIDA
.
D
ZONA
TEMPERATA
BOR
.
E
ZONA
FRIGIDA
.
SEPTENTRIO
must
needes
bee
esteemed
verye
hotte
,
bycause
the
Sonne
runneth
alwaies
betwene
thē
,
so
that
in
the
myddle
betwene
the
two
Tropiks
is
the
equinoctial
line
,
from
the
which
the
Son
is
neuer
fully
24.
degres
so
must
it
seem
to
be
as
hotte
there
in
the
myddle
of
winter
,
as
it
is
in
Spaine
in
the
myddle
of
Sommer
,
and
for
this
cause
all
the
olde
Cosmographers
dydde
thynke
that
that
countrye
myghte
not
be
inhabited
for
heate
:
and
therefore
called
all
that
space
betweene
the
twoo
Tropykes
,
the
Burnynge
Zone
,
The
Burning
zone
.
called
in
latine
Zona
torrida
.
And
of
eche
syde
of
it
,
they
noted
twoo
Zones
,
one
vnder
eche
Pole
,
whiche
they
called
the
Frosen
zones
,
(
and
are
named
in
latine
,
Zonae
Frigidae
)
where
for
extreme
could
,
The
Frosen
zones
.
they
thought
that
no
man
might
dwell
.
and
betweene
those
Frosen
zones
,
&
the
Burning
zone
,
they
appointed
two
Temperat
zones
,
(
called
Zonae
temperatae
of
latine
men
)
which
were
partakers
of
the
heat
on
the
one
side
,
The
Temperate
zones
and
of
the
cold
on
the
other
side
,
so
that
of
bothe
,
there
was
made
a
temperate
mixture
.
Now
se
you
that
betwene
the
Equinoctiall
and
the
one
tropike
,
there
is
no
other
qualitie
,
then
is
betwene
the
same
equinoctiall
and
the
other
tropike
,
wherfore
all
men
(
except
only
Polybius
)
did
accompt
the
space
betwene
the
Tropikes
but
as
one
Zone
:
so
that
the
Equinoctiall
is
the
bounde
of
no
Zone
,
but
passeth
by
the
middle
of
the
Burning
zone
.
Schollar
.
Nowe
I
see
(
as
I
haue
had
at
other
tymes
often
occasion
)
that
we
learn
many
things
when
we
be
children
,
which
we
vnderstande
not
all
when
we
bee
menne
,
for
by
this
talke
I
remember
that
both
in
Ouide
&
Vergile
I
learned
the
distinction
of
those
5.
Zones
,
but
what
was
to
be
vnderstande
by
them
,
I
neuer
knowe
till
now
.
And
nowe
I
see
reason
that
betwene
the
2.
Tropikes
,
all
may
well
be
accompted
the
Burninge
Zone
,
where
no
man
can
dwell
,
as
bothe
my
authors
affirme
.
Master
.
They
had
spoken
more
modestly
,
yf
they
had
said
that
ther
had
been
painful
dwelling
for
heat
.
&
likwaies
of
the
cold
Zones
,
that
ther
is
hard
dwelling
for
cold
:
but
of
this
wil
I
more
exactly
reason
in
an
other
place
,
and
for
this
time
(
as
the
truth
by
experience
is
knowen
)
I
suppose
that
all
the
5.
Zones
haue
their
inhabitants
,
though
not
so
plentifully
as
the
two
Temperat
zones
now
haue
,
especially
this
temperat
zone
that
we
dwell
in
.
Who
is
it
that
hathe
not
hearde
of
the
isles
of
Molucca
,
and
of
Samatra
,
where
the
Portingales
gette
the
greate
plentye
of
riche
drugges
and
fine
spices
?
and
all
that
haue
been
there
,
confesse
that
those
places
ar
right
vnder
the
Equinoctiall
line
:
and
Calecut
is
but
little
from
it
,
for
it
is
diagram representing the circles of latitude on the celestial sphere.
-
A.
C.
The
Horizonte
.
-
B.
The
pointe
ouer
the
heade
.
-
*
.
The
Poles
of
the
worlde
.
The
Zodiake
and
the
other
circles
doth
appeare
of
them selfe
.
more
thē
19.
degres
beyond
the
Tropike
of
Cancer
toward
the
south
so
that
it
is
within
5.
degrees
of
the
very
equinoctial
line
.
Now
therfore
I
thinke
it
moste
apt
place
for
my
purpose
to
begin
at
these
cuntries
,
ouer
whose
hed
the
equinoctiall
dothe
rightly
passe
,
so
that
they
muste
nedes
see
both
the
Poles
in
their
Horizonte
.
Sc.
That
doth
reasonably
folow
,
bicause
half
the
heauen
iustly
appeareth
aboue
the
Horizont
,
and
the
other
halfe
is
vnder
the
Horizont
.
And
also
I
perceaue
that
if
I
set
the
sphere
so
that
the
Equinoctiall
stand
full
vprighte
,
then
will
bothe
the
Poles
be
in
the
very
Horizonte
.
as
this
position
of
the
Sphere
doth
shewe
.
Master
.
You
consider
it
righte
.
And
bicause
the
Equinoctiall
doth
crosse
the
Horizont
with
right
angles
(
for
all
4.
angles
are
equall
)
therfore
is
this
placing
of
the
sphere
called
a
Righte
sphere
:
A
ryghte
Sphere
.
so
that
all
other
nations
,
whiche
haue
the
one
Pole
aboue
their
Horizonte
,
must
needes
haue
the
other
Pole
vnder
their
Horizonte
,
and
the
Equinoctiall
declinith
from
the
point
right
ouer
their
heddes
,
that
waye
as
the
hidden
Pole
is
,
whether
it
be
toward
the
South
,
or
els
toward
the
Northe
.
Schollar
.
The
vse
of
the
materiall
sphere
.
All
this
seemeth
easye
to
me
,
as
longe
as
I
beholde
this
materiall
sphere
?
but
when
I
doo
not
conferre
it
wyth
your
woordes
,
then
your
saynges
appeare
the
more
doubtefull
.
Master
.
For
that
cause
did
I
teache
you
the
making
of
it
,
before
I
instructed
you
in
the
vse
of
it
,
knowing
how
greate
a
helpe
the
sighte
of
the
eye
doth
minister
to
the
righte
and
speedye
vnderstandyng
of
that
,
whiche
the
eare
doth
heare
.
But
againe
to
our
matter
:
in
all
places
where
the
equinoctial
doth
decline
from
the
pointe
ouer
the
heddes
of
any
inhabitauntes
(
whiche
pointe
is
commonly
called
the
Zenith
)
there
the
Equinoctiall
maketh
vnequall
corners
with
the
Horizont
,
The
Zenith
and
therfore
is
that
called
a
Bowyng
sphere
,
A
bowing
Sphere
.
or
a
Leanynge
sphere
;
bycause
the
Equinoctiall
boweth
or
leaneth
toward
one
syde
of
the
Horizont
,
more
then
towarde
the
other
side
.
Schollar
.
I
haue
hearde
it
called
a
Crooked
sphere
also
.
Master
.
That
name
is
vnapte
for
this
arte
,
for
there
can
bee
no
crooked
corner
betweene
the
Equinoctiall
and
the
Horizonte
,
which
myght
make
that
name
meet
for
the
matter
:
and
(
as
I
haue
sayde
)
the
Sphere
taketh
those
seuerall
names
of
his
diuers
position
,
diagram representing the zodiac on the celestial sphere.
-
A.
C.
The
Horizonte
.
-
B.
The
Zenith
.
-
*
.
The
Poles
.
The
Zodiake
,
the
Equinoctiall
and
the
other
circles
do
appeare
of
them selfe
.
and
accordyng
to
the
corners
that
the
equinoctial
doth
make
with
the
Horizonte
.
And
this
may
you
consider
herein
,
that
there
is
no
Zone
but
one
that
canne
haue
a
right
Sphere
:
and
to
speake
precisely
,
but
one
tracte
in
that
zone
,
whiche
is
the
very
middle
of
the
Burninge
zone
,
righte
vnder
the
Equinoctiall
where
as
there
be
innumerable
places
that
haue
Leaninge
spheres
,
whiche
you
may
call
Oblique
spheres
or
Declininge
spheres
,
if
you
delite
more
in
latinelyke
names
then
englishe
.
Schollar
.
So
I
perceaue
that
bothe
we
and
all
other
nations
whiche
dwell
not
righte
vnder
the
Equinoctiall
lyne
,
muste
be
named
to
haue
a
Leaning
sphere
.
And
this
I
consider
resonably
,
that
in
some
cuntries
the
sphere
dothe
leane
and
bowe
more
then
it
dothe
in
other
,
whiche
difference
I
wolde
gladly
vnderstande
.
Master
.
The
diuersitye
in
leaning
of
any
sphere
,
is
agreable
to
the
eleuation
of
the
Pole
in
euerye
cuntrye
,
so
that
where
the
Pole
is
hyghest
aboue
the
Horizonte
,
there
the
sphere
leaneth
most
:
and
where
the
Pole
is
lower
and
nearer
to
the
grounde
,
there
the
sphere
leaneth
lesser
.
Schollar
.
The
height
of
the
Pole
Howe
shall
I
iudge
truly
the
height
of
the
Pole
?
Master
.
That
true
and
exacte
iudgement
will
I
not
treate
of
as
now
,
to
auoide
interruption
in
teaching
:
it
shall
be
sufficient
for
this
place
to
shewe
you
a
plaine
and
easye
forme
,
with
the
vse
of
an
instrument
that
may
helpe
you
sumwhat
in
markinge
the
height
of
the
Sonne
and
Moone
and
anye
other
starres
that
you
lyste
.
and
the
manner
of
it
is
thus
.
You
shall
take
a
Quadrante
depiction of a quadrant.
(
whose
composition
I
haue
taught
amongst
other
instruments
in
the
Gate
of
knowledge
,
but
this
which
you
se
here
,
is
the
forme
of
the
moste
playnest
sorte
)
and
by
the
twoo
syghtes
of
it
,
you
shall
marke
the
height
of
the
Northe
starre
commonly
called
the
Pole
,
and
when
you
se
it
through
both
the
sights
,
thē
mark
what
degree
the
lyne
of
the
plommet
doth
touch
in
the
margent
,
and
,
that
may
you
call
Latitude
of
that
region
,
or
the
heighte
of
the
Pole
,
for
this
tyme
and
place
where
no
precisenes
is
required
.
for
nowe
it
is
sufficiente
for
you
to
vnderstande
generallye
,
that
there
are
suche
diuersyties
of
eleuation
of
the
Pole
in
diuers
countries
:
and
thereby
maye
you
vnderstande
,
that
all
Spheres
bee
not
alyke
in
theyr
position
.
As
for
example
.
In
the
southe
partes
of
Englande
aboute
Sowthehampton
,
Southehampton
.
the
Pole
is
not
fullye
51.
degrees
hyghe
,
and
in
the
isles
of
Orkenaye
,
beyonde
Scotlande
,
the
Pole
is
aboue
62.
degrees
highe
:
this
maye
easilye
bee
tryed
by
them
that
list
to
trauayle
,
but
if
you
lyste
to
go
no
farther
then
Yorke
,
Yorke
.
you
shall
fynde
the
eleuation
aboue
54.
degrees
,
and
so
at
Edynburghe
shall
you
fynde
the
eleuation
aboute
57.
degrees
.
Edynburgh
And
thus
within
your
owne
cuntrye
maye
you
vnderstande
a
greate
diuersitye
,
wherby
you
may
coniecture
the
diuersities
that
bee
in
other
partes
of
the
worlde
.
Schollar
.
This
is
so
appearaunte
to
them
that
will
trauel
any
thing
for
knowledges
sake
,
that
they
cannot
pretend
any
ignoraunce
,
but
wilfull
ignorance
:
but
herein
I
fynde
one
doubte
,
that
maketh
me
to
muse
,
The
alteration
of
the
Horizonte
for
in
trauelyng
thus
from
one
place
to
an
other
,
whereby
the
Pole
is
diuerslye
chaunged
in
his
eleuation
,
I
can
not
thinke
that
the
Pole
it selfe
dothe
chaunge
his
place
,
but
that
rather
the
Horizont
doth
alter
,
from
which
we
muste
take
the
measure
of
height
of
the
Pole
.
Master
.
You
say
well
,
for
in
deed
there
is
no
suche
motion
in
heauen
,
that
maye
make
the
Pole
so
notably
to
chaunge
his
place
:
but
as
we
doo
chaunge
our
standinge
,
so
dooth
there
appear
a
newe
Horizonte
,
whiche
causeth
the
Pole
to
seeme
higher
.
if
we
go
towarde
the
northe
,
for
then
wee
see
more
of
the
skye
(
that
waies
)
aboue
our
Horizont
,
then
we
did
see
before
:
but
if
we
go
toward
the
South
,
then
will
the
Pole
seeme
lower
and
lower
,
still
as
we
go
Southward
:
not
bycause
the
Pole
chaungeth
,
but
our
Horizont
chaungeth
:
for
nowe
wee
see
more
of
the
skye
towarde
the
Southe
,
and
lesse
towarde
the
Northe
:
but
yet
generally
as
much
as
wee
leefe
in
the
one
parte
,
so
muche
wee
wynne
in
the
other
coaste
,
so
that
euermore
we
may
see
halfe
the
skye
.
Whether
the
Horizonte
doo
moue
or
not
.
Schollar
.
Then
this
is
my
doubte
,
how
I
shal
vnderstand
your
former
woordes
:
for
I
remembre
you
sayd
that
the
Horizont
was
a
circle
immouable
,
and
did
not
turne
as
the
circles
in
heauen
do
:
&
now
you
haue
plainly
declared
that
the
Horizonte
dothe
chaunge
,
whiche
can
not
be
without
mouinge
of
it
.
Master
.
You
haue
answered
your
owne
question
,
if
you
marke
it
well
:
for
the
Horizonte
moueth
not
as
the
circles
in
heauen
do
moue
:
that
is
to
say
,
it
goeth
not
round
about
the
earth
by
a
daily
course
,
but
it
standeth
steddye
whyle
the
heauen
moueth
,
so
that
if
you
neuer
chaunge
your
place
,
your
Horizont
will
neuer
moue
.
And
to
speake
more
exactly
:
the
Horizont
moueth
not
,
thoughe
you
moue
neuer
so
farre
:
but
rather
should
we
saye
,
that
you
are
come
into
an
other
Horizonte
,
when
you
are
come
into
an
other
cuntrye
.
Schollar
.
It
muste
needes
appeare
so
,
nowe
that
I
do
consider
the
matter
more
earnestly
:
for
when
I
am
at
London
,
I
see
the
same
Horizonte
that
all
other
men
there
do
see
:
then
if
I
go
to
Yorke
,
I
see
the
Horizont
of
Yorke
,
and
not
of
London
,
so
that
the
Horizont
of
London
remaineth
as
it
was
,
and
so
doth
the
Horizont
of
Yorke
,
whether
I
tarry
or
go
.
And
thus
I
perceaue
great
alteration
in
the
Horizonts
betwene
southe
and
northe
,
wherby
the
pole
is
diuersly
altered
in
height
aboue
the
Horizont
.
What
if
I
go
eastward
or
westward
,
shall
I
not
fynde
the
lyke
alteration
?
Master
.
It
must
needes
appeare
yes
.
for
the
same
reason
that
causeth
you
to
chaunge
your
Horizont
betwene
south
and
north
,
the
same
will
cause
it
to
chaunge
betwene
east
and
weste
.
And
for
declaration
thereof
,
answere
me
to
this
question
:
Do
you
think
that
there
is
any
suche
cuntry
farre
east
from
vs
,
Example
of
Calecut
.
as
the
Portingales
reporte
Calecut
to
be
?
Schollar
.
It
were
as
muche
folly
to
make
a
doubte
of
it
,
as
it
were
to
make
a
doubte
of
Babylon
,
or
Hierusalem
.
Master
.
And
do
you
thinke
that
the
sonne
doth
rise
to
vs
and
to
them
at
one
tyme
?
Schollar
.
It
can
not
be
.
for
this
muche
I
maye
gether
by
that
I
haue
learned
already
,
that
the
rising
of
the
sonne
and
of
all
other
starres
,
is
the
apearing
of
them
aboue
the
Horizonte
,
so
that
they
rise
to
vs
,
when
they
beginne
to
appeare
aboue
our
Horizont
:
and
they
rise
to
them
in
Calecut
,
when
they
appeare
aboue
their
Horizonte
.
And
further
I
gether
now
by
your
briefe
admonition
of
the
chaunge
of
the
Horizontes
,
that
as
betwene
southe
&
northe
in
our
owne
cuntry
,
we
maye
perceaue
notable
diuersitie
,
so
maye
wee
consyder
the
same
much
more
in
so
greate
a
distaunce
,
as
Calecut
is
noted
to
be
from
vs
,
which
I
haue
heard
to
be
named
aboue
15000.
myles
,
and
that
is
farre
greater
(
yea
20.
tymes
)
then
all
the
lengthe
of
Englande
and
Scotlande
togither
.
wherefore
I
gather
that
the
diuersities
of
the
Horizontes
must
be
twenty
times
so
muche
,
as
was
betwene
Southhampton
and
the
northe
parte
of
England
.
Master
.
The
distaunce
is
not
so
muche
,
nor
the
difference
so
great
,
but
by
meanes
that
the
Portingales
do
saile
a
meruailous
compasse
in
goynge
thether
,
they
accompte
the
distaunce
by
that
compassed
course
,
whiche
is
farre
from
oure
talke
now
,
for
we
must
euer
take
right
distaunce
by
a
straight
line
,
as
often
as
we
do
speake
of
any
suche
matter
.
how
be
it
for
examples
sake
,
suppose
it
to
be
.
6000.
miles
east
from
vs
,
The
diuersities
of
the
day
in
dyuers
Regions
.
it
seemeth
to
be
more
then
a
quarter
of
the
whole
compasse
of
all
the
earthe
,
(
as
I
will
proue
it
in
the
nexte
treatise
)
and
therfore
must
the
Sonne
at
the
leaste
rise
6.
houres
to
them
soner
then
it
dothe
to
vs.
do
you
perceaue
that
?
diagram representing the lines of midnight on the celestial sphere.
-
A.C.
The
Horizonte
of
London
.
-
B.
The
Meridian
of
it
.
-
A.
The
easte
to
London
,
and
the
nonesteede
to
Calecut
.
-
D.
B.
The
Horizonte
to
Calecut
.
-
D.
The
easte
to
Calecut
,
and
the
line
of
midnyghte
to
London
.
-
C.
The
weste
to
London
,
and
the
lyne
of
mydnighte
to
Calecut
.
Schollar
.
The
Son
(
as
all
men
knoweth
)
doth
compasse
all
the
earthe
in
24.
houres
,
then
muste
it
compas
halfe
the
earthe
in
12.
houres
,
and
a
quarter
of
the
earthe
in
6.
howers
.
this
is
as
plaine
as
can
be
:
&
thē
it
must
needes
folow
,
that
if
they
bee
a
quarter
of
the
earthe
more
toward
the
east
then
we
,
they
must
see
the
Son
6.
houres
sooner
then
wee
.
Master
.
And
likewaies
they
that
dwell
farther
easte
then
thei
,
as
the
inhabitantes
of
Molucca
doo
,
must
needes
see
the
sonne
before
them
:
and
those
that
dwell
more
westerly
then
they
do
,
as
at
Hierusalem
,
or
at
Constantinople
,
must
haue
the
daye
springe
later
then
they
that
be
at
Calecut
.
And
thus
you
maye
consider
,
that
the
Horizontes
doo
chaunge
as
well
betweene
east
and
weste
,
as
it
dothe
betwene
southe
and
northe
:
As
this
figure
sheweth
for
London
and
Calecut
.
Schollar
.
That
is
plaine
.
for
if
all
those
places
had
one
Horizonte
,
then
should
the
sonne
rise
to
them
all
at
ones
.
Master
.
And
as
their
morninges
do
differ
,
so
must
their
noonetyde
differ
also
.
Schollar
.
No
man
that
hathe
reason
can
denye
that
.
Master
.
Then
muste
their
Meridian
circles
differ
in
lyke
sorte
,
seeynge
they
be
the
limites
of
the
nonetide
.
Schollar
.
So
I
perceaue
that
betweene
easte
and
weste
,
the
Meridianes
do
chaunge
,
as
well
as
the
Horizontes
:
and
hereby
I
vnderstande
,
that
when
it
is
sonne
risinge
at
Calecut
,
it
is
not
day
with
vs
,
by
6.
houres
:
and
when
it
is
noone
with
them
,
it
is
6.
of
clocke
in
the
mornynge
with
vs.
and
so
of
all
other
houres
,
whiche
all
appeareth
by
the
former
figure
.
houres
,
whiche
all
appeareth
by
the
former
figure
.
Master
.
This
standeth
for
the
declaration
of
diuersities
of
dayes
in
diuers
regions
:
but
yet
you
haue
not
heard
what
causeth
the
diuersities
of
dayes
in
one
region
.
Schollar
.
Yes
for
soothe
.
I
remembre
that
you
reproued
me
for
saying
that
the
longe
daies
caused
the
Sonne
to
shine
longe
:
and
you
tourned
that
sentence
,
affirminge
,
that
the
longe
shinynge
of
the
sonne
dothe
make
the
daies
long
,
and
the
shorte
shinynge
of
the
sonne
,
doth
make
shorte
dayes
.
Master
.
And
are
you
satisfied
with
that
reason
?
Schollar
.
I
thinke
it
reason
good
ynoughe
.
Master
.
The
reason
is
good
,
but
not
inough
,
syth
farther
reason
is
to
be
giuen
.
What
maketh
the
son
to
shyne
longe
?
can
you
tell
?
Schollar
.
By
your
helpe
I
truste
to
know
it
.
Mast
.
Set
your
Sphere
before
you
,
and
first
turn
it
so
that
bothe
the
Poles
may
diagram representing the zodiac and circles of latitude on the celestial sphere.
touch
the
Horizont
,
which
is
the
situation
of
the
right
Sphere
.
Then
do
you
se
that
the
horizont
doth
cut
not
only
the
equinoctiall
circle
in
2.
equall
halues
,
but
lykewayes
doth
it
cut
bothe
the
tropikes
,
equally
into
2.
euen
partes
,
so
that
there
is
as
much
of
eche
of
them
aboue
grounde
,
as
there
is
beneth
the
Horizonte
:
and
contrarye
waies
.
Wherfore
it
muste
needes
appeare
,
that
the
son
when
he
runneth
in
anye
of
those
three
circles
,
is
lyke
tyme
aboue
the
Horizont
,
as
he
is
vnder
it
,
so
must
the
daies
and
the
nyghts
be
equall
,
not
only
when
the
son
is
in
the
equinoctiall
circle
,
but
also
when
he
is
in
any
of
the
both
tropykes
:
but
this
equalitye
of
dayes
and
nyghtes
,
when
the
sonne
is
in
any
tropike
,
is
priuately
appropried
to
the
ryght
sphere
:
for
in
all
other
varieties
of
the
Bowinge
spheres
,
then
is
the
greateste
difference
in
all
the
yeare
,
betweene
the
day
and
the
nyghte
,
when
the
sonne
is
in
any
of
the
tropikes
.
as
for
example
:
Set
the
sphere
to
what
eleuation
that
you
lyst
.
that
is
to
saye
:
Raise
the
Pole
as
many
degrees
aboue
the
Horizonte
as
you
will
.
Schollar
.
I
haue
sette
it
nowe
(
as
heere
you
see
)
to
the
eleuation
of
52.
degrees
,
whiche
you
saye
is
the
eleuation
at
Cambridge
.
Master
.
And
nowe
maye
you
see
that
the
Equinoctiall
onlye
is
equallye
dyuided
by
the
Horizonte
,
and
that
the
twoo
Tropikes
are
verye
vnequallye
diuyded
,
so
that
the
tropike
of
Cancer
hath
almost
thre
quarters
aboue
the
Horizonte
,
and
litle
more
diagram representing the zodiac and circles of latitude on the celestial sphere.
then
a
quarter
vnder
the
Horizont
,
wher
contrarye
wayes
the
Tropyke
of
Capricorne
,
hath
almost
thre
quarters
vnder
the
ground
,
and
litle
more
then
one
quarter
aboue
the
Horizont
:
wherof
it
must
nedes
folow
,
that
when
the
sonne
is
in
the
Sommer
Tropyke
,
he
is
almoste
thre
quarters
of
the
Naturall
daye
aboue
grounde
,
and
lyttle
more
then
one
quarter
of
the
same
daye
vnder
grounde
.
Schollar
.
I
knowe
your
mynde
very
well
,
and
I
doo
gather
thereby
,
that
when
the
daye
is
at
the
longest
,
it
is
almost
is
.
howers
daye
,
and
but
lytte
more
then
syx
howers
nyghte
.
And
contrarye
waies
in
the
shortest
of
winter
,
the
daye
is
lyttle
more
then
sixe
howers
longe
,
and
the
nyghte
almoste
is
.
howers
.
And
farther
I
heare
you
call
the
whole
space
of
24.
A
Naturall
Daye
.
howers
a
Naturall
daye
:
But
I
know
not
yet
the
reason
of
that
name
.
Master
.
By
that
name
of
addition
,
the
whole
daye
of
24.
howers
is
distincte
from
the
Artificiall
daye
,
which
is
from
sonne
rysinge
to
sonne
settinge
:
An
Artificiall
Daye
.
and
that
Artificiall
daye
is
moste
commonlye
vnderstande
,
when
men
speake
of
the
daye
.
therfore
for
a
difference
it
is
good
to
vse
suche
an
addition
.
But
nowe
for
the
better
practise
,
set
your
globe
to
some
other
eleuation
.
Schollar
.
I
trow
I
haue
set
the
pole
highe
ynoughe
.
Master
.
Let
it
stande
.
What
is
the
numbre
of
the
eleuation
?
Schollar
.
I
do
see
betwene
the
Pole
and
the
Horizont
in
the
diagram representing the zodiac and circles of latitude on the celestial sphere.
Meridian
dyuers
numbres
,
but
I
take
that
numbre
onli
,
which
touchith
the
horizont
,
and
I
take
that
also
of
the
twoo
orders
of
numbres
,
which
descendeth
from
the
Pole
,
and
that
is
here
now
71.
Master
.
That
is
the
latitude
or
eleuation
of
the
Pole
at
Wardhouse
,
where
our
newe
venteterers
into
Moscouia
do
touch
in
theyr
viage
:
but
now
mark
the
varietie
of
the
tropiks
to
the
Horizont
:
The
Tropike
of
Cancer
is
(
as
you
see
)
more
then
foure
degrees
aboue
the
Horizont
cleare
,
so
that
the
whole
2.
signes
of
Gemini
and
Cancer
,
with
5.
degrees
of
Taurus
,
and
as
muche
of
Leo
,
doth
neuer
sette
vnder
the
Horizont
.
Schollar
.
Then
while
the
sonne
is
goyng
through
those
signes
,
from
the
25.
degree
of
Taurus
,
to
the
6.
degree
of
Leo
,
it
is
continuall
daye
,
bicause
the
sonne
doth
not
set
vnder
their
Horizont
.
but
I
pray
you
how
long
tyme
is
that
?
Master
.
It
is
from
the
7.
day
of
May
vntill
the
19.
daye
of
Iuly
;
The
longest
Daye
at
Wardhous
is
73.
diaes
continuall
.
so
that
it
is
continuall
day
with
them
by
the
space
of
73
of
our
dayes
,
whiche
is
almost
two
monethes
and
an
halfe
.
Schollar
.
This
is
meruailous
straunge
to
me
.
Master
.
Yet
shall
you
hear
more
strang
matter
then
that
:
Sette
your
Sphere
so
,
that
the
Equinoctiall
maye
be
iustlye
in
the
Horizont
,
and
the
north
Pole
righte
vp
in
the
place
of
the
Zenith
.
Schollar
.
That
haue
I
doone
,
as
here
you
maye
see
.
Master
.
Nowe
marke
how
muche
of
the
Zodiake
dothe
neuer
go
vnder
that
Horizont
.
Schollar
.
Howe
shall
I
perceaue
that
?
diagram representing the zodiac and circles of latitude on the celestial sphere.
Master
.
Turne
the
Sphere
rounde
,
as
it
shulde
moue
naturally
on
his
owne
poles
,
but
sturre
not
the
Horizonte
.
Schollar
.
Hereby
I
perceaue
that
6.
signes
,
Aries
,
Taurus
,
Gemini
,
Cancer
,
Leo
,
Virgo
,
doo
neuer
sette
vnder
the
Horizont
,
but
continewe
alwayes
aboue
it
.
Master
.
Then
while
the
sonne
is
in
those
sixe
signes
,
he
can
not
bee
out
of
theyr
syghte
,
that
dwell
within
that
Horizonte
.
Schollar
.
It
is
truthe
,
yf
any
body
doo
dwell
directly
vnder
the
Pole
.
Master
.
It
is
not
now
my
purpose
,
to
prooue
what
partes
of
the
earthe
be
inhabited
,
(
for
that
appertaineth
to
Geographye
)
but
to
declare
howe
the
sonne
doth
shewe
in
all
partes
of
the
worlde
,
as
well
on
the
sea
,
as
on
the
londe
:
and
as
well
in
wyldrenes
,
as
in
populous
countryes
.
Whereby
it
doothe
appeare
sufficientlye
,
that
vnder
the
Poles
of
the
worlde
,
it
is
halfe
a
yeare
continuall
daye
,
and
the
other
halfe
yeare
,
The
length
of
the
daye
vnder
the
Poles
of
the
worlde
.
contynuall
nyghte
,
bicause
so
longe
againe
the
Sonne
is
not
seene
aboue
that
Horizonte
.
Schollar
.
This
is
as
true
as
canne
bee
.
the
reason
of
it
is
so
certayne
and
manifeste
,
that
I
coulde
not
better
vnderstande
the
state
of
that
place
,
if
I
were
there
to
see
it
,
then
I
doo
by
thys
beholdynge
of
the
Sphere
,
and
the
motion
of
it
.
And
thys
(
as
I
take
it
)
is
a
meruaylous
excellencye
in
knowledge
,
The
excellencye
of
knowledge
.
to
bee
able
so
certaynly
to
iudge
of
thinges
absente
,
as
if
they
were
present
:
to
bee
able
to
tell
what
houre
of
the
daye
it
is
in
all
the
partes
of
the
earthe
,
and
when
the
Sonne
ryseth
and
setteth
in
all
nations
vnder
heauen
.
Master
.
Yow
wolde
accompt
this
knowledge
more
meruelous
,
if
you
vnderstoode
other
more
wonderfull
conclusions
in
it
,
whiche
hereafter
I
will
vtter
as
I
shall
haue
occasion
conuenient
:
but
in
the
meane
season
,
I
will
shewe
you
two
or
three
conclusions
,
appertaining
to
our
presente
matter
whiche
we
haue
in
hande
.
As
the
houres
of
the
daye
are
dyuers
in
dyuers
regions
,
so
the
shadowes
that
the
sonne
causeth
in
their
dialles
,
and
all
other
shadows
,
doth
disagree
many
waies
,
not
only
from
our
shadowes
,
but
also
one
of
them
from
an
other
.
Againe
the
times
of
the
yeare
are
not
alyke
through
all
the
worlde
,
but
when
it
is
Sommer
to
vs
,
it
is
winter
to
som
other
:
and
when
it
is
Springe
time
with
vs
,
it
is
sommer
in
an
other
cuntrye
:
and
when
it
is
Haruest
with
vs
,
other
people
haue
sommer
:
so
when
it
is
Winter
with
vs
,
som
nations
haue
sommer
:
yea
when
the
spring
time
beginneth
with
vs
,
it
is
haruest
in
some
cuntries
,
and
in
other
cuntries
it
is
midsommer
at
the
same
time
:
but
when
it
is
midsommer
with
vs
,
it
it
haruest
no
where
in
the
worlde
,
but
midde
winter
it
is
then
in
two
diuers
partes
of
the
worlde
.
Schollar
.
This
talke
is
meruailous
,
and
in
mine
opinion
the
greatest
meruaile
is
,
that
you
can
vnderstand
the
shadowes
of
their
dials
or
any
other
thinges
,
in
all
partes
of
the
world
.
Master
.
Peraduenture
it
wold
seem
more
merueilous
if
I
shoulde
say
,
that
by
the
knowledge
of
the
shadow
of
a
staffe
,
or
any
thing
els
that
standeth
vpright
,
(
if
I
heare
it
trulye
reported
)
I
will
tell
you
in
what
part
of
the
worlde
that
shadowe
was
marked
.
And
thinke
you
this
no
meruell
,
to
tarry
within
Englande
,
and
yet
to
measure
all
the
compasse
of
the
earthe
,
as
certenly
,
as
any
man
can
do
it
,
by
going
rounde
about
the
earthe
?
Schollar
.
These
thinges
do
exceede
credit
,
saue
that
other
thinges
,
whiche
before
I
iudged
impossible
,
and
now
I
know
them
certenly
,
do
perswade
me
to
thinke
many
thinges
possible
by
learning
,
that
seeme
vnpossible
to
the
ignoraunte
,
thoughe
their
wittes
be
neuer
so
good
.
I
heare
suche
men
say
sometimes
,
that
learned
men
and
farre
trauelers
may
be
per
mitted
to
talke
at
their
pleasure
,
syth
no
man
canne
comptroll
them
.
Master
.
By
those
woordes
they
signifie
,
that
they
do
not
credite
all
that
learned
men
do
write
or
saye
:
wherfore
I
will
constantly
saye
to
them
,
that
if
they
wolde
vouchsafe
to
imploye
somtyme
in
learninge
,
they
shoulde
be
easilye
perswaded
,
not
onlye
to
beleue
suche
thinges
as
nowe
they
thynke
impossible
,
but
also
to
know
them
so
certenly
,
as
they
know
howe
many
fingers
they
haue
.
But
to
perswade
you
in
the
meane
ceason
,
Thre
conclusions
.
I
will
presently
shew
you
some
of
these
thre
conclusions
before
named
,
I
meane
for
the
generall
knowledge
of
the
times
of
the
year
:
for
the
declining
of
shadowes
in
diuers
nations
:
and
for
the
ordre
to
measure
the
whole
earthe
,
and
yet
go
not
out
of
England
.
Schollar
.
If
I
maye
vnderstande
but
the
generall
forme
of
those
three
,
I
will
trust
hereafter
to
attayne
all
the
reste
more
certenly
.
Master
.
I
will
begin
with
the
laste
,
whiche
seemeth
moste
hardest
,
and
I
wyll
alleage
nothinge
,
but
that
whiche
you
shall
graunt
vnto
.
Schollar
.
The
declaration
of
the
fyrste
conclusion
for
measuringe
of
the
whole
earthe
.
Then
shall
your
proofe
bee
as
certaine
as
I
can
wishe
.
Master
.
Can
you
with
a
Quadrante
marke
the
eleuation
of
the
Pole
aboue
the
Horizonte
?
Schollar
.
That
is
easye
inoughe
.
Master
.
Then
marke
it
fyrste
at
Southehampton
,
or
in
some
other
more
easterlye
place
,
on
the
south
shore
of
England
.
after
that
go
to
Newcastell
beyond
Yorke
,
and
there
take
the
eleuation
with
your
Quadrante
againe
,
and
marke
it
well
,
and
the
difference
of
those
two
eleuations
shall
you
set
in
your
table
,
and
by
it
you
shall
write
the
numbre
of
myles
diligently
and
truly
taken
betwene
those
two
places
,
where
you
toke
those
two
eleuations
.
Schollar
.
This
can
I
doo
with
diligence
,
although
it
bee
as
harde
to
marke
the
myles
truly
(
the
reportes
of
them
being
so
diuers
)
as
it
is
to
woorke
truly
with
the
Quadrante
,
but
diligence
will
auoide
errour
in
them
bothe
.
Master
.
Then
go
forwarde
to
Edynburghe
in
Scotland
,
and
marke
the
eleuation
there
:
lykewayes
go
to
the
moste
northerlye
pointe
of
Catnesse
,
and
take
the
eleuation
there
also
,
alwaies
markinge
the
difference
of
euerye
twoo
places
in
myles
of
equall
quantitie
,
and
also
the
difference
of
the
degrees
of
the
Pole
in
eche
of
those
places
from
other
,
and
set
them
in
your
tables
in
ordre
the
one
by
the
other
,
as
here
for
examples
sake
only
,
I
haue
set
them
.
The
places
.
|
The
Eleuation
of
the
Pole
.
|
The
difference
in
degrees
.
|
The
distaunce
in
myles
.
|
Southehampton
.
|
51.
|
0.
|
0
|
0
|
000.
|
Newecastell
.
|
55.
|
0.
|
4.
|
0.
|
240.
|
Edynburghe
.
|
57.
|
0.
|
2.
|
0.
|
120.
|
Catnesse
pointe
.
|
62.
|
0.
|
5.
|
0.
|
300
|
The
summe
of
all
|
|
|
11.
|
0.
|
660.
|
Here
you
see
for
Southehampton
,
where
the
fyrste
eleuation
was
taken
,
no
myles
sette
,
bicause
it
is
the
beginning
of
your
iourneye
,
but
the
eleuation
of
the
Pole
there
is
51.
degrees
:
then
at
Newecastell
the
heighte
of
the
Pole
is
55.
degrees
,
and
that
is
more
then
the
other
by
foure
degrees
,
so
that
foure
degrees
muste
be
set
downe
for
their
difference
in
degrees
,
and
their
distaunce
in
equall
myles
,
is
240.
Nowe
to
see
howe
many
myles
do
the
answere
to
a
degree
,
I
do
diuide
240.
by
4.
and
the
quotient
will
be
60.
wherfore
I
saye
,
that
60.
miles
in
earthe
(
by
this
triall
)
doth
answere
to
one
degree
in
heauen
.
Then
at
Edynburghe
I
finde
the
eleuation
of
the
Pole
to
be
57
,
that
is
twoo
degrees
more
then
it
was
at
Newcastell
,
and
the
distaunce
betweene
them
in
myles
,
is
120
,
whiche
if
I
dyuide
by
2
,
the
quotient
will
be
60.
as
it
was
before
:
so
that
one
of
these
workes
doth
confirme
the
other
,
bicause
they
agre
so
iustly
.
Schollar
.
I
vnderstande
all
this
,
as
by
declaringe
of
the
thirde
woorke
it
shall
appeare
to
you
.
At
Catnesse
pointe
,
the
Pole
is
62.
degrees
aboue
the
Horizont
,
whiche
maketh
5.
degrees
more
then
it
was
at
Edenburghe
,
and
the
space
betwene
those
two
places
is
300.
myles
:
now
if
I
diuide
300.
by
fiue
,
there
will
amounte
60
,
whiche
quotient
doth
agree
with
the
other
twoo
before
found
:
so
it
appeareth
that
in
all
Englande
,
60.
mile
in
earthe
,
answereth
to
a
degree
of
latitude
in
the
skye
.
Master
.
Prooue
you
also
the
whole
difference
in
degrees
with
the
whole
distaunce
in
myles
.
Schollar
.
The
whole
difference
in
degrees
betwene
Southhampton
(
where
the
Pole
is
51.
degree
highe
)
and
Catnesse
pointe
,
(
where
the
latitude
is
62.
)
dothe
amount
vnto
11.
degrees
,
and
the
distance
in
myles
is
660
:
nowe
diuidyng
660.
by
11
,
the
quotient
appeareth
60.
agreably
as
it
was
in
all
the
other
woorkes
.
Master
.
What
if
you
dyd
go
farther
northe
,
19.
degrees
moare
?
I
meane
so
farre
Northe
that
the
Pole
were
81.
degrees
hyghe
aboue
the
Horizonte
,
howe
manye
myles
thynke
you
woulde
that
place
be
from
Southe
hampton
.
Schollar
.
That
can
I
quickly
accompt
by
the
Golden
rule
of
proportion
.
The
difference
betwene
those
2.
places
in
degres
is
30.
then
seyng
I
found
before
,
that
11.
degrees
gaue
660.
myles
,
I
sette
the
numbres
thus
in
their
forme
of
woorke
,
and
then
I
multiply
660
by
30
,
whereof
cometh
19800
:
whiche
I
must
diuide
by
11
,
and
the
quotient
wyll
be
1800.
Master
.
Thynke
you
thys
a
true
woorke
?
Schollar
.
This
woorke
is
true
and
without
any
doubte
,
so
that
the
measure
of
myles
in
Englande
were
true
,
whiche
wee
take
for
our
grounde
.
Master
.
And
if
that
measure
bee
not
true
,
yet
by
that
manner
of
woorkynge
you
maye
attayne
to
a
very
true
rate
of
myles
betwene
southe
Hampton
and
Catnesse
.
Schollar
.
That
is
no
greate
matter
,
nother
so
harde
to
bee
doone
.
Master
.
And
it
is
no
greater
matter
,
in
bothe
those
places
to
take
the
altitude
of
the
Pole
.
Schollar
.
That
is
true
also
.
Master
.
So
that
if
this
rate
be
not
true
,
ther
may
be
found
a
true
rate
by
diligence
.
Schollar
.
Yea
surelye
.
Master
.
And
by
that
true
rate
you
could
fynde
how
manye
myles
dothe
answere
to
30.
degrees
in
the
skye
.
Schollar
.
Easilye
.
Master
.
Well
then
:
Take
this
for
a
true
rate
,
tyll
you
can
fynde
an
other
more
certaine
.
And
nowe
answere
me
:
How
manye
myles
are
in
compasse
roude
about
the
whole
earth
?
Schollar
.
Nay
that
is
impossible
for
me
to
discusse
yett
,
tyll
I
haue
farther
knowledge
.
Master
.
Se
how
easye
a
thing
seemeth
impossible
to
you
.
Howe
manye
degrees
is
there
in
the
compasse
of
the
whole
skye
?
Schollar
.
That
can
I
certenlye
say
to
be
360
:
for
as
I
learned
before
,
a
degree
is
no
standynge
measure
,
but
a
rate
of
proportion
,
and
dothe
betoken
the
360.
parte
of
anye
cyrcle
.
Master
.
You
saye
well
.
Now
if
the
whole
circumference
of
heauen
be
360.
degrees
,
I
demaunde
of
you
,
howe
manye
myles
doth
answere
to
360.
degrees
?
Schollar
.
That
maye
I
doo
as
in
the
former
woorke
,
setting
the
numbres
according
to
the
rule
of
proportion
.
Then
multiplying
1800
,
The
compas
of
the
hole
earthe
.
by
360
,
there
ryseth
648000
,
whyche
I
muste
diuide
by
30
,
and
so
the
quotiente
wyll
bee
21600
,
whereby
I
knowe
that
21600
myles
,
doothe
answere
vnto
360.
degrees
in
the
skye
.
And
so
it
shoulde
seeme
that
those
are
the
iuste
numbre
of
myles
aboute
the
earthe
.
Master
.
You
neede
to
make
no
doubte
thereof
,
excepte
you
doubt
whether
there
be
any
part
of
the
earthe
without
the
circuite
of
heauen
:
or
els
that
you
doubte
,
whether
the
earthe
be
in
the
middle
of
the
worlde
.
Schollar
.
The
fyrste
doubte
were
to
foolishe
,
and
for
the
seconde
(
all
bee
it
I
doubte
nothinge
of
it
)
yet
I
adsure
my selfe
by
your
promise
;
of
the
full
proofe
thereof
in
the
next
treatise
.
Master
.
And
other
doubte
there
canne
be
none
,
but
this
:
Whether
the
earthe
and
the
skye
bee
bothe
rounde
.
whyche
both
I
wyll
so
substantially
proue
vnto
you
,
that
no
reasonable
man
will
doubt
of
it
.
Schollar
.
Then
am
I
certified
in
the
possibilitie
of
the
moste
doubtefull
conclusion
of
the
three
,
whiche
you
proponed
:
It
maye
please
you
to
proceede
to
the
other
two
.
Master
.
The
declaration
of
the
seconde
conclusion
,
for
declining
of
shadows
You
do
consider
that
this
conclusion
being
true
,
they
that
dwell
5400
myles
from
vs
,
doo
dwell
a
quarter
of
the
earthe
from
vs.
Schollar
.
That
muste
needes
be
so
:
for
four
times
5400.
doth
make
the
whole
circuite
of
21600.
miles
.
Mast
.
And
so
they
that
dwel
from
vs
any
manner
of
way
,
10800
miles
,
thei
dwel
half
the
compas
of
the
whole
earthe
from
vs.
Scholar
.
It
foloweth
so
by
the
former
reason
.
Master
.
It
is
well
knowen
by
the
nauygations
of
the
Portingales
and
Spaniardes
,
that
there
is
almost
south
from
vs
,
certain
places
inhabited
about
6300.
myles
,
as
namelye
at
the
streight
of
Magellanus
.
Magellanus
streighte
.
The
cape
of
Good
hope
.
Also
at
the
great
forelonde
of
Affrike
,
commonly
called
the
cape
of
Good
hope
,
are
there
diuers
regions
replenished
with
inhabitantes
,
and
they
be
from
vs
southwarde
aboue
5200.
myles
:
then
northward
wee
haue
good
knowledge
of
dyuers
cuntries
beyonde
vs
aboue
1200.
myles
,
whiche
bothe
ioyned
togither
,
do
make
from
the
greate
forelonde
of
Affrike
aforesaid
in
the
south
,
vnto
Wardehouse
in
the
northe
parte
of
Norwaye
,
aboute
6400.
myles
,
whiche
is
more
then
a
quarter
of
the
compas
of
the
earthe
:
but
from
Wardhouse
to
Magellanus
streight
,
it
is
aboue
7500.
myles
,
by
which
distaunce
of
myles
,
you
maye
easilye
gether
how
many
degrees
of
the
heauen
eche
of
those
places
is
from
vs
,
and
from
the
Equinoctiall
.
Schollar
.
Therein
I
praye
you
,
that
I
maye
prooue
my
newe
cunninge
.
The
cape
of
Good
hope
is
from
vs
southwarde
5200.
myles
,
that
is
in
degrees
of
the
skye
86
⅔
,
accordinge
to
the
former
rate
of
60
myles
to
eche
degree
.
from
whiche
numbre
of
86
⅔
,
if
I
abate
so
many
degrees
as
we
be
northe
of
the
Equinoctiall
,
which
are
52
degrees
,
then
doth
there
reste
34
⅔
degrees
.
So
that
it
appeareth
hereby
,
that
the
sayd
forelonde
is
34
⅔
degrees
southe
beyonde
the
Equinoctiall
.
Master
.
Now
for
Magellanus
streight
,
prooue
the
lyke
woorke
.
Schollar
.
It
is
6300.
myles
southwarde
from
vs
:
then
by
the
rule
of
proportion
,
agreablye
to
the
former
rate
,
it
must
yelde
in
degrees
105
,
oute
of
whiche
abatyng
our
distaunce
northe
from
the
equinoctiall
,
(
whiche
is
52
degrees
)
and
so
remaineth
53.
degrees
.
thereby
I
vnderstand
,
that
they
are
so
far
beyond
the
Equinoctiall
southwarde
.
Now
will
I
prooue
for
Wardehouse
,
how
farre
it
is
northe
from
the
Equinoctiall
.
It
is
from
vs
towarde
the
northe
1200.
myles
,
whiche
must
yelde
in
degrees
,
after
our
former
rate
20
,
from
these
20.
degrees
I
maye
not
abate
52
degrees
for
our
latitude
,
as
I
dyd
before
.
Master
.
It
were
againste
reason
,
seynge
that
the
latitude
of
Wardehouse
is
greater
then
our
latitude
is
,
and
lyeth
on
the
same
coaste
of
the
Equinoctiall
:
for
in
the
former
examples
the
two
places
were
on
the
contrarye
coaste
of
the
Equinoctiall
from
vs.
Schollar
.
I
see
it
well
now
,
so
that
by
reason
I
must
needes
adde
it
to
our
eleuation
,
and
so
ther
amounteth
72.
degrees
,
whiche
is
one
degree
more
then
you
did
affirme
it
to
haue
in
latitude
,
in
your
former
declaration
.
Master
.
The
cause
is
this
:
that
rate
of
60
myles
to
eche
degree
doth
serue
in
goyng
precisely
from
southe
to
north
,
but
nother
is
Wardhouse
iust
northe
from
vs
,
but
somwhat
towarde
the
easte
.
nother
yet
in
the
other
two
examples
any
of
bothe
places
was
directly
southe
from
vs
,
for
the
Forelonde
of
Affrike
beareth
towarde
the
easte
,
and
the
Streight
of
Magellanus
bendeth
towarde
the
weste
,
yet
for
this
tyme
it
maye
serue
as
well
for
our
purpose
,
as
if
it
were
more
precisely
doone
.
Schollar
.
An
ordre
in
teachinge
.
Yet
I
thinke
in
teaching
there
shoulde
bee
vsed
nothinge
but
certaine
truthe
.
Master
.
What
so
euer
is
taught
to
be
retained
for
a
truth
,
oughte
to
be
a
very
certaine
truth
in
deede
:
and
they
do
not
well
that
in
suche
manner
doo
teache
fyrste
vntruthes
for
truthes
.
but
where
induction
is
made
by
examples
,
it
is
often
tymes
more
or
at
the
leaste
,
no
lesse
expedient
to
vse
examples
not
exactly
true
,
then
to
take
only
precyse
true
examples
,
for
thereby
it
appeareth
the
proofe
to
bee
of
greater
force
,
if
it
will
procede
in
an
example
whiche
is
not
precisely
true
.
And
in
these
examples
we
haue
so
large
scope
of
triall
,
that
we
neede
not
sticke
for
two
or
thre
degrees
,
for
I
intende
not
to
speake
particularly
of
any
citye
that
is
vnder
one
certain
degree
,
but
of
whole
prouinces
,
whiche
occupieth
diuers
degrees
in
their
latitude
:
as
you
vnderstand
that
the
whole
isle
of
Britayne
doth
occupy
from
51
degrees
,
vnto
62
,
which
containeth
11
degrees
.
But
now
to
come
to
our
purpose
:
thus
much
you
vnderstand
,
that
beyond
the
equinoctial
,
yea
and
beyond
the
tropike
of
Capricorne
also
,
there
be
inhabitantes
.
Schollar
.
Yea
that
ther
be
,
aboue
29
degrees
besouthe
the
tropike
of
Capricorne
:
for
that
tropike
is
but
23
degrees
and
a
half
beyond
the
equinoctiall
:
and
ther
be
inhabitants
53.
degrees
beyond
the
equinoctiall
,
as
before
is
shewed
.
Master
.
Well
if
there
dwell
men
but
6
degrees
besouth
the
tropike
of
Capricorn
(
for
I
sayde
before
,
I
would
not
sticke
with
you
for
a
fewe
degrees
,
sith
I
wold
make
my
proofe
the
more
forceable
)
then
I
demaund
of
you
,
whiche
way
dooth
the
sonne
stande
from
them
at
noonetide
?
Schollar
.
It
must
needes
be
alwaies
northe
from
them
at
noone
,
as
it
is
alwaies
southe
from
vs
at
noone
,
seynge
they
are
beyonde
the
southe
Tropike
,
towarde
the
Southe
,
as
we
are
beyonde
the
north
Tropike
towarde
the
northe
.
Master
.
Then
consider
two
places
that
stande
iuste
south
and
northe
(
bicause
you
like
well
a
precisenes
in
examples
)
as
Venice
that
famous
citie
standeth
north
almost
from
the
cape
of
Good
hope
:
Now
consider
the
matter
thus
:
in
these
two
places
there
is
one
common
meridiane
line
,
sith
thei
do
stand
almost
iuste
southe
and
north
the
one
from
the
other
:
then
when
the
sonne
is
in
the
Meridiane
line
of
Venice
,
is
hee
not
also
in
the
Meridrane
lyne
to
them
that
dwell
at
the
sayd
Cape
of
Affrike
?
Schollar
.
Yes
trulye
.
Master
.
Then
those
twoo
places
haue
their
noone
tydes
at
one
hower
.
Schollar
.
So
haue
they
.
Master
.
And
at
Venice
theyr
shaddowe
goeth
alwaies
at
noone
toward
the
north
&
neuer
toward
the
southe
,
bicause
it
is
far
north
from
the
northerly
tropike
,
called
the
tropike
of
Cancer
,
and
so
is
the
foresaid
cape
of
Affrike
far
southe
,
beyonde
the
southe
tropike
,
whiche
is
the
tropike
of
Capricorne
:
wherefore
(
as
you
haue
confessed
)
their
shaddowe
at
noone
tyde
,
must
needes
go
all
tymes
of
the
yeare
toward
the
southe
.
Schollar
,
So
I
see
that
those
two
places
haue
a
contrarye
propertye
,
touchinge
their
shaddowes
.
Master
.
That
is
parte
of
the
thinge
that
I
did
intende
to
shewe
vnto
you
:
but
yet
they
bothe
do
agree
in
this
pointe
,
that
all
times
of
the
yeare
their
seuerall
shadowes
do
incline
towarde
one
coaste
.
Schollar
.
That
is
true
.
for
at
Venice
it
goeth
stil
north
,
and
at
the
cape
of
Good
hope
,
it
runneth
alwayes
southe
.
Master
.
These
sort
of
people
are
named
of
the
greke
Cosmographers
{αβγδ}
,
{αβγδ}
Heteroscij
Single
shadowed
.
Heteroscij
,
bicause
their
shadowes
goeth
styll
toward
one
coaste
.
Schollar
.
As
though
there
were
other
people
,
whose
shadowes
did
sometime
go
southward
,
and
other
tymes
northward
:
I
meane
their
shaddowes
at
noone
,
for
els
all
nations
haue
in
one
daye
,
at
diuers
houres
,
much
diuersitye
in
theyr
shaddowes
.
Master
.
Ye
vnderstand
the
time
well
.
and
you
shal
perceiue
as
wel
,
that
ther
be
such
places
,
which
chaung
their
shadows
.
You
confesse
that
men
dwel
beyond
the
tropike
of
Capricorne
southward
:
and
other
you
know
to
dwel
beyonde
the
tropike
of
Cancer
northward
:
&
thinke
you
it
not
agreable
to
reason
,
that
betwene
these
two
peoples
there
do
dwell
dyuers
nations
in
so
greate
a
plotte
of
grounde
?
Schollar
.
I
thinke
yes
.
and
I
heare
saye
,
by
our
owne
cuntrye
men
,
whiche
trauaile
to
Guinea
,
that
they
wente
beyonde
the
sonne
,
whiche
alwaies
I
tooke
to
be
a
lye
of
libertye
permitted
to
farre
trauelers
,
but
now
I
perceaue
it
maye
be
true
in
one
sense
.
Master
.
Ther
are
2.
places
of
that
name
,
and
both
are
beyond
the
tropike
of
Cancer
,
toward
the
south
,
and
the
one
of
them
is
almoste
directlye
vnder
the
Equinoctiall
circle
:
and
bicause
you
haue
named
that
cuntry
whiche
our
nation
doothe
well
knowe
,
take
it
for
your
example
.
They
of
Guinea
beeynge
nyghe
vnder
the
Equinoctiall
,
haue
the
Sonne
some
tymes
northe
from
them
at
noone
,
as
when
he
is
in
the
tropike
of
Cancer
:
and
other
tymes
they
haue
the
Sonne
southe
from
them
,
when
hee
is
in
the
Tropike
of
Capricorne
.
and
muste
not
their
shaddowes
chaunge
in
lyke
sort
?
Schollar
.
It
can
not
otherwaies
be
.
And
so
I
see
,
that
when
it
is
midsommer
with
vs
,
then
doth
their
shadows
go
sourth
ward
,
to
as
many
as
dwell
betwene
bothe
the
Tropikes
:
and
in
our
myd
winter
,
their
shaddowes
goeth
northward
.
Master
.
{αβγδ}
Amphiscij
Double
shadowed
.
Those
people
are
named
of
the
greekes
{αβγδ}
,
Amphiscij
,
bicause
the
noone
shadowes
goeth
both
wayes
,
sothe
and
northe
.
Schollar
.
And
farther
I
gather
,
that
there
is
no
quarter
in
the
Horizont
,
but
their
shadowe
runneth
that
waies
somtyme
in
the
yeare
.
Master
.
You
say
truthe
.
but
the
chief
regarde
is
here
gyuen
to
the
shadowe
at
nonetide
,
wherby
you
may
conceaue
,
that
sometime
they
haue
almoste
no
shaddowe
:
for
when
the
Sonne
at
noone
is
righte
ouer
their
headdes
,
then
theyr
shaddowe
is
ryghte
vnder
theyr
feete
,
and
not
on
anye
syde
.
Schollar
.
It
muste
needes
be
so
.
for
seeynge
the
Sonne
is
some
tymes
northe
of
them
,
and
sometymes
southe
from
them
,
hee
muste
needes
twyse
in
the
yeare
bee
right
ouer
their
headdes
,
ones
in
going
southward
,
and
againe
in
commynge
northwarde
.
Master
.
To
helpe
your
memory
and
coniecture
take
this
figure
for
a
presidente
and
example
,
where
I
haue
set
the
line
A.
C.
for
the
horizont
,
and
D.
B.
E.
for
diuers
places
of
the
son
at
noone
.
Now
if
you
call
A.
the
north
point
of
the
horizonte
Geometrical diagram.
zonte
,
and
C.
the
south
pointe
,
then
when
the
son
is
in
D.
toward
the
north
from
their
heds
,
their
shaddow
goith
to
F.
toward
the
south
.
And
when
the
sonne
is
in
E.
toward
the
southe
,
then
is
their
shaddowe
in
G.
bendig
toward
the
north
:
likewaies
the
sonne
being
right
ouer
their
heddes
in
B
,
their
shaddow
must
rest
in
H.
ryghte
vnder
their
feete
.
but
I
see
by
your
countenance
that
your
mind
woorketh
in
some
straung
imagination
:
and
I
coniecture
it
to
bee
for
that
I
haue
drawen
the
shaddowes
beneth
the
Horizonte
,
as
you
take
it
.
Schollar
.
You
haue
truly
coniectured
my
phantasye
.
Master
.
Bicause
this
place
serueth
not
to
declare
conclusions
of
bye
matters
,
I
wyll
exhybite
to
you
this
other
figure
,
Geometrical diagram.
where
the
shaddowes
doo
run
on
the
Horizonte
,
agreablye
to
your
phantasye
,
the
letters
of
demonstration
remayninge
as
they
were
beefore
,
and
bothe
these
tende
to
one
ende
.
Schollar
.
But
heere
are
but
two
shadowes
.
Master
.
Where
wolde
you
haue
the
third
set
?
Schollar
.
Right
vnder
the
tower
that
giueth
the
shaddow
.
Master
.
But
it
may
not
reache
from
the
foot
of
the
tower
,
nother
toward
one
coaste
,
nor
other
.
Schollar
.
No
,
that
it
maye
not
.
Master
.
Then
the
footer
of
the
tower
doth
couer
it
so
,
that
you
can
see
no
shaddow
at
all
.
Schollar
.
That
is
most
certaine
.
Master
.
Yet
remaineth
ther
an
other
sort
of
people
,
which
differ
in
one
point
from
these
other
twoo
sortes
,
by
reason
that
their
shadowe
in
one
daye
runneth
round
about
them
,
and
goeth
toward
all
coastes
of
the
horizont
wherefore
the
Greekes
do
call
them
{αβγδ}
,
Periscij
.
{αβγδ}
Periscij
.
rounde
shadowed
.
Schollar
.
Is
ther
no
english
nor
latin
names
for
these
sorts
of
properties
?
Master
.
The
latin
men
borowed
of
the
grekes
,
both
their
knowledge
and
also
many
names
of
arte
,
bicause
there
is
not
the
lyke
grace
of
facilitie
inborn
position
,
in
the
latyne
tonge
,
as
there
is
in
the
greeke
tongue
,
and
therefore
haue
I
geuen
them
no
englyshe
names
,
bicause
no
one
woorde
can
aptly
expres
these
properties
,
excepte
I
woulde
triflinglye
make
such
an
immitation
,
to
call
theym
,
One
shaddowes
Two
shadowes
,
and
Round
shaddows
:
or
els
,
which
is
not
muche
vnlyke
,
ye
may
call
them
Single
shadowed
,
Double
shadowed
,
and
Round
shadowed
.
Schollar
.
That
immitation
seemeth
straunge
yet
were
it
better
to
make
new
english
names
,
then
to
lacke
words
:
therefore
I
will
not
refuse
to
vse
them
,
till
I
can
learn
more
apt
names
.
but
I
praye
you
,
where
do
those
men
dwell
,
that
haue
their
shaddowes
runnyng
so
about
them
?
Master
.
Within
the
Polare
circles
:
for
all
people
whose
zenith
is
within
23
degrees
and
a
halfe
of
anye
of
bothe
the
Poles
,
haue
their
shaddowes
running
rounde
aboute
them
.
but
as
I
shewed
you
before
,
the
nearer
they
dwell
vnder
the
Pole
,
the
longer
is
theyr
daye
:
and
therefore
the
oftener
doothe
theyr
shaddowes
runne
about
them
for
where
the
daye
is
but
24
houres
longe
,
there
the
shaddowe
runneth
but
ones
aboute
:
and
where
it
is
halfe
a
yeare
longe
,
there
it
runneth
aboute
183
tymes
:
and
in
all
other
meane
places
raccodingly
.
Schollar
.
This
is
manifest
ynoughe
by
your
former
declaration
of
the
lengthe
of
the
dayes
,
and
the
course
of
the
sonne
.
And
farther
I
perceaue
that
when
they
that
be
vnder
the
Northe
pole
haue
their
shadowes
thus
runninge
aboute
them
,
then
they
that
dwell
vnder
the
Southe
pole
haue
no
shadowes
at
all
,
for
it
is
continuall
darkenes
with
them
.
Master
.
You
saye
well
,
Lighte
and
Darknes
vnder
the
Poles
.
concerninge
the
sonne
lyght
,
touching
them
that
dwell
directly
vnder
the
Poles
,
but
yet
they
haue
the
lyghte
of
the
Mone
euery
moneth
more
then
14.
dayes
togither
.
Schollar
.
Then
do
they
not
wante
lyghte
(
thoughe
they
lacke
the
sonne
)
but
only
halfe
a
moneth
togither
,
when
the
Moone
is
in
that
halfe
of
the
Zodiake
,
which
is
out
of
their
Horizonte
.
Master
.
That
is
well
considered
of
you
.
And
yet
euerye
moneth
they
lacke
not
lyghte
,
thoughe
bothe
the
sonne
and
the
Moone
also
bee
oute
of
their
sighte
:
for
as
you
see
with
vs
,
that
we
haue
lyghte
before
the
sonne
rising
,
and
after
the
sonne
setting
,
so
haue
they
suche
a
lyghte
by
the
beames
of
the
Sonne
50
dayes
continuallye
after
they
haue
loste
the
sighte
of
the
sonne
,
and
so
haue
they
the
like
lighte
50.
daies
continuall
,
before
the
sonne
doth
rise
to
them
.
Schollar
.
Then
they
wante
not
the
sonne
lyght
but
only
82.
daies
,
although
they
see
not
the
sonne
in
halfe
a
year
,
and
yet
halfe
that
82.
daies
they
haue
the
mone
in
their
sighte
,
as
I
perceaue
by
your
former
lessons
:
for
seing
she
goeth
about
the
Zodiake
euerye
moneth
,
she
must
needes
bee
halfe
that
tyme
in
that
parte
of
the
Zodiake
whiche
is
alwaies
aboue
their
Horizonte
.
This
contemplation
deliteth
me
muche
,
to
marke
places
absente
,
as
if
I
were
present
,
and
to
see
their
alterations
by
reason
more
certenly
,
then
I
can
do
by
sense
,
if
I
were
there
presently
.
Master
.
Yet
will
I
withdrawe
you
from
this
matter
,
tyll
an
other
more
conuenient
place
:
and
now
will
I
procede
to
the
thirde
conclusion
mentioned
before
:
that
is
the
generall
knowledge
of
the
times
of
the
year
,
in
all
parts
of
the
world
.
When
the
sonne
is
at
the
highest
with
vs
,
The
thirde
conclusion
is
declared
.
it
is
at
the
lowest
with
diuers
other
nations
,
namelye
to
all
them
that
dwell
other
vnder
the
Equinoctiall
circle
directly
,
other
southe
from
it
:
and
therefore
all
those
nations
haue
mydde
winter
,
when
wee
haue
midde
sommer
.
But
amongest
them
all
there
is
one
region
,
whiche
is
as
farre
beyonde
the
equinoctiall
towarde
the
southe
,
as
we
are
towarde
the
northe
.
Schollar
.
That
region
is
about
Magellanus
streight
,
as
I
gether
by
the
seconde
former
conclusion
.
Master
.
In
deede
the
streight
of
Magellanus
is
in
that
region
,
for
here
I
meane
by
a
Region
that
whiche
the
Grekes
do
call
a
Climate
,
whiche
is
in
forme
lyke
to
those
Zones
,
whiche
I
did
describe
before
,
A
Climate
.
saue
that
there
are
more
suche
Climates
or
regions
,
then
there
are
Zones
:
for
the
climates
may
well
be
accompted
48
betwene
the
twoo
polare
circles
,
The
nomber
of
climates
whiche
containeth
but
three
of
the
Zones
.
but
of
those
climats
I
will
say
no
more
at
this
present
,
but
that
euery
region
where
the
longest
day
is
half
an
hour
longer
or
shorter
then
it
is
in
anye
other
region
,
must
bee
accompted
in
a
seuerall
climate
from
it
:
so
that
vnder
the
equinoctiall
the
longest
daye
is
but
12.
houres
,
and
with
vs
in
the
myddle
of
Englande
,
it
is
about
18.
houres
:
wherefore
we
must
accompt
that
the
myddle
of
Englande
is
in
the
12.
clymate
from
the
Equinoctiall
northwarde
,
and
they
that
dwell
66.
degrees
and
a
halfe
north
,
or
southe
from
the
Equinoctiall
,
bicause
their
longest
day
is
of
24.
houres
,
that
is
twelue
howers
longer
,
then
it
is
in
the
myddle
of
the
worlde
vnder
the
Equinoctiall
(
from
which
all
those
accomptes
of
Climates
do
begin
)
they
must
be
iudged
in
the
24.
Climate
.
Schollar
.
Then
are
there
24.
climates
on
eche
syde
of
the
Equinoctiall
,
betwene
it
and
the
polare
circles
,
yet
I
remem
brethat
the
common
authors
make
mention
but
only
of
7.
on
either
side
,
whiche
maketh
but
14.
in
all
.
Master
.
That
shal
be
answered
anone
,
where
I
will
set
out
the
ordre
and
reason
of
the
diuer
sity
of
the
climates
:
but
for
this
time
it
shall
suffise
that
you
consider
this
,
that
all
places
within
one
Climate
,
haue
the
tymes
of
the
yeare
alyke
exactely
,
The
qualities
of
contrarye
climates
.
and
their
dayes
styll
of
lyke
quantitie
the
one
to
the
other
,
and
they
that
dwell
in
the
contrarye
climate
,
as
many
degres
on
the
other
side
of
the
Equinoctial
,
the
haue
bothe
the
times
of
the
yeare
contrary
,
and
also
the
quantity
of
the
daies
disagreable
,
for
when
it
is
sommer
in
the
one
climate
,
it
is
winter
in
the
other
and
when
the
daye
in
the
one
dothe
increase
,
the
nighte
in
the
other
dothe
increase
after
the
same
quantitie
iuste
.
Schollar
.
Then
for
example
:
In
the
cuntrye
about
Magellanus
streighte
,
it
is
sommer
when
wee
haue
winter
:
and
when
our
daye
is
at
the
longest
then
is
their
nyghte
at
the
longest
.
Master
.
Truthe
it
is
,
and
when
wee
haue
springe
,
then
is
their
haruest
:
and
so
is
it
common
to
all
them
that
dwell
ahoue
the
earthe
within
those
twoo
climates
,
yet
is
there
this
difference
,
that
in
our
climate
and
theirs
also
we
maye
imagine
four
quarters
equally
distincte
:
the
firste
quarter
being
that
which
we
dwell
in
,
Euery
Climate
hathe
4
quarters
and
in
the
contrary
climate
,
our
meridian
circle
limiteth
the
first
quarter
,
&
also
the
third
quarter
in
both
places
,
so
that
in
this
first
quarter
in
both
climates
,
the
times
of
the
day
and
night
at
a
like
:
for
when
it
is
noone
to
vs
,
it
is
no
one
to
them
:
and
when
it
is
midnight
to
them
,
it
is
midnight
also
to
vs.
Schollar
.
Then
likewaies
when
the
sonne
riseth
to
them
,
it
riseth
to
vs
,
and
so
setteth
at
one
time
in
bothe
Climates
.
Master
.
Ye
are
far
deceiued
,
for
then
of
necessitie
muste
it
folow
,
that
their
daye
and
ours
at
one
time
should
be
of
(
one
quantity
,
which
is
not
true
,
as
I
said
before
,
but
the
reason
of
that
shal
be
shewed
anone
,
yet
is
it
true
,
that
their
houres
agre
with
our
houres
if
their
meridian
circle
agre
with
ours
.
And
the
same
meridian
circle
vnder
ground
doth
li●…
te
in
both
these
climates
,
the
3
quarter
also
wher
it
is
noone
when
we
in
the
fyrst
quarter
haue
mydnyght
,
and
they
haue
mydnight
anour
noone
.
Now
may
you
easilye
conceaue
by
your
owne
mynd
,
the
places
of
the
other
two
quarters
.
Schollar
.
Ordre
inforceth
them
,
the
one
to
be
in
our
west
,
and
the
other
to
be
in
our
easte
.
Master
.
That
distinction
is
sufficiente
for
you
at
this
time
,
and
it
is
precisely
true
,
if
you
meane
the
easte
,
where
the
Sonne
ryseth
at
the
begynninge
of
the
Sprynge
tyme
,
or
of
the
haruest
,
wherfore
for
that
time
I
wyll
make
myne
example
:
When
the
sonne
riseth
to
vs
in
the
spring
tyme
,
it
is
noone
with
them
that
dwell
aboute
Calecut
,
and
when
the
son
is
in
our
Meridian
line
,
then
doth
he
set
to
them
:
so
that
when
the
son
doth
set
to
vs
,
Calecut
.
Peru
.
it
is
midnight
to
them
about
Calecut
;
&
thē
is
it
noone
to
the
famous
cuntry
of
Peru
:
Again
at
that
time
the
son
riseth
to
thē
that
be
in
the
isles
of
Molucca.
Molucca
.
wherby
you
may
gether
that
Peru
&
Calecut
be
in
2.
contrarye
coastes
of
the
earthe
,
and
therfore
seeme
to
go
wyth
their
feet
the
one
against
the
other
,
and
their
heddes
the
one
from
warde
the
other
,
whiche
sorte
of
people
therefore
are
called
of
the
Greeks
and
Latines
also
{αβγδ}
,
Antipodes
,
Antipodes
.
as
you
myght
say
Counterfooted
,
or
Counterpasers
.
Now
to
our
purpose
.
all
people
that
haue
mydnight
when
other
haue
noone
,
doo
differ
in
sonder
by
halfe
the
compas
of
the
heauens
,
one
waye
:
yet
may
they
not
be
called
Antipodes
,
except
they
differ
in
distaunce
euerye
waye
a
quarter
of
the
skye
,
and
must
haue
one
meridian
circle
.
So
that
our
Antipodes
must
be
vnder
our
meridian
circle
,
and
must
be
halfe
the
compas
of
that
circle
from
vs.
Schollar
.
Then
as
wee
are
52.
degrees
northe
from
the
Equinoctiall
,
so
muste
they
bee
52.
degrees
southe
from
the
Equinoctiall
,
in
that
parte
of
the
Meridian
circle
,
whiche
is
vnder
oure
Horizonte
,
and
then
haue
they
myddenyghte
when
wee
haue
noone
:
and
hereby
I
perceaue
that
they
haue
mydde
nyghte
when
it
is
noone
at
Magellanus
streighte
.
Master
.
In
deede
it
is
daye
then
at
Magellanus
streight
,
but
not
nighe
noone
,
for
Magellanus
streight
is
muche
to
farre
toward
our
weste
:
but
for
examples
sake
that
erroure
maye
be
permitted
,
and
especially
bicause
there
is
no
lond
but
sea
,
where
you
shoulde
meane
that
noone
to
bee
:
so
can
you
giue
it
no
propre
name
:
but
retaininge
that
name
for
example
of
the
true
place
,
you
may
consider
three
fortes
of
people
,
that
is
to
saye
,
our selues
,
and
those
that
dwell
by
east
Magellanus
streight
,
vnder
our
Meridian
circle
,
which
haue
noone
when
we
haue
noone
,
Antipodes
.
and
the
thirde
sorte
which
are
vnder
the
same
Meridian
,
but
haue
midnighte
when
we
haue
noone
,
and
are
as
farre
southe
from
the
Equinoctiall
,
as
we
are
northe
,
whome
I
named
our
Antipodes
,
and
so
ought
they
to
be
called
in
respect
to
vs
,
and
we
are
Antipodes
to
theym
also
:
But
nowe
comparinge
theym
with
those
other
by
easte
Magellanus
straight
,
they
ar
called
eche
to
other
{αβγδ}
Perioeci
,
as
you
may
saye
,
lyke
dwellers
,
bicause
they
dwell
vnder
one
Meridiane
circle
,
and
vnder
one
Parallele
also
,
and
be
like
in
distaunce
from
the
equinoctiall
circle
.
Schollar
.
There
are
manye
places
in
euerye
suche
region
or
climate
,
but
there
are
but
two
proprely
vnder
one
Meridiane
,
and
the
one
of
them
hath
midnight
when
the
other
hath
noone
:
so
the
tymes
of
the
daye
doth
differ
with
them
yet
I
perceaue
that
they
haue
the
seasons
of
the
yeare
agreable
,
bicause
they
dwell
on
one
side
of
the
equinoctiall
.
Then
must
it
folewe
that
those
whiche
vnto
vs
be
Perioeci
,
Perioeci
,
likdwellers
are
An
tipodes
to
them
that
dwell
by
Magellanus
streighte
vnder
our
Meridian
.
Master
.
You
saye
well
.
and
we
vnto
them
by
easte
Magellanus
streighte
,
vnder
our
Meridiane
,
are
called
by
the
greekes
and
latines
{αβγδ}
Antichthones
,
Antichthones
,
Counterdwellers
.
as
you
wold
say
Counterdwellers
,
or
Counterclimates
.
And
thus
haue
you
three
sortes
of
inhabitauntes
by
comparing
the
one
with
the
other
,
wherof
alwaies
Perioeci
(
that
is
Likedwellers
)
haue
like
tymes
of
the
yeare
,
but
not
of
the
daye
.
Antichthones
or
Counterdwellers
,
haue
like
times
of
the
day
,
but
not
of
the
year
.
Antipodes
or
Counterpasers
,
haue
nother
the
parts
of
the
year
,
nother
of
the
day
agreable
togither
,
but
contrary
in
both
,
how
be
it
ther
is
a
farther
consideration
for
exactnes
of
this
knowledg
,
which
I
will
herafter
declare
to
you
in
place
more
conuenient
:
but
hereby
maye
you
gather
the
diuersityes
of
tymes
of
the
yeare
,
and
also
of
the
dayes
,
accordinge
to
the
diuersitie
of
the
inhabitauntes
comparinge
them
all
other
to
your
owne
cuntrye
,
or
one
of
them
to
an
other
,
as
occasion
shall
serue
,
and
oportunitye
of
matter
.
And
thus
will
I
ende
for
this
time
,
if
I
maye
perceaue
by
your
repetition
of
this
thyrde
treatise
that
you
remembre
all
thinges
therein
declared
.
Schollar
.
I
were
els
to
blame
.
but
as
I
haue
learned
in
it
manye
seuerall
thinges
,
so
for
the
ordre
of
the
arte
these
I
note
as
chiefe
matters
.
-
1
The
repetition
of
the
thirde
treatise
.
Firste
the
distinction
of
the
Plages
of
the
worlde
,
accordingly
as
they
be
sette
forthe
in
the
Horizont
of
the
Sphere
.
-
2
Then
the
Paralleles
on
earthe
,
agreable
to
the
Paralleles
in
the
skye
,
of
like
names
,
and
distaunce
proportionable
.
-
3
Thirdly
the
distinction
of
the
.
v.
Zones
,
by
their
qualities
and
limites
,
and
of
their
inhabitantes
.
-
4
The
diuersities
of
Spheres
according
to
their
diuerse
inclinations
,
but
twoo
are
the
generall
distinctions
,
that
is
a
Ryght
Sphere
,
and
a
Bowinge
Sphere
.
-
5
Fyftlye
,
you
gaue
me
a
brefe
ordre
to
take
the
heyghte
of
the
Pole
,
or
any
other
Starre
or
Planete
.
-
6
Then
folowed
the
diuers
alterations
of
the
Horizonte
,
as
wel
betwene
Easte
and
weste
,
as
betweene
Southe
and
Northe
.
-
7
Seuenthlye
,
there
was
declared
the
causes
of
the
diuersities
of
the
daies
,
fyrste
in
diuerse
regions
,
and
then
in
one
region
.
-
8
The
difference
betwene
a
Naturalle
daye
,
and
an
Artificiall
daye
.
-
9
The
quantitie
of
the
longeste
daye
in
certen
partes
of
the
worlde
,
and
namely
vnder
the
Poles
of
the
worlde
.
-
10
How
by
this
excellente
Arte
a
man
maye
measure
all
the
compasse
of
the
earthe
,
and
yet
abyde
styll
in
one
cuntrey
.
-
11
A
distinction
of
sondrye
inhabitantes
,
accordinge
to
the
diuersities
of
their
shaddowes
,
whiche
are
three
principallye
.
-
12
Then
lastlye
folowed
an
other
distinction
of
inhabitantes
,
accordinge
to
the
agreeablenes
and
diuersities
of
tymes
of
the
yeare
,
and
the
quarters
of
the
daye
,
and
these
you
named
by
three
seuerall
names
also
,
whiche
are
names
of
comparison
,
bicause
they
take
not
those
names
,
but
in
comparison
to
other
nations
.
This
I
remembre
to
be
the
summe
of
this
laste
treatise
.
Master
.
You
remembre
it
well
,
and
vnderstande
it
also
well
,
as
it
may
appeare
by
your
repetition
.
Therfore
nowe
shall
you
depart
for
a
time
,
and
you
shall
reade
ouer
againe
your
authors
of
the
Sphere
,
whiche
you
did
name
before
,
and
now
marke
whether
you
can
vnderstande
them
,
and
as
your
returne
,
I
will
instruct
you
more
exactly
in
all
the
premisses
,
and
other
diuers
conclusions
,
whiche
nowe
I
haue
omitted
of
purpose
.
Schollar
.
I
am
moste
earnestly
bound
vnto
you
for
your
great
gentlenes
,
whiche
I
pray
god
to
requite
,
sith
I
cannot
,
and
who
wyll
els
I
knowe
not
.
Master
.
Farewell
then
,
and
remembre
your
owne
profit
▪
Schollar
.
The
author
of
all
profite
,
continew
and
increase
your
profit
,
that
you
may
haue
quiete
time
to
trauaile
for
the
profite
of
manye
.
THE
FOVRTH
TREATISE
OF
THE
CASTLE
OF
KNOWLEDGE
WHEREIN
ARE
THE
PROOFES
OF
ALL
that
is
taught
before
,
and
other
diuers
notable
conclusions
annexed
therto
▪
but
nothing
in
a
manner
with
out
demonstration
and
good
proofe
.
SCHOLLAR
.
IF
THE
INEXPLICABLE
BENEFITE
of
knowledge
did
not
enforce
me
to
forgette
all
bashfulnes
,
I
myghte
thinke
it
to
muche
shame
,
so
often
to
trouble
my
Master
frome
his
earnest
studies
,
and
to
staye
him
from
his
profitable
trauell
with
mine
importune
crauynge
of
knowledge
,
namelye
sithe
I
canne
not
recompence
anye
parte
of
hys
paynes
:
yet
hys
gentlenes
is
suche
,
that
hee
seeketh
more
the
profite
of
other
,
then
his
owne
pleasure
or
peculiare
commoditie
:
and
therfore
will
I
boldly
entre
into
his
house
.
Are
you
at
home
syr
?
Master
.
I
am
alwaies
at
houe
for
my
friendes
,
if
I
bee
not
with
them
from
home
:
yet
some
times
I
can
not
be
at
home
for
my selfe
.
Schollar
.
The
lesse
for
me
and
suche
as
I
am
,
that
often
trouble
you
more
for
our
owne
commoditye
,
then
for
your
gayne
.
Master
.
I
seeke
to
gaine
no
more
then
competentelye
maye
serue
my
necessarye
vses
,
with
conueniente
regarde
to
my
charges
:
but
if
I
offende
anye
wayes
in
couetinge
monnye
,
I
adsure
you
it
is
to
beare
the
charges
in
setting
forth
such
monumentes
of
knowledg
,
as
were
meruailous
profitable
for
all
men
,
very
pleasant
to
many
men
,
&
yet
estemed
only
of
wise
men
.
but
sith
I
cannot
do
the
good
that
I
wold
,
and
other
want
will
which
haue
goodes
in
excesse
,
I
must
do
as
many
other
doth
,
wish
good
to
all
men
,
&
helpe
them
as
I
canne
.
And
for
your
parte
I
looke
none
other
recompense
but
this
,
that
you
alwayes
be
thankefull
to
your
Master
.
and
as
hee
helpeth
you
freelye
,
so
doo
you
healpe
other
againe
,
and
hyde
not
the
knowledge
priuately
,
whiche
may
profite
many
publikely
.
but
now
to
your
matter
:
haue
you
perused
the
authors
of
the
Sphere
which
ar
commonly
readde
?
Schollar
.
To
reade
them
all
,
it
were
to
muche
for
my
lyfe
tyme
,
and
the
profite
not
so
greate
,
as
I
heare
manye
menne
saye
:
for
as
the
noumbre
are
infinite
,
so
the
later
wryters
doo
moste
commonlye
but
repete
that
,
that
twoo
or
three
of
the
auncientes
haue
written
before
.
wherfore
as
I
learned
that
the
beste
wryters
of
them
for
my
studye
,
were
Proclus
,
Ioannes
de
Sacro
bosco
,
and
Orontius
the
Frenche
man
,
so
I
haue
readde
them
,
and
out
of
them
haue
I
collected
a
table
of
theyr
moste
notable
matters
,
whyche
as
yet
I
vnderstande
not
,
or
els
doo
desyre
to
heare
the
demonstrations
for
their
proofe
.
Master
.
You
haue
doone
well
in
bothe
pointes
.
for
as
the
numbre
of
writers
are
infinite
,
so
haue
I
founde
great
tedious
payne
in
readinge
a
great
multitude
of
them
.
Notwithstandyng
as
you
shall
hereafter
seeke
further
knowledge
,
so
muste
you
reade
more
wryters
in
that
matter
:
wherefore
amongest
a
greate
noumbre
wo
orthye
the
readinge
,
I
wyll
name
a
fewe
vnto
you
,
whyche
I
wishe
you
to
studye
:
and
the
resydue
I
leaue
to
your
owne
discretion
.
Cleomedes
the
greeke
authour
,
is
very
woorthye
to
bee
often
readde
:
but
beste
in
hys
owne
tongue
,
for
the
latine
booke
is
muche
corrupted
.
Also
Euclide
his
booke
entituled
Phaenomena
,
and
Stoffler
his
commentaries
vppon
Proclus
Sphere
:
whyche
booke
I
wishe
were
well
recognised
(
as
it
hathe
greate
neede
)
then
myghte
it
serue
in
steede
of
a
greate
numbre
of
other
bookes
.
Dyuers
Englyshe
menne
haue
written
right
well
in
that
argument
:
as
Grostehed
,
Michell
Scotte
,
Batecombe
,
Baconthorpe
,
and
other
dyuers
,
but
fewe
of
their
bookes
are
printed
as
yet
,
therefore
I
will
staye
at
those
three
for
this
tyme
.
As
for
Plinye
,
Hyginius
,
Aratus
,
and
a
greate
manye
other
,
are
to
bee
readde
onlye
of
masters
in
suche
arte
,
that
can
iudge
the
chaffe
from
the
corne
.
and
Prolemye
that
worthye
writer
and
myracle
in
nature
,
is
to
harde
for
younge
schollars
,
except
they
be
fyrste
instructed
not
onlye
in
the
principles
of
the
Sphere
,
but
also
well
traded
in
Euclides
his
Geometrye
,
and
also
well
exercised
in
the
Theorykes
of
the
Planetes
.
But
nowe
let
me
see
the
table
that
you
haue
collected
.
-
1
The
ordre
and
mouinges
of
the
nine
Spheres
.
-
2
The
spaces
of
their
reuolutions
by
their
propre
motions
.
-
3
The
forme
of
heauen
is
rounde
,
and
his
mouynges
circulare
.
-
4
The
earthe
is
rounde
in
forme
,
and
the
water
also
.
-
5
The
earthe
is
in
the
myddle
and
Centre
of
the
worlde
,
and
is
but
as
a
pointe
in
comparison
to
the
Firmamente
,
and
doth
not
moue
anye
waies
.
-
6
The
compasse
of
the
earthe
,
and
the
diameter
of
it
,
what
they
make
in
common
myles
.
-
7
Of
the
circles
in
heauen
what
is
theyr
iuste
quantityes
,
their
numbre
,
their
ordre
,
their
distaunce
,
and
their
offices
.
-
8
Whye
the
Zodiake
hath
that
name
,
and
whether
anye
suche
formes
bee
in
the
skye
.
-
9
The
diuers
significations
of
a
figure
,
and
the
declyninge
of
them
.
There
are
two
Horizontes
,
one
sensible
,
and
the
other
onlye
iudged
by
reason
,
and
what
the
quantities
of
them
bothe
are
.
-
10
The
Greekes
and
the
Latines
doo
not
agree
in
the
description
of
the
circles
Arctike
and
Antarctike
,
and
what
are
theyr
reasons
.
-
11
Whether
there
bee
anye
dwellers
in
the
Vntemperate
Zones
.
-
12
What
bee
the
circles
Verticall
and
circles
of
Heighte
,
the
circles
of
howers
,
and
of
the
twelue
houses
.
-
13
Of
the
rysinge
and
settynge
of
the
Signes
and
other
Starres
,
bothe
in
the
Ryghte
sphere
,
and
also
in
the
Bowing
sphere
,
after
the
Astronomers
.
-
14
Of
the
Latitude
of
the
Sonne
and
the
twelue
Signes
from
the
easte
and
weste
.
-
15
Of
the
risinge
and
setting
of
the
starres
,
after
the
mynd
of
the
poetes
.
-
16
Of
the
diuersitie
of
Naturall
daies
,
as
well
as
of
Artificial
daies
in
diuers
partes
of
the
earthe
.
-
17
The
diuersities
of
howers
,
whereof
some
ar
equall
,
and
other
vnequall
accordinge
to
the
course
of
the
sonne
.
-
18
The
heighte
of
the
sonne
aboue
the
Horizonte
at
all
howers
,
and
in
all
regions
.
-
19
The
diuersyties
of
shadowes
,
whereof
some
be
called
Ryght
shadows
,
and
other
be
called
Turned
shaddowes
.
-
20
The
distinction
of
the
circles
Paralleles
necessary
in
Cosmographye
,
with
the
proportion
of
their
degrees
,
to
the
degrees
of
the
Equinoctiall
.
-
21
The
distinction
of
Climates
and
the
numbre
of
them
,
and
howe
large
in
breadth
eche
of
them
is
.
-
22
Of
the
Longitude
and
Latitude
of
regions
and
other
places
,
and
how
bothe
these
ought
to
be
taken
.
-
23
The
description
of
the
Mylke
waye
in
the
skye
,
whiche
is
commonly
called
Watlynge
streete
,
and
what
is
the
cause
of
that
coulour
in
it
.
-
24
The
numbre
and
names
of
the
chiefe
signes
and
figures
that
be
in
the
skye
,
and
whye
they
be
so
called
.
-
25
Of
the
circles
and
mouinges
of
the
Planetes
,
and
namely
of
the
eclipses
of
the
Sonne
and
the
Moone
.
These
be
the
titles
of
such
matters
as
I
haue
noted
in
them
moste
meete
for
this
tyme
,
syth
manye
other
thynges
are
sufficiently
taughte
in
the
former
treatises
,
and
some
other
thynges
,
namely
in
Orontius
booke
,
appertaine
to
Cosmographye
,
whiche
I
perceaue
by
your
sayinges
,
you
mynde
to
reserue
for
a
peculiar
treatise
of
that
matter
,
and
therfore
I
haue
omitted
them
here
.
Master
.
So
myghte
you
haue
doone
some
other
thynges
also
,
whiche
you
haue
noted
here
:
howe
be
it
I
will
vse
my
libertye
therein
,
to
expresse
in
conuenient
largenes
those
thinges
,
that
be
meet
for
this
place
,
and
the
rest
will
I
touch
with
as
conueniente
briefnes
:
referringe
the
other
to
theyr
more
conueniente
places
.
Schollar
.
Syr
I
know
right
well
,
that
your
iudgement
is
as
well
to
be
folowed
in
the
ordre
of
teaching
,
and
choise
of
matter
,
as
it
is
to
be
esteemed
in
the
teaching
and
explication
of
all
doubtefull
cases
.
Master
.
In
ordre
of
teaching
is
more
credit
to
be
gyuen
to
a
master
,
then
in
affirming
of
anye
doctrine
:
for
the
ordre
is
by
longe
experience
best
knowen
of
such
men
:
but
for
affirming
of
any
doubtefull
doctrine
,
no
man
ought
to
saye
any
more
then
he
can
shewe
good
reason
,
for
thapprouyng
of
the
same
.
And
now
to
your
matter
.
although
you
follow
the
ordre
of
Ioannes
de
Sacro
bosco
in
many
of
your
propositions
,
yet
will
I
beginne
with
your
thirde
proposition
,
and
referre
the
twoo
firste
to
a
more
meete
place
,
sythe
the
proofe
of
them
can
not
well
bee
vnderstande
,
withoute
a
great
numbre
of
other
conclusions
,
which
must
fyrst
be
proued
.
And
for
to
begin
with
the
declaration
of
the
ro
undnes
of
the
skye
,
and
his
circulare
motion
,
I
thynke
it
good
to
folowe
that
ordre
whiche
mouyd
men
fyrste
to
obserue
this
kinde
of
arte
.
The
firste
occasion
to
thinke
the
worlde
to
be
rounde
.
At
the
fyrste
beginning
of
the
worlde
,
when
this
arte
was
vnknowen
,
menne
marked
the
rysinge
of
the
Sonne
and
the
Moone
,
and
other
notable
starres
,
as
the
Broode
henne
,
whiche
is
called
of
many
men
the
Seuen
starres
,
and
other
like
:
and
perceauinge
them
to
rise
alwaies
aboute
the
easte
,
and
so
to
ascende
by
lyttle
and
lyttle
to
the
Southe
,
from
whence
they
dydde
descende
againe
softely
to
the
west
,
where
they
dydde
continuallye
sette
:
and
the
nexte
daye
again
they
perceaued
them
to
begin
their
accustomed
course
and
so
continued
like
as
before
:
wherin
although
they
sawe
some
diuersitye
,
yet
they
perceaued
that
diuersitye
to
bee
vniforme
,
and
after
a
yeare
to
retourne
to
the
olde
state
agayne
.
by
this
occasion
they
beganne
to
ymagine
that
thys
manner
of
mouynge
coulde
not
bee
but
in
a
rounde
and
circulerre
forme
,
and
also
in
a
rounde
and
circulerre
bodye
.
The
second
occasion
.
Then
to
vnderstande
this
matter
the
more
exactlye
,
they
obserued
the
mouinges
of
suche
starres
as
neuer
go
vnder
ground
,
which
be
about
the
north
pole
:
&
ther
thei
perceaued
by
diligent
marking
of
thē
,
especially
in
the
long
winter
nights
,
&
that
at
sundry
times
,
that
thei
turned
round
about
one
point
in
the
skye
:
and
those
starres
that
were
nighe
to
that
pointe
dyd
make
but
a
lyttle
compas
in
their
mouinge
,
and
the
farther
that
any
starres
were
from
that
pointe
,
the
greater
was
the
circle
of
their
reuolution
.
The
thirde
occasion
.
Then
thirdelye
they
marked
certaine
notable
starres
,
whiche
did
rise
and
set
,
but
yet
were
not
farre
from
those
other
starres
,
whiche
do
neuer
rise
nor
sett
,
and
they
might
wel
perceaue
that
they
did
continue
but
a
lyttle
while
vnder
the
Horizont
out
of
sight
,
wher
as
contrarye
wayes
,
those
starres
that
were
farther
from
that
point
or
Pole
,
did
remaine
longer
time
vnder
the
Horizont
,
out
of
their
sighte
,
whereby
they
were
inforced
to
thinke
,
that
these
varieties
and
formes
of
mouynge
coulde
bee
in
none
other
manner
of
body
then
in
a
rounde
forme
,
and
that
the
same
mouynge
was
circulare
and
rounde
,
as
it
did
manifestlye
appeare
in
the
northe
parte
of
the
skye
,
where
the
starres
continually
moue
rounde
aboute
one
pointe
,
and
do
neuer
set
vnder
the
Horizont
.
And
that
point
about
whiche
they
noted
this
motion
to
bee
,
they
called
(
as
reason
inforced
them
)
the
Pole
of
the
worlde
.
A
Pole
.
Schollar
.
What
doth
that
word
signifie
?
Master
.
It
hath
his
name
of
turning
:
as
you
wolde
saye
,
a
Turne
point
.
and
it
doth
betoken
the
ende
and
extreame
pointe
of
any
Axetree
,
howe
be
it
by
speciall
prerogatiue
the
name
is
appropried
to
the
endes
of
the
Axetre
of
the
worlde
.
Schollar
.
This
picture
dooth
some
Geometrical diagram.
what
represent
the
motion
of
the
starres
aboute
the
north
Pole
.
Master
.
You
say
truth
.
howbe
it
aptly
it
can
not
be
perceaued
in
flat
forme
but
in
a
round
body
,
as
a
globe
is
:
but
in
that
point
(
me
thinketh
)
ther
is
no
better
instrument
then
the
sky
it selfe
,
wher
euerye
man
maye
learne
that
lysteth
to
marke
,
and
there
bee
certaine
notable
starres
in
that
place
and
namelye
Charles
wayne
,
whiche
is
called
also
the
greate
Beare
,
whose
motion
is
so
euidente
,
that
euery
childe
may
marke
it
:
Charles
waine
.
And
twise
in
the
yeare
,
that
is
in
the
middle
of
February
and
in
the
middle
of
August
,
they
serue
for
a
iuste
horologe
:
so
that
the
finger
in
a
clocke
doth
not
more
aptely
pointe
the
howers
,
then
doth
that
figure
of
Charles
waine
.
Schollar
.
There
can
hee
no
more
apte
declaration
of
the
roundnes
of
the
heauen
,
and
of
his
circular
motion
,
then
the
sight
of
those
stars
which
moue
so
roundly
,
and
kepe
their
quarters
in
heauen
so
precisely
.
and
yet
I
haue
hearde
of
certaine
great
clerks
,
that
in
no
case
thoughte
it
reas
onable
to
affirme
suche
a
forme
of
roundnes
,
or
suche
a
round
motion
in
heauen
:
but
moste
of
all
I
meruaile
of
that
famous
man
Lactantius
Firmianus
,
which
doth
affirme
(
as
I
haue
hearde
)
that
the
heauen
is
not
rounde
,
but
flat
and
playne
.
Lactantius
Firmianus
his
erroure
.
Master
.
Many
scrupulous
diuines
by
mysse
vnderstandynge
of
scripture
,
haue
abhorred
the
studye
of
Astronomye
,
and
also
of
philosophye
,
and
often
tymes
doo
more
sharply
then
discretely
raile
at
these
bothe
,
and
yet
vnderstande
they
not
any
thinge
in
eyther
of
them
bothe
.
suche
men
are
to
hastye
to
bee
good
iudges
,
that
will
so
quickely
pronounce
sentence
,
before
they
haue
anye
good
euidence
,
and
will
determine
the
case
,
before
they
vnderstand
the
matter
.
for
how
can
anye
man
vnderstand
well
or
iudge
rightly
that
thing
that
he
knoweth
not
?
yet
such
drowsy
dreamers
haue
oftentymes
deceaued
many
wise
men
,
with
their
appearante
reasons
,
but
yet
none
but
such
,
as
either
were
giuen
to
hate
the
name
of
philosophy
,
or
els
at
least
had
no
time
,
or
none
habilitie
to
gette
vnderstandinge
in
it
.
By
some
suche
men
I
may
think
that
Lactantius
was
seduced
:
and
the
more
easily
,
for
that
he
had
conceaued
a
deadly
hatred
against
all
philosophers
and
against
philosophy
it selfe
:
Lactantius
opinion
of
the
forme
of
heauen
.
lib
.
24.
c
.
3
but
I
wil
let
him
and
his
folowers
passe
,
and
retourne
to
the
matter
.
Schollar
.
Yet
if
it
please
you
,
I
wolde
gladly
hear
his
reasons
,
that
he
maketh
for
approuing
his
opinion
,
seyng
hee
is
named
so
greate
an
oratour
and
so
famous
in
learnynge
,
that
many
men
will
beleue
him
without
any
reason
.
Master
.
Who
so
euer
wyll
beleue
him
in
this
point
,
must
do
it
without
reason
:
for
he
alleageth
no
reason
for
his
purpose
,
but
taketh
it
as
a
certaine
truthe
,
thereby
to
improue
the
opinion
of
the
Antipodes
,
as
I
will
more
largely
declare
anone
in
proouing
the
roundnes
of
the
earthe
.
But
seynge
he
coulde
bring
no
reason
for
his
opinion
,
you
shall
heare
some
reason
against
his
phantasye
,
and
then
iudge
as
you
can
.
That
the
skye
is
not
flatte
.
Firste
I
reason
thus
:
If
the
heauen
be
flatte
and
plaine
as
a
borde
,
then
howe
so
euer
it
stande
,
one
parte
of
it
muste
needes
be
nearer
to
the
earth
then
any
other
parte
of
it
.
and
that
parte
by
all
lykelyhod
must
be
right
ouer
our
heddes
,
is
not
that
so
?
Schollar
.
I
can
not
imagin
els
any
forme
of
situation
:
and
Geometrical diagram.
that
doth
appeare
partly
in
this
figure
,
where
A.
B.
C.
standeth
for
the
skye
,
and
lyeth
flatte
ouer
the
earthe
,
whiche
is
heere
represented
by
D
:
and
now
I
see
that
B
,
whiche
is
righte
ouer
D
,
is
muche
nearer
to
it
then
A.
or
C
,
or
anye
other
poynt
in
that
flatte
plaine
forme
,
whiche
is
sette
to
represent
the
flatte
skye
.
Master
.
Nowe
then
what
will
Lactantius
say
,
or
any
man
for
him
?
doth
this
heauen
moueor
not
?
Schollar
.
He
can
not
deny
that
which
we
maye
see
with
our
eies
,
that
bothe
the
Sonne
,
the
Moone
,
and
all
Starres
doo
moue
euery
hour
continuallye
.
Master
.
Yet
peraduenture
he
might
saye
,
as
some
other
like
contemners
of
philosophy
haue
saide
,
that
the
starres
and
Planetes
do
moue
in
the
skye
,
as
fishes
do
swimme
in
the
water
:
and
that
they
go
forwarde
thoughe
the
heauen
stande
styll
.
Schollar
.
I
remembre
I
haue
hearde
of
that
sayinge
,
and
that
a
famous
writer
of
late
doth
maintaine
that
opinion
.
Master
.
What
will
they
saye
then
,
dooth
keepe
the
starres
in
suche
a
iuste
ordre
and
equalitye
of
distaunce
?
whiche
neuer
altered
any
one
whitte
syth
the
beginning
of
the
worlde
,
is
it
possible
that
the
starres
shuld
mouein
the
skye
as
fishes
doo
swimme
in
the
water
,
or
as
birdes
flye
in
the
ayer
,
as
som
terme
it
,
but
that
the
starres
must
stragle
in
their
course
,
as
the
fyshes
do
,
and
as
the
byrdes
also
do
?
Schollar
.
I
haue
seene
both
fyshes
in
the
water
,
and
foules
in
the
ayer
,
to
keepe
a
meruallous
certene
course
in
their
flying
and
swimming
,
and
namely
fishes
that
go
in
sculles
,
as
herringes
commonlye
doo
,
and
other
fyshes
diuers
times
,
and
wilde
geese
also
and
storkes
in
their
flyinge
,
whereof
I
haue
often
mused
.
Master
.
You
maye
often
see
suche
notable
sightes
;
yet
if
you
marke
them
,
you
shall
see
muche
alteration
in
their
flyinge
,
as
well
as
in
the
swimming
of
the
fishes
:
whereby
you
may
think
their
ordre
not
to
be
constant
,
but
somtimes
one
flyeth
a
lyttle
faster
,
and
an
other
a
lyttle
slacker
:
and
sometime
they
swarue
on
the
one
side
,
and
somtime
on
the
other
.
but
were
it
not
a
sonde
ymagination
,
to
thinke
that
starres
doo
flye
and
folowe
one
guide
as
byrdes
doo
,
and
in
5000.
yeare
space
to
keepe
their
places
so
precisely
,
that
they
varye
not
one
minute
of
a
degree
?
Schoollar
.
In
deed
it
were
meruailous
,
and
so
are
all
Gods
woorkes
.
Master
.
Yet
is
there
one
inuincible
reason
againste
that
opinion
,
The
Mylky
way
called
of
the
grekes
Galaxia
gathered
of
the
figure
of
the
Milkye
way
in
heauen
,
whiche
many
men
in
England
do
call
Watlyng
streete
,
comparing
it
to
one
of
the
greate
highe
waies
in
Englande
that
is
called
Watlyng
streete
.
This
Mylkie
way
,
if
it
serued
for
none
other
purpose
,
yet
doth
it
seeme
woorthy
the
noting
,
for
the
exact
consutation
of
the
saide
opinion
,
and
for
that
cause
it
myghte
seeme
to
bee
made
by
God
,
which
hath
wroughte
man
ye
meanes
to
leade
men
vnto
truthe
.
This
way
is
in
the
skye
it selfe
,
as
all
men
hath
confessed
,
and
their
eyes
doo
testifye
,
and
the
starres
that
bee
in
it
are
alwayes
seene
to
keepe
their
places
in
it
:
so
that
it
muste
needes
folowe
,
that
the
same
wayes
doothe
mooue
with
the
starres
,
and
then
consequentlye
the
skye
muste
needes
moue
also
.
Schollar
.
Yet
it
may
be
said
,
that
the
starres
which
bee
in
it
doo
moue
alwaies
so
certainly
in
it
,
that
it
maye
seeme
to
moue
,
as
though
it
stande
still
.
Master
.
Did
you
euer
marke
the
same
Mylke
way
?
Schollar
.
Yea
verily
,
and
that
often
.
Master
.
And
did
you
perceaue
in
it
any
boughts
,
corners
,
partitions
,
or
suche
other
like
markes
,
wherby
you
myghte
knowe
one
part
of
it
from
an
other
?
Schollar
.
That
haue
I
done
also
,
in
so
muche
that
in
som
places
it
seemeth
to
be
diuided
into
two
waies
.
Mast
.
That
is
true
.
And
think
you
if
the
starres
did
moue
in
it
,
and
it
stande
still
,
that
these
starres
which
now
be
by
the
partition
of
those
branches
,
muste
not
within
foure
or
fiue
howers
be
passed
farre
from
that
place
?
Schollar
.
It
shuld
so
folowe
,
yet
that
is
not
so
:
for
I
haue
marked
the
contrary
oftentymes
,
that
they
keepe
those
places
styll
.
Master
.
Then
do
not
the
starres
moue
from
their
places
,
but
as
those
places
moue
with
them
.
Schollar
.
It
appeareth
now
to
plaine
to
bee
made
doubtfull
any
more
.
Master
.
Yet
will
I
prooue
it
better
:
Dydde
you
euer
marke
anye
notable
place
of
that
Mylke
waye
at
the
beginnynge
of
the
nyghte
in
the
easte
,
or
in
any
other
coaste
of
hauen
?
Schollar
.
Yea
for
southe
.
Master
.
And
haue
you
marked
whether
that
place
hathe
gone
anye
farther
westward
that
nyghte
?
Schollar
.
I
haue
marked
it
well
,
and
haue
perceaued
that
it
hathe
moued
a
greate
waye
from
his
firste
place
:
and
who
so
euer
lysteth
to
trye
it
,
let
him
at
sixe
of
the
clocke
in
the
deepe
winter
marke
any
notable
places
in
it
,
and
at
tenne
of
the
clocke
the
same
nyght
,
hee
shall
perceaue
it
to
haue
gon
westward
more
then
a
quarter
of
the
skye
.
Master
.
Your
woordes
are
true
,
meanynge
a
quarter
of
the
skye
aboue
your
Horizonte
:
and
by
this
you
see
,
it
can
not
bee
auoyded
,
but
that
the
skye
dooth
mooue
as
well
as
the
starres
.
Schollar
.
It
is
moste
manifestly
proued
,
so
that
Lactantius
himselfe
can
not
denye
it
,
onlesse
he
will
deny
that
hys
owne
senses
may
iudge
in
sensible
thinges
.
Master
.
Then
if
the
heauen
be
flat
,
as
he
doth
imagyne
it
to
be
,
and
it
doth
moue
westwarde
,
as
all
men
dooth
see
,
other
the
muste
say
that
the
skie
is
infinite
in
length
,
and
that
wee
neuer
see
any
parte
of
it
againe
after
it
is
ones
past
our
sighte
:
and
therby
affirme
,
that
there
be
infinit
many
sonnes
and
as
many
moones
,
and
an
infinite
numbre
also
of
all
other
Planetes
,
and
of
all
seuerall
kinde
of
starres
,
or
els
hee
must
declare
whiche
wayes
that
the
Sonne
,
the
Moone
,
and
the
other
starres
doo
com
into
the
easte
againe
.
Schollar
.
He
can
not
saye
that
they
come
backwarde
the
same
waye
that
they
went
forwarde
,
for
then
wee
shoulde
see
them
in
their
retourninge
:
and
to
saye
truthe
,
there
can
bee
none
other
forme
of
mouinge
,
but
in
rounde
forme
,
that
may
bringe
them
into
the
easte
againe
:
But
peraduenture
he
may
say
,
that
though
the
skie
be
flat
and
plain
in
forme
,
yet
it
hath
a
rounde
motion
.
Master
.
Some
other
man
may
say
so
:
for
he
thinketh
the
contrarie
as
his
woordes
importe
,
for
in
reprouing
Astronomers
,
hee
saithe
:
Ex
motu
syderum
opinati
sunt
coelum
uolui
.
By
the
mouing
of
the
Starres
they
imagined
that
the
heauen
doth
turne
rounde
by
which
wordes
hee
seemeth
to
meane
that
the
starres
moue
,
but
not
the
skie
Schollar
.
That
is
fully
improued
before
.
Master
.
If
it
were
not
,
I
myghte
reason
with
him
thus
:
Seyng
he
affirmeth
as
reason
inforceth
him
,
that
the
starres
do
moue
,
and
will
not
confesse
that
the
skye
turneth
round
,
then
(
as
I
declared
before
)
one
parte
of
the
skye
whiche
is
ouer
oure
headdes
,
is
nearer
to
the
earthe
then
the
bothe
endes
be
.
Schollar
.
That
appeareth
plaine
,
excepte
hee
wolde
saye
against
all
reason
,
that
the
earthe
were
as
large
as
the
skye
.
Master
.
an
argument
against
the
flatnesse
of
the
skye
.
The
maior
or
maxime
.
Yet
thoughe
hee
woulde
saye
so
,
my
reason
shall
proceede
in
full
strengthe
,
syth
some
partes
of
the
skye
by
his
meaninge
muste
needes
bee
farther
from
vs
then
some
other
.
Therfore
I
frame
my
reason
thus
:
All
thinges
that
men
can
see
,
seeme
greattest
when
they
bee
nyghest
vnto
menne
,
and
the
farther
they
bee
from
their
sight
,
the
lesses
they
shewe
.
Schollar
.
I
thynke
no
man
so
childishe
to
denye
that
.
for
euery
hower
our
sighte
doth
approue
that
it
is
so
:
if
we
see
a
man
a
farre
of
,
he
seemeth
no
bygger
then
a
lyttle
child
:
and
a
greate
shippe
farre
in
the
sea
,
dooth
shewe
no
bigger
then
a
crow
sometimes
.
Master
.
The
minor
.
Then
takinge
that
for
a
maxime
in
argumente
,
I
annexe
this
minor
,
that
the
starres
mouynge
it
that
imagined
flat
skye
,
are
most
nighest
to
vs
,
when
they
bee
ouer
our
headdes
:
and
they
are
fardest
from
vs
,
when
they
be
in
the
easte
or
in
the
weste
:
The
conclusion
.
wherefore
I
inferre
the
conclusion
,
that
the
starres
muste
seeme
greatest
,
when
they
be
ouer
our
heddes
:
and
they
muste
seeme
muche
lesser
,
when
they
be
in
the
easte
or
weste
.
Schollar
.
This
conclusion
is
plainly
false
.
for
our
eyes
doo
testifye
the
contrary
,
syth
alwaies
the
sonne
,
the
moone
and
the
starres
doo
seeme
greatest
at
the
rysinge
in
the
east
,
and
at
their
settinge
in
the
weste
.
And
they
shewe
smallest
,
when
they
be
nyghest
ouer
our
headdes
.
Master
.
If
the
conclusion
be
false
,
and
the
argument
good
as
Lactantius
can
not
comptroll
it
,
then
I
maye
obiecte
to
him
his
owne
rule
:
Necesse
est
falsa
esse
,
quae
rebus
falsis
congruunt
.
It
can
not
be
chosen
but
those
muste
be
false
sentences
that
doo
agree
with
false
matters
.
and
so
muste
they
needes
bee
salfe
premisses
,
that
do
inferre
a
false
conclusion
.
Scholar
.
In
good
faithe
I
thinke
nother
Lactantius
,
nother
any
man
els
is
able
to
auoide
this
reason
,
except
he
will
auoide
that
fonde
opinion
of
imagining
a
flatte
skye
,
and
the
standing
of
the
same
vnmouable
:
yet
if
anye
man
wolde
saye
,
that
the
heauen
were
square
,
or
of
any
other
forme
of
diuers
angles
,
as
here
you
se
many
varieties
in
these
figures
.
An
other
reson
by
auoi
ding
of
emptines
whiche
nature
cannot
bere
Geometrical diagrams.
How
might
I
aptly
reproue
their
opinion
,
if
thei
will
affirme
farther
,
that
the
skye
with
suche
a
forme
doth
moue
round
?
for
by
saying
they
mighte
auoide
the
danger
of
this
last
inconueniene
.
Master
.
While
they
mighte
seeme
to
auoide
one
danger
,
they
fall
into
an
other
:
as
for
a
proofe
.
I
tourne
those
figures
round
,
whereby
in
deed
it
appeareth
,
that
euery
part
of
them
keepe
styll
theyr
owne
distaunces
vnchangeably
frome
the
centre
,
but
yet
is
one
parte
more
nerer
the
centre
then
an
other
parte
is
,
and
euerye
parte
in
their
turning
seemeth
to
describe
a
circle
about
the
centre
,
eche
circle
in
bignes
according
to
the
distaunce
of
that
parte
whereby
it
is
described
,
and
so
the
greatest
circles
are
made
by
the
extreame
angles
,
of
euery
figure
.
Scholar
.
All
that
is
easily
perceaued
,
at
the
first
sighte
in
tourning
the
figures
aboute
.
Master
.
Then
if
the
heauen
bee
cornered
,
it
maye
haue
no
lesse
roome
to
moue
in
,
then
the
compasse
of
the
vttermoste
circle
doth
require
.
Scholar
.
That
appeareth
certaine
,
for
els
it
woulde
staye
by
those
corners
,
or
els
break
the
corners
in
the
tourning
,
wherof
nether
is
to
be
fantasied
but
of
fools
,
whose
thoughts
are
pardonable
in
all
those
that
refuse
not
their
common
felowshippe
,
but
not
in
other
,
although
for
their
woorthines
they
might
be
Wardens
of
that
company
.
Master
.
Then
if
for
their
motion
they
require
so
large
a
circle
,
as
may
compas
their
corners
,
there
appeareth
voyde
roome
against
euery
side
,
in
which
roome
what
shal
be
set
to
auoide
emptines
,
which
nature
can
not
beare
?
Schollar
.
Let
them
answere
that
lyketh
that
phantasy
,
for
I
can
imagine
nothing
,
except
I
shuld
name
Ayre
,
but
that
by
his
nature
can
not
ascend
so
highe
.
Master
.
You
gesse
well
,
that
it
muste
be
some
subtile
and
liquide
thinge
,
that
might
change
his
place
as
fast
as
the
heauens
do
turne
:
for
in
turning
,
the
corners
will
come
anone
where
the
emptines
is
now
,
and
so
successiuely
eche
chaunge
place
with
other
.
but
Ayer
you
say
can
not
come
thither
,
sith
it
may
not
ascend
so
highe
:
the
lyke
may
you
saye
of
fier
and
water
,
and
muche
more
of
thearth
.
Againe
if
they
could
ascend
,
how
shuld
they
pearse
through
the
substance
of
the
heauens
?
beside
that
being
elementes
,
and
therefore
corruptible
and
subiecte
to
daily
alterations
,
they
are
vnmeet
to
be
matched
with
the
vnchangeable
substance
of
the
heauens
.
Scholar
.
This
is
reason
inough
against
that
imagination
,
sith
nature
can
not
suffre
it
to
bee
emptye
,
and
nothinge
els
but
part
of
the
skye
can
supplye
it
.
Master
.
The
thirde
reason
for
apt
mouing
Yet
considre
farther
:
syth
the
motion
of
heauen
of
all
other
muste
bee
iudged
the
moste
swiftest
,
whiche
in
24.
howers
dooth
runne
so
large
a
race
,
that
is
manye
folde
greater
then
the
compasse
of
all
the
earthe
,
so
that
euery
hower
it
runneth
many
thousand
miles
,
dooth
not
this
swyfte
motion
require
that
forme
,
which
is
of
all
other
most
apte
for
mouing
?
&
doth
it
not
repugne
to
such
formes
as
be
full
of
corners
,
&
therfore
vnapt
to
moue
swiftly
or
vniformly
?
Sc.
It
appeareth
plain
madnes
to
dream
ones
the
contrary
.
Mast
.
Then
all
men
know
that
as
cornered
bodies
be
most
vnapt
for
to
run
,
so
is
a
round
globe
most
apt
for
all
other
.
Sc.
Euery
common
turner
can
skil
in
that
reason
,
&
know
that
a
litle
altering
of
the
one
side
,
maketh
the
boul
to
run
biasse
waies
.
Master
.
If
the
reason
be
so
plaine
that
common
artificers
can
skyll
of
it
,
it
were
to
great
a
folly
for
learned
menne
to
doubte
of
it
.
Scholar
.
They
that
doubt
of
it
,
neuer
waied
their
opinion
with
any
reason
,
as
I
maye
thinke
,
for
these
reasons
suffice
to
persuade
any
man
.
Master
.
The
fourth
reason
for
capacitie
.
Yet
ones
againe
way
this
for
thee
for
me
of
heauen
.
sith
it
incloseth
all
thinges
,
and
is
the
greatest
of
all
other
,
were
it
not
meete
that
it
shuld
haue
the
greatest
forme
which
is
most
large
and
apte
to
compas
and
inclose
all
other
?
Schollar
.
It
is
bothe
meete
and
necessary
also
.
Master
.
Then
is
it
well
knowen
of
yonge
schollars
in
geometry
,
that
as
of
all
flatte
formes
of
like
circumference
,
the
circle
is
the
greatest
,
so
of
all
sounde
formes
of
lyke
circuite
the
Globe
is
moste
largest
,
and
therefore
moste
aptest
for
the
forme
of
the
skye
,
whiche
incloseth
all
thynges
that
man
canne
see
.
Sch.
I
myght
be
ashamed
to
demaunde
anye
more
profe
for
the
roundnes
of
heauen
or
his
circulare
motion
,
yet
are
the
reason
so
pleasante
,
that
I
delite
muche
in
the
hearinge
of
them
,
and
therefore
canne
bee
contente
to
imploye
as
muche
time
in
hearing
them
,
as
you
thinke
good
to
bestow
in
framynge
them
.
Master
.
I
coulde
occupye
you
so
a
greate
tyme
:
but
I
thinke
it
not
best
to
staye
thereon
to
longe
,
syth
wee
haue
many
other
matters
to
prooue
,
and
at
other
tymes
we
maye
talke
hereof
againe
.
These
reasons
whiche
you
haue
hearde
do
proue
not
only
that
the
motion
of
heauen
is
round
,
but
also
that
the
rounde
forme
doth
best
agree
to
the
skye
,
for
largenes
of
capacitye
,
for
aptenes
in
mouing
,
for
auoyding
of
emptines
,
and
for
the
iuste
appearance
of
the
starres
in
vniforme
bignes
,
whiche
I
thinke
sufficiente
for
this
time
.
Schollar
.
There
be
twoo
thinges
by
the
waye
which
I
desire
muche
to
heare
more
largely
declared
:
the
one
is
for
the
appearance
of
starres
,
whiche
seeme
moste
greatest
at
theyr
risinge
and
settynge
:
the
other
is
,
for
the
auoydinge
of
emptines
,
whiche
as
I
haue
often
hearde
,
so
woulde
I
gladly
ones
vnderstande
.
Master
.
The
firste
of
them
appertaineth
to
perspectiue
,
and
the
seconde
vnto
naturall
phylosophye
,
so
that
bothe
doo
require
an
other
place
and
tyme
:
yet
bicause
I
haue
alleaged
it
for
this
present
matter
,
although
the
reasons
why
it
is
so
,
may
not
well
here
be
repeted
,
yet
that
it
is
so
,
shall
be
brefely
declared
.
All
thinges
shew
great
through
vapoures
or
myste
.
In
a
mystie
morning
as
you
walk
,
all
things
diagram illustrating how objects appear larger when viewed through mist or water.
that
you
see
,
seeme
greater
through
the
myste
,
then
in
deede
they
be
a
pennye
in
the
water
seemeth
broader
then
it
is
,
and
the
deeper
that
it
lyeth
,
the
greater
it
appeareth
:
so
the
Sonne
and
the
Mone
and
all
other
stars
being
nigh
to
the
earth
,
do
shew
through
the
vapours
that
ascend
from
the
ground
,
and
therfore
appear
greater
then
they
be
:
&
if
the
vapours
be
many
,
the
starres
shew
the
bigger
:
the
cause
is
,
the
interruption
and
reflection
of
the
sight
beames
by
the
vapours
&
the
water
.
&
liker
is
the
cause
in
seing
throughe
glasse
which
occasioned
weke
sights
to
seke
aid
of
spectakles
Sch.
Many
vse
that
aide
,
that
know
not
the
reason
thereof
.
Master
.
Nature
abhorreth
emptines
.
So
manye
drawe
water
at
a
plompe
,
that
knowe
not
the
cause
,
why
the
water
do
the
ascend
,
whiche
is
onlye
natures
worke
to
auoide
emptines
.
And
many
men
vse
bellowes
to
blow
the
fier
,
whiche
know
not
the
reason
of
their
firste
inuention
,
and
therefore
can
not
mende
them
if
they
be
hard
to
draw
.
many
men
also
draw
waters
by
fountaines
higher
then
the
springe
,
yet
few
of
them
do
knowe
what
is
the
reason
of
their
woorke
,
and
therefore
fewe
canne
amende
it
,
if
the
faulte
be
any
thinge
doubtefull
.
A
greate
numbre
of
other
lyke
thinges
coulde
I
shewe
,
where
natures
abhorfulnes
to
permitte
any
emptines
,
doth
cause
straunge
effectes
,
in
thinges
that
are
vsed
of
many
men
,
and
well
knowen
of
fewe
men
.
But
ass
it
appertaineth
not
to
this
place
to
discourse
largely
in
those
matters
,
so
an
other
tyme
shall
serue
for
them
.
And
nowe
lette
vs
proceede
in
oure
purposed
attempte
,
to
see
what
proofes
I
can
bringe
for
the
roundenes
of
the
earth
:
wherein
I
will
beginne
with
a
distribution
disiunctiue
,
containynge
many
opinions
touching
the
forme
of
the
earth
:
and
eche
of
them
will
I
substantially
improue
,
Diuers
opinions
of
the
forme
of
the
earthe
.
saue
that
onlye
whiche
affirmeth
it
to
bee
rounde
,
and
that
will
I
so
fullye
approoue
,
that
I
doubte
not
but
you
shall
thynke
your selfe
fullye
satisfied
.
Som
menne
consideringe
that
as
for
the
skie
not
forme
was
so
meete
as
a
round
form
,
bycause
of
his
swifte
mouinge
,
so
for
the
earthe
whiche
standeth
so
steddilye
,
they
iudged
no
forme
so
meete
as
diagram of a cube.
a
Cube
forme
,
which
they
esteemed
moste
stable
of
all
other
:
and
therefore
manye
aunciente
Philosophers
by
the
forme
of
a
Cube
dydde
secretely
signifie
constancy
and
stablenes
:
Why
fortun
is
pictured
standing
on
a
globe
.
and
contrarye
waies
by
the
forme
of
a
globe
they
expresse
changable
alteration
,
and
continuall
mouing
.
Scholar
.
That
I
may
perceaue
by
the
placing
of
Fortune
on
a
rouling
globe
,
in
token
of
hir
inconstancy
&
voluble
changinge
.
And
therefore
haue
I
often
phantasied
,
that
dice
,
Why
dice
be
made
in
cubik
form
.
whiche
is
the
image
of
Fortunes
inconstancye
,
and
serueth
onely
for
fortunes
playes
,
myghte
beste
haue
been
made
in
forme
of
a
Globe
,
for
they
are
as
vnconstant
as
fortune
hir selfe
.
Master
.
Ther
seemeth
in
Fortune
two
diuers
natures
,
Diuers
fortune
.
the
one
is
lyghte
and
alwaye
flickerynge
,
the
other
is
heauy
,
and
therefore
more
stable
,
so
that
ofte
tymes
we
see
them
that
haue
a
lyghte
and
pleasunte
fortune
,
as
lightlye
leese
,
that
they
lyghtly
gayned
:
but
where
heauye
fortune
setteth
hir
foote
,
seldom
can
she
be
remoued
,
hir
steppes
are
so
stayed
:
but
to
expres
more
exactly
the
nature
of
the
cube
resembled
in
the
dice
,
bothe
in
forme
and
in
effecte
,
you
shall
marke
well
the
meaning
of
that
olde
prouerbe
:
Iacta
est
alea
,
The
dice
is
caste
.
or
the
lotte
is
drawen
.
or
fortune
is
past
.
by
whiche
saying
is
declared
,
that
the
thinge
that
is
ones
done
,
can
neuer
againe
be
vndone
,
although
it
may
be
altered
,
and
so
constancy
in
that
appeareth
most
certein
.
for
as
your
chance
on
the
dice
beyng
ones
caste
,
you
muste
be
content
to
stand
to
it
:
so
fortune
when
it
is
paste
,
can
not
bee
altered
.
And
that
is
the
cause
why
all
men
vse
to
saye
,
when
they
expresse
their
stay
in
lyuing
:
Suche
is
my
fortune
.
Yet
many
learned
men
put
difference
betwene
chaungable
chaunce
,
and
stable
fortune
,
callyng
the
firste
Fortuna
,
and
the
other
Fatum
:
so
that
destiny
is
stable
,
though
fortune
chaung
right
often
.
But
thus
I
forget
our
purposed
intent
,
with
so
many
digressions
of
other
bye
matters
.
Schollar
.
I
founde
no
faulte
not
thought
no
tyme
loste
,
syth
the
matter
is
pleasunte
and
somewhat
to
our
purpose
.
Master
.
Well
,
this
was
their
imagination
,
that
thoughte
the
earthe
to
be
of
a
cubyke
forme
,
for
that
they
iudged
it
the
most
stedfast
form
.
The
second
opinion
.
Then
an
other
sorte
deuised
a
three
cornered
forme
like
he
rygge
of
an
house
where
tone
syde
lyeth
flatte
,
A
rygge
forme
.
Geometrical diagram.
and
the
other
two
leane
a
slope
.
And
thys
forme
they
iudged
better
for
twoo
causes
.
Firste
they
thought
that
it
was
more
steddy
then
a
cube
form
,
bicause
it
hath
a
broader
foote
,
and
a
lesser
toppe
:
and
secondly
for
that
they
thought
it
a
more
apte
forme
to
walke
on
,
and
more
agreable
to
the
nature
of
the
earth
,
wher
some
times
there
ryseth
highe
hils
,
and
sometime
againe
men
may
see
greate
vales
descendyng
.
Schollar
.
This
imagination
is
grosse
inoughe
.
Master
.
And
so
grosse
is
the
iudgement
of
the
that
folowe
not
,
or
searche
not
for
true
reason
,
but
content
themselues
with
a
lyght
conceaued
fantasye
.
Schollar
.
And
in
this
they
be
deceaued
,
that
they
accompt
this
form
more
apt
to
walk
on
:
for
the
flat
of
the
cube
is
plainer
,
&
therefore
more
apte
to
walk
on
,
then
is
a
slope
ground
.
Master
.
If
the
syxte
parte
of
the
earthe
were
onlye
inhabited
,
then
woulde
it
appeare
so
in
deede
:
but
if
you
go
any
farther
,
then
haue
you
vnapte
plainesse
to
walke
on
in
theyr
imagination
,
whiche
go
so
downe
righte
,
that
they
do
feare
fallynge
.
Againe
they
thinke
this
Rigge
forme
meetest
for
the
standing
of
the
sea
,
and
for
running
of
riuers
:
for
in
the
fyrste
forme
,
if
the
sea
should
reste
on
the
ouermost
plaine
,
then
wolde
it
ouer
runne
all
that
plaine
,
and
so
flowe
ouer
all
the
earthe
:
where
as
in
this
seconde
forme
it
mighte
reste
about
the
foote
of
the
earthe
,
and
yet
the
slope
risyng
wyll
not
permit
it
to
ouer
runne
all
the
earthe
.
And
so
for
riuers
if
there
be
no
slopenes
(
as
in
a
cube
there
is
none
)
then
can
not
the
ryuers
runne
well
.
The
thyrde
opinion
.
A
thyrde
secte
thinkinge
to
amende
A
playne
Flatte
.
Geometrical diagram.
these
bothe
,
imagined
the
earthe
to
be
plaine
and
flatte
:
for
so
they
fantasied
that
it
wold
rest
moste
steddilye
,
and
so
was
it
very
easy
to
walke
on
.
Schollar
.
We
are
more
beholdynge
to
those
men
,
for
deuising
our
easy
walkinge
,
then
we
are
bounde
to
them
for
their
wise
doctrine
.
Master
.
The
fourthe
opinion
.
The
fourthe
secte
,
fearyng
least
by
this
opinion
they
shoulde
leese
the
sea
and
all
other
waters
,
imagined
the
Geometrical diagram.
forme
of
the
earthe
more
apte
to
holde
water
,
and
deuifed
it
hollow
lyke
a
bolle
.
Schollar
.
Those
men
were
verye
studious
for
staying
of
water
,
more
then
they
were
for
framyng
of
their
wittes
.
Master
.
Yet
this
vaine
follye
didde
seeme
to
them
greate
wisedome
.
Schollar
.
Saue
that
I
do
credite
your
report
,
I
wolde
neuer
haue
thoughte
,
and
muche
lesse
haue
beleued
,
that
euer
anye
suche
madde
imaginations
hadde
beene
phantesied
of
anye
men
.
Master
.
Who
lysteth
to
see
the
monstruouse
opinions
of
suche
dreaminge
doters
,
maye
reade
them
often
touched
in
Aristotle
his
naturall
bookes
,
and
aboundantly
in
Plutarche
his
boke
De
philosophorum
placitis
,
and
in
Galene
and
Eusebius
in
bokes
of
the
same
matter
peculiarly
writen
.
But
these
4
opinions
which
I
haue
here
rehersed
,
are
briefly
noted
in
the
firste
boke
of
Cleomedes
sphere
,
though
not
in
like
ordre
:
and
saue
that
in
the
seconde
opinion
I
iudge
his
printe
corrupt
,
and
that
for
{αβγδ}
,
I
do
reade
and
translate
{αβγδ}
:
as
it
may
well
be
gathered
by
his
owne
confutation
,
which
will
not
agree
so
well
for
confuting
al
stiple
sormes
or
spire
formes
,
but
as
mens
iudgment
ought
to
be
free
,
so
if
any
man
list
to
follow
that
print
,
I
wil
not
withstand
him
.
Schollar
.
Although
some
of
these
opinions
are
so
grosse
that
they
neede
no
confutation
,
yet
I
praye
you
repeate
the
confutations
that
Cleomedes
doth
vse
.
Master
.
I
am
well
content
,
and
better
pleased
to
alleadge
them
in
his
owne
name
,
then
to
ascribe
them
to
my selfe
,
for
diuers
causes
.
Firste
he
beginneth
with
the
thirde
opinion
,
and
reproueth
it
thus
.
he
reprose
of
the
third
opinion
.
If
the
earthe
were
flatte
and
plaine
,
then
should
all
nations
haue
one
horizonte
:
for
in
a
plaine
flatte
forme
,
there
can
be
no
iuste
cause
of
alteration
of
the
Horizont
.
Scholar
.
That
foloweth
moste
certenly
.
Master
.
Then
must
the
Sonne
and
Moone
and
all
other
starres
rise
to
all
people
,
when
they
rise
to
anye
one
,
and
so
muste
they
sette
(
eche
one
in
his
course
)
to
all
men
at
one
instante
.
Schollar
.
That
will
followe
also
.
Master
.
If
the
Sonne
rise
to
all
men
at
ones
,
and
sette
likewayes
at
one
time
,
then
muste
the
daye
beginne
to
all
people
at
one
,
&
all
nations
must
haue
night
at
one
time
precisely
.
Schollar
.
That
is
false
as
all
men
confesse
:
for
at
Hierusalem
(
whiche
is
well
knowen
)
it
is
day
thre
houres
soner
then
with
vs
,
and
so
is
it
nyghte
sooner
by
thre
howers
also
.
But
in
Calecut
(
as
learned
men
affirme
,
and
trauelers
thither
,
do
confirme
)
it
is
daye
6.
howers
soner
then
with
vs
,
and
it
is
night
6.
howers
soner
to
them
againe
then
to
vs.
Master
.
Your
sayinges
are
true
if
they
be
well
taken
:
but
and
if
this
conclusion
bee
false
,
as
it
is
in
deede
,
then
muste
that
opinion
be
false
,
whereof
this
conclusion
is
inferred
.
Schollar
.
So
doth
it
well
folowe
,
and
is
fully
prooued
.
Master
.
One
stronge
reason
for
the
varietie
of
howers
is
gathered
by
the
eclipses
duly
obserued
,
and
namely
of
the
Moone
,
,
for
as
it
happeneth
at
one
instance
of
time
,
so
is
it
not
one
hower
to
all
nations
.
As
for
example
:
Examples
of
eclipses
.
This
year
of
1556
,
the
eclipse
of
the
Moone
shall
be
with
vs
the
17
day
of
Nouembre
at
3.
of
the
clocke
in
the
morninge
,
and
to
them
at
Calecut
it
shall
be
at
9.
of
the
clocke
in
the
morning
:
yea
we
shall
see
the
Moone
in
the
southwest
,
and
they
shall
not
see
her
at
the
same
instant
,
for
she
will
be
to
them
vnder
the
horizonte
in
the
northwest
.
like
waies
in
the
yeare
of
1562.
there
shall
be
a
great
eclipse
of
the
Moone
with
vs
,
whiche
shall
endure
aboue
three
houres
and
an
halfe
,
and
yet
shall
they
at
Calecut
see
no
part
of
it
,
by
reason
that
the
Moone
shall
be
farre
vnder
their
horizont
before
that
eclipse
begin
.
And
in
lyke
manner
this
laste
yeare
1555.
was
there
a
greate
eclipse
of
the
Moone
the
fifte
daye
of
Iune
,
at
three
of
the
clocke
in
the
morning
,
yet
in
Calecut
there
was
none
eclipse
seene
then
,
for
the
Moone
was
set
vnder
their
horizont
two
howers
almost
before
the
eclipse
began
.
But
in
the
yeare
of
1551.
when
we
had
the
eclipse
of
the
Moone
at
9.
of
the
clock
at
night
,
the
20.
day
of
February
,
they
at
Calecut
sawe
that
eclipse
at
thre
of
the
clocke
in
the
morning
the
nexte
daye
,
as
the
Portingales
that
were
there
can
testifye
.
Wherby
it
is
manifest
,
that
their
Horizont
doth
not
agree
with
ours
,
and
thereof
doth
it
folowe
that
the
earth
is
not
flatte
.
But
nowe
to
returne
to
Cleomedes
againe
,
(
vnto
whose
wordes
I
haue
added
but
the
examples
of
the
eclipses
)
his
seconde
reason
against
the
flatnesse
of
the
earth
,
is
this
.
An
other
reprofe
of
the
flatnes
of
the
carthe
.
If
the
earth
were
flatte
and
plaine
in
forme
,
then
the
Pole
must
needes
appeare
at
one
height
to
all
parts
of
the
world
,
and
the
artike
circle
(
which
incloseth
the
starres
that
neuer
set
)
shuld
be
but
one
to
all
nations
.
But
bothe
these
thinges
appeare
plainly
false
:
for
as
vnto
vs
about
London
the
Pole
is
not
fully
52.
degrees
highe
,
so
if
you
go
northward
,
you
shall
fynde
the
Pole
to
rise
higher
and
higher
,
till
it
bee
fully
90.
degrees
highe
.
and
in
going
southward
,
the
eleuation
of
the
Pole
waxeth
lesser
and
lesser
,
till
you
come
to
the
middle
of
the
earthe
vnder
the
equinoctiall
,
where
the
pole
is
of
no
height
,
but
is
equall
with
the
Horizont
.
Also
in
all
these
places
,
you
shall
haue
seuerall
arctike
circles
.
Scholar
.
That
must
needes
folow
the
diuersitye
in
the
eleuation
of
the
Pole
,
as
it
hath
been
sufficiently
declared
before
Master
.
As
the
firste
improbation
doth
reproue
the
flatnes
of
the
earth
betwene
easte
and
weste
,
bicause
it
regardeth
chiefly
the
rising
and
settyng
of
the
Sonne
and
other
starres
,
and
their
course
betwene
easte
and
west
,
so
this
second
confutation
improueth
the
opinion
of
plainesse
betwene
south
and
north
.
So
doth
it
folow
,
that
the
earthe
is
flatte
nother
one
way
nother
other
,
but
bothe
waies
hath
some
certain
rising
,
which
anon
I
will
proue
to
be
a
iuste
roundenes
.
The
thirde
confutation
A
thirde
reason
is
alleged
by
Cleomedes
,
touching
the
equalitie
of
daies
to
all
nations
,
which
shoulde
of
necessitye
follow
if
the
earthe
were
flatte
,
and
all
people
had
one
horizonte
,
but
bicause
it
is
so
little
disagreable
from
the
fyrste
reason
of
one
Horizonte
,
and
one
tyme
of
risinge
and
settinge
of
the
sonne
,
I
haue
ioyned
them
both
in
one
,
as
before
it
dothe
appeare
.
These
thre
reasons
are
plaine
inough
.
The
fourth
reason
whiche
Cleomedes
doth
make
,
is
not
so
easye
,
yet
is
it
as
certaine
as
any
of
the
other
:
and
therefore
I
will
shewe
you
what
it
is
,
seyng
you
desire
to
heare
his
owne
arguments
,
although
I
determined
before
to
allege
such
reasons
only
,
as
myght
appeare
easy
to
vnderstand
.
Scholar
.
If
it
be
not
ouer
muche
obscure
,
it
may
please
you
to
declare
it
in
the
moste
playnest
forme
ye
can
.
Ma.
I
will
only
alter
his
ordre
in
the
propositions
,
adding
that
wich
is
not
easye
to
be
gathered
,
to
make
it
the
easier
to
your
vnderstanding
.
This
is
it
.
The
fourth
confutation
of
the
plain
nes
of
the
Earthe
.
If
the
earth
were
plaine
,
it
shoulde
folowe
,
that
the
whole
diameter
of
the
world
from
one
side
of
the
sky
to
the
other
,
shoulde
be
but
100000.
furlonges
,
that
maketh
12500
miles
,
which
saying
appeareth
so
absurd
,
that
no
man
will
graunt
it
.
but
if
any
man
wold
do
it
,
this
argument
folowing
shall
confute
him
.
First
therfore
I
reason
thus
.
If
the
earth
be
plain
,
then
al
places
in
the
earth
ar
as
far
a
sonder
,
as
their
Zeniths
,
or
Verticall
pointes
be
in
heauen
.
This
maxime
must
I
adde
vnto
Cleomedes
,
to
make
his
reason
the
more
plaine
.
Scholar
.
But
this
maxime
do
I
not
vnderstande
,
wherfore
I
beseeke
you
both
to
proue
it
,
and
declare
it
.
Master
.
I
am
content
.
You
knowe
by
the
former
treatises
,
that
the
Zenith
is
the
pointe
right
ouer
the
headde
of
any
people
,
whose
Zenith
it
is
:
whereof
it
muste
folowe
that
euerye
diuers
place
in
carthe
,
muste
needes
haue
a
seuerall
Zenith
in
the
skye
.
Scholar
.
That
is
plaine
.
Master
.
Then
imagining
the
earth
to
be
flatte
,
the
lynes
that
dooth
ascende
from
any
twoo
places
,
vnto
theyr
Zeniches
in
the
skye
,
muste
needes
be
paralleles
,
as
here
in
this
Geometrical diagram.
picture
doth
partly
appear
.
for
if
the
circle
be
set
for
the
skye
,
and
the
flatte
square
within
it
for
the
earthe
,
then
take
two
places
in
the
earth
,
as
A
and
B.
the
zenith
to
A
is
C
,
&
must
needes
be
right
ouer
it
,
and
therfore
the
line
that
is
drawen
from
A
to
C
,
must
be
a
iust
plumb
line
,
&
perpendiculare
to
the
flatte
earth
.
And
likewaies
the
zenith
to
B
is
D
,
which
muste
needes
be
righte
ouer
it
,
and
therfore
the
line
that
goeth
from
D
to
B
,
must
of
necessitye
be
a
perpendiculare
and
plumbe
line
to
the
flatte
earthe
also
.
Then
if
bothe
those
lines
be
per
pendicular
to
one
flatte
plaine
,
or
to
one
line
standinge
for
that
plaine
flatte
,
all
the
angles
that
they
bothe
doo
make
with
the
thyrde
lyne
A
B
,
muste
bee
righte
angles
,
accordinge
to
the
definition
of
a
perpendiculer
line
.
Nowe
if
all
their
angles
be
right
,
then
are
they
all
equall
accordynge
to
the
fourthe
grauntable
request
in
the
seconde
booke
of
the
Pathway
,
that
all
righte
angles
be
equall
eche
to
other
.
And
if
all
their
angles
be
equal
,
then
must
their
matche
angles
be
equall
of
sorce
:
wherby
it
doth
folow
accordinge
to
the
is
.
Theoreme
of
the
seconde
booke
of
the
Pathway
,
that
those
two
perpendicular
lines
be
paralleles
,
seyng
that
on
2
righte
lines
,
as
A
C
and
B
D
,
there
is
drawen
a
thyrde
ryghte
line
A
B
,
crossewayes
,
and
maketh
twoo
matche
corners
of
the
one
lyne
,
equall
wyth
the
lyke
twoo
matche
corners
of
the
other
lyne
.
Scholar
.
Hereby
I
haue
not
onlye
gotten
the
vnderstanding
of
your
proofe
,
but
also
I
perceaue
a
farther
vse
in
he
Theoremes
of
the
Pathway
,
then
I
knewe
before
.
Master
.
I
will
prosecute
my
proofe
.
Syth
those
twoo
lynes
bee
paralleles
,
and
equallye
distaunte
,
then
is
there
as
muche
space
betweene
A
and
B
,
as
there
is
betweene
C
and
D.
Scholar
.
Thus
is
your
maxime
sufficiently
proued
,
and
fully
declared
:
for
A
B
betokeneth
the
distaunce
of
the
two
places
in
earth
and
C
D
,
standeth
for
the
distaunce
of
their
zeniths
in
the
skye
.
Master
.
Nowe
therefore
will
I
retourne
to
Cleomedes
argument
.
They
that
dwell
at
Lysimachia
(
in
Grece
)
&
thei
that
dwell
at
Syene
(
in
the
southe
parte
of
Egypte
)
haue
betweene
them
in
distaunce
20000
furlonges
(
that
is
2500
miles
)
wherefore
it
must
solowe
that
their
zenithes
in
the
skye
be
no
farther
a sonder
,
seyng
they
be
limited
by
two
perpen
diculers
equallye
distaunte
:
but
it
is
well
knowen
by
good
proofe
of
instrumentes
,
that
Syene
is
vnder
the
Tropike
of
Cancer
directly
,
and
Lysimachia
is
vnder
the
hedde
of
the
North
dragon
,
which
2
places
in
the
skye
are
iustly
pro
ued
to
be
a
sonder
the
15
part
of
the
whole
compas
of
heauen
,
that
is
the
first
part
of
the
diameter
of
the
skye
.
Whersore
if
20000
furlonges
be
the
first
parte
of
the
diameter
,
the
whole
diameter
must
be
but
100000
furlonges
:
&
the
whole
compas
of
the
skie
muste
be
but
300000
furlonges
,
and
of
these
furlonges
it
is
prooued
,
that
the
earthe
contayneth
in
compas
250000.
so
is
the
heauen
lyttle
bygger
then
the
earthe
in
compas
whiche
absurditie
maye
easily
be
confuted
by
the
Sonne
,
whiche
in
comparison
to
the
skye
,
is
a
verye
lytle
parte
of
it
,
and
yet
is
bygger
than
the
earthe
mannye
folde
:
whereby
anye
manne
maye
see
what
absurditye
foloweth
that
opinion
,
to
thynke
that
the
earthe
is
flatte
.
Scholar
.
I
doo
metely
well
vnderstand
this
reason
,
but
I
shuld
better
haue
conceaued
it
,
if
I
had
knowen
the
two
places
whiche
hee
alleageth
for
examples
sake
.
A
like
reason
.
M.
Then
will
I
for
your
pleasure
make
the
like
argument
by
example
of
2
places
which
ar
better
knowen
to
english
men
.
you
knowe
the
castle
of
Arundell
.
Scholar
.
The
name
is
auncient
and
famous
.
Master
.
And
Newe
castle
vppon
Tine
is
well
knowen
to
you
also
.
Scholar
.
So
is
it
.
Master
.
To
go
the
next
waye
betwene
these
two
places
it
is
270
englysh
myles
.
Arundel
castle
.
And
the
Zenith
of
Arundell
castle
(
whiche
is
the
iuste
point
of
the
latitude
of
it
)
is
50
degrees
and
30
minutes
,
as
ones
I
remembre
I
tooke
note
of
it
in
riding
that
waies
.
The
Zenith
also
of
Newcastle
is
from
the
equinoctiall
55.
degrees
,
so
is
the
difference
betwene
their
zeniths
4
degrees
and
30
minutes
.
Now
(
as
I
haue
declared
before
)
If
the
earthe
be
flatte
and
the
perpendicularre
lines
bee
paralleles
and
equidistant
,
that
go
vp
from
these
two
places
to
their
zeniths
,
then
is
4
degrees
and
30
minutes
,
iust
equal
in
quantity
to
270
myles
.
Sc.
That
is
true
,
as
it
is
proued
before
in
the
third
treatise
.
Master
.
You
are
farre
deceaued
:
it
is
declared
there
,
that
270
myles
in
earthe
,
muste
answere
in
proportion
to
foure
degrees
and
an
halfe
,
and
not
that
they
are
equall
togyther
.
Scholar
.
I
perceaue
mine
owne
negligence
in
markinge
the
propretye
of
speache
.
I
shoulde
haue
sayd
,
that
as
foure
degrees
and
an
halfe
is
the
eight
score
part
of
the
whole
compas
of
heauen
,
so
270
myles
is
the
eighte
score
parte
of
the
circuite
of
the
earthe
.
Geometrical diagram.
Master
.
That
is
true
:
but
yet
these
2
partes
are
as
farre
vnequal
in
quantity
as
heauen
&
earth
ar
vnlike
in
their
compas
,
wherfore
to
the
intent
that
from
henceforth
you
shall
not
mistake
it
againe
,
I
wil
by
lineary
demonstration
set
before
your
eyes
the
declaration
and
difference
of
them
bothe
more
plainly
then
curiously
.
Here
in
this
figure
you
see
two
circles
drawen
vppon
one
centre
,
their
common
centre
being
G
,
from
which
there
are
drawen
to
the
vttermost
circle
two
right
lines
G
A
,
&
G
D
,
these
lines
do
crosse
the
lesser
circle
in
2
pointes
E
and
F
,
fro
whiche
two
pointes
I
haue
drawen
twoo
paralleles
,
vnto
the
circumference
of
the
greater
circle
,
whiche
two
paralleles
be
B
E
,
and
C
F.
Nowe
may
I
say
,
that
bicause
these
two
circles
be
made
vpon
one
common
centre
,
and
twoo
lynes
drawen
from
that
centre
to
the
circumference
of
the
both
circles
,
bicause
A
G
D
is
one
common
angle
in
them
bothe
,
therfore
are
there
arche
lynes
inclosed
betweene
those
two
ryght
lynes
lyke
in
proportion
.
Scholar
.
I
perceaue
it
well
:
so
that
if
the
arche
lyne
A
D
in
the
greater
circle
,
be
the
syxte
parte
of
it
,
then
is
E
F
the
arche
lyne
of
the
lesser
circle
,
the
syxte
parte
of
his
owne
circle
,
in
lyke
manner
.
but
yet
that
arche
of
the
lesser
circle
is
not
so
greate
as
the
lyke
arche
in
the
bygger
circle
.
Master
.
Then
what
saye
you
of
the
arche
B
C
,
in
comparison
to
the
arche
E
F
,
whiche
bothe
arches
are
betweene
twoo
lines
paralleles
?
Schollar
.
They
muste
needes
bee
equall
,
seynge
there
is
iuste
as
muche
distaunce
betweene
E
F
,
as
there
is
betweene
B
C.
Master
.
So
maye
you
nowe
perceaue
what
difference
it
is
to
saye
,
that
two
arches
of
two
seuerall
circles
,
are
like
in
proportion
;
and
to
saye
that
they
are
equall
in
quantity
.
Schollar
.
Nowe
I
perceaue
it
plainly
,
that
although
4
degrees
and
an
half
(
as
your
former
reason
did
import
)
be
like
in
proportion
to
the
whole
circumference
of
heauen
,
as
270
miles
are
in
comparison
to
the
compasse
of
the
earthe
:
yet
it
foloweth
not
that
they
should
be
equall
togither
.
Master
.
But
supposynge
the
earthe
to
bee
flatte
,
then
it
foloweth
as
I
haue
declared
beefore
,
that
they
are
equalle
in
quantitye
,
seeynge
bothe
beetoken
the
distant
of
one
couple
of
paralleles
.
And
thē
it
foloweth
,
that
seinge
4
degrees
&
a
half
is
the
four
score
part
of
the
compas
of
heauen
,
if
I
multiply
270
myles
(
whiche
is
equall
to
it
)
by
80
,
therof
will
amounte
the
numbre
of
myles
that
make
the
compasse
of
heauen
,
whiche
are
21600
myles
.
Nowe
to
know
the
diameter
of
it
,
I
take
the
two
receaued
numbres
for
the
proportion
betweene
the
circumference
of
a
circle
and
the
diameter
of
it
,
whiche
are
22
and
7
,
(
as
in
the
Pathway
is
declared
more
largely
)
and
by
the
rule
of
proportion
I
work
in
saying
:
if
22.
giue
7
,
what
shal
21600
yelde
?
and
there
amounteth
6872
8
/
11
,
whiche
must
be
the
whole
diameter
of
the
skie
,
if
the
earth
were
flatte
.
Geometrical diagram.
Scholar
.
That
is
to
greate
an
inconuenience
for
any
man
to
affirm
.
for
therby
I
se
it
wold
folow
that
if
we
go
any
waye
from
our
owne
cuntry
,
3436
miles
,
we
shal
com
hard
to
the
sky
,
which
is
to
childishe
a
fantasye
,
sith
not
only
reason
,
but
dayly
trauell
declareth
the
contrarye
.
Againe
I
remembre
that
in
the
thirde
treatise
you
declared
that
the
earthe
was
so
muche
in
compasse
,
whiche
muste
needes
bee
many
fold
lesse
then
the
heauens
,
whiche
ar
so
farre
distaunt
from
the
earthe
on
euery
side
.
Master
.
Thus
are
all
Cleomedes
reasons
against
the
flatnes
of
the
earth
fully
alleaged
,
&
somewhat
largely
declared
:
Now
wil
I
proceede
to
the
confutations
which
he
vseth
against
the
other
opinions
,
folowing
his
own
ordre
.
wherfore
next
doth
folow
the
confutation
of
them
which
say
that
the
earth
is
holowe
like
a
bolle
.
The
consutation
of
the
fourthe
opinion
.
Against
whose
phantasticall
imagination
he
reasoneth
thus
:
If
the
earthe
were
hollowe
as
a
bolle
,
then
should
the
Sonne
,
the
Moone
and
all
Starres
in
their
rising
appeare
soner
to
them
that
dwell
in
the
weste
,
then
to
them
that
dwell
in
the
easte
:
whiche
thinge
is
contrary
to
daily
experience
.
Geometrical diagram.
For
declaration
of
which
saying
by
lineari
demonstration
I
think
good
to
drawe
a
figure
,
wherin
you
may
aptly
se
the
force
of
his
reason
.
The
vttermost
circle
of
the
figure
doth
represent
the
skye
,
and
the
inner
most
half
circle
standeth
for
the
imagined
holownes
of
the
earthe
,
&
the
halfe
roundelet
A
B
,
representeth
the
massy
substance
of
the
earth
,
the
right
line
K
L
,
expresseth
the
diameter
of
the
world
,
and
therfore
the
right
Horizont
of
the
earthe
,
K
beinge
the
east
and
L
the
west
.
Now
for
explication
of
Cleomedes
reason
:
If
the
earthe
were
holow
,
as
here
the
forme
of
it
is
drawen
,
then
when
the
Sonne
is
risen
,
in
the
easte
aboute
E
,
it
wold
appeare
to
them
that
dwell
in
the
west
by
B
,
&
not
vnto
them
that
dwell
in
the
east
by
A.
for
the
brow
of
the
holow
ground
by
C
,
doth
hide
the
Son
yet
from
them
,
so
that
he
must
ascend
as
high
as
F
,
before
they
that
dwel
in
the
east
by
A
may
see
hym
.
Again
when
the
Son
goeth
doune
,
by
this
opinion
he
shuld
set
to
them
that
dwel
in
the
west
by
B
,
as
sone
as
he
came
to
G
,
by
occasion
of
the
browe
of
the
ground
by
D.
and
yet
they
that
dwell
in
the
easte
by
A
,
should
see
him
a
great
while
longer
:
for
that
browe
of
grounde
by
D
,
wyll
not
yet
hynder
their
sighte
,
vntill
he
be
descended
as
low
as
H.
So
shoulde
they
that
dwell
in
the
west
see
the
Sonne
soonest
in
the
morning
,
and
they
that
dwell
in
the
east
shoulde
see
him
latest
at
eueninge
.
Schollar
.
This
thinge
is
so
false
,
that
euery
chylde
knoweth
the
contrarye
.
Master
.
Yet
of
that
opinion
dooth
there
folowe
farther
inconueniency
,
An
other
reproofe
of
the
same
opinion
.
as
Cleomedes
doth
shew
:
for
by
this
fantasye
,
they
that
dwell
in
the
southe
should
see
the
northe
Pole
more
higher
aboue
ground
,
and
so
should
haue
a
larger
arctike
circle
,
then
they
that
dwell
in
the
northe
,
as
by
the
same
figure
it
may
be
declared
.
Scholar
.
I
perceaue
it
well
:
for
if
I
make
K
to
be
the
south
,
and
L
the
north
,
then
it
appeareth
in
this
form
of
the
earth
,
that
they
which
dwel
in
the
south
by
A
,
may
see
as
low
as
H
:
and
they
that
dwell
in
the
northe
by
B
,
canne
see
no
farther
northe
then
G.
whiche
is
so
farre
against
reason
and
daylye
experience
,
that
it
must
needs
appeare
to
be
a
vaine
fantasy
,
that
bringeth
for
the
so
mad
and
monstruous
conclusions
.
Master
.
Yet
an
other
confutation
of
the
same
opinion
Yet
doth
there
folow
more
fonde
conclusions
of
it
:
for
by
this
opinion
all
nations
that
dwell
within
that
holownes
,
should
see
lesse
then
halfe
the
skie
,
lesse
then
halfe
the
Zodiak
,
and
lesse
then
halfe
the
Equinoctiall
,
wherof
it
wold
follow
(
beside
other
absurdities
)
that
they
shuld
haue
their
nighte
commonly
longer
then
their
daye
,
bicause
that
parte
of
heauen
which
they
se
is
lesse
(
especially
to
them
that
dwell
in
the
botome
of
that
holownes
)
then
that
part
which
is
vnder
their
horizonte
:
Yea
they
that
dwell
in
the
botome
of
that
holownes
,
canne
neuer
haue
their
daye
so
longe
as
their
nighte
,
bicause
they
do
see
so
litle
a
portion
of
the
skye
.
As
a
man
that
is
in
a
deepe
trenche
or
in
a
pitte
,
can
see
but
a
litle
of
the
heauens
.
And
thus
hath
Cleomedes
sufficientlye
confuted
those
two
opinions
:
whiche
kinde
of
confutation
Ptolomye
doth
vse
also
against
bothe
those
opinions
.
Scholar
.
Then
must
they
needes
be
good
:
Ptolemye
.
for
as
I
heare
all
learned
men
say
,
Ptolemye
is
the
father
of
that
arte
,
and
proueth
all
his
woordes
by
stronge
and
inuincible
reasons
.
Master
.
No
man
can
worthely
praise
Ptolemye
,
his
trauell
being
so
great
,
his
diligence
so
exacte
in
obseruations
,
and
conference
with
all
nations
,
and
all
ages
,
and
his
reasonable
examination
of
all
opinions
,
with
demonstrable
confirmation
of
his
owne
assertion
,
yet
muste
you
and
all
men
take
heed
,
that
both
in
him
and
in
al
mennes
workes
,
you
be
not
abused
by
their
autoritye
,
Autority
of
writers
.
but
euermore
attend
to
their
reasons
,
and
examine
them
well
,
euer
regarding
more
what
is
saide
,
and
how
it
is
proued
,
then
who
saieth
it
:
for
autoritie
often
times
deceaueth
many
menne
,
as
here
by
and
by
in
Cleomedes
it
shall
appeare
,
whose
argumentes
in
confuting
the
other
two
opinions
ar
nothing
substantiall
:
which
chanced
other
bicause
he
sawe
the
fondenes
of
these
opinions
so
great
,
that
he
sought
no
great
reasons
to
confute
them
,
other
els
hastinge
in
his
writinge
caused
him
to
vse
the
lesse
diligence
in
framynge
his
reasons
.
but
nowe
will
I
repeat
them
.
Cleomedes
argumente
against
the
first
opinion
.
If
the
earth
were
of
cubike
forme
,
then
should
all
nations
haue
syxe
howers
daye
only
,
and
18
howers
nyght
,
seing
ther
be
rounde
about
the
cube
four
sides
,
so
that
on
eche
of
them
the
Sonne
shoulde
shine
6
howers
only
:
this
is
a
very
weake
argument
.
Schollar
.
Yet
vnto
me
it
seemeth
a
strong
reason
:
for
seing
that
the
Son
doth
go
round
about
the
skie
and
aboute
the
earth
also
iust
in
24
howers
,
it
must
needs
folow
that
he
spendeth
only
6
howers
in
euerye
quarter
:
and
a
cube
hathe
but
four
sydes
in
his
compasse
,
(
althoughe
it
haue
6
sides
in
all
)
wherfore
in
mine
opinion
it
is
well
concluded
,
that
euery
one
of
tose
four
sides
,
doo
see
the
Sonne
6
howers
iustlye
.
Master
.
Often
haue
I
readde
in
Galene
,
and
more
often
haue
I
seen
it
by
experience
,
that
better
it
is
for
men
to
want
all
arte
of
reasoninge
cleane
,
then
to
haue
suche
confidence
in
a
meane
knowledg
therof
,
that
may
occasion
them
to
deceaue
them selfe
,
and
to
seduce
other
.
You
are
fully
perswaded
that
this
argument
is
good
:
whereby
it
appeareth
that
you
espied
not
the
want
of
that
meane
proposition
,
whiche
should
make
the
argument
good
,
which
muste
be
this
:
that
euery
quarter
of
the
sky
,
agreeth
to
one
quarter
of
thearth
.
Schollar
.
That
not
only
I
thinke
to
be
true
,
but
your selfe
affirmed
it
also
before
this
time
,
as
a
true
sentence
.
Master
.
And
so
will
I
do
still
,
affirming
it
of
the
true
form
of
the
earthe
,
but
not
of
this
imagined
cube
forme
.
Scholar
.
Why
,
is
there
anye
difference
in
the
quarters
of
any
formes
?
is
not
a
quarter
of
a
cube
the
fourth
part
of
it
,
as
well
as
a
quarter
of
a
Globe
is
the
fourth
part
of
the
globe
?
Ma.
Yes
,
but
yet
doth
not
the
quarters
of
the
cube
so
agree
with
the
quarters
of
a
globe
,
as
the
quarters
of
two
globes
agree
togither
.
Scholar
.
That
I
vnderstand
not
.
Mast
.
Then
will
I
declare
it
manifestly
by
lineary
demonstration
.
Geometrical diagram.
Marke
these
figures
.
Here
you
se
first
for
the
true
opinion
,
2.
circles
drawen
one
with
in
the
other
vpon
one
centre
,
and
the
same
are
diuided
into
four
quarters
ech
of
them
,
so
that
the
four
quarters
of
the
lesser
circle
,
E
F
G
H
,
do
answere
agreably
to
the
four
quarters
of
the
greater
circle
A
B
C
D
,
but
in
the
second
figure
,
where
the
cube
is
made
in
lue
of
the
earthe
,
the
quarters
do
not
agree
,
as
you
may
perceaue
by
the
draught
of
the
right
lines
,
agreable
to
eche
side
of
the
cube
:
for
euery
side
of
the
cube
hath
almost
halfe
the
circle
aboue
his
horizontall
line
.
Wherfore
if
you
will
haue
a
cube
drawen
in
a
globe
,
in
such
sorte
that
the
quarter
of
the
one
in
compasse
shall
agree
to
the
like
quarter
of
the
other
,
that
cube
muste
be
so
great
,
that
his
Geometrical diagram.
corners
may
touch
the
globe
on
eche
side
,
so
muste
it
bee
as
greate
a
cube
as
maye
bee
made
within
that
globe
.
And
I
am
sure
you
will
not
say
that
the
earthe
is
so
great
in
comparison
to
the
skye
.
Schol
.
Now
I
se
mine
owne
erroure
,
and
the
fault
of
Cleomedes
argument
.
Geometrical diagram.
Master
.
And
if
anye
man
wold
excuse
Cleomedes
,
he
must
say
,
that
Cleomedes
did
make
that
reason
against
suche
as
affirmed
two
errours
at
ones
,
that
is
the
cubike
form
of
the
earth
,
&
the
greatnes
of
it
also
to
bee
suche
,
as
mighte
touche
the
skye
with
euery
corner
:
but
if
this
had
been
his
meaninge
he
might
easily
haue
expressed
it
so
:
but
what
so
euer
he
ment
he
framed
the
confutation
of
the
second
opinion
in
the
like
sorte
.
for
this
is
his
argument
.
Cleomedes
confutation
of
the
second
opinion
.
If
the
earthe
be
of
a
three
cornered
forme
,
then
shuld
the
Sonne
shew
8
houres
iustly
on
eche
side
of
it
,
and
so
wold
it
be
to
al
people
8
houres
day
,
&
16
houres
night
:
which
thing
is
to
appearant
false
:
so
can
not
that
opinion
be
true
.
for
declaration
of
this
argument
I
haue
drawen
first
a
circle
for
the
sky
,
and
then
a
small
triangle
forme
D
E
F
,
vnto
whose
thre
Geometrical diagram.
sides
I
haue
drawen
3
streight
lynes
,
representing
three
seuerall
horizontes
.
but
it
appeareth
at
the
firste
sight
,
that
eche
of
those
horizontes
doo
contayne
aboue
them
almost
halfe
the
skye
.
So
that
in
this
quantitye
of
the
earth
,
Cleomedes
reason
taketh
no
place
,
nother
generally
in
any
other
but
one
,
where
the
three
corners
of
the
earth
may
touch
the
skye
,
for
whiche
forme
I
haue
drawen
the
greate
triangle
A
B
C.
Scholar
.
Yet
although
Cleomedes
argumentes
bee
not
sufficient
to
confute
their
opinion
,
that
would
say
the
earth
were
of
any
of
these
bothe
formes
,
their
opinion
is
false
neuerthelesse
.
thinke
you
not
so
?
Master
.
Yes
verely
:
for
a
weake
confutation
of
an
vntruth
doth
not
make
that
vntruth
to
become
true
.
And
bicause
you
shall
not
thinke
that
these
opinions
haue
anye
sure
grounde
,
I
wyll
repeate
Ptolemye
hys
confutation
of
them
both
,
by
one
vnfallible
reason
.
Ptolemy
his
confutation
of
the
firste
and
seconde
You
see
in
bothe
these
imagined
formes
of
the
earthe
,
that
there
can
be
no
more
horizontes
,
then
there
be
sides
in
the
fygure
.
Scholar
.
That
is
certaine
:
for
all
that
dwell
on
one
plain
side
,
must
needes
haue
one
horizont
:
wherfore
if
the
forme
of
the
earth
wer
four
square
in
his
compas
,
then
could
ther
bee
but
fower
Horizontes
,
that
waye
:
I
vnderstande
it
betweene
easte
and
weste
,
and
in
all
varieties
there
canne
be
but
syxe
,
syth
a
cube
hath
but
syx
sydes
:
lykewaies
in
the
thre
cornered
forme
,
there
canne
be
but
three
diuers
horizonts
betwene
easte
and
west
.
Master
.
You
saye
well
.
And
seeynge
all
that
dwell
on
one
plaine
syde
haue
all
one
horizonte
,
they
muste
haue
day
all
at
one
instant
both
for
the
sonne
risinge
and
also
for
the
setting
,
so
can
ther
be
no
more
variety
in
the
beginning
and
ending
of
daies
,
then
there
are
sides
in
the
figure
of
the
earthe
,
whiche
by
the
firste
opinion
must
be
but
4
,
and
but
3
by
the
seconde
opinion
,
where
as
the
contrary
is
well
knowen
by
dailye
experience
,
as
well
as
by
reason
,
that
euerye
15
degrees
in
distaunce
westwarde
maketh
the
daye
an
hour
later
:
and
contrarye
waies
euery
15
degrees
of
distaunce
estward
,
causeth
the
daye
to
be
rather
by
one
howers
space
.
Sch.
That
is
proued
also
before
,
in
confutation
of
the
third
opinion
,
and
namelye
by
examples
of
eclipses
.
But
what
if
any
wolde
affirme
that
the
earth
were
made
of
many
flattes
,
as
of
24
(
for
an
example
)
betwene
east
and
west
,
then
shuld
there
be
no
more
horizontes
,
then
there
bee
howers
in
one
naturall
daie
,
and
yet
so
the
difference
of
howers
could
not
confute
them
.
Master
.
You
must
thinke
that
learned
men
canne
as
well
marke
the
difference
in
euerye
minute
of
an
hower
,
as
the
common
people
can
obserue
diuersities
in
howers
:
yea
the
learned
obseruations
are
more
exactly
taken
thē
the
60.
part
of
a
minut
of
an
hower
,
wherfore
seyng
it
is
so
well
proued
by
sondry
obseruations
,
and
especiallye
by
eclipses
,
bothe
of
the
sonne
and
the
moone
,
that
euerye
mile
distaunce
betwene
easte
and
west
,
dooth
make
a
seuerall
horizonte
,
there
can
bee
no
other
forme
of
the
earthe
aptlye
assigned
,
but
a
rounde
circular
forme
.
And
by
the
lyke
reason
,
by
the
ordrely
ascending
of
the
Pole
,
in
goinge
northward
,
and
by
the
vniforme
descending
of
it
in
going
southwarde
,
it
must
needes
appeare
that
there
can
bee
none
other
forme
of
the
earthe
betweene
southe
and
northe
,
but
a
rounde
forme
also
.
Scholar
.
Nowe
canne
I
ende
your
argumente
of
the
distribution
disiunctiue
,
whiche
maye
be
framed
thus
.
The
collection
of
the
argumente
The
earth
must
haue
some
forme
,
either
cubike
,
thre
cornered
,
flatte
,
or
holow
,
or
some
suche
lyke
,
other
els
a
round
forme
,
but
his
forme
can
not
be
cubike
,
nor
threcornered
,
nother
flatte
,
nother
holow
,
nor
anye
suche
lyke
,
as
before
is
fully
prooued
,
wherefore
it
muste
needes
be
rounde
.
Master
.
It
foloweth
well
.
for
it
is
not
possible
that
in
any
other
imagined
forme
of
the
earthe
,
the
horizontes
should
alter
toward
euery
coaste
so
vniformely
,
and
the
dayes
differ
so
proportionably
,
the
Pole
to
be
eleuate
so
ratably
,
or
to
be
depressed
so
ordrely
,
and
all
other
appearances
to
answer
so
agreably
.
A
roller
forme
.
Yet
some
men
(
as
Ptolemy
doth
reporte
)
had
inuented
an
other
forme
lyke
a
roller
,
or
a
rounde
pyller
,
whose
endes
shoulde
lye
north
and
south
,
by
whiche
forme
althoughe
they
thought
none
of
the
varieties
of
appearances
myghte
bee
hindered
,
yet
in
that
forme
the
eleuation
of
any
one
of
the
Poles
could
haue
but
two
varieties
for
euer
more
it
muste
appeare
other
ouer
their
heddes
,
as
to
them
that
dwell
on
the
flatte
eandes
of
that
roller
,
or
els
to
all
other
that
dwell
about
the
compas
of
the
roller
,
it
must
still
appeare
in
their
horizonte
,
so
shoulde
ther
bee
no
starres
about
either
Pole
alwaies
appearant
aboue
ground
,
nother
all
wayes
hydde
vnder
grounde
,
but
all
starres
should
ryse
and
set
to
all
them
that
dwell
about
the
roller
.
And
againe
they
that
dwell
on
the
flatte
endes
of
the
roller
,
shoulde
haue
but
one
Horizont
,
so
large
in
distaunce
of
ground
,
as
the
whole
thicknes
of
the
earthe
is
:
all
whiche
imaginations
are
bothe
well
knowen
to
be
vaine
,
&
also
easye
to
be
confuted
by
the
former
reasons
,
which
serue
so
largely
,
that
you
can
imagine
no
forme
other
then
round
,
but
those
reasons
will
confute
it
.
wherefore
your
argument
doth
proceede
well
.
That
the
water
is
round
by
diuers
profes
Yet
farther
for
the
roundenes
of
the
water
also
,
and
namely
of
the
sea
,
you
maye
frame
argumentes
by
the
lyke
forme
of
appearances
:
for
where
so
euer
you
bee
on
the
sea
,
you
shall
see
halfe
the
skye
iustlye
,
and
the
farther
west
that
you
go
,
the
later
dooth
the
Sonne
rise
:
and
contrarye
waies
the
farther
easte
that
you
saile
,
the
sooner
in
the
morning
will
the
Sonne
appeare
to
you
.
whereof
I
will
declare
vnto
you
a
notable
example
,
and
a
iuste
proofe
.
An
example
of
the
roundnes
of
the
sea
by
a
shippes
ceurse
.
Imagine
a
ship
swift
of
saile
to
be
at
the
cape
of
Cornwall
ready
to
make
sayle
towarde
the
weste
directly
,
and
to
haue
a
greate
gale
of
winde
,
it
is
possible
that
she
maye
run
240
myles
in
24
howers
:
for
I
haue
beene
at
the
triall
of
a
greater
course
,
therefore
I
speake
(
as
men
say
)
within
my
boundes
:
after
which
rate
she
shall
runne
in
16
howers
160
myles
.
Now
let
hir
hoise
saile
at
the
sonne
rising
,
and
let
the
time
of
the
year
be
somwhat
before
midsommer
,
or
little
after
,
when
the
Artificiall
day
from
sonne
rising
to
sonne
settinge
,
is
16
howers
longe
:
by
this
meanes
at
the
end
of
16
howers
,
she
shall
be
west
of
the
cape
of
Cornwall
where
she
began
her
course
160
myles
:
and
then
shall
the
sonne
be
at
setting
to
their
sight
that
dwell
at
the
saide
cape
,
but
the
shippe
shall
haue
the
Sonne
aboue
foure
degrees
hyghe
at
that
instaunte
,
by
reason
that
she
dydde
runne
with
the
Sonne
,
and
that
the
roundenes
of
the
sea
doth
chaunge
the
horizont
so
many
degrees
in
160
myles
.
Scholar
.
Althoughe
this
example
bee
pleasaunt
,
yet
it
passeth
myne
vnderstandinge
,
sith
that
I
beleued
hitherto
,
accordinge
to
your
former
doctrine
,
that
160
myles
would
not
haue
altered
any
waies
three
degrees
,
seyng
60
myles
do
answere
to
one
degree
.
Master
.
That
sayinge
is
true
all
wayes
for
the
eleuation
of
the
Pole
,
for
going
betwene
south
and
northe
in
all
places
;
but
for
going
betwene
easte
and
weste
,
it
serueth
onlye
for
the
myddle
of
the
worlde
,
that
is
vnder
the
Equinoctiall
circle
:
and
in
all
other
places
,
the
farther
you
bee
from
the
Equinoctiall
,
the
fewer
myles
answere
to
eche
degree
,
by
reason
that
the
paralleles
growe
lesser
styll
towarde
the
Poles
:
yet
the
leaste
of
theym
is
dyuided
into
thre
hundreth
and
sixtie
degrees
as
well
as
the
greatest
,
whereof
hereafter
I
will
instructe
you
more
exactelye
.
in
the
meane
ceason
,
you
shall
vnderstande
,
that
for
the
latitude
of
the
cape
of
Cornewalle
,
euerye
degree
requyreth
onlye
37
myles
:
How
many
myles
aunswere
to
a
degree
at
the
southe
coaste
of
Englande
.
whiche
beynge
multiplied
by
4
,
maketh
but
148
:
and
therefore
I
sayd
aboue
4
degrees
did
answere
to
160
myles
,
as
the
truthe
is
.
Scholar
.
Nowe
I
perceaue
somwhat
better
the
reason
ther
of
by
the
proportion
of
the
parallele
circles
in
the
Sphere
.
and
surely
this
proofe
is
pleasante
,
and
easye
inoughe
to
bee
tried
.
Master
.
A
lyke
example
may
this
be
.
Suppose
at
the
same
tyme
of
the
year
when
the
day
is
at
the
longest
,
A
lyke
example
of
a
shippes
course
.
that
there
is
a
swifte
shippe
at
the
weste
pointe
of
the
isle
of
Islande
,
wher
the
longest
day
is
20
howers
from
Sonne
rising
to
sonne
setting
,
in
those
20
howers
,
that
shippe
might
sayle
westwarde
200
myles
.
Then
considering
that
at
that
latitude
whiche
is
aboue
63
degrees
,
there
answereth
but
27
miles
to
a
degree
.
when
the
ship
is
at
the
ende
of
his
course
,
the
sonne
will
sette
to
them
that
bee
in
Islande
;
and
then
shall
the
shippe
haue
the
sonne
7
degrees
and
almost
a
halse
,
aboue
the
horizont
,
(
which
maketh
halfe
an
hower
in
time
)
so
that
by
the
roundnes
of
the
sea
,
they
haue
chaunged
their
horizont
so
much
in
twentye
howers
saylinge
.
Nowe
turne
his
course
and
let
the
shippe
haue
like
wind
homeward
againe
the
nexte
daye
,
and
let
him
make
saile
at
the
sonne
rysinge
,
then
shall
it
bee
after
sonne
set
halfe
an
hower
,
before
she
shall
ariue
at
the
former
porte
:
by
reason
that
the
sonne
rysse
halfe
an
hower
later
to
the
shippe
,
where
shee
was
in
the
weste
,
then
it
dyd
to
them
at
Islande
:
and
therefore
muste
it
set
halfe
an
hower
rather
at
Islande
,
so
hathe
the
shippe
loste
halfe
an
hower
,
by
comming
eastwarde
against
the
sonne
.
Scholar
.
I
vnderstand
that
.
As
15
degrees
doth
answer
to
an
hower
,
so
7
degrees
and
a
halfe
maketh
halfe
an
hower
:
wherefore
if
the
shyppe
sayle
iuste
twentye
howers
,
and
that
artificiall
daye
is
iust
20
howers
longe
,
then
shall
they
come
to
their
port
in
Island
halfe
an
hour
after
son
setting
,
bicause
it
was
halfe
an
hour
after
Sonne
rising
in
Island
,
before
they
began
to
make
saile
.
Master
.
This
varietie
coulde
not
happen
,
except
the
water
also
were
rounde
as
well
as
the
earthe
.
An
other
proofe
that
the
water
is
rounde
.
And
for
farther
proofe
of
the
roundnes
of
the
sea
,
daily
experience
doothe
teache
vs
,
if
we
wold
diligently
obserue
it
,
howe
that
when
a
shippe
doth
draw
towarde
londe
out
of
the
maine
sea
,
the
lowe
grounde
doth
not
appeare
at
the
firste
vnto
the
shippe
but
the
toppes
of
high
hilles
and
cliffes
:
like
waies
they
that
be
on
the
londe
and
looke
to
the
shippe
,
they
see
the
toppe
of
the
ship
firste
,
and
after
that
,
the
mastes
,
sayles
,
and
shroudes
before
they
can
see
the
hulle
,
and
body
of
the
ship
.
Now
I
demaund
of
them
that
thinke
the
water
to
be
flatte
,
what
is
it
that
letteth
the
syghte
,
so
that
it
canne
not
as
well
see
the
lowere
grounde
from
the
shippe
,
or
the
hulle
of
the
shippe
from
the
londe
.
Scholar
.
They
can
name
nothing
but
water
:
for
there
is
nothinge
els
betwene
them
,
hable
to
stay
the
sight
.
But
then
peraduenture
they
will
saye
,
it
is
the
waues
of
the
sea
,
whiche
rise
verye
highe
often
times
.
Master
.
That
were
to
childish
an
answer
,
sith
the
lyke
doth
appeare
,
and
that
most
exactlye
,
in
a
greate
calme
,
when
the
sea
seemeth
as
plaine
and
as
smothe
as
a
borde
:
so
that
they
muste
shewe
som
such
thing
,
as
is
higher
between
them
then
any
of
both
theyr
syghts
,
when
the
sea
is
as
quiete
as
can
be
.
Scholar
.
Then
is
there
nothinge
but
water
.
But
then
it
seemeth
to
me
,
that
if
the
water
did
rise
rounde
,
the
farther
the
shippe
were
from
the
lande
the
higher
she
should
be
,
and
therfore
the
better
myghte
be
seene
.
Master
.
Your
imagination
hath
small
ground
of
reason
:
for
although
the
earthe
and
the
water
both
ioyntlye
and
seuerally
bee
rounde
of
nature
,
and
therefore
haue
in
deed
no
place
hygher
then
other
in
their
circumference
,
yet
all
vulgar
men
shall
thinke
by
apparance
that
that
place
is
highest
wher
thei
stand
,
&
that
from
them
on
ethe
syde
ther
is
a
round
descente
,
vntill
by
imagination
they
come
to
the
right
contrary
pointe
where
their
Antipodes
be
,
whome
they
shall
think
to
be
right
vnder
thē
,
wher
as
those
Antipodes
haue
the
contrarye
imagination
,
that
they
dwell
on
the
highest
parte
of
the
grounde
,
and
that
their
sea
is
hyghest
,
and
so
bothe
descendeth
compassedlye
vnto
the
contrarye
poynte
to
them
againe
.
and
thus
euerye
other
sorte
of
people
think
that
they
dwell
on
the
highest
parte
of
the
londe
,
and
also
of
the
sea
,
(
if
they
dwell
on
the
sea
)
and
they
shall
thynke
that
bothe
the
sea
as
well
as
the
londe
doothe
descende
from
them
eche
waies
.
Geometrical diagram.
As
in
this
circularre
forme
of
the
earthe
and
sea
,
the
menne
that
dwell
by
A
,
thinke
them selues
to
dwell
hyghest
of
all
other
,
so
that
on
eche
syde
of
them
the
londe
&
sea
seemeth
to
descend
,
&
therefore
they
iudge
the
ship
that
is
by
B
,
to
bee
lower
then
they
,
where
as
that
shippe
,
contrarye
waies
,
seemeth
to
them
that
be
in
it
,
to
bee
on
the
hyghest
parte
of
the
worlde
:
and
therefore
they
thinke
that
the
londe
by
A
,
is
lower
then
they
are
.
Againe
they
that
dwell
by
C
,
and
the
shippe
that
is
by
D
,
are
of
like
imaginations
,
eche
in
his
fantasie
thinking
him selfe
hyghest
,
and
the
other
lower
.
And
so
of
them
that
dwell
by
A
and
by
C
,
eche
meruayleth
how
the
other
canne
go
,
and
his
headde
downewarde
:
yet
in
deede
none
is
lower
then
other
,
sith
eche
of
them
is
equallye
distaunte
from
the
centre
of
the
earthe
,
whiche
is
the
lowest
place
of
all
other
.
and
therfore
no
waye
is
accompted
lower
except
it
be
nearer
to
that
centre
.
wherby
also
it
may
appeare
contrary
to
your
sayinge
,
that
although
the
sea
bee
rounde
,
yet
shall
not
the
ship
seem
to
ascend
still
,
but
rather
seem
to
descend
,
thoughe
in
deed
it
doth
none
of
both
,
but
moueth
circularly
about
the
centre
of
the
world
,
so
that
it
can
not
aptly
be
called
a
right
motion
,
but
a
compassed
motion
that
a
shippe
maketh
,
saue
that
it
is
tollerably
to
be
borne
in
vulgare
speache
,
bycause
euery
small
arche
of
a
great
circle
,
seemeth
to
be
a
right
lyne
to
the
syght
of
the
eye
.
And
in
this
figure
is
somwhat
represented
the
declaration
how
the
compassed
form
of
the
water
doth
let
the
sight
to
see
the
ship
,
and
like
waies
how
that
thei
on
the
londe
may
se
the
toppe
of
the
ship
when
they
can
not
see
the
hulle
,
and
they
in
the
bulle
of
the
ship
can
not
se
those
places
on
the
londe
,
whiche
other
in
the
top
of
the
ship
may
see
,
by
reason
that
their
sight
is
aboue
the
height
of
the
water
.
And
this
may
stande
for
a
conuenient
proofe
.
Scholar
.
So
dooth
it
appeare
manifestly
,
now
that
my
former
misconceaued
fantasye
is
reproued
.
And
so
I
remembre
when
I
haue
loked
after
a
shyp
that
departed
from
the
porte
where
I
stoode
,
first
I
lost
the
sighte
of
the
hulle
as
thoughe
it
had
sonke
into
the
sea
,
and
yet
I
saw
the
toppe
still
:
but
at
lengthe
I
loste
the
sighte
of
it
also
,
as
thoughe
all
had
sonke
into
the
water
.
which
by
your
declaration
I
perceaue
doth
folow
of
the
roundnes
of
the
water
:
for
other
reason
I
can
find
none
.
Master
.
Although
you
could
fynd
other
reasons
neuer
so
many
,
yet
this
reason
doth
enforce
that
effect
.
this
is
the
reason
that
Ptolemy
,
Cleomedes
,
and
after
them
Ioannes
de
Sacro
bosco
,
and
other
also
do
alleage
,
A
physicall
reason
for
the
roundnes
of
the
water
.
but
the
same
Iohn
hathe
an
other
reason
more
physicall
thē
geometricall
,
borowed
out
of
naturall
phylosophy
,
which
is
this
:
Seing
that
the
water
is
a
body
of
vniforme
substance
,
the
partes
of
it
must
be
of
lyke
condition
as
the
whole
bodye
is
:
but
the
partes
of
water
dooth
all
wayes
couette
a
rounde
forme
,
(
as
wee
see
in
euerye
droppe
that
falleth
from
any
thinge
,
or
standeth
on
anythinge
)
wherefore
of
iuste
congruence
the
whole
body
of
the
sea
and
water
must
needs
couet
the
same
forme
.
Schollar
.
In
deede
all
droppes
that
fall
from
the
ayer
in
a
mylde
rayne
,
when
menne
maye
marke
it
,
doo
fall
in
a
rounde
forme
,
and
so
the
droppes
that
fall
from
the
eaues
of
the
house
,
or
from
any
thing
els
,
yea
and
the
drops
of
dewe
that
stande
vppon
anye
leaues
of
herbes
,
or
other
lyke
thinge
.
Master
.
For
a
farther
experience
,
fyll
anye
vessell
brym
full
of
water
,
and
you
shall
perceaue
by
tryall
,
that
the
water
is
higher
ouer
the
myddle
of
that
vessels
mouth
,
then
it
is
by
the
brimmes
.
And
againe
pour
out
water
on
a
borde
or
on
a
stone
,
and
you
shall
soone
see
that
it
will
shewe
in
a
round
forme
,
and
will
be
deeper
in
the
middle
,
then
it
is
by
the
sides
.
Erasmus
Rheinhold
.
Yet
farther
reasons
there
be
alleged
,
whiche
were
to
tediouse
to
repeate
:
but
twoo
of
them
I
can
not
omytte
,
whiche
are
declared
by
Erasmus
Rheinholt
a
manne
not
onlye
of
greate
learning
,
but
also
of
as
greate
honesty
in
seekinge
to
profite
all
men
by
his
trauaile
,
although
sometime
hee
wanted
leasure
to
examine
some
of
his
writinges
,
as
it
may
appeare
by
one
of
those
two
reasons
,
whiche
is
this
.
An
other
reason
.
By
the
longe
course
of
euerye
greate
ryuer
(
sayth
hee
)
it
maye
appeare
that
the
water
doth
couet
a
rounde
forme
,
els
could
it
not
so
much
rise
in
roundnes
,
as
it
doth
in
running
so
longe
a
course
.
for
example
he
bringeth
the
course
of
the
greate
ryuer
Danubius
,
which
springeth
in
the
Alpes
,
beesyde
Vlma
in
Swicerlande
,
and
entrith
into
the
sea
Euxine
,
aboue
Constantinople
,
whiche
is
from
Vlma
312
germanye
myles
,
that
is
20
degrees
,
whiche
is
the
eightenth
part
of
the
whole
circuite
of
the
earthe
:
whereby
it
muste
needes
folow
that
the
myddle
of
that
ryuer
is
higher
then
the
fountaines
or
the
mouthe
,
by
13
germanye
myles
(
that
is
52
englyshe
myles
)
in
plumbe
heighte
.
for
declaration
whereof
hee
maketh
this
demonstration
linearye
,
supposynge
A
E
B
C
,
to
be
as
one
of
the
greatest
circles
about
the
earthe
,
whose
centre
is
D.
this
circle
must
be
imagined
so
to
passe
agreably
to
the
course
of
Danubius
,
that
A
maye
represente
the
fountaines
of
it
,
and
B
the
mouthe
of
it
,
so
E
shall
stand
for
the
myddle
parte
of
the
riuers
course
and
A
E
B
,
for
the
whole
Geometrical diagram.
course
.
Now
is
it
sayd
before
,
that
betwene
A
and
B
are
20
degrees
,
then
if
you
draw
a
right
line
from
the
one
to
the
other
,
as
heere
you
se
A
F
B
,
it
will
be
lower
vnder
the
myddle
of
the
arche
,
by
the
length
of
the
line
E
F
,
whiche
is
almoste
the
60
parte
of
the
semidiameter
of
the
earthe
,
and
maketh
iustlye
52
englysh
myles
,
sumwhat
lesse
then
57
:
whiche
is
the
60.
part
of
the
semidiameter
of
the
earthe
.
Scholar
.
This
reason
seemeth
pleasaunte
,
but
I
perceaue
not
the
reason
of
the
iuste
quantitye
of
the
lyne
E
F.
Master
That
dependeth
of
the
arte
of
Sines
and
Cordes
and
is
very
certaine
without
any
sensible
errour
,
of
whiche
in
an
other
place
ye
muste
learne
the
vse
.
And
in
deed
as
you
saye
,
this
reason
is
pleasaunt
,
and
the
author
muche
to
bee
praysed
and
loued
,
and
as
muche
is
it
to
be
lamented
,
that
the
shortnes
of
his
life
would
not
permitte
him
to
haue
recognised
his
workes
againe
:
wherfore
that
he
can
not
do
by
preuention
of
deathe
,
I
truste
some
of
his
friendes
will
do
:
for
althoughe
they
be
but
litle
faultes
,
yet
pittye
it
is
that
in
so
good
woorkes
there
shoulde
remaine
any
litle
spottes
,
as
in
this
argument
there
are
two
,
which
yet
hinder
not
the
argumente
.
And
althoughe
it
might
bee
truely
sayde
that
the
heighte
of
the
myddle
of
Danubius
is
not
52
myle
,
and
is
but
36
mile
,
yet
is
the
forme
of
his
argumente
good
,
for
that
height
is
sufficient
to
proue
that
the
middle
appeareth
muche
higher
then
the
fountaines
of
it
:
the
cause
of
this
ouersyght
was
,
that
hee
did
esteeme
the
course
of
Danubius
to
runne
by
one
of
the
greatest
circles
of
the
earth
,
which
is
not
so
:
for
it
hathe
in
latitude
from
the
equinoctiall
46
degrees
,
so
must
the
parallele
of
his
course
bee
litle
more
then
two
third
parts
of
the
greatest
circle
:
but
as
this
is
somwhat
to
straunge
for
you
yet
beyng
vnexpert
in
the
arte
of
Cordes
and
Sines
,
and
in
the
knowledge
of
Cosmographye
,
so
I
wyll
lette
it
passe
with
this
lyghte
admonyshmente
,
wysshynge
that
hee
hadde
also
more
aptelye
expressed
hys
meanynge
,
and
the
vse
of
his
termes
,
for
auoidinge
of
slanderouse
tongues
,
for
it
myghte
nowe
bee
answered
hym
,
that
Danubius
is
no
hygher
in
one
place
,
then
in
an
other
,
seeynge
all
distaunce
of
heighte
is
to
bee
accompted
from
the
centre
:
and
the
middle
of
the
riuer
by
E
,
is
no
farther
from
the
centre
D
,
then
is
the
fontayne
A
,
or
the
mouthe
B.
Schola
.
Marye
that
obiection
is
certaine
,
and
therefore
is
his
errour
manifest
,
and
his
argument
of
no
force
.
Master
.
Erasmus
Rheinholt
excused
.
You
triumphe
to
muche
before
the
victory
.
his
argument
is
better
then
you
do
considre
it
his
intent
was
to
proue
that
the
water
doth
not
run
by
a
right
line
and
dounwarde
still
,
as
the
vulgare
sorte
doothe
imagine
,
but
that
it
runneth
circularlye
.
wherefore
it
foloweth
well
against
the
vulgare
opinion
,
to
say
that
the
water
of
Danubius
is
hygher
in
the
middle
of
this
his
course
,
by
so
manye
miles
in
height
plumb
vpright
,
then
it
shuld
be
by
their
imagination
So
is
there
none
other
fault
in
this
point
,
but
the
want
of
distinction
of
the
true
opinion
of
highnes
and
lownes
,
from
the
wronge
takinge
of
the
same
names
,
wherby
those
which
do
not
know
his
great
learning
,
and
myght
happen
to
hear
his
argument
,
wold
iudge
that
other
he
were
wonderfullye
deceaued
,
other
els
that
he
did
to
much
abuse
hys
tearmes
:
but
if
deathe
hadde
not
preuented
him
,
hee
woulde
haue
declared
his
meaninge
,
I
doubte
not
,
as
I
haue
declared
it
.
Erasmus
Rheinholt
his
seconde
argument
.
Nowe
to
hys
seconde
argument
.
he
proueth
that
there
can
be
no
such
holownes
in
the
sea
,
as
there
is
betweene
two
hylles
for
seeynge
the
sea
is
a
heauye
bodye
,
and
presseth
towarde
the
centre
of
the
worlde
,
euerye
parte
of
it
wyll
doo
the
lyke
if
it
be
not
stayed
.
And
the
water
beynge
a
lyquide
and
fluxible
bodye
,
can
not
be
stayed
by
his
owne
partes
:
wherefore
it
foloweth
that
there
can
remaine
no
valyes
nor
dales
,
nor
hollowe
partes
in
it
,
but
it
shall
quickly
be
fylled
with
water
.
and
therfore
wee
see
,
that
nothinge
can
be
more
plainer
then
is
the
toppe
of
water
,
syth
euery
part
so
exactly
ioyneth
with
other
,
in
fyllinge
vp
all
vnequalitie
:
whereof
it
foloweth
,
that
if
the
toppe
of
the
water
be
iuste
equall
and
lyke
distaunte
from
the
lowest
part
of
the
world
,
(
which
hath
been
often
declared
to
be
the
centre
of
the
earth
)
then
muste
the
face
of
the
water
needes
be
round
,
according
to
the
definition
of
a
circle
.
Scholar
.
Why
the
water
doth
not
couer
all
thearth
.
That
foloweth
well
in
deede
:
for
as
eche
parte
of
the
circumference
in
a
circle
is
equally
distaunt
from
the
eentre
,
so
if
all
partes
of
the
face
of
the
water
be
equally
distant
from
the
centre
,
it
must
needes
be
circular
,
as
the
circumference
of
a
circle
is
.
But
if
it
be
so
round
,
and
ought
to
haue
his
place
aboue
the
earthe
,
how
doth
it
happen
that
it
doth
not
couer
the
whole
face
of
the
earthe
?
and
so
shoulde
there
be
no
earth
seene
.
Master
.
Haue
you
forgotten
what
you
readde
in
Ioannes
de
Sacro
Bosco
,
for
to
answere
that
question
?
Scholar
.
In
deede
he
sayth
that
the
other
three
elementes
doo
compas
the
earthe
round
about
,
saue
that
for
the
preseruation
of
man
and
beastes
,
the
drinesse
of
the
earth
doth
withstande
the
moysture
of
the
water
.
Master
.
That
reason
sauoreth
more
of
the
determinations
theological
,
then
of
the
demonstrations
mathematical
,
wherfore
I
will
adde
therto
a
proof
by
good
demonstration
that
it
can
not
compasse
the
earthe
rounde
:
That
the
water
1.
can
not
compas
the
arth
II
.
for
whiche
purpose
firste
I
saye
,
that
the
water
beinge
inclosed
within
the
boundes
of
the
earthe
,
can
not
be
so
greate
as
the
earthe
is
.
Againe
considering
that
one
portion
of
water
being
mixed
with
4
tymes
so
muche
earth
,
wold
make
it
all
softe
and
slabby
,
it
may
not
be
thought
that
the
water
of
the
sea
and
of
all
ryers
and
springes
ioyned
togither
,
is
so
muche
as
the
firste
parte
of
the
earthe
.
III
.
Farthermore
if
you
consider
the
firme
stablenes
of
the
earthe
,
and
the
vnstable
swaruynge
of
the
water
,
you
wolde
thinke
that
if
the
water
were
able
to
matche
the
twentith
parte
of
the
earthe
,
it
woulde
make
the
earthe
more
vnstable
then
the
nature
of
the
earthe
,
and
the
preseruation
of
earthly
creatures
could
beare
.
Yea
it
would
be
a
weak
ground
to
bear
so
wondrefull
a
waight
as
it
doth
,
IIII
.
if
the
quantity
of
water
were
notable
,
in
comparison
to
the
quantity
of
the
earth
.
V.
Yet
now
for
farther
triall
,
suppose
(
as
I
thinke
it
true
)
that
on
the
flatte
face
and
circumference
of
the
earthe
,
there
is
as
muche
water
as
londe
,
so
mighte
it
appeare
that
the
water
were
as
muche
as
the
londe
,
as
manye
men
doo
affirme
.
Scholar
.
And
moste
part
of
learned
men
(
as
I
haue
heard
say
)
do
vouche
that
as
a
moste
certaine
truthe
.
Master
.
It
is
true
,
as
I
iudge
also
,
yf
they
meane
lyke
cosmographers
that
halfe
the
face
of
the
earthe
(
as
I
sayde
)
is
couered
with
water
,
but
then
imagine
what
depthe
maye
that
sea
be
of
.
Scholar
.
No
manne
can
tell
.
Master
.
Yet
by
triall
of
mariners
it
hath
been
founde
in
fewe
places
,
a
hundreth
fathomes
deepe
,
whiche
is
litle
more
then
the
tenthe
parte
of
a
myle
.
Scholar
.
That
not
withstandinge
,
it
maye
bee
deeper
in
some
places
.
Master
.
For
a
supposition
,
imagine
it
were
in
all
places
a
myle
deepe
,
taking
one
place
with
an
other
.
Sch.
I
thinke
that
to
to
muche
a
great
deale
,
consideringe
that
all
knowen
partes
are
not
in
the
deepest
,
accomptinge
one
place
with
an
other
,
as
good
mariners
can
testify
,
aboue
40
fadome
,
and
so
groweth
shallower
still
to
the
shore
.
Master
.
The
more
that
that
supposition
excedeth
truth
,
the
stronger
shall
the
proofe
be
of
the
smalnes
of
the
water
in
comparison
to
the
earthe
.
Scholar
.
Then
for
trials
sake
,
I
suppose
it
were
so
.
Master
.
How
deepe
thinke
you
now
the
earth
to
be
?
Scholar
.
I
remembre
you
saide
before
,
that
57
myle
was
but
the
60
parte
of
the
semidiameter
of
the
earth
:
then
must
the
whole
earth
be
in
thicknes
6840
myles
.
Master
.
That
is
agreable
to
that
rate
:
but
as
I
sayde
before
,
the
diameter
is
6872
8
/
11.
And
nowe
if
you
abate
one
fifte
parte
of
that
depthe
,
the
rest
will
make
the
side
of
a
cubike
forme
,
almoste
as
great
as
the
globe
of
the
earthe
:
as
it
appeareth
in
the
workes
of
Geometrye
.
Scholar
.
The
fyfte
parte
of
6872
is
1374.
which
beyng
deducted
from
6872
there
resteth
5498.
Master
.
That
numbre
is
somewhat
to
lyttle
,
but
5541
is
very
nigh
the
side
of
a
cube
,
equal
to
the
globe
of
the
whole
earthe
,
therefore
multiplye
it
cubikly
,
as
you
haue
learned
in
Arithmetike
,
and
then
shall
you
see
,
howe
manye
miles
square
are
in
the
whole
globe
of
the
earth
.
Schol
.
If
5541
be
multiplied
by
it self
,
it
maketh
in
square
numbre
30702681
,
which
being
multiplied
again
by
5541
,
doth
yeld
170123555421
:
which
is
the
cubike
numbre
to
5541
,
and
so
consequently
must
it
be
that
cube
whiche
is
equall
to
the
earthe
,
in
his
whole
globe
.
Master
.
So
is
it
very
nighe
.
But
now
for
the
quantitye
of
all
the
sea
,
this
way
must
you
worke
.
Firste
to
know
all
the
plat
face
of
the
earth
,
you
must
multiply
his
circumference
by
his
diameter
,
as
it
is
declared
in
the
Pathwaye
,
and
so
will
there
amounte
148450909
:
whiche
is
the
full
platte
forme
of
all
the
face
of
the
earth
:
whereof
presupposing
(
as
the
truth
doth
inforce
vs
)
that
halfe
the
same
is
sea
and
water
:
then
dooth
it
followe
,
that
the
whole
platte
face
of
the
sea
and
water
is
74225454
myles
and
a
halfe
in
all
togither
,
which
is
not
the
2000
parte
of
the
earthe
.
Scholar
.
But
muste
not
this
numbre
be
multiplied
by
the
depthe
of
the
sea
?
Master
.
Seynge
that
depthe
is
not
in
one
place
with
an
other
aboue
one
myle
,
and
1
dooth
nother
multiplye
nor
diuide
,
it
will
remaine
as
it
is
.
Scholar
.
Then
dare
I
thinke
farther
,
that
the
depthe
of
the
sea
beynge
not
a
quarter
so
muche
generallye
,
the
earth
must
nedes
bee
10000
tymes
so
greate
as
the
sea
,
and
all
other
waters
.
Master
.
Your
woordes
erre
not
muche
from
the
truthe
:
and
therfore
by
this
reason
it
doth
appear
,
that
the
water
being
so
little
in
comparison
to
the
earth
,
can
not
aptlye
compas
the
earthe
.
And
by
this
it
appeareth
also
how
childishlye
they
doo
erre
,
that
thinke
the
water
to
bee
tenne
tymes
so
greate
as
the
earthe
:
for
if
it
were
but
twise
so
greate
as
the
earthe
,
it
muste
of
necessitye
couer
all
the
face
of
the
earthe
:
yea
I
will
saye
constantlye
,
if
all
the
water
were
as
muche
as
the
hundreth
parte
of
the
earthe
,
it
would
ouer
runne
all
the
earthe
,
and
couer
it
cleane
:
whiche
I
maye
easilye
prooue
,
but
not
brieflye
:
and
seeynge
the
same
thinge
is
all
readye
declared
in
the
Pathwaye
,
I
will
omytte
it
heere
,
syth
it
is
a
more
appropried
proofe
for
Geometrye
,
then
for
Astronomye
:
and
nowe
will
I
returne
to
the
prosecutinge
of
our
former
matters
,
accomptynge
this
sufficiente
for
the
declaration
of
the
roundnes
of
the
earthe
and
also
of
the
water
seuerallye
,
and
now
wyll
I
adde
one
reason
to
approue
that
bothe
they
do
make
one
perfect
rounde
globe
.
That
the
earthe
and
water
togither
doo
make
a
perfect
globe
.
Euerye
grosse
and
sounde
bodye
doth
gyue
a
shadow
like
vnto
his
owne
forme
the
earth
is
a
grosse
and
sound
body
,
therefore
muste
it
gyue
a
shadow
lyke
hys
owne
forme
:
but
in
all
eclipses
of
the
Mone
,
which
are
caused
by
the
shadow
of
the
earth
,
his
shadowe
is
alwaies
constantly
round
,
whether
the
shadow
doo
runne
easte
,
weste
,
southe
,
or
any
other
waies
mixtly
:
wherfore
it
foloweth
,
that
the
forme
of
the
earth
is
round
,
whiche
giueth
that
rounde
shaddow
.
Scholar
.
How
shall
a
man
vnderstand
that
the
shadowe
of
the
earthe
is
rounde
?
Master
.
In
the
eclipse
of
the
moone
,
other
all
the
mone
is
darkened
,
or
els
but
one
part
of
hir
:
If
all
the
mone
be
darkened
,
then
doth
the
darkenes
begin
on
the
easte
syde
of
the
moone
in
circularre
forme
,
and
encreaseth
still
in
the
same
forme
,
tyll
all
the
whole
moone
be
eclipsed
,
and
then
decreaseth
the
darkenes
againe
,
so
that
the
weste
syde
of
the
mone
is
darkened
,
but
the
darkenes
vadeth
by
lyttle
and
litle
,
and
yet
styll
in
circularre
forme
.
And
if
the
moone
be
darkened
only
in
one
parte
,
whether
it
be
the
south
part
,
or
the
north
parte
,
yet
still
is
the
shadowe
round
in
forme
:
where
as
if
the
earthe
were
square
or
cubike
,
other
three
cornered
,
or
of
other
suche
forme
,
the
shaddow
wolde
so
appear
in
the
mone
as
by
the
thirde
and
fourthe
figure
,
you
maye
partlye
perceaue
.
diagram of the eclipses of the moon.
Examples
of
the
firste
forme
where
all
the
moone
is
eclipsed
at
the
full
eclipse
.
diagram of the eclipses of the moon.
Example
of
the
thirde
and
fourth
formes
.
diagram of the eclipses of the moon.
Examples
of
the
thyrd
and
fourth
formes
.
Examples
of
the
other
two
sortes
,
of
one
parte
eclipsed
.
The
southe
parte
.
diagram of the eclipses of the moon.
The
northe
parte
.
That
the
earth
is
but
a
pricke
in
respecte
of
the
skye
.
But
I
will
omitte
this
matter
tyll
anone
,
bicause
it
is
not
easye
to
vnderstande
without
farther
explication
of
other
matters
incident
therto
.
And
bicause
I
haue
begon
to
speak
of
the
shaddowe
of
the
earthe
:
I
will
alleage
one
argument
more
,
taken
by
the
same
shaddowe
to
approoue
the
smalnes
of
the
earthe
in
comparison
to
the
skie
.
wherfore
thus
I
frame
mine
argument
.
The
Sonne
is
but
a
very
small
portion
in
comparison
to
the
whole
skie
,
and
yet
the
Sonne
is
manyfolde
bigger
then
the
earthe
:
wherfore
the
earthe
muste
needes
bee
but
a
verye
small
thinge
in
comparison
to
the
heauens
.
Scholar
.
Your
arguments
is
good
,
and
the
maior
is
manifest
to
euery
mans
sight
:
but
how
do
you
proue
the
minor
?
Master
.
Euery
darke
body
giueth
shadow
accordinge
to
the
quantitie
that
it
beareth
to
that
shyning
body
,
which
giueth
the
light
,
so
that
if
the
shining
body
be
equall
to
the
dark
body
,
thē
doth
the
shadow
run
in
form
of
a
piller
,
or
of
a
roller
,
like
byg
at
both
the
ends
:
but
if
the
bright
body
be
greater
then
the
dark
body
,
then
doth
the
shadow
growe
lesser
&
lesser
in
spyre
forme
,
or
taper
fashion
,
and
at
lengthe
doth
ende
in
a
sharpe
pointe
.
Contrarye
wayes
,
if
the
lyghte
bodye
be
lesser
then
the
darke
bodye
is
,
then
doth
the
shaddow
grow
greater
and
greater
,
still
as
it
goeth
from
the
dark
body
,
and
is
smallest
at
the
beginning
;
contrary
to
the
taper
forme
,
whiche
is
greatest
at
the
beginninge
:
and
this
forme
maye
be
called
maundforme
,
or
bell
forme
,
bicause
it
is
like
a
maunde
basket
,
or
a
bell
.
Examples
of
these
thre
diuers
shaddowes
.
The
Piller
forme
.
diagram of a shadow cast by the earth.
The
Taper
forme
.
diagram of a shadow cast by the earth.
The
Bell
forme
.
diagram of a shadow cast by the earth.
A
representeth
the
son
or
other
lyght
body
.
B
the
earth
,
or
any
dark
body
,
and
C
the
shadow
.
Scholar
.
This
may
stand
as
a
sure
maxime
,
sith
both
reason
&
sense
doo
testify
it
to
be
tru
.
Master
.
Then
do
I
infer
farther
:
that
if
the
sonne
were
lesser
then
the
earthe
,
the
shadowe
of
the
earthe
would
grow
greater
and
greater
,
and
would
be
infinite
in
lengthe
:
wherby
it
wold
darken
the
most
parte
of
the
starres
,
euery
night
:
&
very
often
it
wold
shadowe
the
mone
,
and
that
for
a
long
space
togither
.
as
you
may
gather
by
this
figure
,
Astronomical diagram.
wher
A
representeth
the
son
in
lesser
form
then
the
earth
,
which
is
signified
by
the
circle
marked
with
G
,
&
the
shadowe
that
commeth
by
this
form
,
is
marked
with
D
,
which
occupieth
a
great
part
of
the
skye
,
and
therefore
woulde
darken
all
the
starres
is
so
muche
space
of
the
skye
,
which
is
nyghe
hande
a
quarter
of
that
hemisphere
that
is
aboue
our
horizont
.
And
as
the
shaddow
tourneth
about
accordyng
to
the
motion
of
the
Sonne
,
so
in
four
and
twentye
howers
all
the
starres
that
be
nyghe
vnto
the
zodiake
,
should
suffre
eclipse
:
whiche
thinge
is
contrary
to
dayly
experience
,
for
wee
see
there
(
about
the
zodiake
and
againste
the
sonne
)
the
starres
very
bright
.
Scholar
.
This
reason
doth
suppose
,
that
the
starres
do
receaue
their
light
of
the
sonne
,
which
thinge
was
not
yet
proued
by
you
,
althoughe
I
thinke
it
to
be
true
,
yet
in
a
good
argument
,
no
doubtfull
sentence
may
be
alleged
.
Master
.
Then
seing
this
place
doth
not
conueniently
permit
so
longe
a
digression
to
prooue
that
,
I
will
vse
the
mone
for
an
example
,
which
appeareth
so
manifestlye
to
borrowe
her
lyghte
of
the
Sonne
,
that
according
as
she
receaueth
the
lyghte
from
him
,
so
dooth
shee
appeare
greater
or
lesser
in
lyght
,
according
to
hir
distance
from
him
.
and
when
so
euer
she
commeth
into
the
shaddowe
of
the
earth
,
she
leeseth
her
lyght
,
other
fully
or
in
part
,
accordingly
as
she
passeth
and
toucheth
the
shaddowe
of
the
earthe
.
wherefore
as
longe
as
the
moone
shoulde
be
within
that
shaddow
,
she
must
needs
be
in
the
eclipse
:
and
the
shaddowe
beinge
so
great
,
she
shuld
be
eclipsed
not
only
euery
moneth
at
the
full
,
but
she
should
continue
almoste
foure
dayes
to
gither
in
that
eclipse
,
seing
that
shaddowe
dooth
occupye
as
muche
of
the
skye
,
as
shee
doth
moue
by
hir
propre
course
in
foure
dayes
.
Schol
.
That
absurditie
is
to
manifest
to
graunt
vnto
:
and
yet
the
greatnes
of
the
shaddow
inferreth
no
lesse
,
syth
it
occupyeth
so
muche
of
the
skie
.
Master
.
The
like
inconuenience
will
follow
,
if
the
son
and
the
earth
were
both
of
one
greatnes
,
as
are
B
&
G
in
the
former
figure
,
for
so
wolde
the
shaddow
run
of
one
bignes
like
a
roller
,
as
is
represented
by
E
,
and
wold
darken
diuers
stars
,
and
namelye
all
that
bee
in
the
myddle
of
the
Zodiake
,
and
the
moone
should
both
oftener
be
eclipsed
(
then
in
deed
she
is
)
by
the
greatnes
of
the
shaddowe
,
and
wold
tarry
longer
in
the
eclipse
,
by
that
same
reason
,
then
good
reason
wold
allowe
.
But
seing
we
perceaue
no
starres
directlye
against
the
sonne
to
be
eclipsed
,
nother
yet
the
mone
,
in
suche
forme
as
that
pyllerlyke
shaddow
would
cause
,
we
must
needes
thinke
that
the
shaddowe
is
muche
abated
,
beefore
it
come
to
the
sphere
of
the
moone
,
and
is
cleane
consumed
before
it
come
at
anye
of
the
starres
,
whiche
kinde
of
abatement
could
not
be
,
but
where
the
light
is
much
greater
then
is
the
body
that
maketh
the
shaddow
,
as
is
C
in
comparison
to
G.
Scholar
.
So
must
it
followe
,
that
seyng
the
Sonne
is
the
lyghte
body
,
and
the
earthe
giueth
the
shaddowe
,
of
necessitye
the
Sonne
muste
be
greater
then
the
earthe
.
Master
.
Yea
in
deede
,
and
that
manye
folde
.
Scholar
.
Then
of
more
force
muste
the
earthe
bee
a
verye
small
body
in
respecte
to
the
whole
skye
,
which
is
infinitely
greater
then
the
sonne
,
as
euery
childe
may
perceaue
.
Master
.
Yet
haue
I
farther
matter
of
profe
,
that
the
earth
is
not
only
a
very
small
bodye
in
regarde
to
the
skie
,
but
is
without
anye
vewe
of
greatnes
in
that
comparison
.
If
the
earthe
had
anye
notable
quantitye
in
respecte
of
the
skye
,
The
second
reason
for
the
quantitie
of
the
earthe
.
&c
then
muste
the
diameter
of
the
earthe
haue
as
greate
a
quantitie
,
in
comparison
to
the
diameter
of
the
skie
.
for
as
in
twoo
circles
the
proportion
of
the
diameters
is
equall
to
the
proportion
of
the
circumferences
,
so
is
the
proportion
of
the
shorter
to
the
longer
,
greater
then
is
the
proportion
of
their
two
platte
formes
:
but
in
two
globes
the
proportion
of
the
shorter
diameter
to
the
longer
,
is
muche
greater
then
is
the
rate
of
their
platte
formes
:
and
yet
muche
more
greatter
then
the
proportion
of
the
lesser
globe
to
the
bygger
.
Scholar
.
That
is
sufficiently
proued
in
Geometry
,
wherfore
you
may
proceede
with
your
conclusion
.
Master
.
If
the
diameter
of
the
earth
haue
notable
quantity
in
comparison
to
the
diameter
of
the
skie
,
then
the
stars
which
ar
ouer
our
headdes
,
be
nygher
vnto
vs
by
a
notable
quantitie
,
then
when
they
be
in
the
easte
,
or
in
the
west
.
Scholar
.
In
deede
they
are
nearer
by
the
semidiameter
of
the
earthe
:
whiche
of
it selfe
muste
needes
bee
accompted
a
notable
quantitie
.
Master
.
But
if
it
shall
be
so
accompted
in
regarde
to
the
halfe
diameter
of
the
skie
,
then
must
the
stars
ouer
our
heds
seeme
bigger
by
a
notable
quantitye
,
then
when
they
are
in
the
easte
or
weste
.
Scholar
.
That
reason
is
not
only
approued
by
Geometrye
,
but
also
by
common
sight
and
daily
experience
,
that
the
nigher
any
thing
is
to
the
sighte
,
the
greater
it
seemeth
:
and
the
farther
from
the
sighte
,
the
lesser
it
sheweth
.
Master
.
There
is
no
suche
diuersity
perceaued
in
the
quantitie
of
the
starres
,
but
that
they
appeare
styll
constantly
of
one
bignes
:
wherfore
it
must
follow
,
that
their
distance
is
all
one
in
all
partes
of
the
skye
,
and
then
doth
not
the
semidiameter
of
the
earth
make
anye
notable
diuersitie
in
distance
:
wherefore
it
must
be
thought
that
the
quantitye
of
it
is
not
sensible
in
comparison
to
the
semidiameter
of
heauen
,
nother
the
circumference
of
it
in
comparison
to
the
circumference
of
the
skye
,
and
muche
more
may
not
the
whole
quantitye
of
it
bee
accompted
sensible
in
respecte
to
the
whole
quantitie
of
the
worlde
.
Schol
.
That
foloweth
well
:
for
as
I
learned
in
Geometry
,
if
the
diameters
of
any
two
Globes
,
be
in
suche
proportion
that
the
greater
do
contain
the
lesser
a
thousand
times
,
then
be
their
circumferences
in
the
same
rate
:
but
the
platte
forme
of
the
greater
,
is
1000000
folde
greater
then
the
lesser
:
and
the
whole
substance
of
the
bigger
globe
,
doth
containe
the
smaller
globe
,
1000000000
tymes
.
Master
.
Vndoubtedly
it
maye
bee
perceaued
by
sight
as
well
in
dialles
,
as
other
greater
instrumentes
made
for
obseruations
,
that
the
semidiameter
of
the
sonne
his
sphere
is
more
then
a
thousand
times
longer
then
the
semidiameter
of
the
earthe
,
els
wolde
not
the
shadowes
agree
so
exactly
as
they
do
:
for
they
moue
as
duely
and
ordrely
about
the
centre
of
all
suche
instrumentes
,
as
if
their
centre
were
the
very
centre
of
the
world
.
which
thinge
could
not
be
,
if
those
two
centres
dyd
differ
notably
,
in
respecte
to
the
sphere
of
the
Sonne
.
And
if
it
were
not
,
that
an
introduction
dooth
not
admitte
the
exacte
proofes
of
the
arte
,
I
could
herby
declare
the
proportion
of
these
two
semidiameters
so
exactly
,
that
you
should
confesse
that
proofe
to
bee
righte
certaine
and
good
.
But
now
wil
I
procede
to
the
declaration
of
this
third
reason
by
linearye
demonstration
,
although
it
be
somwhat
obscure
,
without
other
helpe
.
In
this
figure
,
which
representeth
the
three
notable
circles
in
a
diall
,
The
thirde
reason
.
that
bee
made
by
the
course
of
the
Sonne
,
in
the
thre
notable
places
of
the
zodiake
,
that
is
in
the
two
tropikes
and
in
the
equinoctiall
,
the
vttermoste
arke
B
L
C
,
representeth
the
tropike
of
Capricorne
,
and
is
heere
made
no
bygger
,
then
the
quarter
of
a
circle
,
by
cause
the
Sonne
doth
shine
but
syxe
howers
vnto
vs
,
when
hee
is
in
the
signe
.
the
equinoctiall
is
set
as
halfe
a
circle
,
bicause
the
son
being
in
it
,
doth
shine
to
vs
12
howers
,
and
is
here
limited
by
E
I
F.
Geometric diagram.
The
tropike
of
Cancer
containeth
thre
quarters
of
a
circle
,
bicause
that
when
the
Sonne
is
in
it
,
then
is
there
18
howers
from
Sonne
rising
to
sonne
setting
:
and
that
circle
here
is
signified
by
G
K
H.
The
centre
of
this
diall
is
A
,
and
the
stile
that
giueth
the
shaddow
is
D
A
,
whose
toppe
being
D
,
doth
describe
those
cantylles
of
circles
,
in
suche
precisenes
,
as
if
that
diall
stood
in
the
centre
of
the
earth
.
and
like
waies
the
distinction
of
the
howers
is
suche
exactlye
in
that
diall
,
as
if
the
centre
of
the
diall
,
wer
the
very
centre
of
the
world
.
Scholar
.
I
do
conceaue
good
reason
of
profe
hereby
,
but
yet
I
thinke
I
shall
perceaue
muche
more
,
when
I
shall
vnderstande
the
iuste
vse
of
those
dials
,
as
well
as
of
other
seuerall
instruments
of
lyke
vse
.
Master
.
You
say
truthe
:
and
therefore
wyll
I
passe
from
this
thirde
reason
,
and
come
to
the
fourthe
proofe
,
whiche
is
thys
.
The
fourthe
reason
for
the
smalnes
of
thearth
.
If
the
earthe
were
of
anye
bygnes
in
comparison
to
the
worlde
,
then
shoulde
his
semidiameter
beare
some
vewe
of
byggenesse
to
the
semidiameter
of
the
skie
.
and
so
consequently
the
horizont
that
we
haue
on
the
ouer
parte
of
the
earthe
,
should
not
diuide
the
skie
into
two
equall
partes
,
for
that
part
which
shuld
be
vnder
the
horizont
,
would
alwaies
be
the
greater
,
and
the
lesser
parte
aboue
the
horizonte
,
as
in
this
figure
it
doth
appear
.
Geometric diagram.
where
A
C
D
B
is
the
circle
of
the
skie
,
and
the
lesser
circle
is
the
earthe
,
the
centre
B
,
being
common
centre
to
them
bothe
.
and
E
F
is
the
semidiameter
of
the
earthe
,
as
E
A
is
the
semidiameter
of
the
skye
.
Nowe
if
E
F
bee
notable
in
quantitie
in
comparison
to
E
A
,
then
will
the
line
C
F
D
(
beyng
the
horizonte
on
the
toppe
of
the
earth
)
differ
notably
from
the
line
A
E
B
,
beynge
the
diameter
of
the
worlde
,
and
the
horizonte
to
the
centre
of
the
earthe
.
And
so
shall
not
that
horizont
C
F
D
diuide
the
worlde
into
two
equall
halues
,
but
the
ouer
part
aboue
the
horizonte
shall
be
lesser
then
the
other
parte
that
is
beneth
the
same
horizonte
,
whiche
thinge
is
contrary
to
daily
experience
,
and
to
all
obseruations
:
for
we
may
see
in
the
longe
winter
nights
those
starres
that
be
in
the
horizont
in
the
easte
at
the
beginning
of
the
nyght
,
to
be
in
the
same
horizont
in
the
weste
,
at
the
ende
of
twelue
howers
;
and
contrarye
waies
those
starres
that
did
set
in
the
west
,
when
those
other
did
rise
in
the
easte
,
shall
rise
againe
when
the
other
do
do
set
.
And
so
of
the
sonne
and
the
moone
when
they
be
in
contrarye
pointes
of
the
Zodiake
.
Scholar
.
That
is
at
the
full
of
the
moone
.
Master
.
In
deede
then
are
they
right
opposite
the
one
against
the
other
:
but
if
the
moone
be
at
the
full
,
long
before
the
sonne
setting
,
then
will
she
rise
somewhat
after
the
same
:
and
contrary
waies
if
she
be
at
the
ful
after
the
sonne
setting
,
then
will
she
rise
somwhat
sooner
,
by
reason
that
she
moueth
eastwarde
euery
hower
33
degrees
.
And
although
vnto
them
that
be
meanly
acquainted
with
the
motions
of
the
planets
,
the
declination
of
the
moone
and
hir
latitude
,
may
occasion
some
doubtefulnes
to
rise
,
yet
vnto
the
learned
,
those
many
folde
varieties
in
the
motion
of
hyr
and
thother
planets
,
do
confirme
the
principles
of
astronomy
more
adsuredly
:
but
this
will
I
omitte
tyll
an
other
more
conuenient
tyme
.
Scholar
.
This
is
well
proued
nowe
,
that
the
earth
in
comparison
to
the
whole
world
is
but
as
a
pricke
or
a
mote
,
and
lykewaies
in
comparison
to
the
other
spheres
.
Master
.
You
muste
except
the
spheres
of
the
thre
planets
Geometric diagram.
whiche
bee
beneth
the
son
.
for
vnto
them
the
diameter
of
the
earthe
beareth
a
notable
quantity
:
for
the
semidiameter
of
Venus
Sphere
,
is
but
167
tymes
so
long
as
the
semidiameter
of
the
earth
:
and
the
semidiameter
of
Mercury
his
sphere
is
shorter
muche
,
for
it
is
litle
more
then
64
times
the
semidiameter
of
the
earthe
,
but
the
moone
hath
hir
semidiameter
only
33
tymes
and
a
halfe
longer
then
the
earthes
semidiameter
:
all
which
proportions
with
the
residue
,
I
haue
set
forth
in
this
figure
,
wherby
you
may
perceaue
,
that
vnto
the
semidiameter
of
ech
sphere
,
is
annexed
the
numbre
that
importeth
howe
often
it
containeth
the
semidiameter
of
the
earthe
.
that
is
to
say
:
the
sonne
his
semidiameter
containeth
it
1120
times
,
Mars
1220
times
,
Iupiter
8876
tymes
,
Saturne
14405
tymes
an
:
d
the
eight
sphere
or
starry
skie
.
20110
tymes
.
Sch.
I
remembre
that
Faber
on
the
Sphere
doth
accompt
those
distances
by
miles
,
which
is
a
pleasant
matter
to
read
.
Ma.
In
that
place
Faber
foloweth
the
accompt
of
Alphraganus
the
Arabitian
,
which
speaketh
of
myles
much
longer
then
the
Italian
myles
be
:
for
6
of
the
Italian
miles
do
make
but
5
of
Alphraganus
miles
:
of
which
diuersity
at
an
other
tyme
I
will
instructe
you
,
namely
in
the
treatise
of
Cosmographye
:
where
I
wyll
set
forth
diuers
varieties
and
appearante
repugnances
of
sondry
writers
,
for
the
measuringe
of
the
earthe
:
and
proue
it
to
be
a
disagrement
more
in
wordes
then
in
meaning
:
and
to
come
by
reason
of
their
diuers
miles
,
or
other
in
constant
measures
.
And
bicause
you
like
that
table
so
well
,
lo
heere
is
an
other
drawen
accordinge
to
the
rate
of
60
myles
to
eche
degree
.
But
heere
by
the
compas
is
vnderstande
the
inner
concauitie
of
eche
sphere
.
The
eyght
Spheres
.
|
The
myles
that
theyr
semidiameter
containeth
.
|
The
myles
of
euery
sphere
in
compas
.
|
☽
The
Moone
|
115278.
|
724604
4
/
7
|
☿
Mercurye
.
|
220500
2
/
33
|
1386000
4
/
231
|
♀
Venus
.
|
573872
8
/
11
|
3607200
|
☉
The
Sonne
.
|
3848367
3
/
11
|
34189737
1
/
7
|
♂
Mars
.
|
4192363
7
/
11
|
26352000
|
♃
Iupiter
.
|
30501163
7
/
11
|
191721600
|
♄
Saturne
.
|
49500818
2
/
11
|
311148000
|
The
eight
sphere
.
|
69105272
8
/
11
|
434376000
|
And
his
conuexitie
or
vtter
compas
is
equall
to
the
concauitye
of
the
nexte
sphere
aboue
it
.
Scholar
.
If
the
whole
circuite
of
the
skye
bee
434376000
myles
,
and
the
same
compasse
is
360
degrees
,
then
muste
it
needes
follow
,
that
euery
degre
of
that
sky
contayneth
iust
1206600
miles
,
as
by
diuision
it
may
be
sufficiently
well
proued
.
But
howe
is
this
supposition
of
distaunces
approued
to
be
true
?
Master
.
That
profe
dependeth
of
more
knowledge
,
then
this
introduction
teacheth
,
and
therefore
must
be
referred
to
a
higher
treatise
.
But
in
the
meane
ceason
admitting
this
supposition
,
you
maye
easilye
tell
,
howe
manye
myles
the
sonne
and
the
moone
are
in
breadthe
,
seeinge
eche
of
them
is
accompted
about
31
minutes
by
theyr
diameter
,
eche
in
the
myddle
of
his
owne
sphere
.
Scholar
.
Nowe
I
vnderstande
the
forme
of
woorkinge
for
tryall
of
this
matter
.
Fyrste
I
muste
searche
how
manye
myles
make
a
degree
in
eche
of
those
spheres
,
and
then
take
a
parte
proportionable
of
that
numbre
agreable
to
31
minutes
&
a
halfe
.
Therfore
to
begyn
with
the
sonne
.
As
his
whole
sphere
in
the
middle
is
in
compas
25270868
myles
,
so
tryinge
it
by
diuision
,
I
fynde
that
euerye
degree
in
that
sphere
doth
containe
70197
miles
nygh
hande
.
Then
say
I
by
the
golden
rule
,
if
60
minutes
(
whiche
make
one
degre
)
do
require
70197
,
what
doo
31
and
a
halfe
make
?
After
iuste
multiplication
and
diuision
,
as
that
rule
dooth
importe
,
I
fynde
the
whole
diameter
of
the
sonne
to
containe
in
myles
,
36853
:
where
as
the
earth
(
as
before
is
noted
)
dooth
containe
in
his
diameter
but
6872
myles
.
So
that
therby
it
appeareth
,
that
the
sonne
is
more
then
5
tymes
so
broade
as
the
earthe
is
ouerthwart
.
Master
.
That
is
well
limited
.
for
els
if
the
flat
of
the
greatest
circle
of
the
whole
earthe
myght
appeare
vnto
vs
,
as
the
flatte
forme
of
the
sonne
doth
,
the
flatte
forme
of
the
sonne
ought
to
be
accompted
about
29
times
so
great
as
the
earth
is
,
in
lyke
forme
.
And
the
whole
globe
of
the
sonne
muste
needes
be
about
155
tymes
so
greate
as
the
earth
in
his
whole
Globe
.
Scholar
.
I
perceaue
that
dooth
followe
by
twoo
rules
of
Geometrye
,
wherof
the
firste
is
this
.
In
what
proportion
so
euer
the
sides
of
any
twoo
squares
be
,
those
squares
are
in
the
square
of
that
proportion
:
so
that
if
the
sides
be
as
2
to
1
,
the
squares
are
as
4
to
1
:
and
if
the
sydes
be
as
3
to
1
,
the
squares
are
as
9
to
1.
&c.
The
seconde
rule
is
this
:
In
what
rate
so
euer
the
sydes
of
any
cubes
be
,
the
cubes
do
beare
the
lyke
rate
cubikly
multiplied
.
as
if
the
sydes
be
as
two
to
one
,
the
cubes
are
as
8
to
1
:
and
if
the
sydes
be
as
thre
to
one
,
the
cubes
are
as
27
to
1.
&c.
Master
.
This
is
well
applied
of
you
,
that
you
can
frame
your
common
rules
in
Geometry
to
suche
speciall
matters
.
And
nowe
may
you
proue
the
lyke
in
the
moone
.
Sc.
You
say
,
that
the
circumference
of
the
sphere
of
the
mone
is
724604
myles
,
and
4
/
7
:
then
diuidyng
it
by
360
,
ther
wil
amount
the
quantitie
of
one
degree
:
whiche
yeldeth
in
this
rate
2012
myles
and
71
/
90
:
but
accomptinge
the
breadth
of
the
moone
31
minutes
and
a
halfe
,
the
myles
that
answere
vnto
it
,
are
but
1057
:
wherby
it
foloweth
,
that
the
diameter
of
the
earthe
being
6872
,
is
6
times
and
a
halfe
greater
then
the
diameter
of
the
moone
.
And
therfore
the
flatte
of
the
earthe
in
his
greatest
circle
,
is
aboue
42
tymes
so
greate
,
as
the
like
flatte
forme
in
the
moone
:
and
the
whole
globe
of
the
earth
is
273
tymes
so
greate
,
as
the
whole
globe
of
the
moone
.
Master
.
In
this
accompt
you
take
the
innermost
circumference
of
the
sphere
of
the
moone
,
and
in
the
like
accompt
manye
other
take
the
vttermoste
circumference
,
but
it
appeareth
more
reasonable
to
take
the
myddle
distaunce
beetweene
them
bothe
,
whiche
is
1055302.
(
as
here
by
example
dooth
appeare
)
and
in
that
place
of
distaunce
to
take
the
rate
of
hir
diameter
.
Scholar
.
So
it
seemeth
most
indifferent
reason
.
And
then
the
measure
of
one
degree
wyll
be
2931
71
/
180
and
of
that
there
will
aunswere
to
the
diameter
of
the
mone
(
being
accompted
31
minutes
and
a
halfe
)
1539
myles
.
Nowe
if
I
diuide
the
diameter
of
the
earthe
(
whiche
is
6872
)
by
it
,
there
wyll
be
in
the
quotient
4
and
a
halfe
almost
:
so
wyll
it
appeare
that
the
diameter
of
the
earth
is
4
times
and
a
halfe
almoste
so
longe
as
the
diameter
of
the
moone
:
and
the
flat
of
the
earth
20
times
so
large
as
the
flat
of
the
moone
.
And
the
whole
earthe
nynetye
tymes
so
greate
as
the
globe
of
the
Moone
.
Master
.
Yet
according
to
the
common
accompt
,
the
earth
is
but
39
tymes
so
muche
as
the
moone
:
but
hereof
and
of
many
other
thynges
that
seeme
aboue
the
reache
of
mannes
witte
,
I
will
an
other
time
instructe
you
farther
.
for
it
is
no
meete
mater
for
an
introduction
.
And
thys
is
broughte
for
exaumples
sake
onlye
,
that
you
myghte
vnderstande
the
ordre
of
suche
sorte
of
woorkynge
,
and
therby
learne
to
trye
your
authors
sayinges
.
But
nowe
it
is
tyme
to
proceede
to
other
matters
,
and
to
declare
the
true
place
of
the
earthe
,
and
to
prooue
that
it
standeth
in
the
myddle
of
the
worlde
,
whiche
thinge
althoughe
it
may
sufficientlye
bee
gathered
by
that
that
is
written
beefore
,
That
the
earthe
is
in
the
middle
of
the
worlde
.
yet
I
wyll
declare
certayne
inuincible
reasons
for
confutation
of
them
that
mysseplace
it
.
And
to
begyn
with
all
,
there
can
be
but
three
dyuersities
of
places
in
generall
,
without
the
centre
of
the
worlde
:
for
other
it
muste
bee
beside
the
Axetree
of
the
worlde
,
and
yet
equallye
distaunte
from
bothe
the
Poles
,
or
els
it
muste
bee
on
the
Axe
tree
of
the
worlde
,
and
yet
nearer
to
one
Pole
then
to
an
other
:
or
thyrdlye
it
muste
bee
beside
the
Axe
tree
of
the
worlde
,
and
also
nearer
to
the
one
Pole
then
to
the
other
.
beside
these
three
varieties
there
is
lefte
but
one
more
(
whyche
is
the
true
placynge
of
it
)
and
that
is
to
be
on
the
Axe
tree
of
the
worlde
,
equallye
distaunte
from
bothe
the
Poles
:
wherefore
if
the
firste
three
opinions
bee
reproued
as
false
,
this
fourthe
must
needes
remaine
as
onlye
true
.
And
nowe
for
the
confutynge
of
the
three
fyrste
opinions
I
will
vse
Ptolemyes
argumentes
,
augmentyng
them
with
a
larger
explication
.
The
confutation
of
the
first
opinion
If
the
earthe
were
out
of
the
centre
of
the
worlde
,
and
yet
stode
in
the
middle
betweene
bothe
the
Poles
,
then
shoulde
not
the
Horizonte
cutte
the
skye
into
twoo
equall
halues
.
And
thereof
woulde
followe
,
that
in
the
righte
sphere
the
daye
and
the
nyghte
shoulde
not
be
of
one
lengthe
.
Geometric diagram.
As
for
example
:
If
you
would
imagine
the
earthe
to
stand
as
L
dooth
in
this
figure
,
then
woulde
the
Horizont
be
the
righte
line
E
L
F
,
and
so
the
parte
that
is
vnder
the
Horizont
is
greater
then
the
other
parte
of
the
skye
aboue
the
Horizonte
:
wherefore
in
the
ryghte
Sphere
the
nyghte
muste
needes
alwaies
be
longer
then
the
daye
.
but
if
you
would
imagine
the
earth
to
stand
where
M
,
is
set
vnderneth
K
,
which
is
the
verye
centre
of
the
worlde
,
then
woulde
that
Horizonte
G
M
H
,
whiche
answereth
to
that
centre
,
be
vnder
the
true
horizont
of
the
centre
of
the
world
,
that
is
the
right
line
A
K
C.
And
so
shoulde
the
nighte
alwaies
in
the
righte
sphere
be
shorter
then
the
daye
,
bicause
the
greater
parte
of
the
skye
is
aboue
the
Horizonte
,
and
the
lesser
parte
vnder
it
.
And
by
the
like
reasons
in
al
other
bowing
sphers
ther
shoulde
bee
no
equalitye
betweene
the
daye
and
the
nyght
:
and
if
there
were
any
,
it
should
not
be
in
that
time
when
the
sonne
were
in
the
iuste
middle
betweene
the
twoo
Tropikes
,
(
that
is
vnder
the
Equinoctiall
line
)
bicause
that
the
Equinoctiall
line
is
not
equally
parted
by
the
Horizont
,
but
the
greater
parte
is
aboue
the
Horizont
,
after
the
one
supposition
,
and
after
the
other
supposition
it
is
vnder
the
Horizont
of
the
earthe
.
Scholar
.
This
I
doo
vnderstande
well
,
accomptinge
the
circle
A
B
C
D
,
to
represent
the
Equinoctiall
lyne
.
Master
.
And
farther
you
may
perceaue
(
as
all
men
,
in
all
ages
,
and
in
all
nations
do
confesse
)
that
the
increase
of
the
dayes
from
the
shortest
to
the
meane
,
and
from
the
meane
daye
to
the
longest
are
not
onlye
agreeable
betweene
them selues
,
but
are
lyke
also
exactlye
to
the
decrease
of
the
daies
from
the
longest
to
the
meane
,
and
from
the
meane
to
the
shorteste
.
whiche
thynge
coulde
not
bee
,
excepte
that
the
myddle
circle
betweene
the
twoo
Tropikes
(
whiche
is
ryghtlye
called
the
Equinoctiall
circle
)
were
equallye
dyuided
by
the
horizonte
into
twoo
iuste
halues
.
And
farther
:
seeyng
there
can
be
no
position
of
suche
obliquity
(
except
it
be
righte
vnder
the
Pole
)
but
some
one
circle
of
the
Sonnes
course
must
be
diuided
equallye
into
two
partes
by
the
Horizonte
,
so
that
when
the
Sonne
were
in
that
circle
,
the
daye
woulde
be
equall
with
the
nyght
:
which
thing
as
all
nations
confesse
,
happeneth
at
one
tyme
to
all
menne
,
and
that
is
when
the
Sonne
is
in
the
beginning
of
Aries
or
Libra
,
precisely
vnder
the
Equinoctiall
lyne
:
wherefore
not
onlye
that
circle
dooth
ryghtly
agree
with
hys
name
,
but
also
it
foloweth
that
the
same
Equinoctiall
line
is
equallye
parted
into
twoo
iuste
partes
by
the
Horizonte
.
And
therefore
the
earthe
muste
needes
bee
iudged
to
bee
in
the
centre
of
the
worlde
.
Farthermore
,
if
the
earthe
were
supposed
to
bee
toward
the
easte
or
toward
the
weste
,
An
other
confutation
of
that
firste
opinion
.
from
the
myddle
of
the
world
,
(
as
in
this
figure
it
is
set
toward
the
easte
,
which
is
limited
by
A
)
thē
as
the
space
toward
the
one
side
is
shorter
thē
the
space
to
the
other
side
from
the
earth
,
so
the
stars
woulde
seeme
bigger
in
that
nearer
part
,
and
lesser
in
that
farther
parte
.
Geometric diagram.
Sc.
Which
thing
is
before
reproued
,
and
by
daily
experience
may
be
confuted
.
Master
.
Therfore
can
not
it
be
a
true
opinion
,
that
inferreth
so
false
a
conclusion
.
And
yet
there
woulde
follow
of
it
more
absurditie
:
that
from
the
morning
vntill
noone
should
bee
shorter
tyme
,
or
els
longer
then
from
noone
vntill
nyght
.
Scholar
.
That
must
needes
folow
also
,
seeyng
that
noone
is
that
time
of
the
daye
,
when
the
sonne
is
in
the
circle
which
goeth
right
ouer
our
headdes
from
south
to
north
,
whiche
here
in
this
figure
is
represented
by
the
right
line
B
E
D
,
as
I
gather
by
your
former
doctrine
.
Master
.
An
abbridged
argument
of
all
the
premisses
.
You
gesse
well
.
and
by
the
contrarye
of
all
these
you
may
conclude
thus
:
that
seyng
the
tyme
before
noone
is
equalle
to
the
tyme
after
noone
,
and
the
starres
appeare
nother
bygger
nor
lesser
in
the
weste
,
then
they
doo
in
the
easte
:
And
that
when
the
sonne
is
in
the
Equinoctiall
lyne
,
the
dayes
are
equall
to
the
nightes
,
it
foloweth
certainlye
,
that
thee
earthe
canne
bee
no
wayes
out
of
the
Axe
tree
of
the
worlde
.
And
now
for
the
seconde
opinion
I
reason
thus
.
Against
the
second
opinion
.
If
the
earthe
were
on
the
Axe
tree
of
the
worlde
nygher
to
the
one
Pole
then
to
the
other
,
then
woulde
the
Horizonte
onlye
in
the
righte
Sphere
dyuide
the
skye
into
twoo
equall
partes
,
and
in
no
forme
of
bowing
sphere
,
as
by
this
figure
you
may
gather
,
wher
E
standeth
for
the
earth
,
and
A
E
C
for
the
right
horizont
.
B
E
D
and
F
E
G
for
two
oblique
horizontes
,
in
2
seuerall
bowing
sphers
:
and
K
limiteth
the
centre
of
the
worlde
.
Geometric diagram.
Scholar
.
Here
I
see
manifestly
that
only
the
right
horizont
dooth
diuide
the
greater
circle
(
whiche
is
sette
for
the
skie
)
into
2
equall
partes
,
and
none
other
:
wherby
it
would
folowe
,
that
wee
whiche
dwell
52
degrees
northwarde
from
the
Equinoctiall
lyne
,
shoulde
see
muche
lesse
then
halfe
the
skye
:
but
that
is
false
,
as
it
hath
beene
often
tymes
proued
,
wherfore
I
perceaue
that
opinion
can
not
be
true
.
Master
.
An
other
argumente
against
the
second
opinion
.
Yet
an
other
argumente
againste
that
opinion
,
may
this
be
.
Yf
the
earthe
were
nygher
to
the
one
Pole
then
to
the
other
,
when
the
Sonne
is
in
the
iuste
easte
,
the
shaddowes
of
anye
thinges
in
earthe
,
woulde
not
runne
full
weste
:
but
all
shaddowes
in
earthe
runne
full
weste
,
when
the
Sonne
is
iuste
easte
:
(
and
contrarye
wayes
)
therefore
canne
not
the
earthe
bee
nygher
to
one
Pole
,
then
to
the
other
.
Scholar
.
This
argumente
is
good
,
and
the
minor
is
well
knowen
to
euerye
sensible
man
:
so
is
there
no
doubte
but
of
the
maior
.
Master
.
For
the
proofe
of
it
,
I
sette
this
figure
.
Wher
the
great
circle
A
B
C
D
betokeneth
the
Horizont
,
and
the
lesser
circle
E
F
G
H
,
standeth
for
the
earthe
.
The
centre
of
the
worlde
is
E
:
the
east
is
D
:
and
the
weste
is
B
:
the
southe
is
A
:
and
the
northe
is
C.
In
the
earthe
the
lyne
F
G
,
standeth
as
a
Parallele
,
wyth
the
ryghte
Geometric diagram.
line
BED
,
and
the
righte
line
DH
runneth
crosse
thē
bothe
,
and
maketh
an
angle
on
the
centre
of
the
earth
,
equal
to
the
angle
by
D
:
whose
largenes
is
agreable
to
the
imagined
distance
of
the
centre
of
the
earthe
from
the
centre
of
the
world
.
wherfore
the
greater
that
that
distance
is
,
the
larger
is
the
angle
of
that
declination
,
and
the
lesser
distaunce
,
causeth
a
lesser
angle
:
but
yet
if
the
distaunce
be
any
thing
,
then
will
that
angle
of
declination
be
notable
inoughe
.
Scholar
.
The
reste
is
easye
to
considre
:
I
meane
that
all
shaddowes
runne
in
a
right
line
from
the
lyght
bodye
,
that
causeth
that
shadow
:
so
that
the
sonne
being
in
D
,
which
is
the
iuste
easte
,
wolde
cast
the
shaddowes
in
the
earthe
,
not
to
F
(
which
is
the
west
in
the
earth
)
but
to
H
,
which
is
almoste
northwest
:
and
therefore
is
your
maior
duely
proued
,
and
the
seconde
opinion
fully
confuted
:
but
how
may
the
thirde
opinion
be
answered
?
Master
.
Against
the
thirde
opinion
.
The
thirde
opinion
is
,
that
the
earthe
standeth
out
of
the
axe
tree
of
the
worlde
,
and
also
nearer
to
the
one
pole
then
to
the
other
:
so
doth
it
containe
both
the
other
opinions
:
wherfore
seyng
they
both
are
reproued
,
this
third
muste
needes
see
me
falser
then
ony
of
them
bothe
,
bycause
it
includeth
all
the
vntruthe
of
them
bothe
.
And
therfore
to
conclude
with
Ptolemye
,
A
confirmation
.
the
increase
and
decrease
of
dayes
coulde
neuer
be
so
ratable
and
iustly
proportioned
as
they
be
,
if
the
earthe
stoode
any
where
els
,
then
in
the
very
centre
of
the
worlde
.
And
farther
more
the
eclipses
of
the
moone
shuld
not
happen
,
An
other
reason
.
(
as
now
they
do
)
at
the
precise
hour
of
ful
opposition
,
if
the
earthe
were
not
in
the
very
centre
of
the
worlde
:
for
considering
that
all
the
thre
bodies
of
the
Son
,
the
moone
,
and
the
earthe
muste
needes
be
in
one
right
line
(
as
in
the
doctrine
of
those
eclipses
it
is
taught
)
there
is
no
place
in
the
worlde
,
where
the
earth
may
stand
in
that
right
line
common
to
all
suche
eclipses
,
but
only
the
centre
of
the
worlde
:
Geometric diagram.
as
for
examples
sake
I
haue
noted
4
seuerall
eclipses
of
the
moone
:
the
first
was
in
the
year
of
Christes
incarnation
1551
,
the
20
day
of
Februarye
,
when
the
Sonne
was
aboute
the
12
degree
of
Pisces
,
and
the
moone
aboute
the
12
degre
of
Virgo
.
The
seconde
eclipse
was
in
the
yeare
of
1553
,
the
sonne
being
in
the
eleuenth
degree
of
Leo
,
and
the
moone
in
the
eleuenth
degree
of
Aquarius
:
The
thirde
eclipse
happened
on
the
fifte
daye
of
Iune
,
1555
,
the
sonne
being
in
the
23
degre
of
Gemini
,
and
the
mone
in
the
23
of
Sagittary
.
The
fourth
eclipse
,
shal
be
this
yeare
1556
,
the
17
daye
of
Nouembre
,
at
whiche
time
the
sonne
shal
be
in
the
fifte
degre
of
Sagittary
,
and
the
moone
in
the
fifte
degree
of
Gemini
.
Nowe
if
you
lyste
to
take
more
examples
,
for
farther
tryall
you
maye
so
doo
.
yet
two
seuerall
eclipses
serue
as
well
for
this
proofe
as
10000.
And
then
drawing
lines
for
eche
eclipse
from
the
place
of
the
sonne
to
the
place
of
the
moone
,
all
those
lines
muste
needes
passe
by
the
earthe
,
and
there
is
none
other
pointe
,
whereby
they
all
(
or
any
two
of
them
)
can
passe
,
but
onlye
the
centre
of
the
Zodiak
,
(
which
is
the
centre
of
the
world
)
therefore
muste
that
centre
of
necessitie
bee
accompted
the
place
of
the
earthe
.
And
this
may
suffice
for
this
time
touchinge
the
earthe
and
his
accidentes
,
principallye
appertaininge
to
Astronomye
:
for
althoughe
manye
other
thinges
are
to
bee
considered
in
it
,
they
appertaine
rather
to
philosophers
or
Cosmographers
,
then
to
Astronomers
,
and
namely
in
the
doctrine
of
the
principles
.
Whether
the
earthe
moue
or
not
.
As
touching
the
distinction
of
the
zones
,
I
haue
sayde
somwhat
before
,
&
somwhat
more
wil
I
say
anon
.
But
as
for
the
quietnes
of
the
earth
I
neede
not
to
spende
anye
tyme
in
proouing
of
it
,
syth
that
opinion
is
so
firmelye
fixed
in
moste
mennes
headdes
,
that
they
accompt
it
mere
madnes
to
bring
the
question
in
doubt
.
And
therfore
it
is
as
muche
follye
to
trauaile
to
proue
that
which
no
man
denieth
,
as
it
were
with
great
study
to
diswade
that
thinge
,
which
no
man
doth
couette
,
nother
any
manne
alloweth
:
or
to
blame
that
which
no
manne
praiseth
,
nother
anye
manne
lyketh
.
Schol
.
Yet
sometime
it
chaunceth
,
that
the
opinion
most
generally
receaued
,
is
not
moste
true
.
Master
.
And
so
doo
some
men
iudge
of
this
matter
,
for
not
only
Eraclides
Ponticus
,
a
great
Philosopher
,
and
two
great
clerkes
of
Pythagoras
schole
,
Philolaus
and
Ecphantus
,
were
of
the
contrary
opinion
,
but
also
Nicias
Syracusius
,
and
Aristarchus
Samius
,
seeme
with
strong
arguments
to
approue
it
:
but
the
reasons
are
to
difficulte
for
this
firste
Introduction
,
&
therfore
I
wil
omit
them
till
an
other
time
.
And
so
will
I
do
the
reasons
that
Ptolemy
,
Theon
&
others
doo
alleage
,
to
prooue
the
earthe
to
bee
without
motion
:
and
the
rather
,
bycause
those
reasons
doo
not
proceede
so
demonstrablye
,
but
they
may
be
answered
fully
,
of
him
that
holdeth
the
contrarye
.
I
meane
,
concerning
circularre
motion
:
marye
direct
motion
out
of
the
centre
of
the
world
,
seemeth
more
easy
to
be
confuted
,
and
that
by
the
same
reasons
,
whiche
were
before
alleaged
for
prouing
the
earthe
to
be
in
the
middle
and
centre
of
the
worlde
.
Scholar
.
I
perceaue
it
well
:
for
as
if
the
earthe
were
alwayes
oute
of
the
centre
of
the
worlde
,
those
former
absurdities
woulde
at
all
tymes
appeare
:
so
if
at
anye
tyme
the
earthe
shoulde
mooue
oute
of
his
place
,
those
inconueniences
would
then
appeare
.
Master
.
That
is
trulye
to
be
gathered
:
howe
bee
it
,
Copernicus
a
man
of
greate
learninge
,
of
muche
experience
,
and
of
wondrefull
diligence
in
obseruation
,
hathe
renewed
the
opinion
of
Aristarchus
Samius
,
and
affirmeth
that
the
earthe
not
only
moueth
circularlye
about
his
owne
centre
,
but
also
may
be
,
yea
and
is
,
continually
out
of
the
precise
centre
of
the
world
38
hundreth
thousand
miles
:
but
bicause
the
vnderstanding
of
that
controuersy
dependeth
of
profounder
knowledg
then
in
this
Introduction
may
be
vttered
conueniently
,
I
will
let
it
passe
tyll
some
other
time
.
Scholar
.
Nay
syr
in
good
faith
,
I
desire
not
to
heare
such
vaine
phantasie
,
so
farre
againste
common
reason
,
and
repugnante
to
the
consente
of
all
the
learned
multitude
of
Wryters
,
and
therefore
lette
it
passe
for
euer
,
and
a
daye
longer
.
Master
.
You
are
to
yonge
to
be
a
good
iudge
in
so
great
a
matter
:
it
passeth
farre
your
learninge
,
and
theirs
also
that
are
muche
better
learned
then
you
,
to
improue
his
supposition
by
good
argumentes
,
and
therefore
you
were
best
to
condemne
no
thinge
that
you
do
not
well
vnderstand
:
but
an
other
time
,
as
I
sayd
,
I
will
so
declare
his
supposition
,
that
you
shall
not
only
wonder
to
hear
it
,
but
also
peraduenture
be
as
earnest
then
to
credite
it
,
as
you
are
now
to
condemne
it
.
in
the
meane
ceason
let
vs
proceede
forwarde
in
our
former
ordre
,
wherin
by
ordre
of
your
table
I
should
speake
of
the
circles
in
heauen
,
both
of
their
numbre
,
how
many
they
be
,
and
also
of
their
quantities
,
how
great
they
are
,
Of
the
circles
in
the
skye
.
which
is
to
be
vnderstand
in
comparison
to
the
Equinoctiall
,
or
some
other
greate
circle
.
Then
of
their
ordre
,
and
their
distance
a
sonder
:
and
likewaies
what
is
their
offices
,
whervnto
they
serue
.
of
all
whiche
thinges
,
although
I
haue
all
ready
sayde
inoughe
for
so
briefe
an
Introduction
,
yet
bicause
in
theyr
numbre
there
may
be
some
disagreement
,
and
in
their
quantities
.
distances
and
ordre
there
maye
bee
some
varietie
,
at
the
leaste
in
diuers
places
,
therefore
I
will
speake
a
little
of
them
againe
.
Equinoctial
First
for
the
equinoctiall
,
there
is
but
one
thoroughe
all
the
world
,
and
he
is
equally
distaunt
from
eche
Pole
,
and
therefore
is
called
the
Girdle
of
the
skye
:
hys
office
was
declared
beefore
to
bee
the
lymite
of
the
myddle
of
the
world
,
in
whiche
the
Son
maketh
the
dayes
equall
to
the
nyghtes
.
Also
hee
declareth
the
true
easte
and
west
,
and
is
not
onlye
the
common
measure
wherby
all
other
circles
are
iudged
in
quantitye
,
but
also
it
is
the
true
measure
of
motions
celestiall
,
and
the
very
rule
to
iudge
all
ascentions
by
,
the
tropiks
as
hereafter
more
largely
shall
appeare
.
Nexte
vnto
this
circle
are
there
2
Tropike
circles
,
one
on
eche
side
of
it
,
depiction of a quadrant.
whose
distaunce
a
sonder
may
well
be
marked
by
a
quadrant
set
so
in
place
conuenient
,
that
it
may
stand
iust
plumbe
with
the
flatte
of
the
horizont
,
and
be
tourned
full
southe
.
Then
obserue
many
daies
aboute
the
middle
of
Iune
the
hyghest
point
that
the
sonne
wyll
ascend
vnto
,
and
shine
duely
thoroughe
those
two
sightes
in
the
ruler
,
mouinge
it
hygher
or
lower
,
as
occasion
serueth
,
tyll
it
stande
exactely
pointinge
the
heyghte
of
the
Sonne
at
no
one
beynge
at
the
highest
.
The
lyke
obseruation
shall
you
make
diuers
dayes
before
,
at
and
after
the
myddle
of
Decembre
,
tyll
that
you
be
assured
of
the
iuste
heighte
at
noone
of
the
sonne
,
beynge
at
the
lowest
then
toward
the
southe
.
The
pointes
of
these
two
obseruations
well
marked
in
the
edge
of
the
quadrante
are
the
true
places
of
the
two
Tropikes
:
and
the
distaunce
of
those
two
markes
a
sonder
by
numbre
of
degrees
,
is
the
very
true
distaunce
of
the
twoo
Tropikes
.
In
the
iuste
myddle
between
these
twoo
tropikes
is
the
place
of
the
Equinoctiall
circle
.
Example
.
With
vs
,
where
the
pole
is
52
degrees
highe
,
the
winter
tropike
wyll
be
14
degrees
and
a
halfe
aboue
the
Horizont
.
the
sommer
tropike
61
and
a
halfe
.
and
the
Equinoctiall
iuste
38
degrees
in
heighte
.
The
gretest
declination
of
the
sonne
And
the
numbre
of
degrees
that
are
betweene
this
Equinoctiall
and
any
one
of
the
tropiks
is
named
the
Greatest
declination
of
the
sonne
,
whiche
in
our
time
is
about
23
degrees
and
28
minutes
.
The
other
pointes
of
declination
of
the
degrees
in
the
ecliptike
line
from
the
equinoctial
circle
,
bicause
they
be
many
in
numbre
and
diuerse
in
vse
,
I
thinke
it
good
to
expresse
in
a
table
which
hereafter
shall
serue
you
for
sundry
vses
.
Scholar
.
The
like
table
is
in
Orontius
.
Master
.
Not
euen
the
lyke
,
as
by
conferring
you
maye
perceaue
:
but
for
the
vse
of
it
,
take
what
degree
you
list
of
anye
Signe
,
and
by
this
table
you
maye
knowe
his
declination
from
the
Equinoctiall
circle
.
The
Signes
are
written
partelye
on
the
headde
of
the
table
,
and
partelye
on
the
foote
of
the
same
.
The
degrees
in
the
fyrste
THE
TABLE
OF
DECLINATION
PARTICVLARLY
FOR
EVERY
DEGREE
of
the
Ecliptike
lyne
,
and
so
for
the
Sonne
.
|
Aries
,
Libra
,
|
Difference
.
|
Taurus
,
Scorpius
.
|
Difference
.
|
Gemini
,
Sagittarius
|
Difference
.
|
|
deg
.
|
degr
.
|
min.
|
min.
|
deg
.
|
min.
|
|
degr
.
|
min.
|
|
deg
.
|
1
|
0
|
24
|
24
|
11
|
50
|
21
|
20
|
23
|
12
|
29
|
2
|
0
|
48
|
12
|
11
|
20
|
35
|
28
|
3
|
1
|
12
|
|
12
|
32
|
20
|
20
|
47
|
11
|
27
|
4
|
1
|
36.
|
|
12
|
52
|
20
|
58
|
26
|
5
|
1
|
59
|
|
13
|
12
|
|
21
|
9
|
10
|
25
|
6
|
2
|
23
|
|
13
|
32
|
|
21
|
20
|
24
|
7
|
2
|
47
|
|
13
|
52
|
19
|
21
|
30
|
9
|
23
|
8
|
3
|
11
|
|
14
|
12
|
21
|
40
|
22
|
9
|
3
|
34
|
|
14
|
31
|
|
21
|
49
|
|
21
|
10
|
3
|
58
|
|
14
|
50
|
|
21
|
58
|
|
20
|
11
|
4
|
21
|
|
15
|
9
|
18
|
22
|
7
|
8
|
19
|
12
|
4
|
45
|
|
15
|
27
|
22
|
15
|
18
|
13
|
5
|
8
|
23
|
15
|
45
|
|
22
|
23
|
7
|
17
|
14
|
5
|
32
|
16
|
3
|
|
22
|
30
|
16
|
15
|
5
|
55
|
|
16
|
21
|
17
|
22
|
37
|
6
|
15
|
16
|
6
|
18
|
|
16
|
39
|
22
|
44
|
14
|
17
|
6
|
41
|
|
16
|
56
|
|
22
|
50
|
5
|
13
|
18
|
7
|
4
|
|
17
|
13
|
|
22
|
55
|
12
|
19
|
7
|
27
|
22
|
17
|
29
|
16
|
23
|
1
|
4
|
11
|
20
|
7
|
50
|
17
|
46
|
23
|
5
|
10
|
21
|
8
|
12
|
|
18
|
2
|
|
23
|
10
|
|
9
|
22
|
8
|
35
|
|
18
|
17
|
|
23
|
13
|
|
8
|
23
|
8
|
57
|
|
18
|
33
|
15
|
23
|
17
|
3
|
7
|
24
|
9
|
19
|
|
18
|
48
|
23
|
20
|
2
|
6
|
25
|
9
|
41
|
|
19
|
2
|
|
23
|
22
|
|
5
|
26
|
10
|
3
|
|
19
|
17
|
|
23
|
24
|
|
4
|
27
|
10
|
25
|
21
|
19
|
31
|
|
23
|
26
|
1
|
3
|
28
|
10
|
47
|
19
|
44
|
|
23
|
27
|
2
|
29
|
11
|
8
|
|
19
|
58
|
|
23
|
28
|
0
|
1
|
30
|
11
|
29
|
|
20
|
10
|
|
23
|
28
|
0
|
degr
.
|
degr
.
|
min.
|
|
degr
.
|
min.
|
|
degr
.
|
min.
|
|
deg
.
|
|
Virgo
.
Pisces
.
|
Difference
.
|
Leo
.
Aquarius
.
|
Difference
.
|
Cancer
.
Capricorn
.
|
Difference
.
|
|
columpne
doo
serue
for
the
signes
that
bee
on
the
heade
of
the
table
,
and
the
degrees
in
the
laste
columpne
doo
serue
for
the
signes
in
the
foote
of
the
table
,
and
the
common
angle
against
the
signe
:
and
the
degree
that
you
seeke
for
,
doth
containe
the
degrees
and
mynutes
of
the
declination
due
to
it
.
Scholar
.
I
perceaue
it
well
:
if
I
would
knowe
howe
muche
the
tenth
degree
of
Leo
doth
decline
from
the
equinoctiall
,
I
must
looke
in
the
columpn
ouer
Leo
right
against
the
numbre
oftenne
in
the
laste
columpne
,
where
I
fynd
17.46
.
Master
.
That
is
17
degrees
,
and
46
minutes
,
which
is
the
declination
of
the
10.
degree
of
Leo
from
the
equinoctiall
circle
.
Schollar
.
I
must
alwaies
vnderstande
that
60
minutes
do
make
a
degree
:
so
these
46
minutes
are
¾
of
a
degree
and
1
/
60
more
.
But
what
is
the
vse
of
this
table
?
Master
.
That
shall
you
knowe
in
the
next
treatise
.
in
the
meane
ceason
to
procede
with
the
parallele
circles
:
there
foloweth
next
,
the
Arctike
and
Antarctike
circles
,
The
Artik
and
Antartik
circles
whiche
are
in
numbre
two
,
and
there
office
is
to
enclose
those
starres
,
whiche
euer
appeare
aboue
our
horizont
,
or
neuer
appeare
aboue
the
same
,
as
before
is
declared
:
but
bycause
euerye
seueralle
Climate
hathe
those
cyrcles
disagreeynge
frome
other
Climates
,
therefore
theyr
distaunce
frome
the
other
cyrcles
Paralleles
canne
not
bee
certaine
,
(
but
for
one
region
certaine
)
nother
yet
theyr
quantities
,
nother
theyr
ordre
:
for
where
the
eleuation
of
the
pole
is
lesse
then
66
degrees
and
a
halfe
,
there
are
those
circles
lesser
then
the
tropikes
,
and
are
in
ordre
betwene
them
and
the
Poles
,
beinge
alwaies
distaunt
from
the
Pole
iust
so
many
degrees
as
the
Pole
is
in
height
aboue
the
Horizont
in
that
region
.
Scholar
.
It
canne
not
bee
other
waies
.
And
therefore
it
foloweth
,
that
where
the
pole
is
more
then
66
degrees
and
a
halfe
in
heighte
,
there
the
Tropike
is
aboue
the
Horizonte
,
as
at
Wardehouse
you
declared
it
to
be
:
and
therefore
in
that
climate
the
Arctik
circle
is
greater
then
the
Tropike
of
Cancer
.
Master
.
Of
the
fiuc
zones
against
the
Greekes
.
Hereby
appeareth
the
ouersighte
of
moste
parte
of
the
Greekes
in
limiting
the
Zones
:
for
they
appoint
the
Arctike
and
Antarctike
circles
for
boundes
of
the
Temperate
Zones
on
the
one
side
,
and
the
Tropikes
on
the
other
side
:
whereof
neither
bounde
can
be
well
admitted
,
after
their
owne
explication
of
the
qualities
of
the
Zones
.
for
if
the
temperate
Zones
shall
be
called
those
Zones
that
be
inhabited
,
as
they
do
so
name
them
,
then
bycause
there
was
knowen
inhabitauntes
innumerable
besouthe
the
tropike
of
Cancer
,
it
muste
needes
followe
,
that
the
tropike
canne
be
no
bounde
of
the
temperate
Zone
:
but
yet
otherwaies
accomptinge
the
distinction
of
the
Zones
,
not
by
that
they
are
inhabited
or
vninhabited
,
but
by
the
varietie
of
the
motion
of
the
sonne
in
respect
to
them
,
and
by
other
accidents
of
shaddowes
,
there
maye
be
good
reason
to
make
the
tropikes
boundes
of
the
temperat
zones
:
mary
there
is
not
the
like
reason
for
the
Arctike
and
Antarctike
circles
.
for
confutation
therfore
of
that
opinion
,
I
make
this
argument
.
An
argument
in
Ferio
.
No
vncertaine
and
variable
boundes
can
limite
anye
certaine
place
:
the
temperate
Zones
are
places
certaine
,
and
the
Arctike
circle
with
the
Antarctike
are
chaungable
,
and
vncertain
limites
,
Therfore
can
not
they
be
the
boundes
of
the
temperate
Zones
.
Scholar
.
This
is
a
good
argument
,
made
in
Ferio
,
the
fowerth
moode
of
the
fyrste
figure
.
And
the
maior
is
moste
true
,
sith
nothing
can
more
disagree
,
then
certain
and
vncertain
,
stable
&
vnstable
,
being
contraries
togither
.
The
minor
hathe
2
partes
in
it
,
which
both
seeme
as
true
:
for
as
long
as
the
Sonne
keepeth
one
yearely
course
,
so
longe
the
regions
muste
remaine
as
they
were
,
and
that
is
for
euer
,
other
styll
temperate
,
other
styll
vntemperate
.
And
so
is
that
part
of
the
minor
true
.
The
other
part
for
the
inconstancy
&
chan
gablenes
of
the
circles
arctik
&
antarctik
,
must
needs
be
true
by
their
definitions
,
approued
of
the
same
Greekes
:
for
euery
region
hath
a
seuerall
Actike
circle
.
Wherfore
I
meruaile
muche
that
the
Greekes
beynge
so
wise
men
,
and
so
greately
learned
,
shuld
be
so
muche
ouerseen
and
so
foroly
deceaued
:
but
peraduenture
ther
are
but
few
of
that
opinion
,
and
such
as
were
leaste
learned
.
Master
.
Parmenides
,
Aristotle
,
Cleomedes
and
Proclus
may
not
be
accompted
vnlearned
,
and
yet
they
with
manye
other
haue
written
that
as
truth
.
But
hereby
may
you
perceaue
what
folly
it
is
,
when
men
receaue
any
doctrine
as
true
,
and
do
not
well
weigh
it
,
but
credite
the
autority
of
the
first
teacher
.
So
it
appeareth
in
this
matter
,
that
bicause
Parmenides
,
whiche
was
a
great
Philosopher
,
had
fyrst
taught
that
whiche
was
a
great
Philosopher
,
had
fyrst
taught
that
distinction
of
the
zones
,
all
the
reste
did
folowe
his
opinion
as
a
plausible
doctrine
,
without
examination
of
it
,
till
Posidonius
began
to
espye
that
errour
&
to
confute
it
:
as
Strabo
dothe
declare
in
his
second
boke
of
Geographye
,
which
place
in
the
latine
translation
is
so
euell
expressed
,
that
no
sentence
in
it
importeth
anye
sence
:
wherefore
as
well
for
the
commoditie
of
you
as
of
other
,
I
will
sumwhat
amend
that
place
,
wisshinge
them
that
haue
leasure
and
learning
to
help
to
amend
many
other
faultes
of
that
good
booke
and
other
lyke
.
The
Latine
translation
is
this
.
A
place
of
Strabo
amended
.
Ad
Septentriones
,
neque
penes
omnes
existentem
;
neque
eisdem
vbicunque
.
Quisnantemperatas
quae
immutabiles
sunt
diuideret
?
Cum
igitur
non
penes
vniuersos
sit
septentrionales
esse
,
nihil
esset
ad
argumentum
.
si
enim
penes
habitatores
temperatae
omnes
,
ad
quos
dicitur
,
so
los
temperata
?
Quod
autem
non
vbique
eodem
modo
,
sed
mutari
,
bene
comprehensum
est
.
ipse
autem
in
zonas
partiens
,
quinque
ad
coelestia
quidem
vtiles
esse
asserit
.
Ex
his
duas
circumstantes
subter
polos
vsque
ad
eas
quae
septentrionales
habent
tropicos
,
diuersarum
vmbrarum
esse
ab
alijs
duabus
,
quae
deinceps
sunt
vsque
ad
habitantes
sub
Polis
.
Quae
vero
inter
Tropicos
est
,
vtrinque
vmbras
habere
.
Scholar
.
Other
the
matter
is
very
obscure
,
or
els
there
wanteth
lyghte
in
the
declaration
of
it
.
Ma.
Ther
is
litle
sence
in
all
these
words
:
&
that
sence
that
may
be
gathered
of
it
is
very
false
.
And
yet
is
the
greek
boke
both
vn
corrupt
(
except
it
be
in
a
worde
or
two
)
and
full
of
perfect
,
sensible
and
pleasaunt
sentences
.
this
is
it
.
The
prited
booke
hath
〈◇〉
falsely
.
{αβγδ}
,
The
greke
booke
hath
〈◇〉
falselye
.
{αβγδ}
.
Whiche
I
doo
translate
thus
.
Arcticis
verò
circulis
(
vt
qui
nec
apud
omnes
existant
,
nec
ijdem
vibique
perseuerent
)
quis
vnquam
temperatas
Zonas
(
quae
immutabiles
sunt
)
terminaret
?
Caeterum
illud
quod
non
apud
omnes
existant
Arctici
circuli
,
nihil
facit
ad
reprehensionem
.
quum
satis
sit
,
si
modo
sint
apud
omnes
incolas
temperatae
ipsius
zonae
,
ad
quos
solos
temperata
dicitur
.
quod
verò
adiecit
,
non
vbique
seruare
eos
eandem
rationem
,
sed
varie
mutari
,
hoc
quidem
rectè
adsumptum
est
.
Atque
ipse
Po
sidonius
dum
Zonas
destinguit
,
quinque
inquit
vtiles
esse
ad
coelestes
obseruationes
.
quarum
duae
,
quae
Polis
subiacent
,
vmbras
circumfluas
habent
,
vndè
Perifciae
dicuntur
:
ibique
finiuntur
vbi
tropici
ipsi
pro
arcticis
circulis
habentur
.
has
sequuntur
aliae
totidem
,
eò
pertingentes
,
vbi
Tropici
verticibus
incolarum
imminent
,
atque
in
his
vmbrae
me
ridianae
in
vnam
plagam
porriguntur
semper
,
hinc
Heterosciae
vocan
tur
.
quinta
verò
quae
inter
tropicos
iacet
,
in
vtrunque
latus
vicissim
vmbras
mittit
,
atque
Amphiscia
nuncupatur
.
Which
words
may
be
englished
thus
.
What
man
(
saith
Posidonius
)
wold
assigne
the
Arctike
circles
to
be
as
bounds
to
the
tempera
te
zones
?
seing
those
circles
ar
not
in
euery
Climate
:
nother
do
they
continue
vniforme
and
of
one
sort
to
all
cuntries
.
These
wordes
(
saith
Strabo
)
that
they
be
not
in
euery
climate
,
maketh
nothing
to
the
reproofe
.
for
it
is
sufficient
that
they
be
incident
to
all
the
inhabitants
of
the
temperate
zone
,
in
respect
to
whom
alone
that
temperate
zone
beareth
his
name
:
but
those
other
woordes
,
that
they
keepe
not
one
vnforme
manner
in
all
places
,
but
are
diuersly
changed
▪
that
is
well
alleaged
.
Also
Posidonius
him selfe
when
he
distincteth
the
zones
,
doth
say
,
that
fiue
zones
are
needefull
and
sufficient
for
celestiall
obseruations
:
whereof
two
which
be
vnder
the
poles
,
are
caled
Perisciae
,
or
Round
shadowed
,
bicause
their
shaddowes
run
round
about
them
.
And
these
zones
extend
to
that
place
;
there
the
tropik
circles
and
the
Arctike
circles
are
all
one
.
After
these
there
do
follow
two
other
,
which
reache
from
thence
vnto
those
partes
,
that
are
directly
vnder
the
tropiks
:
and
these
haue
their
noone
shaddowe
running
one
waies
styll
▪
and
therfore
are
called
Heterofciae
,
or
Single
shadowed
.
The
fift
zone
lyeth
betwene
the
tropikes
,
and
casteth
the
noone
shadows
2
waies
,
wherefore
the
Greekes
call
it
Amphiscion
,
that
is
Double
shadowed
.
Scholar
.
By
this
translation
(
which
is
worth
a
paraphrasis
)
I
doo
not
onlye
perceaue
the
sence
of
these
wordes
,
whiche
before
were
darke
,
partly
for
the
hardnes
of
the
matter
,
and
partlye
for
the
hypallage
,
in
changinge
of
the
speakers
person
,
but
also
I
espye
the
monstrous
shape
of
the
old
translation
.
And
by
this
I
gather
also
that
Strabo
woulde
not
haue
the
Temperat
zones
to
be
bounded
by
the
Arctik
and
Antarctike
circles
.
Master
.
His
mynde
appeareth
more
manifest
anon
after
where
he
blameth
Polybius
,
for
assigninge
those
circles
as
boundes
of
the
zones
:
whereof
one
should
be
inclosed
with
in
that
circle
,
and
the
other
should
extend
from
it
to
the
next
tropike
then
he
concludeth
thus
:
that
those
vnconstant
circles
,
may
be
no
boundes
of
certentye
.
{αβγδ}
Dictum
enim
est
,
quod
per
signa
transmigrantia
,
ea
quae
non
mutantur
,
terminate
non
conuenit
.
For
I
haue
sayde
before
,
that
chaungable
limites
may
not
be
appointed
as
boundes
to
vnchaungable
places
.
Sch.
Thus
it
appeareth
,
that
the
distinction
of
zones
by
the
Arctike
and
Antarctike
circles
were
no
constant
distinction
.
and
so
is
autoritye
of
one
sorte
repelled
by
thauctoritie
of
an
other
sorte
.
Master
.
You
maye
not
weighe
the
matter
by
auctoritye
,
for
so
shoulde
that
former
doctrine
continue
styll
,
seynge
I
aleaged
for
it
Parmenides
,
Aristotle
,
Polybius
,
Cleomedes
and
Proclus
,
&
against
them
only
Posidonius
and
Strabo
,
which
maye
seeme
the
weaker
in
numbre
:
but
then
considre
that
the
firste
sort
bring
only
affirmation
for
their
testimony
,
and
bare
autoritye
:
the
other
,
confute
theym
by
good
reason
and
substantiall
argumentes
,
whiche
are
farre
to
bee
esteemed
aboue
anye
autoritye
.
Scholar
.
Then
credityng
reason
against
autority
,
I
must
say
,
that
the
Zones
must
be
otherwaies
diuided
,
peraduenture
as
I
dyd
learne
of
you
before
,
agreable
to
Iohn
de
Sacro
bosco
his
mynde
,
whom
you
called
the
restorer
of
the
Zones
.
Master
.
Yea
in
deede
:
for
although
Posidonius
and
Strabo
did
teache
the
like
distinction
,
yet
did
they
not
so
openly
name
the
true
limites
,
howe
bee
it
in
effecte
they
meane
the
same
:
for
when
Strabo
saith
,
that
the
Cold
zone
doth
reach
to
that
place
,
where
the
Tropike
is
the
Arctike
circle
,
hee
dooth
meane
that
there
,
where
this
firste
Zone
endeth
,
and
the
temperate
Zone
beginneth
,
the
Pole
is
66
degrees
and
a
halfe
aboue
the
horizonte
,
and
so
muste
the
same
Pole
bee
from
the
toppe
of
their
headdes
in
that
place
23
degrees
and
a
halfe
:
in
whiche
distaunce
bicause
the
Poles
of
the
Zodiake
do
describe
a
circle
,
therfore
doth
Iohn
de
Sacro
bosco
call
that
circle
the
Arctike
circle
,
in
that
confounding
▪
it
in
name
with
an
other
circle
of
the
Greekes
:
wherfore
I
thinke
it
more
reasonable
for
auoyding
confusion
,
to
gyue
it
a
seuerall
name
,
and
call
it
the
Polare
circle
,
and
the
other
to
be
called
styll
the
Arctike
circle
,
The
Polare
circles
.
as
the
greeks
longe
before
did
name
it
.
And
this
distinction
of
the
zones
by
the
two
Tropikes
,
and
the
two
Polare
circles
doth
distinct
exactly
those
three
varieties
of
shaddowes
before
mentioned
.
whiche
is
a
certaine
and
notable
difference
,
not
imagined
by
men
whiche
may
erre
,
but
wrought
by
the
sonne
,
which
can
not
erre
.
But
heere
muste
I
admonish
you
of
an
other
erroure
,
An
other
erroure
.
gathe
red
not
of
grounded
reason
,
but
of
phantasticall
imagination
,
by
occasion
of
whiche
,
this
fonde
distinction
of
zones
was
imagined
.
Bicause
the
elder
Grekes
had
no
trade
into
the
south
parts
of
Afrike
,
nother
the
Ethiopians
again
into
Grece
,
and
farther
by
reason
the
sonne
runneth
still
ouer
their
headdes
,
that
dwell
betweene
the
tropikes
,
manye
of
the
Latines
as
well
as
of
the
Grekes
phantasied
that
there
did
dwell
no
inhabitantes
,
neither
could
dwell
there
for
the
vehement
heat
:
wherfore
they
called
it
the
Burned
Zone
.
And
of
lyke
occasion
where
they
moued
to
accompt
two
other
zones
,
that
be
nigh
the
poles
,
to
be
vninhabited
for
cold
,
by
reason
that
the
sonne
doth
neuer
come
nigher
to
them
then
the
Tropik
circles
:
but
how
muche
herein
they
were
deceaued
,
it
maye
be
declared
not
only
by
reason
,
and
by
experience
,
but
also
by
autority
of
many
of
their
owne
writers
,
as
namely
Eratosthenes
,
Posidonius
,
Polybius
,
and
Ptolemye
.
but
as
this
is
a
matter
more
agreeable
to
the
treatise
of
Geographye
or
Cosmography
,
then
of
the
Sphere
,
so
will
I
ouerpasse
it
for
this
time
,
and
will
returne
to
the
reste
of
the
circles
of
the
sphere
,
amongest
which
the
Zodiake
as
principall
,
The
Zodiake
.
doth
offre
it selfe
,
as
the
common
theatre
and
stage
of
all
the
planets
motion
,
and
of
the
chiefe
signes
and
celestiall
figures
.
Scholar
.
Are
there
I
pray
you
suche
figures
in
the
Zodiake
,
as
Astronomers
do
describe
?
Master
.
There
are
some
that
affirme
no
lesse
,
and
testifye
that
they
haue
in
a
cleere
ayre
perceaued
them
:
but
for
the
reste
of
the
forme
,
I
will
say
nothinge
now
:
onlye
this
I
doo
affirme
whiche
I
know
,
that
all
the
starres
whiche
astronomers
do
name
to
be
there
,
maye
easily
be
seene
there
,
and
in
lyke
forme
as
they
doo
place
them
.
Scholar
.
If
the
formes
of
beasts
be
not
there
,
why
do
they
call
it
by
that
name
of
Zodiake
,
whiche
name
is
deriued
as
many
do
affirme
,
of
{αβγδ}
,
that
signifieth
a
beaste
.
Master
.
The
Signes
doo
beare
the
names
of
beastes
,
and
therfore
may
that
circle
take
the
like
denomination
also
:
but
yet
I
denyed
not
that
the
verye
formes
were
there
,
but
that
they
are
not
easilye
seene
in
suche
exacte
shapes
as
they
be
portured
,
and
as
some
mem
write
that
they
haue
seene
them
:
but
howe
so
euer
it
bee
,
the
certenty
is
,
that
the
12
signes
are
contained
in
that
zodiake
,
and
therfore
doth
Tullye
with
other
latine
men
call
it
Signifer
,
that
is
,
the
Circle
of
the
Signes
:
but
whye
those
names
were
giuen
to
euerye
signe
rather
then
other
,
dooth
not
appertaine
so
muche
to
this
treatise
,
as
to
that
Iudiciall
arte
,
whiche
hath
more
ground
of
reason
then
many
men
thinke
.
Scholar
.
What
is
to
bee
in
a
Signe
.
When
you
saye
that
the
Sonne
is
in
anye
signe
,
you
do
not
meane
(
I
am
sure
)
that
the
Sonne
hath
lepte
so
high
from
his
owne
sphere
,
into
the
sphere
of
the
Fixed
starres
,
where
the
zodiake
and
the
signes
be
,
but
that
the
Sonne
is
directly
vnder
the
same
signe
,
and
in
a
righte
line
betwene
that
signe
and
the
centre
of
the
earthe
.
Master
.
You
saye
well
.
That
is
the
common
vnderstandinge
,
when
we
speake
of
the
place
of
the
sonne
:
but
bicause
other
Planettes
doo
decline
from
the
myddle
of
that
zodiake
,
some
tymes
towarde
the
north
,
and
other
times
toward
the
southe
,
therfore
haue
all
astronomers
appointed
a
conuenient
breadth
to
the
zodiake
,
according
to
the
declination
of
the
Planets
:
howe
bee
it
proprelye
they
doo
call
that
the
Latitude
of
the
Planetes
,
The
latitude
of
Planetes
.
Their
declination
.
Their
longitude
.
The
second
signification
of
a
signe
.
when
they
swarue
frome
the
Ecliptike
line
:
and
the
Declination
of
them
is
their
distaunce
southe
or
northe
from
the
equinoctiall
line
:
so
doo
they
call
the
motion
of
them
in
Longitude
,
theyr
distaunce
by
theyr
naturall
course
frome
the
beginninge
of
Aries
,
which
is
the
beginning
of
the
zodiak
.
And
now
appointing
the
latitude
of
the
zodiake
to
bee
twelue
degrees
(
although
some
planetes
may
runne
in
latitude
on
the
one
side
almost
8
degrees
)
bycause
that
quantitie
is
moste
receaued
,
then
is
euerye
signe
twelue
degrees
broad
,
and
thirtie
degrees
long
.
and
so
maketh
a
longe
square
:
frome
the
corners
of
whiche
long
square
,
you
may
imagin
lines
to
be
drawen
to
the
centre
of
the
earth
:
and
what
so
euer
commeth
within
the
boundes
of
those
lines
,
is
accompted
to
bee
in
that
signe
:
and
this
is
the
second
signification
of
a
signe
.
The
thyrde
signification
of
a
signe
.
Arcturus
.
The
Pole
starre
.
A
third
signification
ther
is
,
which
we
vse
when
we
say
that
the
bright
starre
Arcturus
is
in
Virgine
,
where
as
in
deed
he
is
aboue
30
degrees
north
from
the
Ecliptike
line
:
which
is
farre
out
of
the
breadth
of
the
Zodiake
:
and
so
we
say
that
the
pole
starre
is
in
Taurus
,
whiche
is
from
the
Ecliptike
line
66
degrees
.
and
likewayes
we
name
all
the
starres
in
the
skye
to
bee
in
some
signe
,
bee
they
neuer
so
farre
from
the
Ecliptike
line
,
and
the
Zodiak
.
Therfore
to
know
what
is
vnderstand
by
the
name
of
a
signe
in
this
signification
,
you
must
imagin
6
circles
to
be
so
drawen
about
the
Globe
,
that
they
may
passe
by
the
beginning
of
all
the
signes
(
for
euery
circle
will
serue
for
two
signes
beinge
contrarye
one
against
the
other
)
and
so
shall
the
whole
Zodiake
and
all
the
globe
also
be
parted
into
twelue
equall
partes
,
yf
you
haue
drawen
those
circles
rightly
&
that
they
do
passe
al
by
the
two
poles
of
the
Zodiak
.
Now
mark
how
those
2
lines
that
do
inclose
any
signe
,
ar
widest
a sonder
in
the
myddle
of
the
Zodiake
,
and
from
thence
toward
eche
pole
of
the
zodiake
they
come
nearer
and
nearer
,
tyll
they
touch
in
the
Pole
it selfe
.
All
the
space
betweene
anye
two
suche
semicircles
from
one
Pole
to
the
other
,
is
named
a
sign
in
the
thyrde
signification
:
so
that
what
so
ueuer
starres
bee
within
that
space
,
are
named
to
bee
in
that
signe
which
is
within
the
same
space
:
of
all
these
three
diuers
formes
of
signes
heere
maye
you
see
examples
.
of
the
fyrste
by
A
,
where
the
Sonne
standeth
vnder
the
signe
of
Cancer
.
of
the
seconde
forme
you
haue
an
example
by
B
,
and
of
the
thirde
sorte
you
haue
two
varieties
,
one
by
,
C
and
an
other
by
D.
So
that
what
Astronomical diagram.
so
euer
Planet
doth
come
within
the
boundes
of
that
figure
B
,
is
named
to
be
in
the
signe
of
Taurus
:
&
what
so
euer
Planete
or
fixed
star
is
within
the
compas
of
the
figure
C
,
is
iudged
to
be
in
Cancer
:
as
the
Moone
is
ther
represented
to
be
and
all
the
starres
there
portured
,
&
so
maye
you
iudge
of
anye
other
signe
.
Nowe
this
maye
suffise
for
the
explication
of
the
zodiake
,
The
colures
.
after
whom
foloweth
nexte
the
Colures
,
whiche
take
their
names
in
Greeke
of
vnperfectnes
,
bycause
they
bee
neuer
seene
all
aboue
the
grounde
in
any
oblique
sphere
:
whereby
it
appeareth
,
that
good
Iohn
de
sacro
bosco
was
much
deceaued
in
comparing
them
to
the
compassed
bowing
of
a
wild
bulles
tayle
,
as
thoughe
they
tooke
their
names
thereof
:
but
men
must
bear
with
the
ignorance
of
that
time
,
for
lack
of
knowledge
in
the
Greeke
tonge
.
These
Colures
serue
principally
for
the
distinction
of
the
four
chiefe
pointes
in
the
zodiake
,
as
before
is
declared
.
and
bycause
the
pointe
of
the
intersection
or
crossinge
of
the
ecliptike
line
and
the
equinoctiall
,
doothe
sufficiently
expresse
two
of
those
pointes
in
the
beginning
of
Aries
and
Libra
,
therfore
the
greekes
do
assigne
commonly
but
one
Colure
,
for
the
other
two
tropike
pointes
,
and
none
for
these
equinoctiall
pointes
.
How
be
it
,
bycause
they
serue
also
for
the
declinations
and
latitudes
of
fixed
starres
and
Planetes
,
I
thinke
it
better
to
describe
them
,
then
to
omitte
them
.
And
thus
haue
I
lyghtly
touched
all
the
circles
that
be
fixed
in
the
sphere
,
and
moue
with
it
.
Nowe
remaineth
other
two
,
which
stand
styll
alwaies
and
moue
not
,
of
whiche
the
fyrste
is
the
Horizonte
,
and
the
nexte
is
the
Meridiane
.
The
horizont
is
of
twoo
diuers
sortes
.
the
one
doth
extend
on
euery
syde
vnto
the
firmament
,
The
Horizonte
.
The
celestial
horizont
and
serueth
as
it
were
pecularly
for
the
partition
of
the
heauens
,
and
diuideth
the
skie
iustly
into
two
halues
,
wherof
the
one
appeareth
vnto
vs
aboue
that
Horizonte
,
and
the
other
is
hidde
from
vs
,
vnder
the
same
horizont
:
this
horizonte
hath
his
name
of
the
skie
,
and
is
called
the
Celestial
horizont
,
and
his
diameter
is
as
large
as
the
diameter
of
the
eight
spher
,
which
is
the
farthest
and
highest
part
of
the
skye
that
we
canne
see
:
this
large
horizont
our
sight
doth
inforce
vs
to
acknowledg
as
a
iuste
horizont
,
although
reason
canne
fynde
in
it
some
wante
of
exacte
precisenes
.
And
therfore
Proclus
doth
not
well
distincte
this
horizont
from
the
other
,
by
naminge
the
other
a
sensible
horizont
,
and
affirming
this
to
be
considered
only
by
reason
,
where
as
in
deede
we
neede
reasons
helpe
more
in
iudging
the
other
horizont
,
whiche
I
thinke
moste
aptlye
to
bee
called
the
Earthly
horizont
,
The
Earthly
horizont
bycause
it
serueth
for
sightes
on
the
earthe
and
water
onlye
,
and
reacheth
not
vnto
the
skie
:
no
,
his
semidiameter
excedeth
not
(
as
Macrobius
saith
)
180
furlongs
,
that
is
22
myles
and
a
halfe
:
and
his
whole
diameter
comprehendeth
but
only
45
myles
in
length
.
So
that
if
any
man
do
stande
on
a
plaine
grounde
or
on
the
sea
,
he
maye
see
rounde
about
him
euery
waies
22
myles
and
a
halfe
:
that
is
in
round
compas
of
the
whole
horizonte
141
miles
&
3
/
7.
Geometric diagram.
I
meane
that
seing
the
right
line
A
,
C
,
is
45
miles
,
the
whole
circle
A
B
C
D
,
must
bee
accompted
141
3
/
7
myles
in
compas
.
This
saynge
of
Macrobius
is
more
nygher
to
the
truth
then
Proclus
assertion
,
which
is
that
the
diameter
shuld
be
in
this
horizont
,
2000
furlonges
,
that
is
250
myles
,
wherby
he
meaneth
that
a
manne
may
see
euery
waye
in
:
a
playne
125
myles
from
him
:
whiche
assertion
euery
maryner
dooth
knowe
to
be
false
:
for
it
is
well
knowen
by
often
and
good
obseruation
,
that
in
plaine
ground
,
or
on
the
sea
,
they
can
not
discern
.
well
aboue
20
myles
,
and
therefore
do
all
mariners
call
that
distaunce
commonly
a
Kenninge
:
A
kenning
.
whiche
is
as
muche
as
a
manne
maye
well
see
:
yet
from
a
hill
or
highe
grounde
men
maye
see
farther
,
and
especially
they
maye
see
other
hilles
or
clyffes
,
but
that
is
no
certaine
vewe
,
nor
iuste
kenninge
:
yet
in
that
sort
men
may
see
60
miles
,
or
at
the
moste
80
miles
:
but
125
myles
is
to
greate
a
distaunce
,
for
to
vewe
any
thing
from
a
high
place
,
and
therfore
of
more
force
it
is
to
excessiue
a
distaunce
to
vewe
any
thinge
in
an
equall
plaine
,
A
demonstration
against
proclus
.
as
the
horizont
must
needes
be
,
for
declaration
wherof
,
I
suppose
this
figure
to
represent
the
whole
globe
of
the
earthe
,
Geometric diagram.
and
the
earthly
horizont
to
be
expressed
by
the
ryghte
lyne
F
B
G
:
vnto
which
line
ther
is
an
other
drawen
as
a
iuste
parallele
,
which
is
H
K
L.
of
lyke
lengthe
precisely
with
the
earthly
horizonte
,
and
two
other
lines
ioyninge
them
at
the
eandes
,
makinge
a
longe
square
of
all
righte
angles
,
so
that
two
of
those
angles
do
lyght
on
the
circumference
of
the
circle
of
the
earthe
.
Then
draw
I
a
right
line
from
E
which
is
the
centre
of
that
circle
,
vnto
B
,
and
an
other
from
the
same
centre
E
vnto
G
:
wherby
ther
is
made
two
triangles
E
B
G
,
and
E
K
L.
Nowe
presupposing
that
B
is
the
place
where
we
stande
on
the
earth
,
and
H
and
〈…〉
vnto
whiche
the
Semidiameter
of
1000
furlonges
of
oure
earthlye
Horizont
,
dothe
extende
on
bothe
sides
:
and
frome
the
one
of
them
is
drawen
a
right
line
to
the
other
,
that
line
must
needes
fall
within
the
circle
.
Scholar
.
That
is
true
,
accordinge
to
the
47
Theoreme
of
the
Pathwaye
.
Master
.
Then
muste
the
line
K
E
,
be
shorter
then
the
lyne
B
E
,
and
so
B
and
K
,
are
notably
distaunte
.
Scholar
.
That
is
certaine
.
Master
.
And
bicause
the
righte
line
F
B
G
,
is
parallele
to
the
righte
line
H
K
L
,
there
must
be
as
muche
distaunce
betweene
G
,
and
L
,
as
there
is
betwene
B
and
K.
Scholar
.
That
foloweth
by
the
definition
of
Paralleles
.
Master
.
Then
as
K
,
is
notably
vnder
B
,
so
must
L
be
notably
vnder
G
:
that
is
to
say
vnder
the
Horizont
,
and
therfore
can
not
be
seene
.
Scholar
.
It
is
against
the
definition
of
an
horizonte
,
that
anye
thinge
vnder
it
shoulde
be
seene
.
Master
.
Then
if
the
semidiameter
of
the
Horizonte
shall
extend
no
farther
then
that
a
meane
quantitie
maye
be
seene
on
the
earth
,
it
maye
not
be
so
longe
as
Proclus
hath
limited
it
.
Also
by
the
two
triangles
aforesaide
,
whose
angles
are
like
,
and
therfore
their
sides
proportionable
,
&
other
waies
diuersly
,
by
the
former
figure
,
it
may
be
domonstrate
,
that
the
righte
line
E
G
is
muche
longer
then
E
L
,
whiche
is
the
semidiameter
of
the
earthe
,
so
that
the
horizont
in
so
much
distaunce
is
farre
hygher
then
the
earth
is
there
,
and
therfore
canne
not
bee
aptelye
called
a
Sensible
Horizonte
,
nor
an
Earthly
Horizonte
,
as
Proclus
meaneth
.
But
is
appeareth
that
Proclus
dydde
rather
in
this
doctrine
followe
some
other
mennes
opinion
then
hys
owne
reason
,
as
he
dooth
also
in
the
declaration
of
the
chaunge
of
the
Horizontes
and
the
Meridianes
,
for
betweene
easte
and
weste
,
hee
saythe
that
the
Meridianes
chaunge
at
the
eande
of
300
furlonges
:
but
betweene
southe
and
northe
hee
dooth
assigne
no
chaung
vnto
the
Horizonts
within
400
furlongs
.
In
whiche
woordes
there
are
two
errours
included
:
the
one
that
the
horizonts
be
not
like
in
chaunge
betwene
easte
and
weste
,
and
betwene
southe
and
northe
.
Scholar
.
Nay
he
speaketh
only
of
the
Meridianes
(
I
trow
)
betwene
easte
and
west
,
and
not
of
the
Horizontes
.
Master
.
As
thoughe
we
might
chaunge
the
one
,
and
not
vniformely
chaunge
the
other
.
Scholar
.
Truthe
it
is
,
that
seing
the
meridiane
doth
cutte
the
Horizonte
with
right
angles
,
they
both
must
needes
other
stand
bothe
still
,
other
chaunge
bothe
a
like
:
wherefore
this
firste
erroure
can
not
be
excused
.
Master
.
And
the
seconde
errour
is
as
manifest
as
it
:
for
therby
he
supposeth
that
the
Climates
do
chaunge
by
equal
quantity
of
furlonges
or
miles
,
which
errour
is
to
manifest
:
for
nighe
vnto
the
equinoctiall
,
2150
furlonges
northwarde
do
cause
increase
but
of
a
quarter
of
an
hower
in
the
longest
daye
.
And
with
vs
in
the
southe
parte
of
England
,
700
furlonges
north
warde
dooth
cause
increase
of
a
quarter
of
an
hower
in
the
longest
daye
,
and
in
the
north
partes
of
Scotlande
,
320
furlonges
doo
giue
as
great
an
increase
:
in
Iselande
4
furlonges
yeldeth
the
lyke
increase
:
and
so
styll
the
farther
northe
you
go
,
the
smaller
space
of
ground
bringeth
the
like
increase
in
the
longest
daye
.
Scholar
.
Hereby
I
perceaue
,
that
who
so
euer
will
trauaile
in
these
sciences
with
profit
,
must
lean
rather
to
reason
,
then
to
authoritye
,
els
he
may
be
deceaued
.
Master
.
That
rule
is
generall
in
all
artes
.
Scholar
.
And
if
Proclus
rule
be
not
certen
,
what
rule
may
I
haue
more
certen
?
M.
For
the
alteration
of
the
Horizonte
betwene
south
&
north
,
bicause
not
only
the
climats
do
chang
therwith
,
but
also
the
quantities
of
the
daies
,
I
wil
anon
before
the
doctrine
of
the
ascensions
,
giue
you
a
table
generall
for
all
climates
in
the
earthe
.
And
as
for
the
chaunge
of
the
horizontes
or
of
the
meridianes
betweene
easte
and
weste
,
you
A
TABLE
FOR
THE
DIFErence
of
howers
accordinge
to
the
distaunce
of
myles
from
easte
to
weste
,
vnder
the
Equinoctiall
.
The
distaunce
of
miles
.
|
The
minutes
of
an
hower
.
|
The
distaunce
of
myles
.
|
Howers
.
|
The
minutes
of
an
hower
.
|
The
distaunce
of
myles
.
|
Howers
.
|
The
minutes
of
an
hower
.
|
The
distaunce
of
myles
.
|
Howers
.
|
The
minutes
of
an
hower
|
15
|
1
|
465
|
0
|
31
|
915
|
1
|
1
|
1365
|
1
|
31
|
30
|
2
|
480
|
0
|
32
|
930
|
1
|
2
|
1380
|
1
|
32
|
45
|
3
|
495
|
0
|
33
|
945
|
1
|
3
|
1395
|
1
|
33
|
60
|
4
|
510
|
0
|
34
|
960
|
1
|
4
|
1410
|
1
|
34
|
75
|
5
|
525
|
0
|
35
|
975
|
1
|
5
|
1425
|
1
|
35
|
90
|
6
|
540
|
0
|
36
|
990
|
1
|
6
|
1440
|
1
|
36
|
105
|
7
|
555
|
0
|
37
|
1005
|
1
|
7
|
1455
|
1
|
37
|
120
|
8
|
570
|
0
|
38
|
1020
|
1
|
8
|
1470
|
1
|
38
|
135
|
9
|
585
|
0
|
39
|
1035
|
1
|
9
|
1485
|
1
|
39
|
150
|
10
|
600
|
0
|
40
|
1050
|
1
|
10
|
1500
|
1
|
40
|
165
|
11
|
615
|
0
|
41
|
1065
|
1
|
11
|
1515
|
1
|
41
|
180
|
12
|
630
|
0
|
42
|
1080
|
1
|
12
|
1530
|
1
|
42
|
195
|
13
|
645
|
0
|
43
|
1095
|
1
|
13
|
1545
|
1
|
43
|
210
|
14
|
660
|
0
|
44
|
1110
|
1
|
14
|
1560
|
1
|
44
|
225
|
15
|
675
|
0
|
45
|
1125
|
1
|
15
|
1575
|
1
|
45
|
240
|
16
|
690
|
0
|
46
|
1140
|
1
|
16
|
1590
|
1
|
46
|
255
|
17
|
705
|
0
|
47
|
1155
|
1
|
17
|
1605
|
1
|
47
|
270
|
18
|
720
|
0
|
48
|
1170
|
1
|
18
|
1620
|
1
|
48
|
285
|
19
|
735
|
0
|
49
|
1185
|
1
|
19
|
1635
|
1
|
49
|
300
|
20
|
750
|
0
|
50
|
1200
|
1
|
20
|
1650
|
1
|
50
|
315
|
21
|
765
|
0
|
51
|
1215
|
1
|
21
|
1665
|
1
|
51
|
330
|
22
|
780
|
0
|
52
|
1230
|
1
|
22
|
1680
|
1
|
52
|
345
|
23
|
795
|
0
|
53
|
1245
|
1
|
23
|
1695
|
1
|
53
|
360
|
24
|
810
|
0
|
54
|
1260
|
1
|
24
|
1710
|
1
|
54
|
375
|
25
|
825
|
0
|
55
|
1275
|
1
|
25
|
1725
|
1
|
55
|
390
|
26
|
840
|
0
|
56
|
1290
|
1
|
26
|
1740
|
1
|
56
|
405
|
27
|
855
|
0
|
57
|
1305
|
1
|
27
|
1755
|
1
|
57
|
420
|
28
|
870
|
0
|
58
|
1320
|
1
|
28
|
1770
|
1
|
58
|
435
|
29
|
885
|
0
|
59
|
1335
|
1
|
29
|
1785
|
1
|
59
|
450
|
30
|
900
|
1
|
0
|
1350
|
1
|
30
|
1800
|
2
|
0
|
shall
vnderstande
that
15
myles
difference
from
easte
toward
west
,
doth
make
the
sonne
risinge
,
the
none
steed
,
and
Sonne
setting
,
to
be
later
by
one
minut
of
an
houre
.
and
so
30
miles
2
mynutes
:
120
myles
8
minutes
:
225
myles
.
15.
minutes
.
which
is
a
quarter
of
an
hower
.
And
for
exaumples
sake
more
then
for
any
other
cause
I
giue
you
here
this
table
,
which
you
may
easylye
increase
by
the
lyke
fourme
,
vntyll
you
haue
accomplysshed
the
whole
24
howers
,
yf
you
lyste
.
howe
bee
it
hee
that
is
readye
in
accompte
of
Arithmetike
,
needeth
not
anye
suche
tables
of
ayde
.
This
table
is
calculate
onlye
for
suche
places
as
dyffer
not
aboue
1800
myles
beetweene
easte
and
weste
,
hauynge
no
difference
or
verye
lyttle
in
their
distaunces
betweene
southe
and
north
,
as
touching
this
consideration
.
And
it
serueth
onlye
for
the
middle
climate
of
the
worlde
vnder
the
equinoctiall
circle
.
for
euerye
other
climate
,
yea
and
euerye
degree
in
latitude
of
eche
climate
,
must
haue
a
seuerall
table
,
whiche
maye
not
well
be
set
forth
in
this
brief
introduction
,
but
an
other
time
shall
serue
herafter
for
it
,
yf
you
call
on
me
and
put
me
in
mynde
therof
,
els
the
necessitye
of
prouision
for
my
familye
will
make
me
forget
suche
promises
:
howe
be
it
by
cause
you
shall
not
thinke
that
I
haue
done
more
for
them
that
dwell
vnder
the
equinoctiall
(
or
nygh
vnto
it
in
Guynea
or
in
Calecut
)
then
for
our
own
cuntrie
,
I
haue
drawen
the
like
table
for
the
eleuation
of
52
degrees
,
whose
vse
is
euen
one
with
the
other
before
.
wherefore
if
I
knowe
the
distaunce
of
myles
beetweene
anye
twoo
places
vnder
this
latitude
of
52
degrees
,
or
nyghe
thereto
,
as
soone
as
I
haue
founde
out
that
numbre
of
myles
in
the
table
vnder
that
title
,
in
the
nexte
columpne
on
the
righte
hande
,
I
maye
see
howe
manye
minutes
they
do
differ
in
theyr
howers
.
Scholar
.
So
that
the
miles
exceede
not
1110
,
for
this
table
hathe
no
greater
numbre
.
Master
.
If
you
lyste
by
this
president
,
you
may
increase
the
table
as
muche
as
you
wyll
.
A
TABLE
OF
THE
DIFFERENCE
of
howers
,
according
to
the
distaunce
of
miles
from
easte
to
west
;
for
the
eleuation
of
51
degres
,
55
minutes
.
The
distaunce
of
miles
.
|
The
minutes
of
an
hower
.
|
The
distaunce
of
myles
.
|
The
howers
.
|
The
minutes
of
an
hower
.
|
The
distaunce
of
myles
.
|
The
howers
.
|
The
minutes
of
an
hower
.
|
The
distaunce
of
myles
.
|
The
howers
.
|
The
minutes
of
an
hower
.
|
9
¼
|
1
|
286
¾
|
0
|
31
|
564
¼
|
1
|
1
|
841
¾
|
1
|
31
|
18
½
|
2
|
296
|
0
|
32
|
573
½
|
1
|
2
|
851
|
1
|
32
|
27
¾
|
3
|
305
¼
|
0
|
33
|
582
¾
|
1
|
3
|
860
¼
|
1
|
33
|
37
|
4
|
314
½
|
0
|
34
|
592
|
1
|
4
|
869
½
|
1
|
34
|
46
¼
|
5
|
323
¾
|
0
|
35
|
601
¼
|
1
|
5
|
878
¾
|
1
|
35
|
55
½
|
6
|
333
|
0
|
36
|
610
½
|
1
|
6
|
888
|
1
|
36
|
64
¾
|
7
|
342
½
|
0
|
37
|
619
¾
|
1
|
7
|
897
¼
|
1
|
37
|
74
|
8
|
351
½
|
0
|
38
|
629
|
1
|
8
|
906
½
|
1
|
38
|
83
1
/
4
|
9
|
360
¾
|
0
|
39
|
638
¼
|
1
|
9
|
915
1
/
4
|
1
|
39
|
92
½
|
10
|
370
|
0
|
40
|
647
½
|
1
|
10
|
925
|
1
|
40
|
101
1
/
4
|
11
|
379
¼
|
0
|
41
|
656
¾
|
1
|
11
|
934
1
/
4
|
1
|
41
|
111
|
12
|
388
½
|
0
|
42
|
666
|
1
|
12
|
943
½
|
1
|
42
|
120
¼
|
13
|
397
¾
|
0
|
43
|
675
¼
|
1
|
13
|
952
¾
|
1
|
43
|
120
½
|
14
|
407
|
0
|
44
|
684
½
|
1
|
14
|
962
|
1
|
44
|
138
¾
|
15
|
416
¼
|
0
|
45
|
693
¾
|
1
|
15
|
971
¼
|
1
|
45
|
148
|
16
|
425
½
|
0
|
46
|
703
|
1
|
16
|
980
½
|
1
|
46
|
157
¼
|
17
|
434
¾
|
0
|
47
|
712
¼
|
1
|
17
|
989
¾
|
1
|
47
|
166
½
|
18
|
444
|
0
|
48
|
721
½
|
1
|
18
|
999
|
1
|
48
|
175
3
/
4
|
19
|
453
¼
|
0
|
49
|
730
3
/
4
|
1
|
19
|
1008
¼
|
1
|
49
|
185
|
20
|
462
½
|
0
|
50
|
740
|
1
|
20
|
1017
½
|
1
|
50
|
194
¼
|
21
|
471
¾
|
0
|
51
|
749
¼
|
1
|
21
|
1026
¾
|
1
|
51
|
203
½
|
22
|
481
|
0
|
52
|
758
½
|
1
|
22
|
1036
|
1
|
52
|
212
¾
|
23
|
490
¼
|
0
|
53
|
767
¾
|
1
|
23
|
1045
¼
|
1
|
53
|
222
|
24
|
499
½
|
0
|
54
|
777
|
1
|
24
|
1054
½
|
1
|
54
|
231
¼
|
25
|
508
¾
|
0
|
55
|
786
¼
|
1
|
25
|
1063
¾
|
1
|
55
|
240
½
|
26
|
518
|
0
|
56
|
795
½
|
1
|
26
|
1073
|
1
|
56
|
249
¾
|
27
|
527
¼
|
0
|
57
|
804
¾
|
1
|
27
|
1082
¼
|
1
|
57
|
259
|
28
|
536
½
|
0
|
58
|
814
|
1
|
28
|
1091
½
|
1
|
58
|
268
¼
|
29
|
545
¾
|
0
|
59
|
823
¼
|
1
|
29
|
1100
¾
|
1
|
59
|
277
½
|
30
|
555
|
1
|
0
|
832
½
|
1
|
30
|
1110
|
2
|
0
|
Scholar
.
Bicause
examples
do
make
rules
manifest
,
I
pray
you
let
me
proue
one
example
.
London
and
Bristow
are
94
myles
a
sonder
,
and
as
I
haue
hearde
you
saye
,
they
are
not
muche
different
in
latitude
:
I
desire
to
know
their
difference
in
howers
,
therfore
I
seeke
for
94
vnder
the
title
of
distaunce
of
myles
,
and
I
can
not
find
it
there
,
for
92
and
a
halfe
is
to
lyttle
,
and
101
¾
is
to
greate
.
Master
.
And
in
lyke
rate
is
there
difference
of
minutes
:
for
10
minutes
is
to
lytle
,
and
11
minutes
is
to
greate
.
but
to
gesse
moste
nearest
:
as
92
and
a
halfe
is
nigher
to
94
then
101
¾
:
so
is
10
minutes
more
nearer
their
true
difference
then
11.
And
for
this
time
this
maye
suffise
,
althoughe
I
can
giue
you
a
precise
rule
by
the
part
proportionable
to
fynde
oute
the
iuste
parte
of
euery
minute
,
but
that
were
more
curious
then
profitable
in
this
place
:
Therfore
will
I
leaue
it
,
and
declare
vnto
you
,
how
you
may
make
the
lyke
table
for
any
latitude
of
euen
degrees
.
Scholar
.
I
do
perceaue
by
these
two
tables
,
that
it
I
haue
ones
the
fyrst
numbre
which
must
be
set
against
one
minute
of
tyme
,
then
must
I
double
it
for
two
minutes
,
and
triple
it
for
thre
minutes
,
and
so
forth
,
styll
multiplying
the
fyrste
numbre
of
myles
by
the
numbre
of
minutes
against
which
it
shall
stende
.
Master
.
You
take
it
well
,
and
therfore
seyng
you
doubte
only
of
the
fyrst
numbre
,
I
will
giue
you
a
table
by
whiche
you
may
easily
find
out
that
firste
numbre
for
all
degrees
of
latitude
of
any
region
.
And
this
is
it
.
where
in
the
first
columne
you
see
placed
the
degrees
of
latitude
,
and
in
the
seconde
columne
are
set
the
myles
with
their
fractions
,
which
serue
for
one
degree
of
longitude
,
in
eche
of
those
dyuers
latitudes
.
By
this
table
may
you
make
any
table
for
any
eleuation
of
hole
degrees
,
accordinge
to
the
example
of
the
former
two
tables
.
Scholar
.
That
do
I
perceaue
nowe
very
well
,
and
can
do
it
,
I
doubt
not
,
sufficiently
for
anye
Climate
,
yf
I
were
as
A
TABLE
DECLARINGE
how
many
myles
do
answere
to
one
minute
of
tyme
,
in
euery
seuerall
latitude
.
Degrees
of
latitude
.
|
Miles
agreig
to
i
.
minute
of
time
.
|
0
|
15
|
1
|
14
230
/
240
|
2
|
14
79
/
80
|
3
|
14
47
/
48
|
3
|
14
77
/
80
|
5
|
14
113
/
120
|
6
|
14
11
/
12
|
7
|
14
71
/
80
|
8
|
14
41
/
48
|
9
|
14
40
/
60
|
10
|
14
37
/
80
|
11
|
14
87
/
120
|
12
|
14
162
/
240
|
13
|
14
37
/
60
|
14
|
14
133
/
240
|
15
|
14
117
/
240
|
16
|
14
101
/
240
|
17
|
14
83
/
240
|
18
|
14
4
/
15
|
19
|
14
11
/
60
|
20
|
14
23
/
240
|
21
|
14
11
/
240
|
22
|
13
100
/
120
|
23
|
13
97
/
120
|
24
|
13
160
/
240
|
25
|
13
143
/
240
|
26
|
13
29
/
60
|
27
|
13
11
/
30
|
28
|
13
50
/
240
|
29
|
13
29
/
240
|
30
|
12
119
/
120
|
31
|
12
103
/
120
|
32
|
12
173
/
240
|
33
|
12
139
/
240
|
34
|
12
21
/
48
|
35
|
12
69
/
240
|
36
|
12
2
/
16
|
37
|
11
47
/
48
|
38
|
11
197
/
240
|
39
|
11
79
/
120
|
40
|
11
59
/
120
|
41
|
11
77
/
240
|
42
|
11
7
/
48
|
43
|
10
233
/
240
|
44
|
10
10
/
24
|
45
|
10
73
/
120
|
46
|
10
101
/
240
|
47
|
10
11
/
48
|
48
|
10
9
/
240
|
49
|
9
101
/
120
|
50
|
9
77
/
120
|
51
|
9
53
/
120
|
52
|
9
7
/
80
|
53
|
9
1
/
240
|
54
|
8
40
/
60
|
55
|
8
29
/
48
|
56
|
8
93
/
240
|
57
|
8
41
/
240
|
58
|
7
10
/
20
|
59
|
7
87
/
120
|
60
|
7
½
|
61
|
7
13
/
48
|
62
|
7
1
/
24
|
63
|
6
97
/
120
|
64
|
6
69
/
120
|
65
|
6
81
/
240
|
66
|
6
1
/
10
|
67
|
5
207
/
240
|
68
|
5
140
/
340
|
69
|
5
⅜
|
70
|
5
31
/
240
|
71
|
4
53
/
60
|
72
|
4
19
/
30
|
73
|
4
31
/
80
|
74
|
4
2
/
15
|
75
|
3
53
/
60
|
76
|
3
101
/
240
|
77
|
3
⅜
|
78
|
3
7
/
60
|
79
|
2
207
/
240
|
80
|
2
29
/
60
|
81
|
2
83
/
240
|
82
|
2
7
/
80
|
83
|
1
109
/
240
|
84
|
1
17
/
30
|
85
|
1
37
/
120
|
86
|
1
11
/
240
|
87
|
47
/
240
|
88
|
21
/
40
|
89
|
21
/
80
|
90
|
0
|
certaine
of
their
boundes
.
Of
the
climates
.
but
that
maye
I
learne
by
suche
tables
as
Orontius
and
dyuers
other
haue
sette
forthe
all
readye
.
Master
.
In
deede
bothe
Orontius
and
other
haue
set
forth
suche
tables
,
whiche
maye
suffice
for
an
Introduction
,
but
Orontius
extendeth
not
his
table
aboue
the
latitude
of
66.
degrees
and
a
halfe
,
so
there
resteth
vnto
the
northe
Pole
23
degrees
and
a
halfe
,
The
famous
aduenture
vnto
Moscouia
by
the
northe
Ocean
.
whiche
coaste
hytherto
hath
been
knowen
to
very
fewe
men
,
but
nowe
of
late
by
the
famous
aduenture
of
that
woorthye
companye
of
our
Englishe
marchauntes
for
Moscouia
,
that
coast
is
discouered
vnto
75
degrees
of
latitude
nighe
hande
:
and
our
hope
is
that
if
they
doo
continue
as
they
haue
valiantlye
begonne
,
they
shall
disclose
those
vnknowen
people
whiche
dwell
directlye
vnder
the
Pole
,
or
at
the
leaste
waies
discouer
that
climate
,
suche
as
it
is
,
to
the
full
satisfaction
of
that
importune
desire
,
whiche
hathe
forced
manye
thousandes
to
wisshe
,
that
whiche
not
one
yet
(
that
we
knowe
)
coulde
attayne
:
whereby
they
shall
not
onlye
profite
their
countrie
,
but
shall
procure
to
theim selues
greate
ryches
and
treasure
:
and
that
whiche
is
moste
to
bee
desired
,
immortall
same
.
Wherefore
for
my
parte
to
further
their
knoweledge
in
the
atchiuinge
of
their
woorthye
attempte
,
as
I
haue
all
readye
in
this
booke
giuen
some
lighte
,
so
wyll
I
(
God
wyllinge
)
hereafter
gyue
more
lighte
:
and
for
an
earneste
thereof
I
will
nowe
exhibyte
to
you
a
table
of
the
Climates
extended
to
the
verie
Pole
,
whereby
you
maye
learne
not
onlye
the
beginninge
and
eande
of
euerye
climate
,
but
also
the
iuste
quantitie
of
the
longest
and
shorteste
daye
in
eche
of
theim
,
and
in
all
other
places
to
the
Pole
selfe
:
the
reason
whereof
you
shall
better
vnderstande
by
the
diuersities
of
the
ascensions
.
But
bicause
(
as
I
saide
beefore
)
that
euerye
Climate
differeth
frome
other
,
by
the
space
of
halfe
an
hower
in
the
quantitye
of
their
longest
daye
,
therfore
did
the
greekes
and
namely
Ptolemye
,
for
a
more
precisenes
make
a
certain
distinction
for
euery
quarter
of
an
howers
difference
,
whiche
he
calleth
only
by
the
generall
names
of
paralleles
,
as
it
doth
at
large
appear
in
the
sixte
chapter
of
the
second
boke
of
his
Almagestes
,
wherof
at
anye
other
tyme
I
will
more
largelye
intreate
.
And
for
this
present
time
will
onlye
sette
forthe
the
summe
of
that
matter
in
a
table
,
whose
firste
columpne
doth
containe
the
numbre
of
the
paralleles
as
Ptolemye
did
distincte
them
.
The
seconde
columpne
contayneth
a
more
exacte
partition
of
those
paralleles
accordinge
vnto
the
increase
of
the
longest
daye
,
by
a
quarter
of
an
hower
,
whiche
Ptolemye
obserued
not
,
after
hee
came
to
is
howers
of
lengthe
:
but
I
obserue
styll
,
vntill
24
howers
of
length
.
after
which
time
and
place
,
bicause
the
increase
of
the
longest
daye
is
greater
and
greater
continuallye
,
I
thinke
it
not
good
to
make
so
curious
a
table
for
euery
quarter
of
an
hower
,
but
(
as
Erasmus
Reynhold
doth
)
to
make
the
distinction
thence
forthe
by
halfe
a
degree
of
difference
in
eleuation
of
the
Pole
,
as
by
the
table
you
maye
see
.
In
this
table
are
sette
for
the
96
paralleles
iustlye
:
and
but
38
by
Ptolomies
partition
:
the
cause
whereof
,
I
will
shewe
you
an
other
time
.
Of
these
paralleles
are
made
24
Climats
betweene
the
Equinoctiall
circle
&
the
Tropike
of
Cancer
.
eche
differinge
frome
other
by
halfe
an
hower
,
as
the
laste
columpne
of
the
table
declareth
.
but
the
elder
Greekes
dyd
not
knowe
verye
well
those
North
cuntries
,
and
therefore
did
they
assigne
only
7
climats
according
as
I
haue
set
them
annexed
to
the
firste
columne
of
this
table
.
A
TABLE
FOR
THE
IVSTE
distinction
of
Climates
,
with
the
quantities
of
their
longest
dayes
,
and
the
Eleuation
of
the
Pole
.
The
numbre
of
the
7
climates
accordinge
to
the
olde
Greekes
.
|
Parallels
after
Ptol
|
Parallels
more
exact
|
Eleuation
of
the
Pole
.
|
The
quantitie
of
the
longest
daye
.
|
The
Climates
.
|
The
names
|
Parallels
after
Ptol
.
|
Parallels
more
exact
|
Eleuation
of
the
Pole
.
|
The
quantitie
of
the
longest
daye
.
|
The
Climates
.
|
De
.
|
Mi.
|
H.
|
M.
|
De
.
|
Mi.
|
H.
|
Mi.
|
1
|
1
|
0
|
0
|
12
|
0
|
1
|
of
the
7
climates
after
|
25
|
25
|
58
|
27
|
18
|
0
|
13
|
2
|
2
|
4
|
18
|
12
|
15
|
26
|
59
|
15
|
18
|
19
|
3
|
3
|
8
|
34
|
12
|
30
|
2
|
some
chiefe
place
in
thē
|
26
|
27
|
59
|
59
|
18
|
30
|
14
|
4
|
4
|
12
|
43
|
12
|
45
|
28
|
60
|
40
|
18
|
45
|
1
|
5
|
5
|
16
|
44
|
13
|
0
|
3
|
by
Meroe
|
27
|
29
|
61
|
18
|
19
|
0
|
15
|
6
|
6
|
20
|
34
|
13
|
15
|
30
|
61
|
53
|
19
|
19
|
2
|
7
|
7
|
24
|
11
|
13
|
30
|
4
|
by
Sienc
.
|
28
|
31
|
62
|
25
|
19
|
30
|
16
|
8
|
8
|
27
|
36
|
13
|
45
|
32
|
62
|
55
|
19
|
45
|
3
|
9
|
9
|
30
|
48
|
14
|
0
|
5
|
by
Alexandria
.
|
29
|
33
|
63
|
22
|
20
|
0
|
17
|
10
|
10
|
33
|
46
|
14
|
15
|
34
|
63
|
47
|
20
|
15
|
4
|
11
|
11
|
36
|
30
|
14
|
30
|
6
|
by
the
Rodes
.
|
|
35
|
64
|
10
|
20
|
30
|
18
|
12
|
12
|
39
|
3
|
14
|
45
|
36
|
64
|
31
|
20
|
45
|
5
|
13
|
13
|
41
|
23
|
15
|
0
|
7
|
by
Rome
|
30
|
37
|
64
|
49
|
21
|
0
|
19
|
14
|
14
|
43
|
32
|
15
|
15
|
38
|
65
|
6
|
21
|
15
|
6
|
15
|
15
|
45
|
31
|
15
|
30
|
8
|
by
Ponte
Euxine
.
|
|
39
|
65
|
22
|
21
|
30
|
20
|
16
|
16
|
47
|
21
|
15
|
45
|
40
|
65
|
35
|
21
|
45
|
7
|
17
|
17
|
49
|
1
|
16
|
0
|
9
|
by
Boristhenes
.
|
31
|
41
|
65
|
47
|
22
|
0
|
21
|
18
|
18
|
50
|
34
|
16
|
15
|
42
|
66
|
58
|
22
|
15
|
|
19
|
19
|
51
|
59
|
16
|
30
|
10
|
by
Englande
.
|
|
43
|
66
|
7
|
22
|
30
|
22
|
20
|
20
|
53
|
17
|
16
|
45
|
44
|
66
|
15
|
22
|
45
|
|
21
|
21
|
54
|
30
|
17
|
0
|
11
|
|
32
|
45
|
66
|
21
|
23
|
0
|
23
|
22
|
22
|
55
|
36
|
17
|
15
|
46
|
66
|
25
|
23
|
15
|
|
23
|
23
|
56
|
38
|
17
|
30
|
12
|
|
|
47
|
66
|
29
|
23
|
30
|
24
|
24
|
24
|
57
|
34
|
17
|
45
|
48
|
66
|
31
|
23
|
45
|
|
|
|
|
|
|
|
|
|
33
|
49
|
66
|
31
½
|
24
|
0
|
|
Parallels
after
Ptol
.
|
Parallels
more
exact
|
Eleuation
of
the
Pole
.
|
Quantitye
of
the
longest
daye
.
|
|
Parallels
after
Ptol
.
|
Parallels
more
exact
|
Eleuation
of
the
Pole
.
|
Quantitye
of
the
longest
daye
.
|
Deg
.
|
Mi.
|
Dai
.
|
Ho
.
|
Deg
.
|
Mi.
|
Dai
.
|
Ho
.
|
34
|
50
|
67
|
0
|
23
|
11
|
|
|
74
|
79
|
0
|
127
|
19
|
51
|
67
|
30
|
33
|
17
|
75
|
79
|
30
|
130
|
17
|
|
52
|
68
|
0
|
41
|
14
|
|
|
76
|
80
|
0
|
133
|
13
|
53
|
68
|
30
|
48
|
6
|
77
|
80
|
30
|
136
|
8
|
|
54
|
69
|
0
|
54
|
3
|
|
|
78
|
81
|
0
|
139
|
3
|
55
|
69
|
30
|
59
|
12
|
79
|
81
|
30
|
141
|
21
|
35
|
56
|
70
|
0
|
64
|
11
|
|
|
80
|
82
|
0
|
144
|
14
|
57
|
70
|
30
|
69
|
4
|
81
|
82
|
30
|
147
|
7
|
|
58
|
71
|
0
|
73
|
13
|
|
|
82
|
83
|
0
|
150
|
0
|
59
|
71
|
30
|
77
|
17
|
83
|
83
|
30
|
152
|
16
|
|
60
|
72
|
0
|
81
|
17
|
|
38
|
84
|
84
|
0
|
155
|
8
|
61
|
72
|
30
|
85
|
14
|
85
|
84
|
30
|
158
|
0
|
36
|
62
|
73
|
0
|
89
|
8
|
|
|
86
|
85
|
0
|
160
|
15
|
63
|
73
|
30
|
92
|
22
|
87
|
85
|
30
|
163
|
5
|
|
64
|
74
|
0
|
96
|
10
|
|
|
88
|
86
|
0
|
165
|
19
|
65
|
74
|
30
|
99
|
21
|
89
|
86
|
30
|
168
|
9
|
|
66
|
75
|
0
|
103
|
9
|
|
|
90
|
87
|
0
|
170
|
23
|
67
|
75
|
30
|
106
|
11
|
91
|
87
|
30
|
173
|
13
|
|
68
|
76
|
0
|
109
|
16
|
|
|
92
|
88
|
0
|
176
|
2
|
69
|
76
|
30
|
112
|
20
|
93
|
88
|
30
|
178
|
16
|
|
70
|
77
|
0
|
115
|
22
|
|
|
94
|
89
|
0
|
181
|
5
|
71
|
77
|
30
|
118
|
22
|
95
|
89
|
30
|
183
|
19
|
37
|
72
|
78
|
0
|
121
|
22
|
|
|
96
|
90
|
0
|
186
|
7
|
73
|
78
|
30
|
124
|
21
|
Howe
be
it
bicause
you
shall
know
what
names
thelder
grekes
dyd
giue
them
(
whyche
names
hath
beene
retayned
euer
sith
that
time
)
I
haue
here
drawen
a
lyke
table
as
your
other
authors
haue
sette
forthe
,
that
you
may
the
better
conferre
the
figure
with
the
table
,
and
the
more
easilye
vnderstande
the
one
by
the
other
.
in
whiche
figure
the
circle
A
,
B
,
C
,
D
,
diagram illustrating the globe.
representeth
the
Horizont
,
&
the
righte
line
A
C
,
standeth
for
the
Meridiane
line
.
The
names
and
ordre
of
the
Climates
.
A
is
the
north
pole
and
C
,
the
south
pole
.
B
the
easte
,
&
D
the
west
.
B
D
betokening
the
Equinoctiall
,
and
EF
the
tropike
of
Cancer
,
GH
,
the
tropike
of
Capricorne
.
and
al
the
other
lines
are
the
boundes
of
the
Climats
eche
in
his
order
.
The
first
Climat
taketh
name
of
Meroe
,
a
famous
Iland
in
Ethiopia
vnder
Egypt
,
inclosed
by
the
riuer
Nilus
.
the
second
Climat
is
named
of
Syene
,
a
city
of
Egypt
,
lying
directli
vnder
the
tropik
of
Cancer
.
The
third
Climate
is
called
after
Alexandria
,
a
notable
city
&
an
ancient
vniuersity
in
egypt
also
,
lying
on
the
north
shore
of
it
.
The
fourth
climate
beareth
the
name
of
the
Rodes
,
an
island
better
knowen
then
kept
,
and
yet
better
loste
then
kepte
so
derely
.
The
fifte
Climate
is
expressed
by
the
name
of
Rome
,
a
citye
in
Italye
well
ynoughe
knowen
.
The
sixte
climate
is
called
after
the
Euxine
sea
,
commonlye
called
Ponte
.
The
seuenth
Climate
reacheth
from
the
parallele
that
passeth
by
the
mouthe
of
the
riuer
Boristhenes
,
and
extendeth
to
the
parallele
that
runneth
by
the
south
partes
of
Englande
,
as
Ptolemy
witnesseth
in
the
second
booke
of
his
Almagestes
.
And
although
more
maye
bee
saide
of
the
Climates
,
yet
I
will
reserue
it
to
the
treatise
of
Cosmographye
,
and
at
this
time
will
saye
no
more
,
but
that
on
the
other
side
of
the
Equinoctiall
towarde
the
Southe
,
there
are
the
like
Paralleles
,
and
the
like
Climates
,
The
southe
Climates
.
with
the
same
quantities
of
distaunce
from
the
Equinoctiall
,
and
the
like
increase
of
daies
.
Scholar
.
The
distaunce
of
anye
Climate
or
Parallele
frome
the
Equinoctiall
is
equall
all
wayes
with
the
eleuation
of
the
Pole
aboue
the
Horizonte
,
as
I
maye
easilye
coniecture
:
so
that
when
I
knowe
the
one
,
I
muste
needes
knowe
the
other
:
and
that
maketh
me
nowe
to
thinke
that
yf
I
knowe
anye
eleuation
of
the
Pole
,
I
maye
by
thys
table
easilye
declare
howe
farre
that
Parallele
whiche
serueth
for
that
eleuation
,
The
vse
of
the
table
of
Climates
.
is
frome
the
Equinoctialle
circle
:
and
howe
longe
the
longest
daye
is
in
that
place
:
and
if
it
chaunce
that
the
latitude
of
anye
region
whyche
I
doo
seeke
for
,
bee
not
in
thys
table
iustelye
expressed
,
I
muste
then
gesse
by
the
proportion
of
those
twoo
numbres
,
betweene
whyche
it
standeth
,
what
the
precise
lengthe
of
the
longest
daye
is
.
Master
.
Thys
table
it selfe
suffiseth
for
eche
quarter
of
an
hower
betweene
the
longest
nighte
of
24
howers
,
and
the
longest
daye
of
24
howers
:
but
for
more
exacter
partes
of
tyme
,
I
woulde
not
wisshe
you
to
trauaile
yet
,
tyll
I
maye
hereafter
gyue
you
full
rules
for
it
:
especiallye
seeynge
thys
quarter
of
the
hower
is
the
difference
of
the
whole
daye
,
whiche
muste
be
parted
into
twoo
partes
,
and
the
one
halfe
quarter
to
bee
assygned
to
the
difference
of
the
Sonne
risinge
,
and
the
other
halfe
quarter
the
difference
of
the
sonne
setting
.
Scholar
.
That
difference
is
more
precise
then
our
clocks
or
dials
do
serue
vnto
,
and
therfore
I
may
well
ynoughe
bee
satisfied
with
it
for
this
time
:
wherefore
I
pray
you
now
proceede
to
the
Ascensions
.
Master
.
The
vse
of
the
name
of
the
Ascensions
,
hathe
greate
diuersitye
in
it
,
Of
the
Ascentions
.
therfore
I
muste
by
diuision
and
definition
distincte
so
those
diuers
varieties
,
that
you
may
iustly
knowe
them
eche
in
his
kinde
.
And
fyrst
,
for
the
name
of
Ascension
in
generall
,
it
doothe
betoken
the
risinge
of
anye
starres
or
signes
(
what
so
euer
they
be
)
aboue
the
Horizont
.
But
nowe
is
there
dyuers
obseruations
of
seuerall
persons
touching
the
risinge
of
the
starres
,
for
Astronomers
vse
to
obserue
theyr
rysinge
in
fourme
,
that
is
to
saye
,
whether
they
ryse
ryghte
or
obliquely
,
not
regardynge
(
in
that
consideration
)
the
difference
in
the
time
of
the
daye
:
where
as
the
conninge
Maryners
,
and
authors
of
husbandrye
,
yea
and
good
Physicians
also
as
well
as
Astronomers
do
marke
their
risinge
at
twoo
times
principallye
,
that
is
when
they
rise
iuste
at
the
Sonne
settinge
,
or
els
iuste
at
the
Sonne
rysynge
.
Scholar
.
If
Astronomers
doo
nonsider
onlye
the
fyrste
forme
,
then
these
other
formes
do
not
appertaine
to
thys
treatise
,
whiche
is
of
Astronomye
peculiarly
.
Master
.
Althoughe
those
risinges
and
settinges
of
the
starres
which
Physicions
and
other
good
writers
of
husbanddrye
and
writers
also
of
nauigation
,
doo
ofte
times
speake
of
in
their
writinges
,
as
beynge
suche
,
whiche
in
aunciente
Kalendars
haue
beene
sette
forth
plainlye
for
all
menne
to
vnderstande
,
and
so
myghte
bee
at
this
tyme
also
,
yet
he
that
shoulde
well
sette
theym
so
forthe
,
oughte
to
bee
skylfull
in
Astronomye
,
els
canne
hee
not
doo
it
woorthy
the
readynge
,
and
therefore
it
belongeth
to
Astronomers
to
determine
their
true
times
.
Howe
bee
it
bycause
Poetes
haue
oftener
made
mention
of
suche
rysinges
,
then
Astronomers
haue
doone
,
therefore
doothe
Ioannes
de
Sacro
Bosco
and
others
also
call
them
Ascensions
Poeticall
:
not
as
fayned
matters
,
but
as
thinges
often
remembred
in
Poetes
bookes
.
And
as
I
sayde
,
they
putte
difference
betweene
the
rysynge
of
those
starres
in
the
mornyng
wyth
the
Sonne
,
and
the
risynge
of
the
same
at
the
Sonne
settynge
.
The
fyrste
manner
of
risinge
with
the
Sonne
,
they
call
in
Latine
,
Ortus
Cosmicus
,
Mundanus
and
Matutinus
:
whiche
maye
well
bee
named
in
Englyshe
the
Mornynge
rysinge
:
the
other
sorte
whiche
in
English
ought
to
bee
called
the
Euenynge
risinge
,
is
named
truely
in
Latine
ortus
Vespertinus
or
Acronychus
,
and
not
Temporalis
or
Chronicus
.
Scholar
.
Yet
manye
doo
call
it
so
,
and
Ioannes
de
Sacro
bosco
sheweth
a
reason
of
that
name
,
bicause
(
sayth
he
)
that
Astronomers
vse
that
time
after
the
Sonne
settinge
best
for
markinge
the
course
of
the
starres
.
Master
.
Ignorance
of
the
Greeke
tongue
hathe
hindred
muche
manye
good
wittes
:
whiche
maye
often
appeare
not
only
in
good
Iohn
de
sacro
bosco
,
but
also
in
many
writers
within
these
300.
yeares
especiallye
:
but
wee
muste
wynke
at
suche
faultes
,
whiche
rather
were
the
faultes
of
the
time
,
then
of
the
persons
.
and
for
this
name
Acronychus
,
is
easilye
tourned
into
Chronicus
.
The
fyrste
name
is
often
readde
in
Ptolemye
and
other
Greeke
wryters
,
and
is
named
of
the
begynnynge
of
the
nyghte
,
whiche
name
by
ignoraunce
was
tourned
into
Chronicos
in
Greeke
,
and
so
accordinglye
was
called
Temporalis
in
Latine
,
and
then
an
ymagined
reason
clouted
thereto
:
lykewaies
also
in
the
thyrde
kinde
of
rysynge
and
settinge
,
whereof
the
same
author
doothe
make
mention
,
hit
appeareth
that
hee
was
somewhat
deceaued
,
for
that
owghte
not
to
bee
called
proprelye
rysynge
of
anye
Starre
when
it
getteth
oute
of
the
Sonne
beames
,
and
maye
shewe
or
shine
at
eueninge
or
mornynge
.
The
thyrde
kinde
of
settynge
.
but
it
oughte
rather
to
be
called
Apparition
or
appearynge
of
that
starre
.
And
contrarye
wayes
when
anye
starre
is
so
nyghe
vnto
the
Son
that
the
Sonne
doothe
take
awaye
or
hyde
the
lyghte
of
it
,
it
oughte
to
bee
called
the
Hydynge
or
occultation
of
that
starre
,
and
not
the
settynge
of
that
starre
,
syth
settynge
and
rysynge
haue
propre
relation
to
the
Horizonte
,
and
yet
doothe
hee
and
mennye
other
contrarye
to
the
learned
Greekes
call
the
fyrste
,
the
Sonnelye
rysynge
of
the
starre
,
and
the
other
,
the
Sonnelye
settyng
of
him
where
as
Ptolemye
and
the
learned
Greekes
call
the
one
{αβγδ}
,
that
is
in
Latine
Apparitio
,
the
shewynge
of
the
starre
.
and
the
contrarye
is
called
in
Greeke
{αβγδ}
,
and
in
Latine
Occultatio
,
the
darkenynge
or
hidynge
of
the
starre
.
whiche
chaunce
happeneth
commonly
to
any
starre
being
within
15
degrees
of
the
Sonne
.
this
passion
is
called
of
many
men
Combustion
:
Combustion
.
Oppression
.
Other
contract
the
name
of
combustion
to
syxe
degrees
,
and
call
this
Oppression
.
but
of
all
these
,
I
will
an
other
time
declare
my
full
mynde
,
for
the
iust
knowledge
hereof
appertaineth
to
a
higher
Arte
.
And
so
will
I
hereafter
giue
you
a
table
declaringe
the
morninge
and
euenynge
rysynge
and
settinge
of
all
the
moste
notable
starres
,
for
the
matter
is
not
so
easye
as
it
seemeth
to
bee
.
Scholar
.
I
vnderstande
it
thus
:
that
when
the
Sonne
is
in
anye
parte
of
a
Signe
,
those
starres
whiche
be
in
the
same
parte
of
that
Signe
,
doo
rise
with
the
Sonne
,
and
those
whiche
be
in
the
like
degree
of
the
contrarye
signe
,
they
rise
at
the
Sonne
settynge
.
Master
.
Your
taking
is
true
,
for
suche
starres
as
are
nigh
vnto
the
Ecliptike
line
:
but
yet
such
starres
as
be
farre
from
the
ecliptike
line
,
may
rise
or
set
with
the
Son
,
although
thei
be
in
an
other
Signe
then
the
Sonne
is
,
&
so
may
they
ryse
or
set
before
or
after
the
son
,
although
thei
be
in
one
degre
of
any
Signe
with
the
Sonne
.
And
here
maye
you
not
forgette
that
the
starre
that
setteth
with
the
Sonne
,
The
euening
settig
The
morning
settig
is
named
to
haue
an
euening
setting
:
and
the
starre
that
setteth
in
the
weste
at
the
Sonne
rising
,
is
iudged
to
haue
the
morning
setting
:
wherby
it
foloweth
,
that
the
starre
that
hath
the
morning
rising
,
hath
also
the
euening
setting
:
and
he
that
hath
the
eueninge
risinge
,
hath
the
morning
setting
:
thus
haue
I
spoken
rudely
and
lyghtly
for
this
time
,
but
in
the
table
of
these
risinges
and
settinges
,
you
shall
haue
a
more
exacte
forme
of
knowledge
set
out
for
you
,
touching
this
matter
.
And
nowe
to
retourne
to
those
ascensions
which
be
peculiarly
called
Astronomicall
,
fyrste
,
for
the
definition
you
muste
vnderstande
,
that
Ascension
astronomicall
is
the
certaine
limitation
of
som
pointe
of
the
equinoctiall
circle
,
Ascention
astronomical
whiche
riseth
iustelye
with
anye
starre
,
and
largely
taking
the
vse
of
that
name
.
It
betokeneth
also
the
arke
of
the
Equinoctiall
circle
,
whiche
lyeth
betweene
the
beginninge
of
the
same
Equinoctiall
at
Aries
,
and
extendeth
to
the
iuste
degree
that
riseth
with
any
starre
or
signe
.
Thirdly
the
ascension
of
a
signe
or
constellation
(
whiche
includeth
a
certaine
measure
in
lengthe
,
)
is
that
iuste
arke
of
the
equinoctiall
,
which
doth
passe
the
Horizont
with
that
whole
signe
or
constellation
.
This
ascension
is
commonly
dyuided
into
twoo
kyndes
,
the
one
is
called
Ryghte
ascension
,
and
the
other
Oblique
or
Crooked
ascension
.
Ryghte
ascension
,
is
defined
to
bee
that
,
Ryght
ascention
.
Croked
ascention
.
with
whiche
a
greater
portion
of
the
Equinoctiall
dooth
ascende
.
And
that
is
called
Crooked
or
Oblique
ascension
,
with
whiche
a
lesser
portion
of
the
Equinoctiall
doth
ascende
.
Scholar
.
I
heare
you
speake
of
a
lesser
portion
and
a
greater
portion
,
but
where
vnto
those
comparisons
ought
to
be
referred
,
I
can
not
tell
,
excepte
I
shall
referre
the
one
to
the
other
.
Master
.
That
maye
you
not
doo
,
for
so
one
ascension
depiction of two globes.
mighte
bee
called
right
&
croked
also
,
at
the
least
in
diuers
comparisons
:
but
that
can
not
be
,
nother
is
it
permitted
by
any
astronomers
Scholar
.
How
may
it
appeare
that
suche
absurditie
woulde
follow
?
Master
.
To
the
intente
that
I
maye
alleage
nothinge
,
but
that
whiche
shall
not
only
be
certaine
and
true
,
but
also
shall
be
manifest
to
you
,
I
will
firste
instructe
you
in
the
vnderstanding
of
those
Ascensions
,
and
after
that
I
will
return
to
the
proof
of
these
my
woordes
.
And
for
the
better
vnderstandinge
of
both
definitions
,
I
will
name
vnto
you
a
thirde
Ascension
,
which
must
be
as
the
rule
of
those
other
2
,
and
that
is
the
Meane
ascension
,
for
seyng
you
can
not
well
refer
greater
and
lesser
but
other
to
one
common
meane
,
or
els
eche
to
other
:
and
I
haue
said
before
(
and
wil
proue
it
anon
)
that
they
can
not
be
compared
togither
,
The
meane
Ascension
.
therfore
must
they
bee
referred
and
compared
to
one
common
meane
,
whiche
I
call
the
Mean
ascension
,
bicause
that
with
it
ther
ascendeth
not
so
muche
of
the
Equinoctiall
,
as
with
the
right
ascension
,
nor
so
lytle
as
doth
ascende
with
the
crooked
ascension
.
and
for
this
cause
may
it
well
be
called
a
Mean
ascension
.
Again
it
maye
be
called
a
Meane
ascension
,
bicause
it
is
without
all
excesse
:
for
the
portion
of
the
Equinoctiall
whiche
ascendeth
with
it
,
is
equall
to
it
in
precisenes
of
degrees
,
so
that
neither
of
them
excedeth
other
.
Scholar
.
It
seemeth
reasonable
that
all
excesses
beinge
referred
to
anye
one
thinge
,
do
approue
that
one
as
a
meane
betwene
them
,
namely
when
the
excesses
decline
to
both
extremities
,
as
more
and
fewer
,
greater
&
lesser
do
.
but
in
al
this
kinde
of
doctrine
,
the
wordes
are
more
easye
to
bee
vnderstande
,
then
the
matter
.
Therfore
excepte
ye
do
with
examples
declare
these
varieties
of
Ascensions
,
I
doubte
it
wyll
be
longe
before
I
shall
well
conceaue
them
and
rightlye
distincte
them
.
Master
.
You
haue
learned
before
,
that
there
is
two
varieties
of
Spheres
,
a
Righte
Sphere
,
and
a
Bowing
sphere
:
and
as
in
eche
of
these
the
Equinoctiall
doth
kepe
one
vniforme
ascension
,
that
is
to
say
,
that
in
24
houres
iustlye
all
the
equinoctiall
doth
ascende
,
and
so
consequently
in
euerye
hower
of
the
daye
15
degrees
of
the
Equinoctiall
doo
passe
the
righte
horizont
,
so
the
Zodiake
whiche
is
the
circle
of
the
signes
,
by
meanes
of
his
obliquitie
,
dooth
not
keepe
vniforme
ascension
anye
where
in
any
position
of
Sphere
.
for
although
the
whole
Zodiake
do
ascend
iustly
in
24
howers
,
yet
in
euery
hower
,
vnequal
portions
of
it
do
ascend
,
and
that
diuersly
,
according
to
the
diuersities
of
the
Climates
.
Certain
generall
rules
in
a
righte
Sphere
.
But
in
a
generaltye
of
differences
,
you
may
take
these
generall
rules
.
In
the
right
sphere
,
euerye
quarter
of
the
Zodiak
hath
an
equall
or
Meane
ascension
,
with
euery
quarter
of
the
equinoctiall
,
beginning
the
quarters
at
the
4
principall
points
,
whiche
I
haue
before
set
forthe
:
for
if
you
shoulde
take
three
signes
in
other
partes
of
the
Zodiak
,
their
ascensions
wyll
not
agree
with
a
quarter
of
the
Equinoctiall
,
sith
there
is
no
one
signe
that
doth
equally
agree
in
ascension
with
the
lyke
portion
of
the
Equinoctial
,
that
is
to
say
,
with
30
degres
in
it
.
Scholar
.
This
rule
is
in
Ioannes
de
Sacro
bosco
,
and
in
Orontius
also
.
Master
.
Then
you
beleue
it
the
better
.
Scholar
.
Yea
in
deede
.
Master
.
Then
tell
me
whether
the
ascension
of
one
of
those
quarters
of
the
Zodiake
,
ought
to
be
called
a
Right
ascension
,
or
a
Crooked
ascension
.
Scholar
.
Neither
of
bothe
,
as
I
do
vnderstande
their
definitions
,
seeyng
the
arke
of
the
Equinoctiall
that
ascendeth
with
them
,
is
nother
greater
nother
yet
lesser
then
they
,
as
these
definitions
do
importe
,
but
is
equal
with
them
,
and
therfore
it
seemeth
to
me
more
apte
to
call
it
a
Meane
ascension
after
your
definition
.
Master
.
You
saye
truthe
,
and
therefore
is
their
doctrine
imperfecte
,
that
make
but
two
ascensions
,
where
thre
ought
to
be
distincte
,
(
and
them selues
name
thre
in
vse
,
and
but
2
in
distinction
and
definition
)
namely
seyng
(
as
Tullye
hath
sayd
)
it
is
the
greatest
faulte
that
can
be
,
to
omitte
any
membre
in
diuision
:
but
to
omitte
their
faultes
in
omission
,
and
to
retourne
to
their
better
declaration
.
This
second
rule
do
they
also
approoue
,
yea
and
natures
ordre
doth
necessarily
inferre
the
same
,
that
euerye
twoo
signes
or
partes
of
Signes
equall
in
quantitie
,
and
lyke
distaunte
from
anye
one
of
the
4
principall
pointes
,
haue
equall
ascensions
eche
to
other
.
Scholar
.
That
is
to
meane
,
that
Taurus
,
and
Aquarius
haue
equall
ascension
,
bicause
they
are
equally
distaunt
from
the
Equinoctiall
pointe
of
Aries
.
Master
.
And
so
haue
Taurus
and
Leo
,
bicause
they
differre
equallye
frome
the
Tropicall
pointe
of
Cancer
,
and
so
of
all
the
other
.
But
to
the
intente
that
you
maye
the
better
vnderstande
all
this
that
is
saide
,
and
the
reste
that
is
to
be
saide
,
I
haue
here
set
forthe
in
a
table
the
iuste
numbres
of
degrees
of
the
Equinoctiall
circle
,
which
do
answer
to
the
degrees
of
euery
signe
in
their
ascensions
in
the
right
Sphere
.
So
that
if
you
desire
to
knowe
the
ascension
of
any
degree
of
anye
signe
,
firste
seeke
out
the
signe
,
and
then
in
the
firste
columne
looke
for
the
noumbre
of
the
degree
,
against
whiche
in
the
common
corner
vnderneth
the
Signe
you
may
see
the
numbre
of
the
degrees
and
Minutes
of
the
Equinoctiall
,
that
do
ascende
with
that
degree
of
the
signe
.
And
those
degrees
be
accompted
from
the
beginning
of
the
Equinoctiall
at
Aries
,
and
so
orderly
after
the
naturall
course
of
the
signes
.
wherby
you
maye
perceaue
,
that
Aries
,
Taurus
and
Gemini
all
three
togither
haue
for
their
ascension
90
degrees
,
whiche
numbre
agreeth
with
the
quantitie
of
3.
signes
,
and
therfore
is
their
ascension
Meane
.
Also
I
maye
A
TABLE
FOR
THE
ASCENSIONS
of
the
twelue
Signes
in
the
Righte
Sphere
.
Degrees
of
signes
.
|
Aries
|
Taurus
|
Gemini
|
Cancer
|
Leo
|
Virgo
|
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
1
|
0
|
55
|
28
|
52
|
58
|
51
|
91
|
5
|
123
|
14
|
153
|
3
|
2
|
1
|
50
|
29
|
49
|
59
|
54
|
92
|
11
|
124
|
16
|
154
|
0
|
3
|
2
|
45
|
30
|
47
|
60
|
57
|
93
|
16
|
125
|
18
|
154
|
57
|
4
|
3
|
40
|
31
|
45
|
62
|
0
|
94
|
22
|
126
|
20
|
155
|
54
|
5
|
4
|
35
|
32
|
43
|
63
|
3
|
95
|
27
|
127
|
21
|
156
|
50
|
6
|
5
|
30
|
33
|
41
|
64
|
7
|
96
|
32
|
128
|
23
|
157
|
47
|
7
|
6
|
26
|
34
|
39
|
65
|
10
|
97
|
37
|
129
|
24
|
158
|
44
|
8
|
7
|
21
|
35
|
38
|
66
|
14
|
98
|
43
|
130
|
25
|
159
|
40
|
9
|
8
|
16
|
36
|
36
|
67
|
18
|
99
|
48
|
131
|
26
|
160
|
36
|
10
|
9
|
11
|
37
|
35
|
68
|
21
|
100
|
53
|
132
|
27
|
161
|
32
|
11
|
10
|
7
|
38
|
34
|
69
|
26
|
101
|
59
|
133
|
28
|
162
|
48
|
12
|
11
|
2
|
39
|
33
|
70
|
30
|
103
|
3
|
134
|
28
|
163
|
24
|
13
|
11
|
57
|
40
|
33
|
71
|
34
|
104
|
8
|
135
|
28
|
164
|
20
|
14
|
12
|
53
|
41
|
32
|
72
|
38
|
105
|
12
|
136
|
28
|
165
|
16
|
15
|
13
|
49
|
42
|
32
|
73
|
43
|
106
|
17
|
137
|
28
|
166
|
11
|
16
|
14
|
44
|
43
|
32
|
74
|
48
|
107
|
22
|
138
|
28
|
167
|
7
|
17
|
15
|
40
|
44
|
32
|
75
|
52
|
108
|
26
|
139
|
27
|
168
|
3
|
18
|
16
|
36
|
45
|
32
|
76
|
57
|
109
|
30
|
140
|
27
|
168
|
58
|
19
|
17
|
32
|
46
|
32
|
78
|
2
|
110
|
34
|
141
|
26
|
169
|
53
|
20
|
18
|
28
|
47
|
33
|
79
|
7
|
111
|
39
|
142
|
25
|
170
|
49
|
21
|
19
|
24
|
48
|
34
|
80
|
12
|
112
|
42
|
143
|
24
|
171
|
44
|
22
|
20
|
20
|
49
|
35
|
81
|
17
|
113
|
46
|
144
|
22
|
172
|
39
|
23
|
21
|
16
|
50
|
36
|
82
|
23
|
114
|
50
|
145
|
21
|
17
|
34
|
24
|
22
|
13
|
51
|
37
|
83
|
28
|
115
|
53
|
146
|
19
|
174
|
30
|
25
|
23
|
10
|
52
|
39
|
84
|
33
|
116
|
57
|
147
|
17
|
175
|
25
|
26
|
24
|
6
|
53
|
40
|
85
|
38
|
118
|
0
|
148
|
15
|
176
|
20
|
27
|
25
|
3
|
54
|
42
|
86
|
44
|
119
|
3
|
149
|
13
|
177
|
15
|
28
|
26
|
0
|
55
|
44
|
87
|
49
|
120
|
6
|
150
|
11
|
178
|
10
|
29
|
26
|
57
|
56
|
46
|
88
|
55
|
121
|
9
|
151
|
8
|
179
|
5
|
30
|
27
|
94
|
57
|
49
|
90
|
0
|
122
|
11
|
152
|
6
|
180
|
0
|
THE
SECOND
TABLE
OF
THE
Ascensions
of
the
twelue
Signes
in
the
Righte
Sphere
.
Degrees
of
signes
.
|
Libra
.
|
Scorpius
|
Sagitari
.
|
Capricor
.
|
Aquarius
|
Pisces
|
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
1
|
180
|
55
|
208
|
52
|
238
|
51
|
272
|
5
|
303
|
14
|
333
|
3
|
2
|
181
|
50
|
209
|
49
|
239
|
54
|
272
|
11
|
304
|
16
|
334
|
0
|
3
|
182
|
45
|
210
|
47
|
240
|
57
|
273
|
16
|
305
|
18
|
334
|
57
|
4
|
183
|
40
|
211
|
45
|
242
|
0
|
274
|
22
|
306
|
20
|
335
|
54
|
5
|
184
|
35
|
212
|
43
|
243
|
3
|
275
|
27
|
307
|
21
|
336
|
50
|
6
|
185
|
30
|
213
|
41
|
244
|
7
|
276
|
32
|
308
|
23
|
337
|
47
|
7
|
186
|
26
|
214
|
39
|
245
|
10
|
277
|
37
|
309
|
24
|
338
|
44
|
8
|
187
|
21
|
215
|
38
|
246
|
14
|
278
|
43
|
310
|
25
|
339
|
40
|
9
|
188
|
16
|
216
|
36
|
247
|
18
|
279
|
48
|
311
|
26
|
340
|
36
|
10
|
189
|
11
|
217
|
35
|
248
|
21
|
280
|
53
|
312
|
27
|
341
|
32
|
11
|
190
|
7
|
218
|
34
|
249
|
26
|
281
|
58
|
313
|
28
|
342
|
28
|
12
|
191
|
2
|
219
|
33
|
250
|
30
|
283
|
3
|
314
|
28
|
343
|
24
|
13
|
191
|
57
|
220
|
33
|
251
|
34
|
284
|
8
|
315
|
28
|
344
|
20
|
14
|
192
|
53
|
221
|
32
|
252
|
38
|
285
|
12
|
316
|
28
|
345
|
10
|
15
|
193
|
49
|
222
|
32
|
253
|
43
|
286
|
17
|
317
|
28
|
346
|
11
|
16
|
194
|
44
|
223
|
32
|
254
|
48
|
287
|
22
|
317
|
28
|
347
|
7
|
17
|
195
|
40
|
224
|
32
|
255
|
51
|
288
|
26
|
319
|
27
|
348
|
3
|
18
|
196
|
36
|
225
|
32
|
256
|
57
|
289
|
30
|
320
|
17
|
348
|
58
|
19
|
197
|
32
|
226
|
32
|
258
|
2
|
290
|
34
|
321
|
26
|
349
|
53
|
20
|
198
|
28
|
217
|
33
|
259
|
7
|
291
|
39
|
322
|
25
|
350
|
49
|
21
|
199
|
24
|
228
|
34
|
260
|
12
|
292
|
42
|
323
|
24
|
351
|
44
|
22
|
200
|
10
|
229
|
35
|
261
|
17
|
293
|
46
|
324
|
22
|
352
|
39
|
23
|
201
|
16
|
230
|
36
|
262
|
23
|
294
|
50
|
325
|
21
|
353
|
34
|
24
|
202
|
13
|
221
|
37
|
263
|
28
|
295
|
53
|
326
|
19
|
354
|
30
|
25
|
203
|
9
|
232
|
39
|
264
|
33
|
296
|
58
|
327
|
17
|
355
|
25
|
26
|
204
|
6
|
233
|
40
|
265
|
38
|
298
|
0
|
328
|
15
|
356
|
20
|
27
|
205
|
3
|
234
|
42
|
266
|
44
|
299
|
3
|
329
|
13
|
357
|
15
|
28
|
206
|
0
|
235
|
44
|
267
|
49
|
300
|
6
|
330
|
11
|
358
|
10
|
29
|
206
|
57
|
236
|
46
|
268
|
55
|
301
|
9
|
331
|
8
|
359
|
5
|
30
|
297
|
54
|
237
|
49
|
270
|
0
|
302
|
22
|
332
|
6
|
360
|
0
|
saye
,
that
the
laste
degree
of
Gemini
,
or
anye
starre
in
that
degree
,
or
in
the
laste
degree
of
Virgo
,
Sagittarius
or
Pisces
,
haue
a
Meane
Ascension
,
so
that
the
same
starre
haue
no
latitude
:
how
be
it
in
the
eande
of
Gemini
and
Sagittarye
,
althoughe
they
haue
neuer
so
muche
latitude
,
yet
is
their
ascension
meane
.
whiche
prerogatiue
those
two
points
haue
,
bicause
the
lynes
or
circles
of
their
longitudes
doo
touche
bothe
the
Poles
of
the
Zodiake
and
of
the
Equinoctiall
,
and
so
dothe
no
other
circle
of
longitude
:
wherefore
all
starres
out
of
those
places
limited
where
so
euer
they
be
,
they
haue
no
Meane
ascension
,
but
other
Ryghte
ascension
,
or
els
Crooked
.
Scholar
.
Thus
I
perceaue
that
the
twoo
tropike
pointes
haue
a
priuiledge
aboue
the
two
equinoctiall
pointes
in
the
ascensions
.
Master
.
It
seemeth
so
in
the
righte
sphere
,
but
in
the
Oblique
sphere
the
Equinoctiall
pointes
haue
the
greater
priuilege
:
for
alwaies
in
all
places
where
they
doo
ascende
,
they
keepe
their
meane
ascension
,
but
so
dooth
not
the
tropike
pointes
in
anye
oblique
sphere
.
no
nother
anye
starres
of
their
longitude
,
that
is
to
saye
in
their
Colure
.
for
although
twoo
pointes
in
the
skie
,
where
their
Colure
dooth
cutte
the
Equinoctiall
circle
,
haue
a
meane
ascension
,
yet
in
those
2.
places
is
there
no
starre
that
hath
beene
noted
,
as
hereafter
you
shall
better
vnderstand
.
But
that
you
maye
in
the
mean
season
knowe
what
signes
doo
ascende
righte
,
and
which
do
ascende
crokedlye
in
the
righte
sphere
,
you
shall
marke
this
lytle
table
whiche
I
haue
drawen
out
of
the
former
great
table
,
where
you
see
that
4
signes
agree
styll
in
their
ascension
,
and
the
firste
4
haue
but
27
degrees
and
54
minutes
of
the
Equinoctial
answering
to
eche
of
their
ascensions
:
the
other
4
signes
haue
29
degrees
,
55
minutes
for
their
ascension
:
and
the
laste
4
haue
32
degrees
and
11
minutes
agreeing
to
theyr
rising
,
which
degrees
and
minutes
added
togither
,
do
make
iuste
90
degrees
that
is
exactlye
one
quarter
of
the
equinoctiall
A
briefe
table
for
the
righte
Sphere
.
Ascension
.
|
The
twelue
Signes
.
|
Partes
of
the
Equinoctiall
|
Partes
of
tyme
|
|
|
Deg
.
|
Min.
|
Ho
.
|
Min.
|
Crooked
|
Aries
|
Virgo
|
Libra
|
Pisces
.
|
27
|
54
|
1
|
51
3
/
5
|
Crooked
|
Taurus
|
Leo
|
Scorpius
|
Aquarius
|
29
|
55
|
1
|
59
2
/
3
|
Ryghte
|
Gemini
|
Cancer
|
Sagitarius
|
Capricornus
|
32
|
11
|
2
|
8
14
/
15
|
The
addition
of
those
partes
eche
to
his
owne
kinde
|
90
|
0
|
6
|
0
|
and
so
are
eche
ternary
of
those
Signes
one
iuste
quarter
of
the
Zodiake
.
Scholar
.
And
in
like
case
I
perceaue
,
the
6
howers
of
time
that
answereth
to
those
whole
quarters
,
is
also
the
iuste
quarter
of
the
naturall
day
,
which
amounteth
by
the
addition
of
the
three
seuerall
times
agreing
to
those
3
seuerall
ascensions
.
And
as
I
vnderstand
it
,
the
quantitye
of
tyme
is
gathered
after
the
rate
of
15
degrees
ascendinge
euerye
hower
,
as
you
saide
before
.
so
that
euerye
degree
asketh
4
minutes
of
an
hower
:
and
15
minutes
of
a
degree
in
the
Equinoctiall
doo
ryse
in
one
minute
of
an
hower
:
for
this
is
alwaies
to
bee
remembred
,
that
a
minute
is
euer
more
the
60
part
of
that
thyng
whervnto
it
is
referred
.
But
now
ther
commeth
to
my
mind
the
sayinge
of
Ioannes
de
Sacro
Bosco
,
whiche
longe
hathe
troubled
my
minde
,
and
I
can
not
learne
of
anye
man
howe
to
vnderstande
him
well
:
for
in
mine
opinion
his
woordes
import
an
impossibilitie
.
he
blameth
this
argument
as
euel
:
These
two
arkes
are
equall
,
and
they
begin
to
rise
togither
,
and
continually
ther
riseth
a
greater
portion
of
the
one
arke
then
of
the
other
:
ergo
that
arke
will
bee
full
risen
soonest
,
whose
greater
portion
did
alwaies
rise
.
This
argumente
seemeth
inuincible
in
mine
opinion
,
and
yet
Iohn
de
Sacro
bo
sco
for
improuing
of
it
alleageth
an
example
,
wherby
as
he
seemeth
to
intend
,
the
antecedent
maye
be
true
,
and
the
consequente
false
:
and
therefore
the
argumente
muste
needes
be
naught
.
Master
.
Repeat
you
his
example
,
that
we
may
examine
it
:
Scholar
.
He
willeth
to
take
any
quarter
of
the
Zodiake
,
compared
with
his
like
quarter
of
the
Equinoctiall
,
and
to
begin
with
that
quarter
from
the
fyrste
pointe
of
Aries
,
to
the
latter
ende
of
Gemini
,
alwaies
the
greater
portion
riseth
of
the
Zodiake
,
and
the
lesser
of
the
equinoctiall
,
and
yet
those
two
quarters
ascend
fully
togither
:
and
the
lyke
muste
you
vnderstande
of
the
thirde
quarter
,
from
the
beginning
of
Libra
,
to
the
eande
of
Sagittarye
.
but
contrarye
waies
,
in
the
quarter
that
lyeth
frome
the
fyrste
parte
of
Cancer
,
to
the
laste
of
Virgo
,
the
portion
of
the
Equin
octiall
in
ryfynge
,
is
styll
greater
then
the
parte
of
the
Zodiake
that
riseth
with
it
:
and
yet
those
bothe
arkes
doo
rise
iustly
to
gither
at
the
eande
.
Master
.
Here
is
a
greate
fallation
by
Amphibologye
,
as
Logitians
do
call
it
,
so
that
in
one
sence
it
maye
be
true
,
and
in
an
other
it
is
false
.
And
fyrste
for
declaration
of
Iohn
his
meaning
(
as
I
thinke
)
marke
as
many
partes
of
those
2
firste
quarters
as
you
lyste
,
and
still
by
the
former
table
,
as
well
as
by
tournynge
the
Sphere
it selfe
,
it
wyll
appeare
manyfestly
,
that
the
portion
of
the
Zodiake
is
euer
greater
then
the
matche
portion
of
the
Equinoctiall
.
Scholar
.
That
is
moste
true
.
for
with
12
degrees
of
Aries
there
ascendeth
of
the
equinoctiall
11
degrees
and
twoo
minutes
only
of
the
Equinoctiall
,
that
is
59
minutes
lesse
:
with
30
degrees
of
Aries
there
riseth
but
27
degrees
and
54
minutes
,
whiche
is
lesse
by
two
degrees
and
syxe
minutes
:
also
in
Taurus
,
15
degrees
hath
for
their
ascension
42
degres
and
32
minutes
,
that
is
twoo
degrees
and
28
minutes
to
lytle
:
the
laste
of
Taurus
ascendeth
with
57
degrees
and
49
minutes
,
whiche
shoulde
be
60
if
it
were
equall
with
the
degrees
of
the
Zodiake
.
Againe
the
16
degree
of
Gemini
answereth
to
the
ascension
of
the
74
degree
and
48
minute
of
the
equinoctial
,
whiche
in
equalitye
would
be
76
:
and
the
29
degree
of
Gemini
should
haue
by
ordre
of
equalitie
the
89
degree
of
the
equinoctial
,
&
hath
but
88
degrees
&
55
minuts
,
which
is
lesser
by
5
minutes
then
equalitye
requireth
,
and
so
doth
it
appear
in
all
the
reste
,
saue
in
the
verye
laste
degree
of
Gemini
,
wher
bothe
numbres
appeare
euen
.
Mast
.
Then
are
the
wordes
of
Iohn
desacro
bosco
true
.
Scholar
.
This
matter
troubleth
me
to
muche
:
for
of
this
am
I
assured
,
that
if
anye
two
quantities
be
equall
togyther
,
and
a
lesser
portion
of
the
fyrste
matched
with
a
greater
part
of
the
second
,
then
of
necessitye
that
parte
that
remaineth
of
the
fyrste
quantitie
,
must
needes
be
greater
then
that
that
resteth
of
the
seconde
.
Master
.
That
is
true
also
:
for
if
you
abate
vnequall
partes
from
2
equall
quantities
,
the
portions
that
remaine
will
be
vnequall
,
and
that
parte
will
bee
leaste
,
frome
whiche
the
greater
portion
was
abated
.
Scholar
.
As
that
can
not
be
false
,
so
it
seemeth
to
me
,
that
seyng
there
doth
ascende
with
the
whole
signe
of
Aries
but
27
degrees
,
and
54
minutes
,
there
must
needes
remain
62
de
grees
and
6
minutes
of
that
quarter
,
and
that
is
more
then
the
60
degrees
which
resteth
of
the
like
quarter
of
the
Zodiake
.
Now
those
62
degrees
and
6
minutes
will
ascend
with
the
60
degrees
of
the
Zodiake
,
so
that
then
there
dooth
not
styll
ascende
a
lesser
portion
of
the
Equinoctiall
:
for
as
the
fyrste
portion
was
lesser
,
so
this
seconde
parte
is
greater
.
Master
.
Your
coniecture
is
good
:
and
to
approue
it
the
better
,
you
may
conferre
some
lesser
partes
of
those
2
quarters
togither
,
as
from
the
20
degree
of
Taurus
,
to
the
10
degree
of
Gemini
,
the
degrees
betweene
them
are
20
:
&
to
know
the
arke
of
the
equinoctiall
that
ascendeth
with
those
20
degrees
,
subtracte
the
lesser
from
the
greater
,
and
the
ascension
of
those
20
degrees
wyll
remayne
.
Scholar
.
The
ascension
of
the
20
degree
of
Taurus
is
47
degrees
and
33
minutes
:
the
ascension
of
the
10
degree
of
Geminiis
68
degrees
,
and
21
minutes
.
wherfore
setting
those
numbres
in
conuenient
ordre
,
and
making
subtraction
duly
,
ther
resteth
20
degres
;
&
48
minuts
,
so
is
this
portion
of
the
equinoctiall
the
greater
by
48
minutes
.
Master
.
Proue
again
from
the
28
degree
of
Taurus
,
to
the
28
degree
of
Gemini
:
whiche
difference
is
30
degrees
.
Scholar
.
With
the
28
degree
of
Taurus
there
dooth
ascende
55
degrees
,
and
44
minutes
:
and
with
the
28
of
Gemini
,
87
and
49.
and
by
Subtraction
the
difference
appeareth
to
bee
32
degrees
,
and
5
minutes
.
so
is
the
arke
of
that
Equinoctiall
greater
by
two
degrees
and
5
minutes
,
then
the
matche
arke
of
the
Zodiake
.
And
therefore
are
not
Iohn
de
Sacro
bosco
his
woordes
true
.
Master
.
Prooue
yet
more
before
you
condemne
him
.
try
the
arke
from
the
tenth
degree
of
Taurus
,
to
the
22
degre
of
the
same
signe
,
whiche
arke
includeth
12
degrees
of
the
Zodiak
.
Schol
.
The
10
degre
of
Taurus
,
ascendeth
with
37
degrees
&
35
minutes
of
the
equinoctial
the
22
degre
of
the
same
sign
hath
for
his
ascension
49
degrees
&
35
minuts
,
the
difference
between
them
by
subtraction
is
found
to
be
12
degres
iust
:
and
so
that
arke
of
the
Equinoctiall
is
equall
with
his
matche
arke
in
the
Zodiake
.
Master
.
Yet
ones
more
proue
the
arke
from
the
last
degre
of
Aries
to
the
second
degre
of
Gemini
,
which
ark
is
32
degrees
.
Scholar
.
The
last
degree
of
Aries
riseth
with
27
degrees
,
and
54
minutes
:
and
the
2
of
Gemini
hath
59
degrees
and
54
minutes
in
his
ascension
.
betwene
which
2
numbres
,
the
distaunce
is
32
degrees
exactly
,
and
so
are
those
2
arkes
equall
also
,
and
neither
of
those
2
examples
do
make
the
arke
of
the
Equinoctiall
lesser
then
the
matche
arke
in
the
Zodiake
:
so
that
they
make
agaynst
Iohn
de
Sacro
bosco
.
Master
.
In
deede
as
his
woordes
be
placed
in
the
Present
time
,
they
can
not
be
true
,
but
his
meaning
may
be
more
fauourably
gathered
,
by
turning
the
Present
time
into
the
Perfect
time
,
&
referring
the
name
of
ascension
to
the
whole
arke
that
is
fully
rysen
in
that
quarter
,
as
I
dyd
in
the
explication
of
his
wordes
occasion
you
to
make
proofe
:
wherfore
take
anye
parte
of
the
fyrste
quarter
,
and
accompt
from
the
beginninge
of
Aries
:
or
lykewaies
any
part
of
the
thyrd
quarter
,
and
recken
from
the
beginning
of
Libra
,
and
so
shall
you
see
alwaies
that
the
portion
of
the
Zodiake
whiche
is
ascended
,
shall
be
greater
then
the
parte
of
the
Equinoctiall
that
is
risen
with
it
:
&
so
shall
it
continue
euen
to
the
very
laste
degre
of
them
bothe
,
and
then
at
length
doth
both
the
quarters
end
their
ascensions
exactly
togither
.
Scholar
.
As
you
saye
.
nowe
doo
I
perceaue
it
,
so
that
the
faulte
is
rather
in
his
woordes
then
in
his
meanynge
.
Master
.
Such
meane
matters
must
be
winked
at
in
other
,
but
not
folowed
.
And
nowe
for
the
ordre
of
Ascension
of
the
other
2
quarters
which
begin
at
Cancer
&
Capricorne
,
you
shall
vnderstand
the
lyke
:
but
that
the
greater
portion
the
ascendeth
is
referred
to
the
Equinoctial
circle
&
not
to
the
Zodiak
▪
Scholar
.
So
I
vnderstand
by
this
former
table
that
with
the
28
degree
of
Cancer
there
ascendeth
120
degrees
and
6
minutes
of
the
Equinoctiall
,
which
is
two
degrees
and
6
minutes
more
then
equality
woulde
yelde
:
and
with
the
26
degree
of
Virgo
,
there
riseth
the
176
and
20
minutes
of
the
equinoctiall
,
whiche
is
also
more
then
equallenes
by
20
minutes
:
and
so
if
I
take
anye
degre
of
any
signe
in
that
second
quarter
,
or
in
the
fourth
quarter
,
beginning
at
Capricorn
,
I
may
lyghtly
see
by
the
table
that
the
portion
of
the
Equinoctiall
in
his
ascension
is
greater
then
the
matche
arke
of
the
Zodiake
from
the
beginninge
of
Aries
to
that
degree
.
wherby
it
appeareth
that
al
those
6
signes
do
ascend
right
,
bicause
a
greater
portion
of
the
equinoctiall
ascendeth
with
thē
.
Master
.
Then
by
the
like
reason
,
the
other
6
signes
Aries
,
Taurus
,
Gemini
,
Libra
,
Scorpius
and
Sagittarius
do
ascend
crokedly
,
bicause
the
lesser
portion
of
the
Equinoctial
doth
ascend
with
thē
:
after
the
sort
of
conference
,
which
is
contrary
to
the
I
said
before
,
the
4
signes
only
do
ascend
ryght
in
the
Ryght
spher
:
wherefore
you
muste
vnderstande
,
that
for
to
knowe
the
ascension
of
euerye
signe
,
you
must
consider
that
signe
alone
,
and
the
arke
of
the
Equinoctiall
that
dooth
ascend
with
it
,
and
so
shall
you
see
exactly
the
ascension
of
euerye
signe
seuerally
.
And
here
you
shall
vnderstande
,
that
all
Astronomers
commonly
do
call
the
Right
ascension
so
largely
,
An
other
signification
of
right
ascension
.
that
it
extendeth
to
the
ascension
of
all
the
signes
in
a
Right
sphere
:
and
so
they
name
the
Oblique
ascension
the
rising
of
all
the
Signes
in
anye
Oblique
Sphere
,
whereby
it
appeareth
that
they
giue
the
name
of
Ryghte
and
Crooked
ascensions
,
accordinge
to
the
Horizontes
or
pofitions
of
the
Sphere
,
and
not
after
the
quantities
of
time
in
their
ascension
.
And
this
shall
suffice
at
this
time
touchinge
ascensions
in
the
Righte
Sphere
:
in
which
also
the
descensions
or
settinges
vnder
the
Horizont
,
are
equall
with
the
Ascensions
,
Of
the
descention
of
Signes
.
so
that
they
need
not
to
haue
anye
peculiare
declaration
:
but
in
the
Oblique
Spheres
it
is
not
so
,
but
contrary
waies
.
those
signes
that
do
ascende
righte
,
doo
descende
crooked
:
and
they
that
ascende
crooked
,
doo
descend
righte
:
so
that
the
descension
of
anye
signe
in
an
Oblique
sphere
,
is
equall
precisely
to
the
ascension
of
the
contrarye
signe
.
Schollar
.
You
meane
that
the
defcending
of
Aries
is
equal
to
the
ascendinge
of
Libra
,
and
the
descendinge
of
Taurus
is
one
in
quantity
of
time
with
the
ascension
of
Scorpius
.
Master
.
So
is
it
in
deed
.
And
in
this
greate
varietie
you
shall
marke
one
constaunte
vniformitie
,
that
the
ascension
and
descension
of
any
signe
in
any
croked
sphere
ioyned
by
addition
togither
,
doo
make
an
equall
summe
of
time
with
the
ascension
and
descension
of
the
same
signe
in
a
righte
sphere
,
in
lyke
sorte
ioyned
togither
:
but
to
the
intente
that
you
maye
vnderstande
all
these
thinges
the
better
,
and
also
knowe
the
iuste
ascension
of
euerye
signe
in
this
our
Climat
where
the
eleuation
of
the
pole
is
52
degrees
,
I
haue
drawen
heere
a
speciall
table
for
that
latitude
.
in
whiche
you
shall
vse
the
like
manner
of
entringe
,
as
you
did
in
the
other
,
so
that
A
TABLE
OF
ASCENSION
OF
the
Signes
in
52
degrees
of
Latitude
.
Degrees
of
signes
.
|
Aries
|
Taurus
|
Gemini
|
Cancer
|
Leo
|
Virgo
|
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
0
|
0
|
0
|
12
|
48
|
29
|
42
|
56
|
11
|
94
|
6
|
137
|
0
|
1
|
0
|
24
|
13
|
16
|
30
|
24
|
57
|
17
|
95
|
30
|
138
|
37
|
2
|
0
|
48
|
13
|
45
|
31
|
7
|
58
|
24
|
96
|
54
|
139
|
54
|
3
|
1
|
13
|
14
|
14
|
31
|
50
|
59
|
31
|
98
|
18
|
141
|
20
|
4
|
1
|
37
|
14
|
43
|
32
|
34
|
60
|
39
|
99
|
42
|
142
|
47
|
5
|
2
|
2
|
15
|
12
|
33
|
18
|
61
|
48
|
101
|
7
|
144
|
13
|
6
|
2
|
16
|
15
|
42
|
34
|
3
|
62
|
58
|
102
|
32
|
145
|
40
|
7
|
2
|
51
|
16
|
13
|
34
|
49
|
64
|
9
|
103
|
57
|
147
|
6
|
8
|
3
|
15
|
16
|
43
|
35
|
36
|
65
|
20
|
105
|
22
|
148
|
32
|
9
|
3
|
40
|
17
|
14
|
36
|
24
|
66
|
32
|
106
|
47
|
149
|
58
|
10
|
4
|
5
|
17
|
45
|
37
|
12
|
67
|
45
|
108
|
12
|
151
|
24
|
11
|
4
|
30
|
18
|
16
|
38
|
1
|
68
|
59
|
109
|
38
|
152
|
50
|
12
|
4
|
55
|
18
|
48
|
38
|
51
|
70
|
13
|
111
|
4
|
154
|
16
|
13
|
5
|
20
|
19
|
20
|
39
|
42
|
71
|
28
|
112
|
30
|
155
|
42
|
14
|
5
|
45
|
19
|
52
|
40
|
34
|
72
|
44
|
113
|
56
|
157
|
8
|
15
|
6
|
10
|
20
|
25
|
41
|
26
|
74
|
0
|
115
|
23
|
158
|
39
|
16
|
6
|
35
|
20
|
59
|
42
|
19
|
75
|
17
|
116
|
49
|
160
|
0
|
17
|
7
|
1
|
21
|
34
|
43
|
13
|
76
|
34
|
118
|
15
|
161
|
26
|
18
|
7
|
26
|
22
|
8
|
44
|
8
|
77
|
52
|
119
|
42
|
162
|
52
|
19
|
7
|
52
|
22
|
43
|
45
|
3
|
79
|
11
|
121
|
8
|
164
|
18
|
20
|
8
|
18
|
23
|
18
|
45
|
59
|
80
|
30
|
122
|
35
|
165
|
43
|
21
|
8
|
44
|
23
|
54
|
46
|
56
|
81
|
50
|
124
|
2
|
167
|
9
|
22
|
9
|
11
|
24
|
31
|
47
|
54
|
83
|
10
|
125
|
28
|
168
|
35
|
23
|
9
|
37
|
25
|
8
|
48
|
53
|
84
|
31
|
126
|
55
|
170
|
1
|
24
|
10
|
4
|
25
|
45
|
49
|
53
|
85
|
51
|
128
|
22
|
171
|
27
|
25
|
10
|
31
|
26
|
23
|
50
|
54
|
87
|
12
|
129
|
48
|
172
|
52
|
26
|
10
|
58
|
27
|
2
|
51
|
56
|
88
|
34
|
131
|
15
|
174
|
18
|
27
|
11
|
25
|
27
|
41
|
52
|
59
|
89
|
57
|
132
|
41
|
175
|
44
|
28
|
11
|
53
|
28
|
21
|
54
|
2
|
91
|
20
|
134
|
8
|
177
|
9
|
29
|
12
|
20
|
29
|
1
|
55
|
6
|
92
|
43
|
135
|
34
|
178
|
35
|
30
|
12
|
48
|
29
|
42
|
56
|
11
|
94
|
6
|
137
|
0
|
180
|
0
|
Degrees
of
signes
.
|
Libra
|
Scorpius
|
Sagittari
.
|
Capricor
.
|
Aquarius
|
Pisces
|
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
0
|
181
|
0
|
223
|
0
|
265
|
54
|
303
|
49
|
330
|
18
|
347
|
12
|
1
|
181
|
25
|
224
|
26
|
267
|
17
|
304
|
54
|
330
|
59
|
347
|
40
|
2
|
182
|
51
|
125
|
52
|
268
|
40
|
305
|
58
|
331
|
39
|
348
|
7
|
3
|
184
|
16
|
227
|
19
|
270
|
3
|
307
|
1
|
332
|
19
|
348
|
35
|
4
|
185
|
42
|
228
|
45
|
271
|
26
|
308
|
4
|
332
|
58
|
349
|
2
|
5
|
187
|
8
|
230
|
12
|
272
|
48
|
309
|
6
|
333
|
37
|
349
|
29
|
6
|
188
|
33
|
231
|
38
|
274
|
9
|
310
|
7
|
334
|
15
|
349
|
56
|
7
|
189
|
59
|
233
|
5
|
275
|
29
|
311
|
7
|
334
|
52
|
350
|
23
|
8
|
191
|
25
|
234
|
32
|
276
|
50
|
312
|
6
|
335
|
29
|
350
|
49
|
9
|
192
|
51
|
235
|
58
|
278
|
10
|
313
|
4
|
336
|
6
|
351
|
16
|
10
|
194
|
17
|
237
|
25
|
279
|
30
|
314
|
1
|
336
|
42
|
351
|
42
|
11
|
195
|
42
|
238
|
52
|
280
|
49
|
314
|
57
|
337
|
17
|
352
|
8
|
12
|
197
|
8
|
240
|
18
|
282
|
8
|
315
|
52
|
337
|
52
|
352
|
34
|
13
|
198
|
34
|
241
|
45
|
203
|
20
|
316
|
47
|
338
|
26
|
352
|
59
|
14
|
200
|
0
|
243
|
11
|
284
|
43
|
317
|
41
|
339
|
1
|
353
|
25
|
15
|
201
|
26
|
244
|
37
|
286
|
9
|
318
|
34
|
339
|
35
|
353
|
50
|
16
|
202
|
52
|
246
|
4
|
287
|
16
|
319
|
26
|
340
|
8
|
354
|
15
|
17
|
204
|
18
|
247
|
30
|
288
|
32
|
320
|
18
|
340
|
40
|
354
|
40
|
18
|
205
|
44
|
248
|
56
|
289
|
47
|
321
|
9
|
341
|
12
|
355
|
5
|
19
|
207
|
10
|
250
|
22
|
291
|
1
|
321
|
59
|
341
|
44
|
355
|
30
|
20
|
208
|
36
|
251
|
48
|
292
|
15
|
322
|
48
|
342
|
15
|
355
|
55
|
21
|
210
|
2
|
253
|
13
|
293
|
28
|
323
|
36
|
342
|
46
|
356
|
20
|
22
|
211
|
28
|
254
|
38
|
294
|
40
|
324
|
24
|
343
|
17
|
356
|
45
|
23
|
212
|
54
|
256
|
3
|
295
|
51
|
325
|
11
|
343
|
47
|
357
|
9
|
24
|
214
|
20
|
257
|
28
|
297
|
2
|
325
|
57
|
344
|
18
|
357
|
34
|
25
|
215
|
47
|
258
|
53
|
298
|
12
|
326
|
42
|
344
|
48
|
357
|
58
|
26
|
217
|
13
|
260
|
18
|
299
|
21
|
327
|
26
|
345
|
17
|
358
|
23
|
27
|
218
|
40
|
261
|
42
|
300
|
29
|
328
|
10
|
345
|
46
|
358
|
47
|
28
|
220
|
6
|
263
|
6
|
301
|
36
|
328
|
53
|
346
|
15
|
359
|
12
|
29
|
221
|
33
|
264
|
30
|
302
|
43
|
329
|
36
|
346
|
44
|
359
|
36
|
30
|
223
|
0
|
265
|
54
|
303
|
49
|
330
|
18
|
347
|
12
|
360
|
0
|
althoughe
the
numbres
differ
,
yet
the
woorke
differeth
not
in
this
table
.
the
fyrst
columne
containeth
the
degrees
of
the
Signes
,
and
the
other
columnes
doo
containe
the
degrees
&
minutes
of
the
Equinoctiall
vnder
eche
signe
,
accordingly
as
they
doo
answere
to
the
Ascension
of
the
degrees
of
the
same
Signes
.
By
this
table
may
you
see
a
great
diuersitie
in
the
Ascensions
from
those
in
the
Righte
Sphere
:
And
yet
this
maye
you
certainly
obserue
:
that
euerye
two
signes
beinge
contrarye
to
gither
,
the
one
lyinge
againste
the
other
,
as
they
haue
farre
vnlyke
ascensions
,
so
yet
if
you
adde
their
bothe
ascensions
togither
,
they
will
be
equall
to
the
ascensions
of
the
same
twoo
signes
in
the
Right
sphere
.
Scholar
.
Then
in
as
muche
as
the
ascension
of
Aries
is
in
this
latitude
12
degrees
and
48
minutes
,
&
the
ascension
of
Libra
,
43
degrees
iust
,
(
abating
as
I
ought
108
degrees
)
and
so
they
bothe
by
addition
do
make
55
degrees
,
and
48
minutes
.
And
in
the
right
sphere
eche
of
these
signes
hath
for
his
ascension
27
degrees
and
54
minutes
(
for
the
contrarye
signes
there
are
equall
in
their
ascension
)
wherefore
by
addition
there
will
amounte
the
same
summe
precisely
that
was
gathered
before
:
and
so
likewaies
of
Taurus
and
Scorpius
:
their
ascensions
ioyned
togyther
maketh
59
degrees
and
48
minutes
:
but
in
the
righte
sphere
,
those
two
ascensions
maketh
59
,
50.
that
is
twoo
minutes
only
difference
in
two
signes
,
so
is
it
but
one
minute
in
one
signe
,
that
is
not
to
be
regarded
.
Master
.
Not
greately
,
and
especially
in
an
Introduction
.
But
doo
you
marke
here
the
Signes
that
ascende
ryght
,
and
them
that
ascende
crooked
?
Schollar
.
Although
I
see
a
difference
by
this
table
frome
the
other
:
I
had
thoughte
that
the
more
croked
Sphere
had
made
the
more
croked
ascension
onlye
:
but
yet
that
they
alwaies
had
kepte
one
name
in
generall
,
and
not
haue
chaunged
it
.
but
by
your
question
only
I
am
admonished
of
mine
errour
:
for
I
see
that
Libra
(
as
it
is
easilye
vewed
)
dooth
ascend
here
righte
,
and
hath
for
his
ascension
43
degrees
,
and
in
the
Righte
sphere
it
dyd
ascende
crookedly
,
and
had
but
27
degrees
and
54
minutes
for
his
ascention
,
and
therefore
maye
I
doubte
of
all
the
reste
,
tyll
I
haue
examined
theyr
ascensions
better
.
Master
.
To
ease
you
of
payne
,
lo
here
is
a
table
of
theyr
iuste
ascensions
,
which
you
maye
examine
at
leasure
.
A
BRIEFE
TABLE
FOR
52.
degrees
of
latitude
.
Ascention
|
The
12
Signes
.
|
Parts
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
.
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Crooked
|
Aries
,
Pisces
,
|
12
|
48
|
0
|
51
3
/
15
|
Crooked
|
Taurus
,
Aquarius
,
|
16
|
54
|
1
|
7
9
/
15
|
Crooked
|
Gemini
,
Capricornus
|
26
|
29
|
1
|
45
14
/
5
|
Ryghte
|
Cancer
,
Sagittarius
,
|
37
|
55
|
2
|
31
10
/
15
|
Ryghte
|
Leo
,
Scorpius
,
|
42
|
54
|
2
|
51
9
/
15
|
Ryghte
|
Virgo
,
Libra
,
|
43
|
0
|
2
|
52
|
The
addition
of
those
partes
|
180
|
0
|
12
|
0
|
By
this
table
you
maye
perceaue
what
signes
doo
rise
crokedlye
,
and
whiche
doo
ascend
righte
,
and
that
there
bee
of
eche
sorte
6.
so
that
from
Cancer
vnto
Capricorne
all
the
signes
in
direct
ordre
do
ascende
ryghte
,
and
frome
Capricorne
to
Cancer
,
in
naturall
ordre
of
the
Signes
,
all
those
6
signes
do
ryse
crokedly
.
And
this
rule
is
generall
in
all
these
northe
climates
,
that
lye
from
30
degrees
of
latitude
(
vnder
which
Memphis
and
Alcayre
are
and
mounte
Sinay
:
also
the
yste
of
Madera
,
and
the
parte
of
the
weste
Indies
,
called
Terra
florida
)
vnto
66
degrees
and
a
halfe
of
latitude
,
in
that
Climate
wher
Island
lyeth
and
the
north
partes
of
Nor
wayes
,
and
namelye
Halgoland
,
where
Oht
here
dwelte
,
that
was
the
fyrste
discouerer
of
the
north
viage
towarde
Moscouia
.
Scholar
.
That
viage
I
desire
muche
to
vnderstande
,
and
so
do
manye
other
.
Master
.
An
other
time
shall
serue
for
it
,
for
now
we
haue
an
other
matter
in
hande
.
Scholar
.
Then
for
this
present
matter
:
Is
there
anye
other
varietie
of
ascention
betweene
the
Equinoctiall
circle
and
the
Latitude
of
30
degrees
?
Varietes
of
Ascensions
.
Master
.
Yea
,
muche
diuersitye
:
for
(
as
you
haue
hearde
)
vnder
the
equinoctiall
8
signes
do
ascend
crokedly
,
and
but
4
ryght
:
but
from
the
Equinoctiall
vnto
10
degrees
of
latitude
,
6
signes
ascende
ryght
,
(
Gemini
,
Cancer
,
Leo
,
Scorpius
,
Sagittarius
,
Capricornus
)
and
other
syxe
croked
,
that
is
Aries
,
Tarurus
,
Virgo
,
Libra
,
Aquarius
&
Pisces
.
And
from
10
degrees
vnto
30
there
are
8
signes
that
rise
right
,
as
Gemini
,
Cancer
,
Leo
,
Virgo
,
Libra
,
Scorpio
,
Sagittarius
,
and
Capricornus
:
and
the
other
four
,
Aries
,
Taurus
,
Aqua
rius
and
Pisces
,
rise
crokedly
.
but
to
the
intent
that
you
may
haue
the
better
habilitie
to
iudge
of
suche
varieties
,
I
haue
here
sette
forth
diuers
tables
for
examples
sake
:
and
namely
suche
,
whiche
importe
anye
varietie
of
alteration
,
or
helpe
to
the
apte
vnderstandinge
of
the
same
.
A
TABLE
FOR
THE
LAtitude
of
.
1.
degree
.
Ascention
|
The
12
Signes
.
|
Parts
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
.
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Crooked
|
Aries
,
Pisces
,
|
27
|
42
|
1
|
50
12
/
15
|
Crooked
|
Taurus
,
Aquarius
,
|
29
|
44
|
1
|
58
14
/
15
|
Ryghte
|
Gemini
,
Capricornus
|
32
|
8
|
2
|
8
8
/
15
|
Ryghte
|
Cancer
,
Sagittarius
,
|
32
|
16
|
2
|
9
2
/
25
|
Ryghte
|
Leo
,
Scorpius
,
|
30
|
4
|
2
|
0
4
/
15
|
Crooked
|
Virgo
,
Libra
,
|
28
|
6
|
1
|
52
8
/
15
|
The
summe
of
those
partes
|
180
|
0
|
12
|
0
|
A
table
for
10.
degrees
of
latitude
.
Ascention
|
The
12
Signes
.
|
Parts
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Crooked
|
Aries
,
Pisees
,
|
25
|
51
|
1
|
43
6
/
15
|
Crooked
|
Taurus
,
Aquarius
,
|
28
|
14
|
1
|
52
14
/
15
|
Ryghte
|
Gemini
,
Capricornus
|
31
|
31
|
2
|
6
1
/
15
|
Ryghte
|
Cancer
,
Sagittarius
,
|
32
|
53
|
2
|
11
8
/
15
|
Ryghte
|
Leo
,
Scorpius
,
|
31
|
34
|
2
|
6
4
/
15
|
Crooked
|
Virgo
,
Libra
,
|
29
|
57
|
1
|
59
12
/
15
|
The
summe
of
those
partes
|
180
|
0
|
12
|
0
|
A
table
for
11
degrees
of
latitude
.
Ascention
|
The
12
Signes
.
|
Partes
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
.
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Crooked
|
Aries
,
Pisces
,
|
25
|
38
|
1
|
42
8
/
15
|
Crooked
|
Taurus
,
Aquarius
,
|
28
|
4
|
1
|
52
1
/
15
|
Ryghte
|
Gemini
,
Capricornus
|
31
|
27
|
2
|
5
12
/
15
|
Ryghte
|
Cancer
,
Sagittarius
,
|
32
|
57
|
2
|
11
12
/
15
|
Ryghte
|
Leo
,
Scorpius
,
|
31
|
44
|
2
|
6
14
/
15
|
Ryghte
|
Virgo
,
Libra
,
|
30
|
10
|
2
|
0
10
/
15
|
The
summe
of
the
partes
.
|
180
|
0
|
12
|
0
|
A
table
for
20.
degrees
of
latitude
.
Ascension
|
The
12
Signes
.
|
Partes
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Crooked
|
Aries
,
Pisces
,
|
23
|
39
|
1
|
34
9
/
15
|
Crooked
|
Taurus
,
Aquarius
,
|
26
|
27
|
1
|
45
12
/
15
|
Ryghte
|
Gemini
,
Capricornus
|
30
|
48
|
2
|
3
3
/
15
|
Ryghte
|
Cancer
,
Sagitarius
,
|
33
|
36
|
2
|
14
6
/
25
|
Ryghte
|
Leo
,
Scorpius
,
|
33
|
21
|
2
|
13
6
/
15
|
Ryghte
|
Virgo
,
Libra
,
|
32
|
9
|
2
|
8
9
/
15
|
The
summe
of
the
partes
.
|
180
|
0
|
12
|
0
|
A
table
for
29.
degrees
of
latitude
.
Ascension
|
The
12
Signes
.
|
Parts
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Crooked
|
Aries
,
Pisces
,
|
21
|
25
|
1
|
25
10
/
25
|
Crooked
|
Taurus
,
Aquarius
,
|
24
|
37
|
1
|
38
7
/
15
|
Ryghte
|
Gemini
,
Capricornus
|
30
|
1
|
2
|
0
1
/
15
|
Ryghte
|
Cancer
,
Sagittarius
,
|
34
|
23
|
2
|
17
8
/
15
|
Ryghte
|
Leo
,
Scorpius
,
|
35
|
11
|
2
|
20
12
/
15
|
Ryghte
|
Virgo
,
Libra
,
|
34
|
23
|
2
|
17
8
/
15
|
The
summe
of
the
partes
|
180
|
0
|
12
|
0
|
A
table
for
30
degrees
of
latitude
.
Ascension
|
The
12
Signes
.
|
Partes
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
.
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Crooked
|
Aries
,
Pisces
,
|
21
|
9
|
1
|
24
9
/
15
|
Crooked
|
Taurus
,
Aquarius
,
|
24
|
23
|
1
|
37
8
/
15
|
Crooked
|
Gemini
,
Capricornus
|
29
|
56
|
1
|
59
12
/
25
|
Ryghte
|
Cancer
,
Sagittarius
,
|
34
|
28
|
2
|
17
13
/
15
|
Ryghte
|
Leo
,
Scorpius
,
|
35
|
25
|
2
|
21
12
/
15
|
Ryghte
|
Virgo
,
Libra
,
|
34
|
39
|
2
|
18
9
/
15
|
The
summe
of
the
partes
.
|
180
|
0
|
12
|
0
|
A
table
for
50.
degrees
of
latitude
.
Ascension
|
The
12
Signes
.
|
Partes
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
.
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Crooked
|
Aries
,
Pisces
,
|
13
|
52
|
0
|
55
7
/
15
|
Crooked
|
Taurus
,
Aquarius
,
|
17
|
55
|
1
|
11
10
/
15
|
Crooked
|
Gemini
,
Capricornus
|
27
|
0
|
1
|
48
|
Ryghte
|
Cancer
,
Sagittarius
,
|
37
|
24
|
2
|
29
〈◇〉
|
Ryghte
|
Leo
,
Scorpius
,
|
41
|
53
|
2
|
47
●
/
15
|
Ryghte
|
Virgo
,
Libra
,
|
41
|
56
|
2
|
47
11
/
15
|
The
summe
of
the
partes
.
|
180
|
0
|
12
|
0
|
A
table
for
60.
degrees
of
latitude
.
Ascension
|
The
12
Signes
.
|
Parts
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Crooked
|
Aries
,
Pisces
,
|
7
|
16
|
0
|
29
1
/
15
|
Crooked
|
Taurus
,
Aquarius
,
|
10
|
56
|
0
|
43
11
/
15
|
Crooked
|
Gemini
,
Capricornus
|
22
|
56
|
1
|
31
11
/
15
|
Ryghte
|
Cancer
,
Sagittarius
,
|
41
|
28
|
2
|
45
13
/
15
|
Ryghte
|
Leo
,
Scorpius
,
|
48
|
52
|
3
|
15
7
/
15
|
Ryghte
|
Virgo
,
Libra
,
|
48
|
32
|
3
|
14
2
/
15
|
The
summe
of
the
partes
|
180
|
0
|
12
|
0
|
A
table
for
66
degrees
and
½
of
latitude
.
Ascension
|
The
12
Signes
.
|
Partes
of
the
Equin
.
|
Partes
of
tyme
.
|
|
|
Degrees
.
|
Minutes
.
|
Howers
.
|
Minutes
.
|
Sudden
|
Aries
,
Pisces
,
|
0
|
0
|
0
|
0
|
Sudden
|
Taurus
,
Aquarius
,
|
0
|
0
|
0
|
0
|
Sudden
|
Gemini
,
Capricornus
|
0
|
0
|
0
|
0
|
Ryghte
|
Cancer
,
Sagittarius
,
|
64
|
22
|
4
|
17
7
/
15
|
Ryghte
|
Leo
,
Scorpius
,
|
59
|
49
|
3
|
59
4
/
15
|
Ryghte
|
Virgo
,
Libra
,
|
55
|
49
|
3
|
43
4
/
15
|
The
summe
of
the
partes
.
|
180
|
0
|
12
|
0
|
Scholar
.
Sir
I
thanke
you
moste
hartely
for
these
tables
,
for
I
haue
not
seene
the
lyke
of
them
before
:
and
theyr
ordre
is
so
easye
,
that
I
neede
no
greate
healpe
in
the
vnderstandinge
of
them
:
For
as
in
the
tytle
of
eche
of
them
is
sette
the
degree
of
the
latitude
of
the
Region
for
whyche
the
table
is
calculate
,
so
in
the
fyrste
columne
is
sette
the
differences
of
the
ascensions
in
name
,
and
in
the
seconde
columne
are
the
names
of
the
Signes
,
whiche
haue
those
diuers
Ascensions
,
eche
rowe
contayning
two
Signes
,
whereby
they
differ
from
the
ryght
Sphere
,
for
in
it
4
Signes
agree
in
one
quantitie
of
ascension
,
wheras
in
all
these
Oblique
spheres
,
only
twoo
signes
doo
agree
in
lykenes
of
ascension
.
And
in
eche
of
them
are
there
sette
in
the
thirde
columne
,
the
degrees
of
Ascension
,
and
minutes
after
them
,
whiche
appertayne
to
euerye
signe
:
and
in
the
fourthe
Columne
are
the
partes
of
tyme
,
agreeynge
to
those
partes
of
the
Equinoctiall
circle
:
by
whiche
it
may
appeare
not
onlye
howe
manye
degrees
and
minutes
those
Signes
occupye
in
their
Ascension
,
but
also
howe
manye
howers
or
minutes
doo
answere
to
the
same
.
And
in
eche
table
is
sette
the
full
quantitie
of
halfe
a
daye
,
and
also
of
halfe
the
Zodiake
,
whiche
is
the
full
summe
by
addition
of
all
the
other
percelles
ouer
them
:
The
firste
rule
of
Oblique
Ascention
.
whereby
I
perceaue
it
to
bee
true
,
that
eche
halfe
of
the
Equinoctiall
dooth
equallye
ascende
wyth
eche
halfe
of
the
Zodiake
.
Master
.
Beginninge
the
halues
of
them
bothe
at
the
Equinoctiall
pointes
,
in
Aries
and
Libra
,
it
is
most
true
:
but
not
so
yf
you
begin
at
the
Tropike
pointes
,
or
in
anye
other
partes
of
theym
:
for
yf
you
begynne
at
anye
of
the
northerlye
Signes
betweene
Aries
and
Libra
,
and
so
recken
6
signes
togyther
,
those
Sygnes
shall
haue
a
ryghte
Ascension
:
for
wyth
them
shall
ascende
a
greater
portion
of
the
Equinoctiall
.
But
if
you
doo
recken
syxe
Signes
and
begynne
that
accompte
betweene
Libra
and
Aries
,
in
the
southe
parte
of
the
Zodiake
,
then
doo
those
syxe
signes
ascende
crookedlye
:
for
as
muche
as
the
portion
of
the
Equinoctiall
that
ryseth
with
them
,
is
lesse
then
halfe
of
it
.
Scholar
.
For
proofe
thereof
I
take
the
table
of
tenne
degrees
of
latitude
,
and
I
begynne
with
Taurus
,
and
so
doo
I
recken
syxe
Signes
,
Taurus
,
Gemini
,
Cancer
,
Leo
,
Virgo
and
Libra
,
vnto
which
Signes
these
syxe
numbres
answere
as
they
be
here
set
,
accompting
one
numbre
twise
,
Degrees
|
Minutes
.
|
20
|
14
|
31
|
31
|
32
|
53
|
31
|
34
|
29
|
57
|
29
|
57
|
184
|
6
|
that
is
fyrst
for
Virgo
,
and
then
for
Libra
,
and
so
the
whole
summe
of
partes
of
the
Equinoctiall
is
184
degrees
and
6
minutes
:
that
is
4
degrees
and
6
minutes
more
then
halfe
:
wherefore
those
signes
do
ascende
right
.
And
so
I
perceaue
it
wyll
be
in
the
other
lyke
woorkes
,
if
I
doo
begynne
wyth
anye
Signe
in
that
northe
halfe
of
the
Zodiake
,
for
seeynge
Aries
hathe
the
leaste
of
all
other
Ascensions
,
if
I
take
anye
other
Signe
,
and
omytte
hym
,
I
shall
haue
a
greatter
noumbre
then
the
halfe
of
the
Equinoctiall
circle
.
But
nowe
contrarye
wayes
if
I
begynne
wyth
anye
of
the
southe
Signes
,
and
so
recken
syxe
continuall
Sygnes
,
theyr
Ascension
you
saye
will
bee
an
Oblyque
ascension
,
bycause
theyr
degrees
wyll
bee
more
in
noumbre
then
the
degrees
of
the
Equinoctiall
circle
:
for
example
I
take
my
beginninge
at
Sagittarius
,
and
so
recken
sorthe
directelye
syxe
Signes
,
that
is
Sagittarius
,
Capricornus
,
Aquarius
,
Pisces
,
Aries
and
Taurus
.
and
for
them
I
take
the
numbres
of
their
Ascensions
,
and
set
them
downe
as
here
you
se
:
so
that
by
addition
they
doo
make
172
degrees
,
and
34
minutes
:
that
is
lesse
then
the
halfe
circle
by
seuen
degrees
,
and
26
mynutes
.
wherefore
it
muste
needes
bee
,
that
those
Signes
doo
ascende
crookedlye
.
Deg
.
|
Min.
|
32
|
53
|
31
|
31
|
28
|
14
|
25
|
51
|
25
|
51
|
28
|
14
|
172
|
34
|
Master
.
And
so
muste
it
followe
where
so
euer
you
begynne
after
Libra
in
that
southe
halfe
of
the
Zodiake
:
for
so
muche
as
you
omytte
the
ascension
of
Libra
,
beeynge
29
degrees
and
57
minutes
,
and
in
steed
of
it
you
take
the
ascension
of
Aries
,
whiche
is
but
25
degrees
and
51
minutes
.
Scholar
.
Thys
reason
doothe
appeare
manyfeste
ynoughe
:
and
that
not
only
in
this
table
,
but
also
in
al
the
other
,
saue
that
in
the
laste
table
I
see
a
straunge
dysagreemente
frome
all
the
other
.
for
in
these
syxe
Signes
,
Aries
,
Taurus
,
Gemini
,
Capricornus
,
Aquarius
&
Pisces
,
there
is
set
no
numbres
of
degrees
or
minutes
for
their
ascension
,
but
only
cyphers
,
whiche
thyng
is
straunge
to
me
,
for
thereby
may
it
be
coniectured
,
that
those
6
Signes
haue
none
Ascension
at
all
:
and
yet
I
am
sure
that
the
fyrste
three
of
them
doo
ascende
not
onlye
in
that
Climate
,
but
also
in
all
other
Climates
be
north
that
latitude
euen
to
the
northe
Pole
.
Master
.
A
lyttle
mistakinge
dooth
disturbe
your
mynde
muche
,
but
yf
you
doo
place
the
sphere
in
the
Horizonte
,
in
suche
sorte
,
that
the
northe
Pole
be
66
degrees
and
halfe
aboue
the
Horizonte
,
and
then
tourne
the
fyrste
degree
of
Aries
,
to
the
easte
Horizonte
readye
to
ascende
,
and
afterwarde
yf
you
tourne
the
Globe
towarde
the
weste
,
but
by
the
quantitie
of
halfe
one
degree
in
the
Equinoctiall
,
you
shall
perceaue
that
all
those
sixe
Signes
whyche
lye
from
the
wynter
Tropyke
vnto
the
Sommer
Tropike
,
that
is
to
saye
,
Capricornus
,
Aquarius
,
Pisces
,
Aries
,
Taurus
,
and
Gemini
,
wyll
ascende
sodainlye
in
one
momente
all
6
at
ones
:
so
that
for
their
ascension
there
canne
be
assigned
no
degree
of
the
Equinoctiall
,
nother
anye
sensible
parte
of
tyme
,
syth
it
is
doone
in
a
momente
of
tyme
.
and
therfore
muste
I
putte
no
degree
for
their
Ascension
,
nother
yet
anye
tyme
.
And
bycause
I
thoughte
no
lesse
but
that
this
woulde
seeme
some
thynge
straunge
vnto
you
,
therefore
haue
I
not
touched
anye
thinge
of
the
other
Ascensions
for
these
Climates
that
bee
betweene
the
Tropike
of
Cancer
and
the
Pole
,
beynge
adsured
that
they
woulde
seeme
to
you
muche
more
straunge
,
then
thys
doothe
.
but
hereafter
yf
I
perceaue
that
you
trauayle
well
in
thys
first
Introduction
,
I
wyll
instructe
you
more
largelye
in
all
that
shall
bee
needefulle
for
you
:
and
in
the
meane
ceason
I
wylle
prosecute
the
rules
of
these
Ascensions
in
the
Oblyque
Spheres
:
as
I
dydde
begynne
.
wherefore
you
shall
note
,
that
althoughe
eche
halfe
of
the
Zodiake
doo
agree
in
ascension
with
eche
halfe
of
the
Equinoctiall
,
yet
the
partes
of
those
halues
,
I
meane
the
seuerall
signes
,
and
their
distincte
portions
doo
not
so
agree
,
but
are
ether
more
or
lesse
.
Scholar
.
Iohn
de
sacro
Bosco
his
rules
examined
.
So
I
remembre
doth
Iohn
de
sacro
Bosco
affirm
:
for
(
saithe
hee
)
in
that
halfe
of
the
Zodiake
,
which
is
betweene
the
beginninge
of
Aries
,
and
the
eande
of
Virgo
,
alwaies
the
portion
of
the
Zodiake
whiche
riseth
,
is
greater
then
the
like
halfe
of
the
Equinoctiall
:
and
yet
those
halues
doo
rise
togither
.
Master
.
This
he
speaketh
of
the
Oblique
sphere
.
Scholar
.
So
dooth
he
in
deede
.
Master
.
Propounde
you
an
example
,
that
I
maye
knowe
howe
you
do
vnderstande
it
.
Scholar
.
I
take
an
example
out
of
the
table
of
50
degrees
of
latitude
,
and
for
the
fyrste
fyue
Signes
I
sette
the
quantities
of
their
ascensions
,
as
heere
is
seene
,
whyche
by
Addition
doo
make
138
degrees
and
foure
minutes
.
so
dooth
there
wante
of
150
degrees
,
whiche
are
the
fulle
degrees
for
fyue
signes
,
11
degrees
and
56
minutes
.
that
arke
therefore
of
the
Equinoctiall
is
lesser
then
the
matche
arke
of
the
Zodiake
:
but
nowe
there
resteth
in
that
halfe
of
the
equinoctiall
41
degrees
and
56
minutes
,
whiche
is
the
iuste
ascension
of
Virgo
,
in
that
latitude
.
and
so
those
both
halues
doo
ascend
ioyntly
togither
.
Master
.
Prooue
the
lyke
woorke
in
the
table
of
10
degrees
of
latitude
.
Scholar
.
For
the
firste
5
signes
Aries
,
Taurus
Gemini
,
Cancer
and
Leo
,
I
set
their
ascensions
thus
.
And
by
addition
I
fynde
that
theyr
whole
summe
for
all
that
arkes
ascension
is
150
degrees
and
three
mynutes
.
that
is
three
mynutes
more
thenne
the
degrees
of
fyue
Sygnes
,
whiche
is
5
times
30.
And
so
is
this
example
against
the
rule
,
for
here
the
greater
portion
is
of
the
Equinoctiall
.
Master
.
Proue
yet
againe
in
the
table
of
one
degree
of
latitude
.
Scholar
.
The
ascensions
of
the
fyrste
5
signes
in
that
latitude
,
are
these
:
and
make
in
one
total
summe
,
151
degrees
,
and
54
minutes
:
that
is
1
degree
,
and
54
minutes
more
then
the
like
arke
of
the
5
signes
in
the
Zodiake
,
whiche
contayneth
but
onlye
150
degrees
.
And
so
is
this
example
also
against
the
rule
.
Master
.
So
you
haue
two
examples
contrary
to
that
rule
.
Scholar
.
It
can
not
be
denyed
.
Master
.
Then
is
that
no
certain
rule
.
Scholar
.
It
seemeth
so
.
Master
.
In
deede
it
is
true
onlye
aboue
13
degrees
of
latitude
.
for
in
all
climates
and
paralleles
vnder
13
degrees
of
latitude
,
the
equinoctiall
maketh
greatest
numbre
of
degrees
in
his
arke
.
so
that
Iohn
de
sacro
Bosco
his
woordes
maye
not
be
accompted
true
generally
(
as
they
sounde
)
but
particularly
betwene
13
degrees
of
latitude
,
and
66
and
an
halfe
:
and
so
is
it
to
be
sayde
of
diuers
other
of
his
rules
.
Scholar
.
Is
there
the
lyke
diuersitye
beyonde
66
degrees
and
a
halfe
northward
?
Master
.
There
is
more
diuersitie
,
but
such
and
so
straung
as
I
will
not
at
this
time
trouble
your
head
withall
,
but
wyll
appoint
a
more
conuenient
place
for
it
.
Scholar
.
Then
I
beseeke
you
to
prosecute
the
rest
of
Iohn
de
sacro
Bosco
his
rules
,
touchinge
ascensions
.
Master
.
Repete
you
the
rules
.
Scholar
.
His
nexte
rule
is
:
that
in
the
other
halfe
of
the
Zodiake
,
from
the
beginning
of
Libra
,
to
the
eande
of
Pisces
euermore
there
riseth
a
greater
parte
of
the
Equinoctial
then
of
the
Zodiake
,
and
yet
bothe
those
halues
doo
ryse
fully
togither
.
Master
.
Prooue
it
by
some
examples
.
Scholar
.
In
the
latitude
of
30
degrees
I
take
Libra
onlye
,
and
fynde
against
it
34
degrees
and
39
minutes
:
so
is
there
4
degrees
and
39
minutes
more
of
the
equinoctiall
then
of
the
Zodiake
agreablye
to
the
rule
.
Also
in
the
table
of
60
degrees
with
Libra
,
there
doth
ascende
in
the
equinoctiall
48
degrees
and
32
minutes
.
that
is
to
saye
18
degrees
and
32
minutes
more
then
the
30
degrees
of
Libra
.
Master
.
Assaye
the
lyke
in
the
latitudes
of
one
degree
,
and
of
10
degrees
.
Scholar
.
In
the
latitude
of
10
degrees
,
the
signe
of
Libra
hath
for
his
ascension
29
degrees
,
and
57
minutes
of
the
Equinoctiall
,
that
is
3
minutes
lesse
then
the
degrees
of
the
Zodiake
,
and
so
is
that
contrarye
to
the
sayde
rule
.
Master
.
Nowe
proue
the
other
.
Scholar
.
In
that
parallele
where
the
Pole
is
but
one
degree
hyghe
,
the
Signe
of
Libra
ascendeth
with
28
degrees
and
6
minutes
of
the
Equinoctiall
,
so
is
that
arke
of
the
Equinoctiall
lesser
then
the
degrees
of
the
sayde
signe
of
Libra
,
by
1.
degree
and
65
minutes
,
and
yet
by
the
rule
it
shuld
be
greater
.
wherfore
I
maye
perceaue
,
that
this
rule
dooth
not
serue
for
all
Latitudes
,
but
for
certaine
of
them
.
And
as
I
thinke
,
not
for
anye
aboue
10
degrees
,
althoughe
(
as
you
sayd
)
the
other
exception
did
extend
to
13
degrees
of
latitude
.
Master
.
What
causeth
you
to
thinke
so
?
Scholar
.
The
table
calculate
by
you
for
11
degrees
of
latitude
,
where
I
see
30
degrees
,
and
10
minutes
of
the
Equinoctiall
,
assigned
for
the
ascension
of
the
signe
of
Libra
,
and
there
is
the
portion
of
the
Equinoctiall
greater
by
10
minutes
then
the
portion
of
the
Zodiake
.
Master
.
In
deede
for
whole
signes
this
exception
extendeth
not
aboue
10
degrees
of
latitude
,
and
no
more
doothe
the
other
former
exception
,
but
yet
in
partes
of
signes
it
extendeth
in
them
both
to
13
degrees
,
as
herafter
you
shall
perceaue
more
at
large
.
but
now
go
forth
to
the
nexte
rule
.
Scholar
.
The
fourthe
rule
is
this
:
that
those
arkes
which
succede
after
Aries
vnto
the
eande
of
Virgo
in
the
Oblique
sphere
,
The
fourth
rule
.
do
abate
their
ascensions
in
comparison
to
the
ascensions
that
they
haue
in
the
Right
sphere
:
namely
seeyng
lesse
dooth
rise
of
the
Equinoctiall
.
A
TABLE
OF
ASCENSIONS
showinge
all
diuersities
of
them
,
vnto
the
Polare
circle
,
peculiare
for
euery
seuerall
Signe
.
Degrees
.
of
latitude
.
|
Aries
Pisces
|
Taurus
Aquarius
|
Gemini
Capricor
|
Cancer
Sagittari
.
|
Leo
Scorpius
.
|
Virgo
Libra
|
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
0
|
27
|
54
|
29
|
54
|
32
|
12
|
32
|
12
|
29
|
54
|
27
|
54
|
1
|
27
|
42
|
29
|
44
|
32
|
8
|
32
|
16
|
30
|
4
|
28
|
6
|
2
|
27
|
30
|
29
|
34
|
32
|
4
|
32
|
20
|
30
|
14
|
28
|
18
|
3
|
27
|
17
|
29
|
25
|
32
|
0
|
32
|
24
|
30
|
23
|
28
|
31
|
5
|
26
|
53
|
29
|
4
|
31
|
52
|
32
|
32
|
30
|
44
|
28
|
55
|
8
|
26
|
16
|
28
|
34
|
31
|
40
|
32
|
44
|
31
|
14
|
29
|
32
|
10
|
25
|
51
|
28
|
14
|
31
|
31
|
32
|
53
|
31
|
34
|
29
|
57
|
11
|
25
|
38
|
28
|
4
|
31
|
27
|
32
|
57
|
31
|
44
|
30
|
10
|
15
|
24
|
46
|
27
|
23
|
31
|
10
|
33
|
14
|
32
|
25
|
31
|
2
|
20
|
23
|
39
|
26
|
27
|
30
|
48
|
33
|
36
|
33
|
21
|
32
|
9
|
25
|
22
|
27
|
25
|
27
|
30
|
24
|
34
|
0
|
34
|
21
|
33
|
21
|
30
|
21
|
9
|
24
|
23
|
29
|
56
|
34
|
28
|
35
|
25
|
34
|
39
|
35
|
19
|
43
|
23
|
9
|
29
|
24
|
35
|
0
|
36
|
39
|
36
|
5
|
40
|
18
|
4
|
21
|
45
|
28
|
47
|
35
|
37
|
38
|
3
|
37
|
44
|
45
|
16
|
10
|
20
|
3
|
28
|
1
|
36
|
23
|
39
|
45
|
39
|
38
|
50
|
13
|
52
|
17
|
55
|
27
|
0
|
37
|
24
|
41
|
53
|
41
|
56
|
55
|
11
|
1
|
15
|
5
|
25
|
31
|
38
|
53
|
44
|
43
|
44
|
47
|
60
|
7
|
16
|
10
|
56
|
22
|
56
|
41
|
28
|
48
|
52
|
48
|
32
|
65
|
2
|
4
|
3
|
44
|
15
|
20
|
49
|
2
|
56
|
5
|
53
|
45
|
66
½
|
0
|
0
|
0
|
0
|
0
|
0
|
64
|
22
|
59
|
49
|
55
|
49
|
Master
.
For
tryall
of
this
rule
I
haue
sette
forth
here
a
table
contayninge
all
the
diuersities
(
though
not
all
the
seuerall
degrees
of
latitude
)
that
happen
in
anye
Climate
vnder
67
degrees
of
latitude
,
that
is
vnto
the
Polare
circle
.
So
that
by
thys
table
you
maye
examine
all
the
rules
bothe
of
Iohn
de
Sacro
Bosco
,
and
also
of
others
.
Nowe
therefore
examine
those
arkes
that
followe
Aries
,
and
so
abate
their
ascensions
,
as
your
rule
saythe
,
frome
Aries
,
vnto
the
eande
of
Virgo
.
Scholar
.
Firste
for
Aries
it selfe
:
I
see
that
it
abateth
in
this
table
from
27
degrees
and
54
minutes
vnto
nothinge
.
And
Taurus
abateth
also
frome
29
degrees
and
54
minutes
vnto
nothinge
.
Lykewise
Gemini
abateth
from
32
degrees
and
12
minutes
vnto
nothinge
.
But
contrary
waies
,
Cancer
,
Leo
,
and
Virgo
,
do
not
abate
,
but
increase
the
quantities
of
their
Ascensions
.
so
that
in
the
three
firste
Signes
onlye
(
that
is
Aries
,
Taurus
and
Gemini
)
that
rule
is
true
,
and
in
the
other
three
Signes
,
Cancer
,
Leo
and
Virgo
,
it
appeareth
vtterly
to
be
false
.
Master
.
Yet
in
one
manner
of
consideration
those
words
maye
be
true
as
he
hath
spoken
them
,
though
not
so
largelye
as
the
woordes
do
sound
:
for
it
appeareth
that
your
author
doth
accompt
the
beginning
of
those
arkes
(
whereof
he
speaketh
)
not
from
diuers
and
seuerall
pointes
,
but
from
one
common
beginning
,
which
is
the
fyrst
degree
of
Aries
,
and
in
that
sence
his
rule
is
true
.
for
proofe
whereof
here
is
two
other
tables
sette
forthe
,
in
whiche
is
declared
the
quantities
of
the
Ascensions
of
the
twelue
Signes
,
but
not
in
such
sorte
as
it
was
in
the
table
nexte
before
,
for
there
euerye
arke
of
the
seuerall
Signes
did
take
his
beginninge
at
the
fyrste
degree
of
the
same
Signe
.
but
in
these
twoo
tables
the
arke
of
ascension
is
accompted
from
the
fyrst
degree
of
Aries
,
as
from
the
common
beginning
,
and
eandeth
at
the
laste
degree
of
euery
seuerall
Signe
.
And
now
by
this
fyrst
table
if
you
examine
the
former
rule
you
shal
find
it
to
be
true
A
TABLE
FOR
THE
DIVERSITIES
of
Ascensions
for
the
firste
6
Signes
from
the
Equinoctiall
to
the
Polare
circle
,
accomptinge
the
beginninge
of
euery
arke
,
from
the
firste
degree
of
Aries
.
Theleuation
of
the
Pole
.
|
Aries
|
Taurus
|
Gemini
|
Cancer
|
Leo
|
Virgo
|
|
Deg
.
|
Mi.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
0
|
27
|
54
|
57
|
48
|
90
|
0
|
122
|
12
|
152
|
6
|
180
|
0
|
1
|
27
|
42
|
57
|
26
|
89
|
34
|
121
|
50
|
151
|
54
|
180
|
0
|
2
|
27
|
30
|
57
|
4
|
89
|
8
|
121
|
28
|
151
|
42
|
180
|
0
|
3
|
27
|
17
|
56
|
42
|
88
|
42
|
121
|
6
|
151
|
29
|
180
|
0
|
4
|
27
|
5
|
56
|
20
|
88
|
15
|
120
|
44
|
151
|
17
|
180
|
0
|
5
|
26
|
53
|
55
|
57
|
87
|
49
|
120
|
21
|
151
|
5
|
180
|
0
|
8
|
26
|
16
|
54
|
50
|
86
|
30
|
119
|
14
|
150
|
28
|
180
|
0
|
10
|
25
|
51
|
54
|
5
|
85
|
36
|
118
|
29
|
150
|
3
|
180
|
0
|
11
|
25
|
38
|
53
|
42
|
85
|
9
|
118
|
6
|
149
|
50
|
180
|
0
|
15
|
24
|
46
|
52
|
9
|
83
|
19
|
116
|
33
|
148
|
58
|
180
|
0
|
20
|
23
|
39
|
50
|
6
|
80
|
54
|
114
|
30
|
147
|
51
|
180
|
0
|
25
|
22
|
27
|
47
|
54
|
78
|
18
|
112
|
18
|
145
|
39
|
180
|
0
|
30
|
21
|
9
|
45
|
32
|
75
|
28
|
109
|
56
|
145
|
21
|
180
|
0
|
35
|
19
|
43
|
42
|
52
|
72
|
16
|
107
|
16
|
143
|
55
|
180
|
0
|
40
|
18
|
4
|
39
|
49
|
68
|
36
|
104
|
13
|
142
|
16
|
180
|
0
|
45
|
16
|
10
|
36
|
13
|
64
|
14
|
100
|
37
|
140
|
22
|
180
|
0
|
50
|
13
|
52
|
31
|
47
|
58
|
47
|
96
|
11
|
138
|
4
|
180
|
0
|
55
|
11
|
1
|
26
|
6
|
51
|
37
|
90
|
30
|
135
|
13
|
180
|
0
|
60
|
7
|
16
|
18
|
12
|
41
|
8
|
82
|
36
|
131
|
28
|
180
|
0
|
65
|
2
|
4
|
5
|
48
|
21
|
8
|
70
|
10
|
126
|
15
|
180
|
0
|
66
½
|
0
|
0
|
0
|
0
|
0
|
0
|
64
|
22
|
124
|
11
|
180
|
0
|
Scholar
.
I
perceaue
that
the
fyrste
line
of
numbres
vnder
the
signes
,
against
the
cypher
0
,
doth
represent
the
quantities
of
the
Ascensions
in
the
righte
sphere
,
and
all
the
other
lynes
doo
declare
the
speciall
quantities
of
seuerall
ascensions
A
TABLE
OF
THE
DIVERSITIES
of
Ascensions
for
the
6
southerlye
Signes
,
accomptinge
the
beginninge
of
those
Ascensions
,
from
Aries
firste
degree
.
Degrees
of
latitude
.
|
Libra
|
Scorpius
.
|
Sagittari
.
|
Capricor
|
Aquarius
|
Pisces
|
|
Deg
.
|
Mi.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
Deg
.
|
Min.
|
0
|
207
|
54
|
237
|
48
|
270
|
0
|
302
|
12
|
332
|
6
|
360
|
0
|
1
|
208
|
6
|
238
|
10
|
270
|
26
|
302
|
34
|
332
|
18
|
360
|
0
|
2
|
208
|
18
|
238
|
32
|
270
|
52
|
302
|
56
|
332
|
30
|
360
|
0
|
3
|
208
|
31
|
238
|
54
|
271
|
18
|
303
|
18
|
332
|
43
|
360
|
0
|
4
|
208
|
43
|
239
|
16
|
271
|
45
|
303
|
40
|
332
|
55
|
360
|
0
|
5
|
208
|
55
|
239
|
39
|
272
|
11
|
304
|
3●…
|
333
|
7
|
360
|
0
|
8
|
209
|
32
|
240
|
46
|
273
|
30
|
305
|
10
|
333
|
44
|
360
|
0
|
10
|
209
|
57
|
241
|
31
|
274
|
24
|
305
|
55
|
334
|
9
|
360
|
0
|
11
|
210
|
10
|
241
|
54
|
274
|
51
|
306
|
18
|
334
|
22
|
360
|
0
|
15
|
211
|
2
|
243
|
27
|
276
|
41
|
307
|
51
|
335
|
14
|
360
|
0
|
20
|
212
|
9
|
245
|
30
|
279
|
6
|
309
|
54
|
336
|
21
|
360
|
0
|
25
|
213
|
21
|
247
|
42
|
281
|
42
|
312
|
6
|
337
|
33
|
360
|
0
|
30
|
214
|
39
|
250
|
4
|
284
|
32
|
314
|
28
|
338
|
51
|
360
|
0
|
35
|
216
|
5
|
252
|
44
|
287
|
44
|
317
|
8
|
340
|
17
|
360
|
0
|
40
|
217
|
44
|
255
|
47
|
291
|
24
|
320
|
11
|
341
|
56
|
360
|
0
|
45
|
219
|
38
|
259
|
23
|
295
|
46
|
323
|
47
|
343
|
50
|
360
|
0
|
50
|
221
|
56
|
263
|
49
|
301
|
13
|
328
|
13
|
346
|
8
|
360
|
0
|
55
|
224
|
47
|
269
|
30
|
308
|
23
|
333
|
54
|
348
|
59
|
360
|
0
|
60
|
228
|
32
|
277
|
24
|
318
|
52
|
341
|
48
|
352
|
44
|
360
|
0
|
65
|
233
|
45
|
289
|
50
|
338
|
52
|
354
|
12
|
357
|
56
|
360
|
0
|
66
½
|
235
|
48
|
295
|
36
|
360
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
in
eche
of
those
distinct
latitudes
,
which
be
noted
in
the
first
columne
in
both
tables
.
Therfore
now
I
maye
perceaue
according
to
the
former
rule
,
that
the
greatest
numbre
of
any
doun
right
column
is
the
highest
numbre
in
the
hed
of
the
same
column
,
so
that
it
may
truely
bee
saide
(
as
appeareth
in
this
firste
table
)
that
in
eche
Oblique
sphere
the
ascensions
of
the
arkes
from
Aries
vnto
the
eand
of
Virgo
,
do
abate
still
and
waxe
lesse
and
lesse
,
in
respecte
to
their
ascensions
that
they
haue
in
the
Right
sphere
.
Master
.
Thre
signifiations
of
Ascension
.
Thus
you
see
,
howe
there
may
be
accompted
diuers
formes
of
ascensions
:
firste
(
as
I
sayde
at
the
beginning
of
that
definition
)
it
maye
signifie
that
degree
certenlye
of
the
Equinoctiall
,
whiche
dooth
ascende
with
anye
signe
or
parte
thereof
:
as
for
example
.
in
the
latitude
of
50
degrees
,
the
laste
degree
of
Aries
hath
for
his
ascension
the
13
degree
and
52
minute
of
the
Equinoctiall
,
as
by
the
firste
of
these
twoo
tables
it
dooth
appeare
:
and
in
the
same
table
it
appeareth
,
that
the
laste
degree
of
Taurus
hathe
for
his
ascension
in
the
same
latitude
the
31
degree
and
47
minut
of
the
Equinoctiall
.
And
in
the
seconde
signification
,
the
ascension
of
Aries
whole
signe
is
that
whole
ark
of
13
degrees
and
52
minutes
,
and
so
the
whole
arke
from
the
beginning
of
Aries
,
to
the
eande
of
Taurus
,
hathe
for
his
ascension
that
whole
arke
of
31
degrees
,
and
47
minutes
of
the
Equinoctiall
.
And
in
this
signification
dooth
Iohn
de
sacro
Bosco
vse
the
name
of
Ascension
,
and
in
this
sense
his
rules
be
true
:
accordinge
to
whiche
sense
I
haue
drawen
to
you
certaine
tables
:
the
firste
for
the
ascensions
of
the
twelue
Signes
in
the
right
Sphere
:
the
second
,
for
the
ascension
of
the
Signes
in
52
degrees
of
latitude
:
the
thirde
and
fourthe
are
these
twoo
tables
last
before
,
which
for
diuers
latitudes
doo
declare
the
quantities
of
the
Ascensions
of
al
arkes
of
whole
signes
accompted
from
the
beginning
of
Aries
.
The
thyrde
signification
of
ascensions
is
the
quantitie
of
that
arke
of
the
Equinoctiall
whiche
ascendeth
with
anye
certaine
arke
of
the
Zodiake
:
as
for
example
.
that
arke
of
the
equinoctiall
that
ascendeth
with
any
signe
seuerally
taken
,
is
called
the
ascension
of
that
signe
.
So
haue
you
for
euery
signe
certain
seuerall
arkes
of
ascension
assigned
,
and
set
forthe
here
in
diuers
tables
,
accordinge
to
diuers
eleuations
of
the
Pole
.
And
in
this
signification
must
it
be
vnderstande
,
when
it
is
sayde
that
any
signe
hath
a
Right
ascension
or
an
Oblique
ascension
,
for
if
the
arke
of
the
Equinoctiall
that
riseth
with
that
signe
,
bee
greater
then
30
degrees
,
A
Ryghte
ascension
.
then
hathe
that
signe
a
Righte
ascension
:
and
if
the
arke
of
the
Equinoctiall
be
lesser
then
30
degres
,
then
is
that
ascension
called
an
Oblique
ascension
:
An
Oblique
ascension
.
A
meane
ascension
.
but
if
the
sayd
arke
of
the
Equinoctiall
be
iuste
30
degrees
,
then
is
it
a
Meane
or
Equall
ascension
.
Scholar
.
Nowe
doo
I
better
vnderstande
the
vse
of
these
names
then
I
dyd
before
:
and
also
I
perceaue
howe
the
names
of
greater
and
lesser
portion
are
to
be
referred
,
not
of
eche
greater
to
eche
lesser
,
for
so
the
ascension
of
Taurus
myghte
be
accompted
greater
then
the
ascention
of
Aries
,
and
lesser
then
the
ascention
of
Gemini
,
in
all
climates
with
out
the
Polare
circle
.
And
so
one
ascension
might
be
both
greater
and
lesser
,
and
therefore
bothe
ryghte
and
crooked
whiche
is
an
absurditie
.
Master
.
Thus
hath
ordre
taught
you
,
that
wherof
you
wer
in
doubt
and
manifestly
approued
that
that
seemed
very
obscure
.
Now
therfore
returne
to
your
author
again
.
And
repete
his
other
rules
as
he
doth
teache
them
.
Scholar
.
The
fifte
rule
.
His
fifte
rule
is
this
:
The
arkes
whiche
followe
Libra
,
vnto
the
cande
of
Pisces
,
in
an
Oblique
sphere
,
doo
increase
their
ascensions
aboue
the
ascensions
that
they
haue
in
the
Right
sphere
in
as
muche
as
the
portion
of
the
Equinoctiall
is
augmented
.
And
the
increase
of
those
ascensions
is
agreeable
in
rate
to
the
decrease
of
those
other
ascensions
whiche
succeede
from
Aries
to
Libra
.
Master
.
This
rule
muste
be
vnderstande
of
ascensions
in
the
seconde
signification
:
and
that
may
you
trye
by
the
later
of
those
twoo
tables
which
I
gaue
you
laste
.
Scholar
.
It
appeareth
so
in
deed
.
for
Libra
increaseth
from
207
degrees
and
54
minutes
,
vnto
235
degres
&
48
minutes
.
And
Scorpio
from
237
degrees
&
48
minuts
,
vnto
295
degres
and
36
minutes
.
likwaies
Sagittarius
from
270
degrees
vnto
360
degrees
.
So
dooth
it
appeare
,
that
Libra
dooth
increase
betweene
the
Equinoctiall
and
the
Polare
circle
,
27
degres
,
and
54
minutes
.
And
Scorpio
increaseth
57
degrees
and
50
minutes
.
Also
Sagittarius
augmenteth
by
90
degrees
.
And
now
contrarye
waies
,
Aries
doth
a
bate
from
27
degres
and
54
minutes
to
nothinge
.
Taurus
diminisheth
frome
57
degrees
and
48
minutes
vnto
nothinge
also
.
And
Gemini
abateth
from
90
to
0
:
so
dooth
these
three
in
decrease
agree
with
the
other
in
increase
exactly
.
Master
.
And
so
maye
you
iudge
of
the
other
three
couples
.
And
therefore
sayth
your
author
,
The
sixte
rule
.
that
hereby
it
is
manifest
,
that
two
equall
arkes
lying
one
against
the
other
,
and
in
an
Oblique
sphere
,
haue
their
ascensions
ioyntlye
taken
togyther
equall
wyth
the
Ascensions
of
the
same
arkes
in
a
Ryghte
Sphere
,
ioyntlye
taken
also
:
for
althoughe
those
arkes
bee
vnequall
togyther
,
yet
as
muche
as
the
one
abateth
on
the
one
syde
,
so
muche
the
other
increaseth
on
the
other
syde
,
and
so
bothe
arkes
in
the
Ryght
sphere
are
equall
to
bothe
those
arkes
in
any
Oblique
sphere
.
Scholar
.
But
I
praye
you
,
in
what
signification
of
ascension
is
that
rule
to
be
vnderstande
?
Master
.
In
anye
of
those
twoo
which
be
referred
to
arkes
:
for
the
fyrste
can
haue
no
place
here
,
bicause
it
signifeth
the
ascension
of
one
pointe
only
,
and
not
of
any
arke
as
the
other
twoo
do
,
and
as
this
rule
doth
importe
.
Scholar
.
Then
may
I
proue
by
examples
in
both
sortes
of
tables
.
And
firste
to
beginne
with
those
tables
that
accompt
the
whole
arkes
from
the
beginning
of
Aries
,
I
fynd
the
ascension
of
Aries
in
the
head
of
the
table
,
that
is
in
the
right
sphere
,
to
be
27
degrees
&
54
minutes
,
&
the
ascension
of
Libra
(
which
is
against
it
)
207
degres
&
54
minuts
.
which
both
ioyned
togither
,
make
235
degrees
&
48
minuts
.
Now
to
proue
the
like
in
an
Oblique
Sphere
,
I
take
the
latitude
of
40
degrees
.
and
there
I
fynde
for
Aries
his
ascension
is
degrees
and
4
minutes
:
and
for
Libra
I
fynde
in
the
seconde
table
217
degrees
and
44
minutes
:
whiche
both
beyng
added
togither
,
do
make
235
degrees
and
48
minutes
.
that
is
precisely
equall
with
the
former
ascensions
in
the
right
sphere
.
Also
in
the
eletration
of
60
degrees
I
trye
the
like
,
where
Aries
hath
7
degrees
and
16
minutes
,
and
Libra
hath
228
degrees
and
32
minutes
,
which
by
addition
amount
to
the
same
sum
as
before
.
Master
.
Attempt
the
lyke
in
the
other
tables
.
Scholar
.
I
take
the
arke
of
Aries
ascension
as
before
27
degrees
and
54
minutes
:
and
the
ascension
of
Libra
(
accomptyng
only
the
arke
of
it
from
his
owne
beginninge
)
in
lyke
sorte
27
degrees
and
54
minutes
.
so
that
both
ioyned
togither
,
make
55
degrees
and
48
minutes
.
Then
in
the
latitude
of
55
degrees
,
I
fynde
for
Aries
11
degrees
and
one
mynute
:
and
for
Libra
,
44
degrees
and
47
minutes
.
and
by
addition
I
find
that
they
make
the
same
numbre
as
before
.
Master
.
Make
proofe
in
some
other
arke
.
Scholar
.
I
take
fyrste
the
arke
from
the
beginning
of
Leo
,
to
the
eande
of
the
same
Signe
,
and
fynd
it
to
bee
29
degrees
and
54
minutes
in
the
ryght
sphere
:
and
so
for
the
Ascension
of
the
Signe
of
Aquarius
,
beyng
equall
to
it
,
and
agaynste
it
in
the
Zodiake
,
I
fynde
the
lyke
noumbre
,
whiche
make
by
addition
59
degrees
and
48
minutes
.
Then
in
the
latitude
of
30
degrees
I
trye
the
lyke
,
and
fynde
for
Leo
35
degrees
and
25
minutes
:
and
for
Aquarius
there
dooth
rise
24
degrees
and
23
minutes
:
which
make
also
togither
the
same
sum
of
59
degrees
and
48
minutes
.
So
in
both
those
significations
,
whether
I
accompte
seuerall
arkes
from
seuerall
beginnings
,
on
generall
arks
from
one
generall
beginning
,
the
rule
is
founde
true
.
Now
resteth
but
one
rule
more
of
ascensions
in
this
author
to
be
discussed
,
and
that
is
this
:
The
7
rule
that
in
an
oblique
sphere
echez
arkes
of
the
Zodiake
being
equal
and
equally
distaunt
from
any
one
of
the
Equinoctiall
pointes
,
shall
haue
equall
ascensions
.
Master
.
This
rule
is
partly
a
greeable
with
the
laste
rule
,
and
partly
seuerall
,
in
as
muche
as
euery
contrarye
arke
is
lyke
distaunte
frome
the
one
Equinoctiall
pointe
,
as
the
fyrste
arke
is
frome
the
other
Equinoctiall
pointe
.
thys
rule
dooth
agree
(
after
a
sorte
thoughe
not
proprely
)
wyth
the
other
laste
before
:
but
consideringe
that
Aries
and
Pisces
as
whole
signes
haue
lyke
arkes
,
and
are
equallye
dystaunt
from
one
Equinoctiall
pointe
,
thoughe
in
backe
ordre
:
for
the
eande
of
Aries
is
iuste
equall
in
distaunce
from
the
precise
Equinoctioll
pointe
,
as
the
beginninge
of
Pisces
is
from
the
same
.
And
in
this
pointe
these
Signes
haue
thys
seuenth
rule
as
a
speciall
rule
for
theym
and
their
Ascensions
.
Lykewaies
Taurus
compared
wyth
Aquarius
,
Gemini
with
Capricorne
,
Cancer
with
Sagittarius
,
Leo
with
Scorpius
,
and
Virgo
with
Libra
,
as
this
figure
dooth
diagram of the zodiac.
shew
exactly
,
althoughe
in
the
same
I
haue
marked
also
the
contrary
signes
that
it
might
be
a
common
figure
for
bothe
those
rules
,
so
that
euery
seueral
sign
hath
2
matches
,
with
which
it
may
be
conferred
,
one
of
theym
righte
againste
him
.
and
that
comparison
is
in
the
6
rule
:
and
the
other
lesse
distaunt
,
&
ther
conference
belongeth
to
this
7
rule
.
Scholar
.
As
this
figure
doth
teache
me
what
signes
may
be
conferred
togither
,
so
the
tables
before
written
doo
declare
the
quantities
of
their
ascensions
in
those
seueral
latitudes
:
and
the
true
meaning
of
bothe
those
rules
,
as
well
as
of
other
,
touchinge
ascensions
.
Master
.
But
this
muste
you
farther
knowe
,
that
those
rules
doo
speake
generallye
of
anye
twoo
arkes
,
whether
they
bee
greater
or
lesser
then
a
Signe
,
and
doo
not
meane
of
Signes
onlye
.
Scholar
.
That
muste
needes
follow
ordrely
:
for
if
Aries
bee
equall
in
ascension
with
Pisces
,
and
Taurus
equall
in
risinge
with
Aquarius
,
then
ioyntly
Aries
and
Taurus
must
needes
be
of
one
quantitie
in
ascension
with
Aquarius
and
Pisces
,
by
composition
of
proportions
,
as
is
taughte
in
Geometrye
and
Arithmetike
also
.
Master
.
Lykewaise
(
by
resolution
of
propositions
)
if
al
Aries
be
like
in
ascension
with
all
Pisces
,
then
the
first
degre
of
Aries
shall
ascende
equallye
with
the
laste
degree
of
Pisces
:
and
the
20
degree
of
Aries
,
wyth
the
10
degree
of
Pisces
:
&
in
lyke
manner
of
eche
other
degree
equally
distaunte
from
the
Equinoctiall
pointes
:
and
so
lykewaies
of
euerye
minute
:
for
these
rules
of
equalitie
or
inequalitie
of
Ascensions
of
arkes
,
doo
serue
as
well
for
the
arkes
of
degrees
and
mynutes
,
as
for
the
arkes
of
whole
Signes
,
or
of
greater
quantities
.
Also
this
rule
is
general
,
that
all
arkes
that
ascende
rightly
,
do
descende
crookedly
,
be
they
great
or
small
:
and
contrarye
wayes
,
what
arke
so
euer
ascendeth
crookedlye
,
doth
descende
righte
:
whereby
it
commeth
to
passe
,
that
alwaies
the
one
signe
counteruailyng
with
his
contrary
,
there
is
euermore
one
halfe
of
the
Zodiake
aboue
the
Horizonte
,
as
well
as
there
is
one
halfe
of
the
Equinoctiall
aboue
the
same
.
so
that
when
so
euer
anye
degree
of
the
Zodiake
doth
set
in
the
weste
,
the
contrarye
degree
dooth
rise
in
the
easte
.
Of
this
it
foloweth
,
that
in
the
longeste
daye
in
the
yeare
there
dooth
rise
but
syxe
Sygnes
,
and
in
the
shortest
daye
there
riseth
as
manye
signes
.
Scholar
.
Thereof
it
maye
seeme
to
come
to
passe
,
that
in
aunciente
tyme
the
day
and
the
nyghte
were
euermore
diuiuided
into
12
equall
parts
,
(
how
longe
or
how
short
so
euer
they
were
)
and
those
partes
were
called
Vnequall
howers
,
of
whiche
yet
manye
men
doo
write
,
Howers
vnequall
.
and
doo
call
them
howers
of
the
Planets
:
but
as
I
iudg
by
the
ordre
of
the
ascensions
,
euerye
signe
hathe
not
equall
Ascension
,
nor
equall
time
in
risyng
,
&
therfore
may
those
howers
be
well
called
Vnequall
,
which
depend
of
the
motion
of
the
Zodiake
,
beeyng
in
it selfe
vnequall
in
his
Ascension
.
Master
.
It
is
thought
of
some
men
to
be
a
more
apte
reason
to
call
those
howers
vnequall
,
bicause
not
only
the
sommer
howers
are
vnequall
to
the
winter
howers
,
but
also
the
daye
howers
vnequall
to
the
night
howers
.
Scholar
.
Naturall
howers
.
Iohn
de
sacro
Bosco
doth
call
them
naturall
howers
,
and
defineth
them
to
be
the
measure
of
the
tyme
,
in
whiche
halfe
a
signe
dooth
ascend
.
Master
.
As
the
6
signes
that
rise
in
the
daye
or
in
the
nyghte
keepe
not
one
vniforme
equalitye
in
their
rysynge
,
so
doth
the
Ascensions
of
the
halfe
signes
differ
more
vnequallye
:
and
by
that
meanes
the
howers
of
the
daye
can
not
be
equall
togither
,
nother
yet
the
howers
of
the
nyght
may
be
called
equall
togither
:
wherefore
other
you
must
not
allowe
that
definition
,
or
els
you
must
not
parte
the
daye
and
the
nyght
into
equall
partes
.
Scholar
.
I
knowe
not
what
to
saye
to
this
,
for
nother
can
I
defende
that
definition
,
nother
yet
can
I
improue
that
partition
.
Master
.
Those
howers
haue
beene
the
occasion
of
much
contention
,
and
therfore
were
they
wittilye
reiected
oute
of
the
daylye
vse
,
wherein
they
were
ones
common
,
and
were
lefte
only
to
learned
men
,
Equall
houres
called
Equinoctial
howers
.
for
learned
vses
,
and
in
their
steed
other
howers
more
certaine
and
equall
were
diuised
,
whiche
doo
diuide
the
naturall
day
into
24
equall
partes
,
and
these
keepe
one
iuste
quantitie
,
how
so
euer
the
Artificiall
day
do
varye
his
quantitie
.
Scholar
.
This
I
knowe
well
:
but
yet
touchynge
the
fyrste
howers
,
called
the
Planet
howers
,
I
woulde
gladlye
vnderstande
some
example
for
their
exacte
diuersitie
in
some
one
daye
.
Master
.
You
shall
haue
anone
one
generall
table
for
many
dayes
,
namely
for
euerye
syxte
daye
in
the
yeare
nighe
hande
,
and
that
table
shall
suffice
for
the
whole
yeare
:
and
yt
shall
be
calculate
accordyng
to
that
exact
forme
of
distinction
of
howers
,
by
halfe
Signes
of
the
Zodiake
:
but
in
the
meane
ceason
,
bicause
you
shall
not
be
ignorant
of
the
vulgare
forme
of
vnequall
howers
,
I
haue
heere
sette
forth
an
ordrelye
partition
of
them
,
accordynge
to
the
lengthe
of
euerye
daye
or
nighte
in
the
yeare
,
by
increase
frome
12
minutes
to
12
minutes
,
for
eche
day
or
nyghte
,
from
the
shortest
daye
,
or
nyghte
of
1.
minute
of
length
,
vnto
the
longest
daye
or
nyghte
of
24
howers
.
Scholar
.
But
what
if
the
longest
daye
be
not
so
longe
,
as
it
is
not
with
vs
in
Englande
?
Master
.
The
table
doothe
serue
for
all
places
where
the
dayes
be
of
shorter
lengthe
:
as
by
the
ouermoste
title
and
that
fyrste
columne
on
the
lefte
hande
you
may
perceaue
.
Scholar
.
I
was
to
negligente
,
that
I
did
not
consider
that
,
for
as
it
maye
serue
for
that
daye
in
the
yeare
whiche
is
but
16
howers
longe
,
(
thoughe
the
longest
daye
bee
longer
)
so
maye
it
serue
for
that
place
where
the
longest
daye
is
but
16
howers
in
quantitie
.
Master
.
Yea
and
for
the
myddle
of
the
earthe
vnder
the
Equinoctial
,
where
the
longest
day
is
but
12
howers
,
so
that
it
serueth
from
the
Equinoctiall
circle
,
vnto
the
Polare
circle
,
and
for
all
Climates
that
be
betweene
them
,
as
by
the
howers
in
the
firste
columne
you
may
perceaue
.
The
vse
of
the
table
.
So
that
if
you
will
knowe
the
quantitie
of
anye
hower
vnequall
,
or
hower
of
the
Planetes
,
after
this
forme
:
fyrst
you
muste
knowe
the
A
TABLE
FOR
THE
HOVRES
OF
Planetes
after
the
common
forme
.
Minutes
.
0
|
12
|
24
|
36
|
48
|
Houres
|
Hour
.
|
Minu
.
|
Hour
.
|
Minu
.
|
Hour
.
|
Minu
.
|
Hour
.
|
Minu
.
|
Hour
.
|
Minu
.
|
0
|
0
|
0
|
0
|
1
|
0
|
2
|
0
|
3
|
0
|
4
|
1
|
0
|
5
|
0
|
6
|
0
|
7
|
0
|
8
|
0
|
9
|
2
|
0
|
10
|
0
|
11
|
0
|
12
|
0
|
13
|
0
|
14
|
3
|
0
|
15
|
0
|
16
|
0
|
17
|
0
|
18
|
0
|
19
|
4
|
0
|
20
|
0
|
21
|
0
|
22
|
0
|
23
|
0
|
24
|
5
|
0
|
25
|
0
|
26
|
0
|
27
|
0
|
28
|
0
|
29
|
6
|
0
|
30
|
0
|
31
|
0
|
32
|
0
|
33
|
0
|
34
|
7
|
0
|
35
|
0
|
36
|
0
|
37
|
0
|
38
|
0
|
39
|
8
|
0
|
40
|
0
|
41
|
0
|
42
|
0
|
43
|
0
|
44
|
9
|
0
|
45
|
0
|
46
|
0
|
47
|
0
|
48
|
0
|
49
|
10
|
0
|
50
|
0
|
51
|
0
|
52
|
0
|
53
|
0
|
54
|
11
|
0
|
55
|
0
|
56
|
0
|
57
|
0
|
58
|
0
|
59
|
12
|
1
|
0
|
1
|
1
|
1
|
2
|
1
|
3
|
1
|
4
|
13
|
1
|
5
|
1
|
6
|
1
|
7
|
1
|
8
|
1
|
9
|
14
|
1
|
10
|
1
|
11
|
1
|
12
|
1
|
13
|
1
|
14
|
15
|
1
|
15
|
1
|
16
|
1
|
17
|
1
|
18
|
1
|
19
|
16
|
1
|
20
|
1
|
21
|
1
|
22
|
1
|
23
|
1
|
24
|
17
|
1
|
25
|
1
|
26
|
1
|
27
|
1
|
28
|
1
|
29
|
18
|
1
|
30
|
1
|
31
|
1
|
32
|
1
|
33
|
1
|
34
|
19
|
1
|
35
|
1
|
36
|
1
|
37
|
1
|
38
|
1
|
39
|
20
|
1
|
40
|
1
|
41
|
1
|
42
|
1
|
43
|
1
|
44
|
21
|
1
|
45
|
1
|
46
|
1
|
47
|
1
|
48
|
1
|
49
|
22
|
1
|
50
|
1
|
51
|
1
|
52
|
1
|
53
|
1
|
54
|
23
|
1
|
55
|
1
|
56
|
1
|
57
|
1
|
58
|
1
|
59
|
24
|
2
|
0
|
|
|
|
|
|
|
|
|
iust
quantity
of
the
day
artificiall
,
from
sonne
risyng
to
son
settinge
,
and
thereby
also
the
quantitie
of
the
nyghte
:
then
shall
you
seke
the
houres
of
their
length
in
the
first
column
,
vnder
the
title
of
howers
:
and
if
the
daye
or
nyght
haue
any
minutes
aboue
those
euen
howers
,
you
shall
seke
them
in
the
highestrange
of
numbres
,
where
they
bee
set
from
12
to
12
,
and
take
that
numbre
of
minutes
that
is
nexte
in
quantitye
to
your
minutes
in
the
day
propounded
:
and
in
the
common
angle
,
againste
your
howers
and
vnder
your
minutes
,
you
shall
fynde
the
iuste
quantitie
of
the
minutes
that
make
an
hower
vnequall
,
for
that
daye
or
nyght
:
but
that
must
you
vnderstande
seuerally
.
Scholar
.
I
were
to
grosse
headded
if
I
wold
make
a
doubt
thereof
.
And
bycause
I
will
declare
vnto
you
how
I
vnderstande
the
vse
of
it
,
I
wyll
by
an
example
or
twoo
make
it
appeare
.
When
the
Artificiall
daye
is
14
howers
longe
,
and
20
minutes
,
and
the
nyghte
then
is
9
howers
longe
and
40
minutes
of
necessitye
:
I
woulde
knowe
the
iuste
quantitye
of
the
howers
vnequall
.
Firste
therefore
,
in
the
fyrste
colomne
I
seeke
oute
the
numbre
of
the
howers
,
whiche
is
14
,
then
in
the
highest
raunge
of
numbres
I
seeke
the
odde
minutes
,
beinge
20
,
and
bicause
I
fynde
no
suche
numbre
there
,
I
take
the
nexte
numbre
whiche
is
24
,
and
by
those
2
numbres
in
their
common
angle
againste
14
towarde
the
righte
hande
,
directly
vnder
the
24
minutes
,
I
fynde
1
,
12
,
whereby
I
vnderstande
,
that
eche
vnequall
hower
is
longer
then
the
equall
hower
by
12
minutes
that
daye
.
and
for
the
nyghte
I
fynde
againste
9
and
vnder
the
numbre
of
36
(
whiche
is
nexte
vnto
40
)
the
iuste
quantitie
of
eche
vnequalle
hower
of
the
same
nighte
,
to
bee
0
,
48
,
that
is
but
48
minutes
:
and
so
is
the
vnequall
hower
of
the
nyghte
lesser
by
twelue
minutes
,
then
is
the
equalle
hower
.
And
so
bothe
those
howers
ioyned
togither
,
doo
make
twoo
howers
,
equall
to
twoo
Equinoctiall
or
Equall
howers
.
for
so
muche
as
the
one
is
to
lyttle
,
the
other
is
to
greate
.
Againe
for
an
other
triall
,
I
take
the
artificiall
daye
to
bee
8
howers
and
36
minutes
long
,
and
therfore
to
know
the
quantitie
of
an
vnequall
hower
,
I
seeke
against
8
,
and
vndernethe
36
,
wher
I
fynd
0
,
43
,
which
giueth
me
to
vnderstand
that
the
vnequall
hower
that
daye
is
only
43
minutes
in
quantity
,
&
the
nyghte
then
beynge
15
howers
long
and
24
minutes
,
yeldeth
his
vnequall
howers
of
1
hower
and
17
minutes
longe
:
whereby
it
is
seene
also
,
that
so
muche
is
supplied
by
the
one
hower
as
was
wantinge
in
the
other
.
so
that
euermore
one
vnequall
hower
of
the
day
ioined
with
an
vnequal
hower
of
the
nyghte
,
will
make
two
howers
equall
to
two
equinoctiall
howers
.
Scholar
.
Howers
equall
,
equinoctial
,
vulgare
and
naturall
.
You
meane
those
common
howers
which
we
vse
vulgarlye
,
whiche
are
called
also
of
some
men
Naturall
howers
,
takinge
that
name
of
the
Naturall
daye
,
whiche
they
diuide
into
24
equall
partes
,
(
thoughe
other
men
adscribe
that
name
to
Vnequal
howers
)
and
so
of
their
common
vse
ar
they
named
Vulgare
,
lyke
as
they
are
called
Equinoctiall
howers
,
bycause
(
as
I
haue
learned
)
they
depende
of
the
reuolution
of
the
Equinoctiall
:
and
therefore
keepe
they
one
constante
quantitie
,
eche
beyng
equall
with
other
.
Master
.
You
remembre
it
well
.
And
as
these
are
taken
of
the
motion
of
the
Equinoctiall
,
and
are
nothing
els
but
the
space
or
measure
of
time
wherein
15
degrees
of
the
Equinoctiall
do
passe
the
meridiane
line
,
Vnequall
howers
.
so
againe
it
seemeth
to
the
wisest
sorte
of
men
,
that
the
Vnequall
howers
ought
to
bee
gathered
by
the
motion
of
the
Zodiake
,
whose
seuerall
forme
of
ascension
for
euery
halfe
signe
,
dooth
make
a
seuerall
and
distinct
quantitie
of
Vnequall
howers
,
and
haue
no
fewer
sortes
of
differences
,
then
there
be
distincte
and
seuerall
degrees
or
pointes
,
at
whiche
that
arke
of
15
degrees
maye
beginne
his
ascension
,
The
declaration
of
the
table
.
as
partly
in
this
table
folowing
it
dooth
appeare
:
where
you
may
see
in
the
fyrste
columne
on
the
lefte
hande
,
and
in
the
laste
on
the
right
hand
,
the
degrees
of
the
signes
set
:
not
euery
one
seuerally
,
but
only
from
6
degrees
to
6
degrees
,
whiche
are
so
mennye
as
may
seeme
to
suffice
for
a
conuenient
distinction
of
the
seuerall
diuersities
in
such
hours
,
namely
in
that
latitude
of
52
degres
,
for
whiche
it
is
calculate
.
And
nexte
vnto
those
degrees
in
the
seconde
columne
,
and
in
the
laste
saue
one
,
are
set
the
names
of
the
12
Signes
in
their
conuenient
ordre
,
that
is
to
say
,
in
the
one
parte
the
6
Signes
whiche
be
called
north
Signes
,
as
Aries
,
Taurus
,
Gemini
,
Cancer
,
Leo
,
and
Virgo
:
and
in
the
other
are
set
the
6
south
Signes
,
Libra
,
Scorpio
,
Sagittarius
,
Capricornus
,
Aquarius
,
&
Pisces
.
And
against
those
signes
and
degrees
ar
set
the
quantities
of
euery
hower
in
the
daye
for
that
time
,
when
the
Sonne
is
in
any
suche
degree
of
those
signes
.
And
for
the
better
knowledge
of
the
howers
,
their
names
and
numbres
are
set
forth
in
the
head
of
the
table
:
where
also
is
set
a
distinction
by
diuersitye
of
the
daye
and
nighte
accordinglye
as
the
Sonne
is
then
in
the
southe
Signes
or
in
the
northe
signes
.
Scholar
.
I
doo
perceaue
it
to
bee
reasonable
,
that
the
first
hower
of
the
daye
muste
be
accompted
that
hower
,
in
whose
beginning
the
Sonne
doth
rise
:
so
that
euery
daye
the
fyrste
hower
is
begonne
with
the
ascension
of
that
degree
of
anye
signe
wherein
the
sonne
is
.
And
the
first
hower
of
the
night
is
begonne
with
the
ascension
of
that
degree
,
which
is
opposite
or
contrary
to
the
place
of
the
sonne
:
whiche
place
is
commonly
called
in
latine
Nadir
Solis
,
althoughe
in
deede
the
one
woorde
is
an
Arabike
woorde
,
and
not
latine
.
And
after
that
firste
hower
as
the
other
howers
of
necessitye
doo
follow
in
ordre
of
numbre
,
so
their
distinction
in
quantitie
doth
follow
in
this
table
:
and
the
difference
of
them
is
agre
able
to
the
diuersitye
of
the
ascension
of
eche
halfe
signe
of
the
Zodiake
,
as
they
doo
followe
in
ordre
.
Exaumple
.
So
that
to
come
to
an
example
,
for
declaration
that
I
doo
vnderstande
that
table
.
yf
I
woulde
knowe
the
quantitie
of
the
vnequall
howers
,
when
the
sonne
is
in
Aries
and
in
his
fyrste
degree
,
I
must
entre
the
fyrste
parte
of
the
table
,
where
I
fynde
on
the
lefte
hande
the
Signes
and
their
degrees
:
wherefore
againste
Aries
and
the
cyphar
o
,
which
betokeneth
the
very
beginning
of
the
signe
,
I
note
all
the
howers
as
they
followe
in
ordre
:
whereby
I
perceaue
that
the
fyrste
hower
of
the
day
is
but
25
minutes
of
an
equall
hower
in
lengthe
:
the
seconde
hower
A
TABLE
FOR
THE
DISTINCTION
OF
THE
VNEQVALL
HOWERS
,
calculate
for
the
latitude
of
52
degrees
.
Howers
of
the
daye
,
for
the
northe
Signes
:
and
of
the
nyghte
,
for
the
southe
Signes
.
Signes
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
Hours
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10.
|
11
|
12
|
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
0
|
♈
|
0
|
25
|
0
|
27
|
0
|
30
|
0
|
37
|
0
|
47
|
0
|
59
|
1
|
11
|
1
|
20
|
1
|
25
|
1
|
26
|
1
|
27
|
1
|
25
|
6
|
0
|
25
|
0
|
28
|
0
|
33
|
0
|
41
|
0
|
52
|
1
|
4
|
1
|
16
|
1
|
23
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
26
|
12
|
|
0
|
26
|
0
|
30
|
0
|
36
|
0
|
45
|
0
|
57
|
1
|
9
|
1
|
19
|
1
|
24
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
18
|
0
|
27
|
0
|
32
|
0
|
39
|
0
|
49
|
1
|
2
|
1
|
13
|
1
|
22
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
26
|
1
|
26
|
24
|
♉
|
0
|
29
|
0
|
34
|
0
|
43
|
0
|
54
|
1
|
7
|
1
|
17
|
1
|
24
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
30
|
0
|
30
|
0
|
37
|
0
|
47
|
0
|
59
|
1
|
12
|
1
|
20
|
1
|
25
|
1
|
26
|
1
|
27
|
1
|
25
|
1
|
26
|
1
|
26
|
6
|
|
0
|
33
|
0
|
41
|
0
|
52
|
1
|
4
|
1
|
16
|
1
|
23
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
12
|
0
|
36
|
0
|
45
|
0
|
57
|
1
|
9
|
1
|
19
|
1
|
24
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
27
|
18
|
|
0
|
39
|
0
|
49
|
1
|
2
|
1
|
13
|
1
|
22
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
24
|
0
|
43
|
0
|
54
|
1
|
7
|
1
|
17
|
1
|
24
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
27
|
1
|
26
|
0
|
♊
|
0
|
47
|
0
|
59
|
1
|
11
|
1
|
20
|
1
|
25
|
1
|
26
|
1
|
27
|
1
|
25
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
29
|
6
|
0
|
52
|
1
|
4
|
1
|
16
|
1
|
23
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
24
|
12
|
|
0
|
57
|
1
|
9
|
1
|
19
|
1
|
24
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
22
|
18
|
1
|
2
|
1
|
13
|
1
|
22
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
24
|
1
|
19
|
24
|
♋
|
1
|
7
|
1
|
17
|
1
|
24
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
27
|
1
|
15
|
30
|
1
|
11
|
1
|
20
|
1
|
25
|
1
|
26
|
1
|
27
|
1
|
25
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
25
|
1
|
21
|
1
|
19
|
6
|
|
1
|
16
|
1
|
23
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
24
|
1
|
17
|
1
|
7
|
12
|
1
|
19
|
1
|
24
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
27
|
1
|
16
|
1
|
22
|
1
|
13
|
1
|
2
|
18
|
|
1
|
22
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
24
|
1
|
19
|
1
|
9
|
0
|
57
|
24
|
1
|
24
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
27
|
1
|
15
|
1
|
4
|
0
|
52
|
0
|
♌
|
1
|
25
|
1
|
26
|
1
|
27
|
1
|
25
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
25
|
1
|
21
|
1
|
11
|
0
|
59
|
0
|
47
|
6
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
24
|
1
|
17
|
1
|
7
|
0
|
54
|
0
|
47
|
12
|
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
22
|
1
|
13
|
1
|
2
|
0
|
49
|
0
|
39
|
18
|
1
|
27
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
24
|
1
|
19
|
1
|
9
|
0
|
57
|
0
|
45
|
0
|
36
|
24
|
♍
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
27
|
1
|
15
|
1
|
4
|
0
|
52
|
0
|
42
|
0
|
33
|
0
|
1
|
27
|
1
|
25
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
25
|
1
|
21
|
1
|
11
|
0
|
59
|
0
|
47
|
0
|
37
|
0
|
30
|
6
|
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
24
|
1
|
17
|
1
|
7
|
0
|
54
|
0
|
47
|
0
|
34
|
0
|
33
|
12
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
22
|
1
|
13
|
1
|
2
|
0
|
49
|
0
|
39
|
0
|
32
|
0
|
27
|
18
|
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
24
|
1
|
19
|
1
|
9
|
0
|
57
|
0
|
45
|
0
|
36
|
0
|
34
|
0
|
26
|
24
|
1
|
26
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
27
|
1
|
15
|
1
|
4
|
0
|
52
|
0
|
41
|
0
|
33
|
0
|
28
|
0
|
25
|
30
|
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
25
|
1
|
21
|
1
|
22
|
1
|
59
|
0
|
47
|
0
|
37
|
0
|
30
|
0
|
27
|
0
|
25
|
|
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
Howers
of
the
nyghte
,
for
the
northe
Signes
:
and
of
the
daye
,
for
the
scuthe
Signes
.
7
|
8
|
9
|
10
|
11
|
12
|
Signes
|
1
|
2
|
3
|
4
|
5
|
6
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10.
|
11
|
12
|
Houres
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
25
|
1
|
21
|
1
|
11
|
0
|
59
|
0
|
47
|
0
|
37
|
0
|
30
|
0
|
27
|
0
|
25
|
♎
|
0
|
1
|
26
|
1
|
26
|
1
|
26
|
1
|
24
|
1
|
17
|
1
|
7
|
0
|
54
|
0
|
47
|
0
|
34
|
0
|
33
|
0
|
26
|
0
|
24
|
6
|
1
|
26
|
1
|
27
|
1
|
26
|
1
|
22
|
1
|
13
|
1
|
2
|
0
|
49
|
0
|
39
|
0
|
32
|
0
|
27
|
0
|
25
|
0
|
25
|
|
12
|
1
|
26
|
1
|
26
|
1
|
24
|
1
|
19
|
1
|
9
|
0
|
57
|
0
|
45
|
0
|
36
|
0
|
34
|
0
|
26
|
0
|
25
|
0
|
25
|
18
|
1
|
27
|
1
|
26
|
1
|
27
|
1
|
15
|
1
|
4
|
0
|
52
|
0
|
41
|
0
|
33
|
0
|
28
|
0
|
25
|
0
|
24
|
0
|
26
|
♏
|
24
|
1
|
26
|
1
|
25
|
1
|
21
|
1
|
11
|
0
|
59
|
0
|
47
|
0
|
37
|
0
|
30
|
0
|
27
|
0
|
25
|
0
|
25
|
0
|
27
|
0
|
1
|
26
|
1
|
24
|
1
|
17
|
1
|
7
|
0
|
54
|
0
|
47
|
0
|
34
|
0
|
33
|
0
|
26
|
0
|
24
|
0
|
25
|
0
|
28
|
|
6
|
1
|
26
|
1
|
22
|
1
|
13
|
1
|
2
|
0
|
49
|
0
|
39
|
0
|
32
|
0
|
27
|
0
|
25
|
0
|
25
|
0
|
26
|
0
|
30
|
12
|
1
|
24
|
1
|
19
|
1
|
9
|
0
|
57
|
0
|
45
|
0
|
36
|
0
|
34
|
0
|
26
|
0
|
25
|
0
|
25
|
0
|
27
|
0
|
32
|
|
18
|
1
|
27
|
1
|
15
|
1
|
4
|
0
|
52
|
0
|
41
|
0
|
33
|
0
|
28
|
0
|
25
|
0
|
24
|
0
|
26
|
0
|
29
|
0
|
34
|
24
|
1
|
21
|
1
|
11
|
0
|
59
|
0
|
47
|
0
|
37
|
0
|
30
|
0
|
27
|
0
|
25
|
0
|
25
|
0
|
27
|
0
|
30
|
0
|
37
|
♐
|
0
|
1
|
17
|
1
|
7
|
0
|
54
|
0
|
47
|
0
|
34
|
0
|
33
|
0
|
26
|
0
|
24
|
0
|
25
|
0
|
28
|
0
|
33
|
0
|
41
|
6
|
1
|
13
|
1
|
2
|
0
|
49
|
0
|
39
|
0
|
32
|
0
|
27
|
0
|
25
|
0
|
25
|
0
|
26
|
0
|
30
|
0
|
36
|
0
|
45
|
|
12
|
1
|
9
|
0
|
57
|
0
|
45
|
0
|
36
|
0
|
34
|
0
|
26
|
0
|
25
|
0
|
25
|
0
|
27
|
0
|
32
|
0
|
39
|
0
|
49
|
18
|
1
|
4
|
0
|
52
|
0
|
41
|
0
|
33
|
0
|
28
|
0
|
25
|
0
|
24
|
0
|
26
|
0
|
29
|
0
|
34
|
0
|
43
|
0
|
54
|
♑
|
4
|
0
|
59
|
0
|
47
|
0
|
37
|
0
|
30
|
0
|
27
|
0
|
25
|
0
|
25
|
0
|
27
|
0
|
30
|
0
|
37
|
0
|
47
|
0
|
59
|
0
|
0
|
54
|
0
|
47
|
0
|
34
|
0
|
33
|
0
|
26
|
0
|
24
|
0
|
25
|
0
|
28
|
0
|
33
|
0
|
41
|
0
|
52
|
1
|
4
|
|
6
|
0
|
49
|
0
|
39
|
0
|
32
|
0
|
27
|
0
|
25
|
0
|
25
|
0
|
26
|
0
|
30
|
0
|
36
|
0
|
45
|
0
|
57
|
1
|
9
|
12
|
0
|
45
|
0
|
36
|
0
|
34
|
0
|
26
|
0
|
25
|
0
|
25
|
0
|
27
|
0
|
32
|
0
|
39
|
0
|
49
|
1
|
2
|
1
|
13
|
|
18
|
0
|
41
|
0
|
33
|
0
|
28
|
0
|
25
|
0
|
24
|
0
|
26
|
0
|
29
|
0
|
34
|
0
|
43
|
0
|
54
|
1
|
7
|
1
|
17
|
24
|
0
|
37
|
0
|
30
|
0
|
27
|
0
|
25
|
0
|
25
|
0
|
27
|
0
|
30
|
0
|
37
|
0
|
47
|
0
|
59
|
1
|
11
|
1
|
20
|
♒
|
0
|
0
|
34
|
0
|
33
|
0
|
26
|
0
|
24
|
0
|
25
|
0
|
28
|
0
|
33
|
0
|
41
|
0
|
52
|
1
|
4
|
1
|
16
|
1
|
23
|
6
|
0
|
32
|
0
|
27
|
0
|
25
|
0
|
25
|
0
|
26
|
0
|
30
|
0
|
36
|
0
|
45
|
0
|
57
|
1
|
9
|
1
|
19
|
1
|
24
|
|
12
|
0
|
34
|
0
|
26
|
0
|
25
|
0
|
25
|
0
|
27
|
0
|
32
|
0
|
39
|
0
|
49
|
1
|
2
|
1
|
13
|
1
|
22
|
1
|
26
|
18
|
0
|
28
|
0
|
25
|
0
|
24
|
0
|
26
|
0
|
29
|
0
|
34
|
0
|
43
|
0
|
54
|
1
|
7
|
1
|
17
|
1
|
24
|
1
|
26
|
♓
|
24
|
0
|
27
|
0
|
26
|
0
|
25
|
0
|
27
|
0
|
30
|
0
|
37
|
0
|
47
|
0
|
59
|
1
|
11
|
1
|
20
|
1
|
25
|
1
|
26
|
0
|
0
|
26
|
0
|
24
|
0
|
25
|
0
|
28
|
0
|
33
|
0
|
41
|
0
|
52
|
1
|
4
|
1
|
16
|
1
|
23
|
1
|
26
|
1
|
27
|
|
6
|
0
|
25
|
0
|
25
|
0
|
26
|
0
|
30
|
0
|
36
|
0
|
45
|
0
|
57
|
1
|
9
|
1
|
19
|
1
|
24
|
1
|
26
|
1
|
26
|
12
|
0
|
25
|
0
|
25
|
0
|
27
|
0
|
32
|
0
|
39
|
0
|
49
|
1
|
2
|
1
|
13
|
1
|
22
|
1
|
26
|
1
|
27
|
1
|
26
|
|
18
|
0
|
24
|
0
|
26
|
0
|
29
|
0
|
34
|
0
|
43
|
0
|
54
|
1
|
7
|
1
|
17
|
1
|
24
|
1
|
26
|
1
|
26
|
1
|
26
|
24
|
0
|
25
|
0
|
27
|
0
|
30
|
0
|
37
|
0
|
47
|
0
|
59
|
1
|
11
|
1
|
20
|
1
|
25
|
1
|
26
|
1
|
27
|
1
|
25
|
|
30
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
|
is
27
minutes
longe
:
the
thirde
hower
30
minutes
,
that
is
halfe
an
equall
hower
iuste
:
and
in
the
same
line
goinge
forwarde
,
the
12
and
laste
hower
of
the
daye
is
1
hower
and
25
minutes
in
lengthe
.
Then
for
the
nighte
the
howers
appeare
in
the
other
parte
of
the
table
,
where
the
firste
hower
dooth
containe
one
equall
or
common
hower
,
and
26
minutes
:
the
seconde
hower
and
the
third
be
of
lyke
quantitie
,
and
so
do
they
afterwarde
decrease
vntyll
the
laste
hower
of
the
nyght
.
An
other
example
:
Exaumple
.
when
the
son
is
in
the
10
degree
of
Cancer
,
bicause
I
can
not
fynde
that
degree
in
the
table
,
I
take
the
degree
nexte
vnto
it
,
whiche
is
the
12
degree
,
and
procedynge
with
it
,
I
fynde
the
fyrste
vnequall
hower
to
containe
1.
equall
hower
,
and
19
minutes
:
and
the
second
vnequall
hower
hath
in
it
1.
equall
hower
and
24
minutes
.
Nowe
for
the
nyghte
I
looke
in
the
seconde
parte
of
the
table
,
and
fynde
the
fyrste
vnequall
hower
to
bee
but
49
minutes
in
lengthe
,
and
the
seconde
but
39
minutes
.
and
so
in
ordre
folowinge
.
This
muste
I
doo
when
the
Sonne
is
in
anye
of
the
northe
signes
,
but
if
the
son
be
in
any
of
the
south
signes
,
thē
must
we
accompt
the
day
howers
in
the
second
part
of
the
table
,
&
the
howers
of
the
night
must
be
sought
in
the
firste
parte
of
the
table
:
in
all
other
pointes
I
perceaue
there
is
small
difference
.
Master
.
an
ordre
for
proportion
.
Yet
by
the
way
this
maye
you
note
,
that
if
you
woulde
desire
more
precisely
to
knowe
the
iuste
quantitie
of
the
howers
,
for
anye
suche
degree
of
the
Signes
as
is
not
expressed
in
your
table
,
you
shall
woorke
by
the
rule
of
proportion
,
to
knowe
the
more
exacte
quantitie
of
the
vnequall
howers
.
as
for
example
:
In
the
former
worke
where
you
supposed
the
sonne
to
be
in
the
10
degree
of
Cancer
,
bicause
that
degre
is
not
found
in
the
table
,
you
must
work
by
proportion
to
knowe
it
,
&
that
in
this
forme
:
firste
consider
the
howers
against
the
next
numbre
of
degrees
,
as
well
beneth
your
degre
as
also
aboue
the
same
,
&
marke
the
difference
betweene
them
two
,
which
difference
shall
alwaies
be
the
second
numbre
in
the
Golden
rule
:
and
the
fyrst
noumbre
of
that
woorke
shall
alwaies
be
6
degrees
,
bicause
that
is
the
ordinarye
excesse
in
this
table
of
eche
two
numbres
next
togither
:
Now
for
the
third
numbre
,
you
shall
set
the
excesse
of
your
degrees
proponed
,
aboue
the
lesser
degres
in
that
table
,
next
beneth
your
said
numbre
,
which
in
this
example
is
4
,
for
so
much
is
betwene
6
&
10.
And
the
difference
in
howers
in
the
table
is
but
3
minutes
:
for
against
the
6
degree
of
Cancer
,
ther
is
but
one
hower
and
16
minutes
:
and
against
the
12
degre
is
set
one
hower
and
19
minutes
.
Therefore
thus
doo
I
set
those
numbres
accordyng
to
the
golden
rule
,
saying
:
If
6
degrees
giue
three
minutes
,
then
4
degrees
muste
yelde
twoo
minutes
.
those
two
must
bee
added
to
the
lesser
numbre
,
and
so
dooth
there
ryse
one
hower
and
18
minutes
for
the
exacte
quantitye
of
the
fyrste
vnequall
hower
,
the
Sonne
beeynge
in
the
tenthe
degree
of
Cancer
.
Scholar
.
I
praye
you
lette
me
prooue
the
same
for
the
seconde
hower
of
the
nyght
,
where
against
the
6
degree
I
find
o
hower
and
47
minutes
:
and
againste
the
12
degree
I
see
o
hower
,
and
39
minutes
,
heere
the
excesse
is
8
minutes
:
then
sette
I
the
figures
thus
in
the
golden
rule
,
and
say
:
If
6
yelde
8
,
then
shall
4
giue
5
⅓
:
if
I
adde
these
vnto
the
lesser
numbre
of
time
,
which
is
39
minutes
,
Master
.
You
are
to
farre
deceiued
,
and
therefore
I
interrupt
your
woordes
,
for
all
thinges
are
to
bee
gouerned
by
reason
.
So
that
if
the
howers
do
increase
in
quantitie
,
then
is
it
reasonable
to
adde
the
parte
proportionable
to
the
lesser
numbre
of
tyme
,
as
it
was
in
the
former
example
:
but
in
this
example
you
see
the
time
dooth
not
increase
,
but
decrease
,
(
seynge
the
tyme
against
6
degrees
is
greater
then
the
tyme
against
12
degrees
)
and
therefore
by
good
reason
the
parte
proportionable
is
to
be
abated
from
the
greater
,
and
not
to
be
added
to
the
lesser
.
Schol
.
So
is
it
reasonable
:
therfore
must
I
take
that
5
⅓
from
47
,
&
then
resteth
41
2
/
3
,
whiche
is
the
precise
quantitie
of
that
vnequall
hower
.
And
nowe
I
thanke
you
,
I
am
fully
instructed
touching
that
matter
:
so
that
for
anye
vnequall
hower
accordinge
to
the
place
of
the
sonne
in
this
latter
table
,
and
after
the
lengthe
of
the
daye
in
the
fyrste
table
,
I
canne
fynde
oute
the
quantitie
of
eche
vnequalle
hower
:
but
these
twoo
formes
doo
not
make
exactly
one
quantitye
of
howers
vnequall
.
Master
.
As
in
that
you
shall
haue
more
exacter
declaration
hereafter
.
And
for
this
present
tyme
I
wyll
say
no
more
but
that
eche
of
both
waies
hath
good
vses
.
And
the
fyrst
form
whiche
seemeth
most
plaine
and
leaste
artificiall
,
hathe
comprobation
of
manye
men
,
and
namelye
of
Ptolemye
in
the
ninth
chapter
of
his
second
boke
of
Almagestes
.
but
omittyng
for
a
time
that
that
remayneth
touching
howers
,
I
will
now
speake
somwhat
of
the
quantities
of
daies
,
in
whiche
matter
you
shall
call
to
mynd
,
Daies
artificiall
and
Naturall
.
that
the
Naturall
daye
is
not
one
with
the
Artificiall
daye
:
for
the
firste
is
commonly
accompted
from
Sonne
risinge
one
daye
,
to
Sonne
rising
the
nexte
daye
.
but
the
seconde
,
that
is
the
Artificiall
daye
,
is
reckened
only
from
sonne
risinge
,
to
sonne
setting
:
so
that
there
is
no
night
accompted
in
the
Artificiall
daye
,
as
there
is
in
the
Naturall
daye
.
Scholar
.
This
I
perceaue
well
inoughe
:
and
farther
also
,
that
the
Naturall
daies
are
euer
24
howers
longe
,
in
all
our
knowen
cuntries
,
but
the
Artificiall
daies
do
increase
and
de
crease
diuerfely
.
And
as
I
desire
to
know
the
causes
therof
,
so
I
do
meruail
how
it
cometh
to
passe
,
that
in
any
cuntry
or
climat
the
naturall
daies
shuld
differ
.
Master
.
To
the
intente
that
we
may
proceede
ordrely
,
we
wyll
begin
with
the
one
forte
of
daies
,
and
so
come
to
the
talke
of
the
other
.
And
firste
as
concerning
Naturall
dayes
,
I
sayde
that
they
were
commonly
accompted
from
son
rysing
to
son
setting
:
which
description
being
true
,
what
shal
we
say
of
those
northe
and
southe
cuntries
,
where
the
Sonne
continueth
aboue
the
Horizont
in
some
places
three
weekes
,
in
other
6
weeks
,
and
so
increasing
tyll
it
extend
to
halfe
a
year
.
in
al
which
places
if
we
call
the
naturall
day
the
space
from
son
risyng
to
Sonne
risyng
again
,
then
can
not
the
naturall
day
be
of
one
quantitie
to
all
nations
,
and
so
shuld
those
daies
naturall
differ
in
nature
,
whiche
were
agaynste
nature
vtter
lye
:
and
therefore
dyd
I
vse
that
woorde
commonlye
in
the
former
description
:
but
if
I
shall
define
the
naturall
daye
exactlye
,
I
muste
call
it
that
iuste
tyme
in
whiche
the
eight
Sphere
or
Firmamente
dooth
exactlye
accomplyshe
his
course
,
The
naturall
daye
.
whiche
tyme
of
naturall
daye
is
the
common
meafure
of
all
other
tymes
:
and
thys
tyme
is
alwayes
equalle
in
all
places
,
howe
be
it
accordynge
to
the
former
description
,
yf
the
retournynge
of
the
Sonne
bee
accompted
frome
anye
one
parte
of
the
Meridiane
lyne
,
to
the
same
parte
of
the
sayde
lyne
,
then
maye
that
description
well
extende
to
all
partes
of
the
worlde
:
for
althoughe
some
nations
haue
the
Sonne
in
syghte
halfe
a
yeare
togither
,
yet
dooth
the
sonne
retourne
to
theyr
meridiane
lyne
towarde
the
southe
,
at
the
eand
of
24
howers
within
a
little
,
and
in
all
places
lykewaies
where
the
daye
it
not
full
24
howers
,
the
sonne
doothe
retourne
to
their
horizont
,
at
the
eand
of
24
howers
nygh
hande
.
Scholar
.
I
heare
you
speake
in
bothe
these
declarations
,
with
a
doubtfull
limitation
of
the
24
howers
,
as
thoughe
that
tyme
were
not
the
precise
or
iuste
measure
of
the
naturall
daye
.
Master
.
So
shall
it
appeare
vnto
you
,
yf
you
consider
that
the
sonne
dooth
euerye
daye
runne
one
degree
almoste
towarde
the
easte
,
accordynge
to
the
succession
of
the
signes
,
as
before
is
mentioned
:
for
if
this
daye
the
sonne
be
in
the
fyrste
degree
of
Libra
iustely
at
noone
,
then
to
morowe
at
noone
hee
wyll
bee
in
the
seconde
degree
:
and
so
the
thirde
daye
hence
in
the
thirde
degree
:
and
by
the
same
reason
at
the
monethes
eande
,
wyll
the
sonne
haue
passed
Libra
cleerely
,
and
bee
in
the
beginninge
of
the
nexte
signe
,
whiche
is
Scorpius
:
and
therefore
must
he
be
slacker
in
comming
to
the
Meridian
line
,
by
so
muche
time
as
serueth
for
the
risynge
of
all
the
signe
of
Libra
in
a
Righte
sphere
.
Scholar
.
That
tyme
must
be
an
hower
and
52
minutes
.
for
(
as
I
remembre
)
the
partes
of
the
Equinoctiall
whiche
doo
serue
for
the
ascension
of
Libra
,
are
27
degrees
and
54
minutes
.
Master
.
As
that
is
true
,
so
marke
what
is
the
difference
now
for
euerye
day
of
that
moneth
,
The
firste
cause
of
diuersitye
in
Naturall
dayes
.
and
then
shall
you
perceaue
the
difference
of
the
Naturall
dayes
,
as
muche
as
dependeth
of
that
cause
.
Scholar
.
For
the
fyrste
degree
of
Libra
,
the
quantitye
of
his
ascention
is
55
minutes
of
the
equinoctiall
,
whiche
maketh
in
time
of
an
hower
3
minutes
and
⅔
,
and
so
maye
I
see
for
diuers
degrees
at
the
beginninge
of
Libra
,
by
the
table
of
the
astensions
in
the
Right
sphere
:
but
towarde
the
eande
of
the
same
signe
,
I
see
57
minutes
agreeyng
to
the
ascension
of
one
degree
,
whiche
maketh
some
difference
in
tyme
also
,
thoughe
it
bee
small
.
Master
.
Marke
now
about
the
middle
of
Scorpius
,
how
eche
degree
of
the
Zodiake
hath
one
degree
of
the
Equinoctiall
agreeynge
to
his
ascension
,
whiche
maketh
in
tyme
4
minutes
of
an
hower
:
and
about
the
mydle
of
Sagittarius
one
degree
of
the
Zodiake
hathe
aunswerable
to
him
64
or
65
minutes
of
the
Equinoctiall
.
and
so
in
other
diuers
degrees
of
Signes
shall
you
fynd
diuers
quantities
of
their
ascensions
,
whereby
it
must
needes
appeare
,
that
if
the
Sonne
dyd
moue
forwarde
in
the
Zodiake
euery
daye
one
degree
iustlye
,
that
the
sonne
shoulde
be
4
minutes
after
the
24
howers
slacker
then
he
was
the
daye
before
in
touching
the
meridiane
line
,
if
there
were
not
an
other
cause
of
diuersitye
by
the
sundrye
quantities
of
the
ascensions
.
Scholar
.
This
cause
is
manifest
.
And
bicause
I
see
for
some
degrees
of
the
Zodiake
but
onlye
55
minutes
of
the
Equinoctiall
,
whiche
maketh
in
time
3
minutes
and
⅔
:
and
for
other
degrees
65
minutes
,
whiche
is
4
minutes
and
1
/
3
;
:
so
doth
it
appeare
that
the
greatest
difference
is
but
2
/
3
partes
of
a
minute
:
whiche
is
a
small
matter
.
Master
.
Yet
this
small
matter
will
cause
muche
matter
in
Astronomicall
computations
,
though
there
were
no
more
difference
of
diuersitie
in
Naturall
dayes
but
this
only
:
but
yet
are
there
twoo
other
causes
in
all
Oblique
spheres
,
and
but
one
in
the
Right
sphere
.
The
seconde
common
cause
in
bothe
spheres
,
is
the
eccentricitye
of
the
Sonne
.
The
second
cause
of
vn
equal
daies
naturall
.
Scholar
.
What
meane
you
thereby
?
for
I
doo
not
vnderstande
that
eccentricitye
.
Master
.
It
is
a
matter
not
agreeable
for
this
treatise
,
but
that
by
occasion
I
am
moued
to
name
it
as
a
concurrente
cause
touchinge
inequalitye
of
naturall
dayes
:
yet
somwhat
to
saye
of
it
as
may
suffice
for
this
present
,
by
example
you
shall
vnderstande
both
what
eccentricitye
is
,
and
also
howe
it
maye
cause
diuersitye
in
naturall
dayes
:
for
declaration
Geometric diagram.
whereof
here
in
this
fygure
you
see
two
circles
a
greater
and
a
lesser
:
the
greater
dooth
betoken
the
eighte
sphere
or
firmamente
,
and
the
lesser
dooth
represent
the
eccentrike
circle
of
the
sphere
of
the
Sonne
.
These
2
circles
as
you
see
,
are
eccentrike
,
for
that
they
haue
not
one
common
centre
,
sith
the
centre
of
the
greater
circle
is
by
A
,
and
the
centre
of
the
lesser
circle
is
by
B.
the
distaunce
betweene
A
and
B
is
the
quantitie
of
their
eccentricitye
.
Nowe
maye
you
see
that
eche
circle
is
diuided
into
4
quarters
:
and
lykewise
you
may
se
,
that
the
higher
halfe
of
the
lesser
circle
doth
not
fully
answere
to
halfe
the
greater
circle
:
and
againe
the
nether
halfe
of
the
lesser
circle
doth
occupy
more
then
the
halfe
of
the
greater
circle
.
whereby
it
muste
needes
bee
euidente
to
all
men
,
that
when
the
Sonne
moueth
in
the
higher
part
of
his
eccentrike
circle
,
hee
doth
moue
slowlyer
then
he
dooth
in
the
nether
parte
of
the
same
eccentrike
:
I
meane
in
comparison
to
the
Zodiake
of
the
eyghte
sphere
:
and
thereby
must
it
appeare
that
the
Sonne
doth
not
euerye
daye
moue
lyke
numbre
of
minutes
in
the
Zodiake
:
and
you
maye
easilye
coniecture
hereby
,
that
this
is
an
other
cause
of
diuersitye
in
the
quantitye
of
the
naturall
dayes
.
The
thirde
cause
of
diuersitie
of
daies
Naturall
.
A
thyrde
diuersitye
is
that
whiche
is
peculiare
to
euerye
seuerall
climate
,
and
not
common
to
anye
two
on
one
syde
of
the
Equinoctiall
,
and
that
is
the
obliquitie
of
the
Horizonte
,
yf
the
daye
shall
bee
accompted
from
sonne
risynge
to
sonne
risynge
againe
:
but
this
varietie
is
so
greate
and
so
diuers
,
that
it
is
in
manner
infinite
:
and
therfore
doo
Astronomers
reiecte
the
ordre
of
accompt
of
daies
,
and
recken
the
day
from
noone
to
none
,
whiche
accompte
serueth
generally
for
all
the
partes
of
the
worlde
,
as
if
all
Climates
had
one
Horizont
:
for
as
in
the
ryghte
sphere
bothe
the
Poles
doo
touche
the
Horizont
,
so
the
meridianes
of
euery
climate
and
of
all
regions
do
passe
by
bothe
the
Poles
of
the
worlde
:
and
therefore
all
ascensions
accompted
vnto
that
meridiane
line
,
must
bee
estemed
as
ryghte
ascensions
,
I
meane
ascensions
lyke
vnto
them
that
be
in
the
righte
sphere
.
Scholar
.
Nowe
do
I
perceaue
,
that
although
there
may
be
assigned
thre
causes
of
varietie
in
the
naturall
dayes
,
yet
one
of
them
whiche
is
gathered
by
the
obliquitie
of
the
horizonte
in
not
regarded
of
Astronomers
,
sith
they
doo
accompt
the
beginning
of
the
daye
from
the
noone
steede
,
and
the
sonne
beynge
in
the
meridiane
lyne
.
The
second
cause
by
the
eccentricitie
of
the
sonne
I
may
coniecture
to
appertain
to
a
more
higher
speculation
,
then
this
treatise
doth
admit
:
but
yet
may
be
somwhat
vnderstande
euen
nowe
by
a
small
explication
.
The
thirde
cause
whiche
dependeth
of
the
diuersitie
of
the
ascensions
by
obliquitye
of
the
Horizonte
,
is
peculiare
to
this
treatise
,
and
maye
be
gathered
oute
of
the
tables
of
ascensions
whiche
serue
for
the
Ryghte
sphere
:
of
all
whiche
varieties
at
a
time
of
more
conuenient
leasure
,
I
will
make
for
mine
exercise
a
table
at
large
.
but
in
the
meane
ceason
I
praye
you
,
proceede
as
you
haue
begonne
.
Master
.
Touching
the
diuersities
of
Naturall
dayes
this
maye
suffice
:
and
for
a
common
and
meane
quantitie
you
maye
assigne
24
howers
and
4
minutes
,
bicause
that
is
the
common
nombre
:
for
althoughe
many
be
greater
,
yet
manye
other
bee
lesser
.
and
this
numbre
is
moste
nyghest
the
meane
.
The
diuersitie
of
the
artificiall
daies
.
Nowe
touching
Artificiall
daies
you
shall
fynde
no
fewer
diuersities
:
wherein
although
all
the
former
three
causes
be
concurrent
,
yet
the
principall
cause
is
the
obliquitie
of
the
Horizont
.
And
althoughe
I
haue
twyse
before
made
mention
of
those
daies
,
yet
doth
there
rest
more
to
be
sayd
of
them
.
for
in
bothe
places
before
I
dyd
briefly
touche
the
causes
of
diuersitie
of
suche
Artificialle
daies
in
diuers
climates
,
and
in
the
table
of
the
distinction
of
climates
,
I
dyd
sette
forth
the
quantitie
of
the
longest
daye
in
eche
of
them
:
and
nowe
will
I
shew
you
somwhat
of
the
reason
of
their
inequalitie
in
anye
one
climate
.
Fyrst
therfore
to
begin
withal
,
you
knowe
that
before
the
sonne
in
his
naturall
course
can
passe
the
full
of
one
degre
,
he
is
caried
by
the
violence
of
the
Starrye
skye
rounde
aboute
the
earthe
.
so
that
in
going
betweene
the
firste
degree
of
Capricorne
,
and
the
fyrste
of
Cancer
,
he
dooth
consume
halfe
a
yeare
,
and
therefore
maketh
aboue
is
2
reuolutions
lyke
spirall
circles
,
which
are
diuerslye
parted
by
the
Horizont
,
accordyng
to
the
diuersities
of
the
eleuation
of
the
Pole
.
As
in
the
Ryght
sphere
they
are
all
parted
by
the
Horizont
into
two
equall
partes
:
so
in
euerye
bowing
Sphere
,
they
are
vnequally
deuided
by
the
Horizont
,
so
that
where
the
north
pole
is
eleuate
aboue
the
Horizont
,
there
those
circles
of
the
sonnes
reuolutions
which
be
from
the
equinoctiall
northward
,
haue
the
greater
portion
aboue
the
horizont
,
and
the
lesser
parte
vnder
the
same
:
and
contrarye
waies
those
circles
(
or
spires
if
you
like
better
so
to
call
them
)
whiche
be
from
the
Equinoctiall
to
the
tropike
of
Capricorne
,
and
serue
for
explication
of
the
Sonnes
motion
,
they
haue
their
greater
portion
vnder
the
Horizont
,
and
the
lesser
portion
aboue
the
same
.
And
comparinge
eche
one
of
these
to
other
,
that
circle
whiche
is
farthest
towarde
the
south
,
is
moste
parte
vnder
the
Horizont
of
anye
other
.
and
euerye
one
of
them
the
more
it
departeth
from
the
south
and
draweth
toward
the
north
,
the
greater
is
his
portion
that
is
aboue
the
horizonte
,
and
the
lesser
is
that
other
portion
whiche
is
vnder
the
same
.
wherfore
the
middlemost
bounde
of
those
two
extremes
,
is
iuste
halfe
vnder
,
and
halfe
aboue
the
Horizonte
:
and
therfore
the
sonne
beyng
in
it
,
doth
make
his
abode
iuste
lyke
tyme
aboue
the
earthe
,
as
he
doth
vnder
it
,
and
therby
the
daies
and
nights
are
equall
:
but
from
thence
towarde
Cancer
,
the
daye
dooth
still
increase
aboue
the
nighte
:
and
from
thence
toward
Capricorne
,
the
daye
dothe
still
abate
shorter
then
the
nyghte
:
which
thinge
will
easilye
appeare
to
the
sight
,
bothe
by
these
Geometric diagram.
figures
here
drawen
,
and
also
by
the
diuers
positions
of
the
materiall
Sphere
or
globe
.
And
styll
the
higher
that
the
Pole
is
eleuate
aboue
the
Horizont
,
the
greater
parte
of
the
northerlye
circles
is
aboue
the
Horizont
,
and
the
lesser
parte
of
theym
vnder
the
Horizonte
.
And
contrary
waies
of
the
southerlye
circles
,
the
greater
portions
of
them
are
vnder
the
horizont
,
and
the
lesser
portions
aboue
it
.
Nowe
is
it
easily
perceaued
,
that
seynge
the
sonne
dooth
kepe
hys
dailye
course
in
one
of
those
circles
,
then
accorginglye
as
that
circle
in
whiche
the
sonne
doth
moue
,
is
parted
by
the
horizonte
,
so
is
the
partition
of
the
24
howers
into
daye
and
nyghte
agreeablye
:
so
that
if
the
circle
of
the
sonnes
course
be
more
vnder
the
horizont
then
aboue
it
,
then
shall
the
nyghte
be
longer
then
the
daye
:
and
if
the
greater
parte
of
the
sonnes
circle
be
aboue
the
horizont
,
then
the
day
shal
exceede
the
nighte
,
in
lyke
proportion
as
the
partes
of
the
circles
are
in
comparison
togither
.
Scholar
.
These
diuers
circles
(
I
perceaue
)
are
not
in
the
sphere
of
the
sonne
,
but
are
accompted
in
the
eighte
sphere
betweene
the
two
tropikes
,
so
that
euery
daye
by
the
reuolution
of
the
Firmament
,
the
sonne
is
caried
frome
easte
to
weste
rounde
about
the
earthe
,
and
by
this
violente
motion
doth
describe
a
spirall
circle
(
as
you
call
it
)
and
not
an
exact
circle
:
but
yet
maye
it
serue
in
this
case
,
as
if
it
were
a
iuste
circle
:
the
difference
is
so
lytle
of
the
space
betweene
the
spirall
lynes
in
comparison
to
their
compasse
,
whiche
by
the
table
of
declination
before
expressed
,
I
gesse
to
bee
in
proportion
scarse
1
/
1000
,
which
is
no
part
notable
in
this
case
.
And
this
farther
I
note
:
that
two
circles
on
contrary
partes
of
the
Equinoctiall
equally
distaunt
from
it
,
are
parted
by
the
horizont
after
one
rate
,
and
into
lyke
portions
:
but
yet
in
such
difference
,
that
the
parte
of
the
one
circle
aboue
ground
,
is
equall
to
the
parte
of
the
other
that
is
vnder
ground
:
and
so
contrary
waies
.
wherby
it
foloweth
,
that
the
day
of
the
one
is
equall
to
the
nyghte
of
the
other
,
and
so
contrarye
wayes
also
.
Again
seeyng
that
the
sonne
dothe
descend
from
Cancer
vnto
Capricorne
,
by
the
same
circles
of
reuolution
,
by
whiche
he
dydde
ascende
from
Capricorne
vnto
Cancer
,
it
must
needes
follow
that
euery
two
dayes
in
the
yeare
equally
distaunte
from
the
longest
daye
,
or
from
the
shortest
,
are
equall
in
their
artificiall
daye
,
and
in
their
nighte
.
These
generall
thinges
I
maye
easilye
gather
:
but
howe
I
maye
knowe
iustlye
the
quantitye
of
euerye
Artificiall
daye
from
other
,
and
the
precise
tyme
of
the
sonne
risinge
and
setting
,
I
canne
not
so
easilye
gather
.
wherefore
if
it
please
you
in
those
two
pointes
I
desyre
your
instruction
.
Master
.
Althoughe
for
this
treatise
the
aptest
forme
be
by
the
vse
of
the
sphere
and
the
due
placinge
of
it
,
yet
it
is
harde
to
place
the
sphere
so
well
,
and
to
vse
it
so
aptlye
,
that
it
myghte
declare
a
iuste
precisenes
.
and
therfore
after
that
I
haue
taughte
you
the
vse
of
the
Sphere
for
that
point
,
I
will
also
by
supputation
giue
you
a
table
sufficiente
to
declare
bothe
vnto
you
for
all
partes
vnder
our
parallele
,
and
somwhat
more
.
Firste
for
the
vse
of
the
globe
,
you
muste
set
it
accordinge
to
the
latitude
of
the
Region
that
you
desire
to
know
the
daies
in
,
and
then
marke
the
degree
of
any
signe
that
the
Sonne
is
in
that
daye
,
whose
quantitie
you
desire
to
knowe
:
sette
that
degree
iuste
in
the
horizonte
towarde
the
easte
,
and
marke
what
degree
of
the
equinoctiall
is
in
the
horizonte
at
the
same
tyme
:
then
tourne
the
sphere
westwarde
tyll
the
degree
of
the
sonne
be
iust
in
the
Horizonte
againe
in
the
west
parte
,
and
marke
then
what
degree
of
the
Equinoctiall
doth
lighte
on
the
Horizont
in
the
easte
parte
,
accomptynge
trulye
howe
manye
degrees
bee
betwixte
those
twoo
degrees
which
you
haue
marked
,
and
that
arke
of
the
Equinoctiall
,
is
called
the
arke
of
that
day
:
which
you
may
easilye
tourne
into
howers
,
accomptynge
is
degrees
to
an
hower
,
and
for
euery
degree
lesse
then
15
accompting
4
minutes
of
an
hower
.
Scholar
.
This
were
easye
inough
to
doo
,
if
I
vse
the
helpe
of
the
table
that
I
see
in
some
bookes
,
whiche
teacheth
easily
howe
to
tourne
degrees
of
the
Equinoctiall
into
partes
of
tyme
,
as
here
in
Orontius
worke
it
is
sette
forthe
.
but
I
dyd
abbrydge
it
for
my selfe
as
here
appeareth
:
and
bicause
the
table
was
not
extended
aboue
60
degrees
by
Orontius
,
A
TABLE
FOR
CONVERTINGE
degrees
of
the
Equinoctiall
into
partes
of
tyme
.
The
ark
of
the
Equino
.
|
Partes
of
tyme
.
|
Degree
|
Houres
|
Minuts
.
|
1
|
0
|
4
|
2
|
0
|
8
|
3
|
0
|
12
|
4
|
0
|
16
|
5
|
0
|
20
|
6
|
0
|
24
|
7
|
0
|
28
|
8
|
0
|
32
|
9
|
0
|
36
|
10
|
0
|
40
|
11
|
0
|
44
|
12
|
0
|
48
|
13
|
0
|
52
|
14
|
0
|
56
|
15
|
1
|
0
|
20
|
1
|
20
|
25
|
1
|
40
|
30
|
2
|
0
|
35
|
2
|
20
|
40
|
2
|
40
|
45
|
3
|
0
|
50
|
3
|
20
|
55
|
3
|
40
|
60
|
4
|
0
|
65
|
4
|
20
|
70
|
4
|
40
|
30
|
2
|
0
|
35
|
2
|
20
|
40
|
2
|
40
|
45
|
3
|
0
|
50
|
3
|
20
|
55
|
3
|
40
|
60
|
4
|
0
|
65
|
4
|
20
|
70
|
4
|
40
|
75
|
5
|
0
|
80
|
5.
|
20
|
85
|
5
|
40
|
90
|
6
|
0
|
95
|
6
|
20
|
100
|
6
|
40
|
105
|
7
|
0
|
110
|
7
|
20
|
115
|
7
|
40
|
120
|
8
|
0
|
125
|
8
|
20
|
130
|
8
|
40
|
135
|
9
|
0
|
140
|
9
|
20
|
145
|
9
|
40
|
150
|
10
|
0
|
155
|
10
|
20
|
160
|
10
|
40
|
165
|
11
|
0
|
170
|
11
|
20
|
175
|
11
|
40
|
180
|
12
|
0
|
185
|
12
|
20
|
190
|
12
|
40
|
195
|
13
|
0
|
200
|
13
|
20
|
205
|
13
|
40
|
210
|
14
|
0
|
215
|
14
|
20
|
220
|
14
|
40
|
225
|
15
|
0
|
230
|
15
|
20
|
235
|
15
|
40
|
240
|
16
|
0
|
245
|
16
|
20
|
250
|
16
|
40
|
255
|
17
|
0
|
260
|
17
|
20
|
265
|
17
|
40
|
270
|
18
|
0
|
275
|
18
|
20
|
280
|
18
|
40
|
285
|
19
|
0
|
290
|
19
|
20
|
295
|
19
|
40
|
300
|
20
|
0
|
305
|
20
|
20
|
315
|
21
|
40
|
330
|
22
|
0
|
340
|
22
|
40
|
350
|
23
|
20
|
360
|
24
|
0
|
I
did
for
mine
owne
ease
make
out
the
rest
in
this
for
me
.
Mast
.
This
is
a
table
of
to
much
ease
,
and
therfore
doth
rather
teache
negligence
,
then
anye
thinge
els
.
for
him
that
listeth
to
excercise
his
witte
in
readines
of
accompte
,
it
is
an
easy
matter
to
tourne
degrees
into
howers
without
anye
tables
,
and
therefore
such
tables
myght
well
bespared
,
&
yet
manye
bokes
are
full
of
them
:
but
if
you
lysted
,
you
might
haue
abbridged
it
more
frome
15
vpwarde
,
takinge
onlye
euen
15
styll
.
as
thus
.
15
,
30
,
45
,
60
,
75
,
&c.
so
seemeth
all
the
reste
superfluous
,
excepte
your
numbre
of
degrees
in
the
daye
arke
,
happen
iuste
agreeable
with
some
one
of
those
in
the
table
:
but
nowe
to
procede
,
giue
one
example
for
declaration
of
your
vnderstandinge
herein
.
Scholar
.
Then
to
begin
I
sette
the
globe
to
the
eleuation
of
52
degrees
,
Exaumple
.
and
considre
the
place
of
the
sonne
the
14
day
of
Auguste
,
and
fynde
it
to
be
by
the
Ephemerides
,
in
the
fyrst
beginning
of
Virgo
,
therefore
do
I
set
the
beginning
of
Virgo
in
the
verye
horizont
,
and
then
do
I
see
with
it
the
137
degree
of
the
Equinoctiall
in
the
same
Horizont
,
whiche
I
doo
marke
:
afterwarde
I
tourne
the
sphere
tyll
the
place
of
the
sonne
be
in
the
Horizont
on
the
west
part
,
and
then
in
the
easte
parte
I
marke
the
degree
of
the
Equinoctiall
,
whyche
is
347
degrees
.
Nowe
abatinge
137
oute
of
347
,
there
resteth
the
whole
daye
arke
,
whiche
is
210
degrees
,
whiche
make
14
howers
,
as
by
the
former
table
is
easily
seene
.
wherfore
I
conclude
that
the
14
daye
of
August
,
the
sonne
shineth
14
howers
,
and
then
muste
the
nighte
be
but
euen
10
howers
,
sith
bothe
times
make
iust
24
howers
:
but
yet
I
see
not
howe
to
knowe
the
howers
of
the
sonne
rysinge
,
and
settinge
.
Master
.
I
am
sure
you
thinke
that
the
Noone
is
the
middle
of
the
daye
,
and
that
the
sonne
shyneth
lyke
space
beefore
noone
and
after
noone
.
Scholar
.
That
is
moste
certaine
.
Master
.
Then
partinge
the
whole
time
of
the
sonne
shining
,
or
of
the
artificial
day
into
2
equal
parts
,
the
one
halfe
doth
limite
the
hower
after
none
at
which
the
son
doth
set
.
Scholar
.
That
is
in
this
exaumple
7
,
and
so
muste
it
needes
be
.
And
now
I
see
by
the
same
reason
,
the
sonne
must
ryse
7
howers
before
noone
,
that
is
at
5
of
the
clocke
in
the
mornynge
.
Master
.
So
is
it
.
And
for
that
eande
that
you
maye
haue
a
generall
rule
therein
,
euermore
abate
halfe
the
quantity
of
the
daye
from
12
howers
,
and
then
will
the
remainer
declare
the
iuste
hower
and
minute
of
the
sonne
risynge
.
Scholar
.
Then
by
your
fauoure
I
will
proue
ones
againe
:
Exaumple
.
wherfore
I
take
the
16
daye
of
Iulye
,
the
sonne
beyng
in
the
3
degree
of
Leo
,
which
degree
I
sette
in
the
easte
parte
of
the
horizonte
,
and
then
doth
there
appeare
in
the
same
Horizonte
the
98
and
almost
1
/
3
degree
of
the
Equinoctiall
:
then
turnynge
the
degree
of
the
sonne
to
the
west
part
of
the
horizonte
,
I
fynde
in
the
easte
parte
the
332
and
1
/
3
almoste
of
the
equinoctiall
:
then
subtrayinge
the
lesser
from
the
greater
,
there
resteth
234
:
which
I
turne
into
partes
of
time
,
and
it
dooth
yelde
15
howers
and
36
minutes
.
whiche
is
the
iuste
length
of
that
artificiall
daye
.
and
of
it
the
one
halfe
is
7
howers
and
48
minutes
:
wherby
I
knowe
that
at
48
minutes
,
after
7
of
the
clocke
at
nyghte
,
the
sonne
setteth
on
that
16
daye
of
Iuly
:
and
then
abating
so
much
from
12
,
there
resteth
4
howers
and
12
minutes
:
so
that
the
sonne
risynge
appeareth
to
be
twelue
minutes
after
4.
of
the
clocke
in
the
mornynge
.
And
nowe
I
thinke
my selfe
conninge
inoughe
in
all
this
matter
.
Master
.
Yet
for
more
ease
:
after
that
you
haue
noted
the
degree
of
the
Equinoctiall
that
dooth
rise
with
the
place
of
the
son
,
you
may
marke
the
degree
that
riseth
with
the
contrarye
point
against
the
son
:
and
abate
then
the
fyrst
oute
of
the
second
,
and
so
accomplish
your
woorke
,
as
you
did
before
.
for
it
is
all
one
thinge
,
but
that
you
need
not
to
loke
in
contrary
sides
of
your
sphere
for
your
worke
.
And
this
shall
you
note
farther
:
that
if
the
first
ascension
of
the
place
of
the
son
be
greater
then
the
second
ascension
of
the
Nadir
of
the
son
,
you
shal
put
to
the
second
ascension
,
360
degrees
,
A
Cautele
.
&
then
abate
as
you
are
taught
before
.
As
for
example
:
the
first
day
of
February
the
son
is
by
the
Ephemerides
in
the
22
degree
Exaumple
.
of
February
the
son
is
by
the
Ephemerides
in
the
22
degree
Exaumple
.
of
Aquarius
,
that
degree
I
find
in
the
Zodiak
of
my
spher
,
and
I
sette
it
iuste
in
the
easte
parte
of
the
Horizonte
,
and
ther
may
I
se
that
the
343⅓
degree
of
the
Equinoctiall
doth
ascend
at
the
same
instant
in
the
Horizont
also
:
which
I
must
accompt
for
the
true
ascention
of
that
degre
of
Aquarius
.
Then
tourne
I
to
the
22
degree
of
Leo
,
beinge
the
Nadir
of
the
sonne
,
and
with
it
when
it
is
sette
in
the
Horizonte
,
I
marke
the
125⅓
degree
of
the
Equinoctiall
to
ascende
.
Nowe
when
I
woulde
subtracte
343⅓
out
of
125⅓
,
it
will
not
be
:
and
therfore
I
put
vnto
the
lesser
numbre
360
,
and
so
it
amounteth
to
485¾
,
and
then
from
it
I
abate
343⅓
,
and
there
remaineth
142
5
/
12
:
whiche
if
you
chaunge
into
partes
of
time
,
do
make
9
howers
and
30
minutes
:
and
that
is
the
quantitie
of
the
fyrste
daye
of
Februarye
.
Scholar
.
The
halfe
of
that
is
4
howers
,
and
45
minutes
,
whereby
I
knowe
,
that
at
the
45
minute
that
is
¾
of
an
hower
after
4
of
the
clocke
the
sonne
setteth
:
and
riseth
in
the
mornynge
15
minutes
,
that
is
¼
of
an
hower
after
7
of
the
clocke
.
But
why
doo
you
adde
those
360
degrees
?
Master
.
Seeyng
wee
intende
to
abate
the
fyrste
ascension
oute
of
the
seconde
,
to
thintente
that
their
distaunce
maye
bee
knowen
,
seeynge
the
whole
compasse
of
the
circle
is
but
360
,
from
whiche
if
you
abate
the
fyrste
ascension
being
the
greatest
numbre
,
then
wyll
there
remaine
the
distaunce
betwene
that
ascention
&
the
end
of
the
equinoctial
:
vnto
which
difference
you
must
adde
so
many
degres
as
the
second
ascention
requireth
,
as
both
reason
&
practise
wil
declare
vnto
any
man
.
Scholar
.
It
is
reasonable
.
Therfore
now
it
may
please
you
to
declare
the
same
woorke
by
exactnes
of
tables
.
Master
.
The
declaration
of
the
tables
.
Bicause
you
shall
not
be
driuen
to
seeke
in
the
Ephemerides
for
the
place
of
the
Son
,
but
that
one
table
may
serue
for
it
,
as
well
as
for
the
quantities
of
daies
and
other
conclusions
clusions
also
,
I
wil
make
the
tables
common
for
sundry
vses
,
whose
partes
I
will
fyrste
declare
,
and
after
that
will
expresse
the
vses
of
them
also
.
THE
TABLES
OF
QUANTITIES
of
dayes
Artificiall
,
and
nightes
,
for
all
Englande
.
Signes
for
the
daye
.
|
Eleuation
of
the
Pole
,
or
latitudes
of
Regions
.
|
Signes
for
the
nighte
.
|
daies
of
moneths
|
degres
of
Signes
.
|
daies
of
moneths
|
degres
of
Signes
.
|
51
|
52
|
53
|
54
|
55
|
degres
of
Signes
.
|
daies
of
moneths
|
degres
of
Signes
.
|
daies
of
moneths
.
|
|
10
|
♈
|
0
|
|
13
|
♍
|
30
|
12
|
0
|
12
|
0
|
12
|
0
|
12
|
0
|
12
|
0
|
0
|
♎
|
13
|
|
30
|
|
10
|
|
|
11
|
|
1
|
|
12
|
|
29
|
12
|
4
|
12
|
4
|
12
|
4
|
12
|
4
|
12
|
4
|
1
|
|
14
|
|
29
|
|
9
|
|
|
12
|
|
2
|
|
11
|
|
28
|
12
|
8
|
12
|
8
|
12
|
8
|
12
|
9
|
12
|
9
|
2
|
|
15
|
|
28
|
|
8
|
|
MARCHE
.
|
13
|
|
3
|
|
10
|
|
27
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
14
|
12
|
14
|
3
|
|
16
|
SEPTEMBRE
.
|
27
|
|
7
|
|
|
14
|
|
4
|
|
9
|
|
26
|
12
|
16
|
12
|
16
|
12
|
16
|
12
|
18
|
12
|
18
|
4
|
|
17
|
|
26
|
|
6
|
|
|
15
|
|
5
|
|
8
|
|
25
|
12
|
20
|
12
|
20
|
12
|
21
|
12
|
22
|
12
|
23
|
5
|
|
18
|
|
25
|
|
5
|
|
|
16
|
|
6
|
|
7
|
|
24
|
12
|
24
|
12
|
24
|
12
|
26
|
12
|
26
|
12
|
28
|
6
|
|
19
|
|
24
|
|
4
|
|
|
17
|
|
7
|
|
6
|
|
23
|
12
|
28
|
12
|
28
|
12
|
30
|
12
|
30
|
12
|
32
|
7
|
|
20
|
|
23
|
|
3
|
|
|
18
|
|
8
|
|
5
|
|
22
|
12
|
32
|
12
|
32
|
12
|
34
|
12
|
35
|
12
|
36
|
8
|
|
21
|
|
22
|
|
2
|
MARCHE
.
|
|
19
|
|
9
|
|
4
|
|
21
|
12
|
36
|
12
|
36
|
12
|
38
|
12
|
40
|
12
|
40
|
9
|
|
22
|
|
21
|
|
1
|
|
|
20
|
|
10
|
|
3
|
|
20
|
12
|
40
|
12
|
40
|
12
|
42
|
12
|
44
|
12
|
44
|
10
|
|
23
|
|
20
|
|
29
|
|
|
21
|
|
11
|
SEPTEMBRE
.
|
2
|
|
19
|
12
|
44
|
12
|
44
|
12
|
46
|
12
|
48
|
12
|
49
|
11
|
|
24
|
|
19
|
|
28
|
|
|
22
|
|
12
|
|
1
|
|
18
|
12
|
48
|
12
|
48
|
12
|
50
|
12
|
52
|
12
|
54
|
12
|
|
25
|
|
18
|
|
27
|
|
|
23
|
|
13
|
|
31
|
|
17
|
12
|
52
|
12
|
54
|
12
|
54
|
12
|
56
|
12
|
58
|
13
|
|
26
|
|
17
|
|
26
|
|
|
24
|
|
14
|
|
30
|
|
16
|
12
|
54
|
12
|
58
|
12
|
59
|
13
|
1
|
13
|
3
|
14
|
|
27
|
|
16
|
|
35
|
|
|
25
|
|
15
|
|
29
|
|
15
|
12
|
58
|
12
|
2
|
13
|
4
|
13
|
6
|
13
|
8
|
15
|
|
28
|
|
15
|
|
24
|
|
|
26
|
|
16
|
|
28
|
|
14
|
13
|
2
|
13
|
6
|
13
|
8
|
13
|
10
|
13
|
12
|
16
|
|
29
|
|
14
|
|
23
|
|
|
27
|
|
17
|
|
26
|
|
13
|
13
|
6
|
13
|
10
|
13
|
12
|
13
|
14
|
13
|
17
|
17
|
|
30
|
|
13
|
|
22
|
|
|
28
|
|
18
|
|
25
|
|
12
|
13
|
10
|
13
|
14
|
13
|
16
|
13
|
18
|
13
|
22
|
18
|
|
1
|
OCTOBRE
.
|
12
|
|
21
|
|
|
29
|
|
19
|
|
24
|
|
11
|
13
|
14
|
13
|
18
|
13
|
20
|
13
|
22
|
13
|
26
|
19
|
|
2
|
|
11
|
|
20
|
|
|
31
|
|
21
|
|
22
|
|
9
|
13
|
22
|
13
|
26
|
13
|
28
|
13
|
32
|
13
|
36
|
21
|
|
4
|
|
9
|
|
18
|
|
|
1
|
|
22
|
|
21
|
|
8
|
13
|
26
|
13
|
30
|
13
|
32
|
13
|
36
|
13
|
40
|
22
|
|
5
|
|
8
|
|
17
|
|
|
2
|
|
23
|
|
20
|
|
7
|
13
|
30
|
13
|
34
|
13
|
36
|
13
|
40
|
13
|
44
|
23
|
|
6
|
|
7
|
|
16
|
|
APRIEL
.
|
3
|
|
24
|
|
19
|
|
6
|
13
|
34
|
13
|
38
|
13
|
40
|
13
|
44
|
13
|
48
|
24
|
|
7
|
|
6
|
|
15
|
|
|
4
|
|
25
|
AVGVST
.
|
18
|
|
5
|
13
|
38
|
13
|
42
|
13
|
44
|
13
|
48
|
13
|
52
|
25
|
|
8
|
|
5
|
|
14
|
|
|
5
|
|
26
|
|
17
|
|
4
|
13
|
42
|
13
|
46
|
13
|
49
|
13
|
53
|
13
|
57
|
26
|
|
9
|
|
4
|
|
13
|
FEBRVARYE
.
|
|
6
|
|
27
|
|
16
|
|
3
|
13
|
46
|
13
|
50
|
13
|
54
|
13
|
58
|
14
|
2
|
27
|
|
10
|
|
3
|
|
12
|
|
|
7
|
|
28
|
|
15
|
|
2
|
13
|
50
|
13
|
52
|
13
|
58
|
14
|
2
|
14
|
6
|
28
|
|
11
|
|
2
|
|
11
|
|
|
9
|
|
29
|
|
14
|
|
1
|
13
|
52
|
13
|
56
|
14
|
2
|
14
|
6
|
14
|
11
|
29
|
|
12
|
|
1
|
♓
|
10
|
|
|
10
|
|
30
|
|
13
|
|
0
|
13
|
56
|
14
|
0
|
14
|
6
|
14
|
10
|
14
|
16
|
30
|
|
13
|
|
0
|
|
9
|
|
|
|
|
|
|
|
|
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
|
|
|
|
|
|
|
|
The
seconde
parte
of
the
table
.
Signes
for
the
daye
.
|
Eleuation
of
the
Pole
,
or
Latitude
of
Regions
.
|
Signes
for
the
night
|
daies
of
moneths
|
degres
of
Signes
.
|
daies
of
moneths
|
degres
of
Signes
.
|
51
|
52
|
53
|
54
|
55
|
degr
.
of
Signes
|
daies
of
moneths
|
degr
.
of
Signes
.
|
dayes
of
moneths
|
APRIEL
.
|
10
|
♉
|
0
|
|
13
|
|
30
|
13
|
56
|
14
|
0
|
14
|
6
|
14
|
10
|
14
|
16
|
0
|
♏
|
13
|
|
30
|
|
9
|
|
|
11
|
|
1
|
|
12
|
|
29
|
14
|
0
|
14
|
4
|
14
|
10
|
14
|
14
|
14
|
20
|
1
|
|
14
|
|
29
|
|
8
|
|
|
12
|
|
2
|
|
11
|
|
28
|
14
|
4
|
14
|
8
|
14
|
14
|
14
|
18
|
14
|
24
|
2
|
|
15
|
|
28
|
|
7
|
|
|
13
|
|
3
|
|
10
|
|
27
|
14
|
8
|
14
|
12
|
14
|
18
|
14
|
22
|
14
|
28
|
3
|
|
16
|
|
27
|
|
6
|
|
|
14
|
|
4
|
|
9
|
|
26
|
14
|
12
|
14
|
16
|
14
|
22
|
14
|
26
|
14
|
32
|
4
|
|
17
|
|
26
|
|
5
|
|
|
15
|
|
5
|
|
8
|
|
25
|
14
|
14
|
14
|
20
|
14
|
26
|
14
|
30
|
14
|
37
|
5
|
|
18
|
|
25
|
|
4
|
FEBRVARY
.
|
|
16
|
|
6
|
|
7
|
|
24
|
14
|
18
|
14
|
24
|
14
|
30
|
14
|
34
|
14
|
42
|
6
|
|
19
|
OCTOBRE
.
|
24
|
|
3
|
|
|
17
|
|
7
|
|
6
|
|
23
|
14
|
22
|
14
|
28
|
14
|
33
|
14
|
38
|
14
|
46
|
7
|
|
20
|
|
23
|
|
2
|
|
|
18
|
|
8
|
|
5
|
|
22
|
14
|
26
|
14
|
32
|
14
|
36
|
14
|
43
|
14
|
50
|
8
|
|
21
|
|
22
|
|
1
|
|
|
19
|
|
9
|
|
4
|
|
21
|
14
|
30
|
14
|
34
|
24
|
40
|
14
|
48
|
14
|
54
|
9
|
|
22
|
|
21
|
|
31
|
|
|
20
|
|
10
|
AVGVST
.
|
3
|
|
20
|
14
|
34
|
14
|
38
|
24
|
44
|
14
|
52
|
14
|
58
|
10
|
|
23
|
|
20
|
|
30
|
|
|
21
|
|
11
|
|
2
|
|
19
|
14
|
36
|
14
|
42
|
14
|
48
|
14
|
56
|
15
|
2
|
11
|
|
24
|
|
19
|
|
29
|
|
|
22
|
|
12
|
|
1
|
|
18
|
14
|
40
|
14
|
46
|
14
|
52
|
14
|
0
|
15
|
6
|
12
|
|
25
|
|
18
|
|
28
|
|
|
23
|
|
13
|
|
31
|
|
17
|
14
|
44
|
14
|
50
|
14
|
56
|
15
|
3
|
15
|
10
|
13
|
|
26
|
|
17
|
|
27
|
|
|
24
|
|
14
|
|
30
|
|
16
|
14
|
46
|
14
|
54
|
15
|
0
|
15
|
6
|
15
|
14
|
14
|
|
27
|
|
16
|
|
26
|
|
|
25
|
|
15
|
|
29
|
|
15
|
14
|
50
|
14
|
56
|
15
|
4
|
15
|
10
|
15
|
18
|
15
|
|
28
|
|
15
|
|
25
|
|
|
26
|
|
16
|
|
27
|
|
14
|
14
|
54
|
15
|
0
|
15
|
8
|
15
|
14
|
15
|
22
|
16
|
|
29
|
|
14
|
|
24
|
|
|
27
|
|
17
|
|
26
|
|
13
|
14
|
56
|
15
|
4
|
15
|
11
|
15
|
18
|
15
|
26
|
17
|
|
30
|
|
13
|
|
23
|
|
|
28
|
|
18
|
|
25
|
|
12
|
15
|
0
|
15
|
8
|
15
|
14
|
15
|
22
|
15
|
30
|
18
|
|
31
|
|
12
|
|
22
|
|
|
29
|
|
19
|
|
24
|
|
11
|
15
|
4
|
15
|
10
|
15
|
17
|
15
|
26
|
15
|
34
|
19
|
|
1
|
|
11
|
|
21
|
|
|
30
|
|
20
|
|
23
|
|
10
|
15
|
6
|
15
|
14
|
15
|
20
|
15
|
30
|
15
|
38
|
20
|
|
2
|
|
10
|
|
20
|
|
MAYE
.
|
1
|
|
21
|
|
22
|
|
9
|
15
|
10
|
15
|
18
|
15
|
24
|
15
|
34
|
15
|
42
|
21
|
|
3
|
NOVEMBRE
.
|
9
|
|
19
|
|
|
2
|
|
22
|
|
21
|
|
8
|
15
|
12
|
15
|
20
|
15
|
28
|
15
|
37
|
15
|
45
|
22
|
|
4
|
|
8
|
|
18
|
|
|
3
|
|
23
|
|
20
|
|
7
|
15
|
16
|
15
|
24
|
15
|
32
|
15
|
40
|
15
|
48
|
23
|
|
5
|
|
7
|
|
17
|
|
|
4
|
|
24
|
|
19
|
|
6
|
15
|
18
|
15
|
28
|
15
|
36
|
15
|
44
|
15
|
52
|
24
|
|
6
|
|
6
|
|
16
|
|
|
6
|
|
25
|
|
18
|
|
5
|
15
|
22
|
15
|
30
|
15
|
39
|
15
|
47
|
15
|
56
|
25
|
|
7
|
|
5
|
|
15
|
|
|
7
|
|
26
|
|
17
|
|
4
|
15
|
24
|
15
|
34
|
15
|
41
|
15
|
50
|
16
|
0
|
26
|
|
8
|
|
4
|
|
14
|
|
|
8
|
|
27
|
|
16
|
|
3
|
15
|
28
|
15
|
36
|
15
|
44
|
15
|
54
|
16
|
4
|
27
|
|
9
|
|
3
|
|
13
|
|
|
9
|
|
28
|
|
15
|
|
2
|
15
|
30
|
15
|
40
|
15
|
47
|
15
|
57
|
16
|
7
|
28
|
|
10
|
|
2
|
|
12
|
|
|
10
|
|
29
|
IVLYE
.
|
14
|
♌
|
1
|
15
|
34
|
15
|
42
|
15
|
50
|
16
|
0
|
16
|
10
|
29
|
|
11
|
|
1
|
♒
|
11
|
|
|
11
|
|
30
|
|
13
|
|
0
|
15
|
36
|
15
|
44
|
15
|
54
|
16
|
4
|
16
|
14
|
30
|
|
12
|
|
0
|
|
10
|
IANVARYE
.
|
|
|
|
|
|
|
|
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
|
|
|
|
|
|
|
|
The
thyrde
parte
of
the
table
.
Signes
for
the
daye
.
|
Eleuation
of
the
Pole
,
or
latitude
of
Regions
.
|
Signes
for
the
nighte
.
|
daies
of
moneths
|
degres
of
Signes
.
|
daies
of
moneths
|
degres
of
Signes
.
|
51
|
52
|
53
|
54
|
55
|
degres
of
Signes
|
daies
of
moneths
|
degres
of
Signes
.
|
daies
of
moneths
|
|
11
|
♊
|
0
|
|
13
|
|
30
|
15
|
36
|
15
|
44
|
15
|
54
|
16
|
4
|
16
|
14
|
0
|
♐
|
12
|
|
30
|
|
10
|
|
|
12
|
|
1
|
|
12
|
|
29
|
15
|
38
|
15
|
46
|
15
|
56
|
16
|
6
|
16
|
17
|
1
|
|
13
|
|
29
|
|
9
|
|
|
13
|
|
2
|
|
11
|
|
28
|
15
|
41
|
15
|
49
|
15
|
59
|
16
|
9
|
16
|
20
|
2
|
|
14
|
|
28
|
|
8
|
|
MAYE
.
|
14
|
|
3
|
|
10
|
|
27
|
15
|
44
|
15
|
52
|
16
|
2
|
16
|
12
|
16
|
24
|
3
|
|
15
|
NOVEMBRE
.
|
27
|
|
7
|
|
|
15
|
|
4
|
|
9
|
|
26
|
15
|
46
|
15
|
54
|
16
|
4
|
16
|
14
|
16
|
26
|
4
|
|
16
|
|
26
|
|
6
|
|
|
16
|
|
5
|
IVLY
.
|
8
|
|
25
|
15
|
49
|
15
|
57
|
16
|
7
|
16
|
17
|
16
|
29
|
5
|
|
17
|
|
25
|
|
5
|
|
|
17
|
|
6
|
|
7
|
|
24
|
15
|
52
|
16
|
0
|
16
|
10
|
16
|
20
|
16
|
32
|
6
|
|
18
|
|
24
|
|
4
|
|
|
18
|
|
7
|
|
5
|
|
23
|
15
|
54
|
16
|
2
|
16
|
12
|
16
|
22
|
16
|
34
|
7
|
|
19
|
|
23
|
|
3
|
|
|
19
|
|
8
|
|
4
|
|
22
|
15
|
56
|
16
|
5
|
16
|
15
|
16
|
25
|
16
|
37
|
8
|
|
20
|
|
22
|
|
2
|
IANVARYE
.
|
|
20
|
|
9
|
|
3
|
|
21
|
15
|
58
|
16
|
8
|
16
|
18
|
16
|
28
|
16
|
40
|
9
|
|
21
|
|
21
|
|
1
|
|
|
21
|
|
10
|
|
2
|
|
20
|
16
|
0
|
16
|
10
|
16
|
20
|
16
|
30
|
16
|
42
|
10
|
|
22
|
|
20
|
|
31
|
|
|
22
|
|
11
|
|
1
|
|
19
|
16
|
2
|
16
|
12
|
16
|
22
|
16
|
32
|
16
|
44
|
11
|
|
22
|
|
19
|
|
30
|
|
|
23
|
|
12
|
|
30
|
|
18
|
16
|
4
|
16
|
14
|
16
|
24
|
16
|
34
|
16
|
46
|
12
|
|
23
|
|
18
|
|
29
|
|
|
24
|
|
13
|
|
29
|
|
17
|
16
|
5
|
16
|
15
|
16
|
26
|
16
|
36
|
16
|
48
|
13
|
|
24
|
|
17
|
|
28
|
|
|
25
|
|
14
|
|
28
|
|
16
|
16
|
6
|
16
|
16
|
16
|
28
|
16
|
38
|
16
|
50
|
14
|
|
25
|
|
16
|
|
27
|
|
|
26
|
|
15
|
|
27
|
|
15
|
16
|
8
|
16
|
18
|
16
|
30
|
16
|
40
|
16
|
52
|
15
|
|
26
|
|
15
|
|
26
|
|
|
28
|
|
16
|
|
26
|
|
14
|
16
|
9
|
16
|
19
|
16
|
31
|
16
|
42
|
18
|
54
|
16
|
|
27
|
|
14
|
|
35
|
|
|
29
|
|
17
|
|
25
|
|
13
|
16
|
10
|
16
|
20
|
16
|
32
|
16
|
44
|
16
|
56
|
17
|
|
28
|
|
13
|
|
24
|
|
|
30
|
|
18
|
|
24
|
|
12
|
16
|
12
|
16
|
22
|
16
|
34
|
16
|
46
|
16
|
58
|
18
|
|
29
|
|
12
|
|
23
|
|
|
31
|
|
19
|
|
23
|
|
11
|
16
|
13
|
16
|
23
|
16
|
35
|
16
|
47
|
16
|
59
|
19
|
|
30
|
|
11
|
|
22
|
|
IVNE
.
|
1
|
|
20
|
|
22
|
|
10
|
16
|
14
|
16
|
24
|
16
|
36
|
16
|
48
|
17
|
0
|
20
|
|
1
|
|
10
|
|
21
|
|
|
2
|
|
21
|
|
21
|
|
9
|
16
|
15
|
16
|
25
|
16
|
38
|
16
|
50
|
17
|
2
|
21
|
|
2
|
DECEMBRE
.
|
9
|
|
20
|
|
|
3
|
|
22
|
|
20
|
|
8
|
16
|
16
|
16
|
26
|
16
|
38
|
16
|
51
|
17
|
3
|
22
|
|
3
|
|
8
|
|
19
|
|
|
4
|
|
23
|
|
19
|
|
7
|
16
|
17
|
16
|
27
|
16
|
39
|
16
|
52
|
17
|
4
|
23
|
|
4
|
|
7
|
|
18
|
|
|
5
|
|
24
|
|
18
|
|
6
|
16
|
18
|
16
|
28
|
16
|
40
|
16
|
52
|
17
|
4
|
24
|
|
5
|
|
6
|
|
17
|
|
|
6
|
|
25
|
|
17
|
|
5
|
16
|
19
|
16
|
28
|
16
|
40
|
16
|
53
|
17
|
5
|
25
|
|
6
|
|
5
|
|
16
|
|
|
7
|
|
26
|
IVNE
.
|
15
|
|
4
|
16
|
20
|
16
|
29
|
16
|
41
|
16
|
54
|
17
|
5
|
26
|
|
7
|
|
4
|
|
15
|
|
|
8
|
|
27
|
|
14
|
|
3
|
16
|
20
|
16
|
30
|
16
|
42
|
16
|
54
|
17
|
6
|
27
|
|
8
|
|
3
|
|
14
|
|
|
9
|
|
28
|
|
13
|
|
2
|
16
|
20
|
16
|
30
|
16
|
42
|
16
|
54
|
17
|
7
|
28
|
|
9
|
|
2
|
|
13
|
|
|
10
|
|
29
|
|
12
|
♌
|
1
|
16
|
20
|
16
|
30
|
16
|
43
|
16
|
54
|
17
|
8
|
29
|
|
10
|
|
1
|
♑
|
12
|
DECEMBRE
.
|
|
11
|
|
30
|
|
11
|
|
0
|
16
|
20
|
10
|
30
|
16
|
44
|
16
|
54
|
17
|
8
|
30
|
|
11
|
|
0
|
|
11
|
|
|
|
|
|
|
|
|
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
H.
|
M.
|
|
|
|
|
|
|
|
|
in
the
firste
columne
are
set
the
daies
of
the
monthes
,
and
in
the
second
the
degrees
of
the
Signes
in
the
Zodiake
,
in
whiche
the
sonne
is
that
daye
:
so
likewaies
the
thirde
and
fourth
columne
do
serue
for
the
like
matter
,
seeing
twise
in
the
year
the
daies
are
equall
.
And
bicause
at
other
2
times
in
the
year
the
nights
ar
equall
to
those
daies
,
therfore
on
the
right
hand
of
the
table
are
ther
2
columnes
of
moneths
,
and
other
two
columnes
of
signes
agreeable
therto
,
in
which
those
nights
are
equall
with
the
daies
of
the
monethes
on
the
lefte
hand
,
and
therfore
ar
the
title
set
ouer
the
signes
&
moneths
on
the
lefte
hand
,
signes
for
the
day
:
and
on
the
right
hande
signes
for
the
nighte
:
that
is
to
saye
,
that
if
the
moneth
and
signe
for
which
you
seke
,
be
on
the
left
side
of
the
table
,
then
do
the
numbres
vnder
the
eleuation
of
the
Pole
declare
the
quantitie
of
the
day
:
but
if
the
monethes
&
signes
be
on
the
right
side
,
then
is
that
quantitie
the
length
of
the
night
.
and
ouer
the
5
midle
pillers
,
you
se
the
title
to
be
the
Eleuation
of
the
Pole
,
or
latitude
of
regions
;
whiche
are
there
but
only
5
expressely
set
,
namely
51
,
52
,
53
,
54
,
&
55
:
whiche
may
serue
for
all
England
,
from
the
south
sea
vnto
Scotland
.
And
so
may
it
do
for
diuerse
of
the
northe
partes
of
Europe
and
Asia
.
Nowe
for
the
vse
of
them
,
this
is
the
ordre
.
When
so
euer
you
wold
know
the
quantitie
of
the
daye
Artificiall
and
of
his
night
,
seeke
out
the
day
in
the
columnes
on
the
right
hande
,
or
on
the
lefte
hand
as
it
will
chaunce
,
and
by
it
in
the
next
column
you
may
see
the
place
of
the
Son
in
the
Zodiake
:
then
goyng
right
forth
towarde
the
middle
of
your
table
tyll
you
come
directly
vnder
the
column
that
serueth
for
your
Region
in
latitude
,
there
shall
you
finde
2
numbres
:
the
first
be
tokening
howers
,
and
the
second
minutes
of
howers
,
which
declare
the
iuste
quantitie
of
the
day
for
the
moneths
on
the
lefte
hande
:
or
els
if
the
moneth
that
you
seeke
for
be
on
the
right
hand
,
then
do
those
numbres
of
howers
and
minutes
betoken
the
quantitie
of
the
nyghte
.
Scholar
.
I
perceaue
it
well
,
and
I
se
by
reason
it
must
nedes
be
so
:
as
for
examples
sake
.
the
24
daye
of
Auguste
I
desire
to
knowe
the
lengthe
of
the
day
and
the
place
of
the
Sonne
in
the
Zodiake
:
wherfore
fyndynge
the
saide
24
daye
in
the
fyrste
table
of
those
thre
ryght
against
it
,
I
may
see
the
place
of
the
sonne
,
whiche
is
then
the
11
degree
of
Virgo
:
and
from
thence
proceedinge
forth
righte
towarde
the
myddle
of
the
table
,
I
fynde
vnder
the
numbre
of
52
degrees
of
latitude
13
howers
and
18
minutes
:
whereby
I
perceaue
that
the
Artificiall
daye
from
sonne
rysynge
to
sonne
settinge
,
is
so
longe
with
vs
:
and
the
nyght
is
the
reste
of
24
howers
,
that
is
10
howers
and
42
minutes
.
And
the
lyke
quantities
of
daye
and
nyght
must
needes
be
the
29
daye
of
marche
,
when
the
sonne
is
in
the
19
degree
of
Aries
.
But
on
the
20
daye
of
February
,
the
sonne
beyng
in
the
11
degree
of
Pisces
,
that
13
howers
and
18
minutes
is
the
quantitie
of
the
nyghte
,
and
the
day
then
is
but
10
howers
and
42
minutes
in
length
:
and
so
likewaies
the
seconde
daye
of
Octobre
,
when
the
sonne
is
in
the
19
degree
of
Libra
.
Master
.
This
is
sufficiente
:
for
as
you
haue
doone
in
this
so
maye
you
doo
in
all
other
lyke
.
yet
for
the
more
certenty
I
will
proue
you
with
one
question
more
:
For
London
whiche
is
supposed
to
be
51
degrees
and
24
minutes
in
latitude
,
I
woulde
knowe
the
quantitie
of
the
daye
Artificialle
when
the
sonne
is
in
the
28
degree
of
Scorpio
.
Scholar
.
I
fynde
that
signe
of
Scorpio
in
the
second
table
on
the
right
hand
,
and
the
10
daye
of
Nouembre
answering
vnto
it
.
And
bicause
24
minutes
are
lesse
then
halfe
a
degre
,
I
do
seeke
the
quantitie
of
the
daye
vnder
51
degrees
rather
then
vnder
52
,
and
so
fynde
I
15
howers
and
30
minutes
:
whiche
in
this
case
is
the
quantitie
of
the
nyghte
,
as
the
title
declareth
that
is
ouer
those
signes
:
therfore
the
lengthe
of
the
daye
is
8
howers
and
30
minutes
.
Ma.
A
cautele
for
the
part
proportioble
.
You
haue
done
well
.
But
yet
for
an
exacter
precisenes
,
you
may
take
the
part
proportionable
for
the
odde
minuts
of
the
eleuation
,
as
thus
.
for
the
latitude
of
51
degrees
,
the
daye
is
8
howers
and
30
minutes
:
and
for
52
degrees
,
it
were
8
howers
and
20
minutes
:
so
are
there
10
minutes
difference
betweene
those
two
eleuations
.
Then
saye
by
the
Golden
rule
:
If
60
minutes
giue
10
,
what
shall
24
minutes
giue
?
and
it
will
appeare
to
bee
4
minutes
.
Those
4
minutes
muste
I
abate
frome
the
greater
noumbre
in
this
example
(
and
in
all
this
worke
wher
the
numbres
decrease
)
and
it
will
yelde
8
howers
&
26
minutes
:
where
as
yf
you
did
fynde
the
numbres
to
increase
,
then
should
you
adde
those
partes
porportionable
vnto
the
lesser
numbre
,
as
by
proofe
you
may
try
,
for
that
day
when
the
sonne
is
in
the
seconde
degree
of
Leo
.
Scholar
.
That
is
(
by
the
second
table
)
the
15
daye
of
Iuly
,
and
then
is
the
daye
in
lengthe
15
howers
and
30
minutes
,
in
the
latitude
of
51
degrees
:
but
in
the
latitude
of
52
degrees
,
it
is
15
howers
and
40
minutes
,
so
it
increaseth
10
minutes
:
and
therfore
muste
I
adde
the
parte
proportionable
(
which
is
4
minutes
as
before
)
vnto
30.
and
so
haue
I
the
true
quantitie
34
minutes
aboue
15
howers
.
And
nowe
I
thinke
I
am
perfecte
inoughe
for
all
places
betweene
51
degrees
of
latitude
and
55
:
but
for
other
places
I
knowe
no
suche
waye
.
Master
.
It
were
to
longe
a
woorke
to
sette
out
all
diuersities
of
eleuations
,
and
scarse
agreeable
for
this
treatise
,
wher
these
thinges
are
but
incidente
,
and
not
principall
matters
.
but
at
other
times
in
more
conuenient
place
it
shall
be
done
if
I
maye
vnderstande
this
my
labour
to
be
profitably
imployed
.
And
thē
also
will
I
make
explication
of
dyuers
other
matters
,
whiche
you
did
in
your
table
at
the
beginning
of
this
treatise
propounde
,
although
at
this
time
I
thinke
many
of
them
lytle
appertaining
to
this
booke
.
But
yet
before
I
eande
this
treatise
,
I
must
speak
somwhat
of
twoo
or
three
matters
more
:
Constellations
.
And
firste
of
the
chieffe
Constellations
and
figures
in
the
Starry
skye
.
For
a
ground
you
shall
note
,
that
the
starres
are
not
only
in
multitude
infinite
,
but
many
of
them
also
so
smal
,
that
scarse
any
mans
eye
can
discern
them
.
wherefore
to
auoide
confusion
,
and
to
growe
to
a
certenty
,
the
auncient
Astronomers
did
note
only
1022
starres
,
wherof
the
moste
parte
they
did
assigne
to
certain
limites
,
enclosing
them
in
figures
of
men
,
beastes
,
or
other
formes
,
and
accordinglye
gaue
them
names
,
partly
that
they
might
the
more
easily
bee
remembred
,
partlye
for
remembraunce
of
some
woorthy
facte
,
and
partly
also
for
some
notable
signification
of
the
starres
comprehended
in
eche
of
them
.
All
whiche
matters
I
will
nowe-ouerpasse
,
tyll
a
more
conuenient
place
,
and
will
repeate
onlye
their
names
and
places
generally
,
distincting
them
accordynge
to
the
accustomed
manner
,
into
three
sortes
:
whereof
the
one
sorte
are
called
Northerlye
constellations
,
the
other
sorte
Southerly
constellations
,
and
the
third
sorte
are
the
twelue
signes
,
which
passe
in
the
myddle
betweene
southe
and
northe
:
for
heere
in
this
place
I
meane
not
to
referre
southe
and
north
to
the
Poles
of
the
Equinoctiall
,
but
as
all
learned
men
before
me
haue
doone
,
to
the
poles
of
the
Zodiake
.
And
so
may
the
Zodiake
be
accompted
exactly
in
the
myddle
.
But
nowe
to
beginne
as
Ptolemye
doth
,
The
northe
constellations
with
the
northerly
constellations
:
The
moste
northerly
constellation
is
the
lesser
Beare
,
called
Vrsa
minor
,
and
Cynosura
,
1
Vrsa
miner
and
contayneth
in
it
7
starres
.
This
is
the
chiefe
marke
whereby
mariners
gouerne
their
course
in
saylinge
by
nyghte
,
and
namely
by
2
starres
in
it
,
which
many
do
call
the
Shafte
,
and
other
do
name
the
Guardas
,
after
the
Spanish
tonge
.
Nigh
vnto
it
is
the
greater
Beare
,
called
Vrsa
maior
,
contayninge
27
starres
,
2
Vrsa
maior
wherof
7
are
moste
notable
,
and
are
in
latine
named
Plaustrum
,
and
in
english
Charles
waine
,
which
serueth
also
well
in
sailynge
:
and
manye
of
the
olde
Greekes
obserued
it
onlye
in
their
nauigation
,
3
Dragon
.
4
Cepheus
.
5
Bootes
.
as
the
Sydonians
and
all
the
Phenicians
marked
the
lesser
Beare
.
A
boute
these
2
Beares
is
there
a
longe
trace
of
31
starres
,
commonly
called
the
Dragon
.
Then
foloweth
Cepheus
,
whiche
consisteth
of
11
starres
.
Bootes
also
is
in
the
same
coaste
,
whome
Proclus
and
others
doo
name
Arctophylax
.
and
it
hath
22
starres
,
beside
one
very
bryght
starre
called
Arcturus
,
6
The
northe
Croune
.
7
Hercules
.
which
standeth
betweene
Bootes
legges
.
By
Arctophylax
ryghte
hande
,
is
the
northe
Croune
,
called
also
Ariadnes
Croune
,
and
hath
in
it
8
starres
.
Then
foloweth
Hercules
,
whom
the
greekes
doo
call
Engonasin
,
as
it
were
the
Kneeler
,
bicause
of
his
gesture
:
and
it
containeth
28
starres
.
By
hys
lefte
hande
,
is
there
an
other
constellation
,
8
Lyra
.
whiche
is
called
the
Harpe
,
in
latine
Lyra
and
Fidicula
.
and
also
Vultur
cadens
,
that
is
the
fallynge
Grype
,
9
The
Swan
.
it
comprehendeth
10
starres
.
By
it
is
the
Swanne
;
named
Cygnus
,
and
Auis
generallye
,
as
the
Greekes
call
it
Ornis
,
whiche
some
men
of
to
muche
ouersyght
do
translate
,
10
Cassiopeia
.
11
Perseus
.
Gallina
a
Hen
:
it
consisteth
of
17
starres
.
After
it
dooth
Ptolomye
recken
Cassiopeia
,
which
is
by
Cepheus
,
and
hath
13
starres
.
Nexte
vnto
hir
is
Perseus
,
with
Medusas
headde
,
and
it
includeth
26
starres
.
Then
foloweth
Erichthonius
,
12
The
Carter
with
the
Goate
and
the
2
Kyddes
.
this
constellation
is
also
named
Auriga
the
Cartar
:
and
containeth
14
starres
with
one
in
his
right
foote
,
which
is
common
to
Taurus
also
.
An
other
constellation
is
there
which
ioyneth
heade
to
heade
with
Hercules
,
13
Serpentarius
14
The
serpent
and
is
called
of
the
Greekes
,
Ophiuchus
,
and
of
the
latines
Serpentarius
,
that
is
the
manne
with
the
Serpente
,
or
Serpent
bearer
:
and
it
hathe
24
starres
.
Besyde
the
Serpent
,
which
containeth
18
starres
in
him selfe
,
and
is
named
of
latines
Anguis
,
and
of
greekes
Ophis
.
Then
is
there
an
other
small
constellation
of
5
starres
,
15
The
Dart
.
a
lytle
southe
of
the
swannes
heade
,
and
it
is
named
the
Darte
,
Sagitta
or
Telum
in
latine
,
and
in
greke
Oistos
.
16
The
Egle
.
By
it
towarde
the
southe
,
is
the
Egle
,
includynge
9
starres
:
hee
is
called
not
onlye
Aquila
in
latine
,
but
also
Vultur
volans
,
and
in
greeke
Aetos
.
Vnder
it
towarde
the
south
is
a
constellation
harde
adioyning
named
Antinous
in
all
tonges
,
17
Antinous
.
18
The
dolphin
19
The
Forehorse
.
and
hath
but
6
starres
.
A
lyttle
from
it
is
the
Dolphine
,
whiche
hath
in
it
10
starres
.
Then
foloweth
the
Forehorse
,
noted
with
4
darke
starres
,
and
harde
by
him
is
the
Flying
horse
,
named
Pegasus
:
The
Flying
Horse
.
and
doth
consiste
of
20
starres
.
Vnto
him
ioyneth
Andromeda
,
so
that
hyr
headde
lyeth
on
the
nauell
of
Pegasus
,
21
Andromeda
and
one
starre
is
common
to
them
bothe
.
This
constellation
dothe
containe
23
starres
.
By
hir
lefte
foot
is
ther
a
small
constellation
of
4
starres
,
22
The
triangle
which
is
commonly
called
the
Triangle
,
and
in
latine
Triangulus
,
but
the
greekes
name
it
after
one
of
their
letters
Delta
and
Deltoton
.
And
thus
haue
I
briefly
reckened
all
the
northely
constellations
,
excepte
Berenices
heare
,
of
whiche
I
will
speake
laste
of
all
other
.
And
therefore
nowe
nexte
in
due
ordre
muste
the
12
signes
followe
:
amongest
whiche
Aries
occupieth
the
fyrste
place
,
1
Aries
.
and
contayneth
13
starres
.
Then
Taurus
whiche
is
adorned
with
33
starres
,
2
Taurus
.
Water
stars
wherof
5
be
in
his
forhead
and
face
,
and
are
called
of
the
Greekes
Hyades
,
and
of
the
latines
Succule
:
amongest
whiche
,
one
is
more
notable
then
all
the
reste
,
and
is
called
Oculus
Tauri
,
the
Bulles
eye
:
but
the
Greekes
call
it
Lampadias
,
and
the
latines
Palilicium
:
the
Arabitians
Aldebaran
.
Other
6
starres
(
as
Proclus
numbreth
them
,
though
other
accompt
them
7
)
ar
in
the
backe
of
this
signe
,
and
be
called
Vergiliae
in
Latin
,
and
in
Greeke
Pleiades
,
and
also
Atlantides
:
they
are
named
in
englysh
the
brood
Henne
,
The
seuen
starres
.
and
the
Seuen
starres
,
yet
they
cluster
so
nyghe
togither
,
that
it
is
harde
to
numbre
them
truly
.
and
therfore
many
do
disagre
in
reckenynge
them
.
3
Gemini
.
After
Taurus
,
Gemini
do
followe
,
whiche
comprehend
18
starres
:
of
whiche
twoo
beare
name
as
most
famous
,
and
they
are
in
their
headdes
:
the
formost
is
named
Appollos
headde
,
and
the
nexte
is
called
Hercules
headde
,
bicause
those
two
Twinnes
were
so
named
of
some
men
,
yet
other
doo
call
them
Castor
and
Pollux
.
Before
their
formoste
foote
is
there
one
fayr
star
(
beside
the
18
,
Propus
.
4
Cancer
Crybbe
,
Asses
.
5
Leo
.
)
which
therfore
is
named
in
greke
Propus
.
After
Gemini
foloweth
Cancer
containing
8
stars
,
beside
a
cloudy
tract
which
is
named
the
Manger
or
Crybbe
.
Asses
.
5
Leo
.
Other
two
starres
are
called
the
Asses
whiche
seeme
to
stande
at
the
Crybbe
.
Then
the
Lion
is
nexte
,
as
a
princely
signe
,
in
whome
are
27
starres
,
but
two
of
them
more
notable
then
the
reste
:
the
one
is
in
the
tayle
,
and
therefore
is
called
Cauda
Leonis
,
the
other
in
the
brest
and
is
called
the
Basilyske
or
Kyngely
starre
,
and
also
the
Lions
harte
,
Cor
Leonis
in
Latin
,
and
Basiliscos
in
greke
.
Nexte
after
Leo
,
6
Virgo
.
cometh
Virgo
,
garnished
with
26
starres
,
but
one
especially
glystereth
aboue
the
reste
,
and
is
called
Spica
Virginis
,
the
Virgins
spike
.
A
lesser
starre
there
is
also
,
whiche
yet
is
notablye
marked
,
and
called
Protrigetes
,
Praeuindemiator
.
After
Virgo
cometh
Libra
,
7
Libra
.
the
signe
of
Iustice
and
equitie
:
but
it
is
the
leaste
signe
in
quantitie
of
all
other
in
the
Zodiake
,
for
it
occupieth
scarse
halfe
a
signe
in
lengthe
,
and
no
meruaile
,
syth
that
cruell
Scorpius
dooth
inuade
so
greate
a
portion
,
and
presseth
all
that
Sygne
oute
righte
.
yet
hathe
it
8
starres
,
but
not
one
out
of
the
Scorpions
clawes
.
8
Scorpius
.
Then
Scorpius
with
his
hooked
tayle
,
and
with
his
clawes
doth
reache
so
farre
,
that
two
full
signes
he
taketh
in
length
and
30
degrees
almoste
in
bredth
,
yet
hath
he
but
21
starres
beside
those
whiche
bee
in
his
clawes
,
and
are
common
to
them
&
to
Libra
:
amongest
all
which
the
principall
is
that
,
whiche
is
called
the
Scorpions
harte
,
and
is
named
of
the
Greekes
Antares
,
9
Sagittarius
and
of
Arabitians
,
Calb
alatrab
.
After
him
ensueth
one
of
the
Centaures
lyke
an
archer
on
horse
backe
,
with
manye
fayre
starres
,
though
they
bee
not
of
the
greatest
:
he
hath
in
all
31.
this
signe
is
called
Sagittarius
in
latine
,
10
Capricorn
.
and
in
greeke
Toxotes
.
Capricorn
then
foloweth
with
his
monstrous
shape
,
nother
fysh
nor
flesh
,
but
myxed
of
both
:
a
winterly
signe
and
no
waies
pleasant
,
but
that
he
geueth
hope
of
the
comfort
of
the
Springe
,
bicause
in
it
the
sonne
beginneth
to
retourne
to
vs
againe
.
hee
hath
in
him
29
starres
of
meane
quantitye
.
Aquarius
so
faste
dooth
followe
him
at
hande
,
11
Aquarius
.
that
hee
reacheth
almoste
as
forwardlye
as
Capricorne
,
within
lesse
then
8
degrees
:
this
signe
hath
in
him
22
starres
peculiare
to
him selfe
,
althoughe
Proclus
name
4
of
them
in
hys
ryghte
arme
,
to
be
the
Water
potte
.
The
water
potte
.
But
besyde
these
22
starres
,
there
are
other
19
,
whiche
in
their
dyuers
and
croked
position
doo
make
a
forme
of
a
Ryuer
,
and
are
called
the
Water
whiche
Aquarye
sheddeth
.
With
these
19
starres
Ptolemye
doth
accompte
one
more
,
The
Wauer
whiche
is
a
bewtifull
starre
of
the
bryghtest
sorte
,
and
is
in
the
mouthe
of
the
Southe
fyshe
,
so
that
it
is
common
to
them
bothe
.
this
star
is
called
of
Arabitians
Fomahant
:
so
that
in
all
there
are
reckened
in
this
signe
,
42
starres
.
Laste
of
the
12
signes
commeth
the
Fyshes
,
12
Pisces
.
tyed
by
the
tayles
with
a
common
Lyne
:
The
Lyne
.
the
formoste
Fyshe
hath
but
9
starres
,
and
his
line
hath
10.
the
latter
Fishe
hath
11
starres
,
and
his
lyne
hath
but
5.
and
where
those
two
lines
are
knitte
togyther
,
there
is
one
starre
more
,
whiche
is
called
the
Knotte
,
that
is
in
Greeke
named
Syndesmos
:
so
that
all
the
starres
togither
,
of
this
signe
,
are
34.
Whether
Proclus
did
mistake
any
thinge
in
this
signe
,
I
wishe
other
to
iudge
,
bicause
I
intended
here
not
to
intreat
at
large
,
and
muche
lesse
to
scan
other
mennes
writinges
.
And
thus
wyll
I
eande
the
12
signes
of
the
Zodiake
.
1
The
Whale
Nowe
to
diuerte
vnto
the
southe
signes
:
fyrste
appeareth
the
greate
Whale
,
contayning
22
starres
,
whereof
three
bee
moste
noted
:
the
fyrste
in
the
nether
chappe
,
whiche
is
in
latine
called
Mandibula
ceti
,
and
in
Arabike
Menkar
.
the
seconde
is
called
the
Whales
bellye
,
in
Arabike
Baten
kaitos
,
and
in
Latine
Venter
Ceti
.
the
thirde
is
the
Whales
tayle
,
named
Cauda
ceti
in
latine
,
and
in
Arabike
Deneb
kaitos
.
Nexte
foloweth
Orion
,
the
Stormy
signe
,
2
Orion
.
and
hath
diuers
starres
to
the
numbre
of
38
:
but
the
moste
notable
are
6.
the
fyrste
is
in
his
ryghte
shoulder
,
and
is
called
by
the
Arabitians
Bed
Algeuze
.
The
second
is
in
the
lefte
shulder
and
is
named
Bellatrix
.
Other
thre
stande
as
bullions
set
in
his
gyrdle
,
and
are
called
of
manye
engly
she
men
the
Golden
yarde
.
Then
is
there
in
his
lefte
foote
,
a
greate
starre
of
the
brightest
sort
,
which
is
named
of
Arabitians
Algebar
,
and
Rigel
Algeuze
.
Beside
these
sixe
there
are
other
starres
more
notable
for
their
forme
then
for
their
quantities
.
as
the
two
starres
which
betoken
his
clubbe
in
his
right
hand
,
and
9
starres
by
his
lefte
hande
,
whiche
represente
a
Lions
skynne
:
and
other
three
doo
limite
his
sworde
,
lying
crosse
his
backe
vnder
his
girdle
.
Betweene
Orion
and
the
Whale
is
there
a
greate
tract
of
starres
,
whiche
represent
the
forme
of
a
Riuer
:
and
therefore
are
they
called
the
Ryuer
.
3
The
Riuer
whiche
some
more
peculiarly
name
Eridanus
,
and
other
Nilus
.
Proclus
calleth
it
Orions
ryuer
,
bicause
it
beginneth
at
his
lefte
foote
and
hath
one
starre
common
with
his
foote
,
but
beside
that
it
hathe
34
starres
:
wherof
the
laste
is
one
of
the
greatest
lyght
.
By
the
beginninge
of
this
Ryuer
,
vnder
the
feete
of
Orion
is
there
a
constellation
of
12
starres
,
4
The
Hare
.
named
the
Hare
.
And
after
it
toward
the
easte
is
the
greater
Dogge
,
5
The
great
Dogge
.
(
of
whom
the
Caniculare
daies
bear
name
)
and
is
called
of
the
grekes
Sirius
,
and
of
the
Latines
Canis
,
hauing
18
starres
,
but
one
especially
in
bryghtnes
more
notable
then
anye
of
the
rest
,
and
that
is
in
his
mouthe
,
6
The
lesser
Dogge
.
and
is
called
peculiarlye
Sirius
and
Canis
,
by
the
name
of
the
whole
Signe
,
and
of
the
Arabians
Alhabor
.
Northe
almost
from
this
Dogge
is
ther
a
constellation
of
2
only
starres
named
Canicula
,
the
lesser
Dogge
:
and
in
greeke
Procyon
,
the
fore
dogge
,
whom
Tully
therfore
calleth
Antecanis
,
and
other
name
him
Precanis
.
At
the
tayle
of
the
greater
Dogge
is
the
famous
shippe
Argo
,
7
Argo
the
Shyppe
.
whiche
comprehendeth
45
starres
,
wherof
8
bee
bewtifull
but
one
in
especiall
which
is
in
the
foote
of
the
roother
&
is
called
Canopus
,
&
of
the
Arabitians
Suhel
.
This
star
is
not
seen
in
England
,
France
,
Germany
nor
Italy
,
&
scarsly
in
the
moste
southerly
partes
of
Spaine
.
And
here
by
the
waye
I
will
note
a
place
in
Proclus
very
much
corrupted
,
whiche
nowe
I
will
only
correct
as
I
thinke
good
:
and
an
other
time
will
intreate
more
largely
of
it
and
of
other
mo
.
the
wordes
in
Greeke
are
these
.
{αβγδ}
{αβγδ}
in
all
the
Greeke
bookes
.
{αβγδ}
.
Non
cernitur
.
transtulit
latinus
interpres
,
greaci
codicis
errorem
imitatus
.
Stella
vero
illa
splendida
quea
in
imo
Argus
gubernaculo
sita
est
,
Canopus
dicitur
.
ea
in
Rhodo
vix
conspicitur
,
aut
certè
ab
editis
locis
.
In
Alexandria
vero
prorsus
*
conspicua
est
,
vtpote
ferè
quarta
signi
portione
supra
Horizontem
euecta
.
The
bright
starre
in
the
foote
of
the
roother
of
Argus
is
called
Canopus
,
whiche
in
the
Rodes
can
scantely
be
seene
,
excepte
it
be
from
highe
places
:
but
in
Alexandria
it
maye
well
be
seene
,
for
it
doth
rise
there
nyghe
a
quarter
of
a
signe
aboue
the
Horizont
.
Scholar
.
This
is
contrarye
to
the
common
translation
.
Master
.
And
that
common
translation
is
as
contrary
to
common
sense
,
but
therof
an
other
time
shall
we
talke
,
when
I
mynd
to
teache
you
the
exacte
ordre
of
ascension
for
all
these
constellations
,
and
of
their
chiefe
starres
also
.
And
now
to
proceede
as
we
began
.
8
The
Serpent
of
the
southe
.
Nexte
after
this
ship
ther
foloweth
the
great
Serpent
whiche
is
called
of
the
greekes
and
latines
Hydra
.
it
containeth
25
starres
,
and
stretcheth
in
greate
lengthe
by
the
space
of
3
whole
signes
.
one
starre
there
is
in
it
bryghter
then
the
reste
,
and
that
is
named
by
the
Arabians
,
Alphard
.
On
this
Hydre
there
resteth
other
2
small
constellations
,
the
one
named
the
Cuppe
,
and
the
other
the
Rauen
.
9
The
Cuppe
The
Cuppe
includeth
seuen
starres
all
of
one
bygnes
.
This
Cuppe
standeth
on
the
Hydres
backe
,
almoste
in
the
myddle
of
him
.
10
The
Rauen
.
The
Rauen
standeth
on
the
same
Hydre
,
more
nearer
towarde
the
pointe
of
his
tayle
:
and
it
is
formed
of
7
starres
also
,
of
whiche
that
which
is
in
his
lefte
wing
,
is
called
in
Arabike
,
Algorab
.
11
The
Centaure
.
Vnder
the
taile
of
this
Hydre
and
those
twoo
other
small
constellations
,
there
standeth
the
centaure
Chiron
,
lyke
a
lyghte
horseman
with
his
chasinge
staffe
:
The
Centaurs
spear
he
hath
in
him
37
starres
,
whereof
4
be
in
the
garnishe
or
pensile
of
his
spear
,
and
them
doth
Proclus
recken
as
a
peculiare
constellation
.
and
nameth
it
in
greeke
Thyrsolochus
.
And
Ptolemy
doth
recken
those
starres
naming
them
to
be
in
that
speare
:
wherfore
I
muse
howe
Stofler
seemed
so
ignoraunte
herein
,
to
deny
that
Ptolemye
doth
make
any
mention
of
that
spear
,
and
hym selfe
deuiseth
oute
of
Ptolemye
6
wronge
starres
for
that
purpose
:
it
appeareth
hee
was
deceaued
by
the
olde
translation
,
where
Clypeus
is
translated
for
Hasta
:
that
is
,
shielde
for
speare
.
whiche
wrong
translation
Schoner
,
Copernicus
,
and
Erasmus
Rheinhold
doo
follow
,
and
dyuers
other
learned
men
,
but
against
reason
.
Scholar
.
I
thinke
it
(
as
manye
thinges
els
be
)
is
receaued
by
credite
of
authoritie
,
withoute
disquisition
of
reason
,
whiche
blyndeth
manye
wittye
men
oftentymes
.
Master
.
Yet
is
their
faulte
the
more
pardonable
,
if
they
acknowledg
their
errour
when
thei
be
friendly
admonished
:
but
this
is
beside
our
purpose
at
this
time
,
therefore
to
returne
:
This
Centaure
with
his
righte
hande
dooth
holde
a
Wolfe
,
12
The
Wolfe
.
whiche
is
a
seuerall
constellation
made
of
19
starres
,
althoughe
Hyginus
and
others
doo
recken
fewer
in
him
,
as
they
doo
vntrulye
in
manye
other
.
Vnder
that
beaste
towarde
the
southe
,
harde
vnder
the
Scorpions
tayle
,
standeth
the
Altar
,
13
The
Altar
.
made
of
7
Starres
,
of
the
meanest
lyght
:
but
it
is
not
seene
in
Englande
aboue
the
Horizont
.
By
this
Altar
eastwarde
betweene
the
two
former
feete
of
Sagittarye
,
there
is
the
Croune
of
the
southe
,
14
The
southe
Croune
.
formed
of
13
small
starres
:
Proclus
and
Theon
doo
call
it
also
Vraniscus
,
as
manye
later
writers
in
their
tyme
did
name
it
:
but
Theon
dooth
farther
affirme
that
it
hath
19
starres
:
whiche
muste
seeme
to
bee
an
errour
,
rather
in
the
booke
then
in
the
author
:
wherein
obseruation
canne
not
healpe
vs
in
Englande
,
syth
it
riseth
not
aboue
our
horizont
,
but
only
toucheth
it
.
After
it
foloweth
the
Southe
fyshe
,
containynge
12
starres
:
The
southe
Fishe
.
wherof
one
only
is
of
the
greatest
lyght
,
and
that
is
it
which
standeth
also
for
the
eande
of
the
water
that
runneth
frome
Aquarius
.
This
fysshe
lyeth
betweene
the
constellations
of
Capricorne
and
Aquarye
,
so
that
it
is
partely
vnder
them
bothe
.
These
bee
the
Constellations
most
commonlye
noted
amongest
auncient
writers
:
howebeit
one
more
there
is
named
to
lye
betweene
the
Lions
taile
and
Vrsa
maior
,
whiche
is
called
Berenices
heare
,
some
call
it
in
latine
Trica
,
16
Berenices
heare
.
and
other
Berenicis
crines
.
Conon
that
famous
astronomer
dyd
fyrste
name
it
,
and
Callimachus
did
de●…
re
it
,
and
therefore
doth
Proclus
adscribe
the
fyrste
noting
of
them
vnto
Callimachus
.
The
starres
in
it
are
7
,
as
Hyginus
and
Bassus
do
accompt
them
:
but
they
are
verye
darke
,
and
therefore
Ptolemye
doth
numbre
only
thre
of
them
,
as
the
boundes
of
that
forme
.
Besyde
these
50
constellations
,
there
bee
a
greate
numbre
of
starres
,
whiche
be
not
assigned
to
any
figure
,
but
lye
dispersedly
about
those
other
constellations
,
whereof
61
are
in
the
northe
parte
of
the
skye
,
and
annexed
with
the
northerly
signes
:
and
other
19
in
the
southe
part
of
the
Zodiake
,
vnto
whiche
if
you
adde
337
whiche
be
in
the
northe
constellations
,
and
316
in
the
southe
constellations
,
with
292
in
the
Zodiake
,
so
haue
you
in
all
1025
starres
whiche
be
noted
by
Astronomers
,
but
in
Ptolemyes
accompte
there
appeare
but
1022
,
bicause
he
doth
not
accompte
anye
starre
of
Berenices
heare
,
but
called
it
the
Traces
of
heare
.
These
starres
be
not
of
one
quantity
,
but
som
much
brighter
then
other
,
and
therefore
are
they
distincte
into
diuers
measures
of
lyght
,
and
namely
8
,
whiche
are
called
the
first
greatnes
,
the
seconde
,
the
thirde
,
the
fourthe
,
the
fyfte
an
the
syxte
,
vnder
whiche
they
are
that
be
called
Cloudy
starres
:
and
a
lesser
forte
yet
named
Darke
starres
:
of
all
which
,
and
the
measure
of
their
quantitie
,
I
will
at
an
other
tyme
speak
more
fullye
,
for
this
place
and
time
agreeth
euell
with
the
matter
,
and
that
muche
worse
,
then
at
the
beginning
it
seemed
to
doo
.
Scholar
.
There
remaine
yet
manye
tytles
vntouched
of
them
whiche
I
gathered
.
Master
.
And
manye
of
theym
smally
agreeable
for
this
treatise
,
but
doo
more
aptly
appertaine
to
Cosmography
,
and
therefore
ought
to
be
reserued
for
that
worke
:
saue
that
some
of
them
are
peculiare
for
the
Theorike
of
Planetes
,
and
yet
will
I
lightly
touch
them
in
fewe
words
,
for
so
much
as
may
seeme
to
healpe
to
this
treatise
.
Scholar
.
Howe
the
numbre
of
spheres
is
knowen
.
I
remembre
at
the
beginninge
you
promised
to
shewe
a
cause
why
you
name
but
8
spheres
,
where
as
other
men
do
accompte
more
:
and
also
how
it
may
appeare
,
that
there
are
so
manye
,
for
the
eyes
can
see
but
one
only
,
whiche
is
the
firmament
.
Master
.
Your selfe
sayde
,
you
had
marked
(
as
many
mariners
,
The
Moone
yea
and
all
men
do
almoste
)
that
the
Moone
dothe
euerye
daye
runne
eastwarde
notably
,
so
that
in
a
weeke
shee
passeth
a
quarter
of
the
skye
in
that
course
,
and
in
15
daies
she
runneth
halfe
the
compasse
of
the
skye
,
and
so
in
a
moneth
she
retourneth
to
the
sonne
againe
,
hauinge
passed
all
the
circuit
of
heauen
.
so
of
the
Sonne
you
haue
vnderstand
that
in
a
yeare
he
trauerseth
ouer
all
the
lengthe
of
the
Zodiake
,
The
Sonne
.
contrary
to
the
course
of
the
Firmament
,
whereby
it
muste
needes
appeare
vnto
you
,
that
seeynge
the
sonne
and
the
moone
haue
courses
distinct
from
the
Fixed
starres
,
thei
muste
needes
haue
distincte
spheres
also
,
wherein
they
doo
moue
,
and
accomplishe
their
courses
.
Scholar
.
I
remembre
I
haue
hearde
it
often
repeated
as
a
principle
in
nature
,
that
one
symple
body
can
haue
but
one
symple
motion
.
and
therfore
where
diuers
motions
bee
,
it
muste
needes
followe
that
there
are
diuers
bodyes
as
theyr
workers
,
whiche
you
in
this
talke
do
call
spheres
.
Master
.
As
you
may
thinke
that
their
spheres
are
distinct
from
the
Firmament
by
reason
of
their
seuerall
motions
,
so
are
they
distincte
a
sonder
by
the
same
reason
.
Scholar
.
It
is
moste
certaine
.
Master
.
Then
if
by
good
obseruation
it
haue
bene
proued
,
that
there
be
5
other
starres
which
haue
their
motions
all
distincte
from
the
Starry
skye
,
and
eche
of
them
frome
their
fellowes
,
it
will
appeare
reasonable
that
euerye
one
of
them
hath
a
seuerall
sphere
peculiare
for
him selfe
,
and
for
his
priuate
motion
.
Scholar
.
It
will
followe
of
necessitye
.
Master
.
Then
I
will
beginne
with
your selfe
for
one
of
them
,
whiche
I
am
sure
you
can
not
but
marke
,
as
all
men
,
yea
the
verye
Plowmen
doo
.
And
that
is
Venus
,
whiche
I
dare
saye
,
Venus
.
you
haue
marked
in
the
euenynge
to
set
after
the
son
,
&
then
is
she
named
the
euenyng
star
,
&
yet
doth
she
not
at
al
times
shine
like
space
after
son
setting
,
but
some
times
more
&
somtime
lesse
.
And
if
you
marke
hir
well
,
then
shall
you
perceaue
,
that
the
fyrste
nyghte
that
she
appeareth
,
shee
shyneth
lesse
time
then
she
dothe
the
seconde
nyght
,
and
so
increaseth
the
tyme
of
hir
shyninge
for
a
space
,
and
then
dothe
shee
abate
againe
by
lyttle
and
lyttle
,
tyll
she
ioyne
with
the
sonne
,
and
then
appeareth
no
more
at
euenynge
,
but
shortly
after
will
she
showe
in
the
mornynge
before
the
sonne
rysynge
,
and
increase
the
time
of
hir
shining
by
litle
and
lytle
,
tyll
she
comme
to
the
farthest
of
hir
distaunce
from
the
sonne
,
and
then
will
she
abate
againe
in
lyke
manner
,
till
she
come
within
the
beames
of
the
sonne
,
and
leese
hir
appearynge
for
a
tyme
.
Scholar
.
This
is
moste
certaine
and
knowen
of
all
men
vulgarly
,
althoughe
fewe
men
doo
considre
the
cause
therof
:
but
nowe
I
doo
remembre
,
what
you
taught
me
of
the
ascensions
poeticall
(
as
they
be
named
)
and
namely
of
that
whiche
you
thought
meter
to
bee
called
apparition
,
whose
contrary
you
called
Occultation
:
so
that
when
Venus
doth
shyne
at
euenynge
after
sonne
settinge
,
she
dothe
rise
as
som
tearme
it
,
with
a
sonnely
rysinge
:
and
when
shee
is
hydden
againe
,
she
is
set
with
a
sonnely
settinge
.
but
that
you
iudge
Apparition
and
Occultation
more
apter
tearmes
.
Master
.
You
doo
not
gesse
muche
amysse
.
And
to
the
intent
that
you
may
considre
this
matter
the
better
,
I
think
it
good
that
you
do
marke
hyr
motion
the
more
diligently
hereafter
:
as
in
this
presente
moneth
of
Septembre
,
at
the
beginning
of
the
moneth
she
was
about
36
degrees
behynde
the
sonne
,
and
so
shoulde
she
shine
almoste
2
howers
and
a
halfe
after
the
sonne
,
as
it
myghte
appeare
by
the
degrees
of
distaunce
.
but
consideringe
the
obliquitie
of
the
Zodiake
,
and
the
latitude
of
Venus
at
that
time
,
she
didde
scarse
shine
three
quarters
of
an
hower
after
the
sonne
.
Scholar
.
This
talke
is
to
obscure
for
me
yet
.
Master
.
I
knowe
it
ryghte
well
.
but
yet
I
thoughte
good
to
admonish
you
in
that
matter
,
least
at
any
time
you
shuld
fynde
the
doubte
,
when
you
shall
haue
no
opportunity
to
aske
councell
therein
:
but
now
to
proceede
.
before
the
eand
of
the
same
moneth
of
Septembre
,
the
sayde
Planete
wyll
be
cleane
hydde
with
the
sonne
beames
:
for
within
2
dayes
after
(
I
meane
the
second
daye
of
Octobre
)
she
doth
ioyne
with
the
sonne
by
coniunction
.
And
frome
that
daye
forwarde
the
sonne
doth
outgo
hir
so
faste
,
that
by
the
13
daye
of
Octobre
,
she
wyll
be
out
of
his
beames
againe
,
and
ryse
almoste
an
hower
and
a
quarter
before
the
sonne
.
and
at
the
eande
of
Nouembre
,
she
will
be
46
degrees
behind
the
sonne
,
in
ordre
of
the
signes
,
and
yet
shall
she
rise
4
howers
and
more
before
the
sonne
,
where
as
the
numbre
of
degrees
are
equall
to
lyttle
more
then
three
howers
.
but
the
obliquitie
of
the
Horizont
,
doth
make
all
the
diuersitie
in
this
,
excepte
a
meane
trifle
by
the
latitude
of
Venus
.
And
thus
may
you
marke
Venus
in
all
that
moneth
,
and
in
Decembre
also
vnto
the
eande
of
the
yeare
:
but
then
dooth
she
abate
her
distaunce
againe
,
wherby
it
is
easye
to
vnderstande
that
she
hathe
a
seuerall
motion
from
the
sonne
,
and
a
seuerall
sphere
also
.
Scholar
.
In
Venus
it
doth
appeare
nowe
easye
inoughe
to
considre
,
as
well
as
in
the
Sonne
and
Moone
:
but
is
it
as
easye
in
the
other
four
Planetes
?
Master
.
Yea
in
deede
,
for
three
of
them
which
bee
moste
highest
,
if
you
lyste
to
learne
to
knowe
them
,
and
to
marke
their
courses
:
but
Mercury
is
not
so
well
marked
,
bicause
he
doth
alwaies
keepe
his
course
nigh
about
the
sonne
,
Mercury
.
and
therfore
his
obseruation
requireth
greate
diligence
,
and
his
courses
appeare
most
straunge
,
yet
bothe
he
and
Venus
do
accomplishe
their
course
in
a
yeare
with
the
sonne
:
Saturne
.
but
Saturne
is
so
slacke
a
mouer
,
that
you
shall
not
well
perceaue
his
motion
vnder
4
moneths
.
in
which
time
he
doth
moue
about
4
degrees
:
so
that
if
you
marke
his
place
at
any
time
,
and
within
4
monthes
after
that
time
yf
you
do
marke
him
againe
,
you
shall
perceaue
that
hee
is
gone
4
degrees
eastwarde
,
whiche
you
maye
marke
by
the
fixed
starres
aboute
that
place
:
but
if
you
doo
after
a
whole
yeare
marke
hys
place
,
then
shall
you
perceaue
well
and
manifestly
,
that
hee
is
gone
eastwarde
12
degrees
,
and
somwhat
more
:
as
for
example
.
The
fyrste
daye
of
Septembre
,
the
laste
yeare
1555
,
Saturne
was
in
the
12
degree
of
Aries
,
and
this
year
of
1556
we
see
him
to
be
in
the
26
degree
of
the
same
signe
,
wherby
it
dothe
appeare
,
that
he
hathe
moued
14
degrees
eastwarde
in
that
yeare
space
.
And
if
you
will
haue
farther
proofe
:
In
the
yeare
of
our
Lorde
1549
,
the
laste
daye
of
Nouembre
,
Saturne
was
seene
in
the
26
degree
of
Capricorne
,
and
this
yeare
of
1556
the
fyrste
of
Septembre
,
the
same
starre
was
in
the
26
degree
of
Aries
:
wherby
it
maye
bee
knowen
that
hee
hath
moued
three
whole
signes
(
whiche
is
a
quarter
of
the
Zodiake
)
in
7
year
space
.
And
so
in
lesse
then
30
yeares
,
hee
dothe
go
about
the
whole
Zodiake
.
Iupiter
hath
a
swyfter
course
,
for
he
passeth
the
circuite
of
heauen
in
lesse
then
12
yeares
.
Iupiter
.
so
doth
he
euery
yeare
run
ouer
one
signe
,
and
euery
two
moneths
he
passeth
5
degres
.
Mars
is
yet
swyfter
in
course
then
hee
,
and
compasseth
all
the
Zodiake
in
2
yeare
,
Mars
.
and
euery
moneth
passeth
halfe
a
signe
.
wherby
for
this
point
,
he
is
more
easy
to
be
marked
,
then
anye
of
the
other
.
but
yet
are
his
motions
difficulte
to
marke
in
other
pointes
:
but
this
may
suffice
for
tryall
that
he
moueth
eastwarde
,
as
all
the
other
Planetes
do
:
and
therfore
must
he
be
iudged
,
as
all
the
other
also
oughte
to
haue
seuerall
spheres
in
whiche
they
moue
.
And
although
theyr
spheres
can
not
bee
seene
,
yet
in
as
muche
as
their
starres
maye
be
so
well
perceaued
,
it
muste
needes
follow
,
that
they
haue
spheres
also
:
except
we
shuld
come
to
that
absurditie
to
saye
,
that
they
moue
in
the
Ayer
as
byrdes
do
,
or
as
fyshes
in
the
water
:
whiche
were
to
muche
repugnante
to
any
one
ordrely
motion
,
and
much
more
disagreyng
to
so
many
diuers
motions
as
are
in
the
Planetes
,
but
namely
in
Mars
and
Mercury
.
And
to
the
intent
that
you
may
know
them
the
better
,
it
shall
bee
good
that
you
learne
their
true
places
by
the
Ephemerides
,
and
accustome
your selfe
to
loke
for
them
,
and
to
marke
their
bignes
and
colours
how
they
differ
from
other
starres
.
whiche
is
spoken
by
waye
of
exhortation
only
,
and
not
propouned
as
anye
peece
of
this
booke
,
but
an
other
time
I
will
instructe
you
better
therein
.
Scholar
.
But
in
the
meane
time
,
howe
shall
I
know
whether
there
be
anye
more
spheres
or
no
?
Master
.
There
is
thoughte
to
be
in
the
8
sphere
or
Firmament
,
two
other
motions
,
Of
the
nith
and
tenthe
sphere
.
whiche
be
disagreeable
from
all
other
mouinges
before
mentioned
,
and
therfore
many
thinke
that
they
muste
of
necessitye
confesse
2
other
spheres
from
whiche
those
motions
must
proceede
peculiarly
.
Scholar
.
What
motions
are
those
,
and
howe
are
they
knowen
?
Master
.
Fyrste
there
is
one
notable
obseruation
by
conference
of
learned
men
in
diuerse
ages
,
concernyng
the
Equinoctiall
pointes
,
and
lyke
waies
concerning
those
Tropicall
pointes
,
that
the
Sonne
toucheth
twise
euery
yeare
:
for
about
the
incarnation
of
Christ
,
the
equinoctiall
point
or
instaunte
happened
aboute
the
25
daye
of
Marche
,
and
nowe
it
is
aboute
the
tenthe
of
the
same
moneth
,
whyche
disagreemente
dooth
ryse
partly
by
the
misse
ordre
in
the
Leape
yeares
,
but
moste
principallye
thoroughe
the
anticipation
of
the
Equinoctiall
tearmes
.
For
althoughe
the
Sonne
doo
at
the
yeares
eande
retourne
to
the
same
poynte
in
the
Starrye
skye
where
hee
was
at
the
beginninge
of
the
same
yeare
,
yet
is
he
not
exactlye
so
nighe
vnto
the
Equinoctiall
pointe
as
he
was
before
,
but
doth
ouer
runne
it
euery
yeare
,
and
thereby
in
continuaunce
of
tyme
it
cometh
to
passe
,
that
men
may
sensibly
perceaue
that
the
stars
are
runne
eastward
from
that
equinoctiall
point
.
Scholar
.
This
seemeth
something
obscure
,
excepte
you
can
declare
it
more
plainely
.
Master
.
Do
you
not
considre
betwene
the
sonne
and
the
moone
,
that
when
she
doth
ioyne
with
him
by
coniunction
and
then
ouerpasseth
him
by
her
swyfte
motion
,
that
when
she
retourneth
againe
to
the
same
place
where
she
dyd
leaue
the
sonne
,
she
doth
not
fynde
him
there
,
but
she
must
ouer
go
that
place
,
beefore
shee
canne
ouertake
the
Sonne
againe
,
by
reason
that
the
sonne
dydde
moue
forwarde
after
the
moone
in
the
same
course
,
though
muche
more
slowly
:
So
likewaies
when
the
Sonne
departeth
frome
anye
starre
in
the
skye
,
in
the
verye
instaunt
of
the
equinoctiall
equalitye
,
and
in
the
very
point
of
the
intersection
of
the
Equinoctiall
and
the
Ecliptike
line
,
where
of
necessity
that
equalitie
must
happen
:
if
the
sonne
retourning
after
a
year
vnto
that
Equinoctiall
pointe
,
do
not
fynde
the
starre
there
precisely
,
whiche
he
lefte
there
,
but
that
he
muste
ouer
run
that
point
,
before
he
can
come
again
to
the
said
star
,
may
not
we
yea
and
must
not
we
saye
,
that
that
starre
is
moued
forwarde
in
his
course
eastwarde
,
as
all
the
Planetes
doo
moue
?
Howe
bee
it
the
quantitie
is
so
lyttle
,
that
it
is
not
perceaued
by
syghte
alone
,
nother
yet
by
instrumentes
,
in
lesse
then
an
hundreth
yeare
,
so
that
no
one
man
is
hable
to
marke
anye
greate
diuersitie
in
hys
owne
age
,
but
must
be
fayne
to
conferre
with
other
men
that
hathe
made
obseruations
longe
beefore
and
written
them
:
so
dydde
Ptolemye
conferre
his
obseruations
,
with
Hipparchus
obseruations
,
and
found
that
from
Hipparchus
tyme
vnto
his
owne
age
,
the
Fixed
starres
were
moued
forward
from
the
Equinoctiall
pointe
,
two
degrees
,
and
40
minutes
:
whereby
he
dyd
coniecture
,
that
they
moued
euery
hundreth
yeare
one
degre
,
syth
the
tyme
betwene
their
2
obseruations
was
265
yeare
:
and
after
the
like
rate
was
the
same
motion
found
by
conference
of
the
obseruations
of
Timochares
&
Hipparchus
.
what
other
men
say
for
more
precisenes
herin
syth
their
tyme
,
I
wil
in
the
The
orikes
declare
vnto
you
:
but
all
agree
herein
,
that
the
starres
do
moue
vniformly
with
all
their
sphere
eastward
as
the
Planetes
doo
.
wherefore
many
assigne
that
motion
as
peculiar
to
the
eight
sphere
,
and
the
daily
motion
from
easte
to
west
they
appoint
to
the
nynth
sphere
.
Other
men
perceauinge
that
the
starres
doo
also
ascende
northwarde
,
and
descende
againe
southwarde
,
doo
assigne
a
certaine
motion
,
whiche
is
named
by
them
Motus
trepidationis
,
and
they
note
it
to
bee
peculiare
for
the
eighte
sphere
,
and
the
other
motion
laste
named
before
,
they
accompte
to
be
propre
to
the
nynthe
sphere
,
and
then
of
necessitye
it
foloweth
,
that
a
ten
the
sphere
(
as
they
saye
)
muste
be
assigned
for
the
dayly
motion
.
Scholar
.
If
it
be
true
that
there
be
suche
varieties
of
motions
,
then
it
seemeth
reasonable
to
assigne
so
many
spheres
as
there
be
motions
seuerall
.
Master
.
Although
you
thinke
so
now
,
you
may
be
persuaded
peraduenture
to
thinke
the
contrary
hereafter
,
as
most
wise
men
in
that
arte
do
.
Scholar
.
But
in
the
meane
ceason
what
shall
I
thinke
?
Master
.
Thinke
well
on
that
that
you
haue
learned
,
and
labour
to
be
expert
in
all
that
,
by
often
conference
of
your
learnynge
,
with
the
practise
of
the
globe
,
and
so
shall
you
be
apte
to
bee
instructed
in
all
the
reste
the
more
easilye
.
for
it
will
requyre
a
witte
somewhat
readye
,
and
practised
in
these
former
matters
.
Scholar
.
I
wyll
then
prepare
me
a
Sphere
(
without
which
I
see
I
can
doo
lytle
good
herein
)
and
so
will
I
practise
these
former
lessons
,
that
I
truste
to
be
as
readye
in
them
,
as
any
auditor
in
framynge
of
accompte
.
Master
.
By
that
meanes
shall
all
other
thinges
in
thys
arte
appeare
easye
vnto
you
,
whiche
nowe
myght
seeme
vntimely
put
forth
,
if
I
shoulde
offer
to
teache
them
,
as
the
motions
of
the
Sonne
,
Moone
,
and
other
Planetes
,
with
their
eccentrikes
,
equantes
,
differentes
and
Epicycles
.
Scholar
.
In
deede
I
thinke
this
to
harde
yet
,
but
of
the
progression
,
retrogradation
,
and
station
of
the
Planetes
,
and
also
of
the
eclipses
of
the
Sonne
and
Moone
,
I
knowe
that
Iohn
de
sacro
Bosco
dyd
write
somwhat
,
and
so
myght
you
brieflye
nowe
do
.
Master
.
His
woordes
are
shorte
and
therefore
obscure
,
and
so
should
my
wordes
be
.
beside
that
,
it
is
a
disordrely
forme
to
put
the
carte
before
the
horse
:
I
meane
to
write
of
the
passions
of
the
Planets
,
before
I
haue
sufficiently
taught
the
full
ordre
of
their
motion
.
Therefore
I
will
saye
in
fewe
wordes
,
that
the
reasons
of
the
passions
canne
not
bee
taughte
aptely
,
before
the
Theorikes
of
theyr
motions
.
but
for
contentation
of
your
mynde
,
I
maye
define
after
a
sorte
the
eclipses
of
bothe
the
Sonne
and
Moone
:
wherof
the
fyrste
is
but
an
appearaunte
and
a
countrefete
Eclipse
:
The
Eclipse
of
the
Sonne
.
and
is
no
wante
nor
losse
of
the
lyghte
in
the
Sonne
it selfe
,
but
is
an
impedimente
,
that
hys
lyghte
dooth
not
or
can
not
extende
vnto
vs
,
by
reason
that
the
moone
doth
runne
beetwene
him
and
our
sighte
.
And
this
Eclipse
as
it
hydeth
the
sonne
from
vs
for
a
time
,
so
in
som
partes
of
the
earthe
at
the
selfe
same
instaunte
he
is
not
anye
whitte
eclipsed
,
but
shyneth
cleerely
and
wholly
.
And
therfore
is
that
eclipse
called
no
Generall
eclipse
,
whiche
should
extende
to
all
the
worlde
,
namely
for
that
hemispherye
,
but
is
particulare
for
some
one
climate
,
and
yet
not
vniuersall
to
all
that
climate
.
The
Eclipse
of
the
moone
.
but
contrarye
waies
the
eclipse
of
the
moone
is
a
true
eclipse
in
deede
:
for
there
is
no
thinge
that
runneth
betweene
our
syghte
and
her
,
and
so
hydeth
frome
vs
her
light
,
but
she
leeseth
her
light
certainly
.
As
if
a
glasse
that
standeth
in
the
Sonne
,
doo
receaue
the
lyghte
of
the
Sonne
,
and
doo
caste
beames
(
as
wee
maye
see
)
frome
hym
,
tyll
some
cloude
or
some
other
darke
bodye
passe
betweene
the
Sonne
and
it
,
and
then
it
leeseth
hys
lyght
cleerely
,
and
hathe
no
lyghte
but
hys
owne
bryghtnesse
,
whiche
canne
cast
no
beames
,
nother
deserue
anye
name
of
lyghte
,
in
comparison
to
the
lyghte
that
it
hadde
of
the
Sonne
:
So
the
Moone
kepynge
hyr
course
tyll
shee
bee
at
the
full
,
that
is
to
saye
,
in
the
contrarye
poynte
of
the
Zodiake
to
the
Sonne
,
and
that
then
she
bee
without
all
latitude
,
and
runne
ryghte
vnder
the
Ecliptike
lyne
in
the
Zodiake
,
then
dooth
shee
lyghte
directly
in
the
shaddowe
of
the
earthe
,
and
therefore
canne
not
receaue
the
lyghte
of
the
sonne
,
but
leeseth
it
for
the
time
,
howe
bee
it
not
alwayes
a
lyke
.
for
sometime
shee
commeth
whollye
withoute
the
shaddowe
of
the
earthe
,
and
then
is
shee
whollye
eclipsed
:
at
other
times
shee
commeth
but
partely
into
the
shaddowe
,
and
that
some
tymes
in
the
ouer
parte
,
and
sometime
in
the
nether
parte
,
wherby
shee
is
eclipsed
partly
,
and
not
vniuersallye
:
for
if
the
mone
passe
by
the
northe
or
ouer
part
of
the
shaddow
,
and
touche
it
with
anye
parte
of
hir selfe
,
then
is
that
parte
eclipsed
of
necessity
,
which
is
the
southe
part
of
the
moone
or
the
nether
part
of
her
.
And
again
if
the
mone
do
touch
the
nether
parte
of
the
shaddowe
whiche
is
nexte
to
the
Horizonte
,
then
is
the
hygher
or
northerlye
parte
of
the
Moone
eclipsed
.
To
tell
you
nowe
of
the
Eclipticall
pointes
,
whiche
be
commonly
called
the
Headde
and
the
Tayle
of
the
Dragon
,
it
were
verye
vntymely
,
and
harde
for
you
brieflye
to
conceaue
,
and
therefore
I
do
willingly
omitte
them
.
Scholar
.
Yet
this
I
perceaue
by
you
,
that
the
sonne
is
not
darkened
in
him selfe
,
but
is
hydde
by
the
moone
from
vs
,
whiche
happeneth
diuerslye
:
for
sometyme
all
the
Sonne
is
hyd
,
and
sometyme
the
hygher
part
only
,
and
at
other
times
,
the
nether
parte
onlye
of
all
whiche
formes
,
I
may
see
examples
on
euerye
common
Almanach
after
a
grosse
fort
:
but
this
Figure
doth
Astronomical diagram.
more
aptlye
expresse
the
cause
thereof
:
where
the
Moone
dooth
appeare
to
be
betweene
any
one
Region
and
the
Sonne
,
and
therefore
hydeth
the
Son
frome
the
inhabitauntes
of
that
place
:
but
in
other
Regions
there
appeareth
no
suche
lette
of
the
Moone
,
but
that
they
maye
fully
see
the
Sonne
.
And
other
Nations
beetweene
them
,
see
parte
,
and
leese
other
parte
.
And
thys
I
perceaue
maye
bee
considered
dyuerselye
,
in
as
muche
as
anye
bee
nygher
to
theym
that
see
the
whole
Sonne
,
or
nygher
to
those
that
see
hys
Eclipse
.
Master
.
There
is
in
that
nighnes
double
consideration
:
one
is
of
distaunce
betwene
easte
and
weste
,
and
that
other
is
of
distaunce
betweene
southe
and
north
.
for
when
any
nation
doth
perceaue
the
higher
cantle
of
the
sonne
enclipsed
,
then
they
that
dwell
more
northerly
,
(
vnder
the
same
meridian
)
do
leese
more
of
the
sonne
,
and
iudge
that
eclipse
the
greater
:
and
contrary
waies
they
that
dwell
directly
towarde
the
southe
,
the
farther
south
they
dwell
,
the
lesser
doth
the
part
eclipsed
appeare
to
them
to
be
,
tyll
at
lengthe
vnto
them
that
dwell
more
southe
there
appeareth
no
eclipse
at
all
.
The
seconde
consideration
betwixte
easte
and
weste
,
dooth
cause
only
diuersity
in
time
of
the
Eclipse
,
but
not
in
form
:
&
that
is
common
also
for
the
eclipse
of
the
Moone
,
but
so
is
not
the
first
consideration
,
but
serueth
for
the
sonnes
eclipse
onlye
.
Scholar
.
As
for
the
eclipse
of
the
mone
,
I
thinke
the
former
figures
whiche
you
did
shewe
me
,
do
comprehende
all
varieties
of
formes
sufficiently
,
whiche
be
these
two
,
for
the
Astronomical diagram of the eclipses of the moon.
other
two
do
represent
those
false
formes
,
that
do
follow
of
certaine
false
figures
of
the
earth
:
and
therfore
do
not
serue
here
in
place
of
true
doctrine
.
Master
.
This
may
you
now
also
considre
,
that
although
the
eclipse
of
the
sonne
is
not
general
to
all
nations
,
bicause
it
is
not
a
true
eclipse
or
wante
of
lyghte
,
but
onlye
an
appearaunte
eclipse
,
yet
the
eclipse
of
the
moone
is
a
very
Eclipse
in
deede
,
that
is
to
saye
,
a
wante
of
lyghte
in
hir selfe
,
&
therfore
who
so
euer
doth
see
her
,
dooth
see
also
hir
eclipse
exactlye
as
it
is
:
and
it
appeareth
vniformlye
to
them
all
,
thoughe
at
that
time
the
moone
be
not
,
nor
canne
not
bee
aboue
the
horizonte
to
all
people
:
and
therefore
vnto
them
that
haue
the
moone
vnder
their
horizont
,
it
is
accompted
none
eclipse
.
And
that
is
the
cause
why
many
eclipses
of
the
sonne
and
moone
also
are
not
noted
in
the
common
Ephemerides
and
Almanachs
,
bicause
they
appeare
in
such
time
as
the
Planet
eclipsed
,
is
vnder
the
Horizont
of
that
region
for
whiche
the
Almanach
or
Ephemerides
is
written
.
farther
more
this
is
to
be
considered
as
a
very
truth
and
most
vnfallible
,
that
the
eclipse
of
the
son
can
neuer
happen
but
at
the
verye
chaunge
of
the
moone
,
for
at
other
times
shee
is
so
far
in
ordre
of
hir
course
from
the
sonne
,
that
shee
can
not
hyde
any
parte
of
him
from
anye
nation
in
earth
.
And
for
the
eclipse
of
the
moone
,
the
time
of
opposition
or
full
moone
doth
serue
only
.
for
the
shaddowe
of
the
earth
whiche
alwaye
runeth
towarde
the
Nadir
of
the
sonne
directly
,
can
not
touche
the
moone
,
excepte
she
be
verye
nighe
vnto
the
same
place
.
And
that
is
the
cause
why
the
eclipse
of
the
sonne
whiche
happened
at
the
deathe
of
Christ
,
may
not
be
accompted
a
naturall
eclipse
,
for
so
muche
as
it
happened
in
the
time
of
the
full
moone
,
when
it
is
not
possible
by
natures
ordre
,
that
anye
suche
eclipse
shoulde
happen
.
And
therfore
dyd
Dionyse
the
Areopagite
beyng
in
Alexandria
,
and
Apollophanes
his
companion
,
not
only
wonder
at
this
straung
and
vnnaturall
eclipse
,
but
concluded
that
it
could
not
happen
without
some
meruailous
cause
,
and
a
wondrefull
immutation
of
natures
workes
.
Scholar
.
So
dooth
our
author
of
the
sphere
note
it
,
affirming
that
Dionyse
dyd
say
then
:
Other
doth
the
God
of
nature
suffre
now
,
or
els
the
whole
frame
of
the
world
shall
nowe
be
dissolued
.
Master
.
With
this
good
clause
did
he
eande
his
booke
,
and
so
wyll
we
with
the
same
eande
close
vp
our
talke
.
Learnynge
this
good
vse
in
this
naturall
arte
,
that
it
leadeth
men
wonderfully
to
the
knowledge
of
God
,
and
his
highe
mysteries
.
as
not
only
by
example
of
these
twoo
philosophers
here
it
doth
appear
,
but
by
the
testimonies
of
the
scriptures
in
sundry
places
.
Scholar
.
This
was
that
Dionyse
,
whome
Saincte
Paule
dyd
conuerte
afterwarde
at
Athenes
,
and
rather
muche
bicause
he
hadde
in
remembraunce
that
miraculous
Eclipse
.
Master
.
So
maye
wee
gather
manye
argumentes
by
lyke
maters
against
infideles
and
false
Christians
also
:
but
that
frute
will
I
reserue
for
an
other
place
:
and
for
this
presente
will
only
saye
,
that
there
was
neuer
any
good
Astronomer
,
that
denyed
the
Maiestie
and
prouidence
of
God
,
though
many
other
denyed
bothe
:
but
nowe
farewell
for
a
time
:
I
am
dryuen
to
omytte
teachinge
of
Astrononye
,
and
muste
of
force
go
learne
some
lawe
.
Scholar
.
The
god
that
is
author
of
true
Astronomye
,
and
made
all
the
heauens
for
men
to
beholde
,
keepe
you
in
healthe
and
cleare
from
all
trouble
,
that
you
maye
,
as
you
mynde
,
accomplysshe
your
workes
,
and
finish
well
and
spedily
,
the
frutes
of
your
studye
.
Master
.
Amen
,
and
Amen
.