THE
Arte
of
Nauigation
wherein
is
contained
all
the
rules
,
declarations
,
secretes
,
&
aduises
,
which
for
good
Nauigation
are
necessarie
&
ought
to
be
knowen
and
practised
:
and
are
very
profitable
for
all
kind
of
Mariners
,
made
by
(
master
Peter
de
Medina
)
directed
to
the
right
excellent
and
renowned
Lord
,
don
Philippe
,
prince
of
Spaine
,
and
of
both
Siciles
.
And
nowe
newely
translated
out
of
Spanish
into
English
by
John
Frampton
.
1581.
❧
Imprinted
at
London
,
by
Thomas
Dawson
,
dwelling
at
the
three
Cranes
in
the
Vinetree
,
and
are
there
to
be
solde
.
¶
To
the
right
woorshipfull
,
master
Edwarde
Dier
Esquier
,
Iohn
Frampton
wisheth
health
,
and
perfit
felicitie
with
increase
of
honour
.
COnsidering
with
my selfe
(
right
worshippefull
,
)
that
friendshippe
and
bounden
duetie
,
doth
force
many
times
men
to
doe
thinges
,
which
if
they
were
in
the
free
choyse
of
him
that
doth
them
,
to
leaue
them
vndone
without
any
conceaued
discurtesie
,
not
only
hee
woulde
not
doe
them
,
but
also
,
not
asmuch
as
thinke
of
them
.
This
I
say
that
forced
by
friendshippe
,
and
also
mooued
by
persuasion
of
certaine
pylottes
,
and
Masters
of
shippes
,
I
determined
to
translate
this
booke
of
the
arte
of
Nauigation
,
compiled
by
Master
Peter
de
Medina
a
spaniarde
,
in
the
yeere
of
our
Lorde
Iesus
Christ
.
1545.
And
because
the
worke
is
so
principalle
that
in
our
time
,
the
like
in
all
respectes
hath
not
beene
sette
forth
in
our
tongue
,
considering
it
instructeth
,
and
teacheth
all
the
whole
arte
of
Nauigation
in
all
pointes
,
and
is
in
as
like
sorte
necessary
for
the
Mariner
,
as
the
accidens
is
for
the
Gramarian
,
the
weapon
for
the
soldier
,
the
Toole
for
the
workeman
,
the
Guide
for
the
blinde
,
the
instructor
for
the
learner
:
and
finally
,
comparable
to
a
glasse
,
wherein
all
the
course
of
the
worlde
,
the
Seas
,
the
Windes
,
the
Altitudes
of
the
sunne
,
Moone
,
and
Starres
,
are
to
bee
seene
,
and
knowne
,
as
farre
as
naturalle
reason
may
extende
to
.
And
beesides
,
the
pleasure
that
I
minded
to
doe
,
to
the
aforesaide
persons
,
who
mooued
mee
thereunto
,
as
also
to
satisfie
my
good
and
continual
desire
,
which
I
haue
,
to
helpe
,
and
bringe
to
light
this
good
and
profitable
arte
of
Nauigation
,
whereby
all
men
that
are
desirous
to
knowe
,
the
secreete
of
this
noble
arte
,
may
profite
themselues
threewith
by
reading
it
in
our
Englishe
tongue
,
especially
the
Pylottes
,
Masters
,
and
Mariners
,
considering
their
liues
and
lyuinges
doe
stand
there
vpon
.
And
seeing
as
I
belieue
and
trust
,
they
shall
gather
much
fruite
thereby
,
and
that
by
little
and
little
,
these
sciences
shall
remaine
aswell
in
our
countries
as
in
any
other
whatsoeuer
.
And
seing
this
worke
so
necessary
for
the
common
wealth
,
setting
all
other
priuate
busines
aside
I
tooke
in
hande
to
translate
this
booke
,
being
perused
and
alowed
by
the
chiefe
Pilot
,
&
learned
Cosmographers
of
the
famous
contractacion
house
of
Seuil
for
the
increase
&
knowledge
of
matters
of
Nauigation
,
for
the
subiects
of
Spaine
,
which
worke
so
excellent
tried
&
approued
by
the
learned
:
And
for
this
our
England
so
fit
,
&
by
me
now
thus
translated
out
of
Spanish
into
English
,
I
dedicate
to
your
worship
before
al
others
,
for
that
I
know
you
to
haue
the
arte
of
Nauigation
inhigh
account
,
&
as
highly
to
esteeme
al
men
that
indeuour
the
knowledge
of
the
same
,
beseeching
you
to
accept
of
my
good
wil
and
to
be
a
protector
of
the
same
worke
.
And
so
beseeching
the
almightie
,
to
giue
your
worshippe
long
life
,
and
the
aduancement
in
this
common
weale
,
that
the
good
people
wish
vnto
you
,
that
aucthoritie
may
enable
you
to
doe
,
that
good
,
that
your
good
inclination
doth
naturally
moue
you
vnto
.
From
London
this
fourth
of
August
.
1581.
Your
worshippes
to
commande
.
Iohn
Frampton
.
THE
EPISTLE
DEDICATORIE
TO
THE
right
excellent
and
renowmed
Lorde
,
Don
Phillip
Prince
of
Spaine
,
and
of
both
Siciles
,
&c.
Set
foorth
by
Maister
Peter
de
Medina
,
the
Authour
of
the
Arte
of
Nauigation
.
THE
subiectes
are
accustomed
to
serue
their
Lorde
right
excellent
and
renowmed
Prince
and
Lord
,
with
that
which
seemeth
〈◊〉
them
to
be
most
conformable
to
their
will
,
and
so
some
there
bee
that
serue
with
thinges
that
are
delightfull
to
the
eye
,
and
others
to
the
taste
.
Others
there
are
whiche
doe
imploye
their
persons
in
labours
,
and
also
others
in
diuers
other
matters
:
And
seeing
I
am
desirous
to
bee
of
the
number
of
those
,
I
sought
by
what
meanes
I
might
put
it
in
effect
,
and
for
that
my
abilitie
is
not
sufficient
to
do●
greater
seruice
:
I
determined
to
make
a
booke
of
the
Arte
of
Nauigation
,
and
to
offer
it
in
the
seruice
of
your
highnesse
.
Two
thinges
haue
mooued
mee
to
this
most
mightie
Lorde
.
The
first
is
,
to
see
howe
great
seruice
your
highnesse
〈◊〉
receiue
by
the
Nauigation
,
at
also
howe
great
profite
commeth
thereby
to
all
the
common
●●●alth
of
Christendome
.
And
this
beeing
so
,
it
appeareth
that
by
the
Nauigation
,
your
Royall
Senorie
is
amplified
and
extented
into
so
great
parte
of
the
worlde
.
And
that
whiche
is
newlye
discouered
is
more
then
fiue
thousande
leagues
of
the
Sea
coaste
,
where
doeth
containe
so
many
regions
,
kingdomes
,
and
prouinces
,
where
are
founde
so
many
nations
and
diuersitie
of
people
,
and
many
other
thinges
in
suche
sorte
by
good
reason
it
is
called
the
newe
worlde
.
So
that
by
meanes
of
the
Nauigation
,
there
hath
been
brought
and
is
brought
into
your
highnesse
Countrye
of
Spaine
,
so
many
shippes
laden
with
Golde
and
Siluer
,
that
the
same
thereof
cannot
bee
accounted
.
As
also
such
great
quantitie
of
sweete
Drugges
,
and
other
things
of
great
value
and
price
:
And
this
is
litle
in
respect
,
right
excellent
Lorde
,
of
the
great
number
of
people
whiche
doe
saile
,
not
only
to
places
knowne
,
but
also
to
suche
as
are
farre
of
,
and
vnknowne
,
and
of
such
at
is
no
knowledge
of
,
they
procure
by
sailing
to
seeke
and
knowe
,
And
seeing
how
long
and
dangerous
wayes
they
make
by
Sea
,
and
f●we
of
them
that
saile
doe
knowe
what
doeth
appertaine
to
the
Arte
of
Nauigation
▪
The
cause
is
,
there
are
no
instructors
thereof
,
nor
bookes
whereby
they
may
attaine
to
it
,
so
that
your
highnesse
may
vnderstande
,
although
the
Nauigation
bee
of
such
antiquitie
,
and
more
then
three
thousande
yeares
〈◊〉
it
began
,
and
a
thing
of
such
importance
,
that
the
life
of
man
goeth
therevpon
.
And
who
can
manifest
the
number
of
shippes
and
people
,
which
only
doe
saile
out
of
Spaine
to
all
partes
of
the
world
,
or
who
can
recken
the
multitude
of
people
which
doe
consist
only
vpon
the
Nauigation
,
with
their
goodes
,
riches
,
trades
,
merchandize
,
and
other
thinges
:
And
for
all
this
,
there
are
no
maisters
whiche
doe
teache
this
Arte
,
nor
knowledge
of
an●
that
vnto
this
daye
haue
written
the
manner
of
sailing
:
Euen
so
,
the
most
sorte
of
Pilottes
haue
the
vse
of
Nauigation
,
no
otherwise
but
euerie
one
following
his
owne
opinion
and
iudgement
,
where●f
it
happeneth
many
times
in
one
shippe
two
or
three
Pilottes
,
the
one
saith
according
to
his
reckoning
,
the
shippe
goeth
sailing
vpon
the
lande
,
the
other
sa●eth
,
according
to
his
reckoning
,
the
lande
is
farre
of
from
him
,
and
the
cause
thereof
is
,
that
there
wanteth
true
knowledge
of
Nauigation
,
and
hereby
it
happeneth
many
times
both
shippes
and
people
are
loste
,
and
others
sustaine
great
dangers
and
losses
.
All
whiche
beeing
by
mee
considered
,
and
chiefly
seeing
the
Maiestie
of
the
Emperour
,
father
vnto
your
highnesse
,
and
our
Lorde
many
tymes
putteth
his
imperiall
person
vnto
the
danger
of
the
Sea
.
Wherefore
I
beeing
desirous
to
serue
your
highnesse
in
this
,
and
to
doe
good
to
suche
as
are
Sailers
,
by
giuing
them
rules
and
aduises
howe
they
may
make
their
Nauigation
certaine
without
hazarde
of
ignorance
,
I
haue
framed
and
deuised
an
Arte
of
Nauigation
so
orderly
,
that
the
Pilottes
and
other
persons
whiche
doe
saile
,
shall
finde
them selues
so
able
therewith
,
that
of
it selfe
,
or
with
verie
litle
helpe
,
they
shall
knowe
and
verie
plainly
vnderstande
that
whiche
they
treate
of
,
seeing
it
is
so
necessarie
,
and
so
much
standeth
them
vpon
to
knowe
,
as
a
thing
whiche
doeth
importe
to
many
their
honours
,
liues
,
and
goods
:
Truth
it
is
,
most
mightie
Lorde
,
that
weying
my
strength
with
the
waight
of
my
iudgement
,
and
finding
my selfe
of
small
sufficiencie
,
I
greatly
disputed
with
my selfe
,
if
for
my
small
knowledge
I
should
holde
my
peace
,
seeing
that
I
knewe
it
to
bee
ouermuche
boldnesse
to
make
a
woorke
and
to
directe
it
to
your
highnesse
,
but
animating
my selfe
,
and
trusting
in
your
accustomed
clemencie
and
magnanimitie
,
I
put
my selfe
vnder
the
shadowe
of
your
fauour
,
and
so
most
humbly
beseeching
you
to
receiue
this
my
litle
seruice
with
that
Royall
curtesie
that
vnto
others
you
are
accustomed
to
doe
.
And
beeing
perused
by
your
highnesse
,
it
maye
winne
so
muche
fauour
whereby
it
maye
passe
safely
through
all
places
,
yelding
great
benefite
and
seruice
vnto
your
highnesse
,
as
also
profite
to
suche
as
vse
the
Nauigation
,
that
thereby
they
may
vnderstande
the
perfect
knowledge
thereof
.
❧
A
preamble
of
the
authour
vpon
the
Arte
of
Nauigation
,
wherein
is
declared
the
great
excellencie
of
the
said
arte
.
AMonge
all
other
vertues
some
are
so
much
the
greater
,
by
howe
much
it
is
comunicated
of
amongst
others
,
wherby
the
vertue
of
Iustice
is
most
perfit
among
other
vertues
,
for
it
doth
most
communicate
and
participat
withall
,
so
that
amonge
all
artes
the
arte
of
Nauigation
is
more
excellent
then
others
,
for
it
doth
not
oenly
communicate
with
them
,
but
doth
shut
vp
into
it
,
the
most
principall
of
them
,
that
is
to
say
,
Arithmeticke
,
Geometrie
,
and
Astrologie
.
These
haue
excellencie
among
the
Mathematicals
,
by
the
most
true
shewe
that
is
made
of
their
conclusions
.
And
that
this
arte
hath
his
beginning
and
greatnes
among
other
artes
,
it
appeareth
by
three
reasons
following
.
The
first
,
by
reason
of
his
subtillitie
.
The
second
,
by
reason
of
his
certaintie
▪
The
third
,
by
reason
of
his
profit
.
For
the
first
,
who
is
sufficient
to
speake
of
so
great
a
misterie
that
a
man
with
a
compasse
,
and
certaine
strekes
marked
in
a
carde
,
doth
knowe
howe
to
goe
rounde
about
the
world
,
and
knoweth
both
by
day
and
night
whether
he
shall
come
,
and
from
whence
he
shall
depart
,
and
howe
much
he
shall
go
from
one
place
to
another
,
and
that
he
goe
certainly
in
his
right
way
,
by
so
long
and
so
large
a
thing
as
the
sea
is
,
where
is
no
way
no
signe
therof
,
it
is
a
misterie
very
difficult
.
And
so
it
was
considered
by
Salomon
:
who
saith
,
that
one
of
the
hardest
things
to
be
found
,
is
the
way
of
a
ship
in
the
sea
,
for
she
followeth
not
any
way
,
nor
leaueth
any
signe
where
she
went
,
And
who
is
able
to
speake
of
so
great
a
secret
,
that
with
a
rounde
instrument
no
greater
then
the
palme
of
a
mans
hande
called
Astrolabio
,
the
roundnesse
of
the
heauen
is
measured
,
being
so
great
th●t
the
vnderstanding
of
man
cannot
atteine
thereunto
.
And
therewith
is
taken
the
heigth
of
the
sunne
,
passing
it
by
a
very
litle
and
subtill
place
,
being
much
greater
then
all
the
earth
and
the
sea
.
And
it
is
knowen
howe
nere
and
howe
farre
off
it
is
from
vs
:
And
in
like
manner
the
heigth
of
the
starres
are
taken
,
and
by
this
we
are
so
certainely
guided
,
that
so
much
as
one
point
fayleth
not
.
Likwise
who
can
speak
of
the
secrete
&
●inenes
of
the
compasse
,
that
being
made
with
as
much
paper
as
a
mans
hande
,
and
with
certaine
streekes
marked
thereon
,
doth
note
the
windes
.
And
with
a
litle
iron
put
into
it
,
is
made
an
instrument
that
doth
moue
of
it selfe
,
with
onely
the
naturall
vertue
that
a
stone
hath
giuen
vnto
it
,
and
mouing
without
the
helpe
of
any
thing
,
sheweth
where
is
the
East
,
the
West
,
the
North
,
and
the
South
.
And
likwise
the
thirtie
two
windes
which
the
Nauigation
hath
,
and
this
is
sheweth
not
onely
in
one
place
but
in
all
places
,
and
it
sheweth
it
so
certainly
that
thereby
they
do
it
,
and
are
certaine
of
their
purpose
and
pretence
as
many
as
are
saylers
in
the
sea
.
For
the
second
,
the
certainetie
of
this
art
is
so
great
,
that
it
seemeth
the
knowledge
of
one
man
not
to
bee
sufficient
to
ordaine
it
,
nor
yet
of
many
men
,
more
then
God
prouided
a
speciall
grace
and
vnderstanding
for
that
purpose
,
it
is
proued
wherein
it
happeneth
that
a
pilot
commeth
sayling
,
and
a
storme
taketh
him
three
hundreth
leages
in
the
sea
,
and
the
day
very
cloudie
,
and
the
night
so
darke
that
standing
in
the
poope
of
the
shippe
,
which
is
the
hinder
part
,
he
seeth
not
the
fore part
of
her
,
and
scantly
the
maste
,
and
making
many
turnes
in
the
seas
,
running
from
one
part
to
another
,
rising
and
descending
,
with
a
vehemencie
of
the
windes
and
strength
of
the
sea
,
and
yet
for
all
this
,
by
the
certainetie
of
the
arte
,
he
knoweth
the
way
that
she
hath
gone
,
and
the
place
where
she
is
,
and
being
come
to
the
lande
,
shee
goeth
to
the
port
although
it
be
in
the
night
,
not
seeing
the
lande
,
likewise
it
happeneth
many
times
,
as
the
pilor
goeth
sayling
,
he
findeth
a
rocke
or
shoolde
CC.
leagues
in
the
sea
from
any
lande
,
and
marketh
the
place
where
he
is
,
although
he
seeth
not
wherewith
to
marke
it
,
for
he
seeth
but
the
heauen
and
the
water
,
and
in
it
is
not
any
thing
wherewithal
to
marke
or
make
any
signe
,
because
al
doth
moue
,
but
marketh
it
in
his
carde
by
the
land
,
he
seeth
in
it
and
according
to
the
art
,
which
the
carde
hath
,
it
is
so
certaine
,
that
he
and
others
both
by
day
&
night
do
knowe
howe
to
preserue
and
keep
them selues
from
that
place
going
aside
from
it
,
because
they
would
receiue
no
hurt
,
although
it
be
vnder
the
water
,
that
nothing
of
it
is
seene
,
whereby
is
concluded
that
although
the
other
artes
haue
trueth
,
this
hath
more
by
reason
of
the
demonstration
so
certaine
,
which
sheweth
to
keepe
a
man
from
hurt
and
danger
that
he
seeth
not
.
For
the
third
,
I
say
there
is
no
art
of
any
that
man
vseth
,
so
profitable
nor
so
good
as
this
art
of
Nauigation
is
,
and
this
to
be
true
it
seemeth
well
,
because
by
it
we
haue
knowledge
of
diuerse
and
sundrie
thinges
in
the
worlde
,
and
also
of
the
trade
with
all
partes
of
the
worlde
.
And
if
nauigation
shoulde
cease
,
men
shoulde
be
driuen
to
liue
straightly
,
for
that
they
should
lacke
many
things
which
are
necessarie
for
the
life
of
man
.
Also
here
is
to
be
noted
,
that
amonge
al
artes
which
men
doe
vse
and
practise
,
none
is
of
so
great
peril
and
labour
as
the
art
of
Nauigation
,
and
chiefely
in
these
dayes
,
seeing
it
is
so
greatly
encreased
and
well
neere
the
hol●
roundnes
of
the
worlde
is
sayled
about
:
it
is
strange
to
consider
that
the
auncient
writers
,
neyther
sawe
it
,
no●
thought
of
it
,
but
rather
helde
it
for
vnpossible
:
it
is
worthie
to
be
noted
,
that
I
haue
seene
many
times
a
Pilote
come
from
the
East
India
,
who
hath
bene
one
yeere
vpon
the
way
,
and
from
our
Indias
foure
or
fiue
monethes
,
passing
such
great
daungers
and
troubles
that
many
times
they
haue
beene
at
the
point
of
death
,
and
being
come
home
to
their
naturall
countrey
,
all
hath
beene
so
forgotten
of
them
,
as
if
it
had
past
in
adream
,
and
so
they
procure
to
returne
with
so
geart
good
will
,
as
though
they
went
to
a
thing
of
pleasure
.
I
thinke
that
couetousnesse
of
goods
is
not
the
cause
thereof
,
nor
any
other
worldly
gaine
,
but
I
take
it
to
come
of
the
will
of
God
,
that
although
it
be
a
thing
so
naturall
to
feare
death
,
and
great
labour
,
yet
all
these
labours
and
feares
which
they
passe
in
the
same
Nauigation
,
are
by
them
forgotten
,
for
if
they
shoulde
remember
and
feare
them
,
there
is
none
that
woulde
sayle
on
the
sea
:
And
seeing
the
wise
pilot
that
so
often
times
putteth
his
life
in
hassarde
;
and
not
onely
his
owne
,
but
in
his
knowledge
is
put
in
trust
the
liues
and
goodes
of
many
:
wherefore
if
any
person
will
vnderstand
the
arte
of
Nauigation
,
let
him
peruse
this
booke
and
arte
,
and
studie
therein
,
and
he
shall
finde
plainly
all
things
set
forth
necessarie
for
the
same
,
whereby
pleasing
God
he
will
graunt
,
to
his
way
the
ende
which
hee
desireth
.
The
ende
of
the
preamble
.
Errours
escaped
.
-
Fol.
1.
page
2
,
line
14.
he
in
.
for
he
is
in
.
-
Fol.
2.
page
2
,
line
36.
and
in
planetes
.
for
and
in
plantes
.
-
Fol.
3.
page
1.
line
31.
prospectiue
.
for
perspectiue
.
-
Fol.
3.
page
2.
line
2.
the
tenne
heauens
.
for
the
tenth
heauen
.
-
Fol.
11.
page
1.
line
.
23.
the
king
Iuba
.
the
king
I●b●
.
-
Fol.
14.
page
.
1.
line
47.
one
high
.
for
no
high
.
-
Fol.
15.
page
1.
line
20.
the
1.
for
the
first
.
-
Fol.
30.
pag
1.
line
22.
is
taken
for
one
sphera
Esphera
,
for
is
taken
one
spera
,
Esphera
.
-
Fol.
30.
page
.
2.
line
1.
is
in
auxe
for
is
in
his
auxe
.
-
Fol.
34.
page
2.
line
23.
your
are
distant
.
for
you
are
so
much
distant
.
-
Fol.
45.
page
1.
line
3.
howe
soeuer
it
be
.
for
howe
great
soeuer
it
be
.
-
Fol.
58.
page
2
line
9.
and
of
the
guardes
of
his
mouing
,
for
of
the
guardes
and
of
his
mouing
.
-
Fol.
58.
page
2.
line
22.
the
month
of
bozina
.
for
the
mouth
of
bozina
.
-
Fol.
64.
page
2.
line
3.
he
be
in
the
head
at
three
.
for
he
be
in
the
head
,
at
three
.
-
Fol.
69.
page
2.
line
27.
goe
one
any
viage
.
for
goe
on
any
viage
.
¶
The
table
of
the
bookes
and
Chapters
that
are
conteyned
in
the
Arte
of
Nauigation
.
-
The
first
booke
treating
of
the
worlde
,
of
his
order
and
composition
.
-
CAp
.
1.
What
thing
the
world
is
,
and
how
it
is
compounded
of
the
heauens
and
elements
,
it
declareth
the
number
of
the
heauens
and
their
monings
.
-
Cap.
2.
Wherein
is
declared
the
three
mouings
which
the
eyght
heauen
hath
,
&
how
they
are
knowne
.
-
Cap
3.
Howe
the
heauen
hath
a
rounde
figure
or
shape
,
and
by
5.
reasons
how
it
was
conuenient
it
should
be
so
.
-
Cap.
4.
Of
the
noblenes
of
the
heauen
and
of
his
col●or
.
-
Cap.
5.
Of
the
tenth
heauen
called
the
first
moueable
and
of
his
mouing
.
-
Cap
6.
Of
the
nienth
heauen
called
Christa●ino
or
heauen
of
water
,
it
declareth
how
there
is
a
heauen
of
water
and
of
his
qualitie
.
-
Cap.
7.
Of
the
eight
heauen
which
is
the
firmament
or
the
starrie
heauen
,
and
of
the
light
of
the
starres
and
their
greatnesse
.
-
Chap.
8.
How
it
is
vnderstood
that
the
sun
doth
enter
into
the
signes
,
and
the
cause
wherefore
they
haue
the
name
of
beastes
.
-
Cap.
9.
What
thing
a
signe
is
,
and
what
likenesse
it
hath
with
that
which
it
is
compared
vnto
,
and
what
day
of
the
yeere
the
sunne
entreth
into
euery
signe
.
-
Cap.
10.
Of
the
seuens
heauens
,
of
planets
,
and
of
their
mouings
,
and
howe
they
make
impression
,
and
cause
generation
and
corruption
in
the
lower
bodies
.
-
Cap.
11.
Of
the
elementall
region
,
and
how
it
is
deuided
into
4.
elements
.
-
Cap.
12.
Howe
those
elementes
do
shut
vp
one
another
,
and
why
the
water
doth
not
couer
all
the
earth
.
-
Cap.
13.
How
the
earth
&
the
water
,
both
elementes
do
make
one
round
body
.
-
Cap.
14.
Howe
the
earth
is
scituated
in
the
middest
of
the
worlde
.
-
Cap.
15.
How
the
earth
is
quiet
&
moueth
not
.
-
Cap.
16.
Of
the
foundation
of
the
earth
,
and
howe
it
may
be
saide
that
the
earth
is
the
foundation
of
the
worlde
.
-
The
second
booke
of
the
sea
and
his
mouings
,
and
how
the
Nauigation
was
inuented
.
-
CAp.
1.
What
thing
the
sea
is
,
and
wherefore
it
was
called
Occean
.
-
Cap.
2.
Howe
the
sea
doth
apperteine
to
the
perfection
of
the
world
,
and
without
it
the
world
woulde
perish
,
and
howe
the
water
is
ingendered
in
it
.
-
Cap.
3.
By
what
meanes
the
water
of
the
sea
is
salt
,
and
howe
it
is
more
conuenient
it
shoulde
be
so
,
and
better
for
the
Nauigation
.
-
Cap.
4.
Of
the
difference
of
mouings
which
the
Occean
sea
hath
.
-
Cap.
5.
What
the
cause
is
that
the
sea
neuer
ouerfloweth
aboue
her
bounds
,
nor
is
augmented
.
-
Cap.
6.
Of
the
excellencie
of
the
nauigation
,
and
the
antiquitie
thereof
.
-
Cap.
7.
Howe
that
by
some
tokens
of
the
sun
and
mone
shal
be
knowen
when
will
come
anye
tempest
.
-
Cap.
8.
Of
the
fires
and
lightes
that
appeareth
in
ships
which
do
saile
when
there
is
any
storme
.
-
Cap.
9.
Of
other
certaine
signes
,
whereby
may
be
knowne
when
stormes
will
happen
in
the
sea
.
-
The
third
booke
of
the
winds
,
their
qualities
&
names
,
and
howe
we
ought
to
saile
with
them
.
-
CAp.
1.
What
thing
the
winde
is
,
and
of
what
quallitie
,
and
how
it
is
ingendered
.
-
Cap.
2.
How
the
winde
doth
not
mooue
right
vp
nor
downe
,
nor
contrariwise
,
but
his
mouing
is
in
circle
manner
of
water
and
earth
.
-
Cap.
3.
wherefore
the
winde
is
not
alwayes
equall
alike
,
but
at
sometimes
more
vehemente
,
and
at
other
times
calme
,
and
wherefore
it
moueth
to
contrary
place
.
-
Cap.
4.
Of
the
wherling
of
the
winde
and
what
is
the
cause
thereof
.
-
Cap.
5.
Of
the
windes
which
are
named
in
the
cardes
of
Nauigation
,
and
of
the
number
of
them
and
their
names
.
-
Cap.
6.
How
the
windes
,
conteined
in
the
cardes
of
Nauigation
doe
compasse
aboute
the
roundnesse
of
the
worlde
for
to
sayle
by
them
.
-
A
carde
to
sayle
by
,
wherein
is
conteined
the
Nauigation
of
the
moste
parte
of
Europe
,
Affrica
,
and
Indias
or
new
world
,
with
the
distance
of
leagues
&
height
of
degrees
that
euerything
hath
.
-
Cap.
7.
Of
the
order
that
the
cardes
of
nauigation
hath
.
-
Cap.
8.
Of
the
accounte
which
the
Pilote
ought
to
haue
of
his
way
when
he
sayleth
with
a
winde
that
differeth
from
his
course
.
-
Cap.
9.
Howe
the
Pilot
shoulde
knowe
sayling
by
any
maner
of
course
,
where
the
Meridian
is
.
-
Cap.
10.
Wherein
is
largely
discoursed
this
rule
aboue
written
.
-
Cap.
11.
Howe
the
Pilotte
ought
to
choose
his
course
for
the
place
whether
hee
mindeth
to
saile
.
-
Cap.
12.
Howe
he
ought
to
pricke
his
carde
to
knowe
the
place
that
the
shippe
is
in
.
-
Cap.
13.
Howe
the
Pilotte
ought
to
knowe
that
his
carde
is
iust
and
certaine
,
that
there
bee
no
errour
in
his
Nauigation
.
-
Cap.
14.
Of
the
number
of
leagues
that
is
counted
for
a
degree
in
euerie
course
of
the
Nauigation
.
-
Cap.
15.
Of
the
number
and
measure
,
and
of
howe
many
partes
euerie
degree
is
compounded
.
-
The
fourth
booke
of
the
heigth
of
the
Sunne
,
&
howe
the
Nauigation
ought
to
bee
ruled
thereby
.
-
CHapter
.
1.
Wherein
is
declared
.
17.
chiefe
principles
which
ought
to
be
knowne
in
the
height
of
the
Sunne
.
-
Cap.
2.
Of
the
excellencie
of
the
Sunne
,
and
of
his
mouinges
.
-
Cap.
3.
Of
the
yeare
when
the
Sunne
goeth
in
his
circle
,
and
of
other
maner
of
yeares
,
and
howe
the
leape
yeare
is
counted
.
-
Cap.
4.
What
thing
a
shadowe
is
,
and
howe
the
shadowes
ought
to
be
looked
on
whiche
the
Sunne
maketh
for
to
take
his
heigth
.
-
Cap.
5.
Wherein
is
declared
what
thing
is
the
height
of
the
Sunne
,
and
howe
it
ought
to
be
taken
to
knowe
the
place
wherein
a
man
is
.
Here
followeth
the
rules
of
the
height
of
the
Sunne
.
-
THe
first
rule
when
the
Sunne
and
the
shadow
goeth
towarde
the
North.
-
The
2.
When
the
Sunne
is
at
the
North
,
and
the
shadow
at
South
,
and
the
declination
and
height
is
more
then
90.
degrees
.
-
The
3.
When
the
Sunne
is
at
North
,
&
the
shadowes
at
the
South
,
and
the
declination
and
height
is
iust
.
90.
degrees
.
-
The
4.
The
Sunne
at
the
North
,
and
the
shadowes
at
South
,
and
the
height
and
declination
come
not
to
90.
degrees
.
-
The.
5.
The
Sunne
in
the
Equinoctiall
,
and
the
height
to
be
lesse
then
90.
degrees
.
-
The
6.
When
the
height
is
taken
in
90.
degrees
,
and
whether
there
bee
any
declination
in
the
Sunne
or
no.
-
The
7.
When
the
Sunne
and
the
shadowes
goeth
to
the
South
.
-
The
8.
The
Sunne
at
South
,
and
the
shadowes
at
North
,
and
the
declination
and
height
are
more
then
90.
degrees
.
-
The
9.
The
Sunne
at
South
,
&
the
shadowes
at
North
,
and
the
height
and
declination
are
90.
degrees
iust
.
-
The
10.
The
Sunne
at
South
,
and
the
shadowes
at
North
,
and
the
height
and
declination
come
not
to
90.
degrees
.
-
Cap.
6.
By
the
rules
of
the
height
of
the
Sun
the
degrees
are
to
be
learned
,
a
man
is
of
one
side
or
parte
of
the
Equinoctiall
line
,
more
then
of
any
of
the
other
partes
.
-
Cap.
7.
Wherfore
all
the
rules
of
the
height
of
the
Sunne
are
reduced
into
90.
degrees
,
more
then
any
other
number
.
-
Cap.
8.
Wherefore
doe
we
say
that
a
man
is
from
the
Sunne
the
degrees
that
are
taken
in
the
Astrolabio
,
lesse
then
90.
-
Cap.
9.
Howe
it
is
vnderstoode
that
a
man
hath
the
Sunne
vpon
his
head
.
-
Cap.
10.
Howe
to
knowe
the
height
of
the
sunne
it
must
be
seene
whether
it
be
a
leape
yeare
,
or
what
yeare
it
is
.
-
A
rule
to
knowe
the
leape
yeare
.
-
Tables
of
the
declination
or
a
departing
that
the
Sunne
maketh
from
the
Equinoctiall
line
,
in
euerie
day
of
the
4.
yeares
,
as
well
to
the
North
part
as
to
the
South
.
-
A
Kalender
of
the
Saintes
dayes
through
the
whole
yeare
,
with
a
declaration
of
the
principall
feastes
.
-
A
rule
to
knowe
the
Dominicall
letter
euerie
yeare
.
-
Cap.
11.
Howe
that
by
the
Kalender
aboue
written
,
a
man
shall
knowe
the
moneth
and
the
day
wherein
he
is
.
-
The
fift
booke
of
the
height
of
the
Pooles
.
-
CHapter
1.
What
thing
a
pole
is
,
and
how
among
the
Poles
,
the
roundnes
of
the
world
is
deuided
.
-
Cap.
2.
Howe
the
height
of
the
Pole
Articke
is
to
be
taken
,
and
the
cause
wherefore
hee
is
taken
.
-
Cap.
3.
Howe
the
account
is
to
bee
vnderstood
which
is
taken
of
the
pole
Artick
,
or
North.
-
Cap.
4.
Of
the
North
starre
,
&
of
the
gwards
,
and
of
his
mouing
.
-
Cap.
5.
That
according
vnto
the
course
the
gwardes
are
in
,
shal
bee
knowne
howe
many
degrees
the
North
starre
is
vnder
or
aboue
the
Pole
.
-
Cap.
6.
How
the
rules
of
the
height
of
the
North
starre
ought
to
bee
applied
,
and
how
they
ought
to
bee
added
vnto
,
or
taken
away
,
according
to
the
place
where
the
gwardes
are
.
-
Cap.
7.
Wherin
is
declared
certaine
doubtes
that
in
this
mouing
of
the
North
starre
may
bee
had
.
-
Cap.
8.
Howe
the
height
of
the
North
starre
may
be
taken
,
although
the
gwards
be
not
seene
.
-
Cap.
9.
How
the
altitude
of
the
North
starre
may
bee
taken
,
although
the
Horizon
bee
not
seene
.
-
Cap.
10.
A
Clock
by
the
North
starre
,
wherby
is
knowne
what
houre
of
the
night
it
is
in
any
time
,
or
place
a
man
is
in
.
-
Cap.
11.
Howe
the
height
of
the
Pole
Antarticke
should
be
taken
.
-
The
sixt
booke
of
the
compasses
to
saile
by
.
-
CHapter
1.
Of
the
compasses
of
Nauigation
,
and
of
the
de●ects
they
may
haue
,
and
howe
they
may
bee
amended
.
-
Cap.
2.
Howe
the
windes
of
the
compasse
may
be
vnderstood
,
and
howe
the
Sunne
passeth
by
them
euerie
day
.
-
Cap.
3.
Wherin
is
declared
the
opinion
had
of
the
Northesting
,
&
Northwesting
of
the
compasses
.
-
Cap.
4.
Of
the
inconueniences
that
may
followe
by
the
Northeasting
and
Northwesting
of
the
compasses
.
-
Cap.
5.
Of
the
regard
or
allowance
which
the
compasses
of
Nauigation
haue
,
&
howe
it
ought
not
to
be
giuen
them
.
-
Cap.
6.
Of
an
instrument
wherby
the
compasses
may
bee
marked
and
knowne
if
they
bee
true
.
-
The
seuenth
booke
of
the
Moone
,
and
〈◊〉
her
increasing
and
diminishing
doth
serue
in
the
Nauigation
.
-
CHapter
1.
What
thing
the
Moone
is
,
and
wherefore
her
light
is
not
alwayes
equall
but
continually
it
increaseth
,
or
diminisheth
.
-
Cap.
2.
Of
the
golden
number
,
and
howe
it
amounteth
from
one
to
nineteene
,
and
wherefore
no
more
not
lesse
.
-
A
rule
to
knowe
the
golden
number
of
euerie
yeare
.
-
Cap.
3.
Wherein
is
declared
the
day
&
houre
that
the
Moone
maketh
coniunction
in
euerie
moneth
of
the
yeare
for
euer
.
-
Cap.
4.
Of
the
short
account
or
reckoning
without
any
booke
to
knowe
in
short
time
howe
many
dayes
olde
the
Moone
is
in
any
moneth
of
the
yeare
.
-
Cap.
5.
How
by
the
dayes
of
the
Moone
and
the
course
where
the
Sunne
ought
to
stand
,
may
be
knowne
in
what
houre
the
tide
will
come
.
-
Cap.
6.
Wherein
is
declared
more
at
large
the
Chapiter
aboue
,
with
a
shewe
thereof
.
-
Cap.
7.
How
that
by
the
houre
wherein
the
coniunction
was
,
shal
be
taken
out
the
●ide
,
&
the
regard
or
allowance
that
shal
be
giuen
to
the
Riuers
.
-
The
eight
booke
of
the
dayes
of
the
yeare
.
-
CHapter
1.
What
thing
a
day
is
,
and
howe
it
is
reckoned
,
and
in
howe
many
partes
it
is
deuided
.
-
Cap.
2.
Howe
that
in
all
the
artificiall
daye
the
Sunne
riseth
and
setteth
different
vnto
suche
as
dwell
in
the
world
.
-
Cap.
3.
How
that
vnder
the
Equinoctiall
the
dayes
and
nightes
are
alwayes
equall
.
-
Cap.
4.
Howe
the
dayes
and
nightes
goe
alwayes
increasing
or
diminishing
vnto
suche
as
dwell
out
of
the
Equinoctiall
line
.
-
Cap.
5.
Howe
that
the
increasing
and
diminishing
of
the
day
is
not
equall
in
all
places
.
-
A
Table
of
the
houres
and
minutes
that
such
as
dwell
in
anye
distance
from
the
Equinoctiall
line
,
haue
in
the
greatest
day
of
the
yeare
.
-
Cap.
6.
Of
the
houres
and
minutes
whiche
they
haue
euerie
day
of
the
yeare
in
the
height
of
40.
degrees
.
-
Cap.
7.
Of
the
houres
and
minutes
that
the
Sunne
doth
rise
and
set
euerie
day
in
the
yeare
.
-
The
last
Chapter
,
how
the
Sunne
doth
giue
his
light
in
equall
time
of
the
yeare
,
to
all
suche
as
dwell
in
the
worlde
.
The
ende
of
the
Table
.
¶
The
first
booke
of
the
world
,
his
order
and
Composition
.
THe
first
chapter
,
what
thing
the
world
is
,
how
it
is
compounded
of
heauens
and
elements
,
the
number
of
the
heauens
are
declared
and
there
moouings
.
THe
world
according
to
the
Philosophers
,
is
vniuersall
,
for
all
things
,
it
confesneth
therin
,
the
heuens
,
the
stars
,
the
earth
,
and
the
sea
,
with
all
the
other
elementes
,
and
alltogether
is
called
the
worlde
.
For
as
Ptholomie
sayth
it
is
alwayes
moouing
and
hath
no
time
of
rest
:
Seeing
this
vniuersallitie
whiche
wee
call
worlde
,
is
compounded
and
ordeined
into
twoo
distinct
regions
(
that
is
to
say
)
the
region
Celestiall
,
and
the
Region
elementall
The
first
which
is
the
region
celestial
,
is
altogether
shining
,
void
,
and
free
from
al
variation
,
alteration
and
corruption
.
This
according
to
the
opinion
of
some
auncient
authors
is
diuided
into
niene
heauens
(
that
is
to
say
)
seauen
of
the
planets
,
the
eight
is
the
firmament
where
the
fixed
starres
are
,
the
nienth
the
first
moueable
:
of
that
opinion
was
Ptholomie
the
great
,
and
after
him
Thebit
,
Alfragano
,
Albategni
,
and
others
which
in
astronomy
did
floorishe
,
more
the
late
Astronomers
(
that
is
to
say
)
the
wise
king
Don
Alonso
,
Iohn
de
Liueris
,
George
Purbachio
,
Iohn
de
Monte
Rey
,
and
others
do
bring
it
very
probable
.
That
vppon
the
nienth
sphere
there
is
another
tenth
,
whiche
is
the
first
moueable
,
it
is
alone
,
and
they
prooue
that
there
are
tenne
heauens
moueable
by
the
moouinges
of
the
eyght
heauen
.
Hereof
is
written
vppon
the
first
chapter
of
the
sphere
,
that
the
late
Astronomers
saw
fixed
stars
in
the
heauen
to
haue
three
moouings
,
whiche
were
found
in
the
eyght
sphere
,
whiche
are
these
folowing
one
is
the
first
moueable
,
that
is
to
say
of
the
tenth
sphere
which
is
the
moouing
of
euery
day
,
the
which
in
foure
and
twentie
houres
maketh
a
reuolution
from
the
east
to
the
west
and
this
is
made
vpon
the
two
poles
of
the
worlde
Articke
and
Antarticke
.
It
hath
another
moouing
of
the
nienth
sphere
,
and
is
called
the
second
moueable
,
for
it
is
alwayes
according
too
the
succession
of
the
signes
from
the
Weste
into
the
Easte
,
agaynst
the
moouing
of
the
first
moueable
,
which
moouing
is
made
vppon
the
poles
of
the
Zodiacke
,
and
this
according
as
King
Don
Alonso
sayeth
,
is
called
Auge
of
the
fixed
starres
,
the
third
moouing
is
of
him selfe
,
and
is
called
the
moouing
of
tripidacion
,
or
according
to
the
saying
of
the
sayde
King
the
moouing
of
accesse
and
recesse
of
the
eyghte
Sphere
,
and
is
made
vpon
twoo
little
circles
in
the
concauety
of
the
nienth
sphere
,
in
the
beginning
of
Aries
and
Libra
equally
discribed
in
such
sorte
that
as
to
euery
one
of
the
heauens
shoulde
not
bee
geuen
more
then
one
moouing
of
it selfe
,
and
the
eyght
heauen
should
haue
three
moouings
.
Heereof
it
commeth
that
twoo
of
them
are
vnproper
to
him
but
are
caused
of
other
twoo
superiour
heauens
,
that
is
to
say
of
the
nienth
and
tenth
,
vpon
these
tenne
heauens
or
mouable
spheres
wee
put
the
eleuenth
,
which
according
to
the
learned
is
called
the
imperiall
heauen
,
that
is
by
reason
of
his
great
brightnes
,
which
alwayes
continueth
firme
in
one
manner
of
order
,
without
any
moouing
,
and
of
this
there
are
some
reasons
,
whereby
wee
are
perswaded
,
whereof
there
are
two
thinges
noted
.
The
first
is
,
that
any
manner
of
thing
that
mooueth
from
a
place
modueth
his
place
eyther
in
all
,
or
in
parte
,
so
that
whiche
doeth
mooue
mooueth
into
some
place
,
forotherwise
it
were
immoueable
,
therefore
any
of
the
moueable
heauens
mooueth
place
eyther
altogether
in
him selfe
or
his
partes
,
therefore
he
is
in
some
place
but
not
in
any
inferiour
sphere
,
for
the
place
must
compasse
about
that
which
is
put
into
the
place
,
therefore
hee
in
a
superiour
sphere
.
And
it
is
conuenient
that
there
bee
some
heauen
stedfast
and
greater
,
wherein
it
maye
mooue
.
The
second
reason
,
is
that
there
is
put
a
difference
in
the
heauen
,
that
is
to
saye
,
before
and
after
,
on
the
ryght
side
and
on
the
leaf
,
not
in
respect
of
as
muche
as
toucheth
vs
,
but
for
the
nature
of
the
thinges
,
So
the
Philosopher
sayeth
in
the
seconde
of
the
heauen
and
the
worlde
,
this
cannot
bee
preserued
by
the
moueable
spheres
,
the
cause
is
that
in
the
moueable
Spheres
,
the
parte
that
nowe
is
at
the
ryght
side
,
shall
bee
at
the
left
.
And
the
parte
that
is
nowe
aboue
shall
bee
vnderneath
,
as
experience
sheweth
,
wherevppon
it
followeth
,
that
it
is
conuenient
there
bee
a
fixed
heauen
,
whiche
in
the
behalfe
of
the
thing
,
is
founde
the
difference
that
is
alleadged
.
This
is
the
imperiall
heauen
,
as
it
is
sayde
,
whiche
is
higher
then
all
other
heauens
.
It
hath
greate
dignitie
,
by
reason
of
his
brightnesse
,
cleannesse
,
establitie
,
and
purenesse
,
heere
is
the
Celestiall
Courte
,
where
they
dwell
that
are
of
good
fortune
,
enioying
of
GOD
,
whereas
the
Apostle
sayeth
,
nor
eye
hath
seene
,
nor
eare
hath
hearde
,
nor
canne
enter
into
the
hearte
of
man
,
that
whiche
GOD
hath
made
ready
for
such
as
loue
him
.
The
second
chapter
wherein
is
declared
,
the
three
moouings
which
the
eyght
heauen
hath
and
howe
they
are
knowne
.
I
Haue
sayd
in
the
chapter
before
that
in
the
eyght
heauen
are
found
three
moouinges
different
,
and
that
some
Astronomers
were
of
opinion
,
that
there
were
onely
niene
sphers
moueable
and
others
had
opinion
of
tenne
,
and
because
that
in
this
the
auncient
authors
,
and
the
writers
doe
not
agree
,
I
will
shewe
you
the
reasons
,
that
were
of
these
opinions
of
the
which
is
to
be
vnderstood
,
the
first
,
Astronomers
mainteined
that
there
were
only
eyght
heauens
.
This
they
obteyned
by
the
moouing
of
the
stars
.
For
the
stars
mooue
not
of
themselues
,
but
in
theyr
circles
,
so
sayth
the
Philosopher
in
the
second
of
the
heauen
and
the
worlde
,
that
the
starres
are
fixed
in
the
circle
,
as
the
knot
in
the
table
:
so
that
by
their
moouings
the
difference
that
is
betweene
the
planets
which
mooue
,
and
the
fixed
starres
are
knowne
,
these
in
their
moouinges
are
knowne
to
be
different
〈◊〉
one
from
the
other
,
in
swiftnes
and
in
●lownesse
and
by
their
place
,
but
the
fixed
●ar●es
are
so
many
in
number
that
they
cannot
be
toth
prehended
.
The
long
experience
and
obseruation
of
the
Astronomers
,
attemed
to
the
knowledge
that
●n
doe
mooue
together
in
equall
distance
and
neerenesse
and
continually
the
one
doth
keep
with
the
other
,
so
that
their
moouing
is
one
so
the
Philosopher
vnderstandeth
in
the
first
of
the
heauen
and
the
worlde
,
therefore
I
say
that
these
Astronomers
vnderstood
that
in
the
eyght
heauen
was
onely
the
continual
moouing
,
that
is
from
the
East
to
the
Wea●●
,
and
that
th●
was
the
〈◊〉
moueable
,
it
seemeth
that
the
sayd
Phylosopher
did
so
vnderstand
it
in
the
place
before
aleadged
,
where
he
sayth
that
all
the
fixed
stares
are
〈◊〉
the
first
indueable
,
&
for
this
reason
,
there
are
so
man●e
there
,
and
in
〈◊〉
one
of
the
inferiours
●d
more
but
one
.
There
was
other
Astronomers
,
that
were
not
content
to
put
only
eight
sphers
but
they
atteined
to
the
nienth
.
And
the
reason
was
because
they
sawe
the
eyght
heauen
to
haue
two
moouinges
different
,
the
one
is
as
aforesayd
from
the
East
to
the
Weast
,
and
the
other
contrary
to
it
:
(
that
is
to
say
)
from
the
West
into
the
East
,
and
this
motion
is
so
slowe
,
that
in
A
hundred
yeeres
it
is
scarsely
to
be
perceiued
.
This
moouing
Ptholomie
declareth
in
the
seauenth
of
the
Almagesto
,
with
most
strong
and
certaine
reasons
,
so
that
these
twoo
different
moouinges
beeing
considered
,
they
came
to
the
knoweledge
,
that
the
eyght
heauen
was
not
the
first
moueable
,
for
the
first
mouable
hath
one
only
moouing
of
himself
most
simple
,
the
late
Astronomers
by
their
large
speculation
,
founde
fyxed
Starres
whiche
mooued
sometimes
from
the
Weast
too
the
North
,
And
to
the
South
,
and
more
swiftely
to
the
Easte
then
too
the
Weast
,
and
at
other
times
more
swiftely
towardes
the
North
then
too
the
South
,
The
whiche
Demonstration
,
because
with
onely
twoo
〈◊〉
aforesayde
it
could
not
bee
determined
,
they
put
another
thirde
:
moouing
,
and
this
is
one
of
him selfe
whiche
is
made
in
twoo
small
cyrcles
in
the
heade
of
Aries
and
Libra
,
So
that
as
the
tyght
Sphere
hath
three
moouings
,
it
is
not
onely
necessary
to
put
the
nienth
,
but
also
the
tenth
:
the
reason
is
because
one
simple
body
,
ought
to
haue
but
one
only
simple
moouing
,
and
that
is
vntoo
him
proper
and
naturall
,
so
sayeth
the
Philosopher
in
the
first
of
the
heauen
and
the
worlde
,
if
they
haue
any
more
moouinges
,
they
are
improper
to
him
.
And
seeing
that
the
eyght
heauen
is
a
simple
bodie
,
as
the
Phylosopher
vnderstandeth
it
in
the
same
place
,
it
is
conuenient
that
of
these
three
moouinges
,
one
of
them
be
proper
and
naturall
to
him
and
the
other
two
improper
.
Likewise
the
moouing
that
is
not
proper
to
him
,
vnto
another
is
proper
and
naturall
.
And
seeing
that
it
is
not
an
inferiour
sphere
,
it
is
conuenient
to
graunt
,
that
vppon
the
eyght
heauen
are
other
twoo
moouinges
of
whome
is
caused
these
twoo
moouinges
aforesayde
,
so
that
as
the
Philosopher
saith
,
the
eight
heauen
was
the
fyrst
moueable
.
It
is
to
bee
vnderstoode
,
that
hee
and
the
Astronomers
of
his
time
,
beleeued
that
the
eyght
heauen
had
onely
the
moouing
of
euery
day
.
And
they
came
not
too
the
knowledge
of
the
others
,
because
they
were
not
determined
vppon
,
but
in
a
very
long
continuance
of
time
.
The
thyrde
Chapter
howe
the
heauen
hath
a
rounde
figure
and
of
fiue
reasons
whereby
it
was
conuenient
〈◊〉
should
be
so
.
THE
wisdome
of
the
euerlasting
father
which
treated
and
di●●●sed
all
thinges
,
ordeined
that
the
heauen
shoulde
bee
rounde
vp
these
reason●
following
.
The
first
by
reason
of
the
similietude
.
The
seconde
,
vp
reason
of
the
commoditie
.
The
thirde
for
necessitie
,
Unto
the
firste
,
touching
similitude
or
likenesse
,
because
the
sensible
worlde
,
is
made
vntoo
the
●●●nesse
of
the
worlde
imaginat●●●
,
wherein
is
no
beginning
nor
ending
,
and
for
this
cause
the
sensible
worlde
hath
a
fourme
or
figure
,
after
the
manne●
of
a
sphere
▪
in
the
whiche
cannot
bee
.
assigned
or
marked
,
beginning
nor
ending
,
For
the
second
,
of
the
commoditie
or
profit
this
is
because
in
all
bodies
and
Super
,
fimetros
,
the
whiche
are
foure
principally
Oual
Piramidal
,
Colu●al
,
〈◊〉
the
Sphere
is
of
gra●ter
body
and
of
all
figures
the
rounde
fygure
or
fourme
doeth
co●teiue
most
,
and
seeing
that
the
rounde
bodye
is
the
greater
,
it
followeth
that
all
thinges
which
haue
that
fourme
or
shape
are
profitable
in
the
world
.
The
thirde
whiche
is
of
necessitie
,
for
if
the
world
were
of
another
fourme
or
shape
then
rounde
,
as
like
vnto
a
Tryangle
or
Quadrangle
or
of
another
fourme
it
woulde
followe
that
some
place
shoulde
be
●●●ptie
,
or
some
body
without
a
place
,
therefore
an
empty
place
cannot
be
put
according
to
nature
,
for
nature
it selfe
doeth
abhorre
it
so
muche
,
that
more
easily
it
consenteth
that
whiche
is
heauie
too
rise
vp
,
or
that
which
is
light
too
descende
,
then
too
permitte
an
emptye
place
.
So
saith
the
maker
of
the
commentaries
▪
rather
the
heauen
will
descende
find
the
earth
ascende
,
then
nature
to
permitte
any
thing
emptie
,
A
ristotle
bringeth
in
other
twoo
reasons
,
to
prooue
that
the
heauen
is
round
.
The
first
reason
is
,
that
vnto
the
firste
and
noble
body
is
〈◊〉
the
firste
and
moste
noble
Fygure
or
shape
.
The
heauen
is
the
moste
noble
and
fyrstbodye
and
the
rounde
fygure
is
〈◊〉
perfect
,
therefore
vnto
the
heauen
is
due
the
rounde
houre
〈◊〉
●ording
too
reason
,
for
vnto
euery
one
bodie
nature
gaue
a
fourme
propercionably
vntoo
his
woorke
,
euen
as
it
appeareth
in
Beastes
and
in
planets
.
Therefore
the
proper
woorke
of
heauen
is
to●
mooue
it selfe
continually
like
to
a
circle
.
It
was
conuenient
that
it
shoulde
haue
a
fygure
or
fourme
〈◊〉
and
〈◊〉
for
suche
a
moouing
,
and
that
is
rounde
,
wherefore
this
lacketh
the
〈◊〉
which
doeth
let
the
moouing
.
〈◊〉
sayeth
,
if
the
worlde
were
plaine
some
parte
of
it
woulde
be
more
neere
to
be
the●
other
〈◊〉
euen
as
that
parte
whiche
is
ouer
our
●●ades
,
wherevppon
the
〈◊〉
that
is
there
,
shoulde
bee
more
〈◊〉
too
be
then
that
whiche
is
in
the
Easte
or
in
the
Weste
,
then
those
thinges
whiche
are
neerer
too
vs
doe
seeme
greater
to
vs
,
so
the
Starre
whiche
is
in
the
middest
of
heauen
shall
seeme
greater
to
vs
then
that
whiche
is
in
the
Easte
or
in
the
West
,
which
we
see
contrary
,
For
the
Sunne
or
another
Starre
seemeth
greater
in
the
easte
or
in
the
Weste
,
then
in
the
middest
of
heauen
,
the
cause
of
this
is
,
not
because
the
Sunne
or
the
Starre
is
greater
or
lesser
,
nor
that
hee
is
father
or
neerer
,
But
for
some
vapoures
that
riseth
vppe
and
putteth
them selues
betweene
our
sight
and
the
Sunne
or
the
Starre
,
and
as
these
Uapoures
are
thicke
bodies
they
take
awaye
the
Beames
of
the
Sunne
▪
or
Starre
from
our
sighte
,
in
suche
sorte
,
that
the
thing
in
his
owne
quantity●
cannot
bee
comprehended
.
As
it
may
bee
likened
to
a
peece
of
money
cast
into
〈◊〉
water
,
that
because
of
the
glystering
of
the
Beames
or
strickes
it
seemeth
to
bee
of
greater
quantitie
then
it
is
.
Euen
so
doeth
the
Sunne
or
starre
,
when
the
Uapoures
are
put
betweene
them
and
our
sight
.
The
fourth
Chapter
,
of
the
noblenesse
of
the
Heauen
,
and
of
his
coulour
.
ARISTOTLE
sayeth
that
the
noblenesse
of
the
heauen
,
is
vnderstoode
and
considered
in
the
clearenesse
of
his
shyning
,
in
the
roundnesse
of
his
fourme
,
in
the
vnitie
of
his
equallitie
,
in
the
vertue
of
his
moouing
,
in
the
heyght
of
his
scituation
,
whiche
is
verye
farre
from
the
center
of
the
earth
,
in
the
deminishing
of
his
quantitye
,
whiche
doeth
ouerreach
the
imagination
and
measure
of
reason
.
In
nature
nothing
is
like
too
it
,
neither
comparable
to
it
in
vertue
,
The
heauen
is
none
of
the
elementes
nor
hath
their
qualities
,
nor
is
compounded
of
them
,
if
it
were
it
shoulde
be
corruptible
,
for
all
thing
compounded
of
the
elementes
,
shall
bee
desolued
and
corrupted
.
The
heauen
is
ingenerable
inaugmentable
,
it
cannot
receiue
straunge
impressions
,
it
is
neyther
light
nor
heauie
,
hote
nor
colde
,
drye
nor
moyst
,
formall
or
royall
,
but
vertuous
,
for
his
vertue
and
influence
doeth
heate
,
so
sayeth
the
Phylosopher
in
the
fyrste
of
the
Heauen
and
the
Worlde
,
and
so
improperly
it
may
bee
sayde
,
it
is
not
to
bee
broken
nor
penetrable
,
and
likewise
improper
,
thicke
,
or
congealed
,
improperly
it
hath
his
coulor
bright
.
And
for
as
muche
as
the
coulour
:
which
seemeth
to
vs
it
hath
,
is
to
bee
vnderstoode
,
that
our
sen●es
many
times
deceiueth
vs
,
and
the
sight
maye
sooner
deceiue
vs
their
any
other
of
our
sences
,
for
our
eyes
bee
of
so
tender
a
composition
,
that
any
manner
of
fourme
,
sente
of
any
visible
thing
,
we
feele
griefe
therof
.
So
sayeth
Alacen
in
the
prospectine
;
the
thirtie
niene
rule
.
And
Aristotle
in
the
booke
of
Qualitate
Visus
,
whereby
I
say
that
nothing
aboue
the
Moone
can
bee
seene
,
But
the
Sunne
,
or
the
Starres
,
whiche
Starres
wee
see
by
meanes
of
the
light
that
they
receiue
of
the
Sunne
.
But
as
touching
the
coulour
of
Heauen
,
It
is
to
be
noted
,
that
it
taketh
coulour
in
one
of
twoo
sortes
,
one
is
of
it selfe
.
And
so
is
the
seconde
qualitie
,
caused
of
the
fyrste
,
Euen
as
the
whyte
,
the
blacke
,
and
other
coulours
,
In
this
sorte
the
Celestiall
bodies
haue
no
coulours
,
But
in
another
sorte
it
is
taken
,
that
is
to
saye
,
commonly
by
all
that
which
the
sight
doth
shew
,
&
extendeth
it selfe
to
that
which
is
bright
and
percing
,
and
in
that
manner
the
heauen
hath
his
colour
,
that
is
to
say
,
shining
.
The
fifth
chapter
of
the
tenne
〈◊〉
called
the
first
moueable
and
of
his
moouing
.
SEeing
there
hath
beene
declared
the
number
of
the
heauens
there
shapes
and
qualities
,
I
will
speak
perticularly
of
them
,
and
especially
of
that
which
serueth
for
our
purpose
,
of
the
which
I
say
it
is
manifest
to
our
sight
that
the
heauens
mooue
,
and
it
is
to
be
vnderstood
,
that
a
moouing
is
a
passing
from
one
place
to
another
,
so
that
all
thinges
which
mooue
passeth
from
one
place
to
another
,
or
from
one
limet
to
another
,
this
moouing
may
be
in
one
of
these
three
sortes
,
by
meanes
of
a
circle
or
straight
waye
or
from
aboue
downward
,
and
so
contrary
.
The
first
of
those
three
,
which
is
the
moouing
in
circle
manner
,
mooueth
not
place
according
to
all
his
quantitie
,
but
according
to
his
parts
,
as
it
appeareth
in
a
whele
vnles
it
be
al
mooued
from
one
place
to
another
that
they
make
it
go
round
,
so
they
mooue
all
his
partes
,
such
is
the
moouing
of
the
heauen
,
so
that
,
whiche
is
now
in
the
east
afterward
shal
be
in
the
west
,
and
although
the
heauen
moueth
not
place
according
to
all
the
proportion
which
it
hath
,
yet
it
is
well
mooued
which
in
it
is
mooued
.
And
this
hath
commonly
been
doubted
,
if
the
first
moueable
of
the
heauens
,
were
mooued
by
one
only
moouer
or
by
many
:
And
if
by
many
howe
manye
there
are
,
and
in
what
sort
they
mooue
it
.
Of
the
which
it
is
to
be
noted
that
the
heauens
in
the
first
moueable
are
moued
of
one
mouer
,
and
that
they
are
not
mooued
of
many
,
for
one
only
is
sufficient
,
&
many
would
be
superfluous
,
so
saith
the
Philosopher
or
the
first
of
his
naturall
phylosophie
,
that
it
is
better
to
put
one
beginning
then
many
,
and
a
fewe
rather
then
an
infinite
number
,
therfore
it
is
better
to
put
one
onely
moouer
then
manye
who
maketh
this
first
moueable
:
there
are
diuerse
opinions
,
one
saieth
God
alone
,
bringing
therefore
that
which
Aristotle
saith
that
the
first
moouer
ought
to
be
of
an
infinite
strength-and
seeing
that
God
is
of
an
infinite
strength
and
hath
created
al
thinges
of
a
reasonable
strength
,
it
seemeth
that
God
onely
is
he
that
mooueth
the
first
moueable
.
Others
there
are
that
proueth
that
the
firste
moouer
is
a
certaine
intellectiue
whiche
mooueth
,
the
whiche
they
prooue
in
this
manner
.
If
the
first
moouer
were
God
it
would
folow
either
that
the
mouing
of
heauen
were
done
at
one
instance
,
or
the
doings
of
God
be
measured
with
time
.
Therefore
it
cannot
be
sayde
that
the
heauen
is
mooued
at
one
instant
,
seeing
that
all
Astronomers
holdeth
and
the
sight
sheweth
it
,
that
in
foure
and
twentie
houers
there
is
one
reuolution
a●complished
.
N●●
the
seconde
can
be
.
For
the
saide
Philosopher
in
the
fourth
of
the
naturall
philosophie
sayth
,
the
euerlasting
is
not
in
time
nor
his
dooings
are
measured
with
time
,
but
this
is
it
which
most
commonly
is
vnder
stoode
,
that
an
angell
maketh
the
first
moouing
,
and
likewise
al
the
other
heauens
haue
intellectiue
motion
whiche
mooueth
them
in
their
owne
moouings
and
here
by
it
appeareth
howe
orderly
they
mooue
since
the
time
that
GOD
made
them
,
vntil
the
like
moouing
doe
cease
when
his
will
shal
bee
.
Therefore
I
say
that
the
first
moueable
,
of
the
first
moouing
which
is
of
the
tenth
heauen
according
to
that
as
hath
been
spoken
of
,
geueth
a
turne
once
in
foure
and
twenty
houres
round
about
the
world
,
from
the
east
into
the
west
,
&
with
this
his
mouing
he
catcheth
&
carrieth
with
him
al
the
other
inferiour
heauens
and
maketh
them
giue
a
turne
to
the
world
in
the
time
that
hee
geueth
it
.
Although
that
their
owne
moouinges
be
contrary
to
this
,
this
is
shewed
because
we
see
that
the
starrs
,
the
sunne
,
the
moone
▪
and
the
other
planets
haue
their
first
originall
,
and
are
created
in
the
east
.
And
by
little
&
little
they
rise
vp
and
assend
vntill
they
come
to
the
meridian
and
so
with
one
accord
they
descende
and
come
to
the
west
,
and
alwayes
they
make
this
moouing
in
the
same
foure
and
twentie
houres
as
the
tenth
heauen
doeth
,
so
that
continuallye
they
obeye
the
moouinges
of
the
first
moueable
.
And
it
is
to
be
noted
,
that
for
as
muche
as
it
is
saide
of
this
forceable
moouing
or
catching
which
the
firste
moueable
doeth
,
vntoo
the
other
inferiour
heauens
,
it
is
to
bee
vnderstoode
that
in
the
Celestiall
bodies
is
no
forceable
moouing
or
violence
,
nor
any
resistance
or
contradiction
,
but
all
with
one
conformitie
or
accorde
doe
follows
the
fyrste
moouing
.
And
so
when
it
is
sayde
that
the
first
moueable
doeth
catch
the
other
inferiour
heauens
it
ought
to
be
vnderstoode
soundly
as
if
he
should
say
the
inferiour
or
lower
heauens
are
mooued
of
the
higher
by
an
accedent
,
euen
so
as
the
marriner
mooueth
the
shippe
moouing
her selfe
,
wherin
he
saileth
or
as
the
water
in
a
vessell
,
the
vessel
being
mooued
the
water
also
mooueth
so
it
is
to
be
vnderstoode
,
that
the
inferiour
heauens
doe
mooue
themselues
by
the
moouing
of
the
firste
moueable
,
so
by
that
aforesayde
it
seemeth
that
alwaies
there
may
be
a
dout
saying
.
(
A
doubt
:
)
how
can
it
be
that
the
tenth
heauen
moouing
it selfe
continually
without
ceasing
from
the
easte
to
the
west
,
that
the
other
inferiour
heauens
moouing
them selues
with
him
doe
make
their
owne
moouinges
contrary
,
so
that
in
one selfe
time
there
is
made
by
one selfe
body
different
moouinges
.
A
Declaration
for
the
declaration
of
this
,
the
present
example
is
to
be
noted
,
if
in
the
wheele
of
a
mil
there
were
set
a
flee
or
an
Aunt
,
although
that
the
wheele
doeth
make
his
moouing
very
quicke
and
hastie
yet
the
Aunt
or
Flee
may
be
going
at
their
leisure
,
and
make
their
moouing
contrary
to
that
whiche
the
wheele
doeth
.
As
also
if
the
wheele
carrieth
them
rounde
about
and
in
a
short
space
geueth
a
turne
yet
they
may
make
an
ende
of
their
moouing
at
their
leysure
,
so
that
in
this
sorte
the
moouing
which
the
tenth
heauen
doth
make
which
is
in
euery
foure
&
twenty
houres
,
the
inferiour
heauens
although
they
are
mooued
of
him
they
make
their
owne
moouinges
contrary
,
the
whiche
euerye
one
of
them
by
himselfe
doeth
make
an
ende
in
different
times
.
The
sixthe
chapter
of
the
nienth
heauen
,
called
Christaline
or
heauen
of
water
,
it
is
declared
howe
there
is
a
heauen
of
water
,
and
of
what
qualitie
it
is
of
.
THe
nienth
heauen
called
the
seconde
moueable
,
which
first
of
all
challengeth
the
mouing
from
the
Weste
into
the
Easte
for
his
owne
,
because
of
the
tenne
moueable
heauens
.
This
is
the
first
,
and
that
most
by
leysure
maketh
his
moouing
from
the
West
into
Easte
,
this
is
called
the
Christaline
Heauen
or
Heauen
of
water
,
of
the
whiche
is
written
in
Genesis
the
first
Chapter
.
Where
GOD
sayde
,
let
the
Firmament
bee
made
in
the
middest
of
the
waters
,
So
that
the
waters
remayne
diuided
,
some
aboue
the
Firmament
and
others
beneath
,
the
whiche
Firmamente
is
the
eyght
heauen
.
In
suche
sorte
that
of
waters
which
remayne
aboue
the
Firmament
is
this
nienth
Heauen
,
Of
this
it
seemeth
there
may
bee
a
doubt
,
saying
.
A
Doubt
,
Howe
canne
there
bee
waters
aboue
the
Heauen
,
seeing
that
naturally
water
is
heauie
,
and
all
bodies
whiche
are
heauie
doe
naturallye
descende
,
neither
canne
it
bee
saide
that
GOD
hath
them
there
,
for
any
myracle
,
but
by
a
naturall
meanes
.
A
Declaration
,
to
this
Nicholas
De
Lyra
,
answereth
in
the
glosse
vppon
the
sayd
article
the
first
of
Genesis
,
where
hee
sayeth
that
these
waters
are
taken
here
in
a
double
sence
,
for
those
waters
which
are
aboue
the
firmament
be
of
a
celestiall
nature
,
that
is
to
say
,
of
the
like
qualitie
that
the
heauens
are
of
,
and
of
their
owne
nature
:
And
those
which
are
vnder
the
firmament
are
of
ellymentall
nature
.
This
heauen
is
called
the
heauen
of
waters
or
christaline
heauen
,
because
it
hath
a
pearcing
light
like
to
water
,
and
cleere
shining
like
to
christal
,
of
this
nienth
heauen
,
or
of
the
tenth
we
haue
no
signe
,
nor
there
is
any
in
them
:
nor
our
sight
doeth
passe
the
eyght
heauen
where
the
fixed
stars
are
.
The
seauenth
Chapter
of
the
eyght
heauen
,
which
is
the
firmament
or
starry
heauen
,
and
of
the
light
of
the
starres
,
and
of
their
greatnes
.
THe
eyght
heauen
,
which
is
the
starrie
heauen
,
is
called
the
firmament
by
reason
that
in
it
are
the
fixed
starres
,
in
such
sort
as
none
by
him selfe
moueth
but
altogether
,
of
these
it
is
to
bee
vnderstode
,
that
although
we
see
them
bright
,
yet
there
is
none
of
them
that
haue
any
light
of
them selues
,
but
the
Sunne
giueth
light
vnto
them
all
,
for
he
onely
hath
light
and
no
other
bodie
.
This
light
God
made
the
first
day
,
as
it
is
written
in
Genesis
the
first
chapter
.
And
the
texte
sayth
that
God
saw
the
light
and
it
was
good
.
Saint
Austine
speaketh
of
the
light
that
it
is
a
corporall
substance
,
souereigne
and
simple
,
multiplied
in
vertue
,
and
shyning
with
brightnes
without
resistance
it
is
communicable
and
delightfull
and
therefore
among
all
other
bodies
ther
is
nothing
so
profitable
,
so
quiet
,
so
vertuous
as
the
light
:
The
light
is
sprinkled
abrod
from
the
heauen
to
the
earth
it
is
the
beautie
of
all
visible
creatures
,
and
is
the
cause
wherewithal
the
other
bodies
or
the
world
be
praysed
,
seeing
that
I
say
that
the
stars
haue
no
light
of
themselues
,
more
then
that
which
they
receiue
of
the
sunne
.
So
Albertus
Magnus
writeth
in
the
second
of
the
heauen
and
the
worlde
,
The
sixt
chapter
,
where
he
saith
,
al
the
stars
of
heauen
are
lightned
of
the
sunne
,
as
also
the
moone
,
but
there
is
a
difference
in
receiuing
of
their
light
,
&
so
they
differ
in
receiuing
their
vertu
,
as
they
differ
in
the
noblenes
of
nature
in
such
sort
as
,
some
are
most
pure
and
most
noble
,
&
these
,
receiuing
their
light
at
one
instant
it
doeth
penetrate
them
,
from
the
superficie
which
is
opposite
to
the
sunne
euen
to
the
other
superficie
,
so
that
all
the
starres
remain
cleane
and
full
of
light
,
others
also
are
penetrated
with
the
sunne
,
although
that
by
their
nature
they
decline
to
som
colour
,
but
howsoeuer
it
bee
,
the
sunne
doeth
penetrate
them
at
one
instant
,
&
filleth
them
full
of
light
euen
as
a
candle
is
lighted
with
fire
,
and
heere
it
is
to
be
noted
that
in
this
eyght
heauen
is
the
Zodiacke
where
the
twelue
signes
are
,
or
the
houses
of
the
sun
.
These
signes
are
compounded
euery
one
of
a
certaine
number
of
starres
,
&
besids
the
signes
,
there
are
other
36.
images
,
which
are
also
compounded
of
starres
,
so
that
ther
are
in
all
.
48
,
and
these
starres
,
which
doe
compounde
these
signes
and
images
are
in
number
.
1021.
of
these
speaketh
Alfragano
in
the
third
booke
of
the
assembling
of
the
stars
,
that
the
least
of
the
fixed
Starres
to
a
notable
sight
is
greater
then
all
the
earth
.
And
if
al
the
bodie
of
the
earth
were
put
into
the
place
where
the
fixed
Starres
are
,
although
it
had
light
by
reason
of
the
great
distance
,
it
would
bee
so
little
that
we
should
not
see
it
,
but
this
authoritie
is
not
to
be
vnderstoode
of
the
planets
,
for
all
of
them
bee
not
greater
then
the
earth
,
nor
it
is
to
be
vnderstod
of
all
the
fixed
starres
,
therefore
it
is
to
be
sayd
of
them
that
are
most
notable
to
the
sight
.
For
there
are
some
fixed
starres
so
little
,
that
wee
see
them
not
,
there
be
others
also
that
although
wee
see
them
by
reason
they
are
little
,
they
are
not
accounted
of
the
Astronomers
,
but
onely
such
as
are
great
and
these
be
not
all
of
one
greatnes
or
quantitie
,
but
of
diuerse
quantities
,
and
therfore
they
be
diuided
into
sixe
differences
.
So
Ptholomy
hath
it
in
his
Almagesto
,
and
the
king
Don
Alonso
in
his
tables
.
The
eyght
Chapter
,
howe
it
is
vnderstoode
,
that
the
Sunne
doth
enter
into
the
signes
,
and
wherefore
the
signes
haue
the
names
of
beastes
.
IN
the
Chapter
whiche
goeth
before
,
was
sayde
that
in
the
eyght
heauen
is
the
Zodiack
wher
the
twelue
signes
haue
their
place
or
houses
of
the
Sunne
,
and
of
this
it
seemeth
that
two
things
may
be
douted
.
(
The
first
doubt
)
To
the
fyrst
,
seeing
that
these
signes
or
starres
are
in
the
eight
heauen
and
the
Sunne
in
fourth
,
how
can
the
sunne
enter
into
the
signes
,
seeing
there
is
so
great
distance
betweene
the
sunne
and
them
,
(
The
second
doubt
)
To
the
second
,
if
euery
one
of
the
signes
be
compounded
of
starrs
wherfore
doe
we
say
that
one
signe
is
called
Aries
,
whiche
is
as
much
to
say
a
Ram
,
and
another
Taurus
,
which
is
asmuch
to
say
a
Bull.
And
likewise
of
others
:
seeing
that
in
the
heauen
there
is
not
any
beastes
.
(
The
first
declaration
)
To
the
first
,
although
it
be
true
that
the
signes
be
in
the
8.
heauen
,
&
the
Sunn
in
the
fourth
,
it
is
to
be
vnderstoode
that
the
moouing
which
the
Sunne
maketh
in
all
the
yeere
is
,
that
he
mooueth
himselfe
vnder
the
starres
of
the
signes
,
and
so
when
we
say
that
the
Sunne
is
in
such
a
signe
,
it
is
vnderstood
that
then
he
mooueth
himself
vnder
the
starres
of
that
signe
,
as
also
any
of
vs
may
stande
vnder
any
signe
or
vnder
the
Sunne
,
And
the
distance
that
is
from
the
one
to
the
other
doeth
not
let
it
.
(
2.
Declaration
)
To
the
second
,
it
is
so
,
that
in
the
heauen
are
no
beastes
,
but
these
are
so
named
by
reason
of
the
effectes
whiche
the
Sunne
worketh
,
being
in
euery
one
of
the
signes
which
doe
followe
and
answere
by
propertie
or
likenesse
to
one
of
these
beasts
,
and
by
demonstration
of
suche
an
effect
,
it
compareth
it self
to
the
likenes
of
such
a
beaste
,
or
to
another
thing
that
it
is
likened
vnto
,
as
in
the
chapter
folowing
is
declared
,
that
the
Sunn
entring
into
euery
one
of
these
signes
,
doeth
cause
diuers
effectes
.
Therefore
it
is
to
be
noted
,
that
of
these
twelue
signes
foure
of
them
are
moueable
,
foure
fixed
,
foure
common
.
The
moueable
are
Aries
,
Cancer
,
Libra
and
Capricorne
,
these
signes
are
called
moueable
,
for
the
sun
entring
into
euery
one
of
them
,
it
is
said
,
that
the
disposition
of
the
ayre
doeth
vary
and
not
continue
in
one
estate
,
and
likewise
the
Sunne
entring
into
Aries
,
it
mooueth
from
winter
into
sommer
,
and
entring
into
Cancer
,
it
mooueth
from
Sommer
into
Estio
,
and
entring
into
Libra
it
mooueth
from
Estio
to
Otonno
which
is
haruest
time
.
And
entring
into
Capricorne
it
mooueth
from
Otonno
or
haruest
time
into
winter
.
The
fixed
signes
are
Gemini
,
Virgo
,
Sagitarius
and
Pisces
,
they
are
called
fired
,
for
the
Sunne
entring
into
any
of
them
,
it
is
sayde
,
that
the
time
and
the
disposition
of
the
ayre
doeth
continue
in
his
owne
estate
,
They
which
are
common
,
are
Taurus
,
Leo
,
Scorpio
,
&
Aquarius
,
they
are
called
common
signes
,
for
there
appertaineth
to
them
some
thing
of
the
moueable
and
of
the
fixed
,
and
so
the
common
in
parte
is
moueable
,
and
in
parte
is
fixed
.
The
nienth
Chapter
what
a
signe
is
,
and
what
likenes
it
hath
with
that
whervnto
it
is
compared
,
and
what
day
of
the
yeere
the
Sunne
entreth
into
euery
signe
.
I
Haue
sayde
,
that
the
signes
of
the
Zodiacke
haue
names
of
beastes
,
by
reason
that
the
effects
which
the
Sunne
doth
woorke
by
entring
into
euery
one
signe
,
they
haue
likenesse
or
property
,
with
that
beast
or
with
that
thing
wherof
the
signe
beareth
name
;
And
because
I
thought
good
to
declare
this
at
large
.
I
will
shewe
what
thing
a
signe
is
,
and
how
many
manner
of
wayes
it
is
taken
,
and
the
likenesse
that
euery
signe
hath
with
that
wherewith
it
is
compared
,
and
in
what
daye
of
the
yeere
according
to
the
common
opinion
,
the
Sunne
entreth
into-euery
signe
,
For
the
first
is
to
be
noted
,
that
a
signe
according
to
the
saying
of
Sacro
busto
,
is
a
piramide
of
foure
sides
,
whose
seate
is
that
superficie
,
whiche
wee
call
signe
,
the
sharpenesse
therof
is
towards
the
center
,
the
signes
are
those
starres
,
that
the
Astronomers
were
accustomed
to
contemplate
on
,
loking
on
their
light
or
brightnes
,
wherby
they
knewe
what
wether
would
come
,
and
many
were
accustomed
to
behold
them
,
and
thereby
they
foresaw
the
qualities
of
the
summer
,
winter
,
and
other
times
of
the
yeere
.
For
the
principal
starres
in
their
risinges
and
in
their
setting
,
doe
shewe
the
qualities
of
the
times
,
A
signe
is
also
taken
by
one
parte
of
the
Zodiacke
,
the
which
the
sunne
doeth
passe
,
after
he
hath
gone
thirtie
degrees
from
his
moouing
.
And
because
the
sunne
in
one
yeere
doeth
passe
the
zodiacke
,
whiche
hath
three
hundreth
and
threescore
degrees
,
therefore
the
signes
or
houses
of
the
sunne
are
twelue
,
so
sayth
Ptholomy
in
the
second
Quadri
Partiti
,
that
the
signs
are
twelue
,
answering
to
the
twelue
partes
of
the
earth
,
therefore
of
these
signes
.
The
first
is
Aries
,
and
the
reason
why
this
signe
is
first
named
before
the
others
,
is
because
that
some
holdeth
,
that
in
the
first
degree
of
this
signe
,
the
sunne
made
his
moouing
the
first
day
that
he
began
,
&
that
day
he
was
in
the
equinoctiall
:
and
also
for
because
the
sun
entring
into
this
signe
making
heate
,
bringeth
foorth
moisture
,
by
the
which
it
is
a
liuely
moouing
of
generation
,
This
signe
is
called
Aries
,
by
similitude
euen
as
a
sheepe
is
weake
in
one
parte
of
the
bodie
,
and
is
strong
in
the
other
,
so
entring
the
sunne
into
this
signe
the
11.
of
Marche
,
in
the
first
parte
is
a
little
hote
,
and
in
the
last
with
greater
strength
his
heate
is
felt
.
The
2.
signe
is
called
Taurus
,
to
vnder
stande
,
that
as
the
Bull
is
a
strong
beaste
,
so
entring
the
Sunne
into
this
signe
the
eleuenth
of
Aprill
,
it
heateth
with
more
strength
then
before
.
The
third
signe
is
Gemini
of
this
is
vnderstood
▪
that
the
sunne
entring
into
him
the
eleuenth
of
May
,
with
his
vertue
of
heating
ingendreth
.
The
Iour●h
signe
is
Cancer
,
into
the
which
the
sunne
is
entred
the
eleuenth
of
Iune
,
it
is
marked
like
a
Crabbe
.
The
fifth
signe
is
the
figure
or
shape
of
a
Lion
,
which
is
a
strong
beast
,
collericke
and
full
of
anger
,
so
that
the
Sunne
entring
into
this
signe
the
fourteenth
of
Iuly
,
it
bringeth
a
strong
heat
.
The
sixth
signe
is
Virgo
,
by
the
whiche
is
noted
,
euen
as
the
virgine
is
barren
and
doeth
not
engender
,
so
the
Sunne
entring
into
this
signe
the
fourteenth
of
August
,
the
earth
is
barren
and
bringeth
not
foorth
any
thing
by
reason
of
the
great
heate
.
The
seauenth
signe
is
Libra
,
marked
by
a
payre
of
Ballance
of
like
equalitie
,
to
vnderstand
,
that
the
Sunne
beeing
entred
into
this
signe
the
thirteenth
of
September
,
the
day
is
equall
with
the
night
.
The
eyght
signe
is
marked
with
a
Scorpion
,
which
is
a
Beaste
,
that
with
the
tongue
he
flattereth
,
and
with
the
tayle
he
poysoneth
,
so
when
the
Sunne
is
entred
into
this
signe
the
fourteenth
of
October
,
the
first
part
thereof
is
temperate
,
but
the
last
is
colde
.
The
nienth
signe
is
Sagitarius
which
is
a
beast
offenciue
,
so
that
the
Sunne
entring
into
this
signe
the
thirteenth
of
Nouember
,
offendeth
with
colde
and
snowe
.
The
tenth
is
Capricorne
,
wherein
is
vnderstoode
that
euen
as
the
Gote
from
the
lower
parte
goeth
vp
to
that
which
is
high
,
so
the
Sunne
entring
into
this
signe
the
fourteenth
of
December
,
from
the
lowest
parte
of
our
hemisperio
beginneth
to
goe
to
that
which
is
high
.
The.
11.
signe
is
Aquarius
,
marked
by
a
man
that
sheddeth
water
for
to
shewe
,
that
entring
the
Sunne
into
this
signe
the
11.
of
Ianuary
,
he
sendeth
to
the
earth
water
&
moisture
.
The.
12.
signe
is
Pisces
,
marked
by
2.
fishes
in
the
water
,
which
is
cold
&
moist
,
to
shew
that
entring
the
sun
into
this
signe
the
12.
of
feburary
the
weather
is
colde
and
moist
.
Of
the
aforesayde
it
may
be
knowne
,
the
diuersitie
of
the
effectes
,
that
the
sunne
maketh
in
euery
signe
.
But
it
is
to
bee
noted
that
this
doeth
happen
to
such
as
doe
dwell
from
the
equinoctiall
towardes
the
north
or
pole
articke
,
for
such
as
inhabite
towardes
the
pole
antartike
,
the
sunne
beeing
gone
foorth
of
the
equinoctial
,
doeth
make
contrary
effectes
to
them
,
so
that
when
wee
haue
summer
they
haue
winter
,
in
such
sorte
that
the
order
of
the
signes
in
the
Zodiacke
is
not
conformable
or
agreeable
to
all
for
if
vnto
vs
commeth
forth
first
Aries
before
Taurus
,
to
them
commeth
foorth
first
Taurus
before
Aries
,
&
in
like
sort
of
the
other
signes
as
in
the
materiall
sphere
is
plainely
shewed
.
The
tenth
Chapter
,
of
the
seauen
heauens
,
of
the
planets
,
and
their
moouings
,
and
how
they
haue
impression
,
and
cause
generation
and
corruption
in
the
inferiour
bodies
.
SEeing
that
the
eyght
heauen
hath
bin
treated
of
,
and
of
the
stars
&
signes
that
are
in
it
.
It
is
conuenient
to
speake
of
them
seauen
inferiour
heauens
which
are
named
by
the
planets
,
of
the
which
it
is
to
be
vnderstoode
that
of
the
seauen
heauens
.
The
first
is
Saturn
▪
the
second
is
Iupiter
,
the
third
is
Mars
,
the
●ourth
is
Sol
,
the
fifth
is
Venus
,
the
sixth
is
Mercurie
,
&
the
seauenth
Luna
,
more
neere
vnto
vs
,
then
any
of
the
rest
,
these
seauen
planets
are
called
stars
,
which
are
moueable
not
because
they
erre
,
but
because
their
mouings
be
not
vniform
nor
agreable
,
these
do
moue
the
elements
&
do
corrupt
the
things
that
are
corruptible
they
bring
cloudie
weather
,
and
raiseth
vp
the
waues
of
the
sea
,
they
mooue
tempests
,
and
causeth
flowers
to
grow
,
and
the
heauens
&
planets
haue
natural
vertue
to
cause
these
effectes
,
the
works
of
these
planets
are
diuers
according
to
the
variation
of
the
countries
&
regions
,
&
therby
their
impressions
are
printed
in
beastes
,
birds
,
and
plantes
,
and
in
men
they
incline
more
to
one
then
to
other
.
But
although
they
do
to
incline
&
moue
,
they
doe
not
constraine
nor
binde
by
force
,
But
rather
as
Ptholomie
sayth
,
the
wise
man
is
lord
ouer
the
starres
He
is
wise
that
followeth
not
sensualitie
,
but
reason
,
euery
of
these
planets
haue
a
sphere
of
his
owne
,
wherin
he
moueth
in
circle
wise
,
And
the
superiour
circle
mooueth
round
about
so
nere
to
the
inferiour
,
that
betweene
the
one
and
the
othere
is
no
space
nor
any
thing
emptie
.
so
that
these
heauens
do
shut
one
with
another
,
&
they
are
nere
together
in
such
sort
,
that
any
thing
how
litle
or
smal
soeuer
it
be
,
cannot
put
it self
between
the
one
and
the
other
,
as
it
appeareth
in
the
elementes
,
that
betweene
the
one
and
the
other
their
is
no
place
emptie
:
so
that
we
see
betweene
the
water
&
the
earth
,
or
between
the
ayr
and
the
water
,
or
betweene
the
fire
and
the
ayre
,
remain
no
place
,
that
any
thing
may
be
put
between
:
more
it
is
to
be
noted
,
that
although
the
heauens
are
so
ioyned
together
,
&
neer
one
to
the
other
,
that
this
ioyning
together
doe
not
let
them
of
their
moouing
,
so
that
they
mooue
very
distinctly
in
differente
times
the
one
from
the
other
,
without
any
let
of
their
moouing
or
standing
still
one
onely
pointe
in
such
sorte
,
that
the
tenth
heauen
maketh
his
moouing
in
twentie
and
four
houres
,
&
the
nienth
heauen
that
is
neere
vnto
him
,
in
fortie
niene
thousand
yeres
,
and
likewise
the
eyght
heauen
doeth
make
his
moouing
in
thirtie
&
sixe
thousand
yeeres
,
and
another
in
seauen
thousand
,
and
the
seauenth
heauen
which
is
next
to
him
maketh
an
ende
of
his
moouing
in
thirty
yeres
.
These
are
things
which
doe
teach
vs
the
greatnes
and
power
of
the
maister
&
maker
of
such
workes
,
vnto
whom
the
sayde
woorkes
giueth
praise
,
so
did
the
royal
Prophet
consider
in
the
eyghteene
Psalme
where
hee
sayth
,
The
heauens
doe
shewe
and
manifest
the
glorie
of
the
Lorde
,
and
in
another
place
,
Lorde
the
heauens
shall
confesse
thy
great
maruelles
,
from
the
beginning
thou
madest
the
earth
,
&
the
heauens
are
the
workes
of
thy
handes
.
And
it
is
to
be
noted
that
euery
one
of
these
heauens
haue
twoo
moouinges
one
is
the
first
moueable
,
which
is
made
from
the
east
into
the
west
,
turning
againe
into
the
cast
as
it
is
declared
:
The
other
moouing
which
is
proper
to
euery
one
,
is
made
by
a
circle
oblique
,
contrary
to
the
first
,
that
is
to
saye
,
from
the
west
into
the
east
:
Of
this
is
to
bee
noted
,
that
according
to
the
opinion
of
Frauncis
Capuano
,
it
was
necessary
that
in
the
heauens
were
twoo
contrary
moouinges
,
one
in
the
first
moueable
,
and
another
in
the
lower
spheres
,
and
this
for
twoo
reasons
,
The
first
is
,
because
the
first
moueable
doeth
mooue
so
swift
,
and
with
so
great
hast
,
that
scarsely
his
moouing
can
bee
considered
,
seeing
that
in
twentie
and
foure
houres
hee
passeth
all
the
space
that
he
doeth
occupie
,
whiche
causeth
,
that
he
caryeth
with
him
,
all
the
lower
heauens
,
and
the
fire
,
and
the
measured
region
of
the
ayre
,
as
it
is
written
,
in
the
first
of
the
Metheoros
,
so
that
if
the
eyght
&
nienth
sphere
and
the
heauens
of
the
planets
did
not
mooue
vnto
the
opposite
parte
,
with
a
contrarie
moouing
,
the
sayd
first
moouing
would
not
onely
mooue
vnto
the
Celestiall
Spheres
,
and
to
the
fire
,
but
woulde
mooue
all
the
ayre
,
water
,
and
earth
rounde
about
,
with
his
daily
moouing
,
and
there
woulde
remaine
nothing
quiet
nor
firme
.
The
second
reason
is
because
the
starres
with
their
moouing
doe
cause
influence
in
the
inferiour
,
and
so
they
make
impression
as
they
mooue
,
but
if
euery
one
did
mooue
,
according
to
their
onely
moouing
,
that
is
to
saye
,
from
the
Caste
into
the
Weste
,
so
that
if
they
mooued
altogether
with
one
vniformitie
,
they
would
bring
foorth
one
equall
and
vniforme
effecte
,
the
which
shoulde
bee
an
inconuenience
.
For
that
onely
generation
is
not
sufficient
,
but
it
is
conuenient
,
that
there
bee
corruption
,
and
so
it
was
conuenient
,
that
all
the
Spheres
,
shoulde
modue
in
their
daylye
moouing
,
rounde
about
the
earth
once
in
a
naturall
daye
,
because
all
of
them
may
communicate
with
vs
their
impressions
:
and
likewise
that
they
mooue
in
the
seconde
moouing
in
the
Zodiack
,
comming
together
,
and
deuiding
them selues
one
from
another
to
make
that
the
effectes
shoulde
be
different
.
Aristotle
sayeth
,
in
the
second
of
generation
,
that
the
moouing
of
the
Starres
in
the
circle
,
oblique
,
that
is
to
say
,
in
the
Zodiacke
is
cause
of
the
diuersitie
of
effectes
,
And
so
the
Sunne
in
the
summer
comming
nere
vnto
vs
,
causeth
generation
,
&
likewise
in
Otonno
,
or
Haruest
time
,
and
in
the
winter
going
●rom
vs
causeth
corruption
.
The
eleuenth
Chapter
,
of
the
Region
elementall
,
and
howe
it
is
diuided
into
four
elementes
,
and
why
it
is
not
diuided
into
any
more
or
lesse
.
IN
the
Chapters
before
written
hath
bin
declared
the
order
of
the
heauens
,
their
number
&
mouings
,
therefore
I
will
nowe
speake
of
the
elementes
,
howe
they
are
ordained
and
deuided
,
of
the
which
it
is
to
be
vnderstood
,
that
the
elementes
are
foure
and
no
more
,
by
reason
,
that
first
of
all
they
haue
foure
qualities
,
and
it
maye
bee
sayde
,
that
they
Ioyne
in
sixe
kinde
of
waies
.
Let
vs
see
if
all
sixe
be
possible
.
One
ioyning
is
hote
and
cold
,
another
moist
and
drie
,
the
thirde
hote
and
drye
,
the
fourth
hote
and
moyst
,
the
fifth
moyste
and
colde
,
the
sixth
colde
and
dry
.
The
twoo
first
be
not
possible
,
because
there
cannot
bee
twoo
contraries
in
one
subiect
.
The
foure
which
remayne
are
possible
,
in
the
whiche
the
actiue
one
with
the
other
ioyneth
with
the
passiue
.
These
foure
do
constitute
the
four
first
essentias
which
are
called
elementes
,
And
this
is
by
reason
of
their
fyrste
simple
bodies
,
euen
as
it
seemeth
in
their
quallities
.
That
is
to
saye
,
in
the
fire
,
in
the
ayre
,
in
the
water
,
and
in
the
earth
,
because
we
see
that
the
fire
is
hot
and
drie
,
the
ayre
hote
and
moiste
,
the
water
colde
and
moyste
,
the
earth
colde
and
drye
,
by
the
which
difference
of
qualities
of
the
first
bodies
,
they
are
parted
in
the
same
maner
.
All
these
elements
doe
moone
,
by
the
higher
moouing
except
the
earth
which
is
immoueable
.
So
sayth
Albertus
the
great
in
the
first
of
his
Metheoros
,
the
fourth
Chapter
,
it
is
necessarie
that
wee
saye
the
moouing
,
which
wee
see
from
the
inferiour
,
that
is
to
say
,
the
moouing
of
the
elementes
proceede
of
the
superiour
,
euen
as
of
his
owne
cause
,
but
it
must
be
vnderstoode
of
the
superiour
elements
the
which
in
their
continuall
moouing
,
they
mooue
in
circle
manner
,
onely
the
earth
which
is
most
lowe
,
remayneth
without
moouing
,
not
onely
circuler
neither
yet
straight
.
The
twelfth
chapter
howe
the
elementes
,
doe
compasse
about
one
another
,
and
wherefore
the
water
doeth
not
couer
all
the
earth
.
THese
foure
elementes
,
that
before
are
spoken
of
ought
to
be
vnderstoode
that
the
one
doeth
compasse
about
the
other
in
this
manner
,
the
earth
is
in
the
middest
of
al
,
like
to
a
poynte
or
Center
of
the
worlde
,
neere
vnto
the
which
is
the
water
,
and
vppon
the
water
and
the
earth
is
the
ayre
,
and
vpon
the
ayre
,
the
fire
,
and
the
element
of
the
fire
is
vpon
the
ayre
Albenruys
proueth
it
in
the
fourth
of
the
heauen
and
the
worlde
in
his
thirty
two
commentary
:
where
he
sayth
,
we
see
that
all
fire
moueth
vpwarde
and
is
eleuated
vppon
the
ayre
,
therfore
as
his
mouing
is
not
infinite
it
is
conue●ient
that
it
come
to
one
place
where
it
is
na●●ral
,
and
there
it
is
conserued
,
whereupon
it
is
concluded
that
the
fire
is
aboue
the
ayre
,
it
is
prooued
by
an
example
in
this
sort
.
If
there
be
any
that
haue
not
seene
the
sea
but
seeth
how
all
riuers
goe
to
demain
in
one
pla●●
as
their
moouinges
the
not
infinite
,
it
is
necessarie
to
conclude
and
appoint
some
place
,
where
the
waters
may
ioyne
,
And
this
plate
is
the
sea
,
so
it
is
conuenient
to
graunt
that
vpon
the
ayre
is
a
place
in
the
hollowe
parte
of
the
roundnes
of
the
moone
,
where
the
〈◊〉
is
gathered
together
.
Therefore
I
say
that
these
Elementes
eyther
of
them
doe
compasse
in
roundnesse
equally
from
euery
parte
of
the
earth
,
sauing
the
water
in
that
parte
of
the
earth
,
which
is
discouered
,
for
the
breathing
and
life
of
all
liuing
creatures
,
of
this
it
is
to
be
noted
according
to
the
saying
of
Albertus
the
great
,
that
the
water
did
couer
all
the
earth
,
and
also
he
sayth
in
the
second
of
the
Metheoros
the
thirde
treatie
the
seconde
chapter
,
wee
see
the
order
of
the
elementes
are
in
suche
sorte
,
that
alwayes
the
ioyning
of
the
one
is
in
the
hollownes
of
the
other
,
&
this
is
by
reason
his
roundnes
doeth
girde
him
therevnto
,
and
because
this
is
naturall
,
and
sometimes
it
was
so
,
that
at
somtime
the
earth
was
couered
with
water
,
and
all
bodies
naturally
haue
one
proper
place
,
whereby
it
is
conuenient
,
that
all
be
filled
,
for
otherwise
there
woulde
be
some
thing
superfluous
in
nature
,
so
it
is
euident
,
that
the
proper
place
of
the
waters
is
the
superficie
of
the
earth
,
for
alwayes
they
mooue
by
that
place
.
Also
when
at
any
time
two
elements
doe
not
agree
in
any
quallitie
,
commonly
it
is
called
simbol
,
wherewithall
the
one
doeth
ioyne
with
the
other
.
Therefore
it
is
necessarie
,
that
there
bee
some
meane
that
they
communicate
and
ioyn
together
,
and
seeing
the
earth
and
the
ayre
haue
no
simboll
,
it
is
conuenient
,
that
they
ioyne
together
by
meanes
which
is
the
water
that
hath
a
simboll
with
both
,
and
so
it
is
shewed
that
according
to
nature
all
the
earth
was
couered
with
water
:
Of
this
may
be
asked
what
is
the
cause
,
why
the
roundnes
of
the
elementes
,
fayled
more
in
the
water
then
in
the
others
:
it
is
answeared
that
GOD
did
make
nothing
in
vayne
but
alwaies
woorketh
for
the
best
.
Therefore
as
God
by
his
only
grace
and
wil
made
man
,
and
al
other
things
,
I
leaue
this
part
of
the
discouery
of
the
earth
,
that
man
and
Beastes
might
be
conserued
in
their
owne
likenes
.
Of
this
haue
past
many
questions
,
this
is
certaine
that
GOD
of
his
omnipotencie
made
it
.
And
so
it
is
written
in
Genesis
the
first
chapter
,
that
God
sayd
lette
the
waters
come
together
,
that
are
aboue
the
heauen
,
and
let
the
earth
be
seene
drye
.
The
thirteenth
Chapter
,
how
the
earth
and
the
Water
,
both
Elementes
,
make
one
round
bodie
.
IT
is
to
bee
noted
,
that
these
twoo
Elementes
,
Earth
and
Water
,
both
together
doe
make
one
rounde
body
,
Of
this
speaketh
Iohn
de
Sacro
●usto
in
the
first
chapter
of
the
Sphere
,
The
earth
is
rounde
,
which
is
shewed
by
the
signes
and
the
other
Starres
,
which
rise
not
,
nor
goe
downe
equally
to
all
men
wheresoeuer
they
bee
.
But
first
of
all
they
rise
to
them
that
bee
in
the
east
part
,
rather
then
to
them
that
are
in
the
west
,
and
why
they
appeare
to
one
rather
then
to
the
other
,
the
roundnesse
of
the
earth
is
the
cause
thereof
,
&
that
to
bee
true
,
that
the
stars
are
seene
to
some
rather
then
to
others
,
it
appeareth
by
the
eclipse
,
for
one selfe
eclipse
of
the
moone
,
which
we
see
at
the
first
houre
of
the
night
,
they
which
are
in
the
easte
partes
doe
see
them
in
the
thirde
houre
of
the
night
,
whereby
it
seemeth
,
that
it
was
first
night
,
and
the
sunne
was
first
set
to
them
,
before
it
was
set
to
vs
,
the
●ause
is
,
the
roundnes
of
the
earth
,
&
that
the
earth
is
rounde
from
the
north
vnto
the
south
,
and
so
contrarywise
it
sheweth
it selfe
,
for
vnto
those
which
are
towardes
the
north
,
appeareth
alwayes
some
starres
,
which
are
neere
to
the
pole
artick
,
&
the
other
stars
which
are
neere
to
the
pole
antartik
are
neuer
seene
.
But
if
any
went
from
the
north
towardes
the
south
or
midday
he
might
goe
so
farr
,
that
the
stars
which
he
saw
first
might
be
layde
vnder
the
horizon
that
he
should
not
see
them
,
and
howe
much
more
he
came
towards
the
south
,
so
much
lesse
hee
should
see
the
starres
of
the
north
,
and
then
he
should
see
the
starres
of
the
south
,
that
first
he
coulde
not
see
,
as
contrariwise
,
it
would
happen
to
such
as
went
from
the
south
to
the
north
,
and
the
cause
of
this
is
the
roundnes
of
the
earth
,
likewise
if
the
earth
were
plaine
from
the
easte
to
the
west
,
so
sonne
or
equally
,
the
stars
would
rise
vnto
those
in
the
east
partes
as
to
those
in
the
west
,
whereby
it
seemeth
false
,
by
the
fyrst
reason
.
Item
if
the
earth
were
plaine
from
the
north
to
the
south
,
or
by
the
contrary
,
the
stars
that
one
should
see
should
neuer
be
set
from
him
wheresoeuer
hee
should
goe
,
the
which
is
false
,
by
the
second
reason
,
for
if
in
any
manner
of
wise
the
earth
doe
seem
plain
,
vnto
the
sight
of
men
,
it
is
for
the
great
quantitie
that
it
containeth
,
in
respect
of
our
sight
.
And
if
any
should
say
that
the
mountaines
and
valleis
doe
let
the
roundnes
of
the
earth
.
To
this
is
vnderstoode
,
that
the
mountaines
haue
not
any
proportion
that
should
let
the
earth
to
be
round
And
if
there
be
any
thing
in
that
sorte
they
be
as
the
nayles
of
a
wheele
,
that
very
little
or
nothing
doe
let
his
roundnes
,
but
note
that
in
one
of
twoo
manner
of
wayes
a
round
thing
may
be
spoken
of
,
the
one
is
by
rule
,
that
is
to
saye
,
when
the
lines
which
are
straightly
caried
from
the
center
to
the
circumference
,
be
equall
,
in
this
sorte
the
earth
is
not
perfectly
round
.
In
another
sorte
it
is
sayd
to
be
round
irreguler
,
that
is
,
when
all
partes
are
not
of
equall
distance
from
the
middest
,
so
is
the
roundnes
of
the
earth
.
And
seeing
it
hath
beene
declared
how
that
the
earth
is
rounde
.
I
saye
that
the
water
is
likewise
round
which
is
prooued
by
the
reasons
aforesayde
.
Also
it
is
prooued
,
that
suche
as
sayle
by
the
Sea
,
for
to
discouer
the
Lande
,
they
alwayes
goe
vppe
to
the
toppe
of
the
Shippe
,
whiche
is
the
highest
parte
,
and
happeneth
to
see
the
Lande
from
thence
,
and
from
no
other
place
,
And
this
is
by
reason
of
the
roundenesse
whiche
the
water
hath
.
The
fourteenth
chapter
,
Howe
the
earth
is
scituated
in
the
middest
of
〈◊〉
worlde
.
ALFRAGANO
saith
,
in
the
fourth
difference
,
if
the
earth
were
not
in
the
middest
of
the
world
it
would
not
be
of
equal
distance
from
euery
part
of
the
heauen
.
But
Euclides
bringeth
in
the
firste
of
the
Elementes
,
that
it
standeth
in
the
middest
,
and
is
equall
in
distance
from
all
partes
,
and
prooueth
so
,
for
if
the
earth
were
not
in
the
middest
,
it
woulde
reache
more
to
the
Easte
parte
,
or
too
the
West
.
And
for
a
similitude
,
when
the
Sunne
or
other
Starre
,
were
in
that
parte
,
it
woulde
reach
more
neere
to
the
earth
,
then
it
it
were
in
the
other
part
,
&
so
they
would
seeme
greater
:
Which
is
false
,
for
wee
see
that
all
people
whiche
are
vp●
on
the
face
of
the
earth
the
stars
seemeth
to
them
of
one selfe
quantitie
in
what
parte
of
the
heauen
soeuer
they
be
,
be
it
in
the
middle
heauen
,
in
the
easte
or
in
the
west
.
And
the
cause
of
this
is
,
by
reason
the
earth
is
of
equall
distance
from
the
Sarres
,
it
followeth
therefore
that
it
is
in
the
middest
of
the
Firmament
.
Item
if
the
earth
by
any
of
his
partes
,
were
more
neare
to
the
heauen
in
one
place
then
in
another
,
he
that
were
in
that
part
vpon
the
face
of
the
earth
,
which
were
neerer
to
the
heauen
,
shoulde
not
see
the
halfe
heauen
.
This
is
against
Ptholomie
,
and
all
the
Philosophers
,
that
doe
saye
,
that
wheresoeuer
a
man
standeth
there
riseth
alwayes
with
him
sixe
signes
,
and
other
sixe
setteth
with
him
,
and
the
halfe
heauen
is
seene
of
him
,
and
the
other
halfe
is
hid
from
him
,
so
that
equally
they
are
distant
from
the
heauen
.
Sacro
busto
sayeth
,
that
by
the
selfe
same
signe
or
shewe
is
prooued
,
that
the
earth
is
but
a
poynte
in
respect
of
the
Fyrmament
,
for
if
the
earth
were
of
any
quantitie
in
respecte
of
the
heauen
,
it
woulde
not
happen
that
the
half
heauen
shoulde
bee
seene
.
And
for
the
better
vnderstanding
thereof
,
Imagine
this
,
if
any
plain
superficie
were
put
vppon
the
Center
of
the
earth
,
the
whiche
shoulde
diuide
the
earth
into
twoo
equall
partes
.
And
also
the
firmament
it selfe
.
Then
the
eye
of
him
that
were
in
the
Center
of
the
earth
,
should
see
the
middest
of
the
Fyrmament
,
And
the
selfe
same
eye
standing
vpon
the
face
of
the
earth
,
shoulde
also
see
the
middest
of
the
firmament
,
of
this
is
gathered
,
that
the
quantitie
of
the
earth
is
insencible
in
respect
of
the
firmament
.
The
fiftenth
Chapter
,
how
the
earth
is
quiet
and
mooueth
not
.
THAT
the
earth
is
vnmoueable
and
quiet
,
to
is
prooued
by
two
reasons
,
the
firste
is
,
that
beeing
a
hole
naturall
body
and
altogether
heauie
,
it
goeth
to
the
place
most
lowe
,
whiche
is
the
Center
and
middest
of
the
Firmament
,
and
there
it
remaineth
.
So
sayth
the
Philosopher
in
the
fourth
of
the
naturall
Philosophie
and
in
the
fyrst
and
fourth
of
the
Heauen
and
the
worlde
.
The
seconde
reason
is
to
consider
,
howe
that
the
earth
standeth
in
the
middest
,
and
if
it
shoulde
mooue
and
departe
from
the
middest
,
it
woulde
rise
vppe
,
the
which
woulde
happen
to
it
naturally
or
violentlye
,
not
naturallye
,
because
his
naturall
moouing
is
to
the
middest
,
and
so
his
moouing
contrary
to
the
middest
is
not
naturall
to
it
,
then
it
shoulde
be
with
violence
.
But
it
cannot
bee
with
violence
,
because
there
is
no
body
to
be
found
that
shoulde
doe
violence
to
so
greate
a
body
,
in
greatnesse
and
waight
,
where
it
is
to
bee
concluded
,
that
it
is
alwaies
queit
and
mooueth
not
.
The
same
prooueth
Albertus
the
great
,
in
the
seconde
of
the
heauen
and
the
Worlde
,
in
the
thyrde
Treatie
and
the.
8
,
chapter
where
he
saith
,
the
order
of
the
starrs
doe
learn
the
earth
to
be
quiet
,
and
placed
in
the
middest
,
for
as
the
moone
is
ordeined
to
be
vnder
the
Sunne
,
if
the
earth
were
not
in
the
middest
and
fixed
,
it
would
not
happen
〈◊〉
the
parte
of
the
circle
of
the
signes
,
the
Sunne
and
the
moone
to
be
opposite
to
the
heade
and
tayle
of
the
Dragon
,
and
likewise
the
Astrolabios
,
and
other
instrumentes
of
the
Astronomers
should
be
false
,
and
by
them
woulde
neuer
bee
found
the
courses
and
computations
of
the
starres
,
as
by
the
sayd
iustruments
our
sences
doe
attaine
vnto
,
for
alwaies
they
woulde
happen
to
bee
diuerse
and
different
,
for
from
the
earth
the
circles
of
the
heauen
should
not
be
equally
seen
.
All
the
which
we
haue
prooued
be
Geomitrie
and
Astronomie
.
It
is
to
bee
considered
that
God
made
heauen
and
earth
,
and
all
that
therein
is
,
he
put
the
earth
fixed
in
the
middest
,
because
the
heauen
and
the
starres
should
compasse
it
about
with
their
moouing
,
where
the
diuine
power
doeth
sustaine
it
in
the
nuddest
,
euen
as
a
point
.
Of
this
is
written
,
The
Lorde
sayth
,
I
haue
hanged
,
the
earth
in
one
knot
founded
vpon
his
stabillitie
.
The
sixteenth
Chapter
of
the
center
of
the
earth
,
and
howe
it
may
be
sayd
that
the
earth
is
the
center
of
the
world
.
THE
Center
of
the
earth
may
bee
vnderstoode
in
three
manner
of
wayes
,
The
first
as
touching
the
greatnes
of
the
Center
,
The
second
of
the
waight
of
the
center
.
And
the
third
of
the
mase
or
assemblie
of
the
center
,
the
which
assembly
or
mase
is
in
the
middest
of
the
firmament
,
This
beeing
had
,
foure
thinges
are
to
bee
noted
.
The
first
is
,
that
in
the
land
is
not
one selfe
center
of
greatnes
and
of
waight
,
for
the
earth
is
deformedly
waighty
,
for
that
the
one
parte
is
couered
with
water
,
&
the
other
part
is
discouered
.
The
seconde
,
that
the
center
of
the
waight
of
the
earth
is
not
in
the
middest
of
the
firmament
,
for
if
you
imagine
to
diuide
the
earth
into
2.
equal
parts
,
then
the
part
that
is
couered
with
water
woulde
surmount
the
other
.
The
third
is
that
the
Center
of
the
greatnesse
of
the
earth
,
and
the
Center
of
the
firmament
,
are
not
one
.
For
that
the
earth
is
not
equally
couered
with
water
.
Of
the
which
there
foloweth
,
that
in
the
earth
we
may
imagine
,
three
centers
really
distinct
,
The
firste
,
is
the
center
of
the
greatnes
of
the
earth
,
The
second
the
center
of
the
waight
,
The
third
the
midest
of
the
firmament
,
The
fourth
reason
that
the
,
center
or
poynt
of
the
mase
or
assembly
of
the
water
and
earth
is
in
the
middest
of
the
firmament
.
This
is
because
the
like
assemblie
is
a
waightie
body
,
and
without
lette
,
and
so
the
center
touching
his
wayght
is
in
the
middest
of
the
worlde
,
for
that
he
is
weightie
by
nature
,
wherby
it
may
be
sayde
that
the
earth
is
in
the
middest
of
the
firmament
,
for
that
it
is
a
parte
of
the
mase
,
which
mase
is
in
the
middest
of
the
world
.
¶
The
ende
of
the
first
booke
.
¶
The
seconde
Booke
of
the
Sea
,
and
of
his
moouinges
,
and
howe
the
Nauigation
was
inuented
.
The
first
Chapter
what
thing
the
Sea
is
,
and
wherefore
it
is
called
Occean
.
THe
Sea
is
the
proper
place
of
the
waters
by
reason
of
the
similitude
of
his
forme
.
There
the
waters
doe
ingender
&
are
sutained
.
And
according
as
Albertus
the
great
vnderstandeth
it
,
the
riuers
come
foorth
of
her
and
returne
to
her
againe
.
So
hee
sayth
in
the
third
of
his
Metheoros
the
twelfth
chapter
,
we
see
that
all
riuers
runne
into
the
Sea
,
and
from
the
Sea
they
returne
and
come
foorth
,
that
they
may
runne
agayne
,
wherby
it
seuieth
,
that
the
Sea
is
the
end
and
beginning
of
the
waters
.
It
is
called
the
Occean
Sea
,
for
the
swift
and
continuall
moouing
where
with
it
mooueth
:
for
that
,
Oikis
in
Greeke
is
as
much
to
say
hasty
or
swift
.
The
Greekes
and
Latinists
doe
name
it
by
this
name
,
and
therefore
this
name
hath
continued
common
:
or
else
it
is
called
Occean
Casi
Cianeus
,
because
it
girdeth
or
imbraceth
the
endes
of
the
earth
,
&
by
reason
of
the
diuersitie
of
the
countries
,
it
taketh
diuers
names
,
as
the
Indian
sea
or
Percian
sea
.
&c.
The
Sea
hath
no
colour
,
being
looked
vpon
,
when
one
is
neere
it
:
for
our
sight
remaineth
not
vpon
the
superficies
of
the
water
,
but
desendeth
downe
and
being
looked
vpon
a
farre
of
it
hath
the
colour
of
heauen
,
&
being
moued
of
the
windes
it
hath
the
forme
of
diuers
colours
.
And
it
is
to
be
noted
,
that
the
Sea
for
seuen
dayes
riseth
encreasing
,
and
is
that
which
we
cal
springtides
,
&
other
seuen
she
decreaseth
.
Of
these
flowings
and
ebbinges
.
Aristotle
bringeth
the
causes
to
hee
naturall
,
in
the
seconde
of
his
Metheoro●
:
and
besides
that
,
Hipocrates
,
in
his
booke
of
ayre
and
water
sayth
that
there
is
a
proper
cause
in
Astronomie
,
that
is
by
the
natural
vertue
of
the
moone
,
vpon
the
waters
,
so
likewise
we
see
that
al
shel
fish
with
the
encreasing
of
the
moone
doe
encrease
,
&
with
the
decreasing
do
decrease
:
for
as
the
moone
riseth
aboue
the
Horizon
and
with
his
beames
toucheth
the
sea
,
moueth
a
stitring
vp
,
whereby
it
causeth
her
flowing
and
ebbing
and
to
cast
out
into
her
riuer
or
coast
all
dead
bodies
or
vncleane
thinges
that
are
in
her
.
The
2.
Chapter
how
the
sea
apperteineth
to
the
perfection
of
the
world
,
and
without
her
the
world
woulde
perish
,
and
howe
the
water
is
ingendered
in
her
.
THe
sea
apperteineth
too
the
making
of
the
world
and
to
her
perfection
,
&
the
world
,
should
not
be
perfect
without
her
:
for
if
there
were
no
beginning
of
the
waters
there
shoulde
be
no
simple
waters
.
And
if
there
were
no
simple
waters
there
would
be
no
mixt
waters
,
and
so
there
would
be
nothing
of
that
which
is
ingendered
of
the
water
,
and
if
there
were
no
water
there
would
be
no
bodies
,
as
there
are
continually
,
and
thinges
which
cleeueth
together
,
whereof
it
followeth
,
that
if
the
waters
had
not
a
beginning
the
generation
would
be
destroyed
,
And
so
consequently
all
the
world
.
Also
if
there
were
no
beginning
of
the
waters
there
would
not
be
a
ioyning
together
of
the
contraries
which
are
possible
,
and
so
nature
woulde
dye
in
that
which
were
necessarie
,
and
the
woorke
would
cease
in
the
act
.
Then
it
would
happen
,
not
hauing
a
beginning
of
the
waters
the
woorke
of
nature
would
cease
,
and
so
the
worlde
woulde
perish
,
where
it
concludeth
,
that
the
sea
is
necessary
for
the
sustentation
of
the
worlde
.
And
Aristotle
in
the
seconde
of
his
Metheoros
,
sayth
,
that
the
waters
in
the
sea
doe
ingender
in
the
North
,
which
is
as
much
to
say
,
as
the
greatest
parte
of
the
water
of
the
sea
doth
ingender
in
the
north
.
This
Albertus
the
greate
declareth
in
the
second
of
his
Metheoros
,
chapter
sixe
,
saying
that
the
sea
runneth
from
the
North
into
the
South
,
and
the
cause
is
that
the
north
is
higher
then
the
south
and
the
reason
wherefore
it
is
higher
,
is
,
because
that
with
the
colde
of
the
north
there
is
more
water
ingendred
,
then
that
which
can
containe
in
the
distance
and
height
of
the
riuers
,
and
in
the
south
the
water
consumeth
and
is
wasted
with
the
heate
of
the
sunne
,
and
for
this
cause
in
the
north
,
one
water
pusheth
out
another
,
to
the
place
which
is
lower
then
it selfe
:
And
so
accidently
it
mooueth
,
from
the
place
of
his
generation
.
For
as
it
is
moist
,
it
runneth
vntill
it
come
to
be
deteined
in
some
drye
place
.
The
reason
why
the
water
is
so
consumed
in
the
south
parts
is
,
because
the
sunne
alwayes
mooueth
in
his
circle
,
Excentrik
so
that
his
center
is
not
in
one
place
of
the
earth
,
in
such
sort
that
if
the
Diameter
of
the
circle
of
the
Sunne
were
paste
by
both
centers
,
that
is
to
say
,
his
owne
,
and
that
of
the
earth
,
the
greater
parte
of
the
diameter
shoulde
be
towardes
the
one
parte
,
and
the
lesser
towardes
the
other
,
in
respect
of
the
center
of
the
earth
:
And
so
it
is
shewed
by
reason
of
Geometrie
,
that
the
greater
length
of
the
diameter
is
neere
vnto
the
twentie
degrees
of
Gemini
in
this
our
time
,
and
the
lesser
length
is
in
the
twentie
degrees
of
Sagitarius
whiche
is
a
signe
opposite
to
Gemini
,
whereof
it
appeareth
that
the
sunne
commeth
much
neerer
to
the
earth
in
the
south
partes
then
in
the
north
partes
.
And
so
by
reason
of
his
neere
comming
,
he
heateth
in
such
sorte
,
that
he
consumeth
the
water
and
burneth
the
earth
,
the
which
he
doeth
not
in
the
north
partes
.
The
third
Chapter
,
wherfore
the
water
of
the
Sea
is
salt
,
and
wherefore
it
is
most
conuenient
and
better
for
the
Nauigation
.
EXperience
sheweth
that
the
water
of
the
Sea
is
salte
,
and
so
sayth
Albertus
the
great
,
that
it
is
called
sea
,
by
reason
it
is
bitter
or
salte
,
And
the
Sea
to
be
salts
it
seemeth
to
be
against
his
naturall
kinde
,
wherefore
,
seeing
that
the
sea
is
the
begin●ing
of
the
waters
,
and
his
owne
place
,
and
the
waters
which
ingender
in
her
,
and
those
which
enter
into
her
foorth
of
the
riuers
are
fresh
,
it
seemeth
that
with
more
reason
the
sea
should
be
fresh
,
and
not
salt
.
Also
as
it
is
certaine
that
God
made
all
things
to
the
best
,
it
seemeth
to
be
better
,
that
the
sea
were
freshe
then
salte
.
To
this
answereth
Albertus
the
great
in
the
second
of
his
Metheoros
,
in
the
thirde
treatie
and
fifteenth
Chapter
,
where
he
sayth
that
matter
that
causeth
the
sea
to
bee
salt
is
.
According
to
the
truth
,
there
are
twoo
kindes
of
vapours
,
that
is
to
say
,
hote
and
moyst
,
and
hote
and
drie
,
and
in
the
sea
one
of
these
doth
rise
from
the
superficies
,
&
the
other
riseth
from
the
bottome
,
This
is
by
reason
of
the
heate
of
the
sunne
,
and
of
the
starres
,
which
are
an
efficient
cause
of
these
vapours
,
and
for
the
vapour
of
the
water
it
is
very
subtile
,
betweene
these
two
,
and
therefore
being
risen
into
the
ayre
is
consumed
of
the
sunne
,
and
the
vapour
of
the
earth
remaineth
,
or
more
properly
his
exhalation
dispersed
,
extended
,
&
mingled
in
the
water
.
As
it
appeareth
by
an
example
in
the
meate
digested
,
that
the
thin
substance
thereof
,
is
raised
vppe
and
extended
,
into
the
members
and
is
that
which
nourisheth
,
and
the
grosse
substance
remaineth
,
and
also
that
which
is
vndigested
:
euen
so
doth
the
vapour
of
the
earth
remaine
grosse
,
and
extendeth
into
the
substance
of
the
water
of
the
sea
,
and
the
coldnes
of
the
water
compassing
it
round
about
,
casting
into
it
coldnes
,
and
with
the
coldnes
it
burneth
,
by
reason
they
bee
two
contraries
together
,
they
are
made
stronger
then
before
,
for
the
heate
of
the
salte
exhalation
,
being
come
forth
of
the
depth
of
the
sea
,
by
vertue
of
the
Sunne
fortifieth
it selfe
,
with
his
contrary
,
which
is
the
cold
,
and
so
ouercommeth
the
like
heat
which
is
that
as
is
required
in
the
generation
of
a
salt
fast
,
as
the
Philosopher
hath
it
in
the
second
of
his
metheoros
the
first
chapter
speaking
in
this
matter
,
of
this
there
is
a
similitude
,
that
if
a
freshwater
were
passed
through
ashes
it
would
make
it
salte
,
the
like
is
of
the
water
of
the
sea
,
in
the
time
it
was
made
salt
,
and
because
that
some
say
,
there
is
a
pure
element
insubstance
,
and
the
element
of
the
water
is
in
the
sea
,
and
that
in
the
middest
of
the
sea
,
the
water
is
simple
and
without
tast
,
wherefore
hath
it
not
there
an
obiection
of
contrarietie
.
This
seemeth
to
me
not
to
be
so
,
for
the
heate
of
the
Sunne
,
and
the
starres
,
are
sufficient
to
make
exhalations
come
forth
of
the
bottome
of
the
sea
,
which
being
mingled
with
the
coldnes
and
moisture
of
the
water
caused
a
salt
tast
in
the
highest
parte
of
the
water
:
As
well
&
with
more
reason
they
will
make
it
in
the
middest
or
in
the
bottome
of
the
sea
,
and
so
I
hold
with
Aristotle
,
and
with
Constantine
a
great
Astronomer
,
that
there
is
now
no
element
pure
,
&
for
as
muche
as
the
water
is
salt
,
it
is
more
conuenient
&
better
for
the
nauigation
,
than
the
fresh
,
that
is
because
the
salte
water
is
more
heauie
and
grosse
then
the
freshe
.
And
that
it
is
so
,
Albertus
the
great
saith
in
this
manner
,
that
the
salt
water
is
more
heauie
and
thick
then
the
freshe
,
it
is
gathered
by
many
experiences
,
of
the
which
one
is
.
If
the
freshe
water
be
mingled
,
with
salt
and
made
a
strong
mixture
in
such
sorte
that
all
the
salt
be
melted
in
the
water
,
and
in
to
it
is
cast
an
egge
fresh
layde
,
it
will
swimme
aboue
the
water
,
by
reason
of
the
thicknes
that
the
water
hath
which
is
done
with
the
mixture
of
the
salte
,
and
if
the
sayd
egge
be
put
in
freshe
water
it
will
sinke
,
it
is
sayd
that
it
must
bee
a
newe
laid
egge
,
for
if
it
be
old
or
crackt
,
it
will
sink
.
And
by
the
same
reason
is
shewed
,
that
the
shippes
doe
rather
sinke
in
freshe
water
,
then
in
that
which
is
salt
for
the
fresh
rather
deuideth
it selfe
and
riseth
vp
rather
then
that
which
is
salt
.
The
fourth
Chapter
of
the
different
moouinges
which
the
Occean
sea
hath
.
IT
hath
beene
declared
,
in
the.
2.
chapter
of
this
2.
booke
,
that
a
great
part
of
the
water
of
the
sea
doeth
ingender
in
the
north
,
and
from
thence
it
runneth
to
the
south
,
and
this
is
one
of
the
moouinges
which
the
water
of
the
sea
hath
:
wee
doe
likewise
see
that
the
sea
when
it
floweth
mooueth
towardes
one
parte
and
when
it
ebbeth
it
moueth
to
the
contrary
,
hauing
such
order
,
that
where
it
began
first
to
flowe
▪
there
it
beginneth
first
to
ebbe
,
whereby
it
seemeth
that
the
water
of
the
sea
hath
contrary
moouings
one
from
another
,
and
besides
this
wee
see
that
the
riuers
runne
to
the
sea
,
and
also
the
sea
commeth
vp
by
them
,
and
this
seemeth
meruellous
in
nature
:
for
the
water
naturally
goeth
downwarde
,
as
a
body
which
is
heauie
,
as
it
is
,
and
if
the
riuers
be
higher
then
the
sea
,
the
sea
should
not
goe
vp
into
them
,
and
if
the
Sea
be
higher
then
the
riuers
they
woulde
not
runne
into
the
sea
,
wherby
with
reason
it
may
be
doubted
,
saying
.
(
A
Doubt
,
)
what
is
the
cause
seeing
that
all
the
waters
of
the
sea
,
being
one
bodie
haue
so
many
different
and
contrary
moouinges
,
so
that
some
waters
are
moouing
towardes
one
place
,
and
some
towards
another
,
whereby
it
may
be
sayde
eyther
that
the
sea
mooueth
it selfe
in
these
moouinges
by
chance
,
and
without
any
order
,
or
that
shee
is
mooued
by
different
moouinges
or
mouers
(
A
declaration
,
)
To
these
doubtes
Albertus
magnus
answereth
,
in
the
second
of
the
Metheoros
the
sixth
chapter
of
the
third
treatie
where
he
sayth
,
absoluing
all
the
difficulties
,
which
are
put
,
touching
these
moouinges
of
the
sea
,
wee
say
with
Seneca
that
there
is
no
other
cause
of
the
course
of
the
waters
,
to
one
place
or
other
,
but
the
places
which
are
high
or
low
,
(
except
that
only
mouing
,
whereby
the
sea
ebbeth
or
floweth
,
)
for
in
this
it
followeth
the
circle
of
the
moone
,
as
wee
teach
in
another
place
:
And
that
the
saying
of
Seneca
is
true
,
it
is
prooued
because
the
waters
of
the
sea
doe
come
flowing
to
all
partes
of
the
worlde
,
that
is
to
say
,
to
the
east
,
and
to
the
west
,
to
the
north
&
to
the
south
.
And
▪
likewise
they
goe
ebbing
from
all
the
sayde
partes
.
And
therefore
the
Sea
hath
no
parte
proper
where
his
flowing
and
ebbing
doeth
beginne
,
so
that
by
accedent
the
water
mooueth
it selfe
from
one
place
to
another
,
vnlesse
it
be
downe
right
,
for
because
this
moouing
commeth
not
to
it
by
any
accedent
but
by
proper
essence
,
consequentlie
to
his
forme
.
The
fyfth
Chapter
wherefore
the
Sea
neuer
ouerfloweth
,
nor
is
augmented
nor
made
greater
.
IT
may
be
asked
what
is
the
cause
,
seeing
that
in
the
sea
there
is
so
muche
water
ingendred
,
and
continually
entreth
into
her
so
many
riuers
and
fountaines
,
wherefore
shee
neuer
ouerfloweth
nor
is
augmented
.
To
this
is
some
cause
the
whiche
Albertus
th●
great
bringeth
in
the
second
of
his
metheoros
where
hee
saith
,
the
sea
receyueth
no
augmentation
nor
yet
maketh
it self
greater
,
for
because
she
is
a
naturall
receiuer
of
all
the
waters
,
and
is
their
quiet
place
.
And
the
place
cannot
ouerflowe
,
with
the
comming
in
of
the
thing
which
by
nature
ought
to
bee
in
this
place
:
for
the
place
ought
to
be
conformable
with
that
whiche
it
shutteth
into
it
according
to
nature
,
so
that
the
sea
is
able
to
receaue
into
it
al
the
riuers
.
And
for
the
entrance
of
them
neither
to
ouerflowe
nor
to
augment
it self
.
Likewise
it
ouerfloweth
not
by
reason
that
the
Sea
is
so
great
that
the
riuers
in
the
respect
of
her
are
nothing
,
for
there
is
not
any
thing
in
them
able
to
augment
it
▪
The
third
reason
is
because
the
heate
of
the
sunne
and
the
blowing
of
the
windes
doe
consume
so
great
parte
of
the
water
,
that
although
it
ingender
continually
in
the
sea
and
continually
the
riuers
enter
into
her
:
yet
in
such
order
God
disposed
it
that
it
:
neyther
decreaseth
nor
encreaseth
.
And
so
it
may
be
sayde
that
which
is
written
in
Iob
,
Lorde
thou
diddest
appoint
her
a
precinct
,
that
she
should
not
breake
it
.
And
it
is
to
be
noted
,
that
in
the
floode
of
Noah
.
The
holy
scripture
saith
in
Gene●●s
the
seauenth
chapter
,
that
the
water
did
●ise
vp
fifteene
cubites
vpon
the
most
high
mountaine
that
is
vnder
the
heauen
,
so
that
all
the
earth
was
coueted
with
water
.
But
although
that
this
encreasing
of
the
waters
were
so
great
,
the
sea
did
not
ouerflowe
nor
did
couer
the
earth
,
by
going
foorth
of
her
limmet
and
precinct
.
But
the
great
encrease
of
waters
came
for
two
causes
,
one
was
that
the
windowes
&
cloudes
of
heauen
were
opened
,
and
it
raigned
fortie
dayes
and
fortie
nights
very
leisurly
.
The
seconde
was
that
the
fountaynes
and
riuers
of
freshe
water
did
runne
so
much
that
all
the
earth
was
couered
as
it
is
sayde
,
so
that
all
liuing
things
which
were
vpon
the
earth
did
perishe
(
except
Noah
and
all
that
were
in
the
arke
)
But
the
rayne
being
ceased
,
the
sayde
text
saith
,
that
God
sent
such
great
windes
,
that
they
consumed
the
water
,
&
returned
the
earth
to
his
own
perfectnes
.
The
sixth
Chapter
of
the
excellencie
of
the
Nau●gation
,
and
of
the
antiquitie
therof
.
WIth
reason
it
may
bee
sayde
that
the
nauigation
hath
great
excellency
seeing
that
God
was
the
first
that
commanded
to
make
a
shippe
or
instrument
to
goe
vppon
the
water
:
so
it
is
written
in
Genesis
the
sixte
chapter
where
is
sayde
that
God
commanded
Noah
to
make
a
ship
or
arke
of
timber
.
This
Arke
had
.
300.
cubites
in
length
.
and
50.
in
bredth
,
and
30.
in
hight
,
of
these
cubites
,
there
are
diuerse
opinions
what
length
they
were
of
,
some
say
after
the
manner
of
Geometry
,
others
say
common
,
with
more
reason
it
seemeth
they
were
in
manner
of
Geometrie
,
because
they
should
be
greater
,
for
it
was
conuenient
that
in
the
arke
there
shoulde
be
〈◊〉
for
that
which
shoulde
be
put
there
in
.
S.
Isidore
writeth
of
the
nauigation
in
the
Ethimologias
that
the
Lidians
were
those
that
first
found
out
the
making
of
shippes
,
but
these
did
not
attain
to
more
knowledge
then
to
ioyne
one
timber
with
another
,
and
were
wel
calked
and
nayled
,
they
sayled
in
them
not
departing
farre
from
the
lande
,
after
that
Epaminundas
,
the
Greeke
made
an
end
to
put
shippes
to
sayl
in
perfection
,
and
so
in
the
warres
of
Peloponeso
ther
was
founde
that
notable
captaine
,
Bias
with
shippes
,
carrackes
,
and
Gallies
.
In
the
third
of
the
kinges
in
the
;
10.
chapter
is
reade
that
Salomon
king
of
Hierusalem
sent
two
shippes
to
Tharsis
.
and
euery
three
yeere
they
went
and
came
from
whence
they
brought
golde
siluer
,
woorkes
of
Iuorie
,
and
apes
.
Iulio
Solino
sayth
that
al
the
sea
towardes
the
south
,
which
doeth
compasse
Affrica
about
behinde
and
from
the
India
to
Spaine
was
sayled
,
and
of
this
hee
bringeth
testimonie
of
the
king
of
Inba
for
the
confirmation
&
argument
thereof
he
maketh
mo●tion
of
Ilandes
,
and
of
a
certaine
people
the
manne●s
and
confines
of
the
places
&
the
spaces
of
them
Plato
in
the
.32
.
booke
,
in
the
dialogue
of
Tim●o
,
sayth
that
from
an
Iland
called
the
colūnes
or
pillers
of
Hercules
,
which
is
at
the
mouth
of
a
straight
there
was
failing
to
a
firme
land
,
which
contained
greater
then
all
Affrica
&
Asia
;
wherby
it
appeareth
that
before
the
time
of
Plato
was
sayling
from
the
Iland
of
Cadiz
,
which
is
at
the
mouth
of
the
straite
of
Iebralter
vnto
the
land
of
the
Indias
which
we
now
haue
.
Pliny
writeth
,
that
gouerning
the
thinges
of
the
empire
of
Tiberius
Caesar
there
did
appeare
in
the
coast
of
the
sea
of
Arabia
signes
of
ships
that
the
Spaniardes
had
lost
.
Cornelius
Nepote
geueth
knowledge
that
in
his
time
one
that
was
called
E●do●
〈◊〉
from
the
latine
king
sayling
by
the
sea
of
Arabia
,
and
likewise
sayth
that
he
saw
one
Ce●●
Antipatro
that
called
with
merchandise
from
Spain
Ehiopia
.
In
the
time
of
Augustus
〈◊〉
most
pa●●
the
north
Occean
seas
were
sailed
round
about
.
Al
〈◊〉
vnto
the
cape
of
the
land
of
the
〈…〉
.
Reyhold
Seleuco
and
Anthioco
saye
that
the
riuers
of
the
Caspian
sea
were
sayled
and
known
with
the
armies
of
those
of
Macedonia
:
As
also
they
sailed
all
the
north
parts
from
one
place
to
another
.
Plinie
himselfe
vseth
the
testimony
of
Cornelius
Nepote
who
affirmeth
that
the
king
of
the
Sweuians
or
Esquicaros
gaue
to
Metello
Celeri
chiefe
consull
of
Fraunce
certain
Indians
the
which
sailing
from
the
India
with
merchandise
were
driuen
into
Almain
with
tempest
of
weather
.
Likewise
it
is
read
in
Othō
that
in
the
time
of
the
Iermain
emperours
certaine
ambassadours
of
the
India
were
found
in
the
riuers
of
Almaine
which
were
driuen
thither
with
great
windes
,
&
if
was
not
doubted
that
they
came
from
the
region
towards
the
cast
,
which
could
not
be
if
it
be
as
some
doe
think
that
the
north
seas
be
frosen
Pope
Pio
the
3.
saith
that
in
the
booke
he
wrote
of
Geographie
and
reason
doth
manifest
,
&
shew
the
the
sea
in
old
time
was
sailed
seeing
that
the
men
of
old
time
did
put
names
vnto
the
riuers
of
the
O●cean
sea
,
which
doth
compasse
about
the
farthest
parts
of
the
earth
,
of
the
great
number
&
multitude
of
ships
that
was
molde
time
some
authors
haue
written
.
Homer
.
saith
that
in
the
host
of
the
Greekes
which
came
vnto
Troy
were
1180.
ships
,
likewise
Diodorus
saith
that
Xerxes
king
of
the
Persians
brought
in
his
against
Gretia
,
700000.
men
of
his
owne
,
&
300000.
of
his
friendes
,
and
when
became
to
the
Sea
called
Pontico
,
hee
made
in
the
sea
a
bridge
of
ships
whereby
he
past
with
his
people
so
that
the
ships
being
together
,
reached
from
the
land
of
Asia
vnto
that
of
Europa
,
which
is
at
the
least
a
league
of
sea
.
The
7.
chapter
how
by
some
signes
of
the
sun
&
of
the
moone
may
be
known
when
stormes
wil
come
.
MAny
times
there
happeneth
to
be
in
the
Sea
tempests
of
winds
&
waters
which
doe
cause
greate
stormes
whereof
followeth
to
such
as
are
saylers
death
or
losses
of
ships
and
goods
or
other
great
troubles
:
therfore
here
I
mind
to
declare
the
signes
as
I
find
them
written
by
the
which
the
sayd
tempests
or
stormes
may
be
known
&
being
foreseen
or
known
they
may
do
les
hurt
.
This
pleased
V●rgil
greatly
,
who
sayth
,
that
many
hurtfull
battels
of
windes
doe
come
vpon
the
ignorant
:
it
is
trade
of
Democrito
the
Philosopher
,
that
a
brother
of
his
being
reaping
in
time
of
great
heat
,
who
was
called
Damaso
,
the
sayde
Philosopher
sayde
vnto
him
,
that
he
should
reape
no
more
,
but
shoulde
gather
together
that
he
had
reaped
,
&
keepe
it
,
for
shortly
would
come
a
great
tempest
of
wind
,
that
would
carry
it
away
from
him
,
And
so
a
fewe
houres
being
past
.
It
followed
as
the
Philosopher
had
said
,
after
declaration
made
of
signes
or
prognostication
of
the
tempests
or
stormes
,
there
shall
bee
first
noted
,
those
which
are
shewed
in
the
Sunne
.
The
signes
of
the
Sunne
.
Plinie
in
his
natural
history
the
eighteenth
booke
Chapter
forty
fiue
sheweth
that
if
the
Sunne
when
it
riseth
be
cleere
and
not
cloudie
,
foresheweth
a
fayre
day
,
if
it
seeme
yellow
,
it
foresheweth
rayne
with
hayle
.
It
when
the
sun
doth
rise
it
seemeth
hollow
,
it
foresheweth
rain
and
winde
,
if
when
the
sunne
doth
rise
there
be
cloudes
before
it
,
and
shewe
redde
,
and
parte
of
the
sayde
cloudes
are
dispersed
abrode
towardes
the
north
and
part
towardes
the
south
it
signifieth
windes
with
great
rayne
:
Jf
when
the
Sunne
riseth
&
setteth
doe
appeare
any
streekes
gathered
together
neere
it
,
if
foresheweth
rayne
:
If
before
the
Sunne
rise
do
appeare
vpon
it
round
cloudes
it
foresheweth
great
colde
,
this
is
if
after
Sunne
rising
they
goe
towardes
the
south
,
but
if
they
goe
towardes
the
west
it
signifieth
fayre
weather
.
Jf
cloudes
doe
compasse
the
Sunne
rounde
aboute
the
lesse
light
and
cleerenes
they
geue
signifieth
,
the
greater
tempest
,
and
it
will
be
the
greater
if
her
roundnes
doe
seeme
dubled
.
If
in
the
rising
of
the
Sunne
do
appeare
redde
,
cloudes
lying
ouer
the
sun
being
brought
thither
by
any
manner
of
winde
it
signifieth
that
the
selfe
same
winde
will
blowe
,
but
if
it
be
a
southerly
winde
it
betokeneth
rayne
.
If
when
the
Sunne
riseth
if
be
compassed
aboute
with
cloudes
,
from
that
part
where
the
roundnes
doth
discouer
,
it
is
to
be
loked
for
that
the
wind
will
come
,
but
if
it
discouer
all
,
it
signifieth
equally
faire
weather
.
If
when
the
Sunne
riseth
shee
extend
her
beames
farre
of
,
by
the
clouds
and
in
the
middest
it
seemeth
emptie
,
foresheweth
rayne
.
If
beefore
the
sunne
come
foorth
shee
shew
her
becames
it
foresheweth
water
and
winde
.
If
when
the
sunne
shall
let
,
her
circle
be
white
,
it
foresheweth
some
tempest
that
night
,
and
if
it
be
very
hote
,
there
will
be
winde
.
If
when
the
sunne
doth
set
,
her
round
bodie
doth
seeme
blacke
or
thicke
of
the
parte
which
is
moste
discouered
,
it
will
blowe
much
winde
.
The
signes
of
the
Moone
.
Seeing
there
hath
beene
declared
the
signes
of
the
sunne
,
for
to
know
the
tempestes
or
stormes
that
are
to
come
I
will
speake
of
the
thinges
which
are
to
come
,
that
the
moone
sheweth
.
In
A●gypt
they
keepe
holy
day
,
the
fourth
daye
of
the
moone
the
whiche
if
shee
seeme
shining
with
a
cleane
brightnes
it
foresheweth
a
very
fayre
day
,
and
if
she
shewe
redde
it
betokeneth
much
winde
,
if
blacke
it
signifieth
raine
,
if
in
the
fifth
day
her
hornes
be
not
sharp
&
small
,
but
great
and
brode
,
it
foresheweth
rayne
.
If
the
moone
be
straight
and
shewe
her selfe
vpwarde
it
signifieth
winds
&
chiefelie
when
this
is
in
the
fourth
day
.
If
the
moone
being
foure
dayes
old
,
&
her
roundnes
be
of
an
Alborne
●ulle●
it
signifieth
great
windes
,
the
authour
hereof
is
Var●o
.
Pl●nie
sayth
that
if
in
the
fourth
day
of
the
moone
she
be
vpright
it
betokeneth
tempest
in
the
sea
:
vnlesse
that
all
rounde
about
her
she
hath
a
circle
very
cleere
.
If
at
the
full
moone
in
the
middest
of
her
shee
be
cleere
if
sheweth
a
token
of
fair
weather
,
or
if
she
be
of
an
alborne
colour
or
like
to
a
rose
colour
it
foresheweth
windes
,
if
she
be
blacke
it
foresheweth
rayne
.
When
at
her
rising
shee
rise
with
the
vpper
parte
of
her
horne
blacke
about
,
at
the
decreasing
of
the
moone
,
it
wil
rain
,
and
if
likewise
her
horne
be
blacke
beneath
rounde
aboute
beefore
the
full
moone
it
also
foresheweth
rayne
.
If
the
moone
being
at
the
●ull
haue
a
circle
round
about
her
of
that
parte
which
doeth
shewe
most
bright
,
will
the
winde
come
.
If
at
the
first
appearing
of
the
moon
that
is
to
say
when
shee
is
newe
,
the
bornes
of
her
doe
shewe
great
it
signifieth
tempest
.
And
it
shall
be
the
greater
if
before
the
fourth
day
the
wind
do
not
blows
at
the
west
.
If
at
the
sixteenth
day
of
the
moone
the
seeme
to
be
of
a
great
colour
of
flame
it
foresheweth
tempest
.
The
eyght
Chapter
of
the
fires
and
lightes
,
which
doe
appeare
in
shippes
that
doe
sayle
when
there
is
torment
or
tempest
in
the
Sea
.
IT
happeneth
to
such
as
doe
sayle
when
there
is
stormes
in
the
sea
when
it
seemeth
that
they
should
be
lost
that
al
night
they
see
vpon
the
maste
or
yarde
or
in
some
other
parte
of
the
shippe
a
certaine
fire
or
clearenes
,
the
which
some
saylers
call
,
S.
Edmund
,
which
ought
not
to
be
so
taken
,
seeing
that
it
is
not
as
they
thinke
,
therfore
I
say
that
these
fires
or
lightes
are
a
certain
impression
in
the
ayr
which
the
Greekes
call
Pili
Deuces
,
&
is
so
called
by
meanes
of
the
grosenes
of
the
humor
which
goeth
from
the
earth
&
fighteth
with
the
coldnes
of
the
might
,
&
so
it
gathereth
it selfe
together
and
congealeth
in
the
first
region
of
the
ayre
,
and
when
his
exhalation
findeth
any
body
wherunto
to
cleaue
,
it
kindleth
and
holdeth
it selfe
fast
to
it
vntill
it
be
consumed
and
wasted
.
This
fire
burneth
not
.
And
Plinie
in
his
second
booke
of
the
naturall
historie
,
the
thirtie
seauen
chapter
,
saith
that
when
these
fires
be
two
they
be
called
Pollux
&
Castor
and
it
is
a
good
signe
,
and
when
it
is
but
one
it
is
called
Hellena
,
and
it
is
an
euil
signe
.
These
fires
are
also
seene
in
the
lande
.
And
they
haue
beene
seene
in
the
campes
vpon
the
pikes
which
the
souldiers
carry
,
and
vpon
the
deade
bodies
.
And
Plinie
sayth
also
that
they
haue
beene
seene
vppon
the
heades
of
men
,
and
of
beastes
,
And
so
did
Virgil
affirme
that
it
appeared
vpon
the
head
of
lulio
Escanio
:
In
the
campes
of
the
wars
these
fires
doe
appeare
as
wel
because
of
the
continuall
fumes
,
as
also
because
of
the
heate
of
many
people
:
Jn
the
ships
they
ingender
of
the
fume
of
the
said
ship
and
of
the
heate
of
the
people
gathered
together
into
little
rome
,
and
of
the
Marriners
and
people
in
the
shippe
,
which
in
the
stormes
with
the
greate
moouing
they
haue
,
doe
ingender
heate
:
this
is
when
there
is
disposition
that
the
rising
vp
of
the
vapour
,
shoulde
make
impression
in
the
ayre
,
as
before
is
sayde
:
And
Plini●
saide
that
one
only
fire
is
no
good
signe
.
This
is
because
when
there
are
two
it
seemeth
that
in
the
ayre
is
abundance
of
grosse
smoke
and
signifieth
that
it
is
sufficient
to
consume
the
matter
of
the
tempest
.
Peter
de
Castroboll
,
vpon
the
seconde
of
the
Metheoros
sayth
,
that
whensoeuer
these
fires
are
seene
in
a
tempest
,
it
is
a
good
signe
,
for
it
noteth
faire
weather
.
Likewise
it
happeneth
,
that
there
are
great
stormes
,
&
none
of
these
fires
are
seene
,
and
in
small
stormes
they
see
sometime
one
or
twoo
,
so
that
the
sayle●s
shoulde
haue
no
deuotion
vnto
these
fires
to
beleeue
that
Sainte
Edmunde
is
there
,
for
it
is
a
naturall
thing
.
And
therefore
euery
one
with
his
deuotion
ought
to
commende
himselfe
too
GOD
,
that
hee
keepe
them
,
and
bryng
them
foorth
of
that
Storme
,
and
putte
them
in
the
porte
of
saluation
.
The
nienth
chapter
of
other
certaine
signes
,
wherein
shall
be
knowne
when
stormes
will
come
in
the
sea
.
IN
the
seuenth
chapter
of
this
second
booke
I
haue
declared
some
signes
of
the
sunne
&
the
moone
wherby
may
be
knowne
when
stormes
of
winde
and
raine
will
come
,
as
it
is
declared
:
and
because
these
stormes
are
thinges
,
that
vnto
such
as
saile
is
very
conuensent
they
shoulde
knowe
,
and
preuent
:
it
seemed
well
to
mee
to
adde
this
present
chapter
in
the
which
,
I
will
also
declare
other
fiue
signes
or
prognostications
,
which
I
finde
written
,
that
ought
to
be
looked
on
and
knowne
of
the
saylers
,
which
are
these
following
.
The
first
is
when
in
the
high
places
or
in
the
woodes
there
is
heard
a
noyse
of
winde
,
and
abrode
it
is
not
heard
it
signifieth
stormes
of
winde
.
The
second
when
the
waues
of
the
scaswel
and
giue
great
falles
or
strokes
in
the
bayes
of
the
sea
being
with
great
noyse
or
ratling
,
signifieth
stormes
in
the
sea
:
of
these
2.
Plinie
is
the
author
in
the
eigteenth
booke
of
the
naturall
historie
.
The
thirde
,
if
the
sea
being
calme
doeth
make
a
nosse
within
it selfe
signifieth
great
windes
:
of
this
speaketh
Virgil
in
the
tenth
of
Ac●eados
and
Lucano
.
The
fourth
when
the
Porpisses
of
the
sea
goe
leaping
vpon
the
sea
,
and
shew
them selues
vppon
the
Waues
is
a
signe
of
stormes
,
And
that
the
wind
will
come
from
that
place
that
they
come
,
This
S.
Isidore
bringeth
in
the
twelfth
of
the
Etimologias
.
Of
the
fifth
,
Virgil
,
saith
,
in
the
Georgians
that
when
the
Sea
Meowes
or
Gulles
doe
leaue
the
sea
and
goe
to
the
drye
lande
it
signifieth
stormes
in
the
Sea
.
¶
The
ende
of
the
second
booke
.
¶
The
third
booke
of
the
Windes
,
and
their
quallities
,
and
names
,
and
how
one
should
sayle
with
them
.
The
first
chapter
what
thing
the
winde
is
,
and
what
quallitie
it
is
of
,
and
howe
it
ingendreth
.
FOR
the
declaration
of
the
nature
of
the
winde
,
for
the
diuersitie
of
the
doubtes
that
are
of
it
,
some
say
it
is
the
ayre
and
it
moueth
:
others
say
that
it
is
water
:
others
that
it
is
a
vapour
of
the
earth
:
and
others
,
that
it
is
some
great
celestiall
body
,
or
other
,
that
with
great
force
and
violence
doth
pushe
forwarde
the
ayre
.
And
this
cannot
bee
determined
,
if
his
nature
bee
not
considered
in
that
which
principally
it
is
.
The
which
I
say
that
the
winde
is
a
vapour
of
the
earth
that
riseth
vppe
and
stretcheth
euen
to
the
highest
parte
of
the
ayre
and
strongly
thrusteth
foorth
the
ayre
.
This
vapour
is
hote
and
dry
,
and
by
his
subtiltie
doth
pearce
the
ayre
:
for
as
the
winde
is
of
a
subtile
vapour
in
his
kinde
,
and
being
subtile
and
light
,
it
is
natural
to
rise
vp
&
so
it
riseth
vp
,
&
of
the
subtilt●e
of
the
vapour
of
the
earth
,
he
is
made
,
and
from
thence
he
descendeth
,
&
in
his
descending
he
sheweth
that
the
vapour
mooueth
it selfe
vnto
a
high
place
&
as
he
is
come
to
that
place
is
made
winde
,
and
so
hee
descendeth
blowing
.
And
it
is
to
be
vnderstoode
,
that
the
vapour
riseth
not
so
high
as
the
superiour
parte
of
the
ayre
,
which
is
called
Estus
,
but
riseth
vp
to
the
colde
part
,
&
there
as
Algazel
saith
with
the
colde
,
he
waxeth
thicke
and
descendeth
of
the
which
it
seemeth
,
that
the
vapour
wherof
the
winde
is
made
,
is
not
congregated
with
the
inwarde
colde
as
some
say
,
but
with
the
outwarde
cold
of
the
place
,
by
the
which
as
Algazel
saith
,
he
is
letted
that
he
come
not
to
the
superiour
parte
of
the
ayre
.
Likewise
it
is
proued
,
that
the
vapour
is
raised
vp
with
heate
,
and
for
this
,
if
the
heat
of
ayre
round
about
doe
helpe
him
,
it
heateth
the
more
:
for
the
●●ner
heat
is
holpen
by
the
outward
heat
,
&
so
if
it
were
not
for
the
cold
of
the
place
,
he
would
neither
waxe
thicke
nor
blowe
.
The
2.
Chapter
,
how
the
wind
moueth
not
right
from
aboue
downward
:
nor
contrarywise
,
but
his
mouing
is
in
circle
of
water
and
earth
.
FUrther
for
the
mouing
of
the
winde
,
it
is
to
bee
noted
that
it
moueth
not
from
aboue
downward
,
nor
from
beneath
vpward
but
it
moneth
in
circuler
or
round
manner
,
of
the
water
and
the
earth
:
so
saith
Albertus
the
great
in
the
treatie
of
windes
,
chap.
12.
all
windes
commonly
moue
their
blast
&
mouing
in
circle
manner
,
in
such
sort
,
that
they
moue
not
vp
vnto
that
which
is
high
nor
descendeth
to
that
which
is
lowe
:
but
moueth
by
the
round
superficiall
of
the
earth
,
and
water
in
the
ayre
in
circuler
manner
,
as
appeareth
by
the
cloudes
:
that
with
the
windes
goe
vp
&
descend
down
from
the
East
,
into
the
West
:
euen
like
to
the
moouing
of
the
starres
.
Where
it
is
to
bee
vnderstood
,
by
the
doctrine
of
the
Astronomers
,
that
there
are
some
starres
,
which
moue
the
winds
,
as
lupiter
,
that
moueth
northerly
winds
:
&
the
sunne
moueth
Easterly
winds
:
and
Mars
moueth
the
blast
of
Southerly
winds
:
&
the
Moone
moueth
,
Westerly
windes
.
This
is
as
it
were
a
beginning
,
as
euery
manner
of
cause
,
by
his
owne
meanes
induceth
to
one
effect
,
&
therfore
it
is
conuenient
that
the
effect
doe
immitate
the
moouing
of
the
cause
.
And
seeing
that
the
star●es
doe
moue
in
circuler
manner
,
it
is
conuenient
that
the
wynd
should
moue
like
a
bowe
vpon
his
Horison
.
In
like
manner
it
is
saide
,
when
the
signes
doe
cause
winds
to
blowe
,
because
there
are
three
signes
,
which
haue
hotte
and
drie
qualities
,
which
are
these
,
Aries
,
Leo
and
Sagitarius
:
and
this
is
called
the
triplicitie
of
the
fire
.
And
these
are
called
Easterly
signes
,
because
they
moue
the
winds
of
the
East
part
.
There
are
other
three
signes
,
which
haue
cold
and
drie
qualities
.
These
are
Taurus
,
Virgo
,
and
Capricorne
:
and
this
is
called
triplicity
of
the
earth
,
these
signes
are
called
Meridionales
,
because
they
moue
the
Southerly
winds
continually
.
There
are
other
3.
signes
,
which
haue
their
qualities
hot
and
moyst
:
these
are
Gemini
,
Libra
,
&
Aquarius
:
&
this
is
called
the
triplicitie
of
the
ayre
.
These
are
called
occidentall
or
Westerly
signes
,
because
they
moue
the
winds
of
the
West
part
.
There
is
another
fourth
triplicitie
of
the
other
3.
signes
,
which
are
Cancer
,
Scorpio
,
&
Pisces
,
And
this
is
called
triplicity
of
the
water
:
for
because
his
property
is
colde
and
moyst
,
and
these
signes
doe
moue
the
Northerly
winds
,
&
that
humor
which
they
haue
in
his
propertie
,
they
cause
to
abounde
in
the
times
so
attributed
in
those
bodies
,
where
they
are
ingendred
.
Of
the
aforesaide
,
it
is
concluded
:
that
the
winds
do
moue
themselues
in
r●ūdnesse
of
the
water
and
earth
like
to
the
mouing
of
the
starres
,
and
not
right
going
vpward
nor
descending
.
For
the
vapour
is
eleuated
with
the
heate
,
and
is
expelled
with
the
colde
,
which
congealeth
him
,
and
so
it
is
conuenient
,
that
the
wynde
descende
not
right
downe
,
for
the
heate
that
riseth
vp
,
but
that
it
bee
by
one
side
in
the
circuite
of
water
and
earth
.
And
this
reason
Aristo●le
giueth
.
The
3.
Chapter
,
wherefore
the
wynde
is
not
alwayes
alike
:
but
at
sometime
bloweth
harde
,
and
at
other
times
calme
:
and
wherefore
it
moueth
to
his
opposite
.
WIth
reason
might
be
asked
two
doubtes
concerning
the
wind
,
which
are
these
:
(
the
first
doubt
.
)
What
the
cause
is
wherfore
when
the
winde
beginneth
his
blast
,
it
is
not
equall
,
but
sometimes
harde
,
and
other
times
more
calme
.
And
sometimes
it
ceaseth
,
and
other
times
it
turneth
to
blowe
,
so
that
it
bloweth
not
continuallye
after
one
sort
.
(
the
second
doubt
.
)
The
second
is
,
wherfore
the
winde
mooueth
to
his
opposite
,
for
so
we
cal
it
when
from
the
east
he
goeth
to
the
west
:
And
from
the
north
to
the
south
,
and
likewise
contrary
,
of
this
it
seemeth
that
there
is
no
reason
,
because
the
Uapour
whiche
is
the
roote
of
the
winde
either
followeth
his
moouing
which
is
to
bee
eleuated
because
he
is
hote
,
and
according
as
it
is
straight
so
it
ought
to
goe
vpwarde
,
or
follow
his
matter
which
is
earthly
,
&
at
it
is
straight
,
ought
to
descend
.
Likewise
what
doth
make
the
winde
to
mooue
more
to
one
side
then
to
the
other
,
rather
then
to
moue
it self
straight
so
that
the
east
likewise
should
mooue
it selfe
towardes
the
north
,
or
towardes
the
south
,
as
towardes
the
west
,
and
likewise
of
the
other
windes
.
Item
all
thinges
whiche
are
ingendred
in
one
place
naturally
mooue
not
vnto
the
place
opposite
:
so
that
if
the
easterly
winde
be
ingendered
in
the
east
,
and
the
northerly
wind
in
the
north
,
they
ought
to
mooue
to
their
owne
place
,
and
not
to
the
place
opposite
.
By
the
which
it
is
to
be
said
that
the
windes
mouing
of
them selues
to
their
opposite
is
violent
,
and
against
nature
,
or
the
matter
of
the
windes
is
maruellous
&
vnknowne
to
vs
.
(
The
first
declaration
.
)
The
first
is
to
be
vnderstoode
that
as
the
matter
of
the
winde
,
which
is
the
vapour
of
the
earth
,
riseth
vp
by
little
&
little
,
maketh
a
weake
&
little
moouing
:
But
as
he
is
encreased
in
great
quantitie
:
so
with
a
great
force
hee
descendeth
and
maketh
a
strong
winde
.
Also
the
winde
bloweth
not
continually
alike
because
the
matter
which
riseth
vp
is
not
alwayes
equal
nor
is
equally
put
forward
,
for
the
colde
is
more
or
lesse
,
&
the
vapour
not
equally
congealed
.
And
therfore
the
winde
at
one
time
bloweth
hard
,
and
at
another
time
soft
,
(
The.
2
declaration
.
)
The
2.
is
to
be
vnderstoode
,
that
the
wind
to
mooue
to
his
opposite
is
for
two
causes
.
The
1.
is
as
Alpetragio
sayth
,
the
stars
doe
mooue
in
circle
manner
;
&
so
the
wind
doth
immitate
the
circle
mouing
,
The
2.
as
Albertus
saith
,
that
it
is
more
naturall
,
because
the
vapour
is
ingendred
of
heate
,
&
is
expelled
&
thrust
out
of
the
cold
,
&
the
cold
is
behinde
the
heat
,
&
therefore
is
thrust
out
to
his
opposite
,
so
that
he
cannot
go
vpright
for
the
cold
that
is
in
the
ayre
nor
can
descend
,
for
the
heat
that
riseth
vp
,
nor
can
returne
backward
for
the
colde
which
is
behind
him
:
and
therfore
it
is
necessary
,
that
he
moue
in
circle
manner
to
his
opposite
,
&
as
much
as
that
which
is
said
that
nothing
moueth
forth
from
the
place
of
his
generation
it
is
to
be
noted
,
that
which
is
of
the
nature
of
ayre
,
mooueth
it selfe
to
the
place
of
ayre
,
and
the
ayre
hath
place
in
all
partes
,
and
the
vapour
hath
the
nature
of
aire
as
much
as
apperteineth
to
his
seldom
mouing
so
that
he
moueth
not
forth
of
his
place
.
The
4.
chapter
,
of
the
whirling
of
the
winde
,
and
how
it
is
caused
.
IT
hath
been
spoken
before
that
the
mouing
which
the
winde
maketh
is
mouing
himself
to
his
opposite
by
the
roundnes
of
the
water
&
earth
,
&
not
going
vpright
nor
descending
,
as
it
hath
been
proued
,
&
experience
in
the
nauigation
doth
shew
it
:
and
seeing
that
it
is
so
it
may
be
asked
what
is
the
cause
that
many
times
the
winde
maketh
his
mouing
right
from
beneath
vpward
.
This
we
see
that
the
winde
raiseth
vp
from
the
ground
the
dust
and
the
straw
,
and
carrieth
them
vpright
one
heigh
which
is
commonly
a
whirlwind
,
and
this
is
as
well
caused
or
done
in
the
sea
as
in
the
Lande
.
And
in
the
Sea
it
is
made
wel
neere
like
a
right
sleeue
,
&
by
it
the
water
riseth
upwarde
,
as
many
times
it
is
seen
▪
Wherby
it
s●emeth
that
the
wind
hath
likewise
a
straight
mouing
,
that
is
to
say
from
beneath
vpward
,
as
the
mouing
in
roundnes
before
is
declared
.
To
this
is
to
bee
noted
that
this
moouing
,
which
the
winde
maketh
is
not
naturall
to
it
,
but
accidentall
and
violent
:
for
because
it
is
done
by
force
,
by
meeting
together
in
this
manner
:
when
one
winde
commeth
from
one
part
,
and
another
from
another
part
contrary
,
&
the
strength
of
the
one
,
doth
meete
with
that
of
the
other
as
euery
one
of
them
hath
no
free
running
,
by
the
let
of
the
winde
he
findeth
contrary
:
then
he
that
is
strongest
thrusteth
forwarde
the
other
,
and
so
they
put
themselues
into
roundnes
,
and
make
a
whirlewinde
vntill
they
be
deuided
.
This
appeareth
by
an
example
in
the
water
when
it
runneth
,
that
if
it
finde
another
body
that
doth
make
any
resistance
,
it
maketh
a
whirling
,
moouing
it
in
roundnes
:
euen
so
the
winde
as
it
findeth
resistance
of
another
winde
or
of
some
mountaine
,
or
of
any
like
thing
,
that
doth
resist
his
course
,
it
cannot
goe
forward
.
Therefore
hee
maketh
that
round
whirling
.
and
this
causeth
in
the
Sea
many
times
that
shippes
be
sunke
downe
vnder
the
water
,
when
they
find
themselues
vnder
such
a
whirlwinde
or
spout
:
for
the
water
which
the
winde
raiseth
,
doth
ouerwhelme
&
drown
them
.
Likewise
when
there
are
moouinges
of
contrary
windes
,
they
cause
to
rise
vp
stormes
in
the
Sea
,
which
the
saylers
many
times
may
know
before
hand
considering
and
beholding
the
moouing
of
the
cloudes
if
they
be
contrary
and
different
to
the
winde
that
is
beneath
.
For
when
it
is
so
,
it
is
a
token
that
contrary
windes
doe
runne
abrode
,
of
the
which
continually
the
superiour
doth
ouercome
:
because
he
is
of
more
strength
&
swiftnes
then
the
inferiour
.
The
fifth
chapter
,
of
the
windes
,
of
the
cardes
of
nauigation
,
of
their
number
,
&
names
.
AND
seeing
there
hath
byn
treated
of
the
winds
,
what
things
they
are
,
&
how
they
are
ingendred
and
mooue
,
In
this
I
wil
speake
of
the
winds
that
are
marked
in
the
cardes
of
nauigation
,
their
number
,
&
how
they
haue
their
names
according
to
the
●se
of
the
saylers
.
Of
the
which
it
is
to
be
vnderstood
that
the
windes
of
the
cardes
which
we
cal
courses
,
do
shew
forth
32.
names
of
windes
,
which
are
practised
in
the
nauigation
,
&
no
more
nor
lesse
:
&
the
reason
wherefore
this
number
is
geuen
,
is
because
the
roundnes
of
the
worlde
,
is
imagened
to
be
deuided
into
32.
partes
,
&
in
euery
one
of
these
is
assigned
one
wind
,
&
is
geuen
to
him
a
whole
name
,
or
halfe
,
or
a
quarter
,
according
to
the
part
where
it
seemeth
to
vs
that
he
commeth
;
as
hereafter
shall
be
declared
.
And
to
vnderstand
,
this
is
to
be
noted
,
that
this
roundnes
of
the
world
hath
4.
principal
regions
.
These
4.
partes
are
named
and
knowne
by
4.
windes
,
which
are
east
,
west
,
north
,
south
.
The
east
is
also
called
solan●
,
it
groweth
vnder
the
equinoctiall
line
,
it
is
also
called
lecuāte
,
because
the
sunn●
riseth
there
,
and
beginneth
to
appeare
in
the
morning
.
This
winde
is
called
in
the
nauigation
east
.
The
second
principall
winde
riseth
of
the
Occident
,
vnder
the
equinoctiall
line
,
it
is
called
poniente
,
because
the
sun
setteth
there
,
or
hideth
himselfe
in
the
evening
.
It
is
also
called
,
fauonio
,
and
in
the
nauigation
it
is
called
west
.
The
3.
principall
wind
is
called
,
Cierco
and
groweth
vnder
the
pole
artick
,
he
is
also
called
,
Aquilonall
,
and
Septemtrionall
,
Aquilonal
because
he
groweth
in
the
part
of
Aquilon
Semptentrional
by
the
7.
starres
of
the
Vrsa
minor
.
This
winde
in
the
nauigation
is
called
north
.
The
fourth
winde
is
called
Meridionall
he
commeth
forth
vnder
the
pole
antartike
,
he
is
called
Meridional
:
for
when
he
is
come
to
the
sun
,
there
he
maketh
vnto
vs
the
middest
of
the
daye
.
And
in
the
Nauigation
this
winde
is
called
South
.
These
Windes
are
marked
in
this
manner
.
These
foure
windes
haue
other
four
Colaterales
,
and
are
compounded
of
the
taking
a
name
of
halfe
the
name
of
euery
one
in
this
manner
.
The
1.
is
marked
betweene
the
north
and
the
east
,
and
taketh
name
of
both
,
and
therfore
is
called
northeast
.
The
second
is
between
the
east
and
the
south
,
and
is
called
southeast
.
The
third
is
between
the
south
and
the
west
,
and
is
called
southwest
.
The
fourth
is
betweene
the
west
&
the
north
,
and
is
called
northwest
,
and
is
marked
in
this
manner
.
These
8.
windes
are
called
in
the
nauigation
,
whole
winds
or
principalles
,
among
the
which
there
is
to
bee
marked
other
8.
which
are
called
halfe
windes
not
because
they
haue
lesse
force
than
the
1.
but
because
they
are
described
among
those
8.
winds
afoesaid
,
the
which
also
do
take
their
names
of
the
2.
windes
Colaterales
and
are
called
in
this
manner
.
The
first
is
described
between
the
north
and
the
northeast
,
and
taking
〈◊〉
of
both
of
them
is
called
North
Northeast
.
The
〈◊〉
called
east
,
northeast
,
because
he
standeth
between
the
east
and
the
northeast
.
The
third
is
east
southeast
,
because
he
is
between
the
east
&
she
southeast
.
The
〈◊〉
is
south
Southeast
,
because
he
〈◊〉
betweene
the
south
and
the
southeast
.
The
fifth
is
south
southwest
,
because
he
is
betweene
the
south
and
the
southwest
.
The
sixt
is
west
southwest
,
because
he
is
between
the
west
&
the
southwest
.
The
seuenth
is
west
northwest
,
because
it
is
betweene
the
west
and
the
northwest
.
The
eight
north
northwest
,
because
it
is
betweene
the
north
and
the
north
west
.
And
they
are
ordained
in
this
manner
.
Among
these
xvi
.
courses
of
winds
&
half
windes
,
are
marked
other
sixteene
which
are
named
quarters
,
and
they
are
put
in
this
manner
,
euery
one
of
the
eyght
principal
windes
hath
two
quarters
,
gathered
foorth
of
them
,
and
euery
one
of
them
doth
take
the
name
of
the
windes
nearest
to
him
,
in
this
manner
.
The
north
hath
two
quarters
,
which
is
by
the
part
of
the
northeast
,
and
is
called
North
and
by
east
,
&
that
which
is
by
the
part
of
the
northwest
is
called
north
and
by
west
.
The
northeast
hath
other
2.
&
that
which
standeth
towardes
the
north
,
is
called
northeast
and
by
north
,
and
that
which
standeth
towardes
the
〈◊〉
is
called
northeast
and
by
east
.
The
east
hath
other
two
that
which
is
towardes
the
parte
of
the
northeast
is
called
east
&
by
north
,
&
th●●
whiche
is
towardes
the
〈◊〉
of
the
so●th
is
called
east
and
by
south
▪
The
southeast
hath
two
quarters
,
that
which
is
towardes
the
east
part
,
is
pacled
southeast
and
by
east
,
&
that
whiche
is
towardes
the
south
part
,
southeast
&
by
south
.
The
south
hath
two
quarters
,
that
which
is
towardes
the
east
,
is
called
south
and
by
east
,
and
that
whiche
is
towardes
the
West
is
called
south
and
by
west
.
The
southwest
hath
other
2.
the
which
is
towardes
the
part
of
the
south
is
called
southwest
and
by
south
,
and
the
which
is
towardes
the
west
,
is
called
southwest
and
by
west
.
The
west
hath
two
quarters
,
that
which
is
towardes
the
southwest
is
called
west
and
by
south
,
&
that
whiche
is
towardes
the
part
of
northwest
is
called
west
and
by
north
.
The
northwest
hath
two
quarters
,
that
which
is
towardes
the
part
of
the
west
is
called
northwest
and
by
west
,
&
that
which
is
towardes
the
parte
of
the
north
is
called
northwest
and
by
north
,
They
are
ordayned
in
the
manner
following
.
The
.32
.
●indes
●n
the
com●asse
.
The
sixt
chapter
,
how
the
windes
of
the
cardes
whereby
the
saylers
doe
sayle
doe
girde
or
compasse
about
the
roundnesse
of
the
worlde
for
to
sayle
by
them
.
SEeing
there
hath
beene
declared
,
the
windes
of
the
cards
of
nauigation
,
their
names
,
&
differences
:
I
wil
speak
in
what
manner
and
order
these
windes
doe
compasse
about
the
roundnesse
of
the
world
,
to
know
how
to
saile
by
them
.
Of
this
is
to
be
noted
,
that
this
round
body
of
water
and
earth
,
hath
in
roundnesse
three
hundreth
and
threescore
degrees
.
Therefore
hee
that
is
in
any
part
or
place
,
and
woulde
sayle
towardes
the
North.
All
inconuenience
being
taken
away
,
shall
sayle
with
the
winde
at
South
,
&
with
no
other
.
It
is
to
bee
vnderstood
,
sayling
before
the
winde
.
Although
that
hee
not
hauing
the
wind
at
South
:
But
some
other
wind
sayling
by
the
bowling
:
may
goe
rising
vp
by
other
courses
,
making
boords
,
one
boord
vnto
one
wind
,
&
another
boord
vnto
another
:
vntill
he
come
to
the
place
where
he
pretendeth
to
go
.
Likewise
,
he
that
wil
sayle
from
the
north
to
the
south
,
must
be
with
a
Northerly
winde
,
or
in
the
manner
aforesaide
.
The
nauigation
of
the
east
or
west
,
is
in
this
maner
:
a
shippe
departeth
from
the
Islande
of
Saynt
Thomas
,
or
as
they
cal
it
Saynt
Thome
,
which
is
vnder
the
equinoctiall
,
and
woulde
goe
round
about
the
world
,
if
in
case
,
that
it
might
be
sailed
:
this
ship
if
she
shoulde
saile
toward
the
east
,
her
way
should
be
in
this
maner
,
from
the
said
Island
or
place
where
she
departed
,
she
shall
saile
with
west
,
180.
degrees
,
&
if
from
thence
she
wil
returne
to
the
place
from
whence
she
departed
,
by
the
same
course
that
she
went
,
she
shal
returne
with
east
the
same
way
:
but
if
she
goe
forward
on
her
way
,
you
shal
vnderstand
,
then
all
the
roundnes
wil
serue
you
,
the
west
wherwith
you
departed
,
vntil
you
come
to
the
point
where
you
came
forth
,
in
such
sort
that
in
a
place
where
a
man
is
,
a
circle
beyng
imagined
,
which
gyrdeth
the
worlde
,
all
this
circle
is
sayled
with
one
winde
,
but
if
from
the
halfe
circle
,
or
before
or
after
he
will
returne
by
the
way
that
he
went
,
he
shall
returne
with
the
winde
contrary
.
For
it
is
to
bee
vnderstoode
,
that
from
the
place
that
a
man
departeth
vntill
the
halfe
circle
bee
ended
,
he
goeth
departing
from
the
place
,
from
whence
hee
came
,
and
the
other
half
he
returneth
towards
it
againe
,
as
the
figure
following
sheweth
it
.
I
say
that
one
departeth
from
A.
to
goe
towarde
C.
and
goeth
by
B.
in
A.
which
is
the
place
from
whence
hee
departeth
:
the
wynde
beginneth
,
&
being
come
to
C.
which
is
his
opposite
,
if
hee
returne
from
thence
to
goe
to
the
same
B.
the
wind
which
is
contrary
,
wil
serue
him
.
But
if
he
goe
sayling
from
C.
to
D.
and
from
D.
to
A.
you
shal
vnderstande
that
with
the
winde
hee
began
to
saile
by
,
he
shall
goe
al
the
roundnesse
,
vntill
he
returne
,
where
he
came
foorth
.
The
same
accompt
,
shall
be
made
,
if
you
beginne
to
sayle
towardes
the
West
,
and
that
which
hath
beene
saide
of
the
nauigation
by
the
equinoctial
,
the
same
must
bee
kept
by
any
manner
of
circle
,
whatsoeuer
.
And
it
is
to
bee
noted
,
that
onlie
from
the
East
and
West
,
there
are
circles
or
courses
greater
and
lesser
:
the
greater
circle
passeth
by
the
Center
,
and
the
lesser
passeth
not
by
the
Center
.
But
all
circles
greater
or
lesser
,
haue
three
hundreth
and
sixtie
degrees
of
length
,
but
in
the
leagues
that
euery
degree
hath
,
there
is
difference
of
more
&
lesse
,
euen
as
the
circle
standeth
neere
to
the
equinoctial
,
or
to
the
poles
.
But
the
windes
which
must
serue
the
turne
ought
to
be
of
the
greater
circles
and
none
of
them
of
the
lesser
circles
.
The
nauigation
by
the
other
windes
is
in
this
sorte
.
If
one
sayling
towardes
the
northeast
,
gaue
a
turne
about
the
worlde
,
going
alwaies
by
the
same
course
,
he
shall
returne
by
the
southwest
,
from
the
place
where
he
departed
:
and
the
same
will
bee
done
by
the
contrary
.
And
in
the
rest
let
the
account
be
kept
as
before
hath
beene
declared
.
The
same
doe
I
say
by
the
nauigation
towardes
the
southeast
,
that
he
shall
returne
by
the
northwest
.
And
for
an
example
of
this
,
let
it
be
asked
:
if
two
shippes
bee
in
one
port
,
and
one
departeth
towardes
the
north
and
the
other
towardes
the
south
,
these
shippes
if
they
shall
meete
,
and
if
they
doe
meet
for
to
goe
equall
way
how
much
shall
euery
one
of
them
sayle
?
I
say
that
these
may
meete
,
and
that
sayling
by
these
courses
,
when
euery
one
of
them
haue
gone
.180
.
degrees
they
shall
be
together
.
And
in
like
manner
,
this
acount
is
to
be
kept
departing
by
other
courses
.
And
so
it
is
to
be
vnderstoode
,
that
whensoeuer
two
shippes
or
more
doe
goe
forth
of
one
port
,
and
do
sayle
by
different
courses
,
when
euery
one
of
them
haue
gone
180.
degrees
,
they
shall
returne
and
ioyne
in
the
place
opposite
,
from
whence
they
departed
:
this
is
because
as
it
is
sayde
,
that
all
the
windes
of
the
nauigation
bee
of
the
greater
circles
,
for
all
of
them
doe
passe
by
the
center
,
&
so
euery
one
going
the
half
circle
which
is
the
sayde
.
180.
degrees
shal
finde
him selfe
in
the
point
opposite
from
whence
he
came
forth
.
The
seuenth
chapter
,
of
the
order
of
the
Cardes
of
Nauigation
.
AMong
the
instrumentes
which
are
necessary
for
the
nauigation
,
one
is
the
carde
:
for
without
it
good
nauigation
cannot
be
made
,
seeing
that
in
it
the
Pilot
or
sayler
doeth
see
the
place
where
he
is
,
and
the
place
whether
hee
pretendeth
to
goe
,
&
seeth
the
height
of
degrees
that
euery
place
hath
,
so
that
hee
knoweth
if
he
shall
goe
foorth
right
,
or
if
he
shall
goe
rising
or
descending
:
hee
seeth
also
what
winde
or
windes
will
serue
him
in
his
course
,
and
where
hee
shall
leaue
one
and
take
another
:
he
also
seeth
the
distance
of
the
way
which
he
shal
goe
,
how
many
leagues
it
hath
,
and
so
he
ordaineth
in
all
thinges
that
which
is
best
and
conuenient
for
him
.
But
it
seemeth
that
with
reason
there
may
be
had
a
doubt
in
the
cardes
wherwith
the
nauigation
is
made
▪
And
say
that
they
be
not
certain
nor
true
for
this
cause
following
.
(
A
doubt
,
)
This
being
prooued
that
the
worlde
is
a
round
body
,
and
not
onely
the
heauens
,
but
also
euery
one
of
the
elementes
,
so
that
the
water
whereby
we
sayle
is
round
,
and
the
winde
wherewith
it
is
sayled
mooueth
it selfe
in
roundnes
&
this
being
so
we
see
that
the
cardes
of
nauigation
be
not
made
round
but
plaine
:
Therefore
from
the
round
to
the
plaine
is
great
difference
,
as
appeareth
by
this
present
figure
,
If
two
shippes
should
departe
from
A.
vnto
C.
and
the
one
of
them
went
by
B.
and
the
other
by
D.
so
great
difference
will
be
of
the
way
that
the
one
maketh
to
the
other
by
how
much
the
distance
is
from
the
B.
vnto
the
D.
&
seeing
that
the
way
which
by
the
sea
is
sayled
is
from
the
A.
vnto
C.
by
D.
because
the
water
is
round
,
&
the
cardes
doeth
not
shewe
it
to
bee
so
,
but
it
sheweth
it
in
plaine
manner
which
is
from
A.
vnto
C.
by
B.
whereby
it
seemeth
that
the
way
which
the
ship
maketh
,
is
halfe
more
than
that
which
the
card
sheweth
.
Seeyng
the
ship
goeth
it
in
circle
manner
,
and
the
card
sheweth
it
by
diameter
,
&
the
diameter
hath
but
only
the
thirde
part
and
one
seuenth
part
of
the
circumference
.
Likewise
the
aforesaid
seemeth
to
be
so
:
because
the
round
bodie
is
greater
then
all
other
bodies
,
and
as
the
world
is
a
round
body
,
there
is
no
other
figure
so
great
,
that
may
be
compared
to
it
:
and
so
the
card
which
is
made
in
plaine
,
cannot
bee
equall
with
the
round
.
Also
the
courses
of
the
nauigation
,
as
they
are
put
in
the
cardes
in
euery
hundreth
leagues
:
they
departe
one
from
the
other
twentie
leagues
,
in
such
sort
that
from
the
place
where
the
ship
doth
depart
vnto
the
xc
.
degrees
whiche
doth
amount
to
1575.
leagues
.
An
these
leagues
they
depart
one
ship
from
another
,
or
one
course
from
another
315.
leagues
.
And
seeing
there
are
32.
courses
,
the
world
,
that
is
to
say
,
the
earth
&
the
water
should
haue
in
roundnesse
,
ten
thousand
&
fourescore
leagues
:
this
is
false
,
because
this
roundnesse
hath
360.
degrees
of
17.
leagues
,
and
a
halfe
,
euery
degree
,
which
doth
amount
to
6300.
leagues
and
no
more
.
Of
all
the
aforesaid
,
it
seemeth
that
the
cardes
of
nauigation
because
they
are
made
in
plaine
:
should
be
false
and
vnperfect
.
(
A
declaration
.
)
To
this
is
to
be
noted
▪
that
the
cardes
of
nauigation
are
true
and
altogether
perfect
:
and
the
art
wherwith
they
are
made
and
ordained
,
doth
conteine
all
certeintie
▪
And
aunswearing
to
the
first
is
:
that
the
nauigation
which
the
ship
doth
make
in
roundnesse
,
and
the
card
doth
shewe
in
playne
:
is
to
be
vnderstood
,
that
the
same
quantity
or
distaunce
of
way
,
that
euery
part
hath
in
roundnesse
,
the
selfe
same
is
reckoned
and
giuen
in
playne
:
aswell
in
the
land
,
as
in
the
water
,
by
marking
in
the
leagues
and
degrees
the
distance
that
euery
thing
hath
in
roundnesse
,
without
taking
from
it
any
thing
.
And
this
may
wel
be
done
,
for
although
that
one
body
be
round
,
there
may
bee
giuen
to
it
the
self
same
proportion
and
greatnesse
in
playne
,
as
Ptholome
setteth
it
foorth
in
the
playne
sphere
.
And
Iordan
in
the
treatie
which
he
made
of
the
same
matter
.
This
seemeth
to
be
by
an
example
in
an
apple
,
that
although
it
be
rounde
,
the
length
&
breadth
that
his
roundnesse
hath
,
may
bee
put
in
playne
forme
:
euen
so
in
the
cardes
of
nauigation
,
although
in
their
figure
or
shape
they
be
not
rounde
,
yet
in
the
accounting
of
the
way
,
they
giue
and
hold
in
equalitie
with
the
round
:
And
the
round
body
to
be
greater
then
another
body
.
It
is
to
be
vnderstood
,
that
those
bodies
being
equall
in
circumference
,
for
not
beyng
equal
,
another
figure
may
wel
be
greater
then
the
round
.
And
for
as
much
as
I
say
,
of
the
courses
of
the
cardes
.
It
is
likewise
to
be
vnderstood
,
that
these
be
ordayned
in
Geometry
,
&
because
it
is
so
singuler
among
the
Mathimaticals
,
they
cannot
be
false
as
those
Authours
whiche
I
haue
spoken
of
doe
shewe
.
And
if
by
a
point
of
the
card
there
are
founde
more
Leagues
in
the
courses
then
the
world
hath
:
This
is
not
hurtfull
to
the
carde
,
for
this
arte
and
shew
of
the
courses
,
is
not
only
for
this
number
of
sixe
thousand
and
three
hundreth
Leagues
which
the
worlde
hath
:
but
for
any
manner
of
number
,
so
that
although
the
world
had
a
hundred
thousand
leagues
,
or
had
a
thousande
,
the
selfe
same
woulde
serue
those
courses
in
one
number
as
in
another
:
as
it
appeareth
,
that
such
as
saile
one
hundreth
leagues
doe
goe
in
their
waye
as
well
as
those
which
goe
vnto
the
East
India
,
which
sayle
fiue
thousande
.
And
as
Magalanes
sailed
,
and
suche
as
went
with
him
in
the
yeere
1521.
when
the
straight
was
discouered
,
which
of
Magalanes
is
named
,
that
then
sayling
from
Spayne
,
they
gaue
a
turne
about
the
world
:
of
that
as
is
said
,
it
appeareth
plainely
,
that
the
cardes
of
nauigation
are
so
well
ordayned
,
that
theyr
agreement
and
perfection
is
a
thing
maruellous
:
seeing
a
thing
so
great
as
the
earth
and
the
Sea
is
,
beeing
marked
in
so
little
roome
as
a
Carde
is
,
and
doe
so
muche
agree
,
that
it
doth
not
misse
one
●otte
to
sayle
the
whole
world
thereby
.
The
eight
Chapter
,
of
the
account
which
the
pilot
ought
to
haue
in
his
waye
when
hee
sayleth
with
a
winde
different
to
his
course
.
SEeing
there
hath
beene
declared
the
order
which
ought
to
bee
vsed
,
if
the
roundnesse
of
the
world
were
sayled
:
In
this
I
will
speake
of
shorter
voiages
or
wa●es
,
and
such
as
are
more
commonly
sailed
by
sea
from
one
place
to
another
.
And
howe
the
pilots
&
saylers
should
know
to
keepe
a
good
account
,
&
giue
reason
of
their
nauigations
,
whether
soeuer
they
goe
:
for
the
which
I
saye
,
whensoeuer
the
pilot
will
saile
,
he
ought
principally
to
look
vpon
3.
things
.
First
of
al
,
the
place
where
he
is
,
and
the
place
whither
he
mindeth
to
goe
,
&
to
know
the
distance
,
that
is
from
the
one
place
to
the
other
.
The
second
,
in
what
height
of
degrees
he
findeth
himselfe
,
and
in
what
height
the
place
is
which
hee
mindeth
to
goe
vnto
.
The
third
is
,
to
know
the
winde
or
winds
that
shall
serue
him
in
his
nauigation
,
al
the
which
he
may
see
&
know
in
his
carde
.
And
this
beeyng
knowne
,
let
him
looke
if
he
haue
a
winde
that
is
conuenient
for
his
nauigation
,
and
hauing
it
let
him
proceede
vppon
his
voyage
as
weather
,
&
time
will
permitte
him
.
And
it
is
to
bee
noted
,
that
many
times
it
happeneth
that
for
the
nauigation
which
should
bee
made
,
the
wind
serueth
not
according
to
the
course
,
which
the
ship
should
goe
:
And
therefore
it
is
sayled
with
another
wynde
whiche
is
different
.
Likewise
it
happeneth
,
that
as
a
ship
goeth
sayling
,
there
commeth
such
weather
,
that
causeth
her
to
goe
foorth
of
her
right
way
:
and
take
her
course
by
another
,
by
the
which
how
much
more
she
goeth
,
so
much
the
land
the
they
goe
to
seeke
changeth
it selfe
into
different
courses
of
the
compasse
.
This
is
because
the
shippe
goeth
not
her
right
course
to
the
place
,
whither
she
pretendeth
to
goe
:
so
that
the
selfe
same
place
,
varieth
or
changeth
it selfe
from
one
cour●e
into
another
.
And
likewise
sometimes
it
waxeth
neere
,
and
other
times
farre
of
.
And
when
it
is
so
,
that
the
pilot
sayleth
with
a
winde
,
different
to
that
which
is
conuenient
for
his
course
,
and
sayling
would
knowe
in
what
poynt
or
course
,
the
land
whither
he
mindeth
to
goe
,
lieth
from
him
:
and
howe
manye
leagues
hee
hath
from
him
to
it
,
in
the
figures
&
accounts
following
,
hee
shall
finde
it
:
the
which
shall
profite
him
to
knowe
the
certayne
place
where
hee
is
,
and
thereby
hee
shall
knowe
howe
to
choose
the
true
course
,
(
when
weather
serueth
him
)
for
to
returne
to
the
certaine
place
whither
he
mindeth
to
goe
,
which
is
to
be
vnderstood
in
this
manner
.
I
say
that
you
will
sayle
to
a
land
,
which
beeing
seene
in
your
carde
,
and
the
place
marked
where
you
are
:
You
shall
find
the
it
is
from
you
towards
the
North
or
South
,
or
any
other
course
,
and
so
sayling
towardes
one
place
,
you
runne
towardes
another
:
and
put
the
case
that
the
land
whether
you
pretend
to
goe
,
be
from
you
towards
the
North
,
so
that
you
should
sayle
with
the
winde
at
South
,
&
because
this
winde
bloweth
not
,
you
sayle
with
another
winde
:
Therefore
if
the
nauigation
bee
by
the
first
course
more
neere
to
the
winde
it selfe
,
in
the
first
figure
you
shall
finde
marked
this
first
course
,
and
neere
to
it
the
leagues
which
you
shall
goe
for
to
get
the
land
,
whither
you
pretende
to
goe
towards
all
the
courses
of
the
compasse
:
as
also
how
many
Leagues
the
land
is
of
from
you
,
and
in
the
manner
that
the
nauigation
is
declared
by
this
course
,
so
all
others
are
declared
.
And
when
in
sayling
you
haue
not
the
proper
winde
which
shoulde
serue
,
marke
by
the
winde
which
you
haue
,
how
many
poynts
it
is
of
from
the
proper
wind
,
wherewith
you
should
saile
,
and
seeke
it
in
one
of
the
figures
,
that
is
here
put
,
which
shal
be
one
of
them
marked
with
the
crosse
,
&
nere
to
the
figure
where
the
like
winde
is
,
you
shall
finde
three
accountes
,
these
accountes
serue
in
this
manner
.
In
the
first
account
,
you
shall
finde
how
many
leagues
you
shall
goe
by
the
course
where
you
sayle
.
In
the
second
account
is
the
course
where
you
haue
the
lande
whether
you
pretend
to
goe
,
(
I
will
say
)
that
hauing
gone
those
leagues
which
there
are
declared
you
shall
come
vnto
the
lande
,
which
you
seeke
after
by
the
course
that
is
there
marked
:
the
which
you
shall
knowe
what
course
it
is
,
by
the
number
that
he
hath
,
seeking
the
same
number
in
the
figure
that
is
nexte
to
it
.
In
the
third
account
,
you
shall
finde
how
many
leagues
you
are
distant
of
the
same
lande
whether
you
goe
,
so
that
hauing
gone
the
leagues
of
the
first
account
you
shall
haue
the
land
whether
you
goe
at
the
course
which
standeth
in
the
second
:
And
you
shall
be
from
the
same
land
the
leagues
that
are
marked
in
the
third
account
.
This
being
knowne
,
three
thinges
are
to
be
noted
.
The
first
,
because
heere
cannot
be
put
any
rule
for
the
number
of
the
leagues
that
are
from
the
place
where
you
are
vnto
the
place
where
you
pretende
to
goe
:
because
at
one
time
there
will
be
more
distance
then
at
another
time
.
Therefore
this
account
is
taken
out
for
the
number
of
a
hundreth
leagues
,
I
will
say
that
the
place
where
you
are
vnto
the
place
whether
you
wil
goe
,
is
a
hundreth
leagues
of
way
.
And
it
is
to
be
noted
,
that
although
this
account
,
doe
serue
for
this
number
of
a
hundreth
leagues
,
it
serueth
likewise
for
any
other
number
of
leagues
,
that
the
way
hath
,
in
this
manner
,
if
the
waye
be
of
200
leagues
you
shall
goe
it
twise
as
much
as
the
numbers
of
the
first
account
doe
shewe
:
And
then
you
shall
haue
the
lande
whether
you
goe
in
the
course
which
is
marked
in
the
seconde
account
,
and
you
shall
be
from
the
sayd
land
,
twise
as
many
leagues
of
them
which
are
accounted
in
the
thirde
account
:
and
if
the
way
be
of
300
leagues
you
must
goe
thrise
as
much
as
the
numbers
of
the
first
account
shewe
so
that
of
euery
hundreth
leagues
,
which
is
encreased
of
the
way
you
shall
geue
as
much
more
number
of
that
which
is
in
first
and
third
account
,
&
then
you
shall
haue
the
lande
at
the
same
courses
or
pointes
,
which
are
marked
in
the
second
account
,
and
if
in
the
way
bee
fifties
,
or
more
or
lesse
you
shall
geue
a
halfe
,
a
thirde
,
a
fourth
,
or
a
fifth
,
or
according
as
the
number
is
.
The
second
is
,
that
in
the
figures
which
are
put
here
,
the
nauigation
goeth
marked
by
the
windes
of
the
one
parte
of
the
compasse
:
and
by
the
other
parte
of
the
course
where
you
shall
finde
the
lande
.
This
is
to
be
noted
that
the
same
account
is
when
you
shall
faile
by
the
parte
where
the
courses
goe
,
and
so
it
serueth
for
all
partes
.
The
thirde
is
,
that
towardes
the
wind
that
these
figures
doe
shew
forth
right
,
shal
be
geuen
the
name
of
the
proper
winde
wherewith
you
shoulde
sayle●
¶
When
you
shall
sayle
by
the
first
course
.
I.
Leigues
of
the
way
.
|
Courses
.
|
Leagues
of
distance
.
|
l.
|
1
|
l.
|
lx
vii
.
|
2
|
xl
|
lxx
.
vi
.
|
3
|
xx
viii
|
l●xx
.
|
4
|
xx
v
|
xx
.
|
5
|
xx
ii
.
|
xx
.
iiii
.
|
6
|
xx
.
|
xx
.
viii
.
|
7
|
xx
.
|
c.
|
8
|
xc
.
ii
|
c.
|
9
|
xx
.
v.
|
c.
x
|
10
|
xx
.
v.
|
c
xv
.
|
11
|
xx
.
vi
|
c.
xx
.
|
12
|
xl
|
c.
xl
.
|
13
|
l
|
●●●●●
.
v
|
14
|
c
|
¶
When
you
shall
sayle
by
the
second
course
.
II
Leagues
of
the
way
.
|
Courses
.
|
Leagues
of
distance
.
|
xxx
.
|
1
|
lxxii
.
|
l
iii.
|
2
|
l
i.
|
lxx
.
|
3
|
xl
ii
.
|
lxx
ii
.
|
4
|
lx
ii
.
|
lxx
|
5
|
xl
.
|
xcv
.
|
6
|
xxx
.
|
c
|
7
|
xl
.
|
c
iii.
|
8
|
xl
|
c
xv.
|
9
|
xl
ii
.
|
c
xxx
.
|
10
|
lx
.
|
c
xl
iii.
|
11
|
lxx
.
|
c
lxxx
.
|
12
|
c.
|
cc
lxxx
ii
.
|
13
|
cc.
|
|
|
|
¶
When
you
shall
sayle
by
the
third
course
.
III
Leagues
of
the
waie
.
|
Courses
.
|
Leagues
of
distance
.
|
xx
v
|
1
|
lxxx
.
|
xl
v
|
2
|
lxx
.
|
lx
|
3
|
lx
|
lxx
|
4
|
l
viii
|
lxxx
i
|
5
|
l
viii
.
|
xc
|
6
|
lx
.
|
c
|
7
|
lx
.
|
c
x
viii
|
8
|
lx
v
|
c
xxx
v
|
9
|
lxxx
.
|
c
lxv.
|
10
|
c
|
cc
x
v
|
11
|
c
xl
v
|
ccc
lx
.
|
12
|
cc
xc
|
When
you
shall
saile
by
the
fourth
course
IIII
Leages
of
the
waie
.
|
Courses
.
|
〈◊〉
of
distance
.
|
xx
|
1
|
lxxx
v
|
xl
|
2
|
lxx
v
|
l
viii
|
3
|
lxx
|
lxx
|
4
|
lxx
|
xc
.
|
5
|
lxx
|
c
|
6
|
lxx
v
|
c
x
|
7
|
lxxx
|
c
xl
|
8
|
c
|
c
lxx
v
|
9
|
c
v
|
cc
xxx
v
|
10
|
c
lxxx
|
ccc
lxxx
|
11
|
ccc
x
|
|
|
|
¶
When
you
shall
sayle
by
the
fifth
course
.
V
Leagues
of
the
waie
.
|
Courses
.
|
Leagues
of
distance
.
|
xc
|
1
|
xc
|
xl
|
2
|
lxxx
|
l
v
|
3
|
lxxx
|
lxx
|
4
|
lxxx
|
xc
|
5
|
xc
.
|
c
x
|
6
|
c
|
c
xxx
v
|
7
|
c
x
v
|
c
lxxx
|
8
|
c
xl
v
|
cc
x
|
9
|
cc
xx
v
|
ccc
lx
|
10
|
cccc
xx
v
|
When
you
shall
saile
by
the
sixth
course
VI
Leagues
of
the
waie
.
|
Courses
.
|
Leagues
of
distance
.
|
xx
|
1
|
xc
.
|
xl
|
2
|
xc
.
|
l
v
|
3
|
xc
|
lxx
v
|
4
|
c
|
c
|
5
|
c
x
|
c
xx
v
|
6
|
c
xx
v
|
c
lxx
|
7
|
c
lx
|
cc
l
|
8
|
cc
xx
|
d
x
|
9
|
cccc
lxxx
v
|
|
|
|
❧
When
you
shall
sayle
by
the
seuenth
Course
.
VII
.
Leagues
of
the
way
.
|
Courses
.
|
Leagues
of
distance
.
|
xx
.
|
1
|
xcv.
|
xl
i.
|
2
|
xcv.
|
lx
.
|
3
|
cv.
|
lxxx
.
|
4
|
c
x.
|
c
x.
|
5
|
c
xxxv.
|
c
l
v.
|
6
|
c
lxv.
|
cc
xl
.
|
7
|
cc
xl
.
|
cccc
xc
.
|
8
|
cccc
lxxx
.
|
❧
When
you
shall
sayle
by
the
eight
Course
.
VIII
.
Leagues
of
the
way
.
|
Courses
.
|
Leagues
of
distance
.
|
xx
.
|
1
|
c.
|
xl
.
|
2
|
c
x.
|
lxv.
|
3
|
c
xx
.
|
xcv.
|
4
|
c
xxx
.
v.
|
c
xl
.
|
5
|
c
lxxv.
|
cc
xxxv.
|
6
|
cc
l
viii
.
|
cccc
lxx
.
|
7
|
cccc
lxxx
.
|
|
|
|
❧
When
you
shall
sayle
by
the
nienth
Course
.
IX
.
Leagues
of
the
way
.
|
Courses
.
|
Leagues
of
distance
.
|
xx
.
|
1
|
c
iii.
|
xlv.
|
2
|
c
xv.
|
lxxx
.
|
3
|
c
xl
.
|
c
xxv.
|
4
|
c
lxx
.
|
ccv.
|
5
|
cc
l.
|
ccccxlv.
|
6
|
cccclxx
.
|
❧
When
you
shall
sayle
by
the
tenth
Course
.
X.
Leagues
of
the
way
.
|
Courses
.
|
Leagues
of
distance
.
|
xx
.
|
1
|
c
x.
|
l
v.
|
2
|
c
xxx
.
|
c
|
3
|
c
ix
ii
.
|
c
lxxx
.
|
4
|
cc
xl
.
|
cccc
xl
.
|
5
|
cccclxx
.
|
¶
When
you
shall
sayle
by
the
eleuenth
course
.
XI
.
Leagues
of
●he
way
.
|
Courses
.
|
Leagues
of
distance
.
|
xxx
.
|
1
|
c
xx
.
|
lxx
.
|
2
|
c
l.
|
c
xl
.
|
3
|
cc
x.
|
ccc
xxx
.
|
4
|
ccc
cx
.
|
¶
When
you
shall
sayle
by
the
twelfth
course
.
XII
.
Leagues
of
●he
way
.
|
Courses
.
|
Leagues
of
distance
.
|
xxx
.
|
1
|
c
xx
.
|
c
|
2
|
c
lxxx
.
|
cc
xc
.
|
3
|
ccc
lxx
.
|
❧
When
you
shall
sayle
by
the
thirteenth
Course
.
XIII
.
Leagues
of
the
way
.
|
Courses
.
|
Leagues
of
distance
.
|
l.
|
1
|
c
xl
.
|
c
xc
.
|
2
|
cc
ixxx
.
|
❧
When
you
shall
sayle
by
the
fourteenth
Course
.
XIIII
.
Leagues
of
the
way
.
|
Courses
.
|
Leagues
of
distance
.
|
c.
|
1
|
c
xc
.
|
AND
for
the
better
declaration
of
the
rules
aboue
written
,
this
present
figure
is
to
be
noted
in
the
whiche
I
say
,
that
you
finde
your selfe
,
in
the
poynt
,
A.
And
the
lande
whither
you
will
goe
,
you
haue
it
,
I
put
the
case
at
the
North
,
in
the
poynt
B.
and
there
is
from
you
to
it
an
hundreth
leagues
,
so
that
your
way
should
be
from
A.
vnto
B.
that
is
to
say
,
sayling
from
the
south
towardes
the
North
,
and
because
you
haue
not
this
winde
,
you
sayle
by
the
first
course
,
and
the
account
beeyng
put
in
the
first
rule
,
doth
teache
you
,
that
if
you
goe
fiftie
leagues
by
this
first
course
:
that
the
Lande
,
which
you
had
first
towardes
the
North
,
you
shal
haue
it
at
North
and
by
East
(
you
sailing
by
the
course
of
North
,
&
by
west
)
and
there
shal
bee
from
you
to
it
fiftie
Leagues
,
and
if
you
goe
by
the
same
course
sixtie
seuen
Leagues
,
then
you
shall
finde
it
towards
the
North
North-East
,
and
then
it
will
be
from
you
to
it
fortie
leagues
.
And
if
you
sayle
seuentie
sixe
leagues
,
you
shall
haue
it
towardes
the
Northeast
and
by
north
,
and
there
will
be
from
you
to
it
twentie
eight
Leagues
.
And
so
in
the
rest
,
this
rule
teacheth
you
how
many
leagues
shuld
be
sailed
for
to
get
to
the
lande
whether
you
goe
to
all
these
courses
.
The
second
figure
and
rule
is
,
when
you
shall
sayle
by
the
seconde
course
distant
from
the
proper
winde
:
in
the
whiche
you
shall
find
the
account
that
shal
be
kept
in
that
way
.
And
the
third
for
the
third
course
,
and
so
for
all
the
rest
:
and
it
is
to
be
noted
,
that
to
this
winde
at
North
,
which
was
put
for
an
example
,
shal
bee
giuen
the
proper
name
of
the
winde
,
whereby
you
should
saile
,
and
to
the
others
the
names
of
the
windes
,
that
are
next
to
him
.
Also
it
is
to
be
noted
,
that
alwayes
it
must
be
considered
what
distance
is
from
the
place
where
your
are
,
vnto
the
place
whither
you
mind
to
goe
,
wherby
you
may
make
the
account
,
euen
as
before
is
declared
.
The
nienth
Chapter
,
how
the
pilot
shal
certeinly
knowe
sayling
by
any
manner
of
course
where
the
Meridian
is
.
AND
seeyng
that
in
the
rules
before
written
hath
beene
declared
howe
the
Pilot
shall
knowe
whersoeuer
he
shall
sayle
,
and
to
what
point
or
course
of
the
compasse
he
hath
the
land
whither
he
goeth
,
and
how
many
Leagues
the
lande
is
from
him
.
Here
I
will
speake
,
that
departing
from
one
place
for
to
sayle
to
another
by
anye
manner
of
course
,
you
shall
knowe
howe
muche
you
depart
from
that
Meridian
wherin
you
were
,
and
knowe
the
Meridian
,
wherein
you
finde
your selfe
:
for
this
is
a
thing
most
necessary
in
the
nauigation
,
the
height
or
altitude
only
excepted
.
And
because
this
rule
of
the
Meridian
,
may
bee
the
better
vnderstood
,
you
shall
note
this
example
.
I
saye
that
eight
shippes
beeyng
in
one
porte
,
and
they
goe
foorth
sayling
,
the
one
from
the
North
to
the
South
,
the
seconde
by
the
first
quarter
,
the
third
by
the
seconde
:
and
so
all
the
other
by
different
windes
,
when
euery
one
of
these
shippes
haue
gone
one
degree
,
or
two
,
or
more
,
being
equal
in
degrees
:
they
shal
be
East
and
Weast
all
of
them
one
with
the
other
,
although
not
equal
in
way
,
for
the
one
hath
gone
muche
more
then
the
other
,
in
such
sorte
,
that
that
which
hath
sayled
by
the
seconde
course
hath
gone
more
waye
,
then
that
which
sayled
the
first
,
&
the
thirde
more
then
the
second
,
and
so
of
the
rest
:
by
how
much
they
goe
from
the
first
,
so
much
the
more
way
is
to
be
gone
to
raise
vp
,
or
to
descend
a
degree
.
This
is
caused
by
reason
of
the
obliquitie
of
the
courses
as
more
largely
shal
bee
declared
in
the
14.
Chapter
of
this
third
booke
,
and
this
being
knowne
(
I
say
for
to
know
)
howe
farre
a
man
is
from
the
Meridian
,
from
whence
hee
departed
,
imagine
that
his
nauigation
shoulde
bee
by
the
same
Meridian
:
that
is
to
say
,
from
the
North
,
to
the
South
,
or
from
the
South
to
the
North
:
and
that
hee
saileth
by
the
first
,
the
seconde
the
third
,
or
fourth
course
,
or
by
any
of
the
other
:
according
as
the
course
lieth
whither
you
minde
to
sayle
,
to
one
place
,
or
to
an
other
.
And
this
is
to
bee
vnderstood
in
the
fourteene
courses
colaterales
,
from
the
North
to
the
South
,
or
from
the
South
,
to
the
North
,
according
as
in
the
first
figures
which
are
put
heere
doth
appeare
:
for
because
for
the
other
14.
courses
Colaterals
,
from
the
East
to
the
West
,
in
the
second
figure
or
fable
they
are
declared
:
therfore
I
say
,
when
you
shall
sayle
by
any
of
the
14.
courses
heeretofore
declared
,
two
thinges
must
be
considered
.
The
first
in
what
height
of
degrees
you
were
,
when
you
were
in
them
,
and
in
what
height
you
doe
presently
find
your self
in
:
and
looke
how
many
degrees
of
difference
are
from
the
one
to
the
other
.
The
seconde
is
to
looke
by
what
course
you
haue
come
vnto
the
place
where
you
are
,
and
this
being
knowne
,
looke
into
the
account
hereafter
written
in
the
first
table
,
and
in
it
you
shall
finde
how
many
Leagues
you
haue
departed
from
the
Meridian
,
which
you
had
in
place
from
whence
you
departed
.
An
example
.
I
say
,
that
you
departed
from
the
point
of
these
first
marked
figures
following
,
&
so
you
were
in
20.
degrees
of
height
,
&
after
that
,
taking
your
altitude
,
you
found
your self
in
15.
degrees
,
or
in
25.
in
such
sorte
,
that
you
found
to
haue
raysed
or
destended
fiue
degrees
,
and
this
was
sayling
by
the
fourth
course
,
whose
name
you
shall
know
looking
on
the
fourth
where
he
is
marked
in
the
figures
which
are
heere
put
,
&
the
course
being
knowne
&
agreeed
with
the
which
you
haue
sailed
,
looke
in
the
table
which
is
next
in
the
4.
course
at
the
fiue
degrees
,
and
you
shall
finde
that
you
haue
gone
from
the
Meridian
from
whence
you
departed
87.
leagues
.
And
for
the
better
vnderstanding
of
this
rule
,
immagine
that
from
this
point
of
the
twentie
degrees
,
where
you
were
,
or
from
any
other
place
from
whence
you
departed
,
that
when
from
thence
you
departed
,
there
departed
,
likewise
another
shippe
from
the
same
point
sailing
by
the
same
Meridian
,
and
that
when
you
had
gone
the
fiue
degrees
she
likewise
had
gone
other
fiue
,
in
such
sort
that
you
haue
her
East
and
West
with
you
,
and
so
it
is
to
be
vnderstoode
that
these
87.
leagues
are
of
distance
from
you
to
this
shippe
,
because
you
are
so
farre
distant
of
that
Meridian
,
And
so
knowing
the
distance
which
you
haue
from
the
Meridian
,
where
you
departed
,
foorthwith
you
shal
know
the
Meridian
wherin
you
are
,
and
in
this
sorte
immagine
that
any
manner
of
course
that
you
shall
saile
,
by
any
of
these
that
are
marked
heere
vnder
in
the
two
first
figures
,
you
haue
this
shippe
East
and
West
with
you
,
and
this
shall
be
your
guide
for
to
know
how
farr
distant
you
be
from
the
Meridian
where
you
were
,
this
is
by
seeing
how
many
leagues
you
haue
raised
or
descended
,
and
the
course
wherby
you
haue
sailed
,
and
being
sought
in
the
figures
and
table
following
,
by
it
you
shall
know
the
Meridian
certaine
wherin
you
are
.
The
Nauigation
by
those
courses
Colaterales
from
the
North
to
the
South
.
The
Nauigation
by
those
courses
Colaterales
from
the
South
to
the
North.
A
Table
of
the
nauigation
from
the
north
to
the
south
,
or
from
the
south
to
the
north
.
When
you
shall
sayle
by
the
first
course
Degrees
,
|
i.
|
ii
.
|
iii.
|
iii.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x
|
Leagues
.
|
3
|
7
|
10
|
14
|
17
|
21
|
24
|
28
|
31
|
35
|
When
you
shall
sayle
by
the
second
course
.
Degrees
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
7
|
15
|
22
|
30
|
37
|
45
|
52
|
60
|
67
|
75.
|
When
you
shall
sayle
by
the
third
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
11
|
23
|
34
|
46
|
57
|
69
|
80
|
92
|
103
|
115
|
When
you
shall
saile
by
the
fourth
course
.
Degrees
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
|
ix
.
|
x
|
Leagues
,
|
17
|
35
|
52
|
70
|
87
|
105
|
122
|
140
|
157
|
175
|
When
you
shall
saile
by
the
fifth
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x
,
|
Leagues
.
|
26
|
53
|
79
|
106
|
132
|
159
|
185
|
212
|
238
|
265
|
When
you
shall
saile
by
the
sixth
course
.
Degrees
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
42
|
85
|
127
|
170
|
212
|
255
|
297
|
340
|
382
|
425
|
When
you
shall
sayle
by
the
seuenth
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
85
|
171
|
256
|
342
|
427
|
513
|
598
|
680
|
769
|
855
|
¶
The
Nauigation
by
the
courses
Colaterales
from
the
east
to
the
west
.
The
Nauigation
by
the
courses
Colaterales
from
the
west
to
the
east
.
A
Table
of
the
nauigation
from
the
East
to
the
West
,
or
to
the
contrary
When
you
shall
sayle
by
the
first
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
85
|
171
|
256
|
342
|
427
|
513
|
598
|
680
|
769
|
855
|
When
you
shall
sayle
by
the
second
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
42
|
85
|
127
|
170
|
212
|
255
|
297
|
340
|
382
|
425
|
When
you
shall
sayle
by
the
third
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
26
|
53
|
79
|
160
|
132
|
159
|
185
|
212
|
238
|
265
|
When
you
shall
saile
by
the
fourth
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
|
ix
.
|
x.
|
Leagues
.
|
17
|
35
|
52
|
70
|
87
|
105
|
122
|
140
|
157
|
175
|
When
you
shall
saile
by
the
fifth
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
11
|
23
|
34
|
46
|
57
|
69
|
80
|
92
|
103
|
115
|
When
you
shall
saile
by
the
sixth
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
7
|
15
|
22
|
30
|
37
|
45
|
52
|
60
|
67
|
75
|
When
you
shall
sayle
by
the
seuenth
course
.
Degrees
.
|
i.
|
ii
.
|
iii.
|
iiii
.
|
v.
|
vi
.
|
vii
.
|
viii
.
|
ix
.
|
x.
|
Leagues
.
|
3
|
7
|
10
|
14
|
17
|
21
|
24
|
28
|
31
|
35
|
The
tenth
Chapter
,
wherein
is
declared
,
more
of
this
rule
before
written
.
FOR
it
is
not
onely
necessary
to
knowe
the
nauigation
which
is
made
from
the
north
to
the
south
,
and
so
contrary
:
but
also
that
which
is
made
from
the
East
to
the
West
,
or
from
the
West
to
the
East
(
that
is
to
say
)
by
these
courses
their
Colaterales
.
Therefore
I
haue
put
the
demonstrations
&
table
before
written
,
of
the
whiche
is
to
bee
noted
the
same
order
that
is
in
the
Nauigation
from
the
North
to
the
south
,
or
from
the
south
to
the
north
as
it
hath
been
declared
.
(
The
whiche
is
)
when
you
goe
sailing
you
shall
mark
in
howe
many
degrees
of
height
you
finde
your selfe
in
,
and
after
that
when
you
turne
to
take
the
sayde
altitude
,
you
shall
marke
howe
manye
degrees
you
haue
risen
or
descended
from
the
place
from
whence
you
departed
.
And
this
being
knowne
looke
vpon
the
figures
before
written
,
the
course
whereby
you
haue
sailed
,
and
if
it
be
the
first
the
second
or
third
,
or
any
of
the
others
,
and
the
course
being
knowne
seeke
it
in
the
table
,
&
in
the
same
course
looke
the
number
of
that
degrees
which
you
haue
gone
,
and
nere
to
the
degrees
,
you
shal
finde
the
leagues
which
you
haue
sailed
.
I
speak
of
an
example
,
that
taking
your
altitude
you
found
your selfe
in
30.
degrees
,
and
after
that
you
found
your selfe
in
thirtie
two
,
or
in
thirtie
eyght
in
such
sorte
you
rose
v
p
or
descended
two
degrees
,
and
you
sailed
by
the
third
course
.
Therfore
looke
in
the
table
in
the
third
course
at
the
second
degree
,
and
you
shal
finde
that
you
haue
gone
fiftie
two
leagues
,
and
in
this
order
you
shall
know
the
rest
.
And
note
that
in
these
tables
,
there
are
not
put
more
numbers
than
vnto
ten
degrees
.
(
The
reason
is
)
that
whilest
these
be
a
sayling
by
any
manner
of
course
,
there
will
be
place
to
take
the
altitude
,
and
being
taken
,
to
marke
the
place
,
and
from
thence
to
begin
the
account
as
well
rising
as
descending
,
and
in
this
sort
you
shal
goe
making
a
point
in
your
carde
,
and
knowe
the
certaine
place
where
you
are
.
The
eleuenth
chapter
,
how
the
Pilot
ought
to
choose
the
course
which
is
conuenient
according
to
the
place
hee
mindeth
to
saile
vnto
.
THE
Pilot
or
any
other
person
that
mindeth
to
sayle
,
before
all
thinges
he
ought
to
consider
of
the
waye
that
hee
mindeth
to
goe
,
and
so
to
choose
the
course
or
courses
which
are
necessary
,
according
to
the
way
whiche
he
mindeth
to
make
,
and
for
this
put
before
you
a
certaine
rule
,
and
this
in
any
manner
of
place
where
a
man
standeth
,
is
a
point
or
beginning
where
the
courses
or
winds
of
the
nauigation
doe
proceede
and
come
foorth
.
Therefore
the
Pilot
ought
to
looke
in
his
card
the
place
where
he
is
,
&
the
place
whether
he
mindeth
to
goe
vnto
,
and
this
being
knowne
,
he
ought
to
seeke
for
the
course
that
maye
goe
moste
right
to
it
from
whence
he
doth
depart
vnto
the
place
whether
he
mindeth
to
goe
,
and
if
there
be
a
course
that
will
carry
him
straight
from
one
place
to
the
other
,
let
him
put
the
foreparte
of
his
shippe
into
it
as
his
compasse
will
shewe
him
,
and
by
that
course
let
him
follow
his
way
,
as
long
as
weather
will
serue
him
.
And
when
there
is
no
course
that
goeth
the
right
way
,
let
him
seeke
with
the
compasse
the
course
that
is
most
agreeable
vnto
him
,
which
is
it
that
wil
bring
him
least
out
of
his
way
to
the
place
whether
he
mindeth
to
goe
,
and
by
the
saide
course
let
him
follow
the
degrees
or
leagues
which
are
of
distance
,
vntill
he
finde
another
that
goeth
more
right
to
the
place
,
and
in
this
let
the
Pilot
haue
great
care
,
to
see
how
much
waye
euery
course
serueth
him
,
and
where
he
shall
leaue
that
way
and
take
another
,
and
that
he
keepe
a
good
reckoning
&
knowledge
of
the
way
that
hee
maketh
as
much
as
is
possible
,
and
at
all
times
when
neede
requireth
to
make
a
point
in
his
carde
and
mooue
his
course
,
let
him
doe
it
keeping
alwaies
a
good
reckoning
of
his
waye
,
and
this
to
continue
vntill
hee
finde
a
course
that
may
cary
him
directly
to
the
place
that
he
desireth
.
And
the
Pilot
in
the
beginning
ought
not
to
keep
himself
towards
the
courses
that
are
nearest
adioyning
to
him
where
he
is
,
but
vnto
those
that
are
nearest
to
the
place
whether
he
goeth
.
And
it
woulde
doe
well
to
pricke
his
carde
often
,
and
prouide
diligently
vpon
his
course
:
&
let
the
Pilot
note
,
that
for
to
chose
the
course
the
right
way
as
he
ought
to
doe
,
he
hath
need
to
know
precisely
the
Meridian
wherin
he
is
:
for
not
knowing
it
there
may
follow
great
errour
,
as
by
this
example
appeareth
.
If
one
shippe
goe
sayling
,
the
Pilot
maketh
her
to
be
in
the
point
.
A.
and
would
goe
seeking
for
B
,
and
in
truth
his
point
was
the
C.
it
is
euident
by
reason
he
is
ignorant
&
without
knowledge
of
the
Meridian
beleuing
that
he
sayled
from
A.
vnto
B.
his
nauigation
was
from
C.
vnto
D.
And
therefore
it
seemeth
that
so
much
as
is
erred
in
the
knowledge
of
the
place
where
the
shipp
is
,
as
much
more
she
is
distant
from
the
place
that
she
goeth
to
seeke
:
and
this
is
one
of
the
causes
,
whereby
the
Pilots
doe
finde
themselues
in
great
errour
in
theire
nauigation
,
and
loose
much
time
,
and
other
inconuententies
happen
to
them
.
Therfore
let
the
Pilot
take
this
for
a
good
aduise
,
in
long
wayes
to
keepe
for
him selfe
a
booke
of
account
of
his
nauigation
,
where
he
should
be
put
in
remembrance
of
the
winde
that
serueth
him
euery
day
,
and
in
what
sorte
and
so
how
much
the
singlenes
may
bee
,
that
his
shippe
maketh
,
looking
by
his
clocke
how
many
leagues
he
may
runne
euery
houre
:
and
you
shal
vnderstand
,
that
the
most
which
she
can
runne
is
foure
leagues
in
an
houre
,
and
three
leagues
in
an
houre
is
a
great
tunne
,
and
in
one
houre
two
leagues
is
reasonable
,
and
and
in
an
houre
to
runne
a
league
and
a
halfe
or
sometime
but
a
league
.
It
must
be
well
looked
vnto
,
and
great
aduise
must
be
had
in
this
,
for
it
will
profit
much
to
pricke
the
carde
to
knowe
the
Meridian
,
and
therby
to
choose
the
true
course
as
it
is
sayd
.
The
twelfth
chapter
,
how
you
should
prick
your
carde
to
know
the
place
,
wherein
the
shippe
is
.
ONE
of
the
thinges
that
the
Pilot
ought
to
know
perfectlie
,
is
to
pricke
his
carde
very
precisely
,
for
it
is
verye
necessarye
for
good
nauigation
.
Therfore
when
the
pilot
wil
prick
his
card
for
to
knowe
the
place
where
hee
is
,
he
ought
first
of
al
to
looke
in
his
card
,
the
place
from
whence
he
departed
in
what
height
of
degrees
it
is
in
,
according
as
hee
shall
finde
by
the
graduation
which
the
rard
hath
,
and
let
him
looke
also
in
how
many
degrees
of
height
he
findeth
himselfe
in
according
as
he
tooke
it
,
and
this
being
knowen
let
him
take
his
two
compasses
and
put
the
pointe
of
one
of
them
in
the
place
from
whence
he
departed
,
&
the
other
pointe
of
the
same
compasse
let
him
put
in
the
course
or
winde
which
he
hath
had
,
and
take
the
other
compas
and
put
the
one
pointe
in
the
degrees
of
height
which
he
hath
found
,
seeking
them
in
the
graduation
of
the
card
,
and
the
other
pointe
of
this
compasse
in
the
winde
East
,
and
West
that
is
neerest
,
and
make
these
compasses
to
runne
the
one
vnto
the
other
not
taking
away
the
two
points
which
come
vpon
the
winds
,
(
that
is
to
say
)
the
one
,
is
it
which
the
ship
hath
gone
,
and
the
other
the
East
or
West
and
comming
in
this
manner
where
ioyntly
you
shall
ioyne
the
two
pointes
of
both
compasses
,
the
one
which
was
put
in
the
place
from
whence
the
shippe
departed
,
and
the
other
in
the
height
or
altitude
where
in
ye
found
your selfe
.
In
this
point
is
the
place
wherin
the
ship
is
,
&
to
knowe
if
this
point
be
certeine
make
the
proofe
in
this
manner
.
Look
in
the
point
where
you
finde
your selfe
in
,
and
from
thence
with
the
compasse
measure
how
many
leagues
are
from
it
to
the
place
from
whence
you
departed
,
&
this
being
known
,
looke
into
the
wind
that
brought
you
how
many
leagues
is
to
be
reckoned
for
a
degree
,
according
as
you
shall
finde
in
the
fifteeneth
chapter
of
this
third
booke
,
&
beeing
seene
howe
many
degrees
you
haue
raised
or
descended
from
the
place
where
you
departed
,
vnto
the
place
wher
you
make
your selfe
to
bee
,
you
shall
reckon
the
leagues
that
these
degrees
doe
amount
vnto
,
and
if
the
leagues
of
the
degrees
bee
iust
with
the
leagues
that
you
finde
of
your
way
,
your
reckoning
is
good
,
and
if
the
reckoning
be
not
agreeable
the
one
with
the
other
,
looke
wherein
the
errour
is
,
for
because
that
these
two
summes
or
reckonings
should
come
iust
.
And
if
the
place
where
you
finde
your selfe
be
iust
in
altitude
with
the
place
from
whence
you
departed
,
heere
is
no
rule
that
can
instruct
you
iustly
that
which
you
haue
sayled
,
but
by
iudgement
that
which
your
shippe
may
goe
,
according
to
the
dayes
&
houres
that
she
hath
sailed
,
and
according
to
the
weather
she
hath
had
,
and
so
the
reckoning
is
made
little
more
or
lesse
.
But
let
the
pilot
●●atke
that
●●
this
account
or
reckoning
of
little
more
or
lesse
,
ought
to
be
considered
the
currents
or
tides
that
may
be
in
your
way
,
for
the
many
times
the
winde
and
tide
are
one
way
,
&
when
it
is
so
the
shipp
runneth
more
way
than
the
Pilot
thinketh
:
at
other
times
the
windes
&
tides
are
contrary
in
such
sorte
that
as
much
as
the
winde
carrieth
so
much
the
current
or
tide
reteineth
or
keepeth
backe
,
&
for
this
cause
you
ought
to
consider
that
if
the
winde
doe
cast
the
ship
to
one
parte
&
the
currents
to
another
,
the
race
of
the
ship
will
be
in
that
parte
where
is
lesse
strength
or
power
,
&
if
the
winde
&
the
currents
be
equall
the
race
of
her
will
be
of
the
side
where
the
current
is
.
Let
the
pilot
consider
the
falling
down
or
holding
vp
that
the
shipp
may
make
,
and
so
let
him
make
the
account
that
is
conuenient
.
This
aduise
is
to
bee
had
when
he
pricketh
his
card
by
squarenes
or
by
fancie
,
which
is
by
reckoning
the
singlenes
that
the
ship
hath
made
,
and
arbitrar
or
indg
how
much
way
it
may
be
that
shee
hath
gone
in
euery
one
,
and
by
what
course
,
of
all
these
the
Pilot
must
keepe
a
good
reckoning
in
his
nauigation
as
much
as
in
him
lieth
.
The
13.
chapter
,
howe
the
Pilot
ought
to
looke
that
his
carde
be
iust
&
certeine
that
there
be
no
errour
in
his
nauigation
.
IN
the
chapter
before
hath
beene
declared
the
manner
that
the
Pilot
or
sayler
should
haue
in
the
pricking
of
his
card
&
know
the
place
where
he
is
,
&
be
cause
my
intent
is
to
declare
how
the
sailers
should
know
to
make
their
nauigations
with
out
perill
or
danger
,
as
well
of
the
ignorance
of
the
rules
&
instructions
of
the
nauigation
,
as
also
to
knowe
the
defectes
of
the
cards
&
instrumentes
wherewith
they
gouerne
themselues
by
the
sea
.
I
say
let
the
Pilot
or
any
other
person
that
shall
sayle
,
be
well
aduised
that
the
card
which
he
shal
prick
,
and
order
his
nauigation
by
,
be
iust
&
true
,
as
well
in
the
courses
as
in
the
setting
down
of
the
coast
in
such
sort
that
euery
one
thing
bee
in
his
proper
place
both
true
&
certein
as
well
in
the
course
as
in
the
altitude
.
So
that
the
errour
or
defect
of
the
card
be
not
occasion
that
in
nauigation
you
erre
,
and
you
must
note
that
among
the
cards
of
nauigation
that
vntil
now
haue
byn
vsed
in
the
way
of
the
Indians
of
his
maiesty
,
there
are
many
which
haue
2
graduations
different
one
from
the
other
,
in
such
sort
that
from
one
graduation
to
the
other
is
more
than
3
degrees
of
difference
,
these
cardes
are
false
and
in
the
nauigations
that
by
them
are
made
may
followe
much
hurte
and
greate
inconvenience
by
reason
of
the
difference
,
that
these
2.
graduations
haue
betweene
them
,
because
their
difference
doth
cause
that
al
the
courses
that
reache
from
one
graduation
to
the
other
are
false
,
being
seen
from
the
place
where
they
begin
vnto
the
place
where
they
make
an
end
.
The
reason
is
,
that
as
they
begin
in
one
graduation
,
and
make
an
end
in
another
,
that
is
different
from
that
:
so
the
said
courses
doe
make
the
selfsame
difference
,
&
so
the
way
that
is
sayled
by
them
,
shal
be
erred
,
&
you
shall
not
find
the
place
that
you
doe
seeke
by
it
:
seeing
that
the
ports
,
baies
,
Ilandes
,
&
shooldes
,
&
the
other
thinges
of
the
cardes
,
where
these
said
courses
doe
beginne
,
beeing
looked
on
where
they
end
,
they
bee
foorth
of
their
owne
places
&
true
altitude
,
making
it
equall
with
the
altitude
where
the
nauigation
began
.
Also
looking
in
euerie
course
of
the
card
,
the
distance
of
leagues
,
that
are
from
one
place
to
another
,
or
from
one
porte
to
another
,
I
say
,
from
the
place
where
the
course
began
,
vnto
the
place
where
it
endeth
:
and
these
Leagues
beeyng
taken
with
the
compasse
,
&
the
Leagues
being
seene
which
are
reckoned
for
a
degree
in
euerye
course
of
the
nauigation
shal
be
found
,
that
the
leagues
of
the
courses
be
not
agreable
with
those
leagues
,
which
are
of
the
distance
of
the
way
.
This
is
in
the
courses
that
doe
reach
from
one
graduation
to
another
:
the
which
is
caused
by
reason
of
the
difference
that
the
two
graduations
haue
:
so
that
by
these
saide
cardes
cannot
be
made
any
good
nauigation
,
seeing
that
they
in
themselues
doe
varie
:
likewise
because
they
haue
2.
equinoctiall
lines
,
and
many
other
errors
,
al
the
which
I
haue
made
declaration
of
before
.
The
Counsel
royall
of
the
Indians
,
of
his
Maiestie
,
wherevpon
it
hath
beene
commaunded
that
the
said
cards
be
not
vsed
by
reason
they
haue
two
different
graduations
,
and
therefore
are
false
and
erronious
as
it
is
said
.
Therefore
I
say
,
that
the
Pilot
or
sayler
ought
to
looke
well
that
the
carde
whereby
hee
doth
sayle
,
be
of
one
only
graduation
:
I
wil
say
if
they
haue
two
graduations
or
more
:
let
them
bee
equall
or
vniforme
and
not
different
,
the
one
from
the
other
.
And
likewise
the
other
instruments
,
let
them
bee
certayne
and
true
,
that
they
cause
no
errour
,
whereby
may
followe
hurt
and
daunger
,
as
it
is
most
certeine
that
with
false
instrumentes
it
maye
and
doth
oftentimes
happen
.
The
fourteenth
Chapter
,
of
the
number
of
the
Leagues
,
which
are
reckoned
for
a
degree
in
euery
course
of
the
nauigation
.
FIrst
,
before
I
declare
the
number
of
the
leagues
,
that
ought
to
bee
giuen
to
euery
degree
in
euery
one
of
the
courses
of
nauigation
;
it
is
conuenient
to
speake
here
what
is
the
cause
wherfore
to
the
roundnes
of
the
worlde
,
from
the
East
to
the
West
,
or
from
the
North
to
the
South
,
was
giuen
to
euery
degree
,
17.
leagues
and
a
halfe
,
and
no
more
.
And
in
the
other
courses
,
although
they
be
equal
:
with
these
are
reckoned
more
leagues
for
a
degree
then
in
them
.
To
this
is
to
be
noted
,
what
degree
is
taken
in
one
of
two
sortes
,
is
to
be
vnderstood
a
degree
of
the
roundnesse
of
the
world
,
or
a
degree
of
eleuation
or
height
of
the
pole
.
For
the
first
which
is
a
degree
of
roundnesse
,
in
this
all
the
degrees
of
the
courses
or
winds
be
equal
,
for
all
the
windes
are
as
the
greater
circles
in
the
sphere
,
&
as
it
hath
beene
declared
,
they
haue
three
hundreth
and
sixtie
degrees
of
longitude
,
and
for
that
cause
is
giuen
to
euery
degree
of
roundnesse
seuenteene
leagues
and
a
half
:
but
in
the
second
manner
,
which
is
the
degrees
of
the
eleuation
of
the
pole
,
these
are
different
vnto
those
of
the
roundnesse
.
For
if
in
sayling
towards
the
north
going
17.
leagues
&
a
half
,
the
pole
is
raised
a
degree
,
when
you
saile
towards
the
Northeast
,
although
you
goe
these
17.
&
a
halfe
,
you
haue
not
raised
the
pole
●
degree
:
but
it
is
necessary
that
you
goe
by
this
course
24.
Leagues
and
a
halfe
,
for
euery
degree
of
eleuation
of
the
pole
,
and
like
in
all
the
rest
of
the
courses
,
by
howe
muche
euerie
one
is
more
straight
from
the
pole
vnto
the
Lyne
:
so
manye
more
Leagues
,
or
lesse
shall
be
gone
for
euery
degree
of
eleuation
of
the
pole
,
so
that
the
roundnes
wherwith
the
world
is
girded
,
is
not
to
be
looked
on
in
all
the
courses
of
the
nauigation
.
But
do
you
also
look
how
much
should
bee
gone
by
euery
course
for
to
raise
vp
or
to
put
down
euery
degree
of
the
height
of
the
pole
,
because
this
altitude
of
the
pole
,
is
to
bee
reckoned
from
the
halfe
of
the
world
,
which
is
from
the
Equinoctiall
line
:
for
that
from
thence
they
begin
to
reckon
the
degrees
,
as
well
for
the
part
of
the
North
,
as
for
that
of
the
South
,
so
that
in
the
cardes
of
nauigation
,
are
put
the
coastes
and
all
the
rest
that
are
marked
in
it
according
to
the
degrees
that
euery
thing
is
distant
of
the
sayd
line
:
in
such
sort
,
that
sailing
by
any
manner
of
course
,
from
what
place
a
man
is
in
,
towards
the
Equinoctiall
,
or
from
the
saide
Equinoctiall
or
any
other
part
,
by
as
much
as
the
course
is
more
straight
or
crooked
,
by
so
much
they
shall
reckon
more
or
lesse
leagues
in
euery
degree
in
this
manner
.
The
Equinoctiall
line
.
I
put
the
case
,
that
two
shippes
bee
in
the
poynt
A.
which
is
a
port
towards
the
North
,
sixe
degrees
distant
from
the
Equinoctial
,
and
both
of
them
doe
depart
from
thence
towardes
the
sayde
line
,
&
the
one
departeth
with
North
,
&
the
other
with
Northeast
towardes
the
Southwest
:
It
is
certayne
,
that
she
which
carrieth
the
winde
at
North
,
sailing
by
the
same
course
from
the
North
towardes
the
South
after
shee
hath
gone
a
hundreth
&
fiue
leagues
whiche
are
the
said
sixe
degrees
,
by
that
course
she
shal
be
in
the
Equinoctiall
:
And
the
other
that
saileth
with
Northeast
towards
the
Southwest
,
by
reason
that
that
winde
goeth
more
leaning
towards
the
sayde
line
,
the
way
is
longer
to
her
.
And
so
although
that
in
the
altitude
shee
goeth
not
downe
more
then
sixe
degrees
,
but
for
to
come
to
the
Equinoctiall
she
shall
goe
one
hundreth
fortie
seuen
leagues
,
by
the
which
shee
hath
euery
degree
by
this
course
24.
leagues
&
a
halfe
:
so
that
only
from
the
North
,
to
the
South
,
and
from
the
East
to
the
West
,
&
contrariwise
euery
degree
hath
17.
leagues
&
a
halfe
,
but
in
the
other
courses
euery
degree
hath
the
leagues
following
.
The
second
course
hath
a
hundreth
and
eight
leagues
deuided
into
sixe
degrees
,
which
commeth
foorth
euery
degree
18.
leagues
.
The
thirde
course
hath
a
hundreth
and
fifteene
leagues
and
a
halfe
,
so
that
euery
degree
hath
nieneteene
leagues
and
a
terce
.
The
fourth
course
hath
a
hundreth
twentie
sixe
leagus
,
so
that
euery
degree
hath
21.
leagues
.
The
fifth
course
hath
a
hundreth
fortie
seuen
Leagues
,
so
that
euery
degree
hath
24.
leagues
and
a
halfe
.
The
sixe
course
hath
a
189.
leagues
,
so
that
euery
degree
hath
31.
leagues
and
a
halfe
.
The
seuenth
course
hath
two
hundreth
seuenty
three
leagues
,
so
that
euery
degree
hath
forty
fiue
leagues
and
a
halfe
.
The
eight
course
hath
fiue
hundreth
thirtie
fiue
leagues
,
so
that
euery
degree
hath
eighty
and
niene
leagues
.
The
fifteenth
Chapter
,
of
number
,
and
measure
,
and
of
how
many
parts
a
degree
is
compounded
.
IT
is
written
in
the
book
of
wisedome
,
that
God
made
all
things
in
number
,
waight
,
&
measure
,
therfore
without
knowledge
of
the
numbers
we
can
knowe
nothing
,
of
the
time
,
of
the
houres
,
or
of
the
moouinges
,
or
other
thinges
,
by
the
which
it
seemeth
that
without
knowledge
how
to
reckon
we
cannot
know
any
thing
.
There
are
two
sortes
of
quantities
,
or
numbers
:
one
is
continuall
,
another
is
deuided
or
discrete
:
The
continuall
is
in
3.
sorts
,
that
is
to
say
,
towardes
the
length
only
like
to
a
line
,
and
this
is
called
quantitie
lineall
:
Another
is
continued
in
length
,
&
bredth
,
but
not
deepe
,
&
this
is
called
superficial
:
The
third
is
continued
in
length
,
bredth
,
&
depth
,
&
is
called
corporal
,
or
set
together
.
The
quantity
deuided
or
discrete
,
is
when
we
say
,
one
,
two
,
three
,
&c:
wherby
it
seemeth
by
the
diuersitie
of
the
numbers
are
vnderstood
diuers
meanings
of
writinges
,
&
so
he
that
knoweth
them
not
,
ought
not
to
bee
called
a
man
.
Plato
saith
,
for
this
cause
is
man
so
wise
a
creature
,
because
he
knoweth
the
manner
how
to
account
:
for
the
which
he
had
written
at
the
doore
of
his
Academia
,
that
who
could
not
make
a
reckoning
or
account
,
should
not
enter
in
,
to
heare
him
.
The
measures
,
&
the
reasons
for
them
&
their
properties
haue
sprong
of
Geometry
:
for
Geometry
is
a
science
of
measure
,
the
which
doth
containe
lines
,
superficies
,
and
bodies
,
as
appeareth
in
any
circle
three
square
,
foure
square
,
&
other
figures
,
of
Geometrie
:
many
Authors
haue
written
,
and
principally
Euclides
,
the
father
of
Ypocras
.
Plurtarch
saith
,
that
Archimedes
made
an
artificiall
thing
by
Geometry
,
with
the
which
,
Marcellus
a
captayne
of
the
Romaines
,
hauing
besieged
the
citie
of
Syracula
,
in
Sicilia
with
the
saide
artificiall
thing
Archimedes
tooke
out
the
ships
of
Marcellus
,
that
were
in
the
Sea
,
by
raising
them
vp
into
the
aire
,
he
put
them
within
the
Citie
:
this
science
is
called
Geometry
,
as
Saint
Isidore
saith
,
for
the
distribution
of
landes
and
fieldes
:
Geometry
properly
is
of
the
corporal
things
for
that
all
corporall
thinges
haue
their
proper
measure
.
And
of
the
spaces
or
distances
that
are
from
one
prouince
or
citie
to
another
,
which
are
measured
by
Escadios
,
miles
,
Leagues
,
&
Degrees
:
And
this
measure
whereby
that
all
may
be
alike
in
equalitie
is
ordayned
in
this
manner
.
Foure
graines
of
Barley
doe
make
one
finger
.
Foure
fingers
one
hand
.
Foure
handes
one
foote
.
Fiue
foote
maketh
one
pace
.
An
hundreth
twentie
fiue
paces
maketh
one
Escadio
.
Eight
Escadios
which
are
a
thousand
paces
,
doe
make
a
Mile
.
Three
Miles
doe
make
a
league
.
Seuenteene
leagues
and
a
halfe
doe
make
a
degree
.
Euery
degree
hath
lx.
minutes
.
Euery
minute
60.
seconds
.
Euery
second
60.
thirdes
.
And
so
vnto
tenthes
.
The
reason
why
this
account
is
diuided
into
this
number
of
60.
more
than
into
any
other
.
Ptholome
declareth
in
the
first
of
the
Almagesto
,
the
nienth
chapter
:
where
he
saith
,
that
that
Astronomers
,
sought
a
number
,
that
hath
many
numbers
in
proportionall
partes
,
which
we
call
parts
,
Alicotas
,
and
there
cannot
be
giuen
any
other
number
vnder
sixtie
,
for
that
this
number
may
bee
parted
into
many
diuisions
and
numbers
,
as
in
two
times
thirtie
,
in
three
times
twentie
&c.
The
ende
of
the
thirde
Booke
.
¶
The
fourth
booke
of
the
height
or
altitude
of
the
Sunne
,
and
how
the
nauigation
ought
to
be
ruled
thereby
.
The
first
Chapter
,
wherein
are
declared
17.
Fundamentall
principles
,
which
ought
to
be
knowen
in
the
Altitude
of
the
Sunne
.
ONe
of
the
things
most
subtile
and
of
greatest
vnderstanding
conteyned
in
the
Art
of
nauigation
,
is
the
altitude
of
the
sunne
:
for
it
sheweth
truely
the
way
,
that
hee
which
sayleth
,
maketh
,
or
shall
make
in
suche
sorte
,
that
if
hee
hath
made
any
errour
in
his
voyage
:
by
this
altitude
hee
knoweth
it
:
and
so
by
reason
that
it
is
a
thing
so
excellent
and
subtile
,
the
auncient
writers
in
old
time
did
highly
esteeme
of
the
practise
therof
,
chiefly
that
great
Ptholome
,
&
other
singuler
authors
,
for
the
which
they
used
diuers
instruments
as
the
Astrolabio
,
&
the
3.
rules
,
and
others
.
This
altitude
is
so
effectuall
for
good
nauigation
,
that
those
which
doe
saile
to
farre
countries
,
cannot
make
their
nauigations
:
if
this
should
lacke
.
For
among
all
the
rules
and
aduises
that
I
haue
declared
in
this
art
,
and
will
declare
as
wel
touching
the
altitude
of
the
North
as
of
others
which
serue
in
the
nauigation
:
This
altitude
〈◊〉
the
sunne
hath
excellency
among
all
others
,
because
he
is
as
a
proofe
of
Arithmeticke
,
that
soeweth
the
errours
whiche
are
in
the
numbers
:
so
that
by
the
altitude
of
the
sunne
,
being
precisely
taken
,
the
Pilot
may
know
the
want
or
lacke
that
hath
beene
in
his
nauigation
.
And
because
this
altitude
of
the
Sunne
is
a
matter
delicate
and
subtile
as
I
haue
sayd
.
In
this
fourth
booke
,
I
will
treate
therof
as
plainely
as
possible
I
can
,
shewing
the
rules
by
Text
,
and
giuing
them
their
declaration
&
true
vnderstanding
,
that
they
ought
to
haue
.
And
likewise
giuing
to
euery
one
an
example
and
demonstration
that
they
may
bee
the
better
vnderstood
,
and
for
this
shal
be
noted
17.
fundamental
beginnings
,
which
are
these
following
.
-
Altitude
.
-
Degree
.
-
Horizon
.
-
Zodiake
.
-
Equinoctiall
line
.
-
Declination
.
-
Circles
.
-
Tropikes
.
-
Part
of
the
North.
-
Part
of
the
South
.
-
Longitude
.
-
Latitude
.
-
Parelius
.
-
Meridian
.
-
Hemisphera
.
-
Zenith
.
-
Centrum
.
Altitude
is
the
degrees
which
the
sunne
or
the
●ole
doe
raise
themselues
aboue
the
Horizon
.
Likewise
an
altitude
is
vnderstood
by
those
degrees
,
that
anie
citie
,
port
,
Iland
,
&c
,
are
distant
from
the
Equinoctiall
line
.
A
degree
is
one
part
of
three
hundreth
and
sixtie
:
wherein
the
world
is
deuided
,
it
hath
seuenteene
Leagues
and
a
half
of
way
,
by
the
longitude
which
is
the
length
or
bredth
of
the
water
and
earth
.
Horizon
is
a
circle
which
wee
doe
imagine
vpon
the
vppermost
part
of
the
earth
:
in
the
whiche
our
sight
is
fixed
,
which
is
as
farre
as
our
sight
cāreach
,
and
by
this
circle
half
the
heauen
is
deuided
which
we
see
,
from
the
other
half
which
we
see
not
.
Zodiake
is
a
circle
really
scituated
in
the
eight
heauen
,
vnder
the
which
the
sunne
mooueth
it selfe
in
all
the
yeere
.
This
Zodiake
deuideth
the
Equinoctiall
line
,
into
two
equall
partes
:
the
one
from
the
Equinoctial
line
by
the
part
of
the
north
,
&
the
other
by
the
part
of
the
South
,
by
euery
part
of
these
it
hath
180.
degrees
,
so
that
the
Zodiake
hath
360.
degrees
.
The
Equinoctiall
is
a
s●rcke
or
circle
imagined
by
the
halfe
of
the
worlde
from
the
East
into
the
West
in
equal
distance
from
both
the
poles
,
so
that
from
the
Equinoctiall
vnto
euerye
one
of
the
poles
are
nientie
degrees
.
It
is
called
Equinoctiall
,
because
the
sunne
passing
by
it
causeth
Equinoctio
,
whiche
is
as
much
to
say
,
the
day
and
the
night
to
be
equall
.
Declination
is
the
distance
which
the
sunne
by
his
owne
mouing
maketh
from
the
Equinoctial
line
,
6.
monethes
of
the
yeere
to
the
North
part
,
&
6.
monethes
to
the
South
parte
.
Circles
are
the
waye
whereby
the
poles
of
the
Zodiake
doe
moue
in
roundnesse
from
the
poles
of
the
world
.
These
doe
take
their
names
of
the
said
poles
:
and
so
they
are
called
circle
Articke
,
and
circle
Antartike
,
these
circles
are
distant
of
the
saide
poles
of
the
worlde
,
23.
degrees
,
and
33.
minutes
.
Tropicos
or
Tropikes
are
2.
circles
where
the
sunne
last
of
all
doth
come
once
in
a
yeere
.
One
vnto
the
parte
of
the
North
,
and
the
other
vnto
the
parte
of
the
South
.
It
is
called
the
Tropike
of
Tropos
which
is
a
greeke
name
,
and
is
as
much
to
say
as
conuersion
,
for
the
sunne
being
come
to
euery
one
of
these
Tropickes
conuerteth
her selfe
and
turneth
backe
.
The
parte
of
the
North
is
taken
for
halfe
the
worlde
,
whiche
is
from
the
Equinoctiall
line
vnto
the
Pole
articke
.
The
parte
of
the
South
is
the
other
halfe
of
the
roundnesse
of
the
worlde
,
which
is
from
the
Equinoctial
line
vnto
the
pole
antartike
.
Longitude
or
length
,
is
vnderstood
by
the
way
from
the
East
into
the
West
,
or
from
the
West
into
the
East
,
for
that
this
is
the
length
of
the
world
.
Latitude
or
bredth
is
the
way
which
is
taken
from
the
North
to
the
South
,
which
is
from
one
pole
to
the
other
,
for
this
is
the
bredth
of
the
world
.
Parelius
is
a
way
imagined
to
goe
straight
by
the
heauen
,
or
by
the
Sea
,
or
by
▪
the
land
,
from
the
East
into
the
West
,
or
from
the
West
into
the
East
,
with
,
outcomming
neere
to
the
Equinoctiall
line
,
or
to
the
poles
more
in
one
parte
then
in
another
.
The
Meridian
is
a
line
,
which
is
imagined
from
one
pole
of
the
world
to
the
other
,
right
ouer
our
heades
,
and
when
the
sunne
commeth
to
this
line
,
it
is
the
middest
of
the
day
vnto
suche
as
inhabite
vnder
it
.
Hemisphera
is
as
muche
to
say
,
the
halfe
sphere
▪
and
it
is
to
be
vnderstood
,
that
all
the
worlde
is
one
Sphera
Esphera
,
and
is
taken
for
a
rounde
thing
,
and
because
the
worlde
is
rounde
,
it
is
called
Sphera
,
and
seeing
that
in
what
place
soeuer
a
man
is
,
hee
seeth
the
halfe
of
Heauen
:
This
halfe
of
the
Heauen
,
which
wee
see
,
we
call
Hemisphera
.
Zenith
is
apoynt
imagined
in
the
heauen
very
precisely
put
ouer
our
head
,
&
from
this
point
or
Zenith
to
any
manner
of
place
of
our
Horizon
are
90.
degrees
.
Center
is
a
point
in
the
middest
of
the
sphere
imagined
,
&
so
in
the
middest
that
from
it
to
the
superficie
,
al
the
lines
that
from
foorth
right
shal
be
layde
,
shal
be
equall
:
and
from
any
part
of
the
superficie
to
this
point
is
to
descend
,
and
from
it
to
the
superficie
is
to
rise
vp
.
The
second
Chapter
,
of
the
excellencies
of
the
sunne
,
and
of
his
moouings
.
SAint
Ambrose
saieth
▪
in
the
Exameron
,
that
the
sunne
is
the
fountaine
of
light
,
the
fairenesse
of
the
day
,
the
ornament
of
heauen
,
the
measure
of
time
,
the
vertue
and
strength
of
all
thinges
which
are
borne
,
and
according
as
the
Philosopher
saith
,
is
cause
of
all
generation
and
corruption
.
It
is
of
a
very
great
quantitie
,
so
much
that
Ptholome
saith
in
the
Almagesto
and
Alfragano
,
in
the
difference
22.
that
the
sunne
in
an
hundreth
sixtie
&
sixe
times
greater
then
the
earth
,
his
mouing
is
more
swift
then
any
arrow
,
and
we
doe
not
see
him
mooue
by
reason
of
his
greate
brightnesse
which
is
of
more
strength
to
be
seene
,
then
our
sight
can
see
:
And
to
our
iudgement
hee
goeth
by
leasure
.
But
the
quantity
of
the
way
being
knowen
which
he
goeth
,
his
lightnesse
is
innumerable
:
so
that
for
the
greate
distance
that
is
from
vs
to
him
,
we
cannot
determine
his
moouing
.
And
it
is
to
bee
noted
,
that
the
sunne
hath
two
moouings
contrary
,
which
are
one
forcible
,
and
the
other
proper
:
the
forcible
mouing
is
it
that
we
see
that
euery
day
he
maketh
a
forcible
going
by
the
first
moueable
,
&
in
euery
24.
houres
,
hee
goeth
round
about
the
world
from
the
East
into
the
West
.
The
other
mouing
which
is
naturall
,
with
proper
to
himselfe
,
woorketh
contrary
to
the
first
,
that
is
to
be
vnderstood
from
the
West
into
the
East
,
in
his
circle
Excentrico
:
the
which
moouing
,
he
maketh
in
three
hundreth
sixtie
and
fiue
dayes
&
sixe
houres
,
&
lesse
a
little
quantity
:
And
this
mouing
he
maketh
in
this
maner
,
from
the
eleuenth
day
of
Marche
,
that
the
sunne
passeth
by
the
line
Equinoctial
vntil
the
eleuenth
day
of
June
,
the
sunne
goeth
rising
vp
,
by
the
parte
of
the
North
,
and
so
putting
himselfe
from
the
said
line
,
the
eleuenth
day
of
June
,
he
commeth
to
the
tropike
of
Cancer
,
and
in
this
rising
vp
that
he
maketh
these
three
monethes
hee
departeth
from
the
sayd
line
twenty
three
degrees
and
thirtie
three
minutes
:
which
is
his
greatest
declination
,
or
distaunce
that
hee
maketh
from
the
fayde
line
;
and
from
the
twelfthe
of
June
,
vnto
the
thirteenth
of
September
,
the
sunne
descendeth
from
the
sayde
Tropike
vnto
the
line
:
and
from
the
fourteenth
of
September
,
vnto
the
thirteenth
of
December
:
the
sunne
descendeth
by
the
parte
of
the
South
from
the
line
to
the
Tropike
of
Capricorne
,
from
whence
he
departeth
other
twentie
three
degrees
,
and
thirtie
three
minutes
,
which
is
likewise
his
greatest
declination
of
that
parte
:
and
from
the
fourteenth
of
December
,
vnto
the
tenth
of
Marche
,
the
sunne
goeth
using
vp
from
the
Tropike
of
Capricorne
vnto
the
line
:
so
that
of
the
twelf-monthes
of
the
yeere
,
sixe
of
them
,
the
sunne
goeth
from
the
line
to
the
parte
of
the
North
,
and
the
other
sixe
to
the
parte
of
the
South
.
And
all
the
moouinge
which
the
sunne
maketh
,
is
from
one
Tropike
to
another
:
in
the
whiche
are
47.
degrees
,
and
6.
minutes
.
This
is
the
latitude
of
the
Zona
,
whiche
the
auncient
Writers
called
Torrida
,
which
is
as
muche
to
saye
,
tosted
,
because
alwayes
the
sunne
maketh
his
moouing
by
her
within
these
Tropikes
,
without
going
worth
of
them
at
anye
time
.
And
it
is
to
bee
vnderstood
,
that
the
time
which
the
sunne
goeth
towarde
the
parte
of
the
North
,
and
the
time
hee
goeth
towarde
the
parte
of
the
South
,
Is
not
equall
,
for
the
sunne
goeth
towarde
the
parte
of
the
North
,
a
hundreth
eightie
and
seuen
dayes
,
and
hee
goeth
towardes
the
parte
of
the
South
,
a
hundreth
sixtie
and
eight
:
where
it
appeareth
that
the
sunne
goeth
more
time
of
the
yeere
vnto
the
parte
of
the
North
,
then
vnto
the
part
of
the
South
.
The
cause
is
,
because
this
circle
Excentrico
:
wherein
the
sunne
maketh
his
moouing
,
is
so
shut
into
the
Sphera
,
that
of
one
parte
hee
commeth
more
neere
to
the
firmament
,
then
of
the
other
,
for
the
which
cause
be
is
described
foorth
of
the
Conter
of
the
worlde
.
The
parte
of
this
circle
that
commeth
more
neere
to
the
firmament
,
is
called
auxe
,
which
is
as
much
to
say
eleuation
,
and
this
hee
doth
,
when
hee
commeth
to
the
tropike
of
Cancer
,
and
that
when
he
is
most
distant
is
called
opposite
of
auxe
,
and
this
is
when
hee
commeth
to
the
Tropike
of
Capricorne
:
so
that
when
the
sunne
is
in
Auxe
,
hee
is
more
neere
to
the
firmament
;
and
when
hee
is
in
his
opposite
,
hee
is
more
neere
to
the
earth
,
in
suche
sorte
that
in
the
Sommer
the
sunne
goeth
farre
from
the
earth
,
and
in
the
Winter
,
is
more
neere
to
the
earth
.
This
is
to
bee
vnderstoode
in
respect
of
vs
in
the
Winter
〈◊〉
respect
of
suche
as
inhabite
towardes
the
parts
of
the
South
in
Sommer
.
The
Cardinall
Peter
de
Aliaco
proueth
,
that
aforesaid
in
the
twelfth
question
,
in
the
first
article
of
the
seconde
notable
,
where
hee
sayeth
that
the
sunne
maketh
his
moouing
,
beeyng
come
to
the
ende
of
Gomini
,
is
in
the
Auxe
:
of
his
Excentrieo
,
and
in
the
ende
of
Sagitarius
is
in
the
opposite
.
This
seenteth
by
the
demonstration
that
Ptholome
putteth
in
the
thirde
distinction
of
the
Almagesto
.
And
seeing
that
the
Center
of
the
Excentrico
of
the
sunne
is
distant
from
the
Center
of
the
worlde
,
by
so
muche
when
the
sunne
in
his
Auxe
is
more
distaunt
from
the
earth
;
and
when
hee
is
in
the
opposite
,
hee
is
more
neere
to
it
.
And
so
it
is
prooued
that
the
sunne
is
more
neere
to
the
earth
in
our
Winter
,
then
in
Sommer
.
The
thirde
Chapter
,
of
the
yeere
called
Solar
,
&
other
manner
of
yeeres
,
&
how
the
leape
yeere
is
reckoned
.
THE
yeere
Solar
is
the
time
,
wherein
the
sunne
passeth
the
twelue
signes
of
the
Zodiake
,
and
returneth
where
hee
began
.
It
is
called
a
yeere
,
whiche
is
,
as
if
one
shoulde
say
,
a
ring
,
or
circle
,
because
the
sunne
hath
gone
his
circle
,
he
returneth
to
the
same
place
where
he
began
.
The
Egyptians
as
S.
Isidore
saith
,
before
they
had
the
knowledge
of
learning
,
they
accustomed
to
figure
the
yeere
in
a
dragon
,
that
bitt
the
taile
,
but
since
they
had
learning
and
account
of
the
yeere
,
they
began
it
in
September
,
because
they
say
that
in
that
moueth
the
world
was
made
.
And
the
Arabians
beginne
in
the
same
time
,
the
Hebrues
beginne
in
the
moneth
of
March
,
because
it
was
geuen
to
them
by
lawe
,
wee
begin
it
in
I●nuarie
,
because
then
did
our
〈◊〉
yeere
begin
,
which
was
the
birth
of
the
sonne
of
iustice
,
Christ
our
God
.
And
because
the
sunne
doth
begin
to
come
〈◊〉
vs
,
In
the
scripture
I
finde
fiue
sortes
of
yeeres
.
Anno
Solet
Anno
Lun●●
Anno
Emergence
,
Anno
Grande
,
Anno
Mundano
.
The
yeere
●ol●●
is
it
the
therfore
hath
beene
declared
.
The
yeere
Lunar
is
the
time
which
doth
containe
twelue
moones
,
of
twentie
niene
daies
and
a
halfe
,
which
amounteth
to
th●●
hundreth
fiftie
foure
d●●es
vnto
the
which
is
added
the
eleuen
dayes
of
the
concurrent
,
because
the
yeere
Lunar
which
is
of
the
moone
may
come
with
the
Solar
which
is
of
the
sunne
.
〈◊〉
yeere
Emergente
is
when
there
happeneth
,
a
thing
very
not●●le
,
and
in
the
time
following
is
speech
thereof
,
euen
as
they
talked
in
the
time
of
Caesar
▪
●od
now
of
the
birth
of
our
Lorde
Jesus
Christ
.
Anno
Grande
is
as
much
to
far
,
as
a
great
yeere
,
according
as
the
maister
of
the
histories
sayth
,
that
it
is
a
time
of
sixe
hundred
yeeres
.
Anno
Mundano
according
to
Macrobio
,
is
when
the
Starres
and
all
the
Planets
will
come
to
the
pointe
of
our
degree
where
they
began
their
first
moouing
.
And
this
hee
sayth
shall
bee
in
fifteene
thousand
yeres
,
likewise
the
other
saith
that
it
will
come
in
fortie
&
niene
thousand
yeeres
.
But
any
manner
of
thing
that
the
philosopher
speaketh
of
in
this
matter
,
is
according
to
his
owne
opinion
,
we
ought
to
holde
that
the
time
and
the
moouing
of
the
things
and
the
end
of
them
is
in
the
hand
of
him
that
made
them
of
nothing
,
and
vnto
men
doth
not
appertaine
to
iudge
nor
determine
of
the
time
or
ending
of
the
world
.
For
the
most
high
prouidence
of
the
father
eternall
did
put
it
in
his
owne
bosome
,
as
our
redemer
Jesus
Christ
teacheth
vs
,
answering
to
such
as
asked
him
the
saide
question
,
as
it
is
written
in
the
Actes
of
the
Apostles
the
first
chapter
,
Therefore
I
say
that
the
yeere
called
〈◊〉
hath
three
hundreth
sixtie
fiue
●●●yes
and
sixe
houres
lacking
twelue
minutes
giuing
to
euery
houre
sixtie
minutes
and
because
in
the
yere
are
accounted
sixe
whole
houres
of
this
hath
come
although
the
quantitie
bee
little
,
that
it
is
no
more
but
one
fifth
parte
of
an
houre
ins
euery
one
yere
,
in
so
many
number
of
yeeres
they
haue
not
made
eleuen
dayes
of
difference
in
the
time
,
so
that
these
sixe
houres
which
are
accounted
in
the
yeere
besides
these
sayd
daies
from
foure
to
foure
yeres
doth
amount
to
twentie
foure
●oures
which
maketh
&
natural
day
,
and
so
this
fourth
yeere
bath
three
hundreth
sixtie
sixe
dayes
and
this
is
called
the
leape
yeere
,
it
is
also
called
Bissiesto
by
the
minutes
which
are
as
called
Bises
the
which
minutes
the
sun
tarieth
in
euery
one
signe
most
then
the
thirty
dayes
Bissiesto
is
●●oun●●
to
say
two
times
six
,
for
because
〈◊〉
of
Bissiesto
the
day
that
is
sixe
dayes
before
the
Kalendes
of
march
is
〈◊〉
so
that
in
one
onely
letter
of
the
Kalender
there
are
two
daies
which
are
the
twentie
foure
,
and
twentie
〈◊〉
of
Februarie
,
that
is
to
saye
the
〈◊〉
which
〈◊〉
the
saide
letter
,
and
more
the
day
whiche
is
encreased
by
the
Bissiesto
or
leape
yeere
by
the
which
the
leape
yeere
in
the
moneth
of
February
hath
twentie
nine
dayes
and
the
other
yeeres
twentie
eyght
.
Therefore
it
is
to
be
seene
,
when
the
altitude
of
the
sunne
is
taken
to
knowe
his
declination
if
it
be
a
leape
yeere
,
or
〈◊〉
,
the
seconde
,
or
the
thirde
after
the
leape
yeere
as
is
plainely
to
bee
founde
in
the
seuenteene
Chapter
,
which
treateth
of
the
declination
,
and
according
to
the
yeere
,
so
must
the
declination
of
the
Sunne
bee
sought
for
.
The
fourth
Chapter
,
what
thing
a
shadow
is
,
&
how
the
shadow
which
the
sunne
maketh
ought
to
be
looked
on
,
for
to
take
his
altitude
.
THe
shadowes
are
caused
when
any
darke
body
is
opposite
to
the
light
,
and
so
the
shadow
hath
an
apparance
or
shewe
of
a
body
,
and
it
is
none
The
shadowe
flyeth
away
from
such
as
followe
it
,
and
followeth
such
as
flye
from
it
.
The
shadow
by
how
much
the
sunne
is
higher
,
by
so
muche
it
is
lesser
,
and
how
much
the
lower
,
the
greater
:
whereby
the
shadow
of
a
man
is
greater
in
the
morning
and
in
the
euening
,
then
at
the
middest
of
the
day
,
and
it
is
to
be
noted
,
that
the
sun
goeth
alwaies
is
one
of
these
3
places
,
which
is
toward
the
part
of
the
north
,
or
in
the
equinoctiall
,
or
towardes
the
part
of
the
south
:
&
in
these
three
partes
to
such
as
inhabit
in
the
world
it
maketh
5
shadowes
:
(
That
is
to
saye
,
)
a
shadow
at
the
east
,
a
shadow
at
the
west
,
a
shadow
at
the
north
,
a
shadow
at
the
south
,
&
a
straight
shadow
.
The
shadow
at
the
east
,
is
when
the
sunne
doth
set
.
The
shadowe
at
the
west
is
when
the
sunne
riseth
.
The
shadowe
at
north
is
when
the
sunne
commeth
to
the
middest
of
the
day
,
and
he
that
maketh
the
shadow
is
more
towardes
the
north
then
the
sun
.
And
the
shadow
at
south
is
when
he
that
maketh
the
shadowe
is
more
towardes
the
south
then
the
sunne
there
is
likewise
a
straight
shadowe
,
when
the
sunne
is
in
our
Zen●●●
Al
these
shadowes
,
such
as
dwel
within
the
tropikes
haue
.
Those
which
inhabite
vnder
the
tropikes
,
haue
4
shadowes
,
(
that
is
to
say
)
shadow
at
east
shadow
at
west
and
those
of
the
tropike
of
Cancer
,
haue
the
shadow
at
north
and
those
of
the
tropike
of
Capricorne
haue
the
shadowe
at
south
:
and
once
in
the
yere
a
straight
shadow
,
which
is
when
the
sunne
entreth
into
that
tropike
.
Such
as
dwel
without
the
tropikes
haue
three
shadowes
,
at
east
,
and
at
west
,
and
those
of
the
parte
of
the
north
,
haue
shadowe
at
north
,
and
those
of
the
parte
of
the
south
,
haue
shadowe
at
south
,
and
neuer
any
straight
shadowe
.
But
do
you
note
,
that
although
the
sunne
doth
make
in
the
yeere
fiue
shadowes
to
such
as
dwell
in
the
world
not
onely
in
fiue
partes
,
but
in
xiii
.
differences
of
parts
,
you
may
be
with
the
sunn
and
haue
xiii
.
differences
of
shadowes
,
and
no
more
,
(
that
is
to
say
)
fiue
when
the
sunne
goeth
towardes
the
parte
of
the
north
,
and
three
when
hee
is
in
the
line
,
and
fiue
when
he
is
towardes
the
part
of
the
south
,
the
which
by
xiii
.
rules
with
their
demonstrations
shal
be
noted
in
this
manner
.
When
the
Sunne
is
towardes
the
north
.
The
Sunne
being
towardes
the
north
,
if
the
shadowes
be
towardees
the
north
,
you
are
more
towardes
the
north
then
the
Sunne
,
and
the
Sunne
betweene
you
and
the
line
.
The
Sunne
towardes
the
north
,
if
the
shadowes
be
to
no
parte
,
then
are
you
towards
the
north
as
farre
from
the
line
as
the
Sunne
.
The
Sunne
towardes
the
north
,
if
the
shadowes
be
towards
the
south
,
you
may
be
towardes
the
north
betweene
the
Sunne
&
the
line
.
The
Sunne
towardes
the
north
,
and
the
shadowes
going
towards
the
south
you
may
be
in
the
Equinoctiall
line
.
The
Sunne
towards
the
north
,
and
the
shadowes
going
towardes
the
south
you
may
be
towardes
the
parte
of
the
south
,
and
the
line
betweene
you
and
the
Sunne
.
When
the
Sunne
is
in
the
Equinoctiall
Line
.
The
Sunne
in
the
Equinoctiall
if
the
shadowes
be
towardes
the
north
,
you
are
towardes
the
part
of
the
north
.
The
Sunne
in
the
equinoctiall
,
if
the
shadowes
be
straight
you
are
in
the
equinoctiall
.
The
Sunne
in
the
Equinoctiall
,
if
the
shadowes
be
towardes
the
south
you
are
towardes
the
part
of
the
south
.
When
the
Sunne
is
towardes
the
south
.
The
Sunne
towardes
the
south
,
if
the
shadowes
be
towardes
the
south
you
are
towardes
the
south
,
and
the
sunne
is
betweene
you
and
the
line
.
The
sunne
at
the
south
if
the
shadowes
bee
straight
you
are
towardes
the
south
as
farre
from
the
line
as
the
sunne
.
The
sun
at
south
if
the
shadowes
be
towards
the
north
you
may
be
towardes
the
south
beetweene
the
sunne
and
the
line
.
The
Sunne
towardes
the
south
,
and
the
shadowes
going
towardes
the
north
you
may
be
in
the
Equinoctiall
.
The
sunne
towardes
the
south
,
and
the
shadowes
towardes
the
north
you
may
be
towardes
the
north
,
&
the
line
betweene
you
and
the
sunne
.
The
fifth
chapter
,
wherein
is
declared
what
thing
the
height
of
the
sunne
is
,
and
how
it
ought
to
bee
taken
to
knowe
the
place
where
a
man
is
.
SEing
there
hath
beene
declared
the
difference
of
shadowes
which
the
sunne
maketh
,
or
maye
make
by
all
the
yeere
in
any
manner
of
place
that
a
man
is
,
the
which
shadows
are
necessary
to
be
knowne
.
For
to
knowe
precisely
how
to
take
the
altitude
of
the
sunne
,
I
will
speake
,
what
thing
the
altitude
of
the
sunne
is
,
and
the
manner
that
must
be
had
,
for
to
take
it
well
.
For
this
is
to
bee
noted
,
that
Ptholomie
saieth
in
the
firste
of
Geographia
,
that
wheresoeuer
a
man
is
,
hee
seeth
halfe
the
heauen
and
the
other
halfe
is
hid
from
him
,
in
such
sort
that
of
three
hundreth
and
sixtie
degrees
that
the
heauen
hath
in
roundnes
wee
alwaies
see
the
hundreth
and
foure
score
which
is
the
halfe
wherein
is
contayned
our
Hemispherio
,
so
that
wheresouer
a
man
is
,
and
in
any
manner
of
time
,
from
his
heade
or
Cenith
,
vnto
the
horizon
are
ninetie
degrees
,
and
so
from
what
place
that
a
man
is
in
euen
vnto
the
sunne
,
when
he
riseth
in
the
morning
,
that
hee
doe
begin
to
appeare
in
the
horizon
are
ninetie
degrees
,
and
how
much
more
the
day
goeth
forwarde
,
and
the
sunne
goeth
rising
,
so
much
more
he
commeth
neerer
towardes
our
Cenith
.
And
this
rising
vp
that
the
sunne
maketh
,
is
called
the
altitude
of
the
sunne
,
because
he
goeth
rising
,
and
going
vp
vppon
the
horizon
,
the
which
altitude
he
that
shall
take
him
at
the
middest
of
the
day
,
let
him
vnderstande
that
the
degrees
that
he
shall
finde
in
his
Astrolabio
,
lesse
then
ninetie
,
those
should
be
from
him
to
the
sunne
,
for
that
the
sunne
shall
be
so
many
distant
from
his
Cenith
,
which
is
from
the
right
of
his
heade
.
Therefore
I
say
to
know
the
altitude
that
the
sunne
hath
euery
day
vpon
the
horizon
which
the
pilot
or
any
otherpersō
that
would
take
it
,
ought
,
first
of
all
to
looke
on
fyue
thinges
which
are
these
following
.
The
first
,
that
it
be
taken
in
the
middest
of
the
day
.
The
second
,
that
hee
see
to
whiche
parte
of
the
line
,
the
sunne
goeth
that
day
.
The
third
,
to
what
part
the
shadows
goe
.
The
fourth
,
what
declination
the
sun
hath
.
The
fifth
,
that
he
knowe
how
to
applye
the
rule
that
is
conuenient
according
to
the
time
and
place
wherein
he
findeth
himselfe
.
Vnto
the
first
I
say
,
that
the
altitude
of
the
sunne
ought
to
be
taken
at
the
middest
of
the
day
iustly
,
this
is
because
vntill
the
sunne
commeth
to
the
Meridian
he
goeth
alwaies
rising
aboue
the
Horizon
,
and
if
hee
bee
taken
before
or
after
hee
wil
not
bee
so
iustly
taken
,
but
although
that
in
this
be
some
difference
of
time
being
but
a
little
thing
before
or
after
,
it
is
no
great
inconuenience
,
because
the
most
times
it
cannot
be
punctually
knowne
when
he
commeth
to
the
Meridian
.
Although
you
looke
on
the
clock
,
the
Astrolabio
,
or
any
other
instrument
,
but
alwaies
doe
you
procure
to
take
him
at
the
houre
aforesaide
.
To
the
second
,
it
ought
to
bee
seene
at
what
parte
of
the
line
,
the
sunne
goeth
,
if
it
be
at
the
north
or
at
the
south
,
considering
that
the
time
,
which
the
sun
goeth
to
the
part
of
the
north
,
is
from
the
eleuenth
of
March
vnto
the
thirteenth
of
September
,
and
from
the
fourteenth
of
September
vnto
the
tenth
of
March
hee
goeth
to
the
parte
of
the
south
.
Vnto
the
thirde
,
he
that
taketh
the
altitude
ought
to
see
to
what
parte
the
shadowes
are
from
him
,
(
that
is
to
say
)
the
shadow
of
his
person
,
or
of
the
maste
of
his
ship
,
or
of
any
other
thing
that
is
put
vpright
.
And
so
by
the
shadowe
hee
shall
knowe
at
which
parte
of
the
line
hee
is
,
for
being
knowne
to
which
parte
the
sunne
goeth
,
it
may
be
easily
known
by
the
sayde
shadowe
,
towardes
what
parte
he
is
of
,
as
in
the
fourth
chapter
hath
beene
declared
.
To
the
fourth
,
the
yeere
ought
to
be
looked
vnto
,
if
it
be
a
leape
yeere
,
or
the
first
,
the
second
,
or
third
yeere
after
the
leape
yeere
,
and
according
as
the
yeere
is
,
let
him
looke
on
the
moneth
,
and
day
wherein
he
is
:
and
what
declination
the
sunne
hath
towardes
the
parte
where
he
goeth
,
that
is
how
many
degrees
and
minutes
hee
is
distant
from
the
sayde
line
.
To
the
fifth
,
that
hee
apply
euery
rule
of
the
altitude
in
his
proper
time
and
place
,
and
this
the
pilot
ought
alwais
to
procure
and
knowe
the
rules
of
the
altitude
,
not
onely
the
woordes
but
the
meaning
of
them
for
he
that
onely
knoweth
the
rule
,
and
doth
not
attaine
to
the
reason
or
foundation
thereof
,
as
it
ought
to
be
vnderstoode
,
it
procureth
to
him
many
harmes
,
and
hee
knoweth
not
of
what
they
proceede
,
and
finding
him selfe
in
the
errour
he
putteth
faulte
in
the
instrumentes
and
rules
,
the
fault
being
in
him selfe
,
because
he
vnderstandeth
them
not
.
And
because
these
rules
of
the
altitude
of
the
sunne
may
bee
well
vnderstoode
,
and
that
their
shoulde
be
no
ignorance
in
any
thing
,
here
shal
be
put
euery
one
with
his
declaration
,
figure
,
and
example
,
in
manner
following
.
The
first
rule
,
when
the
Sunne
goeth
towarde
the
parte
of
the
north
,
and
the
shadowes
goes
towardes
the
north
.
THE
Sunne
towardes
the
parte
of
the
North
,
if
the
shadowes
be
towardes
the
North
you
bee
towards
the
north
,
and
the
Sun
is
betweene
you
and
the
line
,
see
howe
many
degrees
you
tooke
of
altitude
and
how
many
doth
lacke
of
ninetie
,
and
with
those
whiche
lacke
,
ioyne
the
declination
of
that
day
,
and
all
ioyned
together
you
are
distant
from
the
line
towardes
the
north
.
This
first
rule
doth
shewe
how
you
shall
knowe
the
altitude
of
the
sunne
,
when
he
goeth
towardes
the
north
,
and
hee
that
taketh
the
altitude
is
more
towardes
the
north
then
the
sunne
,
and
so
he
sayth
.
The
Sunne
towardes
the
parte
of
the
North
,
is
as
muche
to
say
,
that
when
you
doe
take
the
altitude
of
the
Sunne
in
any
day
of
the
sixe
monethes
,
that
he
goeth
from
the
line
vnto
the
parte
of
the
north
.
If
the
shadowes
bee
towardes
the
North
,
if
in
this
daye
that
you
take
the
altitude
of
the
Sunne
the
shadowes
bee
from
you
towardes
the
north
.
You
are
towardes
the
North
and
the
Sunne
is
betweene
you
and
the
line
,
in
such
sorte
that
by
the
shadowes
you
doe
know
that
the
Sunne
is
between
you
and
the
line
,
at
such
time
as
when
they
are
in
this
manner
.
Beholde
how
many
degrees
you
take
of
altitude
,
these
degrees
are
those
that
you
take
the
sunne
in
your
Astrolabio
,
therfore
looke
on
these
degrees
howe
many
they
are
.
And
how
many
lacketh
for
nientie
,
is
to
be
vnderstood
vpon
those
that
you
found
of
Astrolabio
,
looke
how
many
they
are
,
which
doe
lacke
for
to
come
to
nientie
,
And
with
those
whiche
lacke
,
as
if
you
had
taken
fiftie
,
there
lacke
fortye
:
and
if
you
had
taken
65.
there
lacke
25.
Therfore
with
those
forty
,
or
twenty
,
or
more
or
lesse
,
Ioyne
the
declination
of
that
day
,
which
are
those
degrees
&
minutes
which
the
sunne
is
distant
from
the
line
,
as
you
shall
finde
in
the
declination
of
the
sayd
day
,
And
all
put
together
,
that
is
to
say
,
the
declination
of
the
sunne
,
&
the
degrees
which
lacke
for
nienty
,
and
that
which
this
shall
summe
or
amount
vnto
,
you
are
distaunt
from
the
line
towardes
the
North.
An
Example
.
The
sixte
day
of
April
,
I
taking
the
altitude
of
the
sunne
,
the
shadowes
were
from
mee
towardes
the
North
,
and
I
tooke
the
sunne
in
sixtie
degrees
of
Astrolabio
,
there
lacked
30.
for
90.
with
these
30.
I
ioyned
10.
degrees
,
which
the
Sunne
had
this
day
of
declination
,
whiche
did
amounte
to
fortie
degrees
,
so
much
was
I
distant
from
the
line
towards
the
part
of
the
North.
The
reason
is
,
for
because
in
the
moneth
of
Aprill
,
the
sunne
goeth
towardes
the
part
of
the
North
,
&
as
the
shadowes
were
from
me
towardes
the
North
,
I
knewe
that
I
was
more
towardes
the
North
,
then
the
sunne
,
therefore
the
sunne
beyng
taken
in
sixtie
degrees
,
the
thirtie
which
lacked
for
nientie
,
was
I
distant
of
the
sunne
.
This
is
because
alwaies
,
when
that
I
shall
take
the
altitude
of
the
sunne
,
those
degrees
that
I
shall
finde
in
my
Astrolabio
,
lesse
then
nientie
,
the
selfe
same
am
I
distant
from
the
sunne
,
and
the
same
day
,
the
sunne
was
distant
from
the
line
,
ten
degrees
,
which
was
his
declination
,
so
that
from
mee
to
the
sunne
,
were
thirtie
degrees
,
&
from
the
sunne
to
the
liue
,
tenne
whiche
make
fortie
:
so
much
was
I
distaunt
from
the
sayde
line
.
The
seconde
rule
,
that
when
the
sunne
is
towardes
the
North
,
and
the
shadowes
towardes
the
South
,
the
declination
and
altitude
are
more
then
nientie
degrees
.
IF
the
sunne
be
towards
the
North
,
and
the
shadowes
bee
towardes
the
south
,
ioyne
the
declination
with
the
altitude
,
and
if
they
passe
nientie
degrees
,
those
which
are
more
,
you
are
distant
from
the
line
towardes
the
North
,
and
you
are
betweene
the
sunne
and
the
line
.
In
the
firste
rule
hath
been
declared
that
when
the
sunne
is
towardes
the
part
of
the
North
,
&
hee
that
taketh
the
altitude
is
more
towardes
the
North
then
the
sunne
whereby
the
shadowes
goe
from
him
towardes
the
North.
This
rule
is
,
when
the
sunne
goeth
towards
the
selfsame
parte
of
the
North
,
and
he
which
taketh
the
altitude
,
the
shadowes
goe
from
him
towardes
the
South
in
this
manner
.
The
sunne
towardes
the
North
,
the
time
which
the
sunne
goeth
towards
the
North
,
hath
beene
declared
.
Therefore
in
this
time
,
If
the
shadowes
be
towards
the
south
,
the
south
ioyneth
the
declination
with
the
altitude
,
which
is
as
much
to
say
,
looke
on
the
degrees
and
minutes
,
that
this
day
hath
of
declination
,
and
ioyne
them
with
the
degrees
,
that
you
take
the
sunne
in
your
Astrolabio
,
and
if
they
doe
passe
of
nientie
degrees
,
if
altogether
the
declination
of
the
sunne
,
and
the
altitude
whiche
you
tooke
,
were
more
then
nientie
degrees
.
Those
which
were
more
,
you
are
distant
from
the
line
towards
the
North.
It
is
to
be
vnderstood
,
that
if
the
altitude
and
declination
were
nienetie
fiue
degrees
,
you
are
distant
of
the
line
,
fiue
degrees
:
and
if
they
were
an
hundreth
,
you
were
distant
tenne
degrees
:
and
so
are
to
bee
reckoned
those
whiche
are
more
then
nientie
.
And
then
are
you
betweene
the
sunne
and
the
line
.
The
which
you
shall
know
because
the
shadowes
goe
from
you
towardes
the
South
,
and
because
the
altitude
&
dedination
did
passe
of
nienetie
degrees
.
An
Example
.
The
twenty
day
of
May
,
I
tooke
the
sunne
in
80.
degrees
,
this
day
hee
had
of
declination
twentie
and
one
degrees
,
I
ioyned
the
declination
and
the
altitude
,
&
they
amounted
to
an
hundreth
and
one
degrees
,
so
that
they
be
eleuen
degrees
more
then
nienetie
.
These
eleuen
was
I
distaunt
from
the
line
towardes
the
North
,
betweene
the
sunne
&
the
line
,
the
reason
is
,
because
this
day
the
sunne
was
distaunt
of
the
line
,
21.
degrees
:
which
was
his
declination
towardes
the
part
of
the
North
:
so
that
I
hauing
taken
the
sunne
in
fourescore
degrees
,
there
was
from
me
to
the
sunne
,
tenne
degrees
,
and
as
I
am
betweene
the
sunne
and
the
line
,
I
beeyng
tenne
degrees
distaunt
from
the
sunne
towards
the
line
,
there
was
from
mee
to
the
line
eleuen
degrees
,
which
lacketh
for
the
twentie
one
,
which
is
the
declination
of
the
sunne
.
The
third
rule
,
when
the
sunne
is
towardes
the
North
,
and
the
shadowes
towardes
the
South
,
and
the
declination
,
and
altitude
,
are
nienety
degrees
iust
.
THE
sunne
towardes
the
North
and
the
shadowes
towardes
the
South
,
if
ioyning
the
altitude
and
declination
,
they
be
nienety
degrees
,
you
are
vnder
the
Equinoctiall
line
.
Hee
that
taketh
the
altitude
in
the
time
that
the
sunne
goeth
towards
the
North
in
one
of
three
partes
,
hee
may
stande
that
the
shadowes
may
be
from
him
towardes
the
South
,
The
first
is
when
he
is
betweene
the
sunne
and
the
line
,
and
this
hath
beene
already
declared
in
the
rule
,
before
this
.
The
second
is
,
the
sunne
being
towardes
the
North
and
hee
that
taketh
the
altitude
in
the
selfe
same
line
.
The
thirde
is
,
the
sunne
beeyng
towardes
the
North
,
and
hee
that
taketh
the
altitude
towardes
the
parte
of
the
South
,
therefore
of
the
seconde
,
which
is
,
the
man
beeing
in
the
line
,
the
rule
saith
,
The
sunne
at
the
North
parte
if
the
shadowes
goe
towardes
the
South
,
ioyne
the
declination
with
the
altitude
.
It
is
to
bee
noted
,
that
alwayes
when
the
sunne
goeth
to
one
parte
,
and
the
shadowes
to
an
other
,
the
declination
is
to
bee
ioyned
with
the
altitude
,
And
if
they
be
nientie
degrees
iust
.
Euen
like
if
there
were
seuentie
degrees
of
altitude
and
20.
of
declination
,
or
eightie
of
altitude
and
tenne
of
declination
,
or
any
other
number
,
wherin
the
altitude
and
declination
be
nientie
degrees
iust
,
when
it
is
so
:
you
are
vnder
the
Equinoctiall
liue
.
An
Example
.
The
11.
day
of
Iuly
I
tooke
the
sunne
in
my
Astrolabio
,
in
68.
degrees
,
there
was
this
daye
of
declination
,
22.
degrees
,
ioyne
the
altitude
&
declination
,
and
they
amounted
to
nientie
degrees
,
then
was
I
vnder
the
Equinoctiall
line
.
The
reason
is
,
because
the
sunne
was
towardes
the
parte
of
the
North
,
and
the
shadowes
going
from
me
towardes
the
South
,
I
was
more
towardes
the
South
,
then
the
sunne
,
there
,
fore
taking
sixtie
eight
degrees
of
altitude
,
I
was
distant
from
the
sunne
twentie
two
degrees
,
and
this
day
had
the
sunne
twentie
two
degrees
of
declination
,
so
that
the
sunne
was
distant
from
the
line
twentie
two
degrees
,
and
I
distant
from
the
sunne
towardes
the
line
,
the
saide
twentie
two
degrees
,
by
the
which
I
knewe
that
I
was
vnder
the
said
line
.
For
by
how
much
the
sunne
was
distant
from
the
line
,
so
much
was
I
distant
of
the
sunne
from
the
sayde
line
.
The
fourth
rule
when
the
sunne
is
towardes
the
North
,
&
the
shadowes
towardes
the
south
,
and
the
altitude
and
declination
doe
not
amounte
to
nienetie
degrees
.
THe
sunne
at
North
and
the
shadowes
at
south
,
if
ioyning
the
altitude
and
declination
,
they
come
not
to
nientie
degrees
,
those
that
doe
lack
for
nientie
,
you
are
distant
of
the
line
towardes
the
parte
of
the
south
,
and
the
line
wil
be
betweene
you
and
the
sunne
.
It
hath
beene
declared
that
when
the
sunne
goeth
towardes
the
part
of
the
North
,
if
the
shadowes
goe
from
him
that
taketh
the
altitude
towardes
the
South
,
he
may
be
in
one
of
these
three
places
,
that
is
to
say
,
towards
the
North
,
betweene
the
sunne
and
the
line
,
and
in
the
sayde
line
,
and
at
the
parte
of
the
South
,
the
line
beeing
betweene
him
and
the
Sunne
,
for
in
any
parte
of
these
that
a
man
is
,
the
sunne
going
towardes
the
North
part
,
alwayes
at
the
middest
of
the
day
,
the
shadowes
will
goe
towardes
the
South
,
of
these
three
,
two
haue
beene
declared
,
of
the
thirde
this
rule
speaketh
.
The
sunne
towards
the
North
,
if
the
shadowes
be
towards
the
South
,
and
ioyning
the
altitude
and
declination
,
if
they
come
not
to
nientie
degrees
.
If
the
altitude
which
you
haue
taken
in
the
Astrolabio
,
were
fiftie
or
sixtie
degrees
,
and
the
declination
fifteene
or
twentie
,
so
that
all
being
put
together
,
come
not
to
nienetie
.
Those
whiche
doe
lacke
for
nienetie
,
you
are
distaunt
from
the
line
towardes
the
South
.
So
that
those
Degrees
and
Minutes
fewe
or
many
,
that
bee
lesse
then
nienetye
,
You
are
distaunt
of
the
lyne
,
towardes
the
parte
of
the
South
,
&
then
The
line
wil
bee
betweene
you
and
the
Sunne
.
An
Example
.
The
tenth
of
August
,
taking
the
altitude
,
the
shadowe
was
from
mee
towardes
the
South
:
I
tooke
the
sunne
in
the
Astrolabio
,
in
seuentie
degrees
.
This
day
hee
had
of
declination
twelue
degrees
:
I
ioyned
the
altitude
and
declination
,
and
they
amounted
to
eightie
and
two
degrees
,
there
lacked
eight
degrees
for
nientie
,
these
eight
degrees
was
I
distaunt
from
the
line
towardes
the
part
of
the
South
.
The
reason
is
,
that
taking
the
Sunne
in
seuentie
degrees
,
there
was
from
mee
to
the
Sunne
,
twentie
degrees
,
and
this
day
the
Sunne
was
distaunt
from
the
line
,
twelue
degrees
:
which
was
his
declination
towardes
the
parte
of
the
North
:
so
that
the
eight
which
lacketh
for
twentie
,
was
I
distaunt
of
the
line
towards
the
part
of
the
South
,
so
that
from
mee
to
the
line
was
eight
degrees
,
and
from
the
line
to
the
Sunne
twelue
,
these
bee
the
twentie
which
were
from
me
to
the
Sunne
.
The
fifth
rule
,
when
the
sunne
is
in
the
Equinoctiall
,
and
you
take
his
altitude
in
lesse
then
ninetie
degrees
.
WHen
the
sunne
is
in
the
Equinoctiall
,
if
you
take
his
altitude
in
lesse
then
ninetie
degrees
,
those
whiche
are
lesse
then
ninety
,
you
are
distant
from
the
line
towardes
that
part
which
the
shadowes
are
from
you
.
There
hath
beene
declared
the
rules
of
the
altitude
of
the
sunne
,
when
he
goeth
towardes
the
parte
of
the
North
:
nowe
this
rule
serueth
for
the
dayes
of
the
yeere
,
that
the
sunne
is
in
the
Equinoctiall
line
,
and
sayeth
,
when
the
sunne
is
in
the
Equinoctiall
line
.
The
sunne
is
in
the
Equinoctiall
,
the
eleuenth
of
March
,
&
thirteenth
of
September
,
so
that
in
any
of
these
dayes
,
If
you
take
his
altitude
in
lesse
then
ninetie
degrees
,
so
that
if
you
take
it
in
75.
whiche
are
lesse
by
fifteene
then
ninetie
,
or
in
eightie
or
more
or
lesse
:
Those
which
you
take
lesse
then
ninetie
,
These
fifteene
,
or
tenne
,
or
fiue
,
or
as
many
as
are
lesse
then
nientie
,
you
are
distant
from
the
line
vnto
the
parte
whiche
the
shadowes
doc
fall
from
you
.
So
that
if
the
shadowes
goe
from
you
towards
the
North
,
those
degrees
which
you
finde
lesse
then
ninetie
,
you
are
distant
from
the
line
towardes
the
part
of
the
North
,
and
if
the
shadowes
goe
from
you
towards
the
South
,
the
same
degrees
you
shall
finde
your selfe
towardes
the
South
.
An
Example
.
The
11.
of
March
I
tooke
the
sunne
in
eightie
degrees
,
the
shadowes
were
from
mee
towardes
the
North
,
this
day
the
sunne
hath
no
degree
of
declination
,
therfore
the
10.
degrees
,
which
I
tooke
lesse
than
ninetie
,
I
was
distant
from
the
sunne
.
The
reason
is
,
because
the
sunne
was
in
the
line
,
the
same
degrees
that
I
was
distant
from
the
sunne
,
the
selfesame
am
I
from
the
line
,
&
because
the
shadowes
went
from
me
towardes
the
North
,
was
I
towards
the
part
of
the
North
,
the
which
if
they
had
gone
from
me
towards
the
South
,
the
selfe-same
degrees
should
I
haue
been
towards
the
part
of
the
South
.
The
sixt
rule
,
when
the
altitude
is
taken
in
nientie
degrees
,
whether
in
the
sunne
be
a
declination
o●
no.
WHen
you
shall
take
the
altitude
of
the
sunne
in
nienety
degrees
,
the
sunne
is
ouer
your
heade
,
looke
vpon
the
declination
of
this
day
,
&
if
there
bee
no
declination
,
you
and
the
sunne
be
in
the
line
,
&
if
there
be
any
declination
,
that
which
is
,
you
are
distant
from
the
line
,
towards
that
part
which
the
sunne
goeth
.
This
rule
declareth
how
the
altitude
of
the
sunne
shoulde
bee
knowen
,
when
he
that
taketh
him
,
hath
him
in
the
Cenith
,
or
poynte
that
is
right
ouer
his
head
,
the
which
rule
hath
two
partes
,
that
is
to
say
,
one
,
when
the
sunne
is
in
the
Equinoctiall
line
,
&
the
other
when
it
is
foorth
of
it
,
of
the
first
it
speaketh
.
When
you
doe
take
the
altitude
of
the
sunne
in
nientie
degrees
.
It
is
to
be
vnderstood
,
that
the
measurer
of
the
worlde
,
sheweth
in
your
Astrolabio
,
the
nientie
degrees
iust
,
when
it
is
so
.
Knowe
yee
that
the
sunne
is
right
ouer
your
head
:
In
such
sort
,
that
your
shadow
shall
not
goe
to
any
part
,
therfore
then
Looke
on
the
declination
of
this
day
:
Is
to
bee
vnderstood
the
degrees
and
minutes
,
which
the
sunne
is
distant
from
the
Equinoctial
.
And
if
there
be
no
declination
,
Which
will
be
the
eleuenth
of
Marche
,
and
the
thirteenth
of
September
,
them
the
declination
is
of
few
minutes
.
You
and
the
sunne
be
in
the
line
,
the
sunne
beingin
the
●●ne
then
he
hath
no
degrete
nor
halfe
a
degree
of
declination
,
and
you
are
in
the
line
,
seeing
that
you
are
vnder
the
sunne
.
And
if
there
be
any
declination
:
This
is
the
second
part
of
this
rule
,
wherein
is
declared
,
when
the
sunne
,
and
he
that
taketh
the
altitude
be
out
of
the
Equinectiall
,
the
which
will
bee
knowne
in
the
degrees
,
that
the
sunne
hath
of
declination
,
because
it
saith
,
that
which
is
,
is
to
be
vnderstood
few
degrees
,
or
many
.
So
much
you
are
distant
from
the
line
so
that
seesyng
you
are
vnder
the
sunne
,
and
the
sunne
is
distaunt
from
the
line
,
that
the
same
degrees
&
minutes
,
that
the
sunne
hath
of
declination
,
the
same
you
are
distaunt
from
the
line
,
towards
the
part
where
the
sunne
goeth
.
If
it
bee
that
the
sunne
goeth
to
the
North
part
,
you
are
toward
the
North
part
,
&
if
he
goe
towardes
the
South
,
you
are
towarde
the
same
parte
of
the
South
,
and
because
with
this
that
is
declared
,
this
rule
may
be
well
vnderstood
,
there
is
put
in
it
no
more
declaration
.
The
seuenth
rule
,
when
the
sunne
is
towards
the
part
of
the
South
,
and
the
shadowes
goe
likewise
towards
the
South
.
THe
sunne
towards
the
part
of
the
south
,
and
the
shadowes
towards
the
South
,
the
sunne
is
between
you
and
the
line
,
looke
how
many
degrees
of
altitude
,
you
tooke
,
and
how
many
doe
lacke
for
nientie
,
and
with
those
that
lacke
,
ioyne
the
declinacion
of
this
day
,
and
beeing
altogether
the
degrees
that
be
,
you
are
distaunt
from
the
line
,
towardes
the
South
.
This
rule
is
,
when
the
sunne
is
towards
the
part
of
the
South
,
and
the
shadowes
goe
towardes
the
South
,
is
agreeable
with
the
first
rule
,
which
was
declared
when
the
sunne
goeth
towards
the
part
of
the
North
,
and
because
it
is
declared
according
to
his
proper
meaning
,
&
this
is
agreeable
to
that
,
there
shall
not
be
put
here
any
other
declaration
,
but
the
same
that
is
there
declared
,
is
to
be
vnderstood
in
this
.
Onely
making
difference
of
the
names
,
that
is
to
say
,
from
the
North
to
the
South
,
but
because
this
rule
is
for
the
time
when
the
sunne
goeth
towardes
the
South
,
I
wil
put
an
example
of
the
part
of
the
South
,
in
the
manner
following
.
An
Example
.
The
fourth
of
October
,
taking
the
altitude
,
the
shadowes
went
from
me
towards
the
South
,
and
I
tooke
the
sunne
in
85.
degrees
in
my
Astrolabio
,
this
day
the
sun
had
8.
degrees
of
declination
towards
the
south
,
therefore
taking
the
altitude
in
85.
degrees
,
there
lacketh
siue
,
for
nienetie
,
these
fiue
was
I
distaunt
from
the
sunne
,
and
with
these
fiue
,
I
ioyned
the
eight
of
declination
,
they
amounted
to
thirteene
degrees
,
these
thirteene
degrees
was
I
distaunt
from
the
line
,
because
from
mee
to
the
sunne
was
fiue
,
and
from
the
Sunne
to
the
line
eight
,
which
are
thirteene
,
so
that
I
was
distaunt
thirteene
degrees
from
the
line
towardes
the
parte
of
the
South
.
The
eyght
rule
,
when
the
sunne
is
towardes
the
nouth
,
and
the
shadowes
towardes
the
●orth
,
and
the
declination
and
altitude
are
more
then
ninetie
degrees
.
THe
Sunne
towardes
the
south
,
if
the
shadowes
be
towards
the
north
,
ioyne
the
declination
with
the
altitude
,
and
altogether
if
they
passe
of
nientie
degrees
,
those
which
are
more
,
you
are
distant
of
the
line
towards
the
south
,
and
you
are
between
the
sunne
and
the
line
.
This
rule
is
declared
in
the
seconde
rule
before
written
when
the
sunne
goeth
towards
the
north
parte
,
for
the
same
account
or
reckoning
that
is
made
the
sunne
beeing
towardes
the
north
and
he
that
taketh
the
altitude
at
the
same
parte
of
the
north
,
betweene
the
sunne
and
the
line
,
the
selfe
same
is
to
be
done
,
the
sunne
beeing
towardes
the
part
of
the
south
,
and
hee
which
taketh
the
altitude
in
the
same
part
betweene
the
sunne
and
the
line
.
Therfore
the
declaration
which
is
written
for
the
one
,
by
the
selfe
same
fourme
serueth
for
the
other
,
and
to
know
that
he
which
taketh
the
altitude
is
betweene
the
sunne
and
the
line
,
the
rule
declareth
in
what
altitude
and
declination
,
they
shoulde
passe
of
nienty
degrees
,
as
it
is
shewed
in
this
example
.
An
Example
.
The
xiii
.
of
Ianuary
I
tooke
the
sun
in
seuentie
eyght
degrees
,
this
day
hee
had
of
declination
nienteene
degrees
,
I
ioyned
the
declination
and
altitude
as
the
rule
sheweth
and
did
amount
to
nientie
and
seuen
degrees
,
these
seuen
,
degrees
that
past
of
nienty
,
was
I
distant
from
the
line
towards
the
south
.
The
reason
is
,
that
taking
the
sunne
in
seuentie
&
eight
degreees
,
I
was
distant
from
the
sunne
xii
.
degrees
,
&
seeing
that
the
sunne
was
distant
from
the
line
ri●
.
degrees
,
&
I
being
between
the
sunne
&
the
line
,
therfore
there
are
from
me
to
the
sunne
xii
degrees
,
&
from
me
to
the
line
seuen
which
are
nienteene
,
so
many
are
the
degrees
which
the
sunne
is
distant
of
the
line
.
The
nienth
rule
,
when
the
Sunne
is
at
the
south
,
and
the
shadowes
at
north
,
and
the
altitude
and
declination
are
nientie
degrees
iust
.
THE
Sunne
at
south
and
the
shadowes
at
north
if
ioyning
the
altitude
and
declination
they
bee
nientie
degrees
,
you
are
in
the
equinoctiall
line
.
It
hath
beene
declared
that
the
sunne
being
at
north
,
he
which
taketh
the
altitude
,
may
be
in
one
of
3
partes
wherby
his
shadowes
,
may
goe
towardes
the
south
one
of
them
is
towardes
the
parte
of
the
north
,
betweene
the
sunne
and
the
l●n●e
,
another
in
the
sayd
line
,
the
other
towardes
the
parte
of
the
south
▪
the
line
betweene
him
and
the
sunne
▪
the
same
is
vnderstood
the
sunne
going
towardes
the
parte
of
the
south
,
that
hee
whiche
toketh
the
altitude
in
one
of
three
partes
,
he
may
be
that
the
shadowes
goe
from
him
towardes
the
north
,
the
one
being
towarde
the
parte
of
the
south
betweene
the
sunne
and
that
line
,
the
other
being
in
the
saide
line
.
The
thirde
being
towardes
the
part
of
the
north
the
line
betweene
him
and
the
sunne
.
Seeing
of
the
first
it
hath
beene
written
of
,
and
in
the
rule
going
before
,
of
the
second
,
which
is
the
sunne
being
towardes
the
parte
of
the
south
,
&
for
him
which
taketh
the
altitude
in
the
line
is
put
this
present
rule
,
the
which
because
in
the
third
rule
when
the
sunne
goeth
towarde
the
parte
of
the
north
,
it
is
declared
.
Only
here
is
to
be
noted
,
the
example
following
.
An
example
.
The
seconde
of
December
I
tooke
the
sunne
in
sixtie
seuen
degrees
,
this
day
he
had
of
declination
twentie
three
degrees
,
ioyne
the
declination
,
and
the
altitude
they
amounted
to
nientie
degrees
,
and
being
so
I
was
in
the
equinoctiall
,
for
because
the
sunne
at
south
,
the
shadowes
going
from
me
towards
the
north
,
I
was
more
towardes
the
north
then
the
sunne
,
the
sunne
this
day
was
distant
of
the
line
twentie
three
degrees
which
was
his
declination
,
so
that
taking
the
altitude
in
sixtie
seuen
degrees
,
there
was
from
me
to
the
sun
twenty
three
degrees
,
in
such
sorte
that
the
same
twentie
three
degrees
which
the
sunne
was
distant
of
the
line
,
the
same
was
I
distant
of
the
sun
towards
the
line
,
so
thereby
I
knew
that
I
was
in
the
saide
line
.
The
tenth
rule
,
when
the
Sunne
is
towardes
the
South
,
and
the
shadowes
towardes
the
North
,
if
the
Altitude
and
declination
beeing
ioyned
,
they
come
not
to
nientie
degrees
.
THe
Sunne
at
South
,
and
the
shadowes
at
North
,
if
the
altitude
and
declination
doe
not
come
to
ninetie
degrees
,
those
which
doe
lacke
for
〈◊〉
you
are
distant
of
the
line
towarde●
the
parte
of
the
north
,
and
the
line
should
be
betweene
you
and
the
Sunne
.
The
thirde
difference
which
hath
beene
spoken
of
,
wherein
hee
which
taketh
the
altitude
,
may
bee
the
sunne
beeing
towardes
the
South
,
and
the
shadowes
going
towardes
the
North
,
is
,
beeing
towardes
the
parte
of
the
North
,
the
line
betweene
him
and
the
Sunne
,
as
this
rule
sheweth
,
whose
declaration
is
written
in
the
fourth
rule
,
when
the
Sunne
goeth
towardes
the
parte
of
the
North.
And
it
is
to
lie
noted
,
that
at
all
times
when
the
sunne
goeth
towards
one
part
,
&
the
shadowes
towardes
another
,
the
declination
is
to
be
ioyned
with
the
altitude
,
and
if
they
passe
nientie
degrees
,
those
which
are
more
,
you
are
distant
of
the
line
,
towardes
the
parte
which
the
sunne
goeth
and
if
they
bee
nientie
iust
,
you
shoulde
be
in
the
line
,
and
if
they
come
not
to
nientie
,
those
which
are
lesse
you
are
distant
at
the
contrary
parte
where
the
sunne
goeth
,
as
in
this
rule
is
declared
,
and
therefore
in
this
example
following
is
to
be
noted
.
An
Example
.
The
thirtie
of
September
I
tooke
the
sunne
in
sixtie
degrees
,
and
the
shadowes
were
from
me
towardes
the
north
,
and
the
sunne
this
daye
had
sixe
degrees
and
a
halfe
of
declination
,
I
ioyned
the
declination
and
the
altitude
,
and
they
amounted
to
sixtie
and
sixe
degrees
and
a
halfe
,
there
lacked
twentie
three
degrees
and
a
half
for
nientie
.
These
twenty
three
degrees
and
a
halfe
was
I
distant
from
the
line
towardes
the
parte
of
the
north
.
The
reason
is
,
for
that
taking
the
sunne
in
sixtie
degrees
there
was
from
me
to
the
sunne
thirtie
.
I
was
towardes
the
part
of
the
north
,
and
the
sunne
towardes
the
part
of
the
south
distant
from
the
line
,
sixe
degrees
&
a
halfe
,
so
that
of
the
thirtie
degrees
,
which
were
from
me
to
the
sunne
,
taking
out
the
sixe
and
a
halfe
which
the
sunne
is
distant
from
the
line
,
there
will
be
from
me
to
the
line
twenty
three
degrees
and
a
halfe
.
The
sixt
chapter
,
wherefore
the
rules
of
the
height
of
the
sunne
doe
shewe
the
degrees
that
a
man
is
distant
of
the
equinoctiall
line
more
then
by
any
other
parte
.
IN
the
rules
before
written
hath
beene
declared
how
that
euery
day
that
you
wil
take
the
altitude
of
the
sunne
,
you
shall
knowe
at
what
parte
of
the
line
you
are
,
and
how
many
degrees
distant
as
wel
of
the
one
part
as
of
the
other
.
Of
this
may
be
〈◊〉
what
the
cause
is
,
wherefore
all
the
rul●s
of
the
●●●tude
of
the
sunne
,
are
made
and
ord●●ned
that
a
man
should
vnderstand
how
many
degrees
he
is
distant
of
the
equinoctiall
line
,
more
then
from
the
pole
,
or
from
the
other
tropikes
or
from
any
other
parte
.
To
this
is
to
bee
answered
,
that
the
reason
whereby
onely
we
would
know
the
distance
,
that
is
from
the
sayd
line
,
more
then
from
any
other
parte
,
is
,
because
the
sayde
equinoctiall
line
,
as
before
hath
beene
declared
,
is
put
and
●●tuated
in
the
middest
of
the
worlde
,
and
all
the
cardes
of
nauigation
whereby
the
pilots
&
sailers
doe
rule
themselues
by
.
In
the
card
of
nauigation
a●
ordayned
and
put
the
portes
,
and
bayes
,
riuers
,
capes
,
Ilandes
,
and
shooldes
,
&
all
other
thinges
,
which
are
marked
in
them
,
according
to
the
degrees
that
euery
thing
is
distant
from
the
sayd
equinoctiall
line
,
as
wel
towardes
the
part
of
the
north
,
as
of
the
south
:
and
beeing
knowne
by
the
pilot
or
sayler
,
with
the
altitude
which
he
taketh
,
howe
many
degreees
he
is
distant
of
the
sayde
line
,
to
one
parte
or
to
another
,
or
if
he
bee
in
the
sayde
line
,
likewise
he
knoweth
if
he
be
equall
in
altitude
with
the
place
which
hee
goeth
to
seeke
according
as
in
his
carde
he
hath
pricked
,
or
if
he
ought
to
rise
vp
or
goe
downe
,
and
how
many
degrees
,
vntill
he
put
him selfe
right
of
the
place
,
and
for
this
cause
the
line
is
more
sought
for
,
then
any
other
parte
.
The
seuenth
chapter
,
by
what
reason
al
rules
of
the
altitude
of
the
sunne
are
reduced
to
nienty
degrees
,
more
then
to
any
other
number
.
IT
may
be
asked
by
what
reason
all
the
rules
of
the
altitude
of
the
sunne
,
as
before
hath
beene
declared
goe
reduced
to
this
number
of
nientie
degrees
,
more
then
to
any
other
,
for
that
it
is
so
written
,
that
the
degrees
of
altitude
are
to
be
seene
,
wherein
the
sunne
is
taken
in
the
Astrolabio
,
how
many
doe
lacke
,
vnto
nientie
and
in
other
rules
is
sayde
that
the
altitude
and
declination
is
to
be
ioyned
and
seene
if
they
amount
to
nientie
degrees
,
or
if
they
passe
nientie
degrees
,
or
if
they
come
not
to
nienty
degrees
,
in
such
sorte
,
that
all
the
rules
are
made
and
ordained
to
this
number
of
nienty
,
therfore
it
ought
to
be
known
wherfore
more
to
this
number
than
to
any
other
.
For
the
vnderstanding
of
this
doubt
is
to
be
immagined
that
wheresoeuer
a
man
standeth
is
the
middest
of
the
worlde
,
and
he
seeth
half
the
heauen
,
in
such
sort
,
that
as
the
roundnes
of
the
worlde
hath
three
hundreth
&
sixtie
degrees
,
the
horizon
discouereth
the
half
which
are
a
hundreth
and
eyghtie
,
and
they
are
vnderstoode
in
this
manner
▪
from
any
manner
of
part
of
the
horizon
vnto
the
Cenith
are
nienty
degrees
,
and
from
my
Cenith
vnto
the
other
part
of
the
horizon
other
nientie
.
Which
is
to
be
vnderstoode
in
this
manner
,
immagine
that
in
what
place
so
euer
a
man
is
in
,
he
is
right
in
the
middest
of
this
circle
,
which
circle
is
his
horizon
.
Therefore
I
saye
that
I
am
in
the
middest
of
the
circle
,
and
from
the
point
A.
which
is
the
horizon
vnto
my
heade
are
nientie
degrees
,
and
from
my
Cenith
to
the
point
C.
other
nientie
,
which
are
a
hundreth
and
eyghtie
,
and
from
the
point
B.
vnto
my
heade
nientie
,
and
from
my
heade
vnto
the
pointe
D.
other
nientie
,
and
so
there
is
nientie
degrees
from
my
heade
to
any
parte
of
my
horizon
.
Therefore
declaring
the
doubt
,
I
say
that
the
reason
why
the
rules
of
the
altitude
of
the
Sunne
are
reduced
to
this
number
of
nientie
,
is
because
the
Sunne
cannot
rise
vp
aboue
the
horizon
,
more
then
nientie
degrees
,
which
is
vntill
he
come
right
ouer
our
heads
,
and
so
when
we
take
him
in
nientie
degrees
of
Astrolabio
,
wee
saye
that
wee
haue
the
sunne
right
ouer
our
heades
,
&
when
we
take
him
in
lesse
,
that
which
is
lesse
then
nientie
is
the
sunne
distant
from
vs
:
so
that
because
the
sunne
cannot
rise
vp
,
vpon
the
horizon
more
then
nientie
degrees
,
with
the
which
as
I
haue
saide
,
he
commeth
vntill
he
be
vpon
our
heads
:
therefore
the
rules
of
his
altitude
goe
reduced
to
this
number
,
and
not
to
any
other
.
The
eight
Chapter
,
wherein
is
declared
wherefore
we
saie
,
that
the
man
is
distant
of
the
sunne
,
the
degrees
that
he
taketh
in
the
Astrolabio
lesse
then
nientie
.
OF
the
rules
of
the
altitude
of
the
Sunne
before
written
,
hath
been
sayde
,
and
declared
,
that
at
all
tymes
when
the
Altitude
is
taken
,
the
degrees
are
to
bee
looked
for
which
doe
lacke
in
the
Astrolabio
of
nientie
,
and
that
those
same
,
the
man
is
distante
of
the
Sunne
.
And
beecause
it
is
conuenient
and
expedient
that
this
rule
bee
well
and
throughly
vnderstoode
and
knowne
,
I
will
most
euidently
declare
it
,
in
this
manner
following
.
It
is
to
bee
noted
,
when
the
Sunne
doth
beginne
to
appeare
by
our
horizon
which
is
,
when
he
goeth
foorth
in
the
morning
,
then
he
hath
no
Altitude
but
from
thence
hee
goeth
rising
vp
,
and
howe
much
more
hee
ryseth
,
so
much
he
goeth
hauing
more
Altitude
,
vpon
the
Horizon
,
in
such
sort
that
if
one
houre
after
he
is
come
forth
,
hee
hath
raysed
him selfe
vp
fiue
degrees
,
in
two
houres
hee
shall
haue
raysed
him selfe
vp
tenne
or
twelue
,
and
in
three
houres
〈…〉
vp
vn●●●
the
myddist
the
daye
,
and
from
of
thence
hee
t●●●eth
to
desc●●●●
by
the
〈◊〉
order
that
hee
went
risy●g
vp
,
vntyll
hee
put
or
hyde
him selfe
vnder
the
horizon
.
Of
that
which
hath
beene
sayde
,
two
thinges
are
to
bee
noted
,
the
fyrst
is
,
that
from
the
time
the
Sunne
〈◊〉
foorth
,
vntyl
it
be
the
middest
of
the
day
,
he
goeth
alwayes
rising
vp
,
and
aug●●nting
in
his
〈◊〉
,
vntyll
hee
come
to
〈◊〉
,
Meridian
,
and
alwayee
the
Meridian
is
in
the
middest
of
the
bow
,
which
the
Sunne
maketh
,
from
the
time
that
hee
commeth
foorth
vntill
hee
is
sette
▪
This
is
because
alwayes
the
man
is
in
the
middest
of
the
roundnes
,
which
roundnes
is
his
horizon
.
The
seconde
is
,
that
this
Bowe
which
the
Sunne
maketh
vppon
our
horizon
,
is
not
euery
day
equall
,
but
at
some
times
is
greater
then
at
other
some
,
euen
as
the
daye
is
great
or
litle
,
but
although
that
the
bowe
bee
great
or
little
,
alwayes
the
Sunne
goeth
rising
vp
,
vntill
he
come
to
the
Meridian
,
and
from
thence
hee
descendeth
.
And
it
is
to
be
noted
,
that
alwayes
the
Sunne
commeth
forth
,
and
setteth
in
equall
distance
from
vs
,
but
at
the
middest
of
the
day
,
he
is
not
alwaies
in
equal
distance
of
vs
,
but
at
one
time
hee
is
neere
,
and
at
another
time
farre
off
,
this
is
from
the
right
of
our
heads
,
which
is
to
be
vnderstood
in
this
manner
.
I
put
the
case
that
I
bee
distant
from
the
equinoctiall
line
tenne
degrees
,
and
the
Sunne
hath
of
declination
the
same
daye
the
same
tenne
degrees
,
towards
the
part
that
I
am
,
and
beeing
so
,
when
the
Sunne
came
foorth
this
daye
,
and
beganne
to
appeare
in
the
horizon
,
then
hee
was
from
mee
nientie
degrees
,
and
from
thence
hee
went
rysing
vp
vntyll
the
middest
of
the
day
,
and
beeing
come
to
my
Meridian
,
hee
shall
bee
precisely
right
ouer
my
head
.
Insomuch
that
if
a
lyne
be
imagined
▪
that
rightly
doth
descende
from
the
Sun
vnto
the
earth
,
this
line
woulde
come
vpon
my
head
,
and
this
woulde
bee
so
at
all
times
,
when
I
were
as
distant
of
the
line
,
as
the
declination
is
,
which
the
sunne
hath
this
day
,
because
I
am
in
that
way
where
the
Sunne
that
day
doth
make
his
moouing
,
by
the
which
that
day
at
the
middest
of
the
day
,
I
shall
haue
it
vpon
my
head
:
but
if
I
be
distant
of
the
waye
of
the
sunue
,
although
that
when
he
came
foorth
,
hee
was
from
me
ninety
degrees
,
it
is
to
be
vnderstood
,
that
when
it
is
the
middest
of
the
day
,
I
shall
not
haue
it
right
ouer
my
head
,
but
I
shal
haue
it
as
farre
of
,
as
the
distance
is
from
the
place
,
where
I
am
,
to
the
place
of
the
way
of
the
sunne
,
in
such
sort
that
if
the
distance
,
which
is
of
the
place
or
way
,
where
I
am
,
to
the
place
or
way
where
the
Sunne
came
foorth
,
were
fiue
degrees
,
or
tenne
,
or
more
,
or
lesse
:
Those
same
the
Sunne
shal
be
at
the
middest
of
the
day
distant
from
the
right
of
my
head
,
so
that
,
if
there
were
layd
two
straight
lines
or
strekes
,
from
the
East
into
the
West
,
the
one
by
the
place
where
the
Sunne
commeth
foorth
,
and
the
other
by
the
place
where
I
am
:
the
degrees
of
distance
that
shoulde
be
from
one
line
to
the
other
,
the
selfe-same
at
the
middest
of
the
day
,
wil
be
of
distance
of
the
Sunne
to
my
Cenith
.
And
doe
you
note
,
that
in
this
distance
,
which
the
Sunne
maketh
from
mee
is
not
to
bee
looked
,
howe
muche
there
is
from
mee
to
the
Sunne
,
but
doe
you
looke
how
much
the
Sunne
is
distant
at
the
middest
of
the
day
,
from
the
right
of
my
head
,
for
so
much
as
this
distance
is
,
so
muche
will
I
say
,
that
I
am
distant
of
the
Sunne
,
to
one
parte
or
other
.
The
nienth
Chapter
,
wherein
is
declared
,
howe
it
is
vnderstoode
,
that
a
man
hath
the
Sunne
right
ouer
his
head
.
IT
hath
beene
declared
in
the
Chapter
going
before
,
that
when
a
man
findeth
himselfe
in
the
course
where
the
sun
maketh
his
way
,
that
that
day
at
the
middest
of
the
day
,
he
shall
haue
him
right
ouer
his
heade
,
of
this
maye
bee
had
a
greate
doubt
,
(
whiche
is
this
.
)
A
doubt
.
It
hath
beene
declared
in
the
seconde
Chapter
of
this
fourth
Booke
,
according
to
the
opinion
of
Ptholome
,
and
Al●rag●no
,
that
the
Sunne
is
an
hundreth
sixtie
and
sixe
times
greater
then
the
earth
:
and
that
the
Sunne
is
so
great
,
it
appeareth
well
,
seeyng
that
continually
hee
geueth
light
to
all
the
starres
of
the
heauen
,
the
heauen
beeing
so
greate
,
and
the
starres
so
many
in
number
,
as
the
royall
prophet
saith
,
that
God
only
doth
reckon
and
number
them
.
Likewise
the
greatnesse
of
the
Sunne
doth
shewe
,
in
the
which
,
although
that
there
bee
alwayes
put
all
the
roundnesse
of
the
water
and
earth
betweene
the
Sunne
and
the
Heauen
in
such
sort
,
that
continually
,
he
putteth
himselfe
before
,
according
to
the
sight
of
man
,
whereby
wee
see
not
anie
more
then
halfe
the
heauen
:
and
although
the
earth
and
the
water
are
so
great
bodies
,
yet
they
occupie
not
anye
thing
,
nor
deteyne
the
light
of
the
Sunne
,
that
it
doe
not
passe
to
geue
light
to
all
the
starres
.
This
is
because
the
earth
and
water
are
so
little
things
in
respect
of
the
sunne
,
that
well
neere
they
maye
bee
compared
to
a
graine
of
mustard
seed
,
put
before
a
great
torche
lighted
,
which
doth
let
nothing
of
the
light
thereof
,
but
that
it
doth
extende
to
all
partes
.
Therefore
all
the
earth
beeyng
so
little
in
comparison
of
the
Sunne
,
and
the
man
beeyng
well
neere
of
no
quantitie
in
respecte
of
all
the
earth
,
it
seemeth
to
be
farre
out
of
reason
,
to
say
that
a
man
shoulde
haue
the
Sunne
right
ouer
his
head
in
anye
time
or
place
,
euen
as
there
shoulde
bee
no
reason
to
saye
,
that
a
greate
shippe
going
by
the
Sea
,
may
bee
right
vppon
the
poynte
of
a
little
nayle
,
which
were
in
the
depth
of
the
water
:
or
that
a
great
cloude
shoulde
be
right
vpon
a
little
worme
of
the
earth
,
euen
as
wel
it
seemeth
,
that
there
is
no
reason
to
say
,
that
the
sunne
is
right
ouer
the
heade
of
a
man
:
seeing
that
the
sunne
is
alwayes
,
and
sheweth
it selfe
vpon
the
halfe
of
all
the
earth
,
by
the
which
reason
likewise
it
seemeth
,
that
it
ought
not
to
be
thought
,
that
the
sunne
in
one
time
is
in
the
Equinoctial
,
and
another
time
at
the
North
part
,
and
another
at
the
South
parte
,
seeing
that
these
are
partes
of
the
earth
,
and
the
sunne
not
only
is
greater
then
these
parts
,
but
in
very
great
quantity
,
greater
then
all
of
them
,
as
it
is
saide
,
and
so
it
is
prooued
&
seemeth
that
it
is
an
improper
thing
,
to
say
that
the
sunne
is
right
vpon
our
head
,
or
that
he
is
in
one
parte
or
other
of
the
earth
.
A
declaration
.
For
the
declaring
of
this
doubt
,
is
to
be
noted
,
that
although
the
sunne
is
of
so
great
a
quantitie
,
as
before
hath
beene
declared
,
this
doth
not
let
,
that
a
man
may
haue
him
right
ouer
his
head
,
and
in
the
discourse
of
the
yeere
he
be
in
one
part
or
other
of
the
earth
,
the
which
is
vnderstood
in
this
manner
,
that
the
greatnesse
of
the
sunne
is
not
to
be
considered
how
great
it
is
in
it selfe
,
but
how
great
it
is
to
vs
,
I
will
say
according
to
our
sight
,
and
according
to
the
effect
which
it
maketh
with
vs
.
(
An
example
of
this
is
)
that
many
times
it
happeneth
to
men
that
goe
sayling
,
and
they
see
very
farre
of
in
the
Sea
a
ship
,
and
although
shee
be
very
great
,
and
goeth
very
swiftly
,
it
seemeth
to
him
that
beholdeth
her
,
that
she
is
little
,
and
that
shee
moueth
not
:
the
same
doth
happen
to
vs
with
a
great
cloude
,
which
the
wind
doth
carry
with
great
lightnesse
:
this
is
caused
for
the
great
distaunce
that
is
from
the
one
to
the
other
,
in
such
sort
,
that
we
iudge
not
as
it
is
,
but
according
as
the
sight
doth
represent
it
to
vs
:
euen
so
the
sunne
although
he
be
very
great
,
and
mooueth
with
great
haste
,
we
iudge
not
of
it
,
but
according
to
our
sense
,
for
because
in
as
much
as
toucheth
the
hastinesse
of
his
mouing
,
as
the
earth
is
wel
neere
a
point
of
the
circle
,
which
the
sunne
maketh
,
it
is
certayne
,
that
it
cannot
bee
perceiued
or
knowne
according
as
his
moouing
is
,
this
is
by
reason
of
the
greate
distance
that
is
betweeene
him
and
vs
,
and
so
by
this
greate
distance
hee
commeth
to
diminish
himselfe
so
muche
in
our
sight
that
he
may
be
right
ouer
the
heade
of
of
one
man
,
and
not
right
ouer
the
head
of
another
,
that
is
one
league
from
him
.
This
is
shewed
,
that
in
taking
the
altitude
of
the
sunne
,
one
man
will
take
him
very
precisely
right
ouer
his
owne
head
,
&
another
although
hee
bee
neere
,
will
finde
him
sarre
of
from
him
,
this
is
bicause
he
was
more
right
ouer
the
head
of
the
one
then
of
the
other
.
Likewise
this
is
shewed
by
the
shadowes
,
the
which
doe
shew
infallibly
the
moouing
which
the
sunne
maketh
from
one
part
to
another
:
in
such
sort
,
that
in
one
place
one
man
may
haue
his
shadow
so
right
,
that
at
the
middest
of
the
day
,
the
sunne
doth
make
no
shadow
to
any
part
,
and
to
another
that
is
not
farre
from
thence
,
although
he
be
in
the
same
Meridian
,
and
at
the
same
houre
and
minute
,
the
shadow
wil
decline
to
some
part
,
wherby
it
manifestly
appeareth
▪
to
haue
the
sunne
right
ouer
our
head
,
and
howe
if
mooueth
not
onely
by
the
middest
,
but
likewise
by
the
sides
of
the
earth
.
And
for
the
better
declaration
of
that
aforesayd
is
to
be
noted
,
that
naturally
all
things
which
wee
see
,
the
sight
doth
comprehend
it
by
A
piramide
,
so
saith
Alacen
in
the
perspectiue
in
the
17.
rule
,
that
the
comprehension
of
all
thinges
visible
is
by
a
rooted
pyramide
.
The
pyramide
is
to
be
imagined
in
this
manner
.
The
tenth
Chapter
,
to
knowe
howe
the
altitude
of
the
Sunne
ought
to
be
seen
if
it
be
leape
yere
,
or
what
yere
it
is
.
IN
the
sixth
Chapter
of
this
fourth
booke
,
I
said
how
it
is
necessary
when
the
altitude
of
the
sunne
is
taken
to
knowe
the
yere
,
if
it
be
the
leap
yere
,
or
the
first
or
seconde
,
or
thirde
after
the
leap
yere
,
because
the
dayes
of
one
yere
,
with
those
of
the
other
haue
not
the
degrees
and
minutes
equall
,
and
the
reason
is
,
because
as
in
the
third
chapter
of
this
fourth
booke
hath
beene
declared
,
that
the
yere
called
Solar
,
hath
three
hundreth
sixty
fiue
daies
,
&
sixe
houres
,
and
that
those
sixe
houres
of
euery
one
yeere
,
from
foure
to
foure
yeres
,
do
make
a
natural
day
,
and
that
such
a
yeere
is
called
a
leap
yere
,
so
that
the
first
yere
after
the
leape
yeere
,
hath
three
hundreth
sixtie
fiue
dayes
and
sixe
houres
.
And
the
seconde
yeere
,
three
hundreth
sixtie
fiue
dayes
and
twelue
houres
,
the
sixe
of
the
first
yeere
,
and
sixe
his
owne
,
and
the
third
yeere
,
three
hundreth
sixetie
fiue
daies
and
eighteene
houres
,
the
twelue
of
the
two
yeres
the
first
and
seconde
,
and
the
vi
.
his
owne
,
and
the
fourth
yeere
three
hundreth
sixtie
sixe
dayes
,
so
that
in
this
fourth
yere
is
shut
vp
the
houres
of
al
foure
yeres
,
and
the
fourth
yere
being
past
,
The
first
begineth
,
and
so
the
other
yeres
successiuely
as
it
is
said
,
and
for
this
cause
they
bee
not
equall
in
degrees
and
minutes
all
dayes
one
with
another
:
Therefore
it
is
conuenient
,
as
it
is
before
declared
,
when
the
altitude
of
the
sunne
is
to
bee
taken
,
that
it
be
seene
what
yere
it
is
,
and
seeke
what
daye
and
moneth
you
are
in
,
and
there
you
shal
finde
the
declination
,
or
distance
which
the
sun
hath
,
from
the
line
,
as
in
the
tables
folowing
is
conteined
,
therfore
to
knowe
the
yere
that
you
are
in
,
if
it
be
a
leape
yere
,
or
the
first
,
second
,
or
thirde
after
the
leape
yeere
,
looke
ouer
the
two
rules
of
the
discourses
folowing
,
for
in
them
playnely
is
shewed
,
by
reckoning
the
yere
of
our
L●●be
,
a
thousande
fiue
hundreth
fourtie
fiue
in
the
first
house
of
the
which
is
the
first
yere
,
and
so
successiuely
in
euery
yere
one
house
,
&
the
house
being
ended
of
the
last
rule
,
returne
to
the
beginning
,
and
so
this
account
is
for
euer
.
A
rule
to
knowe
the
leape
yere
.
1545.
☜
1.
2.
3.
B
1.
2.
3.
B
1.
2.
3.
B
1.
2.
3.
B
1.
2.
3.
B
1.
2.
3.
B
1.
2.
3.
B.
When
you
will
knowe
if
the
yeere
be
a
leape
yeere
,
or
not
without
looking
in
the
booke
,
looke
in
the
yere
of
the
birth
of
our
Lord
,
&
leaue
the
thousand
fiue
hundreth
,
the
rest
deuide
in
the
middest
,
and
when
euery
halfe
were
of
euen
number
in
payers
or
cupples
it
is
the
leape
yere
.
The
tables
of
the
distance
or
declination
which
the
Sunne
maketh
from
the
equinoctiall
line
euery
day
of
the
foure
yeres
,
aswell
towardes
the
part
of
the
north
as
towardes
the
south
.
¶
The
declination
of
the
Sunne
.
The
first
yeere
.
Ianuarie
.
|
Februarie
.
|
March
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
xxi
|
●i
|
1
|
xiii
|
iviii
|
1
|
iii
|
xxxix
|
2
|
xxi
|
xl●
|
2
|
xii●
|
xxxviii
.
|
2
|
●i
|
xv
|
3
|
xxi
|
xxxi
|
3
|
xiii
|
xviii
.
|
3
|
ii
|
iii
|
4
|
xxi
|
xx
|
4
|
x●
|
lviii
|
4
|
ii
|
xxviii
|
5
|
xxi
|
ix
|
5
|
xii
|
xxxvii
|
5
|
ii
|
iiii
|
6
|
xx
|
lviii
|
6
|
xii
|
xvi
|
6
|
i
|
xli
|
7
|
xx
|
xiv
|
7
|
xi
|
lv
|
7
|
i
|
xvii
|
8
|
xx
|
xxxiii
|
8
|
xi
|
xxxiiii
|
8
|
0
|
liii
|
9
|
xx
|
xxi
|
9
|
xi
|
xii
|
9
|
0
|
xxx
|
10
|
xx
|
viii
|
10
|
x
|
●i
|
10
|
0
|
vi
|
11
|
x●x
|
lv
|
11
|
x
|
xxix
|
11
|
0
|
xviii
|
12
|
x●x
|
xli
|
12
|
x
|
vii
|
12
|
0
|
xiii
|
13
|
x●x
|
xxvii
|
13
|
ix
|
x●vii
|
13
|
i
|
v
|
14
|
x●x
|
xiii
|
14
|
ix
|
●●iii
|
14
|
i
|
xxix
|
15
|
xviii
|
lviii
|
15
|
ix
|
|
15
|
i
|
lii
|
16
|
xviii
|
xlii
|
16
|
viii
|
xxxviii
|
16
|
ii
|
xvi
|
17
|
xviii
|
xxvii
|
17
|
viii
|
xv
|
17
|
ii
|
xl
|
18
|
xviii
|
xi
|
18
|
vii
|
〈◊〉
|
18
|
iii
|
iii
|
19
|
xvii
|
liiii
|
19
|
vii
|
xxx
|
19
|
iii
|
xxvi
|
20
|
xv●i
|
xxxviii
|
20
|
vii
|
vii
|
20
|
iii
|
xlix
|
21
|
xvii
|
●x●i
|
21
|
vi
|
xliiii
|
21
|
iiii
|
xii
|
22
|
xvii
|
v
|
22
|
vi
|
xxi
|
22
|
iiii
|
xxxv
|
23
|
xvi
|
xlv●i
|
23
|
v
|
lviii
|
23
|
iiii
|
lviii
|
24
|
xvi
|
xxix
|
24
|
v
|
xxxv
|
24
|
v
|
xxi
|
25
|
xvi
|
xi
|
25
|
v
|
xi
|
25
|
v
|
xliiii
|
26
|
xv
|
liii
|
26
|
iiii
|
xlviii
|
26
|
vi
|
vi
|
27
|
xv
|
xxxv
|
27
|
iiii
|
xxiiii
|
27
|
vi
|
xxix
|
28
|
xv
|
xvi
|
28
|
iiii
|
●
|
28
|
vi
|
liii
|
29
|
xiiii
|
lvi
|
|
|
|
29
|
vii
|
xv
|
30
|
xiiii
|
xxxv●i
|
|
|
|
30
|
vii
|
xxxvii
|
31
|
xiiii
|
xvii●
|
|
|
|
31
|
vii
|
lix
|
¶
The
declination
of
the
Sunne
.
The
first
yeere
.
April
.
|
May
.
|
Iune
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
viii
|
xxi
|
1
|
xvii
|
14
|
1
|
23
|
●
|
2
|
viii
|
xliii
|
2
|
xviii
|
●
|
2
|
23
|
13
|
3
|
ix
|
v
|
3
|
xviii
|
24
|
3
|
23
|
17
|
4
|
ix
|
xxvi
|
4
|
xviii
|
39
|
4
|
23
|
21
|
5
|
ix
|
xlviii
|
5
|
xviii
|
54
|
5
|
23
|
24
|
6
|
x
|
ix
|
6
|
xix
|
8
|
6
|
23
|
26
|
7
|
x
|
xxx
|
7
|
x●x
|
21
|
7
|
23
|
28
|
8
|
x
|
lii
|
8
|
xix
|
35
|
8
|
23
|
30
|
9
|
xi
|
xii
|
9
|
xix
|
47
|
9
|
23
|
31
|
10
|
xi
|
xxxiii
|
10
|
xx
|
0
|
10
|
23
|
32
|
11
|
xi
|
liii
|
11
|
xx
|
13
|
11
|
23
|
33
|
12
|
xii
|
xiiii
|
12
|
xx
|
24
|
12
|
23
|
33
|
13
|
xii
|
xxxiii
|
13
|
xx
|
36
|
13
|
23
|
33
|
14
|
xii
|
liii
|
14
|
xx
|
47
|
14
|
23
|
32
|
15
|
xiii
|
xiii
|
15
|
xx
|
59
|
15
|
23
|
31
|
16
|
xiii
|
xxxii
|
16
|
xxi
|
10
|
16
|
23
|
29
|
17
|
xiii
|
li
|
17
|
xxi
|
20
|
17
|
23
|
27
|
18
|
xiiii
|
x
|
18
|
xxi
|
30
|
18
|
23
|
25
|
19
|
xiiii
|
xxix
|
19
|
xxi
|
40
|
19
|
23
|
22
|
20
|
xiiii
|
xlvii
|
20
|
xxi
|
49
|
20
|
23
|
18
|
21
|
xv
|
vi
|
21
|
xxi
|
57
|
21
|
23
|
15
|
22
|
xv
|
xxiiii
|
22
|
xxii
|
6
|
22
|
23
|
11
|
23
|
xv
|
xlii
|
23
|
xxii
|
14
|
23
|
23
|
6
|
24
|
xv
|
lix
|
24
|
xxii
|
〈◊〉
|
24
|
23
|
2
|
25
|
xvi
|
xvi
|
25
|
xxii
|
29
|
25
|
22
|
●7
|
26
|
xvi
|
xxxiii
|
26
|
xxii
|
36
|
26
|
22
|
51
|
27
|
xvi
|
l
|
27
|
xxii
|
42
|
27
|
22
|
45
|
28
|
xvii
|
vii
|
28
|
xxii
|
49
|
28
|
22
|
39
|
29
|
xvi●
|
xxiii
|
29
|
xxii
|
58
|
29
|
22
|
32
|
30
|
xvi●
|
xxxviii
|
30
|
xxii
|
0
|
30
|
22
|
25
|
|
|
|
31
|
xxiii
|
4
|
|
|
|
¶
The
declination
of
the
Sunne
.
The
first
yeere
.
Iulie
.
|
August
.
|
September
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
|
1
|
xxii
|
xvii
|
1
|
xv
|
xxxii
|
1
|
iiii
|
xivi
|
2
|
xxii
|
i●
|
2
|
xv
|
xiiii
|
2
|
iiii
|
xxiii
|
3
|
xxii
|
i
|
3
|
xiiii
|
ivi
|
3
|
iiii
|
0
|
4
|
xxi
|
ii
|
4
|
xiiii
|
xxxvii
|
4
|
iii
|
xxxvii
|
5
|
xxi
|
xliiii
|
5
|
xiiii
|
xix
|
5
|
iii
|
xiiii
|
6
|
xxi
|
xxxiiii
|
6
|
xiii
|
0
|
6
|
ii
|
li
|
7
|
xxi
|
xxiiii
|
7
|
xiii
|
xli
|
7
|
ii
|
xxviii
|
8
|
xxi
|
xilii
|
8
|
xiii
|
xxi
|
8
|
ii
|
iiii
|
9
|
xxi
|
iii
|
9
|
xiii
|
ii
|
9
|
i
|
xl
|
10
|
xx
|
〈◊〉
|
10
|
xii
|
xliii
|
10
|
i
|
xvii
|
11
|
xx
|
xli
|
11
|
xii
|
xxii
|
11
|
0
|
liiii
|
12
|
xx
|
xxix
|
12
|
xii
|
iii
|
12
|
0
|
xxx
|
13
|
xx
|
xviii
|
13
|
xi
|
xliii
|
13
|
0
|
vi
|
14
|
xx
|
vi
|
14
|
xi
|
xxii
|
14
|
0
|
xviii
|
15
|
xix
|
li●i
|
15
|
xi
|
●
|
15
|
0
|
xli
|
16
|
xix
|
xl
|
16
|
x
|
xl
|
16
|
i
|
v
|
17
|
xix
|
xxvii
|
17
|
x
|
xix
|
17
|
i
|
xxviii
|
18
|
xix
|
xiii
|
18
|
ix
|
lvii
|
18
|
i
|
lii
|
19
|
xviii
|
●ix
|
19
|
ix
|
xxxvi
|
19
|
ii
|
xvi
|
20
|
xviii
|
xlv
|
20
|
ix
|
xv
|
20
|
ii
|
xl
|
21
|
xxviii
|
xxx
|
21
|
viii
|
liii
|
21
|
iii
|
iii
|
22
|
xviii
|
xv
|
22
|
viii
|
xxxii
|
22
|
iii
|
xxvi
|
23
|
xviii
|
00
|
23
|
viii
|
ix
|
23
|
iii
|
l
|
24
|
xvii
|
xliiii
|
24
|
vii
|
xlvii
|
24
|
iiii
|
xiii
|
25
|
xv●i
|
xxix
|
25
|
vii
|
xxv
|
25
|
iiii
|
xxxvi
|
26
|
xvii
|
xliii
|
26
|
vii
|
iii
|
26
|
v
|
0
|
27
|
xvi
|
●vi
|
27
|
vi
|
xli
|
27
|
v
|
xxiii
|
28
|
xvi
|
xl
|
28
|
vi
|
xvii
|
28
|
v
|
xlvii
|
29
|
xvi
|
xxiii
|
29
|
v
|
lv
|
29
|
vi
|
ix
|
30
|
xvi
|
vi
|
30
|
v
|
xxxii
|
30
|
vi
|
xxxiii
|
31
|
xv
|
xlix
|
31
|
v
|
ix
|
|
|
|
¶
The
declination
of
the
Sunne
.
The
first
yeere
.
October
.
|
Nouember
.
|
December
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
|
1
|
vi
|
iv●
|
1
|
xvii
|
29
|
1
|
23
|
7
|
2
|
vii
|
xix
|
2
|
xvii
|
45
|
2
|
23
|
11
|
3
|
vii
|
xli
|
3
|
xviii
|
2
|
3
|
23
|
16
|
4
|
viii
|
iiii
|
4
|
xviii
|
18
|
4
|
23
|
20
|
5
|
viii
|
xxvii
|
5
|
xviii
|
33
|
5
|
23
|
23
|
6
|
viii
|
xlix
|
6
|
xviii
|
49
|
6
|
23
|
26
|
7
|
ix
|
xi
|
7
|
xix
|
5
|
7
|
23
|
28
|
8
|
ix
|
xxxiii
|
8
|
xix
|
19
|
8
|
23
|
30
|
9
|
ix
|
lv
|
9
|
xix
|
33
|
9
|
23
|
32
|
10
|
x
|
xvii
|
10
|
xix
|
47
|
10
|
23
|
33
|
11
|
x
|
xxxix
|
11
|
xx
|
1
|
11
|
23
|
33
|
12
|
xi
|
●
|
12
|
xx
|
14
|
12
|
23
|
33
|
13
|
xi
|
xx●ii
|
13
|
xx
|
20
|
13
|
23
|
32
|
14
|
xi
|
xliiii
|
14
|
xx
|
38
|
14
|
23
|
31
|
15
|
xii
|
v
|
15
|
xx
|
51
|
15
|
23
|
30
|
16
|
xii
|
xxvi
|
16
|
xxi
|
3
|
16
|
23
|
28
|
17
|
xii
|
xlvi
|
17
|
xxi
|
14
|
17
|
23
|
26
|
18
|
xiii
|
vii
|
18
|
xxi
|
25
|
18
|
23
|
23
|
19
|
xiii
|
xxvii
|
19
|
xxi
|
36
|
19
|
23
|
19
|
20
|
xiii
|
xlvii
|
20
|
xxi
|
46
|
20
|
23
|
15
|
21
|
xiiii
|
vii
|
21
|
xxi
|
5●
|
21
|
23
|
11
|
22
|
xiiii
|
xxvii
|
22
|
xxii
|
4
|
22
|
23
|
6
|
23
|
xiiii
|
xivi
|
23
|
xxii
|
13
|
23
|
23
|
1
|
24
|
xv
|
v
|
24
|
xxii
|
21
|
24
|
22
|
56
|
25
|
xv
|
xxiiii
|
25
|
xxii
|
29
|
25
|
22
|
50
|
26
|
xv
|
xliii
|
26
|
xx●i
|
36
|
26
|
22
|
4●
|
27
|
xvi
|
i
|
27
|
xxii
|
44
|
27
|
22
|
35
|
28
|
xvi
|
xi●
|
28
|
xxii
|
51
|
28
|
22
|
28
|
29
|
xvi
|
xxxvii
|
29
|
xxii
|
56
|
29
|
22
|
20
|
30
|
xvi
|
lv
|
30
|
xxiii
|
1
|
30
|
22
|
12
|
31
|
xvii
|
xiii
|
|
|
|
31
|
22
|
3
|
¶
The
declination
of
the
Sunne
.
The
second
yeere
.
Ianuarie
.
|
Februarie
.
|
March
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
xxi
|
liiii
|
1
|
xiiii
|
iiii
|
1
|
iii
|
xliiii
|
2
|
xxi
|
xliiii
|
2
|
xiii
|
xliii
|
2
|
iii
|
xxi
|
3
|
xxi
|
xxxiii
|
3
|
xiii
|
xxiii
|
3
|
ii
|
lviii
|
4
|
xxi
|
xxiiii
|
4
|
xiii
|
iii
|
4
|
ii
|
xxxiiii
|
5
|
xxi
|
xiii
|
5
|
xii
|
xlii
|
5
|
ii
|
x
|
6
|
xxi
|
i
|
6
|
xii
|
xxii
|
6
|
i
|
xlvi
|
7
|
xx
|
xlix
|
7
|
xii
|
i
|
7
|
i
|
xxiii
|
8
|
xx
|
xxxvii
|
8
|
xi
|
xl
|
8
|
0
|
lix
|
9
|
xx
|
xxiiii
|
9
|
xi
|
xviii
|
9
|
0
|
xxxv
|
10
|
xx
|
xii
|
10
|
x
|
lvii
|
10
|
0
|
xii
|
11
|
xix
|
lviii
|
11
|
x
|
xxxv
|
11
|
0
|
xii
|
12
|
xix
|
xliiii
|
12
|
x
|
xiii
|
12
|
0
|
xxxvi
|
13
|
xix
|
xxxi
|
13
|
ix
|
li
|
13
|
0
|
lix
|
14
|
xix
|
xvii
|
14
|
ix
|
xxix
|
14
|
i
|
xxiii
|
15
|
xix
|
ii
|
15
|
ix
|
vii
|
15
|
i
|
xlvi
|
16
|
xviii
|
xlvii
|
16
|
viii
|
xiv
|
16
|
ii
|
x
|
17
|
xviii
|
xxxi
|
17
|
viii
|
xxii
|
17
|
ii
|
xxxiiii
|
18
|
xxviii
|
xv
|
18
|
vii
|
lix
|
18
|
ii
|
lvii
|
19
|
xvii
|
lix
|
19
|
vii
|
xxxvii
|
19
|
iii
|
xx
|
20
|
xvii
|
xlii
|
20
|
vii
|
xiiii
|
20
|
iii
|
xliii
|
21
|
xvii
|
xxvi
|
21
|
vi
|
li
|
21
|
iiii
|
vii
|
22
|
xvii
|
ix
|
22
|
vi
|
xxvii
|
22
|
iiii
|
xxx
|
23
|
xvi
|
lii
|
23
|
vi
|
iiii
|
23
|
iiii
|
liii
|
24
|
xvi
|
xxxiiii
|
24
|
v
|
xli
|
24
|
v
|
xv
|
25
|
xvi
|
xvi
|
25
|
v
|
xviii
|
25
|
v
|
xxxviii
|
26
|
xv
|
lviii
|
26
|
iiii
|
liiii
|
26
|
vi
|
i
|
27
|
xv
|
xxxvii
|
27
|
iiii
|
xxxi
|
27
|
vi
|
xxiiii
|
28
|
xv
|
xxi
|
28
|
iiii
|
viii
|
28
|
vi
|
xlvii
|
29
|
xv
|
ii
|
|
|
|
29
|
vii
|
x
|
30
|
xiiii
|
xliii
|
|
|
|
30
|
vii
|
xxxii
|
31
|
xiiii
|
xxiii
|
|
|
|
31
|
vii
|
liii
|
¶
The
declination
of
the
Sunne
.
The
seconde
yeere
.
April
.
|
May
.
|
Iune
.
|
Dayes
|
Degrees
.
|
Minutes
|
Dayes
|
Degrees
.
|
Minutes
.
|
Daye●
|
Degrees
.
|
Minutes
.
|
1
|
viii
|
xvi
|
1
|
xvii
|
x●x
|
1
|
23
|
8
|
2
|
viii
|
xxxviii
|
2
|
xviii
|
vi
|
2
|
23
|
12
|
3
|
viii
|
lix
|
3
|
xviii
|
xx
|
3
|
23
|
16
|
4
|
ix
|
xxi
|
4
|
xviii
|
xxxv
|
4
|
23
|
20
|
5
|
ix
|
xlii
|
5
|
xviii
|
l
|
5
|
23
|
23
|
6
|
x
|
iiii
|
6
|
xix
|
iiii
|
6
|
23
|
26
|
7
|
x
|
xxv
|
7
|
xix
|
xviii
|
7
|
23
|
28
|
8
|
x
|
xlvi
|
8
|
xix
|
xxxi
|
8
|
23
|
29
|
9
|
xi
|
vii
|
9
|
xix
|
xliiii
|
9
|
23
|
31
|
10
|
xi
|
xxvii
|
10
|
xix
|
lvii
|
10
|
23
|
32
|
11
|
xi
|
xlviii
|
11
|
xx
|
x
|
11
|
23
|
33
|
12
|
xii
|
x
|
12
|
xx
|
xxii
|
12
|
23
|
33
|
13
|
xii
|
xxviii
|
13
|
xx
|
xxxiii
|
13
|
23
|
33
|
14
|
xii
|
xlviii
|
14
|
xx
|
xliiii
|
14
|
23
|
32
|
15
|
xiii
|
viii
|
15
|
xx
|
lvi
|
15
|
23
|
31
|
16
|
xiii
|
xxvii
|
16
|
xxi
|
vii
|
16
|
23
|
29
|
17
|
xiii
|
xlvi
|
17
|
xxi
|
xviii
|
17
|
23
|
27
|
18
|
xiiii
|
vi
|
18
|
xxi
|
xxviii
|
18
|
23
|
25
|
19
|
xiiii
|
xxv
|
19
|
xxi
|
37
|
19
|
23
|
23
|
20
|
xiiii
|
xiiii
|
20
|
xxi
|
46
|
20
|
23
|
19
|
21
|
xv
|
●
|
21
|
xxi
|
55
|
21
|
23
|
16
|
22
|
xv
|
xix
|
22
|
xxii
|
4
|
22
|
23
|
12
|
23
|
xv
|
xxxvii
|
23
|
xxii
|
12
|
23
|
23
|
7
|
24
|
xv
|
lv
|
24
|
xxii
|
20
|
24
|
23
|
3
|
25
|
xvi
|
xii
|
25
|
xxii
|
27
|
25
|
23
|
58
|
26
|
xvi
|
xxix
|
26
|
xxii
|
34
|
26
|
22
|
53
|
27
|
xvi
|
xiv
|
27
|
xxii
|
41
|
27
|
22
|
47
|
28
|
xvii
|
iii
|
28
|
xxii
|
48
|
28
|
22
|
40
|
29
|
xvii
|
xix
|
29
|
xxii
|
52
|
29
|
22
|
33
|
30
|
xvii
|
xxxiiii
|
30
|
xxii
|
58
|
30
|
22
|
27
|
|
|
|
31
|
xxiii
|
3
|
|
|
|
¶
The
declination
of
the
Sunne
.
The
second
yeere
.
Iulie
.
|
August
.
|
September
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
xxii
|
xix
|
1
|
xv
|
xxxvi
|
1
|
iiii
|
lii
|
2
|
xxii
|
xi
|
2
|
xv
|
xviii
|
2
|
iiii
|
xxix
|
3
|
xxii
|
iii
|
3
|
xv
|
0
|
3
|
iiii
|
vi
|
4
|
xxi
|
liiii
|
4
|
xiiii
|
xlii
|
4
|
iii
|
xliii
|
5
|
xxi
|
xlv
|
5
|
xiiii
|
xxiiii
|
5
|
iii
|
xix
|
6
|
xxi
|
xxxvi
|
6
|
xiiii
|
v
|
6
|
ii
|
lvi
|
7
|
xxi
|
xxvii
|
7
|
xiii
|
xiv
|
7
|
ii
|
xxxiii
|
8
|
xxi
|
xvii
|
8
|
xiii
|
xxvi
|
8
|
ii
|
x
|
9
|
xxi
|
vi
|
9
|
xiii
|
vii
|
9
|
i
|
xlvi
|
10
|
xx
|
lv
|
10
|
xii
|
xlvii
|
10
|
i
|
xxiii
|
11
|
xx
|
xliiii
|
11
|
xii
|
xxvii
|
11
|
0
|
lix
|
12
|
xx
|
xxxii
|
12
|
xii
|
viii
|
12
|
0
|
xxxv
|
13
|
xx
|
xx
|
13
|
xi
|
xlviii
|
13
|
0
|
xii
|
14
|
xx
|
ix
|
14
|
xi
|
xxvii
|
14
|
0
|
xii
|
15
|
xix
|
lvi
|
15
|
xi
|
vi
|
15
|
0
|
xxxv
|
16
|
xix
|
xliii
|
16
|
x
|
xlv
|
16
|
0
|
lix
|
17
|
xix
|
xxx
|
17
|
x
|
xxiiii
|
17
|
i
|
xxiii
|
18
|
xix
|
xvii
|
18
|
x
|
iii
|
18
|
i
|
xlvi
|
19
|
xix
|
iii
|
19
|
ix
|
xii
|
19
|
ii
|
x
|
20
|
xviii
|
xlix
|
20
|
ix
|
xx
|
20
|
ii
|
xxxiiii
|
21
|
xviii
|
xxxiiii
|
21
|
viii
|
iix
|
21
|
ii
|
lvii
|
22
|
xviii
|
xix
|
22
|
viii
|
xxxvii
|
22
|
iii
|
xx
|
23
|
xviii
|
liii
|
23
|
viii
|
xv
|
23
|
iii
|
xliiii
|
24
|
xvii
|
xlviii
|
24
|
vii
|
lii
|
24
|
iiii
|
viii
|
25
|
xvii
|
xxxiii
|
25
|
vii
|
xxxi
|
25
|
iiii
|
xxxi
|
26
|
xvii
|
xvii
|
26
|
vii
|
ix
|
26
|
iiii
|
liiii
|
27
|
xvii
|
i
|
27
|
vi
|
xlvi
|
27
|
v
|
xvii
|
28
|
xvi
|
xliiii
|
28
|
vi
|
xxiii
|
28
|
v
|
xli
|
29
|
xvi
|
●xviii
|
29
|
vi
|
0
|
29
|
vi
|
iiii
|
30
|
xvi
|
xi
|
30
|
v
|
xxxviii
|
30
|
vi
|
xxvii
|
31
|
xv
|
liiii
|
31
|
v
|
xv
|
|
|
|
¶
The
declination
of
the
Sunne
.
The
second
yeere
.
October
.
|
Nouember
.
|
December
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
vi
|
li
|
1
|
xvii
|
25
|
1
|
23
|
5
|
2
|
vii
|
xiiii
|
2
|
xvii
|
41
|
2
|
23
|
10
|
3
|
vii
|
xxxvi
|
3
|
xvii
|
58
|
3
|
23
|
15
|
4
|
vii
|
lviii
|
4
|
xviii
|
14
|
4
|
23
|
19
|
5
|
viii
|
xxi
|
5
|
xviii
|
29
|
5
|
23
|
22
|
6
|
viii
|
xliiii
|
6
|
xviii
|
46
|
6
|
23
|
25
|
7
|
ix
|
vi
|
7
|
xix
|
1
|
7
|
23
|
27
|
8
|
ix
|
xxviii
|
8
|
xix
|
15
|
8
|
23
|
29
|
9
|
ix
|
l
|
9
|
xix
|
29
|
9
|
23
|
31
|
10
|
x
|
xii
|
10
|
xix
|
43
|
10
|
23
|
32
|
11
|
x
|
xxxiiii
|
11
|
xix
|
57
|
11
|
23
|
33
|
12
|
x
|
lvi
|
12
|
xx
|
21
|
12
|
23
|
33
|
13
|
xi
|
xvii
|
13
|
xx
|
23
|
13
|
23
|
33
|
14
|
xi
|
xxxix
|
14
|
xx
|
36
|
14
|
23
|
32
|
15
|
xii
|
0
|
15
|
xx
|
48
|
15
|
23
|
30
|
16
|
xii
|
xxi
|
16
|
xxi
|
0
|
16
|
23
|
28
|
17
|
xii
|
xli
|
17
|
xxi
|
12
|
17
|
23
|
26
|
18
|
xiii
|
ii
|
18
|
xxi
|
23
|
18
|
23
|
23
|
19
|
xiii
|
xxii
|
19
|
xxi
|
33
|
19
|
23
|
20
|
20
|
xiii
|
xlii
|
20
|
xxi
|
43
|
20
|
23
|
16
|
21
|
xiiii
|
ii
|
21
|
xxi
|
53
|
21
|
23
|
12
|
22
|
xiiii
|
xxii
|
22
|
xxii
|
2
|
22
|
23
|
7
|
23
|
xiiii
|
xlii
|
23
|
xxii
|
11
|
23
|
23
|
2
|
24
|
xv
|
i
|
24
|
xxii
|
19
|
24
|
22
|
57
|
25
|
xv
|
xx
|
25
|
xxii
|
28
|
25
|
22
|
51
|
26
|
xv
|
xxxix
|
26
|
xxii
|
35
|
26
|
22
|
44
|
27
|
xv
|
lvii
|
27
|
xxii
|
42
|
27
|
22
|
37
|
28
|
xvi
|
xv
|
28
|
xxii
|
49
|
28
|
22
|
30
|
29
|
xvi
|
xxxiii
|
29
|
xxii
|
55
|
29
|
22
|
22
|
30
|
xvi
|
l
|
30
|
xxiii
|
0
|
30
|
22
|
14
|
31
|
xvii
|
viii
|
|
|
|
31
|
22
|
5
|
¶
The
declination
of
the
Sunne
.
The
third
yeere
.
Ianuarie
.
|
Februarie
.
|
March
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
xxi
|
lvi
|
1
|
xiiii
|
viii
|
1
|
iii
|
l
|
2
|
xxi
|
xlvi
|
2
|
xiii
|
xlviii
|
2
|
iii
|
xxvi
|
3
|
xxi
|
xxxvi
|
3
|
xiii
|
xxviii
|
3
|
iii
|
iii
|
4
|
xxi
|
xxvi
|
4
|
xiii
|
viii
|
4
|
ii
|
xl
|
5
|
xxi
|
xv
|
5
|
xii
|
xlvii
|
5
|
ii
|
xvi
|
6
|
xxi
|
iiii
|
6
|
xii
|
xxvi
|
6
|
i
|
●●i
|
7
|
xx
|
lii
|
7
|
xii
|
vi
|
7
|
i
|
xxviii
|
8
|
xx
|
xxxix
|
8
|
xi
|
xlv
|
8
|
i
|
v
|
9
|
xx
|
xxvii
|
9
|
xi
|
xxiii
|
9
|
0
|
xli
|
10
|
xx
|
xv
|
10
|
xi
|
ii
|
10
|
0
|
xvii
|
11
|
xx
|
ii
|
11
|
x
|
xl
|
11
|
0
|
vi
|
12
|
xix
|
xlviii
|
12
|
x
|
xviii
|
12
|
0
|
xxx
|
13
|
xix
|
xxxiiii
|
13
|
ix
|
ivi
|
13
|
0
|
liiii
|
14
|
xix
|
xx
|
14
|
ix
|
xxxiiii
|
14
|
i
|
xvii
|
15
|
xix
|
v
|
15
|
ix
|
xii
|
15
|
i
|
xli
|
16
|
xviii
|
l
|
16
|
viii
|
l
|
16
|
ii
|
iiii
|
17
|
xviii
|
xxxv
|
17
|
viii
|
xxvii
|
17
|
ii
|
xxviii
|
18
|
xviii
|
xix
|
18
|
viii
|
iiii
|
18
|
ii
|
lii
|
19
|
xviii
|
iii
|
19
|
vii
|
42
|
19
|
iii
|
xiiii
|
20
|
xvii
|
xlvi
|
20
|
vii
|
xix
|
20
|
iii
|
xxxviii
|
21
|
xvii
|
xxx
|
21
|
vi
|
lvi
|
21
|
iiii
|
i
|
22
|
xvii
|
xiii
|
22
|
vi
|
xxxiii
|
22
|
iiii
|
xxiiii
|
23
|
xvi
|
lvi
|
23
|
vi
|
x
|
23
|
iiii
|
xlvii
|
24
|
xvi
|
xxxviii
|
24
|
v
|
xlvii
|
24
|
v
|
ix
|
25
|
xvi
|
xx
|
25
|
v
|
xxiii
|
25
|
v
|
xxxiii
|
26
|
xvi
|
ii
|
26
|
v
|
0
|
26
|
v
|
lvi
|
27
|
xv
|
xliiii
|
27
|
iiii
|
xxxvi
|
27
|
vi
|
xviii
|
28
|
xv
|
xxv
|
28
|
iiii
|
xiii
|
28
|
vi
|
xli
|
29
|
xv
|
vi
|
|
|
|
29
|
vii
|
iiii
|
30
|
xiiii
|
xlvii
|
|
|
|
30
|
vii
|
xxvi
|
31
|
xiiii
|
xxviii
|
|
|
|
31
|
vii
|
xlviii
|
¶
The
declination
of
the
Sunne
.
The
thirde
yeere
.
April
.
|
May
.
|
Iune
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
viii
|
ix
|
1
|
xvii
|
46
|
1
|
23
|
7
|
2
|
viii
|
xxxi
|
2
|
xviii
|
2
|
2
|
23
|
11
|
3
|
viii
|
liii
|
3
|
xviii
|
17
|
3
|
23
|
15
|
4
|
ix
|
xvi
|
4
|
xviii
|
31
|
4
|
23
|
19
|
5
|
ix
|
xxxvii
|
5
|
xviii
|
46
|
5
|
23
|
22
|
6
|
ix
|
lviii
|
6
|
xix
|
l
|
6
|
23
|
25
|
7
|
x
|
xx
|
7
|
xix
|
14
|
7
|
23
|
27
|
8
|
x
|
xii
|
8
|
xix
|
28
|
8
|
23
|
29
|
9
|
xi
|
ii
|
9
|
xix
|
41
|
9
|
23
|
31
|
10
|
xi
|
xxii
|
10
|
xix
|
54
|
10
|
23
|
32
|
11
|
xi
|
xliii
|
11
|
xx
|
7
|
11
|
23
|
33
|
12
|
xii
|
iiii
|
12
|
xx
|
19
|
12
|
23
|
33
|
13
|
xii
|
xxiii
|
13
|
xx
|
30
|
13
|
23
|
33
|
14
|
xii
|
xliii
|
14
|
xx
|
42
|
14
|
23
|
32
|
15
|
xiii
|
iii
|
15
|
xx
|
53
|
15
|
23
|
31
|
16
|
xiii
|
xxii
|
16
|
xxi
|
4
|
16
|
23
|
30
|
17
|
xiii
|
xlii
|
17
|
xxi
|
15
|
17
|
23
|
28
|
18
|
xiiii
|
i
|
18
|
xxi
|
25
|
18
|
23
|
26
|
19
|
xiiii
|
xx
|
19
|
xxi
|
35
|
19
|
23
|
23
|
20
|
xiiii
|
xxxviii
|
20
|
xxi
|
44
|
20
|
23
|
20
|
21
|
xiiii
|
lvii
|
21
|
xxi
|
53
|
21
|
23
|
17
|
22
|
xv
|
xv
|
22
|
xxii
|
2
|
●●
|
23
|
13
|
23
|
xv
|
xxxiii
|
23
|
xxii
|
10
|
23
|
23
|
9
|
24
|
xv
|
l
|
24
|
xxii
|
18
|
24
|
23
|
4
|
25
|
xvi
|
viii
|
25
|
xxii
|
25
|
25
|
22
|
59
|
26
|
xvi
|
xxv
|
26
|
xxii
|
32
|
26
|
22
|
54
|
27
|
xvi
|
xli
|
27
|
xxii
|
39
|
27
|
22
|
48
|
28
|
xvi
|
lviii
|
28
|
xxii
|
46
|
28
|
22
|
42
|
29
|
xvii
|
xv
|
29
|
xxii
|
52
|
29
|
22
|
35
|
30
|
xvii
|
xxx
|
30
|
xxii
|
57
|
30
|
22
|
28
|
|
|
|
31
|
xxiii
|
2
|
|
|
|
¶
The
declination
of
the
Sunne
.
The
third
yeere
.
Iulie
.
|
August
.
|
September
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
xxii
|
xxi
|
1
|
xv
|
xl
|
1
|
iiii
|
lvii
|
2
|
xxii
|
xiii
|
2
|
xv
|
xxiii
|
2
|
iiii
|
xxxiiii
|
3
|
xxii
|
v
|
3
|
xv
|
iiii
|
3
|
iiii
|
xii
|
4
|
xxi
|
ivi
|
4
|
xiiii
|
xlvi
|
4
|
iii
|
xlix
|
5
|
xxi
|
xlviii
|
5
|
xiiii
|
xxviii
|
5
|
iii
|
xxv
|
6
|
xxi
|
xxxix
|
6
|
xiiii
|
ix
|
6
|
iii
|
ii
|
7
|
xxi
|
xxix
|
7
|
xiii
|
l
|
7
|
ii
|
39
|
8
|
xxi
|
xix
|
8
|
xiii
|
xxxi
|
8
|
ii
|
xvi
|
9
|
xxi
|
ix
|
9
|
xiii
|
xii
|
9
|
i
|
lii
|
10
|
xx
|
lviii
|
10
|
xii
|
lii
|
10
|
i
|
xxviii
|
11
|
xx
|
xlvi
|
11
|
xii
|
xxxii
|
11
|
i
|
v
|
12
|
xx
|
xxxv
|
12
|
xii
|
13
|
12
|
0
|
xli
|
13
|
xx
|
xxiii
|
13
|
xi
|
lii
|
13
|
0
|
xviii
|
14
|
xx
|
ix
|
14
|
xi
|
32
|
14
|
0
|
vi
|
15
|
xix
|
lix
|
15
|
xi
|
xi
|
15
|
0
|
30
|
16
|
xix
|
xlvi
|
16
|
x
|
l
|
16
|
0
|
liii
|
17
|
xix
|
xxxiii
|
17
|
x
|
xxix
|
17
|
i
|
xvii
|
18
|
xix
|
xx
|
18
|
x
|
viii
|
18
|
i
|
xl
|
19
|
xix
|
vii
|
19
|
ix
|
xlvii
|
19
|
ii
|
iiil
|
20
|
xviii
|
lii
|
20
|
ix
|
xxv
|
20
|
ii
|
xxviii
|
21
|
xviii
|
xxxviii
|
21
|
ix
|
iiii
|
21
|
ii
|
lii
|
22
|
xviii
|
xxiii
|
22
|
viii
|
42
|
22
|
iii
|
xv
|
23
|
xviii
|
viii
|
23
|
viii
|
xx
|
23
|
iii
|
xxxix
|
24
|
xvii
|
lii
|
24
|
vii
|
lviii
|
24
|
iiii
|
ii
|
25
|
xvii
|
xxxvii
|
25
|
vii
|
xxxvi
|
25
|
iiii
|
xxv
|
26
|
xvii
|
xxi
|
26
|
vii
|
xiiii
|
26
|
iiii
|
xlix
|
27
|
xvii
|
v
|
27
|
vi
|
lii
|
27
|
v
|
xi
|
28
|
xvi
|
xlviii
|
28
|
vi
|
xxix
|
28
|
v
|
xxxv
|
29
|
xvi
|
xxxii
|
29
|
vi
|
vi
|
29
|
v
|
lviii
|
30
|
xvi
|
xv
|
30
|
v
|
xliii
|
30
|
vi
|
●1
|
31
|
xv
|
lviii
|
31
|
v
|
xxi
|
|
|
|
¶
The
declination
of
the
Sunne
.
The
thirde
yeere
.
October
.
|
Nouember
.
|
December
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
|
1
|
vi
|
xlv
|
1
|
xvii
|
21
|
1
|
23
|
4
|
2
|
vii
|
viii
|
2
|
xvii
|
37
|
2
|
23
|
9
|
3
|
vii
|
xxxi
|
3
|
xvii
|
54
|
3
|
23
|
13
|
4
|
vii
|
liii
|
4
|
xviii
|
10
|
4
|
23
|
17
|
5
|
viii
|
xvi
|
5
|
xviii
|
26
|
5
|
23
|
22
|
6
|
viii
|
xxxix
|
6
|
xviii
|
42
|
6
|
23
|
25
|
7
|
ix
|
i
|
7
|
xviii
|
57
|
7
|
23
|
27
|
8
|
ix
|
xxiii
|
8
|
xix
|
12
|
8
|
23
|
29
|
9
|
ix
|
xlv
|
9
|
xix
|
26
|
9
|
23
|
31
|
10
|
x
|
vii
|
10
|
xix
|
40
|
10
|
23
|
32
|
11
|
x
|
xxix
|
11
|
xix
|
54
|
11
|
23
|
33
|
12
|
x
|
li
|
12
|
xx
|
7
|
12
|
23
|
33
|
13
|
xi
|
xii
|
13
|
xx
|
20
|
13
|
23
|
33
|
14
|
xi
|
xxxiiii
|
14
|
xx
|
33
|
14
|
23
|
32
|
15
|
xi
|
lv
|
15
|
xx
|
45
|
15
|
23
|
31
|
16
|
xii
|
xvi
|
16
|
xx
|
57
|
16
|
23
|
29
|
17
|
xii
|
xxxvi
|
17
|
xxi
|
9
|
17
|
23
|
27
|
18
|
xii
|
lvii
|
18
|
xxi
|
20
|
18
|
23
|
24
|
19
|
xiii
|
xvii
|
19
|
xxi
|
31
|
19
|
23
|
21
|
20
|
xiii
|
xxxvii
|
20
|
xxi
|
41
|
20
|
23
|
17
|
21
|
xiii
|
lvii
|
21
|
xxi
|
50
|
21
|
23
|
13
|
22
|
xiiii
|
xvii
|
22
|
xxii
|
0
|
22
|
23
|
8
|
23
|
xiiii
|
xxxvii
|
23
|
xxii
|
9
|
23
|
23
|
3
|
24
|
xiiii
|
lvi
|
24
|
xxii
|
17
|
24
|
22
|
58
|
25
|
xv
|
xv
|
25
|
xxii
|
26
|
25
|
22
|
52
|
26
|
xv
|
xxxiiii
|
26
|
xxii
|
33
|
26
|
22
|
46
|
27
|
xv
|
lii
|
27
|
xxii
|
40
|
27
|
22
|
39
|
28
|
xvi
|
xi
|
28
|
xxii
|
47
|
28
|
22
|
32
|
29
|
xvi
|
xxix
|
29
|
xxii
|
53
|
29
|
22
|
24
|
30
|
xvi
|
xlvi
|
30
|
xxii
|
59
|
30
|
22
|
16
|
31
|
xvii
|
iiii
|
|
|
|
31
|
22
|
7
|
¶
The
declination
of
the
Sunne
.
The
leape
yeere
.
Ianuarie
.
|
Februarie
.
|
March
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
|
1
|
xxi
|
lviii
|
1
|
xiiii
|
xiii
|
1
|
iii
|
xxxii
|
2
|
xxi
|
xlix
|
2
|
liii
|
liii
|
2
|
iii
|
ix
|
3
|
xxi
|
xxxix
|
3
|
xiii
|
xxxiii
|
3
|
ii
|
xlvi
|
4
|
xxi
|
xxix
|
4
|
xiii
|
xiii
|
4
|
ii
|
xxii
|
5
|
xxi
|
xvii
|
5
|
xii
|
liii
|
5
|
i
|
lviii
|
6
|
xxi
|
vii
|
6
|
xii
|
32
|
6
|
i
|
xxxiiii
|
7
|
xx
|
lv
|
7
|
xii
|
xi
|
7
|
i
|
x
|
8
|
xx
|
xliii
|
8
|
xi
|
l
|
8
|
0
|
xlvii
|
9
|
xx
|
xxx
|
9
|
xi
|
xxix
|
9
|
0
|
xxiii
|
10
|
xx
|
xviii
|
10
|
xi
|
vii
|
10
|
0
|
i
|
11
|
xx
|
v
|
11
|
x
|
xlv
|
11
|
0
|
xxiiii
|
12
|
xix
|
li
|
12
|
x
|
xxiii
|
12
|
0
|
xlviii
|
13
|
xix
|
xxxviii
|
13
|
x
|
i
|
13
|
i
|
xi
|
14
|
xix
|
xxiiii
|
14
|
ix
|
xxxix
|
14
|
i
|
xxxv
|
15
|
xix
|
ix
|
15
|
ix
|
xvii
|
15
|
i
|
lix
|
16
|
xviii
|
liiii
|
16
|
viii
|
lv
|
16
|
ii
|
xxii
|
17
|
xviii
|
xxxix
|
17
|
viii
|
xxxiii
|
17
|
ii
|
xlvi
|
18
|
xviii
|
xxiii
|
18
|
viii
|
x
|
18
|
iii
|
ix
|
19
|
xviii
|
vii
|
19
|
vii
|
xlvii
|
19
|
iii
|
xxxii
|
20
|
xvii
|
l
|
20
|
vii
|
xxv
|
20
|
iii
|
lv
|
21
|
xvii
|
xxxiiii
|
21
|
vii
|
ii
|
21
|
iiii
|
xviii
|
22
|
xvii
|
xviii
|
22
|
vi
|
xxxix
|
22
|
iiii
|
xlii
|
23
|
xvii
|
i
|
23
|
vi
|
xv
|
23
|
v
|
iiii
|
24
|
xvi
|
xlix
|
24
|
v
|
lii
|
24
|
v
|
xxvii
|
25
|
xvi
|
xxv
|
25
|
v
|
29
|
25
|
v
|
l
|
26
|
xvi
|
vii
|
26
|
v
|
v
|
26
|
vi
|
xiii
|
27
|
xv
|
xlix
|
27
|
iiii
|
xliii
|
27
|
vi
|
xxxvi
|
28
|
xv
|
xxx
|
28
|
iiii
|
xix
|
28
|
vi
|
iviii
|
29
|
xv
|
i
|
29
|
iii
|
lvi
|
29
|
vii
|
xxi
|
30
|
xiiii
|
lii
|
|
|
|
30
|
vii
|
xliii
|
31
|
xiiii
|
xxxiii
|
|
|
|
31
|
viii
|
v
|
¶
The
declination
of
the
Sunne
.
The
leape
yeere
.
April
.
|
May
.
|
Iune
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
viii
|
xxvii
|
1
|
xvii
|
58
|
1
|
23
|
10
|
2
|
viii
|
xlix
|
2
|
xviii
|
13
|
2
|
23
|
14
|
3
|
ix
|
x
|
3
|
xviii
|
28
|
3
|
23
|
18
|
4
|
ix
|
xxxii
|
4
|
xviii
|
43
|
4
|
23
|
22
|
5
|
ix
|
liii
|
5
|
xviii
|
58
|
5
|
23
|
25
|
6
|
x
|
xv
|
6
|
xix
|
11
|
6
|
23
|
27
|
7
|
x
|
xxxvii
|
7
|
xix
|
25
|
7
|
23
|
29
|
8
|
x
|
lviii
|
8
|
xix
|
38
|
8
|
23
|
31
|
9
|
xi
|
xviii
|
9
|
xix
|
51
|
9
|
23
|
32
|
10
|
xi
|
xxxix
|
10
|
xx
|
4
|
10
|
23
|
33
|
11
|
xii
|
0
|
11
|
xx
|
16
|
11
|
23
|
33
|
12
|
xii
|
xx
|
12
|
xx
|
28
|
12
|
23
|
33
|
13
|
xii
|
xxxix
|
13
|
xx
|
39
|
13
|
23
|
33
|
14
|
xii
|
lix
|
14
|
xx
|
50
|
14
|
23
|
32
|
15
|
xiii
|
xix
|
15
|
xxi
|
2
|
15
|
23
|
30
|
16
|
xiii
|
xxxviii
|
16
|
xxi
|
13
|
16
|
23
|
28
|
17
|
xiii
|
lvii
|
17
|
xxi
|
22
|
17
|
23
|
26
|
18
|
xiiii
|
xvi
|
18
|
xxi
|
33
|
18
|
23
|
24
|
19
|
xiiii
|
xxxv
|
19
|
xxi
|
42
|
19
|
23
|
21
|
20
|
xiiii
|
liii
|
20
|
xxi
|
51
|
20
|
23
|
17
|
21
|
xv
|
xii
|
21
|
xxii
|
0
|
21
|
23
|
14
|
22
|
xv
|
xxx
|
22
|
xxii
|
8
|
2●
|
23
|
10
|
23
|
xv
|
xlvii
|
23
|
xxii
|
16
|
23
|
23
|
6
|
24
|
xvi
|
iiii
|
2
|
xxii
|
24
|
24
|
23
|
0
|
25
|
xvi
|
xxi
|
25
|
xxii
|
31
|
25
|
22
|
35
|
26
|
xvi
|
xxxviii
|
26
|
xxii
|
37
|
26
|
22
|
49
|
27
|
xvi
|
iv
|
27
|
xxii
|
44
|
27
|
22
|
43
|
28
|
xvii
|
xii
|
28
|
xxii
|
50
|
28
|
22
|
37
|
29
|
xvii
|
xxvii
|
29
|
xxii
|
56
|
29
|
22
|
30
|
30
|
xvii
|
xliii
|
30
|
xxiii
|
1
|
30
|
22
|
23
|
|
|
|
31
|
xxiii
|
6
|
|
|
|
¶
The
declination
of
the
Sunne
.
The
leape
yeere
.
Iulie
.
|
August
.
|
September
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
xxii
|
xv
|
1
|
xv
|
27
|
1
|
iiii
|
xl
|
2
|
xxii
|
vil
|
2
|
xv
|
ix
|
2
|
iiii
|
xvii
|
3
|
xxi
|
lviii
|
3
|
xiiii
|
l
|
3
|
iii
|
liiii
|
4
|
xxi
|
l
|
4
|
xiiii
|
xxxii
|
4
|
iii
|
xxxi
|
5
|
xxi
|
xii
|
5
|
xiiii
|
xiii
|
5
|
iii
|
vii
|
6
|
xxi
|
xxxi
|
6
|
xiii
|
lv
|
6
|
ii
|
xlv
|
7
|
xxi
|
xxi
|
7
|
xiii
|
xxxv
|
7
|
ii
|
xxi
|
8
|
xxi
|
xi
|
8
|
xiii
|
xbi
|
8
|
i
|
lviii
|
9
|
xxi
|
0
|
9
|
xii
|
lvi
|
9
|
i
|
xxxiiii
|
10
|
xx
|
xlix
|
10
|
xii
|
xxxvil
|
10
|
i
|
x
|
11
|
xx
|
xxxviii
|
11
|
xii
|
xvii
|
11
|
0
|
xlvii
|
12
|
xx
|
xxvi
|
12
|
xi
|
lvii
|
12
|
0
|
xxiii
|
13
|
xx
|
xiiii
|
13
|
xi
|
xxxvii
|
13
|
0
|
0
|
14
|
xxi
|
il
|
14
|
xi
|
xvi
|
14
|
0
|
xxiiii
|
15
|
xix
|
xlix
|
15
|
x
|
lv
|
15
|
0
|
xlviii
|
16
|
xix
|
xxxvi
|
16
|
x
|
xxxiiii
|
16
|
i
|
xi
|
17
|
xix
|
xxiii
|
17
|
x
|
xiii
|
17
|
i
|
xxxv
|
18
|
xix
|
x
|
18
|
ix
|
li
|
18
|
i
|
lviii
|
19
|
xviii
|
xvi
|
19
|
ix
|
xxx
|
19
|
ii
|
xxii
|
20
|
xviii
|
xli
|
20
|
ix
|
ix
|
20
|
ii
|
xlvi
|
21
|
xviii
|
xxvli
|
21
|
viii
|
xlviii
|
21
|
iii
|
ix
|
22
|
xviii
|
xi
|
22
|
viii
|
xxv
|
22
|
iii
|
xxxiii
|
23
|
xvii
|
ivi
|
23
|
viii
|
iii
|
23
|
iii
|
lvi
|
24
|
xvii
|
xl
|
24
|
vii
|
xli
|
24
|
iiii
|
xix
|
25
|
xvii
|
xxv
|
25
|
vii
|
xix
|
25
|
iiii
|
xliii
|
26
|
xvii
|
ix
|
26
|
vi
|
lvii
|
26
|
v
|
vi
|
27
|
xvi
|
lii
|
27
|
vi
|
xxxiiii
|
27
|
v
|
xxix
|
28
|
xvi
|
xxxv
|
28
|
vi
|
xi
|
28
|
v
|
liii
|
29
|
xvi
|
xix
|
29
|
v
|
xlix
|
29
|
vi
|
xvi
|
30
|
xvi
|
ii
|
30
|
v
|
xxvi
|
30
|
vi
|
39
|
31
|
xv
|
xliiii
|
31
|
v
|
iii
|
|
|
|
¶
The
declination
of
the
Sunne
.
The
leape
yeere
.
October
.
|
Nouember
.
|
December
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
Dayes
|
Degrees
.
|
Minutes
.
|
1
|
vii
|
ii
|
1
|
xvii
|
33
|
1
|
23
|
8
|
2
|
vii
|
xxv
|
2
|
xvii
|
50
|
2
|
23
|
12
|
3
|
vii
|
xlviiii
|
3
|
xviii
|
7
|
3
|
23
|
17
|
4
|
viii
|
x
|
4
|
xviii
|
22
|
4
|
23
|
21
|
5
|
viii
|
xxxiii
|
5
|
xviii
|
38
|
5
|
23
|
24
|
6
|
viii
|
lv
|
6
|
xviii
|
53
|
6
|
23
|
26
|
7
|
ix
|
xxii
|
7
|
xix
|
8
|
7
|
23
|
28
|
8
|
ix
|
xxxix
|
8
|
xix
|
23
|
8
|
23
|
30
|
9
|
x
|
i
|
9
|
xix
|
37
|
9
|
23
|
32
|
10
|
x
|
xxiiii
|
10
|
xix
|
50
|
10
|
23
|
33
|
11
|
x
|
xlvi
|
11
|
xx
|
4
|
11
|
23
|
33
|
12
|
xi
|
vii
|
12
|
xx
|
17
|
12
|
23
|
33
|
13
|
xi
|
xxix
|
13
|
xx
|
30
|
13
|
23
|
32
|
14
|
xi
|
l
|
14
|
xx
|
42
|
14
|
23
|
31
|
15
|
xii
|
xi
|
15
|
xx
|
54
|
15
|
23
|
29
|
16
|
xii
|
xxxi
|
16
|
xxi
|
6
|
16
|
23
|
27
|
17
|
xii
|
lii
|
17
|
xxi
|
17
|
17
|
23
|
25
|
18
|
xiii
|
xii
|
18
|
xxi
|
28
|
18
|
23
|
22
|
19
|
xiii
|
xxxii
|
19
|
xxi
|
38
|
19
|
23
|
18
|
20
|
xiii
|
liii
|
20
|
xxi
|
48
|
20
|
23
|
14
|
21
|
xiiii
|
xiii
|
21
|
xxi
|
57
|
21
|
23
|
10
|
22
|
xiiii
|
xxxii
|
22
|
xxii
|
7
|
22
|
23
|
5
|
23
|
xiiii
|
lii
|
23
|
xxii
|
15
|
23
|
22
|
59
|
24
|
xv
|
xi
|
24
|
xxii
|
23
|
24
|
22
|
54
|
25
|
xv
|
xxx
|
25
|
xxii
|
31
|
25
|
22
|
48
|
26
|
xv
|
xlviii
|
26
|
xxii
|
38
|
26
|
22
|
41
|
27
|
xvi
|
vi
|
27
|
xxii
|
46
|
27
|
22
|
33
|
28
|
xvi
|
xxiiii
|
28
|
xxii
|
52
|
28
|
22
|
26
|
29
|
xvi
|
xlii
|
29
|
xxii
|
58
|
29
|
22
|
18
|
30
|
xvii
|
0
|
30
|
xxiii
|
3
|
30
|
22
|
9
|
31
|
xvii
|
xvii
|
|
|
|
31
|
22
|
0
|
¶
The
Callender
.
Ianuarie
.
|
Februarie
.
|
March
.
|
1
|
a
|
Newe
yeeres
day
.
|
1
|
d
|
|
1
|
d
|
2
|
b
|
|
2
|
e
|
Pruficatiō
of
Ma.
|
2
|
e
|
3
|
c
|
|
3
|
f
|
|
3
|
f
|
4
|
d
|
|
4
|
g
|
|
4
|
g
|
5
|
e
|
|
5
|
A
|
Shroue
Sunday
.
|
5
|
A
|
6
|
f
|
Twelfe
day
.
|
6
|
b
|
|
6
|
b
|
7
|
g
|
|
7
|
c
|
|
7
|
c
|
8
|
a
|
|
8
|
d
|
|
8
|
●
|
9
|
b
|
|
9
|
e
|
|
9
|
e
|
10
|
c
|
|
10
|
f
|
|
10
|
f
|
11
|
d
|
|
11
|
g
|
|
11
|
g
|
12
|
e
|
|
12
|
A
|
|
12
|
A
|
S.
Gregorie
.
|
13
|
f
|
|
13
|
b
|
|
13
|
b
|
S.
Leonard
.
|
14
|
g
|
|
14
|
c
|
|
14
|
c
|
15
|
a
|
|
15
|
●
|
|
15
|
d
|
16
|
b
|
|
16
|
e
|
|
16
|
e
|
17
|
c
|
|
17
|
f
|
|
17
|
f
|
S.
Gabriel
archan
.
|
18
|
d
|
|
18
|
g
|
|
18
|
g
|
19
|
e
|
|
19
|
a
|
|
19
|
A
|
|
20
|
f
|
S.
Fabian
&
Seba.
|
20
|
b
|
|
20
|
b
|
|
21
|
g
|
|
21
|
c
|
|
21
|
c
|
|
22
|
A
|
S.
Uincent
martyre
.
|
22
|
d
|
|
22
|
d
|
|
23
|
b
|
|
23
|
e
|
|
23
|
e
|
|
24
|
c
|
|
24
|
f
|
S.
Matthias
apost.
|
24
|
f
|
|
25
|
d
|
Conuer
.
of
S.
Paul
.
|
25
|
g
|
|
25
|
g
|
Anuntia
.
of
Marie
.
|
26
|
e
|
|
26
|
A
|
|
26
|
A
|
Easter
day
.
|
27
|
f
|
|
27
|
b
|
|
27
|
b
|
|
28
|
g
|
|
28
|
c
|
|
28
|
c
|
|
29
|
A
|
|
|
|
|
29
|
d
|
|
30
|
b
|
|
|
|
|
30
|
e
|
|
31
|
c
|
|
|
|
|
31
|
|
|
¶
The
Callender
.
April
.
|
May
.
|
Iune
.
|
1
|
g
|
|
1
|
b
|
S.
Phil.
and
Jacob.
|
1
|
e
|
|
2
|
A
|
|
2
|
c
|
|
2
|
|
|
3
|
b
|
|
3
|
d
|
Innuenci
.
of
the
crosse
.
|
3
|
g
|
|
4
|
c
|
|
4
|
e
|
Ascention
day
.
|
4
|
A
|
|
5
|
d
|
|
5
|
f
|
|
5
|
b
|
|
6
|
e
|
|
6
|
g
|
|
6
|
c
|
|
7
|
f
|
|
7
|
A
|
|
7
|
d
|
|
8
|
g
|
|
8
|
b
|
|
8
|
e
|
|
9
|
A
|
|
9
|
c
|
|
9
|
f
|
|
10
|
b
|
|
10
|
d
|
|
10
|
g
|
|
11
|
c
|
|
11
|
e
|
|
11
|
A
|
Barnabe
apostle
.
|
12
|
d
|
|
12
|
f
|
|
12
|
b
|
|
13
|
e
|
|
13
|
g
|
|
13
|
c
|
|
14
|
f
|
|
14
|
A
|
Whitsunday
.
|
14
|
d
|
.
|
15
|
g
|
|
15
|
b
|
S.
Isidore
archbish.
of
Seuill
.
|
15
|
e
|
|
16
|
A
|
|
16
|
c
|
16
|
f
|
|
17
|
b
|
|
17
|
d
|
|
17
|
g
|
|
18
|
c
|
|
18
|
e
|
|
18
|
A
|
|
19
|
d
|
|
19
|
f
|
|
19
|
b
|
|
20
|
e
|
|
20
|
g
|
|
20
|
c
|
|
21
|
f
|
|
21
|
A
|
|
21
|
d
|
|
22
|
g
|
|
22
|
b
|
|
22
|
e
|
|
23
|
A
|
S.
George
matyre
.
|
23
|
c
|
|
23
|
f
|
|
24
|
b
|
|
24
|
d
|
|
24
|
g
|
S.
John
Baptist.
|
25
|
c
|
S.
Marke
Euang.
|
25
|
e
|
|
25
|
A
|
|
26
|
d
|
|
26
|
f
|
|
26
|
b
|
|
27
|
e
|
|
27
|
g
|
|
27
|
c
|
|
28
|
f
|
|
28
|
A
|
|
28
|
d
|
|
29
|
g
|
|
29
|
b
|
|
29
|
e
|
|
30
|
A
|
|
30
|
c
|
|
30
|
f
|
S.
Peter
and
Paul
.
|
|
|
|
31
|
d
|
|
|
|
|
¶
The
Calender
.
Iulie
.
|
August
.
|
September
.
|
1
|
g
|
|
1
|
c
|
|
1
|
f
|
|
2
|
A
|
|
2
|
d
|
|
2
|
g
|
|
3
|
b
|
|
3
|
e
|
|
3
|
A
|
|
4
|
c
|
|
4
|
f
|
|
4
|
b
|
|
5
|
d
|
|
5
|
g
|
|
5
|
c
|
|
6
|
e
|
|
6
|
A
|
Transfigu
.
of
our
Lord
|
6
|
d
|
|
7
|
f
|
|
7
|
b
|
|
7
|
e
|
|
8
|
g
|
|
8
|
c
|
|
8
|
f
|
The
natiuitie
of
our
|
9
|
A
|
|
9
|
d
|
|
9
|
g
|
Ladie
.
|
10
|
b
|
|
10
|
e
|
Saint
Laurence
.
|
10
|
A
|
|
11
|
c
|
|
11
|
f
|
|
11
|
b
|
|
12
|
d
|
|
12
|
g
|
S.
Clare
virgin
.
|
12
|
c
|
|
13
|
e
|
|
13
|
A
|
|
13
|
d
|
|
14
|
f
|
|
14
|
b
|
|
14
|
e
|
|
15
|
g
|
|
15
|
c
|
Assumption
of
Ma
|
15
|
f
|
|
16
|
A
|
|
16
|
d
|
|
16
|
g
|
|
17
|
b
|
|
17
|
e
|
|
17
|
A
|
|
18
|
c
|
|
18
|
f
|
|
18
|
b
|
|
19
|
d
|
|
19
|
g
|
|
19
|
c
|
|
20
|
e
|
|
20
|
A
|
|
20
|
d
|
|
21
|
f
|
|
21
|
b
|
|
21
|
e
|
|
22
|
g
|
Marie
Magdalen
.
|
22
|
c
|
|
22
|
f
|
S.
Matthewe
apo.
|
23
|
A
|
|
23
|
d
|
|
23
|
g
|
|
24
|
b
|
|
24
|
e
|
S.
Bartholomewe
apostle
.
|
24
|
A
|
|
25
|
c
|
Saint
James
.
|
25
|
f
|
|
25
|
b
|
|
26
|
d
|
Saint
Anne
.
|
26
|
c
|
|
26
|
e
|
|
27
|
e
|
Saint
Christopher
.
|
27
|
A
|
|
27
|
d
|
|
28
|
f
|
|
28
|
b
|
S.
Austin
.
|
28
|
e
|
|
29
|
g
|
|
29
|
c
|
The
cutting
off
of
saint
John
Baptist
|
29
|
f
|
S.
Michael
archan
|
30
|
A
|
|
30
|
d
|
|
30
|
g
|
S.
Jerome
.
|
31
|
b
|
|
31
|
e
|
head
.
|
|
|
|
¶
The
Callender
.
October
.
|
Nouember
.
|
December
.
|
1
|
A
|
|
1
|
d
|
All
Saintes
day
.
|
1
|
f
|
|
2
|
b
|
|
2
|
e
|
The
remembrance
|
2
|
g
|
|
3
|
c
|
|
3
|
f
|
of
them
that
are
.
|
3
|
A
|
|
4
|
d
|
|
4
|
g
|
dead
.
|
4
|
b
|
Saint
Barbara
.
|
5
|
e
|
|
5
|
A
|
|
5
|
c
|
|
6
|
f
|
|
6
|
b
|
|
6
|
d
|
S.
Nicholas
bisho
.
|
7
|
g
|
|
7
|
c
|
|
7
|
e
|
|
8
|
A
|
|
8
|
d
|
|
8
|
f
|
Conception
of
Ma.
|
9
|
b
|
|
9
|
e
|
|
9
|
g
|
|
10
|
c
|
|
10
|
f
|
|
10
|
A
|
|
11
|
d
|
|
11
|
g
|
Saint
Martin
.
|
11
|
b
|
|
12
|
e
|
|
12
|
A
|
|
12
|
c
|
|
13
|
f
|
|
13
|
b
|
|
13
|
d
|
S.
Luce
virgin
.
|
14
|
g
|
|
14
|
c
|
|
14
|
e
|
|
15
|
A
|
|
15
|
d
|
|
15
|
f
|
|
16
|
b
|
|
16
|
e
|
|
16
|
g
|
|
17
|
c
|
|
17
|
f
|
|
17
|
A
|
|
18
|
d
|
S.
Luke
euangelist
.
|
18
|
g
|
|
18
|
b
|
|
19
|
e
|
|
19
|
A
|
|
19
|
c
|
|
20
|
f
|
|
20
|
b
|
|
20
|
d
|
|
21
|
g
|
The
xi
.
M.
virgins
.
|
21
|
c
|
|
21
|
e
|
S.
Thomas
apost.
|
22
|
A
|
|
22
|
d
|
|
22
|
f
|
|
23
|
b
|
|
23
|
e
|
Saint
Clement
.
|
23
|
g
|
|
24
|
c
|
|
24
|
f
|
|
24
|
A
|
|
25
|
d
|
|
25
|
g
|
Saint
Katheren
.
|
25
|
b
|
|
26
|
e
|
|
26
|
A
|
|
26
|
c
|
Christmas
day
.
|
27
|
f
|
|
27
|
b
|
|
27
|
d
|
S.
Steuen
martyre
.
|
28
|
g
|
S.
Simon
&
Jude
.
|
28
|
c
|
|
28
|
e
|
S.
John
euangelist
.
|
29
|
A
|
|
29
|
d
|
|
29
|
f
|
Holy
Innocentes
.
|
30
|
b
|
|
30
|
e
|
S.
Andrew
apostle
.
|
30
|
g
|
|
31
|
c
|
|
|
|
|
31
|
A
|
|
¶
A
Rule
to
knowe
the
Dominicall
letter
euery
yeere
.
FOr
to
knowe
in
what
day
of
the
weeke
is
euery
feast
of
the
yeere
.
It
is
necessarie
you
know
what
letter
it
is
that
serueth
for
sunday
.
This
is
to
be
knowen
by
the
rules
of
the
letters
vnder
written
,
in
the
which
,
the
first
letter
which
is
D.
serueth
for
the
Dominicall
letter
,
this
yere
of
1545
and
so
successiuely
in
euery
yeere
one
letter
serueth
,
and
the
two
rules
being
ended
,
returne
againe
to
the
begining
,
and
this
is
for
euer
.
And
it
is
to
be
noted
that
in
the
leape
yeeres
are
two
Dominicall
letters
.
The
letter
aboue
being
vppermost
serueth
from
the
first
day
of
Januarie
,
vnto
the
xxv
of
Februarie
,
and
the
other
vnto
the
end
of
the
yeere
.
1545.
D
C
B.
A
F
E
D.
C
A
G
F.
E
C
B
A.
G
B
D
G
E
D
C
B
G
F
E.
D
B
A
G.
F
F
A
C
E
The
eleuenth
Chapter
,
wherein
is
declared
howeby
the
Calender
before
written
,
a
man
may
know
the
moneth
,
and
the
day
wherein
he
is
.
THe
Philosopher
saith
,
that
the
art
doth
emitate
nature
as
much
as
hee
may
,
Likewise
the
saide
art
many
times
helpeth
the
defects
of
nature
,
this
is
prooued
,
wherein
we
see
that
a
man
which
by
nature
doth
want
his
sight
,
the
art
doth
help
and
remedy
his
want
,
that
is
,
by
looking
on
a
payre
of
spectacles
,
whereby
in
such
sort
,
the
sight
is
gathered
together
,
and
is
cause
that
he
seeth
,
the
which
he
doth
not
without
them
for
that
it
is
scattered
abroad
.
The
selfe
same
which
is
said
of
the
sight
,
may
be
said
of
the
memory
,
that
many
times
it
lacketh
in
men
,
but
it
is
certain
that
in
some
it
commeth
by
nature
,
but
in
others
by
their
owne
vncarefulnes
that
they
forget
themselues
so
much
,
that
in
things
which
standeth
them
much
vpon
,
they
take
no
heede
.
And
concerning
this
I
doe
remember
as
we
came
sayling
in
a
shippe
,
nienteene
men
,
which
were
seuen
passengers
,
and
twelue
mariners
,
and
hauing
bin
many
dayes
at
the
sea
,
because
the
weather
was
contrary
,
there
happened
a
cause
whereby
it
was
conuenient
that
the
purser
shuld
write
it
downe
in
his
booke
for
to
giue
reason
thereof
when
time
should
serue
,
and
he
with
the
other
that
were
there
,
knewe
not
what
day
of
the
moneth
it
was
,
nor
there
was
any
that
had
it
in
his
remembrance
,
nor
knew
what
day
was
the
first
day
of
the
moneth
,
vntil
I
told
him
,
nor
any
booke
in
the
ship
to
looke
in
whereby
it
might
be
knowen
.
And
this
being
brought
for
my
purpose
,
I
say
that
here
before
hath
bene
declared
.
that
one
of
the
thinges
which
ought
to
be
seene
and
knowen
,
for
to
take
the
altitude
of
the
sunne
,
is
the
declination
or
distance
which
it
hath
that
day
from
the
equinoctiall
line
,
for
not
knowing
the
declination
how
much
it
is
,
the
said
altitude
can
not
be
knowen
,
whereby
it
is
necessary
that
the
Pilote
or
any
other
person
which
shal
take
the
said
altitude
should
knowe
in
what
moneth
he
is
in
,
and
howe
many
dayes
of
the
moneth
it
is
,
without
hauing
any
errour
or
want
therein
.
And
because
of
that
as
I
haue
spoken
of
before
,
which
happened
,
it
may
happen
the
like
in
others
,
or
likewise
if
hee
that
taketh
the
altitude
be
alone
,
or
with
little
company
,
and
do
not
remember
the
reckoning
aforesayde
,
for
this
it
seemeth
to
me
to
be
a
conuenient
thing
to
helpe
the
memorie
by
putting
here
the
calender
before
written
,
wherby
may
be
kept
a
certaine
remembrance
&
a
reckoning
of
the
moneth
and
day
wherein
he
is
,
by
looking
what
day
euerye
moneth
beginneth
,
without
any
need
to
aske
it
of
any
.
And
because
such
as
do
goe
by
some
wayes
which
hath
not
much
used
it
,
are
accustomed
to
set
marks
to
know
it
the
better
.
So
in
this
Calender
,
for
the
better
knowledge
thereof
,
I
haue
put
marks
which
are
the
saints
daies
.
Therfore
I
saye
to
knowe
what
day
in
the
weeke
is
euery
holy
day
of
them
aforesayde
.
The
letters
must
be
seene
which
standeth
before
those
daies
of
euery
moneth
,
&
see
what
letter
of
these
serueth
in
this
yere
for
sunday
,
and
is
called
the
the
Dominicall
letter
,
which
shall
bee
knowen
by
the
rule
afore
written
,
and
being
knowen
,
to
stay
in
it
which
is
sunday
,
&
in
another
which
is
next
munday
,
&
in
the
other
tewsday
.
And
so
al
the
seuen
dayes
of
the
weeke
named
by
the
seuen
letters
ABCDEFG
.
And
by
reckoning
in
this
maner
,
see
what
day
is
the
letter
that
is
next
to
the
holy
day
,
and
in
that
yeere
that
is
the
proper
day
of
such
a
feast
,
the
leape
yeeres
as
before
hath
beene
declared
,
haue
two
dominicall
letters
,
the
one
serueth
vnto
the
xxv
day
of
Februarie
,
and
the
other
vnto
the
ende
of
the
yeere
.
The
ende
of
the
fourth
booke
.
¶
The
fifth
booke
of
the
Altitude
of
the
Poles
.
The
first
Chapter
,
what
thing
a
pole
is
,
and
how
betweene
the
two
poles
the
roundnesse
of
the
worlde
is
deuided
.
These
Zonas
the
first
is
called
Septentrionall
,
the
second
solstitiall
,
the
thirde
Equinoctiall
,
the
fourth
●emall
,
the
fifth
Australl
.
And
it
is
to
bee
noted
,
that
these
two
poles
▪
the
one
is
superiour
,
and
the
other
is
inferiour
.
And
according
to
Albertus
the
great
in
the
second
booke
of
the
heauen
,
&
the
world
,
the
first
treatie
,
the
sixe
chapter
,
they
are
to
bee
considered
in
this
manner
,
in
as
much
as
toucheth
the
moouing
of
the
circle
of
the
fired
starres
.
The
pole
Antarticke
is
the
superiour
,
and
the
pole
Articke
is
the
inferiour
,
and
according
to
the
circle
of
the
Planets
,
the
pole
Articke
is
the
Superiour
,
and
the
Antarticke
the
inferiour
,
and
it
is
to
be
vnderstood
that
such
as
dwell
in
the
Equinoctiall
line
,
onely
the
place
of
the
one
pole
they
see
,
and
so
we
doe
onely
see
in
the
heauen
,
the
place
where
wee
imagine
the
one
pole
to
be
:
&
this
is
called
Articks
,
likewise
Septeritrional
,
or
Boreal
:
It
is
called
Articke
,
because
it
is
neere
to
the
image
called
Arture
.
It
is
called
Septentrionall
,
by
the
seuen
starres
of
the
Vrsa
minor
,
whiche
doth
mooue
round
about
the
sayde
pole
.
It
is
called
Boreall
by
the
winde
Boreas
,
which
we
cal
North.
The
other
pole
is
called
Antartico
,
which
is
against
,
as
though
it
were
put
contrarye
or
opposite
to
the
Articke
,
and
Australl
,
because
from
that
part
commeth
the
winde
called
Austro
:
it
is
also
called
Meridionall
,
because
it
is
towardes
the
parte
of
the
middest
of
the
day
,
it
is
to
bee
vnderstood
,
that
it
standeth
towards
the
parte
of
the
middest
of
the
day
to
suche
as
doe
dwell
towardes
the
North
,
out
of
the
tropicke
of
Cancer
,
because
in
all
times
of
the
yeere
at
the
middest
of
the
daye
,
wee
haue
the
Sunne
towardes
that
parte
▪
The
seconde
chapter
,
how
the
altitude
of
o●
the
pole
Articke
is
to
be
taken
,
and
of
the
effect
wherefore
he
is
taken
.
THe
P●●ot
or
an●
other
person
that
will
take
the
Altitude
of
the
pole
articke
,
which
commonly
we
call
the
Altitude
of
the
North
,
let
him
take
his
Ballestila
or
quadrant
,
or
the
instrument
that
he
hath
most
vsed
,
let
him
take
the
altitude
of
the
sayde
starre
,
as
precisely
as
hee
can
,
and
for
the
better
taking
thereof
,
let
him
put
himselfe
neere
to
the
maste
of
the
〈◊〉
,
●●there
shall
〈◊〉
feele
lead●●
all
the
moouing
a●
the
〈◊〉
.
And
it
in
to
〈◊〉
,
that
the
altitude
of
the
pole
to
token
,
to
know
the
distance
of
the
degrees
,
that
are
〈◊〉
hori●d
vnto
the
p●le
,
〈◊〉
there
degrees
beeyng
knowne
,
is
knowne
how
many
degrees
are
from
him
which
taketh
the
altitude
vnto
the
Equinoctiall
line
,
and
it
is
knowne
in
this
manner
.
The
pole
articke
,
or
the
antarticke
either
of
them
,
is
distant
from
the
Equinoctiall
line
,
ninety
degrees
,
therefore
let
him
looke
that
taketh
the
altitude
how
many
degrees
he
hath
raysed
the
pole
vpon
the
Horizon
,
&
he
shall
vnderstand
,
that
the
selfe-same
degrees
are
from
the
place
where
he
is
vnto
the
Equinoctial
line
,
so
that
if
hee
be
vnder
the
Equinoctiall
,
hee
shall
not
take
altitude
of
any
of
the
poles
,
because
he
shall
haue
them
in
the
Horizon
.
But
beeing
come
foorth
of
the
Equinoctiall
,
how
much
he
is
distant
from
her
,
so
much
hee
shall
haue
the
one
pole
raised
vp
,
and
the
other
put
downe
,
so
that
how
many
degrees
hee
is
distant
from
the
line
,
in
so
many
he
shall
take
the
altitude
of
that
pole
,
towardes
●he
parte
where
he
is
.
For
so
many
,
hee
hath
raysed
vpon
him
his
Herizon
,
In
such
sort
,
that
if
he
tooke
the
altitude
of
the
pole
in
tenne
degrees
,
the
sayde
tenne
degrees
hee
is
distant
of
the
Equinoctiall
,
&
if
in
twentie
,
twentie
,
and
so
the
rest
.
In
such
sorte
,
that
whensoeuer
the
altitude
of
the
pole
is
taken
,
looking
by
her
the
degrees
that
are
raysed
vpon
the
Horizon
,
the
selfe
same
he
which
taketh
the
altitude
is
distant
from
the
Equinoctiall
line
.
The
thirde
Chapter
,
howe
the
reckoning
whiche
is
taken
of
the
height
of
the
pole
articke
or
North
is
,
to
bee
vnderstood
.
IT
hath
beene
declared
in
the
chapter
before
this
,
that
how
many
degrees
are
taken
of
the
altitude
of
the
pole
,
so
many
is
he
which
taketh
her
distant
of
the
Equinoctiall
line
,
because
for
this
effect
to
know
the
distance
of
the
sayde
line
,
the
sayde
altitude
is
taken
,
therefore
in
this
present
,
I
will
speake
how
this
altitude
which
is
taken
of
the
pole
is
to
bee
vnderstood
.
Of
the
which
it
is
to
bee
vnderstood
,
that
when
a
man
is
in
the
Equinoctiall
line
,
he
hath
both
poles
in
the
Horizon
,
as
before
hath
beene
declared
,
and
by
how
muche
hee
is
going
from
the
sayde
line
,
and
comming
towardes
the
pole
articke
or
North
pole
,
which
is
this
that
wee
speake
of
,
by
so
much
the
sayde
pole
goeth
rising
vpon
his
Horizon
,
so
that
if
the
man
bee
distant
of
the
line
twentie
degrees
,
the
same
twentie
hee
hath
the
pole
,
aboue
his
Horizon
.
Of
this
is
to
be
noted
,
that
the
degrees
which
are
taken
of
the
altitude
of
the
pole
,
are
not
to
bee
vnderstoode
of
those
whiche
are
from
him
,
that
taketh
the
altitude
vnto
to
the
pole
it selfe
:
But
it
is
to
be
vnderstood
,
that
those
haue
gone
raysing
vp
the
saide
pole
aboue
his
Horizon
.
For
because
like
as
in
the
altitude
of
the
sunne
,
is
not
noted
how
much
the
sunne
is
raysed
aboue
him
that
taketh
his
altitude
,
but
it
is
to
be
seene
,
howe
muche
he
is
raysed
aboue
the
Horizon
,
whiche
is
seene
by
these
degrees
,
which
are
taken
in
the
Astrolabio
,
so
that
in
the
altitude
of
the
North
,
it
is
not
to
be
looked
,
howe
muche
the
pole
is
risen
vpon
him
,
which
taketh
his
altitude
,
but
that
which
hee
is
risen
aboue
his
Horizon
,
in
such
sorte
,
that
to
knowe
the
height
of
the
pole
,
there
is
no
account
or
reckoning
,
to
bee
taken
betweene
him
that
taketh
it
and
the
pole
,
but
the
reckoning
is
betweene
the
pole
and
the
Horizon
.
For
if
the
man
shoulde
keepe
reckoning
with
the
pole
,
it
woulde
be
said
in
this
manner
,
from
the
Equinoctiall
line
,
to
the
pole
,
are
nienty
degrees
,
therefore
if
he
which
taketh
the
altitude
is
twenty
degrees
,
distant
from
the
Equinoctial
line
:
then
it
shoulde
bee
threescore
and
tenne
degrees
from
the
pole
,
and
woulde
say
,
seeyng
I
am
in
seuentie
degrees
of
altitude
,
I
am
so
manye
from
the
pole
.
This
ought
not
to
bee
vnderstood
so
,
for
it
woulde
bee
a
verye
great
errour
,
so
muche
that
beeyng
in
twentie
degrees
of
altitude
,
hee
that
should
so
make
his
reckoning
,
shoulde
make
that
he
were
in
seuentie
.
But
let
the
reckoning
be
kept
,
as
aforesayde
,
which
is
,
that
how
many
degrees
I
doe
take
of
altitude
with
my
Ballestisa
,
or
other
instrument
:
these
haue
I
raised
the
pole
,
not
aboue
me
,
but
aboue
my
Horizon
,
&
the
selfe
same
degrees
am
I
distant
of
the
Equinoctiall
line
.
The
fourth
Chapter
,
of
the
North
starre
,
and
of
the
guardes
of
his
moouing
.
THE
North
starre
beeyng
very
well
seene
and
knowne
of
al
the
saylers
,
is
the
first
of
the
7.
starres
,
which
that
Vrsa
minor
doth
set
in
order
,
and
commonly
he
is
called
Bozina
.
These
7.
starres
doe
seeme
cleere
&
bright
,
&
three
of
them
are
like
to
a
halfe
circle
,
&
the
other
4.
like
to
a
quadrangle
in
this
manner
.
The
seuen
starres
doe
alwayes
mooue
rounde
about
the
pole
,
describing
their
circl●s
from
the
East
into
the
West
,
and
alwayes
in
one selfe
distance
one
with
the
other
,
and
in
euery
foure
and
twentie
houres
they
geue
a
turne
about
the
pole
.
But
as
the
North
starre
is
more
neere
the
pole
,
then
any
of
the
others
,
his
turne
is
lesser
and
done
with
more
●eysute
,
then
any
of
the
other
starres
:
because
howe
muche
more
euery
starre
goeth
farther
of
from
the
pole
,
so
much
the
greater
circumserence
hee
maketh
,
and
so
much
the
hastier
hee
mooueth
.
Therefore
I
say
,
that
by
this
statre
of
the
North
is
knowne
,
howe
much
the
altitude
is
,
which
the
pole
hath
vpon
the
Horizon
:
In
suche
sorte
,
that
although
the
pole
is
seene
,
yet
by
this
starre
is
knowne
the
place
where
the
pole
is
,
the
whiche
is
knowen
by
an
other
starre
of
the
same
seuen
,
the
most
shyning
.
Of
the
two
called
guardes
,
which
are
in
the
moneth
of
the
Bozina
,
which
star
is
called
the
formest
guarde
,
and
also
he
is
called
the
horologial
star
,
because
hee
goeth
alwayes
like
to
a
whele
of
a
clocke
,
giuing
to
vnderstand
in
all
times
of
the
yeere
,
what
houre
of
the
night
it
is
,
by
that
reckoning
,
that
is
called
the
middest
of
Aprill
,
midnight
in
the
head
.
And
note
ye
,
that
between
the
north
starre
,
and
the
guardes
,
is
alwayes
the
pole
,
in
suche
sorte
,
that
when
the
guardes
are
aboue
the
pole
,
the
north
starre
is
vnder
,
and
so
contrary
,
seeing
by
the
course
or
place
where
the
guards
are
,
is
knowen
to
what
part
of
the
pole
,
and
in
what
distance
of
him
,
the
sayde
starre
is
.
The
fifth
Chapter
,
howe
that
according
to
the
course
wherein
the
guardes
are
,
is
knowen
howe
many
degrees
the
north
starre
is
vnder
or
aboue
the
pole
.
IT
hath
beene
declared
in
the
chapter
going
before
,
that
the
north
starre
moueth
him selfe
rounde
about
the
pole
,
and
that
likewise
the
two
starres
called
the
guards
,
doe
make
their
mouing
rounde
about
the
saide
starre
,
and
of
the
pole
.
By
the
which
it
is
necessarie
to
know
,
in
what
course
the
guards
are
in
,
with
the
saide
starre
,
because
with
this
,
wil
be
knowne
by
the
rules
here
vnder
written
,
in
what
course
the
saide
starre
is
in
with
the
pole
,
as
also
howe
many
degrees
he
is
vnder
or
aboue
him
:
for
the
which
knowledge
,
the
rules
following
are
so
be
looked
on
,
in
the
which
is
to
bee
noted
that
besides
the
rules
of
the
principall
windes
,
you
shal
finde
rules
for
the
half●
partes
,
because
the
saide
altitude
more
easely
at
any
houre
of
the
night
may
bee
taken
.
The
which
rules
goe
set
with
their
figures
in
such
sort
,
that
in
euery
course
that
the
guards
are
in
,
may
be
knowne
likewise
in
what
course
the
saide
north
starre
is
in
,
it
is
ordayned
in
the
maner
following
.
The
guardes
in
the
east
,
the
most
fore
guarde
is
with
the
north
starre
,
east
and
west
,
and
the
sayde
starre
a
degree
and
a
halfe
vnder
the
pole
.
The
guardes
in
the
east
northeast
,
the
north
starre
is
three
degrees
vnder
the
pole
.
The
guardes
in
the
northeast
,
the
one
guarde
is
with
the
other
east
and
west
,
and
the
north
starre
is
three
degrees
and
a
halfe
vnder
the
pole
.
The
guardes
in
the
north
northeast
,
the
north
starre
is
three
degrees
and
a
halfe
vnder
the
pole
.
The
guardes
in
the
north
,
the
formost
guarde
is
with
the
north
starre
north
and
south
,
and
the
sayd
starre
〈◊〉
three
degrees
vnder
the
pole
.
The
guardes
in
the
north
north
●est
,
the
north
starre
is
two
degrees
〈◊〉
●●r
the
pole
.
The
guardes
in
the
northwest
,
the
one
guarde
is
with
the
other
north
&
south
,
the
sayd
starre
is
halfe
a
degree
vnder
the
pole
.
The
guardes
in
the
west
northwest
,
the
north
starre
is
one
degree
aboue
the
pole
.
The
guardes
in
the
west
,
and
formost
guarde
is
with
the
north
starre
east
and
west
,
and
the
sayde
starre
is
a
degree
and
a
halfe
aboue
the
pole
.
The
guardes
in
the
West
Southwest
,
the
North
starre
is
three
degrees
aboue
the
pole
.
The
guardes
in
the
Southwest
,
the
one
guarde
is
by
the
other
East
and
West
,
and
the
North
starre
is
three
degrees
and
a
halfe
aboue
the
pole
.
The
guards
in
the
South
Southwest
,
the
North
starre
is
three
degrees
aboue
the
pole
.
The
guardes
in
the
South
,
the
North
starre
is
with
the
foremost
guard
,
North
and
South
,
and
the
sayde
starre
is
three
degrees
aboue
the
pole
.
The
guards
in
the
South
,
Southeast
,
the
North
starre
is
two
degrees
aboue
the
pole
.
The
guards
in
the
Southeast
,
the
one
guarde
is
by
the
other
North
,
and
South
,
and
the
North
starre
is
halfe
a
degree
aboue
the
pole
.
The
guardes
in
the
East
Southeast
,
the
north
starre
is
halfe
a
degree
vnder
the
pole
.
The
sixt
Chapter
,
howe
the
rules
of
the
altitude
of
the
North
starre
ought
to
be
applied
,
and
howe
they
ought
to
be
put
to
,
or
taken
away
,
according
to
the
place
where
the
guardes
are
.
THerefore
when
you
take
the
altitude
of
the
pole
,
looke
in
what
place
the
guardes
are
,
&
by
them
you
shall
vnderstande
if
the
north
star
be
vnder
or
aboue
the
pole
,
as
it
is
sayde
.
And
marke
,
if
the
starre
be
vnder
,
you
shall
ioyne
with
the
altitude
that
you
take
,
those
degrees
that
are
vnder
and
altogether
so
much
is
your
altitude
:
and
if
the
star
be
aboue
the
pole
,
you
shall
take
away
from
the
altitude
that
you
tooke
,
the
degrees
that
the
star
is
aboue
,
&
that
which
remaineth
,
is
the
altitude
wherin
you
are
.
Example
.
I
say
the
guardes
being
in
the
northeast
,
you
tooke
xl
.
degrees
of
altitude
;
ioyne
with
these
xl
.
three
degrees
and
a
half
,
that
the
starre
is
vnder
the
pole
▪
which
doth
amount
to
fourtie
three
degrees
and
a
half
,
this
is
your
altitude
▪
and
if
the
guardes
bee
in
the
southwest
,
take
a
way
of
the
fourtie
degrees
,
three
and
a
halfe
that
the
star
is
ouer
the
pole
,
there
doth
rest
thirty
sixe
&
a
half
and
this
is
the
altitude
wherin
you
〈◊〉
to
that
when
the
star
is
vnder
the
poles
you
shall
ioyne
with
the
altitude
those
degrees
that
he
is
vnder
,
and
when
he
is
aboue
,
you
shal
take
away
the
degrees
that
he
is
aboue
,
&
so
you
shall
make
your
account
iust
,
and
you
shall
knowe
the
place
where
you
are
.
The
seuenth
Chapter
,
wherein
be
declared
certain
doubts
that
in
this
mouing
of
the
north
starre
may
be
had
.
IN
the
third
chapter
of
this
fifth
book
hath
bin
said
,
that
the
starres
which
are
nere
to
the
pole
,
do
moue
them selues
more
slowly
then
they
that
are
farre
off
,
&
it
seemeth
that
of
this
may
be
a
doubt
,
because
that
euery
thing
which
mooueth
their
parts
in
rule
,
do
moue
so
equally
,
that
one
moueth
not
more
siow
,
nor
the
other
more
hasty
.
And
as
al
the
heauen
doth
moue
equally
,
as
the
sight
both
manifest
it
,
and
so
is
the
beginning
of
Astronomy
,
that
the
mouing
of
euery
day
is
in
rule
,
whereby
it
ought
to
bee
said
,
that
the
parts
of
heauen
do
moue
equally
,
&
not
the
one
part
more
slowly
then
the
other
Likwise
this
is
proued
because
that
one self
intelligence
,
moueth
al
the
circle
and
all
his
partes
seeing
that
the
parts
nerest
to
the
pole
,
are
lesse
then
those
which
are
far
off
,
therfore
the
said
intelligence
hath
a
greater
proportion
vpon
them
,
and
of
the
great
proportion
commeth
greater
swiftnes
,
whereby
may
be
saide
,
that
the
parts
which
are
most
nere
to
the
pole
,
do
moue
more
speedely
or
with
m●●
hast
then
the
others
.
Item
,
in
the
fifth
chapter
of
the
first
booke
hath
been
declared
how
the
heauen
is
round
,
and
seeing
that
it
is
so
,
it
may
be
said
,
that
in
the
heauen
is
no
part
from
aboue
the
pole
,
nor
part
vnder
the
pole
,
because
that
all
round
bodies
,
naturally
haue
no
part
high
nor
lowe
:
for
if
one
parte
were
more
high
or
lowe
then
the
other
,
then
the
body
should
not
be
rounde
,
whereby
it
seemeth
,
that
it
cannot
bee
saide
,
that
the
starre
of
the
North
,
nor
the
guardes
are
in
no
time
vnder
nor
aboue
the
pole
.
The
third
doubt
is
,
that
likewise
we
say
,
that
the
North
starre
doth
geue
an
equall
turne
rounde
about
the
pole
,
and
seeing
it
is
so
,
that
it
is
equall
:
wherefore
at
sometimes
is
he
distaunt
of
the
pole
vnder
or
aboue
halfe
a
degree
,
and
at
other
times
three
degrees
and
a
halfe
.
To
that
which
is
saide
in
the
first
doubt
,
all
the
Philosophers
and
Astronomers
are
agaynst
,
for
that
al
of
them
holde
that
the
pole
mooueth
not
,
but
is
fixed
,
and
vpon
him
all
the
partes
of
heauen
doe
moue
in
circle
manner
and
in
such
sort
,
that
that
which
is
neere
,
mooueth
slowlie
,
and
that
which
is
farre
of
,
moueth
with
more
haste
,
wherby
that
which
mooueth
it selfe
by
the
Equinoctiall
,
because
that
there
it
is
farthest
of
,
there
the
moouing
is
more
hastie
,
then
in
any
other
part
,
and
this
sheweth
it selfe
by
experience
.
We
see
in
the
moouing
of
a
wheele
,
that
the
Ex
standeth
still
,
and
alwayes
remayneth
in
one
place
,
and
all
the
partes
of
the
wheele
doe
compasse
it
about
,
of
the
which
,
those
partes
that
are
neere
to
the
Ex
,
goe
more
slowly
,
and
those
that
are
farther
of
they
moue
with
more
hastie
mouing
,
so
the
vppermost
part
of
the
wheele
his
moouing
is
more
hastie
then
any
of
the
other
partes
:
as
Aristotle
sheweth
it
in
the
Mechanica
.
To
that
which
is
saide
,
that
the
heauen
mooueth
it selfe
equally
,
it
is
to
be
vnderstood
in
equallitie
of
time
,
but
not
in
equality
of
place
,
in
such
sort
,
that
in
equall
time
they
make
their
partes
in
equall
moouing
,
because
these
parts
cannot
of
continuance
〈…〉
by
themselues
.
A
continuance
is
that
whose
mouing
is
one
,
and
is
to
be
vnderstood
wholly
together
:
so
that
it
cannot
be
,
that
at
one
time
one
parte
is
mooued
,
&
at
another
time
another
,
but
at
the
mouing
of
one
parte
,
all
the
other
partes
,
and
all
together
are
mooued
:
so
that
when
the
Heauen
mooueth
,
because
his
moouing
is
a
pure
mouing
,
of
his
place
to
his
mouing
all
the
partes
doe
moue
place
.
Item
although
that
one selfe
intelligence
doe
moue
the
partes
of
the
poles
&
likewise
the
others
,
which
are
more
distant
,
because
all
be
continuall
,
they
are
mooued
together
.
And
it
is
so
,
because
these
partes
are
not
put
asunder
,
nor
deuided
the
one
from
the
other
.
And
if
they
were
it
is
certayne
that
the
lesser
partes
should
mooue
more
hastily
then
the
greater
partes
,
the
which
is
not
because
the
sayd
intelligence
doth
mooue
them
together
,
&
the
moouer
hath
his
proportion
to
all
,
and
not
to
part
.
And
this
is
manifest
,
because
in
the
continuall
moueable
,
there
are
partes
of
an
infinite
smalnesse
,
for
that
to
any
part
that
is
marked
maye
bee
geuen
a
lesser
.
To
the
second
doubt
which
is
in
the
rounde
bodie
,
that
there
is
no
part
high
nor
lowe
:
truth
it
is
,
that
naturally
there
is
not
,
respectiuely
there
is
.
And
to
saye
that
the
North
starre
is
sometime
aboue
the
pole
,
and
at
other
times
vnder
,
it
is
to
be
vnderstood
,
not
naturally
,
but
to
our
respect
,
and
so
hee
that
were
in
such
a
place
,
that
had
the
pole
for
Cenith
:
the
North
starre
should
not
be
from
him
more
high
nor
more
lowe
,
at
one
time
then
at
another
.
But
to
him
whose
Cenith
is
not
vnder
the
pole
in
the
mouing
which
the
starre
maketh
at
some
time
,
he
wil
bee
vnder
the
pole
,
&
at
other
t●●es
aboue
and
to
know
how
the
North
starre
is
vnder
or
aboue
the
pole
,
doe
you
imagine
the
f●●ure
of
a
●an
in
the
pole
articke
,
which
hauing
his
face
towardes
the
middest
of
the
day
,
and
beyng
so
put
,
the
left
arme
shal
bee
towardes
the
East
,
and
the
right
towardes
the
West
,
therefore
when
the
North
starre
doth
goe
from
the
left
to
the
right
,
which
is
from
the
East
towardes
the
West
by
the
heade
which
maketh
the
halfe
of
his
circle
,
wee
saye
that
hee
is
aboue
the
pole
,
because
then
the
pole
is
betweene
the
starre
and
the
Horizon
,
so
there
are
more
degrees
,
from
the
Horizon
to
the
starre
,
then
to
the
pole
:
and
when
he
goeth
from
the
right
arme
to
the
lefte
,
which
is
from
the
West
to
the
East
,
in
the
other
halfe
turne
that
he
maketh
by
the
foote
,
we
say
,
that
hee
is
vnder
the
pole
,
because
then
the
starre
wil
bee
betweene
the
pole
and
the
Horizon
,
and
then
there
are
more
degrees
from
the
Horizon
to
the
pole
,
then
to
the
starre
,
as
appeareth
by
this
figure
.
The
Horizon
,
And
so
it
is
to
bee
vnderstood
,
that
the
North
starre
to
bee
vnder
or
aboue
the
pole
.
To
the
third
is
to
be
noted
,
that
the
north
starre
doth
goe
rounde
about
the
pole
,
but
although
the
turne
,
which
hee
geueth
,
be
in
equall
roundnes
,
he
goeth
distant
from
the
pole
,
more
in
one
place
then
in
another
,
this
is
to
be
vnderstod
not
as
much
as
toucheth
the
roundnes
,
but
as
muche
as
toucheth
the
straightnesse
of
the
pole
,
in
this
manner
.
When
the
star
is
in
any
of
the
armes
of
the
east
or
of
the
west
,
then
hee
is
neither
more
high
nor
more
low
then
the
pole
but
in
one
equallitie
with
him
.
And
for
as
muche
as
toucheth
his
turne
,
hee
goeth
from
the
sayde
armes
,
by
the
part
of
the
head
,
or
by
the
part
of
the
foote
,
so
much
he
goeth
aside
of
,
from
the
straightnesse
of
the
pole
.
In
such
sort
,
that
when
he
is
in
the
head
,
is
,
when
he
is
farthest
of
the
pole
,
by
the
vppermost
part
:
and
when
hee
is
in
the
foote
,
is
,
when
hee
is
farthest
of
by
the
lower
parte
,
the
whiche
is
not
to
bee
vnderstood
,
that
the
circumference
is
greater
in
the
head
or
the
foote
,
then
in
the
other
partes
.
But
vnto
our
respect
is
that
whiche
he
goeth
distant
aboue
or
vnder
the
pole
as
here
it
is
shewed
.
The
eight
Chapter
,
howe
the
altitude
of
the
North
,
is
to
be
taken
,
although
the
guards
be
not
seene
.
IT
happeneth
manye
times
to
such
as
bee
saylers
,
when
they
goe
neere
the
Equinoctiall
by
reason
the
pole
is
neere
to
their
Horizon
,
they
see
not
wholly
the
turne
which
the
guards
doe
make
,
round
about
the
pole
,
so
that
when
the
guards
doe
descend
from
the
West
;
and
goe
towardes
the
East
,
in
all
those
courses
of
the
west
Southwest
,
South
West
South
Southwest
,
South
,
South
Southeast
,
Southeast
,
East
Southeast
,
they
cannot
take
the
altitude
,
because
he
is
not
seene
when
the
guardes
doe
come
to
euery
one
of
these
sayd
courses
.
And
for
this
in
this
chapter
shal
bee
declared
,
howe
it
shal
bee
knowen
,
when
the
guardes
doe
come
to
euery
one
of
these
courses
aforesayde
,
&
taking
the
altitude
how
much
it
is
that
iustly
shal
be
taken
away
from
the
altitude
,
according
to
the
place
where
the
starre
is
,
is
to
be
vnderstood
,
that
which
is
aboue
the
pole
:
for
the
which
it
is
to
bee
noted
,
that
besides
the
two
starres
which
we
call
guards
,
which
before
haue
been
spoken
of
,
there
are
other
three
starres
,
whiche
goe
well
neere
in
the
same
distance
,
that
the
guardes
goe
in
,
that
goe
rounde
about
the
North
starre
:
and
although
the
guardes
be
not
seene
,
yet
by
these
three
starres
,
or
by
any
of
them
,
the
altitude
of
the
pole
is
to
bee
knowne
,
as
well
as
by
the
guardes
,
which
is
to
be
knowne
in
this
manner
.
These
three
starres
which
before
are
spoken
of
,
are
called
the
third
,
the
sixt
,
and
the
nienth
,
and
although
they
haue
other
names
,
these
names
wee
name
them
by
,
because
it
maketh
for
our
purpose
,
and
the
reason
is
,
because
the
starre
,
which
we
call
Tercera
,
or
thirde
starre
,
goeth
three
houres
,
which
is
one
course
or
winde
before
the
foremost
guard
:
and
the
Sesta
or
sixe
,
two
courses
or
winds
which
are
sixe
houres
:
and
the
Nouena
or
nienth
,
three
courses
or
windes
which
are
nine
houres
.
And
to
know
these
starres
,
doe
you
note
that
the
third
starre
hath
neere
to
him
other
two
starres
,
and
all
three
doe
make
well
neere
one
triangle
,
in
this
manner
.
This
starre
whensoeuer
that
the
foremost
guard
is
in
the
head
,
then
is
she
in
the
Northeast
,
and
if
the
guard
be
in
the
West
,
then
is
she
in
the
Northwest
,
and
if
the
guarde
bee
the
South
,
then
is
she
in
the
Southwest
,
&
so
it
is
to
bee
vnderstood
of
the
other
courses
,
that
alwayes
he
goeth
one
winde
behinde
the
guarde
.
The
sixt
is
one
starre
alone
,
the
which
goeth
wel
neere
as
distant
of
the
North
starre
as
the
guards
.
This
starre
goeth
two
windes
behinde
the
guarde
,
so
that
if
the
guarde
be
in
the
head
,
she
is
in
the
East
,
and
if
the
guarde
be
in
the
West
,
shee
is
in
the
North
,
and
so
it
is
to
bee
vnderstood
in
the
other
courses
.
The
nienth
is
one
starre
alone
which
is
neerer
to
the
North
starre
,
then
the
guards
,
this
starre
goeth
three
windes
behinde
the
guarde
,
so
that
if
the
guard
be
in
the
West
,
shee
is
in
the
Northeast
,
and
so
contrary
.
And
these
three
starres
being
knowne
,
although
the
guardes
bee
not
seene
,
by
these
or
by
any
of
them
is
to
bee
knowen
,
in
what
course
the
guardes
are
in
reckoning
the
courses
in
the
manner
,
as
it
hath
beene
declared
:
the
whiche
rule
I
haue
had
experience
of
,
and
haue
found
it
certayne
.
The
nienth
Chapter
,
how
the
altitude
of
the
North
,
is
to
be
taken
,
although
the
Horizon
be
not
seene
.
IT
happeneth
manye
times
to
suche
as
sayle
,
that
they
cannot
take
the
altitude
of
the
North
,
because
they
cannot
see
the
Horizon
.
This
is
because
either
the
earth
doth
couer
it
,
or
some
cloude
or
vapour
which
riseth
of
the
water
,
or
it
maketh
so
much
darknesse
,
that
it
cannot
bee
discerned
,
or
for
some
other
cause
.
And
howe
to
know
the
Horizon
is
a
thing
so
necessary
,
that
lacking
it
the
altitude
of
the
North
cannot
any
manner
of
way
bee
taken
with
the
Ballestilla
of
this
cause
the
saylers
receiue
very
great
hurte
,
for
that
manye
times
it
happeneth
to
them
,
to
passe
many
dayes
without
taking
the
altitude
and
most
of
all
in
the
winter
.
Therefore
to
take
away
this
hurte
&
inconuenience
,
I
will
declare
in
this
present
Chapter
,
in
what
manner
the
sayde
altitude
may
bee
taken
although
the
Horizon
be
not
seene
,
the
which
is
this
.
The
pilot
or
other
person
,
that
shoulde
take
this
altitude
,
let
him
take
a
staffe
or
rodde
of
the
greathes
of
a
finger
little
more
or
lesse
,
and
so
high
,
that
beeyng
put
vpright
in
the
grounde
,
it
come
iustly
to
his
sight
,
and
beeyng
made
of
this
greatnesse
,
no
more
nor
lese
:
let
him
make
at
the
toppe
of
it
a
Crosse
,
and
when
hee
will
take
the
altitude
,
let
him
ioyne
his
feete
together
,
and
laye
downe
the
rodde
straight
and
equall
from
the
poynt
of
his
feete
,
as
farre
as
the
rodde
will
reache
,
and
let
him
make
two
poyntes
,
the
one
where
he
hath
his
feete
,
and
the
other
as
farre
as
the
rodde
doth
reache
,
and
in
that
poynt
where
the
rodde
doth
reach
,
there
doe
you
take
him
vp
,
and
let
some
bodye
holde
him
vpright
,
and
the
Ballestilla
beeyng
taken
his
feete
beeyng
put
in
the
poynt
that
he
first
had
them
put
,
let
him
take
his
altitude
,
making
the
Horizon
in
the
highest
parte
of
the
rodde
or
staffe
where
hee
marked
the
Crosse.
And
yee
shall
vnderstand
that
this
is
his
Horizon
,
wheresoeuer
hee
findeth
himselfe
.
And
it
is
to
be
noted
,
that
if
the
night
were
as
darke
,
that
the
highest
parte
of
the
rodde
cannot
bee
seene
.
That
which
I
haue
saide
is
his
Horizon
,
then
put
vpon
the
toppe
of
the
rodde
,
a
signe
or
shew
of
fire
,
by
the
sight
of
the
which
hee
may
hit
to
put
his
Ballestilla
right
with
the
sayd
rod
,
and
so
he
shall
take
his
altitude
precisely
doing
in
the
rest
,
to
take
away
or
put
to
the
degrees
,
according
to
the
place
wherein
the
guardes
are
,
as
before
hath
beene
declared
.
The
tenth
chapter
,
of
a
clocke
by
the
north
starre
whereby
may
bee
knowne
what
houre
of
the
night
it
is
,
in
any
manner
of
time
and
place
that
a
man
is
in
.
IN
the
third
Chapter
of
this
fifth
booke
,
I
sayd
,
that
the
foremost
guard
is
called
horologial
,
because
he
goeth
alwaies
round
about
the
North
starre
,
like
to
the
wheele
of
a
clocke
geuing
knowledge
what
houre
of
the
night
it
is
.
And
because
this
knowledge
bringeth
much
profite
,
and
it
is
conuenient
that
euery
one
should
know
it
,
therfore
in
this
present
Chapter
,
I
will
speake
howe
it
should
be
knowne
in
any
manner
of
place
,
whersoeuer
a
man
is
,
&
in
any
time
of
the
yeere
,
what
houre
of
the
night
it
is
,
and
for
to
know
it
,
is
to
bee
noted
that
which
followeth
.
First
of
all
,
looke
vpon
the
North
starre
and
imagine
vpon
him
a
Crosse
in
this
manner
.
Of
this
crosse
the
vppermost
part
,
we
cal
head
,
and
the
lower
most
part
foote
,
and
the
other
two
the
right
arme
,
and
the
left
,
in
this
manner
.
This
being
had
,
is
to
be
vnderstood
,
that
betweene
these
foure
courses
or
strekes
,
wee
put
other
foure
which
doe
deuide
or
parte
these
in
the
middest
which
wee
call
lines
,
in
this
manner
.
So
that
there
is
a
line
betweene
the
right
arme
and
the
head
,
and
a
line
betweene
the
head
and
the
left
arme
,
and
a
line
betweene
the
left
arme
and
the
foote
,
&
a
line
betweene
the
foote
and
the
right
arme
:
this
imagination
beeing
made
,
it
is
to
be
vnderstood
,
that
the
greater
starre
of
the
two
guardes
,
which
is
the
foremost
,
which
before
hath
been
named
the
starre
of
the
clocke
,
this
starre
in
twenty
foure
houres
doth
passe
these
eight
partes
,
tarrying
three
houres
from
the
one
to
the
other
.
So
that
it
at
xii
.
of
the
clocke
in
the
night
,
hee
bee
in
the
head
at
three
,
hee
shal
be
in
the
line
betweene
the
head
and
the
left
arme
,
and
at
sixe
in
the
sayd
arme
,
&
in
that
sorte
,
the
rest
is
to
be
reckoned
.
Of
this
doth
remayne
,
that
beeing
knowne
in
what
part
this
starre
should
be
when
it
is
midnight
,
foorthwith
wil
be
seene
,
that
if
he
be
there
it
is
mydnight
,
and
if
he
be
not
come
thither
it
is
not
,
&
if
he
be
past
,
it
is
more
then
mydnight
.
For
this
,
it
is
necessary
to
knowe
two
thinges
:
the
one
is
,
to
know
in
euerie
moneth
of
the
yeere
,
in
what
parte
the
guarde
starre
ought
to
bee
in
,
to
knowe
when
it
is
mydnight
:
&
the
other
,
howe
it
is
to
bee
knowne
,
what
houre
it
is
,
more
or
lesse
than
mydnight
.
Of
the
first
this
is
to
be
noted
,
that
the
account
or
reckoning
,
that
is
to
bee
vsed
in
this
,
is
,
that
at
the
middest
of
the
moneth
of
Aprill
,
when
it
is
mydnight
,
then
the
sayde
guarde
starre
will
be
in
the
head
,
with
the
North
starre
,
and
from
thence
forwarde
euery
fifteene
dayes
,
the
middle
of
the
night
,
is
one
houre
forwarde
:
for
in
euery
day
hee
goeth
forwarde
foure
poyntes
or
minutes
,
and
geuing
to
euery
houre
threescore
poyntes
,
so
that
it
commeth
to
passe
in
euery
fifteene
daies
one
houre
forwarde
.
But
in
this
I
say
that
I
haue
made
experience
sometimes
with
clockes
of
precise
houres
,
and
setting
them
punctually
,
at
the
poynt
that
the
Sunne
setteth
,
and
I
finde
that
vnto
the
twentie
daye
of
Aprill
,
the
guarde
and
the
starre
,
doe
come
precisely
at
mydnight
in
opposite
,
but
because
the
difference
is
little
:
I
doe
followe
the
order
of
the
figure
following
.
To
the
seconde
is
to
bee
noted
,
as
before
hath
beene
declared
,
that
in
euery
three
houres
the
starre
called
the
guarde
,
doth
passe
from
one
course
to
another
,
by
the
whiche
there
is
to
bee
deuided
with
the
imaginatiue
,
that
space
in
three
partes
,
and
euery
parte
of
space
will
be
one
houre
.
In
such
sort
,
that
the
place
of
the
guarde
starre
beeyng
knowen
where
hee
shoulde
bee
at
mydnight
,
is
to
bee
knowne
,
if
hee
be
there
,
or
if
hee
bee
one
houre
,
two
,
or
three
,
behinde
or
before
,
and
so
it
wil
be
knowen
what
houre
it
is
:
and
to
know
in
what
parte
the
guarde
is
in
at
midnight
,
euery
halfe
moneth
of
the
yeere
,
it
must
bee
seene
in
this
figure
of
following
.
The
eleuenth
Chapter
,
how
the
altitude
of
the
pole
,
antarticke
is
to
be
taken
.
SEeing
there
hath
beene
declared
the
altitude
of
the
pole
articke
,
or
North
with
his
demonstrations
,
it
is
conuenient
to
speake
of
the
altitude
of
the
pole
antarticke
,
how
he
should
be
knowne
,
because
the
saylers
or
any
other
person
finding
himselfe
towardes
the
South
parte
▪
they
may
know
how
to
take
him
,
and
to
gouerne
themselues
thereby
.
Of
〈◊〉
is
to
be
knowen
,
that
the
tokens
or
knowledge
,
that
we
haue
of
the
pole
antarticke
,
are
foure
starres
,
put
Crosse
wise
in
this
manner
.
These
starres
be
not
of
any
of
the
signes
of
the
Zodiacke
,
nor
of
the
other
thirtie
sixe
images
of
the
heauen
,
therfore
they
are
called
Cruzero
,
and
these
foure
starres
we
name
,
head
,
foote
,
&
armes
,
and
to
know
which
starre
is
the
head
,
and
which
are
those
of
the
other
parts
,
is
to
be
vnderstood
,
that
the
starre
of
the
foote
is
greater
then
any
of
the
others
,
&
by
this
,
the
other
are
knowne
.
Therefore
it
is
to
be
noted
,
that
when
these
foure
starres
are
a
crosse
,
the
head
being
right
with
the
foote
,
that
then
the
greater
starre
which
is
the
foote
,
is
more
neere
the
Horizon
,
and
then
he
is
distant
of
the
pole
antarticke
thirtie
degrees
aboue
the
sayde
pole
,
and
the
altitude
of
this
starre
is
taken
,
and
of
no
other
:
And
hee
is
to
be
taken
when
he
is
in
right
of
the
head
,
for
there
is
his
owne
place
.
Therefore
when
you
will
knowe
the
altitude
of
the
saide
pole
,
doe
you
stay
vntill
the
starre
of
the
foote
,
be
in
his
place
,
because
with
the
moouing
of
the
heauen
,
hee
mooueth
with
the
others
,
and
being
in
his
place
,
then
take
his
altitude
,
euen
as
you
take
that
of
the
North
,
and
looke
that
the
altitude
which
you
take
of
him
,
either
they
must
be
thirty
degrees
or
more
or
lesse
,
if
they
be
thirtie
●ust
,
you
are
in
the
Equinoctiall
:
If
they
be
more
then
thirtie
,
those
whiche
are
more
,
you
are
distant
of
the
line
towardes
the
part
of
the
South
,
&
if
they
be
lesse
then
thirtie
,
that
which
is
lesse
you
are
distant
of
the
line
towards
the
part
of
the
North.
An
Example
.
I
say
that
the
saide
starre
beeing
in
his
place
,
I
tooke
his
altitude
in
fortie
degrees
,
then
I
say
that
I
am
in
tenne
degrees
,
distant
of
the
line
towards
the
part
of
the
south
,
the
reason
is
,
because
this
saide
starre
hath
thirtie
degrees
of
declination
or
distance
of
the
pole
,
therfore
if
I
had
taken
him
in
the
saide
thirtie
degrees
,
then
should
I
haue
had
the
pole
in
the
Horizon
,
and
hauing
the
pole
in
the
Horizon
,
I
am
in
the
Equinoctiall
,
and
so
the
degrees
,
which
are
more
then
thirtie
,
in
the
which
I
tooke
the
altitude
those
am
I
distant
of
the
line
towardes
the
parte
of
the
South
:
for
thirtie
from
the
starre
to
the
pole
,
and
tenne
from
the
pole
to
the
Horizon
,
are
forty
,
in
so
many
tooke
I
the
altitude
,
so
that
these
tenne
degrees
,
is
the
pole
raised
aboue
my
horizon
,
so
that
by
howe
muche
,
I
shal
be
distant
of
the
line
,
so
muche
the
pole
shall
rise
vp
aboue
my
horizon
,
and
in
so
many
more
degrees
,
I
shal
take
the
altitude
of
the
saide
starre
and
the
thirtie
being
taken
out
,
whiche
the
starre
is
aboue
the
pole
,
those
which
are
more
,
I
am
distant
of
the
line
towardes
the
sayde
pole
,
and
so
many
shall
the
saide
pole
be
raised
aboue
my
horizon
,
and
if
I
should
take
the
altitude
in
twentie
,
I
am
distant
of
the
line
tenne
degrees
towards
the
part
of
the
North
,
and
if
I
shoulde
take
him
in
tenne
,
I
am
distant
twenty
,
and
if
I
should
take
him
in
fiue
,
I
am
distant
twentie
fiue
,
&
if
I
had
the
saide
starre
in
the
horizon
,
I
am
distant
thirtie
degrees
of
the
said
line
,
towards
the
part
of
the
North
,
so
that
when
I
shall
take
him
in
thirtie
degrees
,
I
am
in
the
Equinoctiall
,
and
when
in
lesse
,
towards
the
part
of
the
North
,
and
when
in
more
,
towards
the
part
of
the
South
.
The
ende
of
the
fifth
booke
.
❧
The
sixt
booke
,
of
the
Compasses
to
sayle
by
.
The
first
Chapter
,
of
the
Compasses
to
sayle
by
,
and
of
the
defectes
which
they
may
haue
,
and
how
they
may
be
amended
.
The
first
is
,
by
the
stiles
not
beeing
well
touched
with
the
Lodestone
,
that
he
lacketh
the
vertue
.
And
this
ceasing
whiche
is
the
cause
,
the
effect
ceasseth
,
which
is
to
shew
the
North.
The
seconde
,
because
the
capitall
is
wrested
,
and
not
vpright
,
that
he
doth
not
suffer
the
rose
to
goe
right
in
his
steppe
.
The
thirde
,
because
the
steppe
is
brode
,
so
that
the
rose
cannot
moue
with
quickenesse
.
The
fourth
,
because
the
rose
lieth
downe
,
and
hangeth
more
to
one
side
then
to
another
.
The
fifth
,
because
the
chest
of
the
rose
is
open
,
in
such
sort
that
the
aire
entreth
into
it
.
The
sixt
,
if
the
sphere
or
the
hinges
,
whe●eby
the
said
boxe
or
chest
is
sustained
,
are
not
so
light
that
the
chest
and
the
rose
may
goe
equall
.
To
the
first
,
the
pilot
ought
to
carrie
in
his
chest
a
Lodestone
,
&
that
he
haue
experience
that
it
be
good
,
and
with
the
face
thereof
to
rubbbe
or
touch
the
points
of
the
compasse
subtlely
vntil
there
cleaue
to
it
,
a
little
of
the
saide
stone
,
&
see
that
it
be
with
the
face
of
the
said
stone
,
the
which
hee
ought
to
haue
marked
,
to
which
parte
it
is
,
for
if
it
bee
with
another
part
it
maketh
not
the
true
effect
.
To
the
second
,
which
is
the
capital
to
be
layde
downe
,
for
to
know
when
it
is
so
,
take
a
compasse
&
put
the
one
point
in
the
head
of
the
capitall
,
and
the
other
in
one
of
the
circles
of
the
rose
,
&
therby
you
shal
know
to
which
part
he
is
wrested
,
&
how
much
it
is
needful
to
dresse
him
,
&
it
is
to
be
vnderstood
,
that
if
the
capital
be
not
very
vpright
,
the
rose
wil
put
him
cleane
out
of
his
place
,
although
he
be
very
well
touched
.
To
the
third
,
if
the
steppe
bee
broade
or
flat
,
he
ought
to
be
finely
filed
,
so
that
it
be
seene
,
that
the
rose
run
not
hastie
nor
to
slowly
,
and
if
by
●yling
of
him
,
it
bee
seene
that
the
rose
doth
run
ouer
much
,
touch
him
subtilly
with
some
yron
in
the
poynt
,
that
he
may
be
somewhat
brode
,
so
that
the
rose
may
run
ordinately
.
To
the
fourth
,
if
the
rose
goe
somewhat
laide
downe
,
&
doe
not
goe
very
equall
,
you
may
put
to
him
some
waxe
,
or
pitche
▪
or
a
thing
that
may
cleaue
fast
to
him
in
the
vnder
part
,
vntill
that
hee
goe
vpright
,
without
leaning
to
one
part
more
then
to
the
other
.
To
the
fifth
,
he
ought
to
look
that
the
boxe
or
chest
where
the
rose
goeth
be
so
neere
,
that
there
goe
not
in
any
ayre
as
well
by
the
parte
of
the
glasse
,
as
by
the
parte
whiche
is
shutte
,
and
if
it
bee
open
in
anye
parte
,
with
the
sayd
waxe
or
pitch
,
it
ought
to
be
shutte
.
To
the
sixt
,
I
saye
that
hee
ought
so
looke
to
the
Sphera
or
hinges
,
wherein
the
said
chest
or
boxe
goeth
put
,
vpon
the
which
it
is
sustayned
or
helde
vp
that
it
bee
so
good
and
light
that
the
sayde
boxe
or
chest
goe
alwayes
equall
,
in
suche
sorte
,
that
although
the
shippe
doe
hilde
or
doe
lye
downe
to
one
side
or
to
the
other
,
the
sayde
boxe
and
rose
bee
alwayes
right
,
for
if
the
yrons
,
wherein
they
mooue
,
be
hurt
they
cause
that
when
the
shippe
doth
hilde
to
one
side
or
other
,
the
boxe
and
the
rose
cannot
iudge
the
North
in
his
proper
place
.
So
that
it
is
conuenient
that
the
sayde
Compasse
or
needle
bee
precisely
made
without
hauing
defecte
or
lacke
,
or
if
there
bee
any
inconuenience
,
although
it
bee
verie
little
,
it
causeth
muche
errour
.
The
seconde
Chapter
,
how
the
windes
of
the
Compasse
ought
to
bee
vnderstood
,
and
how
the
sunne
passeth
euery
day
by
them
.
IT
is
necessary
,
that
the
pilot
vnderstande
two
thinges
in
his
compasse
,
the
one
is
,
how
the
East
&
West
,
which
are
marked
in
the
Compasse
ought
to
be
vnderstood
.
The
seconde
,
howe
that
in
euery
foure
and
twentie
houres
,
the
Sunne
doth
passe
all
the
courses
of
the
Compasse
.
To
the
first
is
to
bee
noted
,
that
this
name
East
and
West
is
taken
two
wayes
,
(
that
is
to
say
)
natural
and
respectiue
:
the
East
and
West
is
naturall
,
and
is
vnderstood
by
the
Equinoctiall
line
,
&
not
by
any
other
part
,
because
it
is
the
middest
betweene
the
two
extreame
partes
,
(
that
is
to
say
)
the
two
poles
,
as
his
definition
declareth
.
The
respectiue
is
by
any
other
manner
of
parte
where
a
man
is
,
now
neare
the
line
,
now
farre
off
,
so
that
if
a
man
be
fiue
degrees
from
the
line
,
or
tenne
,
or
more
or
lesse
,
all
that
he
is
in
the
same
degrees
,
hee
shall
be
towardes
the
east
and
respectiue
towardes
the
west
,
in
such
sorte
,
that
all
that
hee
is
from
the
place
,
where
the
Sunne
riseth
to
the
Meridian
where
the
man
is
,
hee
shal
be
towardes
the
east
,
and
that
which
hee
is
from
the
man
vnto
the
place
where
the
sunne
setteth
,
hee
shal
be
towardes
the
west
,
and
this
likewise
,
is
to
be
vnderstoode
being
in
the
equinoctial
,
as
also
foorth
of
the
equinoctiall
.
An
example
.
Of
this
may
be
asked
,
if
the
citie
Seuill
be
towardes
the
east
or
west
,
that
is
,
towardes
Leuante
or
Poniente
,
it
is
answered
,
that
it
is
not
in
the
east
&
west
naturall
,
and
as
much
as
toucheth
the
respectiue
,
it
is
towardes
the
east
,
and
it
is
towardes
the
west
,
I
will
say
,
that
likewise
it
is
towardes
the
Leuante
,
&
it
is
towards
the
Poniente
,
in
this
manner
.
Of
that
which
it
is
most
occidental
is
towardes
Leuante
,
and
of
that
which
is
most
orientall
,
is
towardes
the
Poniente
,
so
that
if
Seuill
bee
in
thirtie
seuen
degrees
of
the
equinoctial
,
towards
the
part
of
the
north
,
all
that
it
is
in
the
right
course
of
the
thirtie
seuen
degrees
it
is
with
Seuill
east
and
west
,
in
such
sorte
that
all
that
it
is
from
the
Meridian
of
Seuill
vnto
the
parte
of
Poniente
,
Seuill
hath
towardes
the
Leuante
,
and
that
which
is
from
Seuill
towardes
the
parte
of
the
Leuante
,
Seuill
hath
it
towards
Poniente
.
We
haue
an
authour
of
this
,
who
is
Saint
Luke
in
the
first
chapter
,
where
he
sayth
,
that
the
three
kinges
came
from
the
orientall
partes
to
Hierusalem
,
it
is
to
bee
vnderstoode
,
that
as
Hierusalem
was
more
occidentall
,
then
from
whence
they
came
,
so
they
came
from
the
orient
,
to
occident
,
which
is
from
the
east
to
the
west
.
Therfore
I
say
to
our
purpose
it
is
not
to
be
vnderstoode
that
the
course
which
is
marked
in
the
compasse
,
is
the
east
&
west
,
respectiue
,
or
accidentall
,
but
the
natural
which
is
by
that
straight
course
which
the
Sunne
doth
describe
in
that
moouing
which
he
maketh
the
eleuenth
of
march
,
and
thirteenth
of
September
,
for
that
is
east
&
west
,
that
is
marked
in
the
compasse
,
(
that
is
to
say
)
by
the
equinoctiall
,
so
that
from
the
east
vnto
the
north
are
nientie
degrees
,
and
seuen
courses
,
besides
the
east
and
the
north
,
and
the
like
vnto
the
south
,
And
if
the
east
of
the
compasse
were
respectiue
the
nientie
degrees
,
nor
the
seuen
windes
or
courses
,
shoulde
not
bee
reckoned
the
which
woulde
bee
a
verye
great
errour
.
To
the
seconde
,
I
saye
that
how
muche
a
man
is
farthest
of
the
equinoctiall
,
so
much
the
dayes
will
bee
greater
to
him
when
the
Sunne
goeth
of
this
parte
where
he
is
,
and
by
reason
that
the
dayes
are
greater
to
him
,
the
rising
of
the
Sunne
maye
bee
different
to
him
,
in
this
manner
,
those
whiche
inhabite
vnder
the
equinoctiall
,
or
in
any
other
parte
,
when
the
Sunne
doth
describe
the
sayde
lyne
,
alwayes
hee
commeth
foorth
to
them
in
the
east
,
and
setteth
to
them
in
the
west
,
and
they
haue
twelue
houres
of
day
,
and
twelue
of
night
,
so
that
in
the
foure
and
twentie
houres
wherin
the
Sunne
maketh
his
daylie
woouing
hee
passeth
all
the
eyght
windes
or
principall
courses
of
the
nauigation
,
In
suche
sorte
,
that
from
three
to
three
houres
,
hee
goeth
from
one
winde
to
another
,
and
so
hee
riseth
and
commeth
foorth
to
vs
at
si●e
of
the
clocke
,
at
the
east
,
and
at
niene
at
the
southeast
,
and
at
twelue
at
the
south
,
and
at
three
at
the
southwest
,
and
at
sixe
at
the
west
,
and
there
he
setteth
.
So
that
in
xii
.
houres
he
goeth
foure
courses
,
but
out
of
the
equinoctial
,
how
much
the
day
is
greater
so
many
more
courses
the
sunne
goeth
in
the
day
,
and
lesse
in
the
night
,
so
that
if
the
day
be
of
fifteene
houres
,
the
sun
goeth
in
the
day
fiue
courses
and
by
night
three
:
and
if
the
day
be
of
eighteen
houres
the
sunne
goeth
in
the
day
sixe
courses
and
by
night
two
:
and
if
the
day
be
of
one
and
twentie
houres
,
the
sunne
goeth
in
the
day
seuen
courses
,
and
by
night
one
:
and
if
the
day
be
of
foure
and
twentie
houres
the
sunne
goeth
twenty
foure
houres
in
the
day
,
whiche
are
eyght
courses
,
and
that
day
there
is
no
night
:
as
it
happeneth
to
those
whiche
inhabite
in
the
circles
,
when
the
sunne
commeth
to
the
tropikes
.
And
that
which
is
vnderstood
of
the
dayes
when
they
goe
increasing
,
and
the
nightes
deminishing
,
the
same
is
to
bee
vnderstoode
by
the
courses
which
the
sunne
goeth
by
night
when
the
day
goeth
deminishing
,
and
the
night
increasing
:
as
shall
be
declared
in
the
sixt
chapter
of
the
eyght
booke
,
so
that
the
quantitie
of
houres
being
knowne
which
the
daye
hath
,
the
pilot
may
knowe
to
what
course
of
the
compasse
the
sunne
riseth
and
setteth
from
him
euery
daye
,
this
reckoning
will
serue
for
many
thinges
of
the
nauigation
.
The
thirde
chapter
,
wherein
is
declared
,
the
opinion
that
is
had
in
the
northeasting
,
and
northwesting
of
the
compasses
.
THere
is
an
opinion
among
such
as
sayle
that
the
compasses
doe
north
stear
,
and
northwestear
,
and
it
is
sayd
that
in
the
Meridian
of
the
Ilandes
of
the
Acores
,
that
there
the
Compasse
doth
shewe
the
pole
in
his
place
.
And
from
thence
passing
towards
the
west
,
it
doth
Northwestear
,
this
is
that
hee
sheweth
not
the
pole
in
the
place
where
hee
was
first
,
but
that
hee
goeth
aside
towardes
the
Northwest
.
And
if
they
come
from
the
saide
Meridian
,
towardes
the
East
,
that
the
Compasse
doth
Northeastear
,
that
is
,
to
make
the
sayde
difference
towardes
the
parte
of
the
Northeast
,
so
that
they
saye
,
that
onely
in
that
Meridian
the
Compasse
doth
shew
the
pole
,
and
not
in
any
other
place
:
but
to
one
part
or
other
:
and
howe
muche
more
they
departe
from
him
,
so
muche
the
Compasses
haue
more
the
sayde
defect
,
but
those
whiche
vnderstande
this
,
giue
no
cause
nor
any
reason
,
nor
howe
much
this
difference
is
,
which
the
Compasse
maketh
,
nor
howe
farre
it
goeth
,
so
that
they
knowe
not
what
to
saye
more
,
but
marking
their
Compasses
,
it
seemeth
that
whiche
is
sayde
to
bee
so
.
Hereupon
I
haue
procured
to
seeke
some
Authour
or
reason
,
or
some
thing
wherin
this
should
haue
a
foundation
,
and
I
say
that
of
this
variacion
which
is
spoken
of
the
compasse
.
I
finde
not
any
thing
written
,
nor
reason
,
nor
experience
,
that
is
certaine
:
therefore
here
I
will
speake
my
opinion
,
touching
this
,
perswading
my selfe
to
that
which
is
most
naturall
and
true
of
the
nauigation
.
Therefore
comming
to
the
cause
,
I
say
putting
an
example
,
if
I
make
two
compasses
of
one selfe
stile
,
and
of
one
temperance
,
and
touched
with
one selfe
stone
,
and
two
shippes
goe
sayling
with
them
,
departing
from
the
sayde
Meridian
one
towardes
the
east
,
and
the
other
towardes
the
west
,
that
these
compasses
shall
make
,
different
effectes
in
such
sort
,
that
in
the
one
,
the
stone
and
the
stile
,
shoulde
haue
vertue
to
cause
northeasting
,
and
in
the
other
to
cause
northwesting
which
are
contrary
effectes
,
it
seemeth
not
to
mee
,
that
there
is
any
foundation
,
or
reason
to
haue
the
like
.
But
let
vs
see
if
this
bee
in
any
thinge
of
the
nauigation
,
lette
vs
seeke
it
in
three
partes
,
which
is
in
the
pole
or
the
compasse
,
or
in
the
waye
where
sayling
now
is
vsed
.
To
the
first
,
to
saye
that
the
pole
doth
make
any
variation
or
distaunce
from
his
place
or
poynte
,
this
ought
not
to
bee
thought
,
because
it
should
bee
to
put
out
of
order
all
the
order
of
the
Sphera
,
in
such
sort
that
all
the
●ixed
circles
;
should
be
moueable
▪
besides
this
,
if
the
pole
should
moue
with
him
that
saileth
towards
the
east
,
it
would
moue
it selfe
in
the
same
tune
with
him
whiche
saileth
towardes
the
west
.
This
is
vnpossible
how
much
more
,
that
the
pole
cannot
mooue
to
one
parte
or
to
another
because
it
is
a
point
immagined
alwaies
fixed
in
one
place
.
To
the
seconde
,
I
say
that
it
ought
not
to
be
thought
or
vnderstoode
,
that
the
compasse
by
himselfe
maketh
the
sayde
difference
,
for
it
is
certaine
,
that
the
sayde
naturall
vertue
or
propertie
which
the
stone
and
steele
haue
in
the
place
where
the
compasse
was
made
,
the
selfe
same
they
haue
in
the
sayde
Meridian
,
and
in
the
new
Spaine
,
and
in
Calicut
,
and
in
all
partes
.
And
there
is
no
reason
to
say
,
that
this
propertie
is
of
such
qualitie
,
that
in
the
saide
Meridian
it
hath
one
vertue
,
and
in
all
others
,
which
are
well
neere
infinite
,
it
hath
it
in
euery
one
,
different
,
for
if
it
were
so
,
it
woulde
bee
to
geue
a
greate
inconuenience
,
the
which
is
that
〈◊〉
no
parte
foorth
of
the
sayde
Meridian
,
there
coulde
bee
made
a
true
compasse
,
seeyng
that
in
no
parte
the
compasse
doth
shew
the
pole
but
there
,
and
to
say
so
it
were
a
very
greate
errour
,
because
an
instrument
,
so
important
to
the
nauigation
,
should
not
bee
sayde
,
that
in
no
parte
it
coulde
be
made
certayne
,
for
if
it
were
so
,
it
were
to
geue
to
the
nauigation
an
instrument
with
a
knowne
errour
.
To
the
thirde
,
that
is
by
the
way
where
you
sayle
,
this
is
knowne
,
that
in
any
manner
of
place
where
a
man
is
,
there
hee
hath
his
Meridian
,
the
whiche
goeth
precisely
to
remayne
at
the
poynt
,
whiche
is
the
pole
,
without
making
any
distaunt
or
difference
in
any
thing
.
And
if
it
shoulde
bee
sayde
,
that
by
reason
of
the
waye
which
the
Shippe
sayleth
,
the
compasse
maketh
the
saide
difference
as
well
towardes
the
one
parte
,
as
to
the
other
,
this
woulde
be
to
make
manye
Meridians
different
,
the
one
from
the
other
,
and
so
they
shoulde
goe
to
remayne
at
different
poles
in
such
sort
that
how
many
differences
the
compasse
went
making
,
by
reason
of
the
way
:
so
many
different
Meridians
,
the
waye
shoulde
haue
:
and
too
euerye
Meridian
of
necessitie
,
there
shoulde
a
pole
〈◊〉
geuen
,
where
hee
shoulde
make
an
ende
,
for
otherwise
it
woulde
bee
an
infinite
processe
,
so
that
there
shoulde
bee
geuen
an
infinite
number
of
poles
.
And
to
thinke
this
shoulde
bee
a
verye
greate
errour
▪
so
that
it
appeareth
well
,
that
neither
by
the
parte
of
the
pole
,
neither
of
the
compasse
,
nor
of
the
waye
where
you
sayle
,
the
sayde
compasse
doe
make
anye
variation
or
difference
from
his
proper
place
,
but
making
more
inquirie
of
this
variation
,
which
of
the
compasse
is
spoken
:
I
say
that
commonly
is
vnderstood
that
the
compasse
doth
shewe
the
pole
,
but
of
this
there
is
no
writing
which
doth
say
so
:
that
which
I
finde
written
of
the
Lodestone
,
and
of
yron
is
,
that
Plinie
in
his
thirtie
sixe
booke
of
the
naturall
historie
saith
,
and
also
Saint
Isidore
in
the
sixteenth
of
the
Etimologi●s
,
that
the
Lodestone
by
one
hidden
vertue
or
propertie
,
that
it
hath
doth
specifie
that
it
draweth
to
it
yron
of
this
Auicen
speaketh
in
the
Booke
of
Viribus
Cordis
,
the
tenth
Chapter
,
hee
asketh
what
the
cause
is
,
wherefore
the
Lodestone
doth
draw
vnto
it
yron
,
to
the
whiche
hee
aunsweareth
,
that
there
is
no
other
thing
can
bee
sayde
,
but
because
it
hath
a
naturall
vertue
to
drawe
it
to
him
,
and
hee
saieth
that
some
vnderstoode
that
hee
draweth
it
to
him
by
reason
of
heate
or
coldnesse
,
or
because
of
similitude
,
that
both
of
them
haue
in
nature
,
or
for
other
reasons
,
all
the
whiche
hee
saith
is
false
,
for
that
hee
draweth
it
not
,
but
onely
with
his
propertie
,
and
declaring
what
thing
propertie
is
,
he
sayth
,
propertie
is
found
in
nature
in
the
compounded
bodies
,
proceeding
in
them
,
a
most
high
and
full
influence
,
so
that
wee
see
the
loade
stone
doth
drawe
to
him
the
yron
:
likewise
we
see
that
the
yron
being
rubbed
with
the
sayde
stone
,
I
say
in
one
onely
parte
of
it
the
vertue
renia●●●th
with
the
yron
to
shewe
alwayes
one
point
,
which
is
answerable
to
the
place
where
we
doe
shewe
in
the
horizon
the
winde
at
north
:
so
that
●eeing
the
pole
is
imagined
in
the
heauen
,
and
is
not
seene
,
&
the
compasse
doth
shewe
him
in
the
horizon
without
any
rising
,
one
only
degree
aboue
the
horizon
:
it
is
cleare
that
neither
the
compasse
doth
shewe
the
pole
nor
by
the
said
compasse
the
pole
can
be
seene
when
it
is
equall
with
him
,
nor
when
it
is
at
one
parte
nor
at
another
,
euen
as
I
shoulde
not
know
,
when
I
am
right
with
that
which
I
see
not
,
nor
when
to
one
part
nor
to
another
.
This
being
vnderstood
,
I
mind
to
declare
here
whervpon
they
ground
them selues
,
which
are
of
opinion
that
the
compasse
hath
a
Northeasting
&
a
Northwesting
,
and
the
manner
whereby
they
say
,
that
they
know
it
,
which
is
this
.
The
pilots
which
doe
ma●●e
their
compasses
doe
behold
the
North
starre
to
marke
them
by
her
,
but
because
this
starre
doth
alwayes
mooue
,
as
before
it
hath
beene
declared
,
therfore
they
tarrie
vntill
the
guardes
be
in
the
Northeast
,
or
in
the
Southeast
,
for
then
they
thinke
,
that
the
saide
starre
is
in
opposite
of
the
pole
,
vnder
or
aboue
him
,
and
then
they
imagine
a
streke
which
descendeth
from
the
saide
starre
vnto
the
Horizon
,
&
they
imagine
another
streke
which
goeth
from
the
poynt
of
the
flower
of
the
compasse
,
vnto
that
poynt
of
the
Horizon
,
so
that
in
these
two
strekes
,
which
they
put
in
that
poynt
,
they
looke
if
that
poynt
be
straight
vnder
the
North
starre
,
and
so
they
speake
what
their
opinion
is
without
hauing
in
this
anye
other
account
or
reason
.
To
this
is
to
be
noted
two
thinges
.
The
first
that
the
guardes
being
in
any
of
these
sayde
courses
are
not
in
opposite
of
the
North
starre
,
and
the
pole
rather
is
a
poynt
different
,
for
because
to
stand
in
opposite
,
the
guards
ought
to
be
in
the
Northeast
,
and
by
North
,
or
in
the
Southwest
and
by
South
.
The
seconde
,
that
this
making
iust
of
the
compasse
is
alwayes
done
by
night
,
because
by
day
there
is
no
starre
seene
.
And
from
the
starre
vnto
the
Horizon
the
distance
is
very
great
,
by
which
the
true
poynt
that
is
corespondent
to
the
sayde
starre
,
cannot
be
knowen
in
the
Horizon
:
But
that
at
one
time
is
●●dged
one
,
and
at
another
time
another
.
Likewise
for
the
greate
distance
,
that
is
from
the
sayde
compasse
vnto
the
poynt
which
is
imagined
in
the
horizon
:
And
as
that
poynt
is
imagined
,
and
inuisible
,
alwayes
the
sight
goeth
wauering
without
establishing
it selfe
,
whiche
hath
happened
sometimes
to
me
,
making
experience
in
this
.
And
therefore
I
saie
,
that
according
to
the
perspectiue
rule
,
the
precise
poynt
of
the
Horizon
cannot
be
taken
with
the
only
sight
which
is
imagined
vnder
the
said
starre
,
nor
it
can
make
iustly
equall
,
the
poynt
of
the
flower
of
the
compasse
,
by
reason
there
is
no
certayne
poynt
,
and
the
distance
very
great
,
which
is
to
that
as
is
imagined
.
For
the
sight
fayleth
when
the
obiect
is
very
distant
.
Wherby
I
conclude
,
that
it
cannot
bee
precisely
knowen
in
the
compasse
,
by
the
manner
as
it
is
said
,
if
he
make
the
said
distance
of
the
pole
,
nor
howe
muche
it
is
,
nor
I
by
this
waye
coulde
euer
attayne
to
it
.
The
fourth
Chapter
,
of
the
inconueniences
,
which
may
followe
by
the
Northeasting
,
and
Norwesting
of
the
Compasses
.
AMong
other
inconueniences
,
that
will
follow
in
the
nauigation
,
if
the
Compasses
should
make
the
sayde
variation
or
difference
,
I
finde
foure
verye
principals
,
which
are
these
following
.
The
first
if
it
be
true
,
that
the
compasses
haue
a
Northeasting
,
&
a
Norwesting
,
likewise
it
may
bee
sayde
,
that
they
haue
a
southeasting
and
southwesting
,
and
the
reason
is
this
,
it
is
certain
that
the
variation
or
difference
which
the
compasse
doth
make
to
the
parte
of
the
north
,
the
same
ought
to
bee
made
,
towardes
the
parte
of
the
south
,
I
will
say
that
how
much
the
north
pointe
of
the
compasse
departeth
from
his
owne
pointe
,
so
much
the
south
pointe
of
the
sayde
compasse
goeth
distant
to
the
other
parte
,
and
so
the
north
poynt
of
the
compasse
doth
northeast
a
quarter
or
more
,
and
the
south
pointe
doth
southwest
the
like
,
for
the
north
point
cannot
goe
aside
,
but
the
south
pointe
doth
the
like
.
And
so
when
you
shall
sayle
towardes
the
parte
of
the
south
,
seeing
that
there
the
north
star
is
not
seen
to
marke
by
her
,
either
it
must
be
sayde
,
that
of
that
part
the
compasse
doth
not
make
variation
,
or
if
it
doe
,
that
in
the
south
,
it
is
to
be
known
:
and
so
when
you
shall
sayle
to
the
riuer
of
plate
,
otherwise
called
Rio
de
Plata
,
or
to
the
straight
of
Magalanes
,
or
by
the
south
sea
,
or
to
the
cape
of
Buena
Esperanca
which
is
in
englishe
,
good
hope
,
and
from
thence
to
Calicut
or
the
Maluco
,
then
wil
be
said
,
that
the
south
point
of
the
compasse
doth
southeast
or
southwest
,
and
to
say
so
shoulde
be
a
great
errour
.
The
second
if
the
north
point
of
the
compasse
doe
make
the
sayde
distance
of
his
proper
place
and
point
,
it
is
certaine
that
the
selfe
same
difference
and
distance
all
the
other
windes
of
the
nauigation
shoulde
make
from
their
proper
places
,
because
howe
muche
any
winde
doth
departe
from
his
proper
place
,
the
selfe
same
all
the
others
shoulde
doe
by
the
agreeable
order
,
and
equall
distance
,
that
they
haue
in
the
compasse
,
the
one
with
the
other
,
and
so
none
woulde
answere
to
the
certaine
pointe
,
that
is
shewed
in
the
Horizon
,
so
that
likewise
,
there
woulde
mooue
from
theire
place
,
the
east
,
and
the
west
,
and
all
the
other
windes
,
this
woulde
bee
a
great
inconuenience
,
for
the
compasses
,
woulde
neuer
agree
with
the
cardes
,
this
is
because
alwayes
the
windes
of
the
cardes
are
fixed
in
one
pointe
,
without
moouing
from
thence
,
therefore
if
the
windes
of
the
compasse
doe
make
many
differences
,
it
is
certaine
,
that
they
cannot
be
agreeable
,
and
not
agreeing
:
The
place
whiche
you
goe
to
seeke
cannot
in
any
manner
of
wise
,
bee
precisely
hitte
,
but
with
greate
compasse
,
this
will
cause
it
by
reason
the
carde
sayth
one
thing
and
the
compasse
another
,
and
so
there
cannot
bee
had
a
certaine
accounte
,
in
the
degrees
and
leagues
whiche
are
sayled
,
rather
all
the
accountes
or
reckoninges
of
the
leagues
whiche
is
geuen
for
a
degree
in
euery
course
,
shoulde
bee
false
seeing
the
pilot
doth
not
sayle
by
the
course
,
whiche
he
thinketh
he
doth
,
and
so
the
reckoning
whiche
is
made
by
such
a
course
,
should
not
be
certaine
,
and
if
hee
woulde
geue
allowaunce
it
woulde
bee
nothing
woorth
,
for
hee
knoweth
not
of
what
parte
nor
howe
much
,
and
so
it
woulde
bee
to
adde
one
errour
to
another
.
The
thirde
,
if
the
variation
or
difference
whiche
is
spoken
of
the
compasse
,
were
certaine
it
woulde
followe
,
that
the
compasses
which
were
verie
distant
of
the
sayde
Meridian
at
the
east
or
at
the
west
,
they
shoulde
haue
great
difference
,
if
it
be
true
,
that
howe
much
more
they
are
distant
,
so
muche
more
they
haue
the
sayde
defect
,
and
so
all
the
earth
,
that
shoulde
be
discouered
,
with
these
compasses
,
and
should
bee
sette
downe
in
the
carde
,
shoulde
not
be
in
his
true
pointe
,
the
reason
is
,
because
the
principall
windes
of
the
carde
(
that
is
to
saye
)
the
north
and
the
south
,
the
east
and
the
west
,
are
marked
in
foure
fixed
pointes
equally
distant
,
which
are
the
two
poles
and
the
equinoctiall
line
:
and
according
to
these
all
the
other
windes
of
the
carde
are
marked
and
parted
,
for
if
there
were
put
into
the
cardes
any
other
thing
it
woulde
bee
to
make
an
errour
at
the
beginning
,
whiche
is
not
conuenient
in
a
thing
so
certaine
,
as
the
nauigation
is
,
so
that
all
these
windes
are
alwaies
stedfast
and
fixed
,
in
their
owne
poyntes
,
without
making
variation
or
any
difference
,
so
that
all
which
is
placed
with
the
compasse
by
reason
of
his
difference
,
will
not
be
aunswearable
with
the
certayne
point
;
according
to
the
windes
which
are
in
the
carde
.
The
fourth
,
if
the
variation
of
the
Compasse
bee
true
,
immediatly
would
follow
greate
difference
betweene
the
course
and
the
altitude
,
because
if
I
,
by
my
way
or
course
doe
seeke
a
lande
,
whiche
I
knowe
is
in
thirtie
degrees
,
or
more
or
l●sse
,
and
I
sayle
by
one
point
the
whiche
I
haue
chosen
agreeable
to
the
Altitude
.
It
is
certayne
,
that
by
reason
of
the
variation
of
the
sayde
Compasse
.
I
shall
not
goe
by
this
course
to
that
Lande
whiche
I
goe
to
seeke
,
but
rather
when
I
haue
gone
,
the
sayde
way
,
I
shall
finde
my selfe
foorth
of
that
place
,
whether
I
goe
very
different
,
of
the
whiche
,
the
errour
of
the
Compasse
was
cause
thereof
.
And
so
in
long
wayes
will
alwayes
happen
great
hurtes
&
inconueniences
.
Therefore
I
say
,
seeing
that
the
said
opinion
hath
no
more
reason
nor
foundation
,
then
that
which
is
before
saide
,
that
such
as
doe
followe
it
,
let
them
looke
to
the
hurtes
and
daungers
whiche
may
followe
them
.
The
fifth
Chapter
,
of
the
allowance
,
which
the
Compasses
haue
,
and
howe
it
ought
not
to
be
geuen
them
.
SOme
which
make
compasses
haue
a
custome
,
that
at
such
time
as
they
doe
set
the
stiles
in
the
rose
of
the
windes
,
they
doe
not
precisely
put
the
flower
of
the
rose
vpon
the
pointes
of
the
stiles
,
whiche
are
touched
with
the
Lodestone
,
but
they
put
them
aside
of
the
flower
halfe
a
poynt
for
the
Northeast
,
and
this
they
say
they
doe
to
geue
allowance
to
that
whiche
the
Compasses
doe
Northeast
,
so
that
the
Compasse
doth
remayne
,
made
in
suche
manner
that
the
stiles
,
and
the
slower
are
not
vniforme
in
shewyng
the
North
point
,
because
the
flower
doth
shewe
him
to
one
part
,
and
the
stiles
doe
shewe
him
to
another
:
this
is
a
knowne
errour
,
and
it
ought
not
to
bee
done
in
no
manner
of
wise
,
for
the
reasons
following
.
The
first
,
if
it
be
true
,
that
the
Compasses
doe
northeast
and
northwest
:
it
is
also
said
that
they
doe
as
well
northeast
as
northwest
,
so
that
the
difference
which
is
giuen
to
the
one
part
,
the
selfe-same
is
giuen
to
the
other
,
and
if
it
bee
so
,
by
what
reason
shoulde
bee
giuen
to
it
the
allowance
,
alwayes
to
the
one
parte
,
and
not
to
the
other
,
therefore
it
is
certayne
,
that
it
to
the
nauigation
that
is
made
towardes
the
West
,
the
allowance
doth
profite
that
whiche
is
made
towards
the
East
,
it
would
hurt
,
seeing
they
are
different
the
one
with
the
other
,
so
that
what
it
doth
benefite
the
one
,
it
will
hurt
the
other
.
Likewise
,
with
the
selfe
same
compasses
,
which
they
goe
one
any
voyage
,
with
the
selfesame
they
returne
,
without
taking
away
,
or
putting
to
any
thing
in
them
,
thereby
it
is
cleere
,
that
the
saide
errour
is
to
bee
perceiued
,
seeing
that
the
allowance
cannot
serue
to
both
partes
.
The
seconde
,
if
it
bee
true
that
in
the
Meridian
of
the
Acores
the
Compasse
doth
not
make
anie
difference
from
the
pole
,
I
say
that
this
cannot
be
knowne
,
by
the
sayde
compasses
.
(
The
reason
is
)
because
the
vertue
of
the
Compasse
is
in
the
stiles
,
and
not
in
the
flower
,
and
the
pilot
looketh
not
vnto
the
stiles
,
but
to
the
flower
,
because
hee
cannot
see
the
stiles
,
and
the
flower
sheweth
one
,
and
the
stiles
another
,
whereby
as
hee
ruleth
himselfe
by
the
flower
he
cannot
knowe
the
truth
.
Likewise
what
reason
is
there
,
that
there
is
geuen
there
to
the
Compasse
,
as
much
allowance
,
as
in
other
partes
which
are
farre
of
.
Of
this
doth
follow
,
that
for
the
allowance
or
difference
put
in
the
said
compasse
cannot
be
knowne
,
when
the
pilot
is
in
the
saide
Meridian
.
Therefore
it
is
so
as
it
hath
beene
said
,
when
the
stiles
doe
shew
,
the
flower
doth
not
shew
.
And
so
the
said
Meridian
cannot
be
knowen
,
if
it
be
not
in
seeing
the
saide
Ilandes
,
by
reason
of
the
difference
that
is
betweene
the
stiles
&
the
flower
.
The
third
I
say
,
that
there
is
no
reason
,
wherfore
so
much
allowance
should
be
geuen
to
the
Compasse
in
the
sayling
of
a
hundreth
leagues
,
as
in
the
sailing
of
two
thousand
by
the
which
reasons
,
it
is
not
conuenient
,
that
to
any
compasse
the
saide
allowance
or
difference
be
geuen
betweene
the
flower
and
the
stiles
,
but
that
they
be
made
euen
very
precisely
,
so
that
they
may
bee
vniforme
in
their
shewing
.
The
sixt
Chapter
,
of
an
instrument
,
with
the
which
the
Compasses
may
bee
marked
,
and
knowne
if
they
bee
certayne
and
true
.
IT
hath
beene
saide
,
that
by
the
poynt
of
the
Horizon
,
which
is
corespondent
to
the
North
starre
the
compasses
cannot
be
marked
,
because
it
is
an
vncertayne
point
,
so
that
because
the
compasse
is
an
instrument
so
litle
&
so
subtil
,
it
is
necessary
to
bring
him
in
order
with
another
instrument
,
suche
a
one
as
the
sight
and
the
reason
may
rectifie
.
Therefore
when
the
pylot
wil
marke
his
compasse
,
and
know
if
he
be
true
or
not
,
let
him
make
the
instrument
following
:
with
the
which
I
haue
many
times
marked
compasses
,
and
haue
founde
it
certayne
,
set
downe
your
compasse
vpright
,
and
put
vpon
him
a
little
thinne
table
&
plaine
,
a
little
longer
than
the
compasse
,
and
narrower
than
the
rose
,
so
that
the
North
and
the
South
bee
seene
of
the
rose
:
And
in
this
table
make
a
circle
with
the
compasse
,
wel
neere
of
the
greatnesse
of
the
rose
,
&
make
in
the
saide
circle
a
streke
very
equall
&
straight
,
that
may
goe
from
the
North
to
the
South
of
the
rose
,
so
that
the
rose
standing
stil
,
the
streke
of
the
circle
of
the
table
,
bee
such
,
that
he
come
precisely
with
the
North
&
south
of
the
rose
,
this
being
done
,
put
in
the
poynt
with
the
compasse
made
in
the
middest
of
the
circle
of
the
table
,
a
little
small
maste
vpright
,
and
that
he
be
so
great
that
the
shadowe
whiche
he
maketh
goe
foorth
of
the
circle
,
&
being
put
so
,
then
set
your
compasse
in
the
sun
before
the
middest
of
the
day
,
&
there
make
equall
the
streke
of
the
circle
with
the
rose
,
as
before
is
declared
,
&
the
compasse
standing
quiet
&
the
table
fixed
aboue
,
doe
you
stay
vntill
the
shadowe
whiche
the
little
maste
doth
make
,
doe
come
shortning
vntill
he
come
to
the
said
circle
,
and
when
he
is
come
,
make
a
point
there
.
And
after
that
stay
vntil
the
said
shadowe
doe
turne
to
goe
foorth
of
the
circle
,
&
when
hee
commeth
to
it
,
make
there
another
poynt
,
this
being
done
,
take
your
compasse
,
and
part
iustly
that
which
is
from
one
point
to
the
other
.
And
to
this
point
of
the
partition
,
the
Meridian
of
that
place
is
corespondent
,
it
is
to
be
seene
if
the
streke
which
was
made
in
the
circle
of
the
North
&
South
,
of
the
compasse
doe
come
by
the
sayde
poynt
of
the
partition
,
then
the
compasse
is
good
,
and
if
not
,
there
it
is
to
bee
seene
,
to
which
parte
hee
maketh
difference
,
and
howe
much
it
is
.
The
ende
of
the
sixt
booke
.
¶
The
seuenth
booke
of
the
Moone
,
and
how
her
ebbings
and
flowinges
doe
serue
in
the
Nauigation
.
The
first
Chapter
,
what
thinge
the
moone
is
,
and
wherefore
her
light
is
not
equall
,
but
alwayes
increaseth
or
diminisheth
.
THE
Moone
is
one
of
the
seuen
Planettes
,
constituted
in
the
first
Heauen
more
neere
vnto
vs
then
anye
of
the
others
,
of
this
some
had
opinion
,
that
shee
had
light
of
her selfe
,
and
when
shee
was
in
one
signe
with
the
Sunne
,
by
meanes
of
the
greate
light
of
the
Sunne
,
shee
gaue
no
light
,
and
howe
muche
the
more
shee
went
from
the
Sunne
,
so
muche
her
light
began
to
appeare
,
and
the
neerer
shee
was
,
the
lesse
it
did
appeare
.
This
is
not
so
,
because
the
Moone
hath
no
cleerenesse
nor
brightnesse
of
her
owne
,
as
in
the
first
booke
the
seuenth
Chapter
,
hath
beene
declared
,
the
whiche
is
seene
by
experience
,
because
the
Moone
doth
suffer
Eclipses
,
when
shee
is
depriued
of
the
light
of
the
Sunne
,
as
there
is
a
lette
,
that
shee
cannot
receiue
it
,
she
remayneth
darke
.
This
light
is
let
by
meanes
of
the
Earth
,
as
the
Philosophers
and
Astronomers
doe
shewe
,
because
in
the
moouing
which
the
Sunne
and
the
Moone
make
,
as
they
come
into
the
point
,
that
the
earth
is
directly
betweene
the
Sunne
and
the
Moone
,
the
light
of
the
Sunne
geueth
in
the
earth
,
and
so
the
Moone
remayneth
in
her
owne
likenesse
,
whiche
is
darke
,
so
that
of
her selfe
,
shee
hath
no
light
nor
cleerenes
,
but
the
sunne
which
is
ouer
her
,
doth
light
her
,
although
not
euery
day
alike
towards
vs
,
because
as
the
Moone
is
a
body
darke
,
when
shee
is
right
vnder
the
sun
,
she
is
lightened
of
the
vppermost
part
,
&
remayneth
darke
towards
the
earth
,
&
therfore
in
her
coniunction
with
the
sunne
,
we
see
her
not
.
And
it
is
to
be
noted
,
that
in
the
coniunction
of
the
moone
,
she
&
the
Sun
rise
not
in
one selfe
place
,
but
they
rise
at
one selfe
time
,
&
so
by
meanes
of
the
light
of
the
sun
,
the
moone
doth
not
appeare
,
because
comming
foorth
at
one selfe
time
and
in
one
place
the
sunne
woulde
be
eclipsed
,
and
so
the
eclipse
of
the
sunne
happeneth
in
the
coniunction
of
the
moone
,
when
shee
is
in
the
heade
or
tayle
of
the
Dragon
.
And
as
by
her
moouing
,
shee
goeth
away
from
the
sunne
,
shee
beginneth
to
appeare
vnto
vs
,
and
appeareth
in
the
manner
of
a
thinne
horne
,
and
the
farther
she
goeth
from
the
sunne
,
the
more
she
shineth
to
vs
.
And
at
the
eyght
day
she
shineth
parted
in
the
middest
,
and
at
the
fifteenth
day
she
is
full
,
for
then
she
is
farthest
of
the
sunne
,
the
which
is
prooued
because
it
happeneth
,
when
the
sunne
doth
set
to
vs
in
the
west
,
shee
beginneth
to
come
foorth
in
the
east
,
and
then
all
the
brightnes
,
which
the
moone
receiueth
of
the
sunne
descendeth
towards
vs
,
and
after
she
beginneth
to
goe
neerer
to
the
Sunne
,
by
the
same
manner
that
shee
went
departing
,
and
when
the
light
goeth
vpwarde
the
shadow
descendeth
,
and
so
she
turneth
decreasing
,
in
the
like
sort
as
she
went
increasing
.
And
it
is
to
bee
noted
,
that
the
moone
doth
passe
the
circle
of
the
zodiack
,
in
tweentie
seuen
dayes
&
eight
houres
,
and
although
that
in
this
time
,
she
maketh
an
end
of
her
circle
,
there
is
geuen
to
euery
moone
twenty
niene
daies
&
a
halfe
.
The
reason
is
,
because
in
those
said
twentie
seuen
dayes
&
eight
houres
,
she
doth
not
ouertake
the
sunne
,
and
therefore
passeth
forward
other
two
dayes
,
and
foure
houres
,
a
little
thing
more
or
lesse
,
and
so
twentie
nine
dayes
decying
past
,
and
twelue
houres
,
and
a
few
minutes
,
in
some
more
,
and
in
others
lesse
,
the
coniunction
of
the
Moone
and
the
Sun
is
made
.
This
is
according
to
the
halfe
mouing
of
the
Moone
,
wherwith
is
made
equall
,
the
mouing
of
all
the
dayes
,
because
according
to
the
true
mouing
which
she
maketh
,
at
sometime
it
is
sayd
to
be
slow
,
and
at
other
times
swift
,
the
which
moouing
is
also
made
equall
by
the
middle
moouing
,
this
is
largely
declared
by
the
king
Don
Alonso
in
his
tables
.
The
seconde
Chapter
,
of
the
Golden
number
,
&
how
it
is
to
be
reckoned
from
one
to
nienteene
,
and
wherefore
no
more
nor
lesse
.
IT
is
a
necessary
thing
to
take
out
the
reckoning
of
the
Moone
by
the
Golden
number
,
for
that
the
Golden
number
is
a
thing
whereby
many
reckonings
are
made
,
and
therefore
it
is
called
the
number
of
Golde
,
wherof
I
minde
to
declare
in
this
Chapter
,
that
of
the
Golden
number
whiche
maketh
to
our
purpose
,
where
I
saye
that
this
reckoning
of
the
Golden
number
is
,
from
one
to
nieneteene
,
so
that
the
Golden
number
is
accomplished
in
the
time
of
nieneteene
yeeres
,
and
the
nineteene
yeeres
beeing
past
,
returneth
agayne
to
one
and
so
for
euer
.
The
reason
why
it
hath
this
number
,
&
no
more
nor
lesse
is
because
the
nineteene
yeeres
beyng
past
,
the
Moone
turneth
to
one
only
day
,
of
the
yeere
,
of
the
Sunne
,
and
in
this
time
shee
finisheth
and
endeth
all
those
diuersities
of
coniunctions
and
fulnesse
,
and
other
aspectes
,
which
shee
hath
with
the
Sunne
in
one
only
day
,
degree
,
and
minute
,
in
this
manner
following
.
I
put
the
case
that
the
Moone
made
coniunction
the
first
daye
to
Ianuarie
of
this
yeere
.
The
yeere
followyng
shee
will
not
make
the
same
coniunction
in
the
same
poynt
,
but
before
or
after
,
and
so
we
will
speake
the
like
of
the
fulnesse
,
and
other
aspectes
.
And
as
these
bee
not
in
an
infinite
number
,
it
is
certaine
that
they
are
comprehended
vnder
some
number
,
or
space
of
time
.
These
are
those
sayde
nieneteene
yeeres
,
in
the
which
are
to
be
noted
,
as
it
is
saide
,
all
the
diuersities
of
aspectes
,
aswell
of
coniunctions
,
and
fulnesse
,
as
of
any
other
cause
,
which
the
moone
maketh
with
the
Sunne
,
in
such
sorte
,
that
the
nieneteene
yeeres
beeyng
ended
.
The
Moone
doth
not
turne
to
make
a
new
coniunction
or
opposition
in
any
degree
or
poynt
of
the
Zodiacke
,
that
in
the
sayde
time
,
shee
hath
not
already
done
,
and
by
this
reason
this
reckoning
of
the
golden
number
is
ended
and
finished
in
the
time
of
nieneteene
yeeres
,
and
not
in
more
nor
lesse
.
❧
A
Rule
to
knowe
the
Golden
number
of
euerie
yeere
.
TO
knowe
euery
yeere
howe
many
are
of
the
Golden
number
,
looke
on
the
numbers
following
and
counting
in
the
first
house
,
the
yeere
of
our
Lorde
1545.
which
are
seuen
of
the
Golden
number
,
and
one
house
is
to
bee
reckoned
euerye
yeere
,
and
the
last
house
beeyng
ended
,
returne
to
the
first
and
so
for
euer
.
1545.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
1.
2.
3.
4.
5.
6.
WHen
you
will
knowe
in
any
yeere
that
you
are
in
,
howe
many
are
of
the
Golden
number
,
without
looking
on
the
booke
,
see
in
what
yeere
you
runne
,
and
leauing
out
the
thousand
fiue
hundreth
,
of
the
rest
take
out
the
nieneteenes
,
and
that
which
remayneth
,
so
much
is
of
the
Golden
number
that
yeere
,
and
if
the
number
of
the
yeeres
come
iust
in
nieneteenes
,
that
yeere
is
nieneteene
of
the
Golden
number
.
The
thirde
Chapter
,
wherein
is
declared
the
day
and
houre
,
wherein
the
Moone
maketh
coniunction
in
euerye
Moneth
of
the
yeere
for
euer
.
THere
hath
been
declared
in
the
Chapter
before
,
how
it
should
be
known
euery
yeere
howe
manye
are
of
the
golden
number
,
according
as
the
account
in
it
is
declared
,
and
because
it
is
necessary
for
the
nauigation
to
knowe
in
euery
moneth
the
day
and
houre
of
the
coniunction
,
therfore
in
this
Chapter
,
shal
bee
declared
,
how
a
man
may
know
euery
day
what
day
and
houre
the
coniunction
of
the
Moone
was
,
or
shal
be
.
And
for
this
are
to
be
noted
,
two
things
,
the
first
,
that
this
account
goeth
taken
out
by
the
Golden
number
,
and
by
him
you
must
rule
your selfe
,
euen
according
as
the
number
is
,
which
that
yeere
,
wherein
you
are
,
doe
runne
of
the
Golden
number
.
In
that
sayde
yeere
,
looke
the
Moneth
where
you
are
,
or
the
Moneth
that
you
woulde
knowe
,
and
in
him
you
shall
find
the
day
,
and
houre
that
the
Moone
was
or
shal
bee
in
coniunction
.
The
seconde
is
,
that
in
this
account
a
day
is
vnderstood
from
this
day
the
middest
of
the
day
,
vntill
to
morrowe
,
the
middest
of
the
day
,
so
that
if
wee
saye
,
this
day
is
the
fifteenth
day
of
the
Moneth
it
is
vnderstood
,
from
this
day
the
middest
of
the
day
,
vntill
to
morrowe
the
middest
of
the
day
,
and
from
the
middest
of
the
day
to
morrowe
,
doth
sixeteene
beginne
,
because
this
is
the
manner
,
that
the
Astronomers
doe
reckon
the
dayes
,
so
that
those
houres
which
are
ouer
and
aboue
,
the
dayes
are
from
the
halfe
day
forwarde
.
If
they
be
one
of
the
Golden
number
.
|
If
they
be
two
of
the
Golden
number
.
|
If
they
bee
three
of
the
Golden
number
.
|
Monethes
|
Daies
|
Houres
|
Monethes
|
Daies
|
Houres
|
Monethes
|
Daies
|
Houres
|
Ianuarie
.
|
19
|
16
|
Ianuarie
.
|
8
|
20
|
Ianuarie
.
|
27
|
14
|
Februarie
.
|
18
|
6
|
Februarie
.
|
7
|
13
|
Februarie
.
|
25
|
9
|
marche
.
|
19
|
7
|
marche
.
|
8
|
4
|
marche
.
|
27
|
1
|
Aprill
.
|
18
|
1
|
Aprill
.
|
6
|
16
|
Aprill
.
|
25
|
4
|
may
.
|
17
|
9
|
may
.
|
6
|
2
|
may
.
|
25
|
0
|
Iune
.
|
15
|
15
|
Iune
.
|
4
|
9
|
Iune
.
|
23
|
8
|
Iuly
.
|
14
|
23
|
Iuly
.
|
3
|
15
|
Iuly
.
|
22
|
16
|
August
.
|
13
|
8
|
August
.
|
1
|
7
|
August
.
|
21
|
0
|
September
.
|
11
|
21
|
September
.
|
29
|
19
|
September
.
|
19
|
8
|
October
.
|
11
|
12
|
October
.
|
29
|
9
|
October
.
|
18
|
19
|
Nouember
|
10
|
6
|
Nouember
.
|
28
|
1
|
Nouember
.
|
17
|
7
|
December
.
|
10
|
1
|
December
.
|
27
|
20
|
December
.
|
16
|
22
|
If
they
bee
foure
of
the
Golden
number
.
|
If
they
bee
sixe
of
the
Golden
number
.
|
If
they
be
eight
of
the
Golden
number
.
|
Monethes
|
Daies
|
Houres
|
monethes
|
Daies
|
Houres
|
monethes
|
Daies
|
Houres
|
Ianuarie
.
|
15
|
0
|
Ianuarie
.
|
23
|
20
|
Ianuarie
.
|
2
|
3
|
Februarie
|
14
|
19
|
Februarie
.
|
22
|
9
|
Februarie
.
|
31
|
22
|
Marche
.
|
16
|
3
|
marche
.
|
22
|
22
|
marche
.
|
31
|
22
|
Aprill
.
|
14
|
19
|
Aprill
.
|
21
|
8
|
Aprill
.
|
29
|
17
|
May
.
|
14
|
9
|
may
.
|
21
|
4
|
may
.
|
29
|
3
|
Iune
.
|
12
|
11
|
Iune
.
|
19
|
19
|
Iune
.
|
27
|
14
|
Iuly
.
|
12
|
7
|
Iuly
.
|
19
|
9
|
Iuly
.
|
27
|
3
|
August
.
|
10
|
16
|
August
.
|
18
|
0
|
August
.
|
25
|
29
|
September
.
|
9
|
1
|
September
.
|
16
|
13
|
September
.
|
24
|
12
|
October
.
|
8
|
10
|
October
.
|
16
|
2
|
October
.
|
23
|
6
|
Nouember
.
|
6
|
20
|
Nouember
.
|
14
|
14
|
Nouember
.
|
22
|
23
|
December
.
|
6
|
7
|
December
.
|
14
|
1
|
December
.
|
22
|
15
|
If
they
bee
fiue
of
the
Golden
number
.
|
If
they
bee
seuen
of
the
Golden
number
.
|
If
they
bee
niene
of
the
Golden
number
.
|
Monethes
|
Daies
|
Houres
|
Monethes
|
Daies
|
Houres
|
Monethes
|
Daies
|
Houres
|
Ianuarie
.
|
4
|
20
|
Ianuarie
.
|
12
|
11
|
Ianuarie
.
|
21
|
4
|
Februarie
.
|
3
|
11
|
Februarie
.
|
10
|
21
|
Februarie
.
|
19
|
15
|
Marche
.
|
5
|
3
|
March
|
12
|
8
|
Marche
.
|
21
|
0
|
Aprill
.
|
3
|
20
|
Aprill
.
|
10
|
19
|
Aprill
.
|
19
|
8
|
May
.
|
3
|
13
|
May
.
|
10
|
7
|
May
.
|
18
|
16
|
Iune
.
|
2
|
2
|
Iune
.
|
8
|
20
|
Iune
.
|
17
|
0
|
Iuly
.
|
1
|
4
|
Iuly
.
|
8
|
10
|
Iulie
.
|
16
|
9
|
August
.
|
29
|
16
|
August
.
|
7
|
2
|
August
.
|
14
|
21
|
September
.
|
28
|
2
|
September
.
|
5
|
17
|
September
.
|
13
|
12
|
October
.
|
27
|
12
|
October
.
|
5
|
10
|
October
.
|
13
|
|
Nouember
.
|
25
|
22
|
Nouember
.
|
4
|
1
|
Nouember
.
|
12
|
1
|
December
.
|
25
|
8
|
December
.
|
3
|
15
|
December
.
|
11
|
19
|
If
they
bee
tenne
of
the
Golden
number
.
|
If
they
be
twelue
of
the
Golden
number
.
|
If
they
bee
foureteene
of
the
Golden
number
.
|
monethes
|
Daies
|
Houres
|
monethes
|
Daies
|
Houres
|
Monethes
|
Daies
|
Houres
|
Ianuarie
.
|
10
|
12
|
Ianuarie
.
|
17
|
9
|
Ianuarie
.
|
25
|
7
|
Februarie
.
|
9
|
3
|
Februarie
.
|
18
|
15
|
Februarie
|
23
|
23
|
marche
.
|
9
|
16
|
marche
.
|
17
|
21
|
Marche
.
|
24
|
15
|
Aprill
.
|
8
|
●
|
Aprill
.
|
16
|
11
|
Aprill
.
|
23
|
7
|
may
.
|
7
|
9
|
may
.
|
15
|
23
|
May
.
|
22
|
22
|
Iune
.
|
5
|
16
|
Iune
.
|
14
|
8
|
Iune
.
|
21
|
13
|
Iuly
.
|
4
|
23
|
Iuly
.
|
13
|
16
|
Iuly
.
|
21
|
1
|
August
.
|
3
|
7
|
August
.
|
12
|
00
|
August
.
|
19
|
13
|
September
.
|
1
|
18
|
September
.
|
10
|
8
|
September
.
|
18
|
1
|
October
.
|
31
|
8
|
October
.
|
9
|
17
|
October
.
|
17
|
11
|
Nouember
.
|
29
|
19
|
Nouember
.
|
8
|
5
|
Nouember
.
|
15
|
22
|
December
.
|
29
|
14
|
December
.
|
7
|
18
|
December
.
|
15
|
8
|
If
they
be
eleuen
of
the
Golden
number
.
|
If
they
be
thirteene
of
the
Golden
number
.
|
If
they
be
fifteene
of
the
Golden
number
.
|
Monethes
|
Daies
|
Houres
|
Monethes
|
Daies
|
Houres
|
Monethes
|
Daies
|
Houres
|
Ianuarie
.
|
28
|
8
|
Ianuarie
.
|
6
|
10
|
Ianuarie
.
|
13
|
18
|
Februarie
.
|
27
|
1
|
Februarie
.
|
5
|
3
|
Februarie
.
|
12
|
6
|
March
|
28
|
15
|
Marche
.
|
6
|
21
|
Marche
.
|
13
|
19
|
Aprill
.
|
27
|
1
|
Aprill
.
|
5
|
15
|
Aprill
.
|
12
|
9
|
May
.
|
26
|
9
|
May
.
|
5
|
6
|
May
.
|
12
|
0
|
Iune
.
|
24
|
16
|
Iune
.
|
3
|
19
|
Iune
.
|
10
|
20
|
Iuly
.
|
23
|
23
|
Iulie
.
|
3
|
6
|
Iuly
.
|
10
|
5
|
August
.
|
22
|
7
|
August
.
|
1
|
15
|
August
.
|
8
|
20
|
September
.
|
20
|
17
|
September
.
|
29
|
10
|
September
.
|
7
|
10
|
October
.
|
20
|
5
|
October
.
|
28
|
19
|
October
.
|
7
|
0
|
Nouember
.
|
18
|
21
|
Nouember
.
|
27
|
6
|
Nouember
.
|
5
|
13
|
December
.
|
18
|
14
|
December
.
|
26
|
18
|
December
.
|
5
|
0
|
If
they
be
sixteene
of
the
Golden
number
.
|
If
they
be
eighteene
of
the
Golden
number
.
|
monethes
|
Daies
|
Houres
|
monethes
|
Daies
|
Houres
|
Ianuarie
.
|
3
|
10
|
Ianuarie
.
|
12
|
2
|
Februarie
.
|
2
|
20
|
Februarie
.
|
10
|
14
|
marche
.
|
3
|
6
|
marche
.
|
11
|
0
|
Aprill
.
|
1
|
17
|
Aprill
.
|
0
|
7
|
may
.
|
1
|
4
|
may
.
|
8
|
8
|
Iune
.
|
29
|
15
|
Iune
.
|
6
|
23
|
Iuly
.
|
28
|
21
|
Iuly
.
|
6
|
8
|
August
.
|
27
|
13
|
August
.
|
5
|
19
|
September
.
|
26
|
6
|
September
.
|
3
|
8
|
October
.
|
25
|
22
|
October
.
|
3
|
1
|
Nouember
.
|
23
|
13
|
Nouember
.
|
1
|
19
|
December
.
|
24
|
1
|
December
.
|
1
|
14
|
If
they
bee
seuenteene
of
the
Golden
number
.
|
If
they
be
nineteene
of
the
Golden
number
.
|
Monethes
|
Daies
|
Houres
|
Monethes
|
Daies
|
Houres
|
Ianuarie
.
|
22
|
12
|
Ianuarie
.
|
30
|
5
|
Februarie
.
|
20
|
22
|
Februarie
.
|
28
|
14
|
March
|
22
|
7
|
Marche
.
|
30
|
1
|
Aprill
.
|
20
|
16
|
Aprill
.
|
28
|
9
|
May
.
|
20
|
1
|
May
.
|
27
|
16
|
Iune
.
|
18
|
11
|
Iune
.
|
25
|
13
|
Iuly
.
|
17
|
23
|
Iulie
.
|
25
|
6
|
August
.
|
16
|
14
|
August
.
|
23
|
16
|
September
.
|
15
|
7
|
September
.
|
22
|
4
|
October
.
|
15
|
1
|
October
.
|
21
|
20
|
Nouember
.
|
13
|
19
|
Nouember
.
|
20
|
14
|
December
.
|
13
|
11
|
December
.
|
20
|
19
|
It
is
to
be
noted
,
that
for
the
coniunctions
of
the
moone
before
written
,
shal
be
taken
out
,
the
opposition
or
the
fulnesse
of
the
moone
that
is
,
by
reckoning
fourteene
dayes
,
and
sixeteene
houres
,
after
the
coniunction
,
a
little
thing
more
or
lesse
.
The
fourth
Chapter
,
of
a
shorte
account
or
reckoning
to
knowe
without
the
booke
briefly
the
dayes
whiche
the
moone
hath
in
any
mooneth
of
the
yeere
.
OF
the
accounte
of
the
Moone
which
before
hath
beene
declared
,
you
may
at
all
times
when
you
will
,
know
how
many
dayes
olde
the
moone
is
,
&
what
day
&
houre
the
coniunction
was
,
but
because
without
the
booke
it
cannot
be
known
.
I
thought
good
to
put
heere
a
short
account
;
that
by
memorie
it
may
bee
knowne
,
howe
many
dayes
olde
the
Moone
is
,
at
all
times
when
you
will
know
it
:
the
which
is
to
be
reckoned
i●
this
manner
.
In
what
day
soeuer
you
are
in
,
looke
howe
many
bee
of
concurrent
in
that
yeere
which
you
runne
,
according
as
you
shall
finde
in
the
account
before
〈◊〉
and
ioyne
with
them
the
number
of
the
Monethes
whiche
are
past
from
March
vnto
that
moneth
,
&
likewise
ioyne
the
dayes
of
the
moneth
which
you
haue
vnto
the
day
wherein
you
are
:
these
three
numbers
together
if
they
passe
of
thirtie
,
those
whiche
are
more
,
the
Moone
is
olde
,
and
if
they
bee
thirtie
iust
,
the
Moone
is
in
couiunction
,
and
if
they
come
not
to
thirty
,
those
which
are
,
so
many
dayes
old
the
Moone
is
.
An
Example
.
In
the
yeere
of
1545.
we
haue
seuenteene
of
concurrent
,
therefore
the
twentie
of
August
,
I
will
knowe
how
many
dayes
old
the
Moone
is
:
I
say
that
of
concurrent
is
seuenteene
,
ioyne
sixe
of
the
monethes
which
are
from
March
to
August
,
it
amounteth
to
twentie
three
,
and
twentie
of
the
Moneth
are
forty
three
,
take
away
thirty
,
there
remaineth
thirteene
,
so
many
daies
the
Moone
is
old
,
the
twentie
day
of
August
.
And
by
this
manner
you
shall
take
out
the
dayes
that
the
Moone
is
old
,
euery
time
that
you
will
.
1545
17
●8
9
20
1
12
23
4
15
26
7
18
29
11
22
314
25
6
In
the
yeere
of
1545.
we
haue
seuenteene
of
concurrent
,
the
next
yeere
following
,
we
haue
tweentie
eight
,
and
so
reckoning
in
euery
yeere
one
house
of
these
and
it
serueth
for
euer
.
OF
this
account
of
the
concurrent
,
knowe
yee
,
that
it
increaseth
euerie
yeere
eleuen
,
and
it
cannot
passe
aboue
thirtie
,
and
if
they
doe
passe
thirtie
,
you
must
leaue
the
thirtie
,
and
take
that
which
remayneth
.
And
so
know
this
reckoning
of
the
concurrent
quickly
by
the
head
,
doe
you
in
this
manner
set
downe
in
the
roote
of
the
thumbe
,
ten
,
and
in
the
ioynt
of
the
middest
twenty
,
and
the
vppermost
thirtie
,
and
this
being
done
put
the
Golden
number
in
the
three
ioynts
,
reckoning
one
in
the
roote
of
the
thumbe
,
and
in
the
middle
ioynt
,
two
,
and
aboue
three
,
&
turning
againe
beneath
foure
,
and
in
the
middest
fiue
,
and
so
discoursing
vntill
you
come
to
the
Golden
number
of
that
yeere
,
and
if
it
staye
in
the
roote
of
the
thumbe
you
shall
ioyne
that
whiche
it
is
of
Golden
number
,
with
the
tenne
that
was
put
there
,
&
ioyning
one
number
with
as
many
more
:
you
shal
haue
of
concurrent
as
much
as
both
numbers
doth
amount
too
,
and
if
the
Golden
number
d●e
rest
in
the
middle
ioynt
you
shall
ioyne
with
the
Golden
number
,
the
twentie
that
was
put
there
,
and
all
beeyng
ioyned
together
,
it
wil
be
so
many
of
concurrent
,
and
if
the
Golden
number
,
doe
rest
in
the
vppermost
parte
of
the
thumbe
,
ioyne
with
the
Golden
number
,
the
thirtie
which
was
put
there
,
hauing
alwayes
remembraunce
,
when
all
the
number
doth
passe
thirtie
,
you
shall
leaue
the
thirtie
,
and
that
whiche
remayneth
,
is
the
concurrent
.
The
fifth
Chapter
,
how
by
the
dayes
of
the
Moone
,
and
the
course
where
the
Sunne
will
bee
,
shal
bee
knowen
at
what
houre
the
tyde
will
come
euery
day
.
ALL
persons
which
doe
doe
sayle
,
it
is
necessary
that
they
knowe
howe
the
tides
doe
fall
euerye
day
,
&
at
what
houre
it
is
full
Sea
,
or
lowe
water
,
for
this
is
conuenient
,
aswell
for
to
enter
in
by
any
bard
hauen
,
as
for
other
things
,
which
may
serue
in
the
nauigation
.
Therefore
in
this
Chapter
,
I
wil
declare
,
howe
the
reckoning
of
the
sayde
tides
ought
to
be
kept
,
&
at
what
houre
they
come
,
for
to
profite
thereby
,
of
the
whiche
is
to
bee
vnderstood
,
that
the
Moone
goeth
the
thirtie
two
windes
of
the
nauigation
in
24.
houres
,
in
the
which
she
maketh
her
dayly
moouing
,
with
more
that
she
hath
gone
of
her
owne
mouing
,
&
in
this
time
she
bringeth
two
tydes
,
that
is
to
say
,
two
floods
&
two
ebbes
,
so
that
the
sea
floweth
sixe
houres
,
&
ebbeth
other
sixe
,
which
are
twelue
,
and
the
like
is
done
in
other
twelue
,
but
it
is
to
be
noted
,
that
these
flowinges
and
ebbinges
are
not
equall
,
nor
alike
in
all
times
&
places
,
as
muche
as
toucheth
the
time
they
bee
not
equall
,
because
seuen
dayes
the
waters
goe
rising
,
and
wee
call
them
spring
rides
,
&
other
seuen
they
goe
decreasing
or
●ayling
,
&
we
call
them
nepe
tides
:
so
that
from
the
first
day
of
the
Moone
vnto
the
eight
day
,
which
is
the
quarter
,
the
waters
goe
decreasing
,
and
from
the
quarter
vnto
the
fifteenth
which
is
the
ful
Moone
,
they
goe
increasing
,
and
from
the
full
Moone
to
the
thirde
quarter
,
they
goe
decreasing
,
and
from
that
to
the
coniunction
they
goe
increasing
:
&
declaring
this
more
at
large
,
I
saye
that
the
first
daye
of
the
Moone
,
is
the
head
of
the
water
,
and
the
second
day
,
the
increasing
is
as
greate
,
and
the
thirde
day
well
neere
the
like
,
and
the
fourth
day
it
decreaseth
,
and
so
it
goeth
euerye
daye
decreasing
,
vntill
the
Moone
bee
eight
dayes
olde
,
and
then
it
is
altogether
neap
tydes
:
and
the
nienth
is
the
like
,
and
the
tenth
well
neere
alike
.
The
eleuenth
it
beginneth
to
increase
something
,
and
so
it
goeth
increasing
euery
day
vnto
the
fifteenth
which
is
full
Moone
,
whiche
doth
turne
to
bee
the
head
of
the
water
.
And
the
sixeteenth
it
increaseth
the
like
,
and
the
seuenteene
well
neere
the
like
.
The
eighteenth
it
decreaseth
,
and
so
it
goeth
decreasing
euerye
daye
vnto
the
two
and
twentie
,
whiche
is
altogether
nepe
tides
,
and
the
three
and
twentie
it
is
the
point
of
the
water
,
and
goeth
increasing
euerye
day
vnto
the
thirtye
day
which
is
the
coniunction
.
And
the
first
day
it
turneth
to
bee
the
head
of
the
water
,
and
so
successuiely
,
it
goeth
increasing
and
decreasing
as
it
hath
becue●●eclare●
.
Likewise
it
is
to
be
vnderstood
,
that
these
increasinges
,
are
not
at
all
tunes
equall
or
alike
,
but
in
some
〈◊〉
they
are
greater
and
in
other
〈…〉
as
by
experience
wee
see
.
Likewise
it
is
to
bee
noted
that
these
increasinges
and
decreasinge●
in
all
plates
are
not
alike
,
for
th●rauses
that
I
will
speake
of
.
And
for
to
knowe
the
howe
,
when
the
tides
doe
come
,
it
is
to
bee
vnderstood
,
that
alwayes
the
Moone
being
in
the
Northeast
it
is
full
Sea
,
and
in
the
Southeast
lowe
water
,
and
in
the
Southwest
full
Sea
,
and
in
the
Northwest
lowe
water
.
And
to
knowe
when
the
Moone
is
in
euery
one
of
these
courses
,
it
must
bee
taken
out
by
the
course
where
the
Sunne
is
in
this
manner
.
The
first
day
,
of
the
Moone
,
the
Sunne
beeyng
in
the
Northeast
and
by
East
,
the
Moone
is
in
the
Northeast
,
and
that
houre
full
Sea
.
The
seconde
day
,
of
the
Moone
,
the
Sunne
beeyng
in
the
Northeast
is
full
Sea
.
The
thirde
day
,
when
the
Sunne
is
in
the
East
and
by
north
it
wil
be
ful
Sea
.
The
fourth
day
,
the
Sunne
in
the
East
full
Sea
.
The
fifth
day
,
the
Sunne
in
the
East
,
and
by
South
,
the
Moone
in
the
Northeast
.
The
sixte
day
,
the
Sunne
in
the
Southeast
,
the
Moone
in
the
Northeast
.
The
seuenth
day
,
the
Sunne
in
the
Southeast
,
and
by
east
,
the
Moone
in
the
Northeast
.
The
eight
day
,
the
Sunne
in
the
Southeast
,
the
Moone
in
the
Northeast
.
The
nienth
day
,
the
Sunne
in
the
Southeast
and
by
south
,
the
Moone
in
the
Northeast
.
The
tenth
day
,
the
Sunne
in
the
South
Southeast
,
the
Moone
in
the
Northeast
.
The
eleuenth
day
,
the
Sunne
in
the
South
,
and
by
east
,
the
Moone
in
the
Northeast
.
The
twelfth
day
,
the
sunne
in
the
South
,
the
Moone
in
the
Northeast
.
The
thirteenth
day
,
the
sunne
in
the
South
,
and
by
west
,
the
Moone
in
the
Northwest
.
The
foureteenth
day
,
the
sun
in
the
South
,
Southwest
,
the
Moone
in
the
Northeast
.
The
fifteenth
day
,
this
day
we
reckon
two
quarters
together
,
by
reason
that
the
poyntes
are
thirtie
two
,
and
the
daies
thirty
,
we
giue
in
the
middest
one
quarter
,
and
in
the
end
another
,
so
that
at
the
fifteenth
day
the
Sunne
beeyng
in
the
Southwest
,
the
Moone
wil
bee
in
the
Northeast
,
&
this
houre
it
wil
be
full
Sea
.
The
sixeteenth
day
,
the
sun
being
in
the
Southwest
&
by
west
,
the
Moone
wil
be
,
in
the
Southwest
,
&
that
houre
wil
be
full
Sea
.
The
seuenteenth
day
,
the
sun
in
the
West
,
Southwest
,
the
Moone
in
the
southwest
is
full
Sea
.
The
eighteenth
day
,
the
sunne
in
the
West
,
and
by
south
,
the
Moone
in
the
southwest
full
Sea
.
The
nineteenth
day
,
the
sunne
in
the
West
,
the
Moone
in
the
South
West
,
full
Sea
.
The
twentieth
day
,
the
sunne
in
the
West
,
and
by
north
,
the
Moone
in
the
Southwest
.
The
twenty
one
day
,
the
sunne
in
the
West
,
Northwest
,
the
Moone
in
the
Southwest
.
The
twenty
two
day
,
the
sunne
in
the
Northwest
,
and
by
west
the
moone
in
the
Southwest
.
The
twentie
three
day
,
the
sunne
in
the
Northwest
,
the
moone
in
the
southwest
.
The
twentie
soure
day
,
the
sunne
in
the
Northwest
,
and
by
north
,
the
moone
in
the
Southwest
.
The
twenty
fiue
day
,
the
sunne
in
the
nor
northwest
,
the
moone
in
the
southwest
.
The
twenty
sixe
day
,
the
sunne
in
the
North
and
by
west
,
the
moone
in
the
Southwest
.
The
twenty
seuen
day
,
the
sunne
in
the
North
,
the
moone
in
the
southwest
.
The
twenty
eight
day
,
the
sunne
in
the
North
,
and
by
east
,
the
moone
in
the
southwest
.
The
twenty
niene
day
,
the
sunne
at
North
Northeast
,
the
moone
at
southwest
,
and
at
that
houre
full
Sea
.
The
thirtie
day
,
which
is
the
coniunction
is
to
be
reckoned
two
points
,
which
are
the
Northeast
and
by
north
,
and
the
Northeast
.
The
sixte
Chapter
,
wherein
is
declared
more
at
large
,
the
aforesaide
Chapter
,
with
a
demonstration
.
OF
the
account
which
before
hath
beene
declared
,
you
shall
take
out
euery
day
at
what
houre
the
tyde
commeth
,
the
sunne
beeing
in
the
poynt
or
course
as
before
is
mentioned
.
But
for
the
better
vnderstanding
therof
,
it
is
to
be
noted
,
that
alwayes
at
12.
of
the
clocke
in
the
day
you
haue
the
sunne
at
south
,
if
you
be
more
towards
the
North
than
the
sunne
,
so
that
at
sixe
of
the
clocke
in
the
morning
you
had
it
at
East
,
and
at
nine
at
Southeast
,
and
at
three
after
the
middest
of
the
day
,
you
shall
haue
it
at
southwest
,
and
at
sixe
,
at
West
,
and
at
nine
,
at
Northwest
,
and
at
twelue
of
the
night
,
at
North.
And
at
three
after
midnight
at
northeast
,
and
if
the
sunne
be
more
towardes
the
North
,
then
at
the
middest
of
the
day
,
you
shall
haue
him
at
North
,
and
at
twelue
of
the
night
at
South
.
And
by
these
courses
you
shall
take
out
the
rest
,
according
to
the
place
and
time
,
wherein
you
shal
finde
your selfe
.
Likewise
it
is
to
bee
noted
,
as
before
hath
beene
declared
.
The
Moone
beyng
in
the
Northeast
or
Southwest
,
it
is
full
Sea
,
and
in
the
Southeast
and
Northwest
,
it
is
low
water
.
And
to
knowe
when
hee
is
in
these
courses
,
the
course
must
bee
sought
where
the
Sunne
should
stand
according
as
the
dayes
of
the
moone
are
,
And
of
this
is
vnderstood
that
although
here
goeth
written
,
the
courses
where
the
Sunne
ought
to
bee
,
because
the
Moone
should
be
in
the
Northeast
,
and
that
houre
full
Sea
.
Likewise
it
is
to
bee
vnderstood
,
that
the
Sunne
being
in
the
contrary
course
of
that
,
the
Moone
〈◊〉
in
the
Southwest
,
and
it
wil
be
likewise
full
Sea
,
and
the
〈◊〉
wil
be
at
the
lowe
water
.
And
in
this
sort
the
account
serueth
,
as
well
〈◊〉
the
first
tide
,
as
for
the
second
,
the
which
may
bee
,
taken
out
by
the
figure
〈◊〉
lowing
.
Of
this
figure
is
to
bee
noted
,
that
beeyng
knowne
howe
many
dayes
the
moone
is
olde
,
and
seeking
it
in
this
account
,
and
the
Sunne
beeing
come
to
that
course
,
where
the
like
number
is
,
or
to
his
contrary
,
that
houre
will
bee
full
Sea
,
keeping
reckoning
that
at
twelue
of
the
clocke
of
the
day
the
Sunne
is
at
South
,
and
at
twelue
of
the
night
at
North
:
And
that
in
three
quarters
of
an
houre
the
Sunne
passeth
from
one
poynt
to
another
.
The
seuenth
Chapter
,
howe
by
the
houre
wherein
the
coniunction
was
,
the
tyde
may
be
knowen
,
and
the
allowance
that
ought
to
be
giuen
to
the
riuers
.
IT
hath
beene
declared
,
howe
it
shal
be
knowne
,
at
what
houre
the
tides
come
euery
day
,
by
counting
the
number
of
daies
of
the
moone
,
&
by
that
meanes
looking
in
the
course
where
the
sunne
shoulde
bee
,
as
in
the
Chapters
before
written
hath
beene
declared
.
And
besides
this
,
it
seemed
good
to
mee
,
to
put
here
a
rule
,
and
account
,
because
not
only
by
the
dayes
of
the
moone
,
&
courses
of
the
sunne
,
but
by
the
houres
,
the
houre
beeyng
knowen
wherin
the
coniunction
was
,
shal
bee
knowen
euerye
day
,
at
what
houre
of
the
day
or
the
night
,
the
tide
will
come
:
and
for
this
you
must
knowe
the
account
following
.
Looke
in
what
day
and
what
houre
the
moone
was
in
coniunction
,
and
beyng
knowne
,
you
shall
finde
that
euerie
day
the
tyde
doth
come
foure
quintos
or
foure
fiue
partes
of
an
houre
forwarde
,
so
that
if
the
tyde
come
this
day
at
one
of
the
clocke
,
to
morrowe
hee
will
come
at
one
and
foure
fiue
partes
of
an
houre
,
and
the
nexte
day
at
two
,
and
three
fiue
partes
,
and
so
the
rest
of
the
dayes
as
by
this
account
appeareth
.
Dayes
.
|
Houres
.
|
Fifthes
.
|
1
|
|
4
|
2
|
1
|
3
|
3
|
2
|
2
|
4
|
3
|
1
|
5
|
4
|
|
6
|
4
|
4
|
7
|
5
|
3
|
8
|
6
|
2
|
6
|
7
|
1
|
10
|
8
|
|
12
|
8
|
4
|
12
|
9
|
3
|
13
|
10
|
2
|
14
|
11
|
1
|
15
|
12
|
2●
|
16
|
12
|
4
|
17
|
13
|
3
|
18
|
14
|
2
|
19
|
15
|
1
|
20
|
16
|
|
21
|
16
|
4
|
22
|
17
|
3
|
23
|
18
|
2
|
24
|
19
|
1
|
25
|
20
|
|
26
|
20
|
4
|
27
|
21
|
3
|
28
|
22
|
2
|
29
|
23
|
1
|
30
|
24
|
|
IT
is
to
bee
noted
that
the
houres
here
〈◊〉
,
being
ioyned
with
the
houres
of
the
moone
which
she
hath
in
the
coniunction
,
besides
those
dayes
that
bee
more
then
foure
and
twentie
,
there
shal
be
taken
out
once
twelue
,
or
twise
if
it
he
needefull
,
and
t●ose
whiche
remayne
shall
bee
the
houre
in
the
which
the
tide
〈◊〉
come
.
Item
it
is
to
be
noted
that
the
accountes
which
before
hath
beene
declared
,
whereby
may
be
knowne
,
at
what
houre
the
tide
will
come
,
is
as
much
as
to
the
naturall
course
of
the
moone
,
more
it
is
so
that
accidentally
,
it
is
not
in
all
partes
,
or
in
all
coastes
that
the
tides
are
equall
,
although
they
bee
in
one
Meridian
,
they
come
not
so
at
one
time
,
by
reason
of
the
great
currents
,
or
the
straightes
of
the
Sea
,
great
gulfes
,
or
entraunce
of
Lande
into
the
Sea
,
or
windes
,
or
for
other
cause
,
by
the
which
alwaies
the
practise
of
the
Land
ought
to
be
looked
vnto
.
Likewise
,
it
is
to
be
vnderstood
,
that
there
ought
to
bee
giuen
allowance
to
the
riuers
,
because
they
make
not
the
tides
according
to
the
barre
,
and
there
should
be
giuen
them
allowance
,
a
quarter
later
because
in
the
coastes
,
the
tides
beginneth
to
ebbe
more
speedily
,
and
in
the
riuers
it
cannot
bee
done
,
by
reason
of
the
holding
backe
or
stay
of
the
waters
that
commeth
from
aboue
,
and
the
like
is
to
bee
giuen
at
the
flowing
,
this
is
common
,
but
the
allowance
is
not
alwayes
equall
to
all
riuers
,
because
some
doe
flowe
and
ebbe
more
then
other
some
.
This
is
by
reason
that
some
riuers
haue
more
current
then
other
some
,
and
likewise
when
the
flowing
is
holpen
with
winde
,
therefore
the
disposition
of
the
place
is
to
bee
looked
on
.
The
ende
of
the
seuenth
Booke
.
❧
The
eight
booke
of
the
dayes
of
the
yeere
.
The
first
Chapter
,
what
thing
a
day
is
,
and
howe
it
is
reckoned
,
and
in
howe
manye
partes
it
is
deuided
.
In
such
sort
,
that
how
much
the
variation
of
the
Horizon
is
,
so
much
is
the
variation
of
the
daies
in
length
or
shortnesse
,
and
if
this
shoulde
hee
made
euen
for
all
Horizontes
,
it
were
conuenient
,
to
haue
for
euery
one
a
Table
of
equallitie
of
the
dayes
,
where
shoulde
bee
well
neere
an
infinite
number
,
so
that
the
Astronomers
to
flie
so
great
adiuersitie
,
began
the
day
,
in
the
middest
of
the
day
,
because
one
is
sufficient
for
al
parts
,
and
seeing
that
wee
haue
spoken
of
the
natural
day
,
let
vs
speake
also
of
the
artificiall
day
.
The
artificial
day
is
the
time
which
the
sunne
doth
shewe
light
vnto
vs
,
going
aboue
our
Hemispherio
,
and
is
called
the
artificial
day
,
because
he
is
different
in
diuerse
parts
,
&
because
the
Artificers
doe
make
their
woorks
in
him
,
the
which
is
deuided
into
foure
parts
accoring
to
4
differences
,
which
the
Sun
maketh
.
In
the
first
he
shineth
,
in
the
second
he
heateth
,
in
the
third
hee
burneth
,
in
the
fourth
hee
warneth
,
the
night
consequently
hath
foure
partes
.
The
first
is
the
first
sleepe
,
the
second
is
mydnight
,
when
all
thinges
holde
their
peace
,
because
it
is
no
apt
time
to
woorke
anye
thing
,
the
thirde
when
the
Cocke
croweth
,
the
fourth
when
the
day
doth
begin
to
appeare
.
There
is
another
time
called
Cropusculo
,
and
is
,
when
it
is
neyther
day
nor
night
:
so
betweene
day
and
night
,
as
betweene
night
and
day
.
This
Cropusculo
is
that
bright
time
,
whiche
wee
haue
in
the
Morning
,
before
the
Sunne
riseth
,
as
likewise
that
whiche
wee
haue
in
the
Euening
,
after
that
the
Sunne
is
set
:
vntill
the
darknesse
of
the
night
doe
come
.
This
Cropusculo
is
greater
or
lesser
,
according
as
the
day
is
greate
or
little
,
and
so
in
the
Sommer
wee
haue
a
greater
Cropusculo
then
in
the
Winter
,
and
in
that
parte
it
shoulde
bee
greater
,
where
the
dayes
are
greater
,
and
so
we
see
,
that
in
Flaunders
in
the
Sommer
,
at
ten
of
the
clocke
in
the
night
,
although
it
be
two
houres
after
Sunne
let
,
there
is
so
muche
light
,
that
any
letter
may
be
read
.
The
second
Chapter
,
howe
in
the
artificiall
day
the
Sunne
riseth
and
setteth
,
differently
to
suche
as
inhabite
in
the
worlde
.
IT
hath
beene
declared
,
what
thing
a
daye
is
,
and
howe
the
naturall
day
,
and
artificiall
day
,
are
vnderstood
.
In
this
I
will
speake
howe
the
sunne
comming
foorth
in
the
Horizon
,
&
rising
vp
by
our
Hemispherio
,
commeth
to
the
Meridian
,
and
from
thence
descending
,
and
commeth
to
the
orrident
,
where
he
setteth
to
vs
,
and
as
this
is
done
indifferently
to
suche
as
inhabite
in
the
worlde
,
of
the
which
it
is
to
be
vnderstoode
,
that
the
going
foorth
which
the
sunne
maketh
,
euery
day
by
our
horizon
,
is
not
equall
one
day
with
another
,
and
that
this
is
true
,
experience
doth
shewe
it
.
And
to
be
likwise
so
,
the
quantitie
or
greatnes
is
not
equall
one
day
with
another
,
but
of
this
is
to
be
noted
,
that
in
the
degrees
or
distance
of
the
equinoctial
,
wherein
the
sunne
commeth
foorth
euery
day
,
in
the
same
he
setteth
,
likewise
it
is
to
bee
noted
,
that
although
the
day
bee
great
or
litle
,
alwayes
a
man
being
in
one
place
,
the
sun
commeth
euery
day
at
the
middest
of
the
day
,
into
one self
Meridian
,
without
any
manner
of
variation
.
Likewise
it
is
to
be
vnderstood
,
that
because
the
sunne
commeth
not
foorth
equally
at
one
time
to
all
such
as
inhabite
in
the
world
,
nor
all
of
them
doe
see
him
at
one
time
,
so
the
middest
of
the
day
is
not
made
at
one
time
to
all
.
In
such
sort
,
that
how
much
the
more
anie
place
is
more
easterly
,
then
other
,
by
so
muche
,
such
is
inhabite
there
,
doe
see
the
sun
rather
,
&
doth
begin
to
appeare
rather
to
them
then
to
suche
as
are
more
westerly
.
And
in
this
manner
successiuely
,
euen
as
the
sun
goeth
rising
aboue
the
Horizon
of
some
,
so
hee
goeth
shewing
&
appearing
indifferent
partes
to
others
:
so
that
when
to
vs
it
is
the
middest
of
the
day
,
suche
as
are
more
westerly
,
to
some
it
wil
be
xi
.
a
clocke
,
to
other
x
,
&
to
others
it
.
And
so
how
much
more
distant
he
is
of
vs
towardes
the
west
,
so
much
the
later
the
sunne
commeth
foorth
to
them
,
and
so
by
the
saide
reason
,
hee
commeth
later
to
their
Meridian
,
I
say
more
late
to
our
respect
,
and
such
which
are
from
vs
more
easterly
,
because
the
sunne
came
foorth
to
them
first
,
then
to
vs
,
they
had
the
day
first
.
And
in
this
manner
,
is
to
be
vnderstood
that
at
the
xxiiii
.
houres
,
that
the
sunne
goeth
about
the
world
,
when
to
some
it
is
day
,
to
othersome
it
is
night
,
&
when
to
some
it
is
the
morning
,
to
others
it
is
the
Euening
,
and
when
he
riseth
to
some
,
he
setteth
to
othersome
,
and
when
to
some
it
is
midday
,
to
others
it
is
midnight
.
This
is
because
as
the
sunne
mooueth
himselfe
rounde
about
the
world
,
&
alwayes
goeth
lightning
the
halfe
of
the
roundnes
,
doth
cause
the
said
differences
.
And
it
is
to
be
noted
,
that
in
the
moouing
which
the
sunne
maketh
,
he
mooueth
euery
house
by
the
roundnesse
of
water
and
earth
,
262
leagues
,
because
the
vi
.
thousand
three
hundred
leagues
being
parted
,
which
the
roundnesse
hath
in
the
xxiiii
.
houres
of
the
natural
day
,
it
commeth
to
euery
houre
262
leagues
.
And
so
by
this
reckoning
,
looking
what
houre
it
is
of
the
day
in
the
place
where
a
man
as
,
he
shall
knowe
what
houre
it
is
in
any
other
parte
,
knowing
the
distance
of
the
leagues
which
are
to
that
said
place
.
The
third
Chapter
,
howe
that
vnder
the
Equinoctiall
,
the
dayes
and
nightes
are
alwayes
equall
.
IT
was
an
opinion
of
some
auncient
writers
,
that
vnder
the
Equinoctiall
,
and
likewise
all
the
Torrida
Zona
was
inhabitable
,
the
whiche
they
beleeued
,
because
that
there
the
sunne
doth
send
his
perpendiculer
beames
,
there
should
bee
such
excessiue
heate
,
that
it
was
not
habitable
:
of
this
opinion
was
Virgil
,
and
Ouid
,
&
other
singular
men
.
Others
there
were
,
whiche
healde
that
some
parte
was
habitable
,
following
Ptholome
,
which
in
the
booke
that
was
compared
to
the
arte
of
the
Sphera
,
saith
,
it
is
not
conuenient
,
that
we
should
thinke
the
Torrida
Zona
to
be
altogether
inhabitable
.
Other
there
were
,
which
heald
that
there
it
was
not
only
temperate
,
&
without
too
much
beate
,
but
also
most
temperate
.
And
this
is
affirmed
by
S.
Isidore
,
in
the
first
of
the
Etimologias
,
where
hee
saith
that
the
earthly
Paradise
is
in
the
East
part
vnder
the
Equinoctiall
,
a
most
temperate
place
,
and
Ptholome
likewise
saith
in
the
thirde
of
the
Quadri
partiti
,
that
all
the
temperate
complections
doe
proceede
of
the
Equinoctiall
.
The
experience
doth
nowe
shew
vs
,
that
not
only
vnder
the
Equinoctiall
,
but
al
the
Tortida
which
is
from
one
Tropike
to
the
other
,
is
habitable
,
riche
,
and
plentifull
,
because
well
neere
all
the
yeere
,
the
dayes
and
nights
are
almost
equall
:
so
that
the
freshnesse
of
the
night
,
doth
temper
the
heate
of
the
day
,
and
so
continually
the
earth
hath
season
to
bring
foorth
and
increase
her
fruites
.
But
it
is
to
bee
noted
,
that
touching
the
equalitie
of
the
dayes
&
the
nights
,
there
may
be
had
a
doubt
,
and
say
that
the
sunne
in
no
time
doth
make
equalitie
of
the
day
with
the
night
,
but
alwayes
the
artificiall
daye
is
greater
then
the
night
by
these
reasons
following
.
It
is
certaine
that
a
shining
body
being
greater
,
lighteth
the
darknesse
more
than
halfe
,
and
as
the
sunne
is
greater
then
all
the
earth
,
so
that
as
it
hath
beene
saide
,
that
it
is
the
opinion
of
Alfragano
in
the
difference
twentie
two
,
that
the
Sunne
is
166.
times
greater
then
the
earth
,
so
that
the
Sunne
doth
light
the
earth
more
then
the
halfe
.
The
lesser
parte
remayning
darke
,
in
suche
sorte
,
that
the
Sunne
is
seene
in
a
greater
parte
of
the
earth
,
then
in
that
part
where
he
is
hidde
,
and
as
the
presence
of
the
Sunne
is
cause
of
the
day
,
and
his
absence
causeth
the
night
,
it
followeth
,
that
the
sunne
neuer
maketh
equalitie
of
the
day
,
and
of
the
night
.
Likewise
the
aforesaid
is
proued
,
wherin
a
case
is
giuen
,
that
the
halfe
of
the
Equinoctial
,
is
aboue
the
Horizon
,
and
the
other
halfe
beneath
,
for
the
greatenesse
of
the
Sunne
is
the
greater
parte
where
hee
lighteth
,
then
in
that
whiche
he
hideth
himselfe
:
it
seemeth
euident
,
that
the
parte
is
greater
that
the
sunne
lighteth
,
then
that
whiche
hee
leaueth
darke
.
By
the
which
reason
is
proued
that
the
Sunne
maketh
not
equality
of
the
day
with
the
night
.
A
declaration
.
Contrary
to
that
which
is
said
are
many
reasons
,
I
will
speake
of
three
in
short
time
.
The
first
is
,
that
our
sight
doth
manifest
,
how
all
dayes
are
not
equall
,
but
some
daies
greater
,
and
some
lesser
,
by
the
which
whersoeuer
is
giuen
greater
and
lesser
,
is
like
wise
necessary
that
there
be
giuen
an
equalitie
,
so
that
as
there
is
a
day
greater
then
the
night
,
&
a
night
greater
then
the
day
,
of
necessitie
must
be
giuen
day
and
night
equall
,
because
it
cannot
passe
from
one
extremitie
to
another
,
but
by
the
meane
:
To
the
seconde
,
the
Philosopher
saith
in
the
sirt
of
the
naturall
philosophie
,
that
the
sunne
being
come
to
the
Equinoctiall
,
the
moouing
which
hee
maketh
aboue
the
earth
,
is
equall
with
that
which
he
maketh
vnder
.
And
in
like
sort
,
the
time
of
the
day
is
equall
with
the
time
of
the
night
.
The
thirde
,
aunswearing
to
the
reasons
aforesayde
,
I
say
that
it
is
true
,
that
the
Sunite
lighteth
more
then
halfe
the
eart
,
as
the
perspectiue
reason
sheweth
it
,
but
it
is
to
bee
denied
,
that
the
day
in
the
Equinoctial
is
greater
then
the
night
,
not
because
when
soeuer
any
part
of
the
light
of
the
Sunne
is
seene
,
the
day
beginneth
,
but
it
beginneth
when
the
Ce●●er
of
the
sunne
commeth
foorth
,
and
not
the
partes
circumferentials
.
And
so
likewise
when
he
setteth
,
the
night
beginneth
.
The
reason
is
because
the
Planets
,
and
the
starres
doe
occupie
a
great
quantitie
,
and
their
place
,
and
moouing
is
not
to
bee
taken
,
by
any
manner
of
parte
,
but
it
ought
to
bee
taken
by
the
Center
,
and
so
it
is
said
that
the
Sunne
is
in
the
Equinoctiall
,
when
his
Center
is
there
.
The
fourth
Chapter
,
howe
the
dayes
and
the
nightes
goe
alwayes
increasing
or
diminishing
vnto
such
as
inhabite
foorth
of
the
Equinoctiall
.
IN
the
first
Chapter
of
the
fourth
booke
hath
beene
declared
,
that
from
the
Eqniuoctiall
,
to
the
pole
articke
is
called
the
North
part
,
&
from
the
Equinoctiall
to
the
pole
antarticke
,
is
called
the
South
part
.
Therefore
it
is
to
bee
vnderstood
,
that
such
as
inhabite
from
the
Equinoctiall
,
towards
the
North
part
,
or
the
pole
articke
,
as
the
sunne
commeth
to
the
tropike
of
Capricorne
,
the
thirteenth
of
December
,
&
so
beginneth
to
returne
to
the
line
,
howe
much
hee
commeth
from
the
said
tropike
,
so
much
the
dayes
goe
increasing
,
and
to
such
as
inhabite
towardes
the
South
parte
,
they
goe
decreasing
.
And
the
sunne
beeyng
come
to
Aries
the
eleuenth
of
Matche
,
he
describeth
the
Equinoctiall
line
,
and
maketh
in
all
partes
the
dayes
and
nightes
equall
,
and
beeing
past
the
first
poynt
of
Aries
,
the
daies
begin
to
waxe
greater
then
the
nights
&
to
those
of
the
other
part
,
the
daies
lesser
,
&
the
nights
greater
,
&
the
sun
being
come
to
Cancer
the
eleuenth
of
June
,
the
day
is
greater
,
and
the
night
lesser
,
&
to
the
other
parte
the
contrary
:
for
then
the
sunne
is
more
neere
to
some
and
more
distant
to
other
some
,
&
from
thence
the
sun
turneth
to
descend
,
&
as
he
goeth
away
from
that
parte
,
the
daies
goe
decreasing
,
&
the
nights
increasing
,
&
being
come
to
Libra
,
the
13.
of
September
,
he
returneth
to
describe
the
Equinoctiall
,
and
the
dayes
&
the
nights
are
to
al
equal
,
&
from
thence
he
goeth
descending
to
Capricorne
,
&
the
nights
begin
to
be
greater
then
the
daies
,
&
towards
the
South
part
,
the
dayes
greater
,
and
the
nightes
lesser
,
&
as
he
commeth
to
the
saide
tropike
,
it
maketh
a
greater
night
,
and
a
lesser
day
,
&
to
those
of
the
other
parte
,
the
day
greater
,
and
the
night
lesser
,
for
there
the
Sunne
goeth
more
distant
from
some
,
and
commeth
neerer
to
other
some
.
Wherby
it
is
to
be
noted
,
that
if
there
be
taken
two
dayes
of
the
yeere
,
equally
distant
of
the
Equinoctiall
line
,
of
contrary
partes
,
that
howe
greate
the
artificiall
day
is
of
the
one
,
so
greate
the
artificiall
night
is
of
the
other
.
Likewise
it
is
to
bee
vnderstood
,
that
howe
much
in
euerye
habitation
,
the
pole
is
more
raysed
aboue
the
Horizon
,
so
muche
the
daies
&
the
nightes
are
greater
,
so
that
those
whose
Cenith
is
in
the
circle
articke
.
To
whom
the
pole
riseth
aboue
the
Horizon
,
sixtie
sixe
degrees
and
a
halfe
,
when
the
sunne
commeth
to
the
first
point
of
Cancer
,
the
eleuenth
of
June
is
to
them
one
day
24.
houres
,
and
the
night
very
short
,
because
in
one
moment
the
sunne
toucheth
that
day
his
Horizon
and
immediatly
commeth
foorth
,
and
that
touching
they
haue
for
night
.
And
the
thirteenth
of
December
,
when
the
sunne
commeth
to
the
first
degree
of
Capricorne
,
then
he
is
to
then
a
night
of
24.
houres
,
and
a
little
moment
for
the
day
,
for
in
one
instant
,
the
sunne
toucheth
his
horizon
,
&
foorthwith
he
hideth
himselfe
,
and
that
touching
they
haue
for
a
day
,
by
the
contrary
,
such
as
inhabite
vnder
the
circle
antartike
,
haue
the
like
.
And
those
whose
Cenith
is
betweene
the
circle
and
the
pole
of
the
worlde
,
whiles
the
Sunne
goeth
towardes
the
North
parte
,
it
wil
bee
to
him
one
day
,
that
whiche
his
Horizon
doth
discouer
of
the
Equinoctiall
,
continually
without
night
,
and
if
that
were
of
the
quantitie
of
one
signe
that
day
woulde
bee
of
one
Moneth
.
And
if
of
two
signe
,
it
would
bee
of
two
Monethes
,
and
so
the
rest
:
and
hee
that
were
vnder
anye
of
the
poles
,
all
the
yeere
would
be
to
him
one
day
and
one
night
:
In
such
sort
,
that
if
he
were
vnder
the
pole
articke
,
the
sixe
monethes
whiche
the
Sunne
goeth
to
the
part
of
the
North
,
woulde
bee
to
him
one
day
without
any
night
,
and
the
other
sixe
which
he
goeth
towards
the
part
of
the
South
,
woulde
bee
one
night
,
without
day
,
and
so
contrary
it
woulde
bee
,
if
he
were
vnder
the
pole
antarticke
,
so
that
halfe
the
yeere
,
it
would
bee
to
him
one
day
,
and
the
other
halfe
,
one
night
.
The
cause
is
,
by
reason
the
roundnesse
of
the
worlde
,
how
much
it
goeth
towardes
the
poles
,
so
muche
it
goeth
to
be
lesser
,
and
so
the
Horizon
of
such
as
are
neerest
to
the
poles
,
doe
discouer
more
parte
of
the
turne
whiche
the
Sunne
giueth
in
the
heauen
,
when
hee
goeth
from
that
parte
:
In
suche
sorte
,
that
the
earth
,
nor
the
water
,
doth
not
occupy
the
sight
of
the
Sunne
,
all
the
time
that
hee
goeth
,
rising
vp
,
and
turneth
descending
,
vntill
hee
commeth
where
his
Horizon
doth
not
discouer
any
thing
of
the
circle
or
turne
,
that
the
Sunne
maketh
to
the
worlde
,
and
so
how
much
more
,
the
part
is
which
is
seene
of
this
turne
,
so
muche
the
day
wil
be
greater
.
The
fifth
Chapter
,
how
the
increasing
and
diminishing
of
the
day
is
not
in
all
parts
alike
.
MAny
thinges
are
put
in
the
common
opinion
of
the
people
that
reason
,
&
truth
doth
shewe
it
to
be
in
another
manner
.
And
among
others
,
one
is
that
many
doe
thinke
that
the
increasing
,
&
decreasing
of
the
dayes
through
all
the
yeere
are
made
equall
,
I
will
say
that
the
time
,
whiche
those
dayes
goeth
increasing
,
so
muche
increaseth
one
day
as
another
,
and
so
when
they
decrease
euen
by
the
like
sort
.
And
according
to
the
quantity
of
houres
which
the
day
increaseth
,
from
the
lesser
day
to
the
greater
,
those
being
parted
by
the
time
of
the
6.
monethes
,
which
the
day
doth
increase
,
they
consider
how
muche
it
is
that
it
increaseth
euery
day
,
giuing
equall
number
or
quantitie
of
time
to
one
day
,
&
so
much
to
another
.
And
likewise
when
the
day
goeth
decreasing
how
much
it
is
that
it
decreaseth
:
in
such
sort
,
that
the
lesser
day
,
hauing
nine
houres
,
and
the
greater
15.
these
6.
houres
which
he
increaseth
,
deuided
into
6.
Monethes
,
the
dayes
shoulde
increase
one
houre
euery
Moneth
.
And
so
by
the
contrary
in
the
other
6.
Monethes
,
it
woulde
decrease
an
houre
euery
Moneth
:
(
This
is
not
so
)
for
in
truth
only
in
the
Moneth
of
March
,
the
dayes
doe
increase
as
much
as
they
did
increase
in
the
2.
Monethes
of
Januarie
and
Februarie
,
and
by
the
contrary
,
they
doe
decrease
so
muche
in
the
onely
Moneth
of
September
,
as
they
doe
decrease
in
July
and
August
:
also
in
the
Kalenders
,
in
the
head
of
all
the
Monethes
is
written
,
that
the
dayes
haue
in
euery
Moneth
,
so
many
hours
,
and
the
night
so
many
.
Of
this
is
to
be
vnderstood
,
that
neyther
the
dayes
are
equall
in
all
the
Moneth
,
nor
the
number
of
the
houres
are
one
in
all
places
.
For
in
the
citie
of
Ceuill
,
the
dayes
are
of
one
quantitie
,
and
in
Toledo
,
of
another
,
&
in
Burgus
another
,
and
so
proceeding
to
the
place
where
the
daye
is
of
24.
houres
:
so
that
the
dayes
of
euerye
Moneth
be
not
equall
in
houres
,
nor
the
dayes
bee
not
equall
in
all
partes
,
the
cause
is
,
as
the
sunne
maketh
difference
from
one
Moneth
to
another
in
comming
neere
,
or
going
from
the
Equinoctiall
line
,
so
the
daies
goe
increasing
or
diminishing
this
comming
neere
,
or
going
away
of
the
sun
,
he
doth
it
not
alwaies
alike
,
but
he
doth
it
in
this
manner
.
From
the
12.
of
Marche
,
that
hee
goeth
foorth
of
the
Equinoctiall
,
he
beginneth
to
rise
vp
,
by
the
part
of
the
north
,
from
thence
vntill
the
12.
of
Aprill
,
hee
hath
gone
from
the
saide
line
,
12.
degrees
,
and
from
the
12.
of
Aprill
,
to
the
12.
of
May
,
he
hath
gone
distant
other
8.
degrees
,
&
from
the
12.
of
May
,
to
the
11.
of
June
,
which
hee
commeth
to
the
Tropike
,
hee
goeth
distant
other
three
degrees
and
a
halfe
,
whiche
are
in
all
23.
degrees
and
a
halfe
,
whiche
the
sunne
hath
of
declination
or
distance
,
from
the
saide
line
,
in
such
sort
,
that
the
first
Moneth
hee
goeth
distant
,
the
halfe
of
the
said
declination
,
and
the
seconde
Moneth
the
thirde
parte
,
and
the
thirde
,
the
sixt
part
,
and
so
in
the
increasing
of
the
dayes
.
The
11.
of
Marche
,
the
daies
&
nightes
are
equall
,
and
from
thence
to
the
11.
of
Aprill
,
the
day
increaseth
halfe
of
all
the
time
that
hee
will
increase
,
&
from
the
12.
of
Aprill
,
to
the
12.
of
May
,
he
increaseth
the
thirde
parte
,
and
from
the
12
of
May
to
the
11.
of
June
,
hee
increaseth
the
sixt
part
,
whereby
that
in
the
straight
course
,
where
the
greatest
day
hath
15
:
houres
,
the
12.
of
March
,
it
hath
12.
and
the
12.
of
Aprill
,
13.
&
a
halfe
,
and
the
12.
of
May
14.
and
a
halfe
,
and
to
the
11.
of
June
15.
And
by
this
reason
in
the
straight
course
,
where
the
greatest
day
hath
16.
houres
,
and
in
him
where
hee
hath
14.
or
more
,
or
lesse
:
the
12.
of
May
,
or
in
any
other
day
,
except
in
the
Equinoctials
,
the
dayes
will
not
bee
equall
,
but
one
wil
be
greater
then
another
,
in
suche
sorte
,
that
the
day
hath
more
increased
to
them
which
haue
16.
houres
then
to
them
which
haue
foureteene
,
so
that
such
as
haue
sixeteene
,
the
twelfth
of
May
,
the
day
hath
increased
two
houres
,
and
to
such
as
haue
foureteene
,
it
hath
not
increased
more
then
one
,
And
as
the
day
went
increasing
at
the
rising
vp
of
the
sunne
,
so
hee
returneth
diminishing
or
decreasing
,
when
hee
descendeth
.
And
so
the
reckoning
ought
to
bee
kepte
in
all
partes
,
according
to
the
quantitie
of
the
time
and
houres
,
whiche
the
greatest
day
hath
.
And
it
is
to
bee
noted
,
that
howe
much
the
day
increaseth
of
twelue
houres
vpwarde
:
so
much
hee
decreaseth
of
twelue
houres
downward
,
therfore
to
knowe
the
quantitie
of
houres
,
and
points
,
that
the
greatest
day
of
the
yeere
hath
in
euery
degree
of
distance
of
the
Equinoctiall
line
:
In
the
table
hereafter
written
,
shal
bee
declared
,
the
which
is
likewise
to
bee
vnderstood
for
the
part
of
the
South
,
as
for
the
part
of
the
North.
And
it
is
to
be
knowen
what
day
it
is
called
in
this
reckoning
from
the
time
that
halfe
the
body
of
the
sun
riseth
,
vntill
the
other
half
be
set
,
&
all
the
other
is
night
,
also
the
houres
or
parts
of
the
day
are
not
vnderstood
by
the
twelfth
part
of
the
day
,
or
of
the
night
,
but
by
these
vulgar
things
of
the
clocke
,
for
by
another
name
they
are
called
Equinoctials
:
for
in
euery
one
of
them
riseth
fifteene
degrees
of
the
Equinoctiall
,
&
other
fifteene
setteth
.
And
likewise
it
is
to
bee
vnderstood
,
that
in
this
account
threescore
points
or
minutes
doe
make
an
houre
,
&
thirtie
,
half
an
houre
.
And
so
of
the
rest
.
A
Table
of
the
houres
,
and
minutes
which
the
greatest
day
of
the
yeere
hath
,
to
such
as
inhabite
in
any
manner
of
distance
of
the
Equinoctiall
.
Deg.
|
Hour
.
|
Minut.
|
Deg.
|
Hour
.
|
Minut.
|
Degrees
|
Houres
|
Minuts
.
|
1
|
12
|
1
|
23
|
13
|
27
|
45
|
15
|
27
|
2
|
12
|
3
|
24
|
13
|
30
|
46
|
15
|
33
|
3
|
12
|
5
|
25
|
13
|
34
|
47
|
15
|
40
|
4
|
12
|
8
|
26
|
13
|
39
|
48
|
15
|
50
|
5
|
12
|
12
|
27
|
13
|
43
|
49
|
16
|
2
|
6
|
12
|
17
|
28
|
13
|
48
|
50
|
16
|
11
|
7
|
12
|
21
|
29
|
13
|
52
|
51
|
16
|
22
|
8
|
12
|
25
|
30
|
13
|
57
|
52
|
16
|
34
|
9
|
12
|
29
|
31
|
14
|
2
|
53
|
16
|
45
|
10
|
12
|
34
|
32
|
14
|
7
|
54
|
17
|
0
|
11
|
12
|
40
|
33
|
14
|
12
|
55
|
17
|
15
|
12
|
12
|
45
|
34
|
14
|
17
|
56
|
17
|
30
|
13
|
12
|
49
|
35
|
14
|
22
|
57
|
17
|
45
|
14
|
12
|
54
|
36
|
14
|
27
|
58
|
18
|
0
|
15
|
12
|
57
|
37
|
14
|
32
|
59
|
18
|
20
|
16
|
13
|
0
|
38
|
14
|
38
|
60
|
18
|
40
|
17
|
13
|
4
|
39
|
14
|
45
|
61
|
19
|
0
|
18
|
13
|
7
|
40
|
14
|
52
|
62
|
19
|
30
|
19
|
13
|
11
|
41
|
14
|
59
|
63
|
20
|
0
|
20
|
13
|
15
|
42
|
15
|
6
|
64
|
21
|
0
|
21
|
13
|
19
|
43
|
15
|
12
|
65
|
22
|
0
|
22
|
13
|
23
|
44
|
15
|
19
|
66
|
23
|
0
|
66m
|
24
|
0
|
The
sixt
Chapter
,
of
the
houres
,
pointes
or
minutes
,
that
euery
day
of
the
yeere
hath
in
the
altitude
of
fortie
degrees
.
IN
the
table
before
written
,
hath
beene
declared
the
number
of
the
houres
and
minutes
,
or
points
that
the
greatest
day
of
the
yeere
hath
in
any
manner
of
distance
,
of
the
Equinoctiall
line
,
and
because
it
is
likewise
profitable
,
to
knowe
the
houres
&
points
,
that
successiuely
,
euery
day
in
the
yeere
,
hath
in
euery
parte
.
But
for
to
make
this
apparant
,
to
al
persons
,
it
were
needfull
to
haue
many
tables
.
Therefore
this
is
only
taken
out
for
the
altitude
of
fortie
degrees
,
where
the
greatest
day
hath
foureteene
houres
&
,
and
fiftie
two
minutes
,
which
are
well
neere
fifteene
houres
.
For
in
this
altitude
,
is
the
middest
of
Spayne
,
so
that
with
little
difference
or
more
or
lesse
,
it
may
serue
in
all
Spayne
.
In
the
other
partes
may
bee
taken
out
the
reckoning
,
according
to
the
greatnesse
of
the
greatest
day
,
agreeable
to
the
Table
before
written
.
Ianuarie
.
|
Februarie
.
|
March
.
|
Daies
|
Houres
|
Points
|
Daies
|
Houres
|
Points
|
Daies
|
Houres
|
Points
|
1
|
9
|
22
|
1
|
10
|
22
|
1
|
11
|
34
|
2
|
9
|
23
|
2
|
10
|
24
|
2
|
11
|
36
|
3
|
9
|
24
|
3
|
10
|
26
|
3
|
11
|
39
|
4
|
9
|
25
|
4
|
10
|
29
|
4
|
11
|
43
|
5
|
9
|
26
|
5
|
10
|
3
|
5
|
11
|
44
|
6
|
9
|
28
|
6
|
10
|
34
|
6
|
11
|
47
|
7
|
9
|
30
|
7
|
10
|
37
|
7
|
11
|
50
|
8
|
9
|
32
|
8
|
10
|
40
|
8
|
11
|
53
|
9
|
9
|
34
|
9
|
10
|
42
|
9
|
11
|
56
|
10
|
9
|
36
|
10
|
10
|
44
|
10
|
11
|
59
|
11
|
9
|
38
|
11
|
10
|
46
|
11
|
12
|
2
|
12
|
9
|
40
|
12
|
10
|
48
|
12
|
12
|
4
|
13
|
9
|
42
|
13
|
10
|
50
|
13
|
12
|
8
|
14
|
9
|
44
|
14
|
10
|
53
|
14
|
12
|
11
|
15
|
9
|
46
|
15
|
10
|
56
|
15
|
12
|
14
|
16
|
9
|
48
|
16
|
10
|
59
|
16
|
12
|
16
|
17
|
9
|
50
|
17
|
11
|
4
|
17
|
12
|
18
|
18
|
9
|
52
|
18
|
11
|
7
|
18
|
12
|
21
|
19
|
9
|
54
|
19
|
11
|
10
|
19
|
12
|
24
|
20
|
9
|
57
|
20
|
11
|
12
|
20
|
12
|
26
|
21
|
9
|
0
|
21
|
11
|
15
|
21
|
12
|
29
|
22
|
10
|
2
|
22
|
11
|
18
|
22
|
12
|
32
|
23
|
10
|
4
|
23
|
11
|
20
|
23
|
12
|
35
|
24
|
10
|
6
|
24
|
11
|
23
|
24
|
12
|
37
|
25
|
10
|
8
|
25
|
11
|
26
|
25
|
12
|
39
|
26
|
10
|
10
|
26
|
11
|
28
|
26
|
12
|
41
|
27
|
10
|
12
|
27
|
11
|
30
|
27
|
12
|
43
|
28
|
10
|
15
|
28
|
11
|
32
|
28
|
12
|
45
|
29
|
10
|
46
|
|
|
|
29
|
12
|
48
|
30
|
10
|
18
|
|
|
|
30
|
12
|
50
|
31
|
10
|
20
|
|
|
|
31
|
12
|
53
|
Aprill
.
|
May
.
|
Iune
.
|
Daies
|
Houres
|
Points
|
Daies
|
Houres
|
Points
|
Daies
|
Houres
|
Points
|
1
|
12
|
56
|
1
|
14
|
4
|
1
|
14
|
47
|
2
|
12
|
59
|
2
|
14
|
6
|
2
|
14
|
47
|
3
|
13
|
2
|
3
|
14
|
8
|
3
|
14
|
48
|
4
|
13
|
4
|
4
|
14
|
10
|
4
|
14
|
48
|
5
|
13
|
6
|
5
|
14
|
12
|
5
|
14
|
49
|
6
|
13
|
9
|
6
|
14
|
14
|
6
|
14
|
49
|
7
|
13
|
12
|
7
|
14
|
16
|
7
|
14
|
49
|
8
|
13
|
14
|
8
|
14
|
18
|
8
|
14
|
50
|
9
|
13
|
16
|
9
|
14
|
20
|
9
|
14
|
50
|
10
|
13
|
18
|
10
|
14
|
22
|
10
|
14
|
51
|
11
|
13
|
20
|
11
|
14
|
24
|
11
|
14
|
52
|
12
|
13
|
22
|
12
|
24
|
26
|
12
|
14
|
52
|
13
|
13
|
24
|
13
|
14
|
27
|
13
|
14
|
52
|
14
|
13
|
26
|
14
|
14
|
28
|
14
|
14
|
51
|
15
|
13
|
28
|
15
|
14
|
29
|
15
|
14
|
50
|
16
|
13
|
31
|
16
|
14
|
30
|
16
|
14
|
50
|
17
|
13
|
34
|
17
|
14
|
32
|
17
|
14
|
49
|
18
|
13
|
36
|
18
|
14
|
33
|
18
|
14
|
49
|
19
|
13
|
39
|
19
|
14
|
34
|
19
|
14
|
48
|
20
|
13
|
42
|
20
|
14
|
36
|
20
|
14
|
48
|
21
|
13
|
44
|
21
|
14
|
38
|
21
|
14
|
47
|
22
|
13
|
46
|
22
|
14
|
39
|
22
|
14
|
47
|
23
|
13
|
48
|
23
|
14
|
40
|
23
|
14
|
46
|
24
|
13
|
50
|
24
|
14
|
41
|
24
|
14
|
46
|
25
|
13
|
52
|
25
|
14
|
42
|
25
|
14
|
45
|
26
|
13
|
54
|
26
|
14
|
43
|
26
|
14
|
45
|
27
|
13
|
56
|
27
|
14
|
44
|
27
|
14
|
44
|
28
|
13
|
58
|
28
|
14
|
45
|
28
|
14
|
43
|
29
|
14
|
|
29
|
14
|
45
|
29
|
14
|
42
|
30
|
14
|
2
|
30
|
14
|
46
|
30
|
14
|
41
|
|
|
|
31
|
14
|
46
|
|
|
|
Iulie
.
|
August
.
|
September
.
|
Daies
|
Houres
|
Points
|
Daies
|
Houres
|
Points
|
Daies
|
Houres
|
Points
|
1
|
14
|
40
|
1
|
13
|
50
|
1
|
12
|
38
|
2
|
14
|
39
|
2
|
13
|
48
|
2
|
12
|
33
|
3
|
14
|
38
|
3
|
13
|
46
|
3
|
12
|
29
|
4
|
14
|
37
|
4
|
13
|
44
|
4
|
12
|
26
|
5
|
14
|
36
|
5
|
13
|
42
|
5
|
12
|
23
|
6
|
14
|
35
|
6
|
13
|
39
|
6
|
12
|
19
|
7
|
14
|
34
|
7
|
13
|
36
|
7
|
12
|
17
|
8
|
14
|
33
|
8
|
13
|
34
|
8
|
12
|
15
|
9
|
14
|
31
|
9
|
13
|
32
|
9
|
12
|
11
|
10
|
14
|
30
|
10
|
13
|
30
|
10
|
12
|
7
|
11
|
14
|
28
|
11
|
13
|
28
|
11
|
12
|
4
|
12
|
14
|
26
|
12
|
23
|
26
|
12
|
12
|
2
|
13
|
14
|
25
|
13
|
13
|
24
|
13
|
12
|
0
|
14
|
14
|
24
|
14
|
13
|
22
|
14
|
11
|
59
|
15
|
14
|
22
|
15
|
13
|
20
|
15
|
11
|
57
|
16
|
14
|
20
|
16
|
13
|
18
|
16
|
11
|
55
|
17
|
14
|
18
|
17
|
13
|
16
|
17
|
11
|
52
|
18
|
14
|
16
|
18
|
13
|
14
|
18
|
11
|
49
|
19
|
14
|
14
|
19
|
13
|
12
|
19
|
11
|
46
|
20
|
14
|
12
|
20
|
13
|
9
|
20
|
11
|
44
|
21
|
14
|
10
|
21
|
13
|
6
|
21
|
11
|
41
|
22
|
14
|
8
|
22
|
13
|
4
|
22
|
11
|
38
|
23
|
14
|
6
|
23
|
13
|
1
|
23
|
11
|
36
|
24
|
14
|
4
|
24
|
12
|
59
|
24
|
11
|
33
|
25
|
14
|
2
|
25
|
12
|
56
|
25
|
11
|
30
|
26
|
14
|
1
|
26
|
12
|
53
|
26
|
11
|
28
|
27
|
14
|
0
|
27
|
12
|
50
|
27
|
11
|
25
|
28
|
13
|
59
|
28
|
12
|
48
|
28
|
11
|
22
|
29
|
13
|
58
|
29
|
12
|
46
|
29
|
11
|
20
|
30
|
13
|
56
|
30
|
12
|
43
|
30
|
11
|
17
|
31
|
13
|
54
|
31
|
12
|
40
|
|
|
|
October
.
|
Nouember
.
|
December
.
|
Daies
|
Houres
|
Points
|
Daies
|
Houres
|
Points
|
Daies
|
Houres
|
Points
|
1
|
11
|
15
|
1
|
10
|
|
1
|
9
|
15
|
2
|
11
|
12
|
2
|
9
|
58
|
2
|
9
|
15
|
3
|
11
|
9
|
3
|
9
|
56
|
3
|
9
|
14
|
4
|
11
|
6
|
4
|
9
|
54
|
4
|
9
|
14
|
5
|
11
|
4
|
5
|
9
|
52
|
5
|
9
|
13
|
6
|
11
|
1
|
6
|
9
|
50
|
6
|
9
|
12
|
7
|
10
|
58
|
7
|
9
|
34
|
7
|
9
|
11
|
8
|
10
|
56
|
8
|
9
|
46
|
8
|
9
|
11
|
9
|
10
|
53
|
9
|
9
|
44
|
9
|
9
|
10
|
10
|
10
|
50
|
10
|
9
|
4●
|
10
|
9
|
9
|
11
|
10
|
48
|
11
|
9
|
40
|
11
|
9
|
9
|
12
|
10
|
46
|
12
|
9
|
38
|
12
|
9
|
8
|
13
|
10
|
44
|
13
|
9
|
36
|
13
|
9
|
8
|
14
|
10
|
42
|
14
|
9
|
34
|
14
|
9
|
8
|
15
|
10
|
39
|
15
|
9
|
33
|
15
|
9
|
9
|
16
|
10
|
36
|
16
|
9
|
32
|
16
|
9
|
9
|
17
|
10
|
34
|
17
|
9
|
30
|
17
|
9
|
10
|
18
|
10
|
31
|
18
|
9
|
28
|
18
|
9
|
10
|
19
|
10
|
29
|
19
|
9
|
26
|
19
|
9
|
11
|
20
|
10
|
26
|
20
|
9
|
24
|
20
|
9
|
12
|
21
|
10
|
23
|
21
|
9
|
23
|
21
|
9
|
13
|
22
|
10
|
20
|
22
|
9
|
22
|
22
|
9
|
13
|
23
|
10
|
18
|
23
|
9
|
21
|
23
|
9
|
14
|
24
|
10
|
16
|
24
|
9
|
20
|
24
|
9
|
14
|
25
|
10
|
14
|
25
|
9
|
19
|
25
|
9
|
15
|
26
|
10
|
12
|
26
|
9
|
18
|
26
|
9
|
16
|
27
|
10
|
10
|
27
|
9
|
17
|
27
|
9
|
17
|
28
|
10
|
8
|
28
|
9
|
17
|
28
|
9
|
18
|
29
|
10
|
6
|
29
|
9
|
16
|
29
|
9
|
19
|
30
|
10
|
4
|
30
|
9
|
16
|
30
|
9
|
20
|
31
|
10
|
2
|
|
|
|
31
|
9
|
21
|
The
seuenth
Chapter
,
of
the
houre
,
and
point
which
the
sunne
riseth
,
and
setteth
in
euery
one
day
of
the
yere
.
ANd
seeing
there
hath
bin
declared
in
the
Chapter
going
before
,
the
houres
,
and
minutes
which
euery
day
hath
,
it
is
conuenient
to
speake
in
this
at
what
houre
and
minute
the
sunne
riseth
and
setteth
,
in
euery
day
of
the
yeere
:
for
the
which
first
of
all
,
it
is
to
be
noted
,
that
for
to
take
out
the
houre
when
the
sun
shall
rise
,
is
to
be
reckoned
from
xii
.
of
the
clocke
in
the
night
.
And
the
houre
when
it
shall
set
,
is
to
be
reckoned
from
xii
.
of
the
clocke
in
the
day
.
Therfore
looke
ouer
the
houres
and
pointes
which
the
sunne
hath
,
and
deuide
them
in
the
middest
,
&
that
which
one
half
doth
amount
to
,
take
it
out
of
twelue
,
and
that
which
remaineth
shal
be
the
houre
,
wherin
the
sunne
riseth
,
and
the
same
halfe
shal
bee
the
houre
wherin
the
sunne
setteth
,
so
that
for
when
hee
riseth
take
out
of
xii
.
half
of
the
number
which
the
day
hath
:
And
to
that
which
remaineth
,
is
the
point
,
where
the
sunne
riseth
and
setteth
him self
after
the
middest
of
the
day
,
at
the
point
which
is
halfe
of
the
number
that
the
day
hath
.
An
example
.
The
first
day
of
Januarie
,
hee
hath
niene
houres
,
and
xxii
.
points
,
halfe
this
is
iiii
.
houres
,
and
fourtie
one
pointes
,
therefore
these
foure
houres
,
and
fourtie
one
pointes
,
taken
out
of
xii
.
houres
,
remaineth
vii
.
houres
&
nienteene
points
,
and
so
the
first
day
of
Januarie
,
the
sun
commeth
forth
at
vii
.
of
the
clocke
,
and
nienteene
pointes
after
midnight
,
and
setteth
at
foure
of
the
clocke
,
and
fourtie
one
points
,
after
the
middest
of
the
day
,
which
was
halfe
the
number
that
the
day
hath
.
The
eyght
Chapter
,
howe
the
sunne
giueth
his
light
at
equal
time
of
the
yeere
to
such
as
inhabite
in
the
worlde
.
IN
the
rules
and
accounts
beefore
declared
,
there
might
bee
a
doubt
saying
,
seeing
that
in
some
parts
of
the
world
,
The
dayes
be
great
,
and
in
other
partes
litle
,
let
vs
see
if
in
any
one
part
of
the
world
the
sunne
shineth
in
al
the
yeere
more
time
then
in
other
.
To
this
is
to
be
noted
,
that
although
it
bee
true
,
that
in
some
part
of
the
world
,
&
times
of
the
yeere
,
the
dayes
&
nights
be
greater
then
in
other
some
,
it
is
to
be
taken
,
that
the
sunne
by
his
owne
mouing
,
that
hee
maketh
in
the
yeere
,
at
equal
time
of
the
yeere
is
seene
and
giueth
light
in
all
partes
,
so
that
as
long
time
of
the
yeere
he
is
seene
in
the
part
where
the
dayes
be
little
,
as
in
the
part
where
they
bee
great
,
the
which
is
knowen
in
this
manner
,
consider
that
which
euery
part
hath
in
it
,
of
the
day
,
and
that
which
it
hath
of
the
night
in
this
manner
,
such
as
inhabite
vnder
the
equinoctiall
,
as
they
haue
continually
,
the
dayes
equall
with
the
nights
,
euery
one
of
them
xii
.
houres
,
it
is
certaine
that
halfe
the
time
of
the
yere
they
haue
day
,
and
they
see
the
sun
,
and
he
sheweth
light
to
them
,
and
the
other
half
they
haue
night
,
that
they
see
him
not
,
and
such
as
dwell
in
fourtie
and
two
degrees
which
haue
the
greatest
day
of
xv
houres
,
they
haue
also
day
of
niene
houres
,
and
so
as
the
day
goeth
increasing
from
xii
.
to
xv
.
houres
,
so
they
come
decreasing
vnto
niene
,
in
such
sorte
that
the
said
time
,
which
they
haue
of
day
,
the
same
they
haue
of
night
,
so
consequently
those
which
inhabite
in
sixtie
degrees
which
haue
the
greatest
day
of
xx
.
houres
,
they
haue
likewise
day
of
foure
houres
,
and
as
the
sunne
goeth
lighting
of
them
,
&
the
daies
increasing
vnto
twentie
houres
,
likewise
they
goe
decreasing
vntill
the
day
be
no
more
but
iiii
.
houres
,
and
the
night
goeth
increasing
and
diminishing
the
like
.
And
of
those
which
inhabite
in
sixty
sixe
degrees
and
a
half
,
haue
the
greatest
day
of
twentie
foure
houres
,
likewise
they
haue
night
of
the
said
xxiiii
.
houres
,
and
such
as
haue
day
of
one
moneth
without
night
,
haue
likewise
a
moneth
of
night
without
day
,
and
such
as
shoulde
haue
sixe
monethes
of
day
without
night
,
shoulde
haue
other
sixe
monethes
of
night
without
day
,
and
so
the
time
beeing
considered
which
euery
part
hath
of
day
,
and
being
seene
,
that
as
much
iustly
it
hath
of
night
:
So
shal
be
founde
that
not
onely
in
the
torrida
zona
,
by
the
which
the
sunne
continually
moueth
,
but
likewise
in
the
other
partes
very
distant
and
farre
off
,
and
also
vnder
the
poles
them selues
,
so
long
time
of
the
yeere
it
is
that
the
sunne
is
seene
,
as
the
time
that
he
is
not
seen
,
in
such
sort
,
that
the
sunne
giueth
his
light
in
equall
time
in
all
parts
,
and
not
in
one
more
then
in
another
.
So
the
omanipotent
God
,
maker
of
the
heauens
,
of
the
earth
,
&
of
all
that
is
in
them
,
did
dispose
and
ordeine
,
whose
name
be
blessed
,
in
the
worlden
worldes
.
Amen
.
The
ende
of
this
booke
of
Nauigation
.
God
saue
the
Queene
.