A
FRIEND
OF
NAVIGATJON
.
CHAP.
I.
Of
the
Cosm●graphicall
discription
of
the
World.
THat
which
the
onely
wise
God
made
f●●
mans
behoofe
,
euen
all
the
world
of
nothing
,
Genesis
the
first
,
is
said
to
be
round
by
all
moderne
Writers
:
it
is
proued
by
reason
,
and
the
holy
Scripture
saith
it
,
Psal.
98.
It
was
diuided
in
two
parts
by
the
same
God
,
the
part
seene
,
and
the
part
vnseene
:
But
by
faith
search
the
Scriptures
,
there
is
the
part
and
vse
in
this
our
Christian
Nauigation
discouered
.
The
part
seene
is
well
defined
to
bee
a
Booke
,
In
which
wee
may
see
and
learns
to
praise
God
in
his
workes
.
And
is
said
to
bee
of
two
parts
,
Celestiall
,
and
Elementall
:
In
the
Celestiall
part
may
be
considered
the
Arts
,
as
Musicke
,
the
harmony
of
the
Spheres
:
of
Soule
and
Body
,
for
whose
health
Phisicke
is
next
,
in
which
we
consider
that
Miraculous
Medicine
of
preseruing
life
,
be
it
Philosopher
stone
,
Salt
,
Virgin-earth
,
or
other
denomination
,
or
Mathematicall
,
as
the
knowledge
of
Points
,
Lines
,
Circles
,
Signes
,
Constelations
,
Planets
,
and
their
Influence
and
power
ouer
bodies
Elementall
.
It
may
be
said
and
that
by
good
reason
,
I
should
begin
at
the
Centor
of
the
Earth
,
&
so
consider
of
the
things
contained
therein
,
with
the
Sea
,
The
face
of
the
Earth
and
Sea
,
and
the
things
thereon
;
The
Aire
couering
the
other
two
,
and
the
Fire
inclosing
them
all
,
making
one
round
body
of
these
Elementall
parts
,
being
as
a
Centor
to
the
rest
,
and
so
p●●●e
vpwards
vnto
the
first
m●●●er
,
shewing
the
relation
and
agreement
they
haue
together
,
I
liuing
now
nearer
the
Centor
of
the
Earth
(
as
it
is
obserued
)
by
many
thousand
miles
.
But
if
I
end
my
worke
so
high
may
bee
proud
(
as
some
are
)
or
dazelled
in
the
Celestiall
brightnesse
,
being
mortall
,
be
cast
downe
with
Pl●●●●
.
In
the
name
of
God
therefore
,
and
in
his
feare
,
I
will
begin
with
the
first
mouer
,
which
going
with
great
violence
,
turneth
the
whole
frame
of
the
heauen
within
it
,
round
in
24.
houres
,
from
East
to
West
:
Which
heauen
is
said
to
haue
no
impression
in
it
,
being
almost
invisible
,
yet
carrying
the
light
and
darknesse
,
making
differ●nce
of
time
in
daies
and
nights
,
according
to
the
difference
of
Longitude
and
Latitude
of
places
on
Earth
.
In
it
are
all
the
circles
and
points
in
the
whole
fabricke
of
the
world
said
to
be
described
,
their
plaines
defending
and
meeting
in
the
Centor
of
the
Earth
,
or
on
their
other
Centors
.
The
two
principall
points
,
are
the
two
poles
of
the
world
,
the
North
pole
eliuated
with
vs
heere
at
London
51.
degrees
,
30.
or
there
about
;
and
the
South
pole
is
right
opposite
to
it
.
Therefore
depressed
iust
as
much
(
vnder
the
horizon
of
which
I
will
speake
anon
.
)
These
〈◊〉
points
are
fixed
fast
and
vnmoueable
,
betweene
which
and
through
the
Centor
of
the
Earth
,
there
passeth
▪
right
line
,
which
is
called
the
Axe-tree
of
the
world
on
which
it
turneth
.
Now
we
must
consider
both
this
right
line
,
and
all
other
right
lines
,
cords
,
signes
,
great
circles
and
paralels
,
to
be
diuided
into
360.
degrees
,
each
degree
subdiuided
into
60.
minutes
,
each
minute
into
60.
Seconds
,
each
Second
in
60.
thirds
,
&c.
as
the
case
may
require
.
The
Herman
is
a
great
circle
,
whose
Centor
is
in
the
middest
of
the
Earth
,
and
his
plaine
reacheth
not
onely
to
the
face
of
the
Earth
,
diuiding
the
vpper
part
from
the
lower
,
the
day
from
the
nights
●ut
through
the
Or●e●
of
the
planits
and
fixed
starres
,
euen
to
the
first
mouer
.
This
circle
hath
two
poles
,
one
is
called
Zon●th
,
and
is
right
ouer
our
head
,
from
the
which
if
a
right
line
passe
through
the
Center
of
the
Earth
,
touching
the
concaue
superficies
of
the
first
Mouer
,
it
pointeth
out
the
other
Pole
,
called
Mador
.
In
this
Circle
we
count
the
Amplitude
of
the
Sunne
or
Starres
;
and
the
Point
of
the
Compasse
or
Wind.
All
the
Circles
called
Azimuthes
,
crosse
the
Horizon
at
Rectangles
and
passe
through
the
Poles
thereof
:
His
Parallels
are
Circle●
of
Altitude
,
in
which
are
obserued
the
position
of
the
Planets
and
fixed
Starres
aboue
the
Earth
,
at
all
howres
of
the
day
or
night
:
Or
Circles
of
Depresion
diuiding
the
length
of
twilight
.
The
Equator
is
a
great
Circle
,
deuiding
the
World
into
two
equall
parts
,
the
North
part
and
the
South
:
His
parallels
sets
out
the
Latitude
of
places
on
Earth
,
and
declination
in
the
Heauens
.
All
the
Meridians
doe
crosse
the
Equator
at
Rectangles
and
go
through
the
Poles
of
the
World.
On
this
is
counted
the
Longitude
of
places
on
the
Earth
or
Sea
:
For
euerie
4
of
equall
time
made
by
the
equall
motion
of
the
Equator
doth
make
1
degree
.
And
7
deg.
30
min.
of
Longitude
,
either
East
or
West
,
doth
cause
●
houre
difference
in
time
of
day
or
night
,
and
they
that
dwell
15
,
or
30
deg.
East
haue
it
12
or
11
a
clocke
,
when
we
haue
it
10
or
11
,
and
those
that
dwell
so
much
West
of
vs
,
haue
it
10
or
11
when
it
is
midnight
with
vs
.
These
that
dwell
at
the
East
part
of
our
Horison
haue
it
noone
when
it
is
but
6
in
the
morning
with
vs
,
and
when
it
is
noone
with
vs
,
it
is
6
at
night
with
them
,
but
with
them
in
the
West
part
of
our
Horizon
it
is
6
in
the
morning
.
Our
Antipodes
haue
it
●oo●e
when
it
is
midnight
with
vs
,
and
when
it
is
Summer
with
vs
,
it
is
Winter
with
them
.
All
other
Circles
not
yet
named
are
likewise
supposed
to
bee
in
the
first
Heauen
,
as
in
the
rest
of
the
inferior
Orbes
of
which
we
suppose
11
after
Maginus
.
And
to
good
purpose
:
For
the
Lord
of
Heauen
and
Earth
hath
so
layd
the
Foundations
of
the
Earth
that
they
cannot
be
moued
,
Ps.
14.2
.
Though
Co●●●●●
to
bring
some
good
purpose
about
hath
imagined
so
.
Let
the
tenth
Heauen
be
(
if
you
please
)
the
Wa●ers
aboue
the
Firmament
,
for
ther
are
so
,
Gen.
1.6
,
7.
CHAP.
II.
Of
the
measure
of
the
heauens
THe
Zodiaque
is
a
great
broad
circle
crosing
the
heauens
,
like
a
b●n●●●re
or
girdle
,
of
12ᵈ.
broad
at
the
●east
;
in
the
midest
●hereof
is
a
little
circle
called
the
ecliptique
line
,
which
crosseth
the
Equator
at
two
opposit
points
,
swar●eth
from
it
23ᵈ.
30.
at
the
least
,
as
I
ha●e
●ound
by
obseruation
this
present
yeare
1627.
So
the
poles
of
the
Ecliptique
are
distant
from
the
poles
of
the
world
23ᵈ.
30.
by
reason
of
his
obliquitie
:
Betweene
which
poles
there
passeth
a
right
liue
or
Axetree
on
which
the
second
●ouer
or
tenth
heauen
is
carried
in
his
owne
motion
(
contrary
to
the
first
)
from
West
to
East
,
and
is
most
slowe
,
making
his
reuolution
in
3434
yeares
,
and
10.
daies
.
The
third
mouer
or
ninth
heauen
,
hath
his
two
poles
in
the
two
po●●ts
of
the
equator
and
ecliptique
,
and
his
motion
is
from
North
to
South
:
making
his
reuolution
in
1717.
yeares
and
5
daies
.
But
it
will
be
sufficient
for
our
necessary
vse
here
to
obserue
the
motion
of
the
8.
Sphere
,
wherein
are
all
the
Celestiall
bodies
of
the
fixed
Starres
placed
:
whose
motion
is
from
West
to
East
,
(
some
say
but
one
degree
in
100.
yeare
.
But
the
Planets
mone
in
their
Or●es
〈…〉
,
as
〈…〉
in
30.
yeare
,
♃
Iupiter
in
12.
yeares
,
♂
Mars
in
2.
yeare
,
●
Sol
in
one
yeare
,
♀
Venus
and
☿
Mercury
like
☉
,
Luna
☽
in
a
month
from
West
to
East
.
Diuers
learned
Mathematicions
haue
set
downe
the
magnitude
of
the
Starres
to
be
farre
bigger
then
the
earth
:
making
6.
differences
in
bignesse
be
sides
du●ke
and
obscure
.
The
Planets
also
are
said
to
be
of
〈◊〉
bignesses
and
distances
.
The
Orbe
of
♄
is
〈…〉
miles
,
and
his
distance
from
♃
78721
〈◊〉
The
Orbe
of
♃
189●●54●
m.
His
distance
to
♂
78721.
m.
That
of
●
2630●800
.
m.
his
distance
from
☉
15725.
m.
☉
343996
4/●
.
m.
His
distance
from
♀
23437
½
m.
The
Orbe
of
♀
3274494
6/12.
Her
distance
from
☿
12812.
m.
☿
Orbe
253372
●/●
.
m.
His
difference
from
☽
12812
,
The
☽
to
be
in
bignes
105222
●/11.
her
distance
from
the
earth
15750.
m.
♄
his
bignesse
compared
to
the
Earth
i●
as
95.
to
1.
and
his
distance
to
the
Firmament
2●0445
.
m.
〈◊〉
his
magnitude
to
the
Earth
is
a●
〈…〉
91.
to
●
.
And
♂
as
●
.
to
1.
And
the
distant
from
the
Fir●●ment
to
the
Earth
35
846
3½
.
m.
It
hath
appeared
manifestly
that
both
by
Sea
and
Land
,
who
so
trauaileth
60.
miles
on
a
great
Circle
,
altereth
a
degr●e
in
his
Trauaile
:
which
taketh
360.
times
tho
number
of
the
whole
circle
,
maketh
21600.
miles
the
conpasse
of
the
whole
Earthland
Sea
.
The
Diameter
then
will
be
6872
●/11.
the
semyd●amiter
3436
4/1●
m.
which
maketh
the
firmament
to
be
from
the
Center
of
the
Earth
361899●●/●
.
Therefore
it
seemeth
there
is
something
to
worke
vpon
to
measure
these
things
by
.
Likewise
I
may
say
,
considering
that
from
the
earth
to
the
Moone
is
15750.
miles
,
and
the
☽
is
the
lowest
Planet
.
Therefore
the
two
vppermost
elements
of
Ayre
and
Fire
are
both
together
15750
mi.
in
thicknesse
:
Againe
,
because
the
hill
Atlas
is
said
to
reach
to
the
midle
region
of
the
ayre
,
that
hill
(
which
I
take
to
be
Teneriffe
)
may
easily
be
measured
,
and
so
the
measure
of
all
the
rest
is
had
.
The
motion
of
the
Eclipticke
causeth
other
foure
circles
to
be
described
,
two
are
described
of
the
motion
of
the
Poles
therof
,
being
distant
from
the
●●●es
of
the
world
23.
degrees
30.
min.
making
two
round
circles
about
them
:
that
next
the
North
pole
is
called
the
circle
Articke
,
the
other
is
called
the
circle
Antarticke
.
The
other
two
are
described
by
the
motion
of
the
tow
.
Tropicall
points
of
the
eclipticke
,
that
on
the
North
side
of
the
equanox
is
called
the
tropicke
of
Cancer
,
the
other
is
called
the
tropicke
of
Capricorne
.
The
Zodiacke
is
diuided
in
12.
equall
parts
,
beginning
at
the
one
intersection
of
the
same
with
the
equanoctiall
circle
,
and
so
going
round
:
And
these
are
called
the
12.
signes
of
the
Zodiacke
,
for
as
much
as
they
extend
them
to
the
full
breadth
of
the
Zodiacke
,
and
are
the
cause
thereof
.
There
are
two
other
circles
also
of
speciall
vse
in
this
Art
,
one
is
the
Equinoctiall
colure
,
the
other
is
the
Solititiall
colure
:
These
two
are
great
circles
,
the
first
parteth
the
Equator
and
Zodiacke
euen
,
so
as
the
North
signes
are
from
the
South
signes
parted
by
the
first
point
of
the
first
signe
,
and
the
first
point
of
the
sca●outh
signe
:
and
these
signes
are
called
Aries
♈
,
and
Libra
♎
,
beginning
the
Spring
and
Autumne
,
the
other
passeth
by
the
two
tropicall
points
of
Cancer
♋
,
and
Capricorne
♑
,
making
the
beginning
of
Summer
and
winter
;
both
passing
through
the
poles
of
the
world
,
parting
the
Zodiacke
in
foure
equall
parts
,
and
the
equator
also
with
all
his
paralels
.
The
first
point
of
♈
,
beginneth
the
Spring
:
that
is
,
when
the
Sunne
in
his
motion
commeth
first
to
that
point
,
and
going
through
three
signes
♈
,
Taurus
♉
,
Gemini
♊
:
then
comming
to
the
first
point
of
♋
,
beginneth
the
Summer
:
and
passing
through
other
three
signes
♋
Leo
♌
,
Virgo
♍
,
so
commeth
to
Libra
♎
,
Scorpio
♏
,
Sagitarius
♐
,
to
the
first
point
of
♑
:
beginneth
the
winter
,
from
thence
through
♑
,
Aquarius
♒
,
Pisses
♓
making
the
whole
yeares
reuolution
.
And
these
12.
signes
are
called
Constellations
,
and
there
are
other
Constellations
,
some
North
,
some
South
,
in
which
is
had
a
number
of
Starres
bearing
names
,
according
to
their
nature
:
and
these
constellations
beare
rule
ouer
diuers
Regions
,
Countries
and
Cities
.
Now
we
may
passe
the
Orbes
of
the
other
superior
Planets
,
&
onely
note
their
friendly
aspect
as
we
passe
by
them
:
And
consider
the
☽
motion
with
the
☉
for
the
Eclipses
of
vse
,
for
finding
of
longitude
on
earth
or
Sea
.
Her
monthly
motion
,
full
change
and
quarters
,
for
the
ebbing
and
flowing
of
the
waters
,
spring
and
nepe
tides
:
her
aspect
with
the
planets
,
good
or
euill
,
for
Physicke
:
Her
place
in
the
Zodiacke
,
for
bloud
letting
either
for
Man
or
Beast
.
C●AP
.
III.
Of
the
Elements
.
FIre
is
the
most
noble
and
superiour
of
all
the
Elements
,
pure
,
subtle
,
most
spirituall
,
putting
heat
into
all
substances
,
lightsome
,
hauing
motion
Lionous
,
choloricke
.
Ayre
is
diuided
into
three
Regions
,
that
next
the
Fire
is
most
hot
,
that
in
the
middle
most
cold
,
vnto
the
which
some
hill
tops
doe
clime
,
as
hath
been
seene
,
the
lowest
is
that
in
which
wee
liue
,
the
Clouds
and
the
Fowles
doe
flye
,
which
God
of
his
mercy
make
wholesome
vnto
vs
.
God
said
let
the
waters
vnder
heauen
be
gathered
into
one
place
,
and
let
the
dry
land
appeare
,
Gen.
1.9
.
And
God
called
the
dry
land
Earth
,
and
the
gathering
together
of
the
waters
,
he
(
euen
God
)
called
Sea
,
ver
.
10.
Sea
,
which
together
with
the
earth
make
one
huge
massiue
body
,
round
,
as
may
be
proued
by
the
artificall
Globe
,
:
but
most
truely
by
a
perfect
Artsman
,
who
vsing
his
skill
in
his
Trauell
,
both
by
Sea
and
Land
,
is
able
to
salue
such
small
irrigularities
,
as
high
tydes
,
lowe
ebbes
,
high
Mountaines
lowe
Vallies
:
For
experience
is
the
mother
of
Acts
,
and
th●●●
〈◊〉
partly
conceiue
in
this
(
I
hauing
a
brother
in
Saint
Christophers
Isle
of
the
West
Indies
,
who
hath
sent
me
Letters
from
Meri●rs
Hope
there
)
I
went
to
Gresham
Colledge
in
London
of
purpose
to
looke
on
the
biggest
Terrestriall
Globe
they
had
,
and
found
such
an
I
le
to
lye
in
some
16.
deg.
of
North
Latitude
,
and
in
321
deg.
of
longitude
,
or
there
about
:
But
there
I
could
finde
neither
Cape
,
nor
Bay
,
Port
nor
Hauen
;
therefore
no
vniuersall
Map
will
serue
that
turne
:
And
Master
♄
,
being
there
with
mee
at
that
time
,
made
a
doubt
,
saying
:
How
know
I
that
Saint
Christophers
Ile
lyeth
there
except
I
had
seene
it
,
or
know
some
body
that
had
bin
there
?
meaning
no
doubt
some
Arts-man
,
who
(
I
confesse
)
may
not
onely
obserue
the
longitude
and
latitude
;
but
may
also
set
out
the
Capes
and
Bayes
,
Ports
,
Bounds
,
Riuers
,
and
giue
the
dimention
of
the
superficis
.
Of
the
innumerable
multitude
of
creatures
in
the
Sea
,
and
of
her
riches
,
I
will
not
speake
;
but
the
artificiall
making
and
vse
of
Shipping
therein
is
admirable
,
as
may
appeare
in
the
whole
Art
of
Nauigation
:
A
wonderfull
secret
thereof
is
the
variation
of
the
compasse
;
a
cause
thereof
is
imagined
to
be
the
hollownesse
of
the
Earth
or
depth
of
the
Sea
,
and
for
that
nature
abhorring
emptinesse
,
the
excellent
vertue
of
the
Load-stone
doth
alwayes
draw
towards
it
in
all
places
,
where
the
needle
being
touched
therewith
shall
draw
most
neere
;
but
I
thinke
it
is
a
speciall
gift
of
God
,
sent
for
mans
vse
,
but
farre
aboue
his
knowledge
.
Sea
and
earth
are
diuided
as
the
heauens
:
the
beginning
of
the
Equator
or
first
Meridian
being
with
Saint
Michael
and
Saint
Maries
Iles
,
the
circle
of
the
equator
passing
by
Saint
Thomas
I
le
,
Abasa●●●
,
the
famous
I
le
of
Sa●●●ta
,
B●rni●
,
Pap●os
,
New
Guinny
,
G●na●●s
,
and
fo
round
,
from
Meridian
to
Meridian
Eastward
we
count
Longitude
on
any
paralell
:
but
Latitude
is
counted
from
the
Equator
towards
the
Poles
of
the
World
on
the
Meridian
or
colure
.
The
Paralels
sets
out
the
Zones
and
Climates
.
Of
creatures
without
life
,
or
such
as
are
in
the
earth
onely
,
are
Gold
,
Siluer
,
precious
Stones
,
Minerals
,
Mettals
.
But
the
Bodies
which
shall
one
day
rise
againe
,
are
chiefely
to
be
considered
.
Of
Creatures
with
life
,
some
are
fixed
,
as
Plants
,
Hearbes
,
Flowers
,
Spices
,
Trees
,
bearing
fruit
,
without
fruit
.
Gen.
2.19
.
Out
of
the
ground
God
formed
beasts
and
fowles
:
and
in
another
place
it
is
said
All
flesh
is
grasse
.
Therefore
of
mouing
things
some
are
in
the
Earth
,
as
Wormes
,
Serpents
,
Moles
,
Co●●e●
:
some
in
the
Ayre
,
as
Fowles
:
in
the
Water
,
as
Fishes
.
Monsters
on
the
face
of
the
earth
,
as
all
manner
of
Beasts
and
Cattell
wilde
and
tame
.
The
most
excellent
thing
made
is
man
(
a
shame
for
him
to
become
so
wicked
)
Being
wonderfully
made
,
Psal.
139.
an
epitomy
of
the
whole
World
;
to
seeke
and
set
forth
Gods
glory
:
surely
flesh
and
bloud
cannot
set
forth
his
glory
,
whose
workes
doe
amaze
the
sences
of
the
most
learned
.
Therefore
be
not
proud
O
ye
learned
,
nor
vaineglorious
O
ye
wise
;
but
seeke
and
set
forth
Gods
glory
,
that
the
vnwise
and
vnlearned
,
may
see
,
marke
,
and
learne
:
and
be
incouraged
O
thou
that
art
ignorant
(
of
which
I
am
chiefe
)
to
see
the
workes
of
the
Lord
in
heauen
and
in
earth
,
and
his
wonders
in
the
deepe
Sea
,
Ps.
107.
CAHP.
IIII.
The
ground
of
the
Art
,
the
Instrument
,
Astronomycall
propositions
,
with
the
Geographicall
and
Hidrographicall
description
of
the
Earth
and
Sea
.
REason
doth
teach
,
and
this
36.
yeares
experience
I
haue
had
,
that
to
the
gaining
of
these
knowledges
,
quantitie
is
to
bee
considered
,
either
Geometrically
or
Arithmetically
,
or
most
vsually
of
both
together
.
Arithmeticke
is
the
Art
of
numbering
,
and
euery
number
is
expressed
by
certaine
Characters
,
figures
,
and
Ciphers
,
as
:
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
0.
or
:
2
●
.
3ᵈ.
30.
50.
20l
:
But
the
figures
and
Ciphers
whether
they
be
abstract
or
contract
,
haue
a
double
signification
to
expresse
them
,
which
is
called
their
numeration
,
Psal.
90.
ver.
12.
O
Lord
,
teach
vs
so
to
number
our
daies
,
that
we
may
apply
our
hearts
vnto
wisedome
.
Figures
do
either
signifie
themselues
onely
,
as
1.
is
one
,
2.
is
two
,
&c.
or
are
valued
according
to
their
place
:
Position
of
this
kinde
is
knowne
as
men
read
the
Hebrew
tongue
.
This
Art
giueth
the
numerall
solution
in
all
dementions
,
and
hath
these
kindes
:
Addition
,
Subtraction
,
Multiplication
,
Diuision
;
and
these
all
haue
a
diuers
property
in
their
vse
,
either
in
working
proportion
,
or
otherwise
.
Another
Arithmatique
there
is
(
not
of
numbers
)
but
of
parts
of
number
,
hauing
like
species
,
properties
and
passions
,
and
fetch
either
their
beginning
from
vnity
,
but
with
a
difference
,
for
as
number
increaseth
in
multitude
Infinitly
:
so
doe
Fractions
decreaseth
infinitly
but
most
commonly
,
as
in
this
worke
,
they
are
compound
:
for
if
I
take
in
account
of
Time
,
Motion
,
Measure
,
Signes
,
Degrees
,
Minut●
,
Seconds
,
&c.
As
in
reckoning
of
the
☽
place
,
Thus
:
suppose
the
☽
in
the
day
of
♂
to
be
in
the
first
degree
of
♈
;
and
a●
20.
daies
old
,
I
would
know
her
place
;
say
if
the
☽
go
in
one
day
12.
degrees
from
the
☉
,
and
the
☉
goe
each
day
one
degree
,
Therefore
the
☽
goes
in
20.
dayes
260ᵈ.
which
diuided
by
30ᵈ.
giueth
8
●
:
20ᵈ.
where
●
.
is
the
number
20
,
the
Fraction
,
and
his
place
the
20ᵈ.
of
Sagitarius
:
But
where
deg.
are
taken
for
numbers
,
there
Minuts
,
Seconds
,
Thirds
,
are
Fractions
:
as
15ᵈ.
to
an
houre
4.
to
a
degree
,
or
20ᵈ.
is
as
much
as
one
houre
20
:
or
20ᵈ.
50.
30.
is
as
much
as
1250
miles
½
:
and
generally
all
circles
and
paralels
,
are
numbered
with
these
kinde
of
Astronomicall
Fractions
or
numbers
.
Geometry
giueth
a
punctuall
termination
to
all
dementions
,
either
in
length
,
bredth
,
or
thicknesse
:
which
number
many
times
cannot
doe
;
as
in
diuiding
a
line
by
extreame
and
meane
proportion
.
But
number
and
parts
do
helpe
Geometry
to
expresse
the
quantitie
,
bee
it
in
length
,
bredth
,
or
thicknesse
.
Linne●●●mall
as
angles
right
lined
,
of
Sphericall
:
&
may
serue
to
tel
some
distance
〈…〉
Instruments
necessary
in
any
worke
,
are
of
necessity
,
and
to
this
worke
which
conteineth
so
many
Arts
,
it
may
be
obiected
that
one
poore
though
of
a
good
capassity
shall
be
neuer
able
to
attaine
.
Say
not
so
man
,
for
the
best
instrument
in
any
worke
is
a
willing
minde
:
Againe
,
shall
I
be
ashamed
to
indeuour
to
doe
well
,
because
some
more
learned
then
I
,
will
despise
my
simplicity
and
weakenesse
in
knowledge
?
No
sure
,
the
vertuous
will
commend
it
,
God
bee
thanked
there
are
as
many
good
Instruments
as
Arts
,
let
euery
man
bee
content
with
such
as
hee
hath
,
and
God
no
doubt
will
blesse
the
good
indeauours
of
the
godly
honest
.
2ˢ.
6ᵈ.
on
a
paire
of
Compasses
,
and
two
pence
on
a
straight
ruler
is
not
much
:
with
these
thou
maiest
beginne
in
spending
some
spare
houres
time
to
worke
thus
:
first
make
a
circle
,
diuid
it
in
360.
parts
,
or
¼
into
90
,
and
besides
abundance
of
necessary
conclusions
,
which
the
malicious
ignorant
will
not
beleeue
,
these
following
are
not
the
least
,
and
are
most
meet
to
be
knowne
:
Radius
or
any
signe
,
cord
,
arke
,
Tangent
,
Secant
,
great
circle
,
parralell
:
example
:
I
did
take
the
☉
height
,
May
the
26.
1627.
and
so
found
his
declination
22ᵈ.
30.
North
,
his
place
being
in
15d
d
♊
.
right
assention
,
61ᵈ.
30.
difference
assentionall
28ᵈ.
15.
height
of
the
North
pole
51ᵈ.
30.
Amplitude
37ᵈ.
30
North.
oblique
assention
33ᵈ.
15.
:
semydiurnall
arke
118ᵈ.
15.
semynocturnall
arke
61ᵈ.
45.
his
course
from
rising
to
his
setting
,
15
houres
40.
length
of
twilight
8
houres
14.
length
of
the
night
darke
0.
houre
.
Likewise
about
December
the
12.
1627.
☉
place
0
♑
merid
height
15ᵈ.
declination
23ᵈ.
30.
South
,
amplitude
40ᵈ.
30.
south
,
right
assention
270ᵈ.
oblique
assencion
298.
deg.
30
,
difference
assencional
28.
d.
30.
Likewise
may
the
fourth
1629.
suppose
the
sonnes
place
which
is
his
longitude
,
found
by
the
rules
before
going
to
be
53.
d.
or
the
23.
of
♉
.
in
the
latitude
of
51.
deg.
30.
min.
his
merid
.
height
is
found
by
these
rules
to
be
55.
deg.
declination
18.
deg.
north
,
amplitude
28.
north
,
right
assention
50.
deg.
oblique
27.
deg.
difference
assentionall
23.
deg.
semydiurnall
arke
7.
hou.
32.
min.
semynocturnall
arke
4.
hou.
28.
min.
length
of
twilight
2.
hou.
4.
min.
from
noone
to
euening
shut
in
9.
hou.
33.
min.
length
of
the
day
19.
hou.
6.
min.
night
darke
4.
hou.
54.
min.
Son
rise
at
4.
hou.
28.
m.
setteth
at
7
hou
.
and
32.
min.
Sun
aboue
the
Horizon
1●
hou.
4
min.
vnder
the
Horizon
8
hou.
56
min.
And
here
remember
,
that
,
The
workes
of
the
Lord
●p
g●●●●
sought
out
of
all
them
that
haue
pleasure
therein
.
Ps.
111.2
.
The
mercifull
and
gracious
Lord
hath
so
done
his
maruilous
workes
,
that
they
ought
to
be
had
in
remembrance
,
v.
4.
The
Lord
is
high
aboue
the
Heauens
,
Ps.
113.4
.
Who
is
like
the
Lord
our
God
,
that
hath
his
dwelling
so
high
,
and
y●●
humbleth
himselfe
to
behold
the
things
that
are
in
Heauen
and
in
Earth
,
v.
5.
He
taketh
the
simple
out
of
the
●●st
.
v.
6.
The
Heauens
declare
the
glorie
of
God
,
and
the
Fir●●●●●●
sheweth
his
handiworke
,
Ps.
19.1
.
As
Arcturius
Orio●
pleades
the
hiden
Chambers
of
the
South
,
the
great
Lauiathan
that
mo●eth
in
the
water
,
but
beyond
all
our
Redemption
in
Christ
,
God
commanded
Noah
to
build
an
Arke
,
and
to
build
Shiping
were
but
vaine
except
God
blesse
it
and
bee
the
Sea-mans
guide
.
Say
then
,
is
it
not
a
great
blessing
we
receiue
from
him
in
guiding
our
Ships
and
Selues
both
by
Sea
and
Land
with
such
excellent
Rules
of
Art
:
Surely
the
learned
in
the
Geographicall
,
Hidrographicall
and
Nauticall
Sciences
must
needs
confesse
it
,
especially
those
that
trauell
.
Neither
need
any
be
so
sottish
as
to
thinke
it
a
shame
to
spend
ten
min.
of
his
idle
time
euerie
day
to
some
such
good
purpose
,
which
may
add
him
more
comfort
perhaps
in
distresse
,
then
all
the
friends
in
the
world
besides
.
By
the
Seale
made
on
a
straight
Ruler
and
Compasses
distance
is
had
easily
without
measuring
to
them
,
for
make
a
Circle
and
diuide
it
in
foure
equall
parts
with
straight
lines
ouer
the
Centor
,
then
diuide
¼
in
two
equall
parts
,
and
ech
of
them
in
3
then
againe
these
subdiuision●
in
3
and
lastly
those
into
5
,
so
is
one
quarter
of
the
Circle
diuided
into
90
deg.
by
the
same
reason
you
may
diuide
a
right
line
as
your
Ruler
into
Foots
,
ech
Foot
into
Inches
or
Tenths
,
ech
10
into
●●
3.
4.
5.
7.
11.
12.
16.
20
parts
or
what
you
please
,
and
then
begin
to
worke
thus
,
Imagin
to
stand
on
some
Hill
as
at
High
〈◊〉
from
thence
to
all
the
highest
Hilles
round
about
you
cast
your
eye
,
and
by
your
Circle
diuided
you
may
take
the
quantitie
of
the
Angle
from
your
eye
to
the
two
next
Hilles
from
you
and
neerest
one
to
another
.
Suppose
that
Shutors
Hill
and
●urfleet
Hill
doe
make
an
Angle
of
1/●
of
the
quadrant
or
30
deg.
Or
Harrow
Hill
and
Saint
Albones
make
an
Angle
of
40
deg.
and
the
distance
between
High-gate
and
Shuters
Hill
to
be
10
mil.
more
or
lesse
,
and
from
High-gate
to
Harrow
12
mil.
you
shall
goe
to
Shuters
Hill
and
obserue
the
Angle
between
High-gate
and
Purfleet
,
be
it
right
or
oblique
,
acut
or
obtuse
make
2
lines
,
whereof
one
to
be
laid
downe
by
the
Scale
on
your
Ruler
of
the
iust
distance
between
your
2
first
stations
,
at
the
one
end
make
the
first
Angle
,
at
the
other
end
make
the
other
looking
one
towards
the
other
,
and
the
two
lines
continued
will
point
you
our
Purfleet
,
doe
so
by
the
other
and
it
will
point
you
out
Saint
Albones
,
then
by
your
Scale
you
may
know
their
distance
,
hauing
them
distances
you
may
easily
find
all
the
distances
and
angles
of
position
or
situation
of
all
the
Hilles
,
Townes
,
Riuers
,
Borders
,
in
any
one
Countie
,
and
from
thence
ye
may
doe
the
like
by
the
rest
,
and
so
take
a
true
su●●eigh
of
a
Kingdome
,
and
of
all
the
Iles
,
&
Rockes
in
the
Sea
,
and
Kingdomes
adioyning
,
as
Scotland
with
his
Iles
,
and
ouer
the
Sea
,
as
Ireland
with
his
Iles
,
likewise
from
Douer
to
Callice
,
and
so
take
the
Countrey
and
Kingdome
of
France
,
with
his
Riuers
,
Iles
,
Rockes
,
and
euerie
remarkeable
thing
that
commeth
in
view
of
your
eye
.
But
note
,
that
if
you
measure
such
great
distances
,
you
must
haue
regard
to
Longitude
and
Latitude
,
for
if
you
shall
measure
from
France
to
Spaine
,
Portugale
,
and
so
ouer
the
mouth
of
the
St●i●●
of
Guib●ater
into
Barbarie
,
Guiny
,
by
the
Coast
of
Saint
Thomas
I
le
,
Monomotapa
,
Cape
Good-hope
,
the
Coast
of
Saint
Latence
,
Mosamque
,
Prester
Iohn
,
the
head
of
the
ancient
Riuer
Nilus
,
the
Arabian
,
Iudean
,
Notalia
,
Grecian
,
Italian
Countreys
,
so
come
to
Germany
,
Polonia
,
and
all
those
North
parts
to
the
Pole
if
you
can
,
or
to
Sweden
,
Moscouia
,
and
the
North
part
of
Tartaria
,
and
th●●
way
discou●r
all
the
North
parts
round
about
the
Pole
,
and
so
if
you
can
come
into
North
America
,
if
not
,
then
come
ouer
Land
neere
the
Caspian
Sea
,
Parthia
,
Persia
,
Ormuse
,
Gus●●●
Goa
,
Cochin
,
and
all
the
Iles
to
the
South
thereof
,
the
Gulph
of
Bengala
,
Malaca
,
Sumatra
,
the
Strait
of
Sunda
,
Iaua
maior
,
Iaua
minor
,
new
Ginny
,
Papoos
,
Hiland
,
Timor
,
so
to
Beach
,
and
to
the
discouerie
of
the
parts
of
Maletor
Kingdome
to
the
South
Pole
if
you
can
,
or
by
the
Moluce●e
,
Bernie
,
Ca●●bia
,
Cochin
China
,
Iapan
China
,
to
Cathay
,
from
thence
East
a
little
North
to
the
Straits
of
Annian
,
and
so
into
the
most
Westerly
parts
of
North
America
,
Portray
all
that
new
world
,
to
be
short
,
come
by
the
Gulph
of
Mexico
down
to
the
Strait
of
Land
called
Noua
Hispaniola
to
Peru
,
goe
ouer
the
●trait
of
Ma●●●nica
and
discouer
all
the
vnknowne
Land
round
about
the
South
Pole.
Which
thing
may
be
done
by
Gods
permission
no
doubt
,
and
when
thou
hast
done
this
most
truly
,
with
all
the
Coasts
of
the
Seas
,
thou
wilt
say
the
circompherence
of
the
Sea
is
also
had●
True
,
yet
neuerthelesse
ye
shall
neuer
be
able
to
lay
the
true
semetry
of
both
Earth
and
Sea
on
a
plaine
superficies
by
this
way
.
The
like
may
you
proue
by
the
Hidrographicall
discription
of
the
Sea
,
by
the
common
Sea
Card.
And
here
note
,
that
this
may
serue
likewise
to
proue
that
the
Earth
and
Sea
make
one
round
Body
.
CHAP.
V.
Of
certaine
considerations
to
be
remembred
,
briefly
set
downe
.
AS
I
conceiue
,
there
are
these
three
things
to
be
considered
,
without
which
fayling
cannot
be
performed
.
The
first
,
is
an
exact
obseruation
of
the
Sunne
,
Moone
,
and
Starres
.
The
second
,
is
the
perfect
finding
out
of
the
vari●tion
of
the
Compasse
.
Lastly
,
a
true
reckoning
of
the
Ships
way
.
These
all
doe
helps
one
another
,
and
should
be
precisely
had
.
Againe
,
the
Earth
and
Sea
making
one
round
Body
,
we
may
consider
that
to
sayle
between
2
places
,
may
be
either
by
a
Par●a●ll
,
a
Rui●●
,
or
a
gr●●●
Circle
,
as
ye
may
perceiue
by
the
artificiall
Globe
.
Therefore
if
ye
can
draw
some
blanke
Charts
to
carrie
with
you
in
your
voyages
,
such
whose
Meridians
and
Parralels
beare
such
proportion
one
to
the
other
in
ech
Latitude
,
as
those
in
the
Globe
,
you
shall
doe
well
.
In
the
Globe
you
may
perceiue
the
degrees
in
the
Equator
to
agree
and
be
equall
with
the
degrees
in
the
Meridian
.
Now
the
degrees
in
the
Meridians
〈…〉
where
equal
,
but
the
degrees
in
the
Parralels
to
the
Equator
are
lesse
and
lesse
,
so
that
a
degree
of
Longitude
in
the
60
deg.
of
Latitude
is
but
½
of
that
degree
of
Longitude
in
the
Equator
,
and
as
the
whole
signe
is
to
the
number
of
parts
in
a
degree
of
Longitude
at
the
Equator
,
so
is
the
fight
of
the
complement
of
any
Latitude
to
a
fourth
number
(
by
the
rule
of
proportion
of
geometricall
demostration
)
which
number
tels
you
how
many
parts
of
a
degree
of
the
Equator
serueth
a
degree
of
Longitude
in
that
Latitude
,
but
in
a
plaine
Card
where
the
Meridians
are
all
Parralels
,
there
because
the
degrees
of
Longitude
in
ech
Latitude
are
equall
,
you
must
increase
the
degrees
of
the
Meridian
in
ech
Latitude
in
such
proportion
as
is
aboue
said
,
which
is
easie
to
be
done
with
the
Scale
on
your
Ruler
.
This
to
looke
on
to
the
eye
will
be
strange
,
and
to
such
as
loue
to
st●oke
to
their
old
errors
,
in
the
plaine
Card
they
will
thinke
it
cleane
against
reason
,
but
let
such
describe
some
portion
of
the
world
in
it
,
they
may
compare
it
with
a
Globe
,
and
see
it
beare
a
true
semetry
,
but
in
their
plaine
Card
it
will
appeare
monstrous
.
Here
is
now
a
view
of
the
world
from
Centor
to
Circomference
,
Here
is
an
entrance
to
the
meanes
of
obtaining
to
some
abilitie
in
the
vse
and
practise
thereof
:
But
aboue
all
and
in
all
things
giue
vnto
the
Lord
the
glorie
due
vnto
his
name
,
Ps.
29.2
.
And
this
indeed
is
the
verie
thing
wherein
we
ought
to
reioyce
,
and
for
which
God
made
vs
,
namely
,
to
seeke
his
glorie
,
which
is
wonderfully
seen
:
and
for
forth
in
the
frame
of
the
World
,
but
most
mightily
in
the
part
vns●●●
but
by
Faith
,
with
which
eye
thou
must
looke
into
Heauen
by
viewing
here
on
Earth
Gods
holy
Word
,
and
hearkening
with
the
eare
of
Faith
,
to
the
Ministers
of
his
Word
,
who
doe
breake
the
Bread
of
Life
vnto
the
faith
〈◊〉
●●reable
virgins
strong
meat
vnto
men
,
&
〈◊〉
vnto
babes
,
so
shalt
thou
be
the
better
able
to
worship
the
Lord
in
the
beautie
of
his
holinesse
,
Ps.
19.2
.
It
appeareth
,
G●●
.
1.14
.
that
God
made
the
Lights
in
the
Firmament
to
diuide
the
day
from
the
night
,
and
to
be
for
signes
and
seasons
,
dayes
and
yeeres
.
And
v.
15.
to
giue
light
vpon
the
Earth
,
according
to
the
roundnesse
of
the
Earth
,
and
motion
of
the
☉
the
light
and
darkenesse
doe
differ
,
for
the
Sunnes
body
being
bigger
then
the
body
of
the
Earth
,
maketh
that
the
Sunne
being
at
the
Equator
,
although
from
Sunne
rysing
to
Sunne
setting
be
iust
12
howres
,
yet
the
light
will
appeare
from
breake
of
day
to
euening
shut
in
14
h.
24
m.
and
the
darkenesse
will
continue
9
h.
36
m.
Now
if
two
men
be
one
vnder
the
North
Pole
,
another
vnder
the
South
Pole
,
they
shall
both
see
the
Sunne
in
their
Horizon
,
if
the
☉
decline
towards
the
North
,
he
will
rise
aboue
the
Horizon
to
him
in
the
North
,
but
to
him
in
the
South
the
☉
setteth
and
when
the
☉
is
in
the
tropicke
of
♋
it
is
noone
with
him
in
the
North
,
but
with
him
in
the
South
it
is
midnight
(
&
contra
.
)
By
this
it
appeareth
the
time
betweene
Sunne
rising
and
Sunne
set
to
either
of
them
is
about
436.
houres
,
on
●/●
yeere
,
sauing
that
the
Lords
louing
kindnesse
hath
been
of
old
,
Psa
5
,
6
to
this
Christian
part
of
the
world
,
in
placing
the
Suns
Apoge
in
this
part
,
by
which
we
receiue
a
double
benefit
,
the
one
of
light
so
much
the
longer
by
the
Sunnes
slow
motion
,
the
other
,
that
when
the
Sun
is
come
so
neere
our
Zeneth
,
it
hath
pleased
God
to
draw
it
vp
neerer
Heauen
and
further
from
the
Earth
,
that
we
be
not
burned
with
his
heat
,
as
it
is
written
,
The
Sunne
shall
not
burne
thee
by
day
,
nor
the
Moone
by
night
,
Ps.
121.6
.
Et
〈◊〉
in
the
South
part
of
the
World
among
the
Heathen
that
know
not
God.
But
in
the
Poles
the
twilight
lasteth
so
long
as
the
Sun
is
within
18
deg.
of
the
Horizon
,
which
is
about
the
first
of
May
,
so
the
darke
night
lasteth
1968
h.
and
the
twilight
is
about
1200
h.
that
is
50
dayes
with
vs
.
From
these
two
differences
in
a
right
Spheare
you
may
make
to
your selfe
a
Theoricke
of
the
oblique
by
considering
the
difference
of
light
betweene
any
number
of
degrees
from
the
Equator
to
the
Poles
as
you
please
,
or
after
this
example
:
I
did
obserue
the
height
of
the
Sunne
this
yeere
1627
,
and
found
him
to
be
more
then
62
deg.
in
Meridian
height
,
proues
that
the
Sun
hath
more
then
a
●
deg.
30
min.
declination
,
or
else
the
Poles
eleuation
to
be
lesse
then
51
d.
30
m.
here
at
London
,
which
the
learned
haue
likewise
proued
in
the●●
most
exact
obseruations
,
but
for
the
lesse
learned
,
and
the
honest
Sea-mans
vse
,
the
declination
of
23
d.
30
m.
will
make
no
〈◊〉
.
Now
that
in
a
Countrey
of
knowne
Latitude
you
may
fin●lly
the
height
of
the
Sun
his
Azimuth
and
declination
in
any
Longitude
,
by
which
you
may
find
the
variation
of
your
Compasse
at
all
houres
of
the
day
,
or
by
the
day
of
the
month
the
Suns
Meridian
height
being
giuen
,
is
had
the
Latitude
of
the
place
,
or
height
of
the
Pole
,
then
the
amplitude
or
azimuth
as
before
,
and
to
speake
truly
,
these
prepositions
depend
on
one
another
,
and
what
is
said
of
the
Sun
,
may
likewise
be
done
by
the
Stars
being
knowne
,
their
Longitude
,
Latitude
,
and
Declination
being
likewise
had
.
If
any
man
shall
say
,
I
haue
discouered
my
wants
herein
,
he
saith
truly
,
if
my
malice
my
good
will
,
let
him
know
I
care
not
,
if
any
man
will
further
my
willing
mind
,
to
him
I
will
send
this
Boaste
for
Patronage
,
and
for
euer
pray
for
him
,
if
any
fleare
and
scoffe
at
mee
,
it
were
much
better
for
his
Soule
that
he
were
at
prayers
,
and
leaue
scoffing
.
Euerie
good
man
may
if
please
him
,
amend
this
,
and
so
further
me
.
If
no
ignorant
man
will
profit
by
it
,
yet
let
such
as
are
honestly
minded
,
suffer
this
to
liue
with
me
,
because
all
that
I
haue
,
or
can
doe
,
is
but
to
imploy
my
time
in
such
meane
knowledge
as
I
haue
,
to
Gods
glorie
,
and
the
benefit
of
my
Countrey
.
Wherein
if
knowledge
and
a
purse
did
agree
with
heart
and
good
will
,
I
would
striue
with
the
best
Subiect
.
In
the
meane
time
I
will
striue
to
doe
my
best
,
as
my
dutie
doth
bind
me
.
CHAP.
VI.
Of
Shipping
and
going
out
of
the
Harbor
.
THese
things
afore
spoken
of
,
are
most
vsefull
,
and
now
I
hold
it
a
good
method
to
examine
your
Ship
whether
shee
be
for
your
turne
or
not
,
in
all
things
well
appointed
for
the
Sea
,
if
new
,
how
well
built
,
and
strong
,
and
how
well
fitted
in
her
ge●re
,
if
old
,
whether
she
be
able
to
indure
the
surging
waues
of
the
Sea
,
to
goe
another
voyage
,
and
likewise
for
her
burthen
,
proportioned
according
to
the
businesse
ye
vse
her
for
.
But
if
ye
wi●●
build
a
new
Ship
in
any
proportion
assigned
,
ye
shall
iudge
〈◊〉
better
how
to
haue
it
done
,
by
learning
so
much
in
Arithmeticke
,
as
to
be
able
to
extract
the
Square
and
Rube
root
,
then
may
you
doe
after
this
example
next
following
,
or
otherwise
at
your
pleasure
.
Let
the
proportion
be
as
two
to
one
,
and
suppose
you
haue
a
Ship
of
100
tun
,
in
all
things
so
well
framed
,
that
thou
doest
desire
to
haue
one
of
200
tun
,
and
like
to
the
other
to
do
this
,
first
take
the
measures
of
your
first
Ship
,
which
suppose
to
be
these
,
the
Keele
44
foot
,
at
the
Beame
20
foot
,
in
Houle
9
,
foot
,
her
Rake
afore
13
foot
,
after
7
foot
,
here
is
giuen
sixe
numbers
,
and
the
proportion
assigned
,
and
seeing
the
proportion
is
to
be
doubled
,
therfore
take
ech
number
&
cube
it
,
then
double
that
cube
number
,
and
extract
the
cube
root
of
that
number
,
and
you
shall
find
the
second
Ship
must
haue
in
Keele
55½
foot
neere
,
and
Beame
25
and
about
½
,
in
Houle
11½
,
Rake
afore
16●
,
after
almost
9
,
and
her
burthen
will
be
200
tun
,
or
this
may
be
found
by
that
excellent
Instrument
of
the
memorable
Mast
.
Edmund
Gu●●●r
,
lately
set
forth
by
him
in
his
life-time
,
and
is
called
a
Sector
,
his
proportionall
Ruler
and
Crosse-staffe
is
well
knowne
to
bee
an
excellent
Instrument
for
these
purposes
following
,
and
also
for
many
other
,
Take
in
equall
parts
of
the
Sector
44
,
and
fit
it
ouer
in
the
Cubes
at
44
,
the
Sector
so
resting
,
take
with
your
Compasses
the
distance
ouer
in
88
of
the
Cubes
,
and
apply
it
to
the
equall
parts
,
giueth
55½
,
as
before
,
do
so
by
the
rest
,
and
you
shall
find
the
like
numbers
.
But
say
it
be
demanded
to
haue
her
of
any
other
proportion
,
namely
,
as
20
to
15
,
or
4
to
3
,
take
the
measures
of
the
first
,
an
before
,
and
cube
them
,
then
say
,
if
15
giue
such
a
Cube
,
what
Cube
shall
20
giue
,
it
will
giue
a
number
,
whose
Cube
root
in
the
number
sought
.
But
by
the
Sector
take
the
numbers
〈◊〉
&c.
in
equall
parts
,
and
fit
them
ouer
in
15
of
the
Cubes
,
then
take
the
distance
ouer
in
20
of
the
same
lines
,
and
that
applyed
to
the
equall
parts
,
giueth
the
number
sought
.
And
now
being
fitted
with
a
Ship
for
thy
purpose
and
hauing
launched
,
and
going
downe
the
Riuer
take
heed
to
the
set
of
〈◊〉
Tyde
,
not
onely
for
running
fowle
of
other
craft
,
but
least
ye
bring
your selfe
on
ground
on
a
Lee
shore
,
on
a
Shelfe
,
Sand
,
or
Shole
,
as
Barking
shelfe
,
a
Shole
against
Grayes
,
Blacke
shelfe
,
the
Piles
below
Tilberie
,
Milton
shore
,
or
in
a
darke
night
gape
for
a
sho●e
,
and
thinke
to
gaine
the
point
,
but
run
your
Ship
cleane
out
of
the
Thames
as
I
see
one
had
done
,
the
18
Decemb.
1627
,
and
layd
her
on
the
March
below
Greene-hiue
in
Kent
.
Going
out
or
in
any
Riuer
whatsoeuer
,
note
what
marke
yee
see
with
the
opening
of
any
Point
,
as
Yoke
on
a
Wall
,
Tree
,
House
,
Hill
,
Wood
,
Wind-mill
,
Steeple
,
Castle
,
or
Towne
,
and
learne
to
describe
the
Semetry
of
it
,
and
note
it
in
a
Booke
,
remembring
to
sound
the
depth
,
and
note
it
likewise
,
and
what
grounds
for
ancoring
good
or
bad
,
with
the
swiftnesse
and
indraft
or
outlet
of
the
waters
,
ye
may
also
describe
the
windings
thereof
by
the
Compasse
,
with
the
lengths
and
breadths
on
a
Paper
,
and
be
sure
to
note
the
magniticall
Azimuth
,
for
your
variations
,
be
it
of
the
Sonne
or
Starres
,
which
to
be
able
to
do
,
learne
so
much
in
Geometry
,
as
to
be
able
to
describe
the
Spheare
in
plaine
,
and
to
know
the
vse
of
the
Globes
,
or
at
least
to
vse
your
plaine
Scale
,
and
keep
your
trauice
on
your
Card
,
&
a
Iournall
or
daies
Book
,
and
know
both
in
Riuer
and
at
Sea
,
thou
must
make
vse
of
these
two
Globes
,
namely
,
the
Scriptures
where
the
good
shine
like
Starres
,
and
Christ
Iesus
is
the
true
Load-stone
.
CAHP.
VII
.
Of
the
Iournall
,
obseruation
,
and
proiection
.
WHen
you
are
come
into
the
Sea
,
begin
your
Iournall
on
this
wife
:
In
the
Name
of
God
,
Amen
.
The
daies
Booke
for
the
Voyage
intended
,
for
Saint
Christophers
,
and
C●●●e
de
Mine
.
The
24
of
May
wee
came
out
of
Portsmouth
,
and
●●cored
in
Stokes
Bay.
The
25
wee
weighed
,
and
with
a
g●●e
Basterly
.
The
26
we
put
thorough
the
Needles
.
The
27
wee
put
in
at
Dartmo●th
,
the
wind
South
South
West
,
verie
fo●●e
.
And
you
may
make
a
●alender
after
such
like
order
a●
this
.
heare
though
I
haue
set
but
some
dayes
of
the
mouth
:
yet
I
meane
you
should
set
downe
each
day
,
and
in
the
last
space
to
note
each
dayes
variation
,
and
which
Pole
is
eliuated
in
the
end
,
say
:
This
31.
of
Iuly
,
saying
on
an
east
winde
by
Gods
protection
,
we
had
sight
of
Matalena
,
and
at
noone
our
latitude
found
by
the
Sunne
pearing
thorow
the
Vane
of
your
Instrument
15.
de.
3.
mi.
and
by
the
North
Starre
the
next
morning
the
like
:
so
at
noone
the
South
East
part
of
Matalena
South
,
and
the
Meridian
distance
from
the
Lizard
1009
leagues
,
and
diference
of
longitude
57.
de
.
and
dominico
South
end
58.
de
.
and
in
your
way
note
thus
,
for
example
in
a
booke
by
it selfe
:
May
the
24.
from
the
23.
at
noone
,
from
South
to
East
10.
de.
17.
mi.
latitude
23.
de.
18.
mi.
☉
.
magnitude
,
Azimuth
130.
de.
5.
mi.
True
Azimuth
117.
de.
12.
mi.
the
variation
12.
de.
53.
mi.
as
in
chap.
4.
and
set
downe
whatsoeuer
is
remarkable
in
your
way
,
as
well
in
the
Sea
as
else
for
example
being
in
the
Latitude
of
46.
S.
the
body
of
the
Iles
of
Babe
North
East
,
7
leagues
being
to
the
North
of
the
Maine
shole
that
lyeth
in
mid
way
betweene
Mintain
and
Iles
Babe
the
West
Land
of
Babe
Iles
North
West
½
.
North
5.
leagues
from
the
South
I
le
of
Babe
towards
the
East
by
North.
20.
leagues
in
Latitude
20.
is
a
dry
shole
that
hath
to
the
W.
N.
W.
of
it
a
shole
or
Ledge
that
is
3.
leagues
off
.
Also
from
the
dry
shole
is
on
to
the
N.
E.
and
from
the
dry
shole
another
to
the
E.
S.
E.
from
the
dry
shole
the
pike
of
Pasamond
Hill
31.
de
.
Mag.
E.
to
N.
42.
miles
,
which
I
found
by
obseruation
:
for
being
6.
miles
from
shole
,
my
Angle
of
shole
and
Hill
85.
de
.
and
the
Angle
from
shole
to
hill
and
Ship
87
de
.
from
Hill
to
Shole
and
Ship
8.
de
.
by
which
the
distance
was
found
,
and
the
Hill
appeared
thus
.
And
for
the
soundings
doe
thus
,
Aprill
29.
euening
Bautum
hill
17.
de.
2.
mi.
from
S.
to
W.
14.
fatham
Poloubaus
and
neare
point
26.
from
S.
to
W.
14.
fatham
,
at
the
same
time
A.
N.E.
by
●
.
3.
leagues
.
4.
fatham
.
And
now
left
any
should
say
I
haue
prescribed
many
things
to
others
,
and
can
doe
nothing
my selfe
;
I
will
make
an
euident
and
plaine
demonstration
of
most
of
these
things
,
wherein
I
shall
make
more
easie
the
booke
of
M.
Thom●s
Addison
,
sometime
of
Ratcliffe
▪
in
his
life
time
a
good
Sea-man
,
and
Mr.
of
the
Ship
called
the
Palsgraue
,
bound
to
the
East-Indies
in
the
yeere
1624.
where
he
dyed
before
he
had
diuulged
them
:
his
widdow
not
knowing
what
to
doe
in
the
matter
,
and
I
hearing
of
the
same
,
did
purchase
the
said
bookes
at
my
owne
charge
:
Thinking
it
but
my
duty
to
quicken
and
raise
vnto
life
for
the
benifit
of
my
Country-men
,
according
to
the
minde
and
intent
of
the
Author
,
that
which
would
haue
dyed
,
or
at
lest
was
like
to
haue
dyed
in
the
shell
.
First
,
the●efore
as
I
haue
spoken
of
the
cirkles
of
the
m●tteriall
Spheare
and
Globe
,
so
I
would
haue
vnderstand
them
,
though
they
be
described
in
plano
after
this
manner
.
This
discription
is
common
:
but
I
haue
described
the
parralell
lines
with
prickes
,
the
horison
and
cirkle
of
depression
with
blacke
,
the
almacanter
with
the
other
parralells
are
red
,
the
sigments
within
are
to
shew
the
houre
lines
as
that
which
croseth
the
equator
as
it
were
at
r●ct
Angles
:
that
which
croseth
the
horizon
:
likewise
to
shew
the
Azimuth
and
that
which
croseth
the
Ecliptike
to
shew
the
Longitude
and
Latitude
in
the
Heauens
,
and
though
there
3.
inscribed
sigments
be
somthing
hard
to
doe
by
Geometricall
demonstration
,
and
for
so
much
as
they
are
of
singular
vse
:
Therefore
when
thou
wilt
finde
the
true
Azimuth
,
Longitude
,
or
houre
on
a
parralell
;
Take
thy
Sector
(
see
chap.
6.
)
and
open
it
to
the
distance
of
the
Semidiameter
of
that
parralell
in
the
totall
Sine
,
then
take
the
distance
in
the
Sine
giuen
,
and
apply
it
in
the
paralell
from
the
centor
it
sheweth
the
true
place
.
Now
I
haue
giuen
a
rule
before
for
finding
the
Sunnes
place
in
the
Zodiack
,
see
chap.
4.
which
we
will
for
examples
sake
suppose
to
be
the
30.
day
Aprill
1629.
which
is
by
the
Tables
of
Origanus
19
de.
21.
m.
2.
se
.
of
♉
.
and
by
my
rule
iust
19.
de
.
the
point
in
this
demonstration
for
that
place
is
at
B.
and
this
point
is
found
by
the
cirkle
deuided
as
is
before
spoken
of
,
chap.
4.
by
taking
fromward
the
poies
of
the
Zodiack
,
the
Sunnes
Longitude
in
degrees
,
which
in
this
example
is
49.
de
.
hauing
the
day
of
the
month
,
and
the
☉
.
place
found
,
the
rest
followeth
most
easily
:
For
a
parralell
drawne
to
the
equator
thorow
the
point
at
B.
sheweth
the
declination
at
C.
from
A.
right
Ascencion
B.
C.
Amplitude
A.
D.
Meridian
height
F.
H.
the
difference
Ascencionall
C.
D.
and
all
the
rest
followeth
,
and
are
measured
by
degrees
on
the
limbe
.
By
the
same
I
may
say
if
the
declination
be
giuen
,
as
from
A.
in
the
Centor
,
to
C.
the
☉
parralell
,
which
by
Origanus
for
the
30.
day
of
Aprill
1629.
●●
17.
de.
46.
m●
.
and
by
this
it
is
17.
de.
30.
which
is
but
little
lesse
;
and
that
was
by
the
neglect
of
the
minute
in
the
Sunnes
Longitude
.
I
will
giue
one
demonstration
more
,
and
that
shall
suffise
for
this
paper
,
for
my
purpose
is
to
include
all
this
worke
within
these
few
sheets
.
This
proiection
is
of
that
chapter
the
4.
May
the
4.
1629.
☉
.
place
the
23.
d.
12.
m.
41.
se
.
♉
.
Origanus
Tables
,
declination
18.
d.
32.
mi.
N.
☉
.
Longi
.
53.
de.
12.
mi.
41.
se
.
but
by
this
proiection
,
Suns
place
23.
de
.
and
A.
C.
declination
18.
de.
30.
mi.
Longitude
53.
de
.
and
at
B.
from
A.
A.
D.
the
Amplitude
●8
.
de
.
E.
F.
the
Meridian
height
55.
de
.
B.
C.
right
Ascencion
50.
de
.
C.
D.
difference
Ascencionall
23.
de.
0.
mi.
B.
G.
Obligue
Ascencion
27
de
.
o.
mi.
D.
E.
semydiurnall
arke
7.
ho
32.
mi.
D.
E.
semynocturnall
arke
4.
ho.
28.
D.
H.
length
of
twilight
2.
ho.
4.
mi.
H.
E.
time
from
noone
to
euening
shut
is
9.
ho.
33.
mi.
that
double
is
the
length
of
the
day
.
19.
ho.
6.
mi.
This
last
taken
from
24.
leaueth
the
length
of
the
night
darke
4.
ho.
54.
mi.
Sun
riseth
at
D.
4.
ho.
28.
mi.
seteth
at
7.
ho.
32.
mi.
Time
from
rising
to
setting
15.
ho.
4.
from
Sun
setting
,
to
his
rising
8.
ho.
56.
mi.
Height
of
the
Pole
N.
R.
51.
de.
30.
mi.
Though
many
more
propositions
may
be
wrought
by
this
kinde
of
proiection
,
yet
to
make
some
good
vse
of
this
marke
,
the
last
which
is
the
height
of
the
Pole
found
,
so
that
if
ye
doe
but
remember
the
day
of
the
month
;
which
you
must
needs
doe
by
your
Kalender
in
the
beginning
of
this
chap.
or
his
declination
:
take
his
amplitude
Azimuth
,
or
Meridionall
height
,
hauing
with
you
your
Compasses
:
Compasse
,
crostafe
,
Sea-quadrant
,
Card
,
and
some
good
Tables
of
the
fixed
Starres
,
that
yee
may
vse
them
for
obseruation
in
the
night
:
and
by
all
meanes
I
would
haue
you
get
the
reconing
of
your
Ships
way
by
that
excellent
way
of
Mr.
Addisons
of
the
〈◊〉
glasse
,
the
Log-line
,
and
also
by
what
true
way
soeuer
the
experienced
Sea-man
can
bring
to
light
;
and
then
may
you
cast
vp
your
Trauerse
by
that
excellent
way
of
the
Arithmeticall
Nauigation
,
by
your
Card
and
Trauerse
bord
,
and
by
this
Kalender
,
whose
vse
is
this
;
Iune
the
23.
being
in
Latitude
48.
de.
14.
found
by
obseruation
,
we
failed
vntill
the
24.
noone
that
is
24.
●●
.
there
is
the
month
,
day
,
houre
,
in
the
2
first
columes
vpon
a
course
of
33.
de
.
from
S.
to
W.
20.
leagues
,
the
winde
being
N.
N.
E.
all
this
is
in
the
3.
next
columes
:
the
Latitude
then
obserued
to
be
47.
de.
25.
mi.
Longitude
in
miles
88.
from
Lizard
west
and
the
variation
12.
de
.
53.
●●
.
depth
90.
fatham
,
(
if
it
were
sound
so
)
and
these
in
the
2.
last
columes
,
and
from
Iuly
the
19
in
Latitude
17.
de.
40.
mi.
to
Iuly
the
21.
noone
,
that
is
48.
ho.
we
sayled
on
a
course
of
18.
de
.
from
W.
to
S.
74.
leagues
.
The
winde
being
at
E.
N
E.
which
brought
vs
into
the
Latitude
of
16.
de.
35.
mi.
and
into
Longitude
1834.
miles
:
or
611
1/●
.
leagues
W.
from
Lizard
vad
10.
de.
0.
mi.
Depths
60.
fatham
,
S.
W.
7.
leagues
a
Rock
,
&
S.
by
W.
land
thus
.
Note
that
if
you
get
your
height
and
course
exactly
,
it
will
correct
your
way
,
height
and
way
will
correct
your
course
:
course
and
way
will
correct
your
height
:
but
striue
to
doe
all
as
exact
as
posible
you
can
,
to
doe
which
,
note
what
followeth
.
Propositions
of
Nauigation
,
Arethmetically
,
Geometrically
,
and
Instrumentally
shewed
.
Chap.
8.
1.
To
finde
the
leagues
run
on
any
course
,
the
difference
of
Latitude
and
course
being
giuen
.
AS
the
sine
of
the
course
from
the
parralell
is
to
the
miles
in
difference
of
Latitude
:
so
is
the
totall
sine
to
the
leagues
run
.
As
the
Tangent
of
the
course
,
from
the
parralell
is
to
the
miles
in
a
degree
of
Latitude
;
so
is
the
Secant
of
the
course
to
the
way
.
As
the
totall
sine
is
to
the
miles
in
the
difference
of
Latitude
;
so
is
the
Secant
of
the
course
,
from
the
Meridian
to
the
miles
run
.
As
the
sine
of
the
course
from
the
Meridian
is
to
the
miles
in
difference
of
Latitude
;
so
is
the
Tangent
of
the
course
from
Meridian
to
the
way
.
Let
the
Logarithme
of
the
course
from
the
parralell
be
taken
out
of
the
Logarithme
of
miles
in
difference
of
Latitude
,
the
remainder
is
the
Logarithme
of
the
miles
in
way
.
Instrumentally
by
the
Sector
,
take
in
the
equall
parts
the
miles
in
difference
of
Latitude
and
set
it
ouer
in
the
equall
fine●
of
the
course
from
the
parralell
,
the
Sector
so
opened
,
take
the
distance
ouer
in
the
totall
signe
and
that
distance
applyed
to
the
equall
parts
giueth
the
miles
of
way
run
.
2
The
difference
of
Latitude
and
Longitude
giuen
to
finde
the
leagues
run
.
SQuare
both
sides
,
then
ad
the
2.
squares
together
and
extract
the
square
roote
is
the
miles
in
way
run
.
Looke
which
is
the
greater
side
,
either
the
Lat.
or
the
Lo●
,
Open
the
Sector
to
a
rectangle
:
then
take
the
miles
in
Longitude
and
set
it
on
one
side
,
the
Sector
from
the
Centor
in
equall
parts
,
and
the
miles
in
Latitude
on
the
other
side
:
then
take
the
distance
ouer
with
a
paire
of
Compasses
,
and
apply
that
distance
to
the
equall
parts
,
giueth
the
number
of
miles
in
way
.
3
To
finde
the
difference
of
Longitude
,
the
course
and
difference
of
Latitude
being
giuen
.
AS
the
sum
of
the
course
from
the
parralell
is
to
the
difference
in
Latitude
,
so
is
the
fine
of
the
course
from
the
Meridian
to
the
difference
in
Longitude
.
As
the
totall
sine
is
to
the
difference
in
Latitude
:
so
is
the
Tangent
of
the
course
from
the
Meridean
to
the
Longitude
.
As
the
Tangent
of
the
course
,
from
the
parralell
to
the
miles
in
Latitude
:
so
is
the
totall
sine
to
the
miles
in
Longitude
.
As
the
Secant
of
the
course
from
the
parralell
is
to
the
difference
of
Latitude
:
so
is
the
Secant
of
the
course
from
the
Meridian
to
the
Longitude
sought
.
Take
the
Logarithme
difference
of
the
Angle
from
the
Meridian
out
of
the
Logaritme
of
the
difference
of
Latitude
in
miles
the
remainder
is
the
logaritme
of
Longitude
in
miles
.
Take
the
number
of
equall
parts
(
in
the
Sector
)
which
are
the
difference
of
Latitude
,
&
fit
that
distance
ouer
in
the
liues
of
sines
of
course
from
the
patrid
all
,
and
the
i●strument
opened
to
that
widnesse
:
the
distance
ouer
in
the
sine
of
the
course
from
the
Meridian
:
that
distance
applyed
to
the
equall
parts
,
sheweth
the
Longitude
in
miles
.
4
To
finde
how
many
miles
off
the
equator
or
Meridian
is
a
degree
of
Longitude
in
any
parralell
of
Latitude
.
AS
the
totall
sine
is
to
the
miles
in
a
degree
of
the
equator
:
so
is
the
sine
of
the
complement
of
Latitude
to
the
miles
sought
.
As
the
Tangent
of
the
Latitude
is
to
a
degree
in
the
Meridian
:
so
is
the
line
of
the
Latitude
to
the
miles
sought
.
As
the
Secant
of
the
L●●●tude
is
to
the
miles
in
the
equator
or
Meridian
:
so
is
the
totall
sine
to
the
miles
sought
As
the
Secant
of
the
complement
of
Latitude
is
to
the
miles
of
Meridian
:
so
is
the
Tangent
of
the
complement
of
Latitude
to
the
miles
,
answering
a
degree
.
Let
the
logarithme
of
the
complement
of
Latitude
be
added
to
the
logarithme
of
miles
in
a
meridians
degree
;
the
totall
is
the
logarithme
of
miles
sought
.
Instrumentally
,
take
the
number
of
equall
parts
in
a
degree
of
the
Meridian
or
equator
by
the
Sector
,
&
fit
them
ouer
in
the
sines
totall
:
then
take
the
distance
ouer
in
the
sines
of
the
complement
of
Latitude
,
and
apply
that
to
the
equall
parts
,
sheweth
the
miles
that
make
a
degre
of
Longitude
in
that
parralell
.
5
To
finde
the
Longitude
answering
to
a
Meridian
distance
in
any
parralell
of
Latitude
.
AS
the
sine
of
the
complement
of
Latitude
is
to
the
Meridian
distance
:
so
is
the
totall
sine
to
the
Longitude
.
As
the
sine
of
the
Latitude
is
to
the
Meridian
distance
:
so
is
the
Tangent
of
the
Latitude
to
the
Longitude
.
As
the
totall
sine
to
the
Meridian
distance
:
so
is
the
Secant
of
Latitude
to
the
Longitude
.
As
the
Tangent
of
the
complement
to
the
Meridian
distance
:
so
is
the
Secant
of
the
complement
to
the
Longitude
.
Let
the
Logarithme
of
the
complement
be
taken
out
of
the
Logarithme
of
Meridian
distance
,
the
remainder
is
Logarithme
of
Longitude
.
Take
from
the
scale
of
equall
parts
in
the
Sector
the
Meridian
distance
;
and
fit
with
your
Compasses
in
the
sines
of
the
Latitudes
complement
:
then
the
distance
taken
betweene
90.
and
90.
applyed
to
the
same
scale
,
giueth
the
Longitude
.
6
To
finde
the
signe
of
any
Arke
in
any
parralell
.
AS
the
totall
sine
is
to
the
complement
:
so
is
the
sine
giuen
in
the
great
Cirkle
to
the
sine
in
the
Latitude
.
As
the
Tangent
of
Latitude
to
the
sine
of
Latitude
:
so
is
the
sine
of
the
Arke
in
the
great
Diameter
to
the
sine
of
the
Arke
in
the
lesser
.
As
the
Secant
of
Latitude
to
the
totall
sine
:
so
is
the
sine
in
the
greater
,
to
the
sine
in
the
lesser
Semy
diametor
.
As
the
Secant
of
the
complement
is
to
the
Tangent
thereof
:
so
is
the
sine
in
the
greater
to
the
sine
in
the
lesser
.
Ad
to
the
Logarithme
of
the
Arke
giuen
,
the
Logarithme
of
the
complement
of
Latitude
,
the
totall
is
the
Logarithme
of
sine
demanded
.
By
the
Sector
let
the
distance
from
the
Centor
to
the
Arke
giuen
be
put
ouer
in
90.
and
90.
then
the
distance
betweene
the
sines
of
the
complement
of
Latitude
,
applyed
from
the
Centor
,
giueth
the
Arke
whose
sine
is
the
demanded
.
7
By
a
sine
giuen
in
a
parralell
,
to
finde
the
Arke
.
AS
the
sine
of
the
complement
of
the
Latitude
is
to
the
sine
giuen
▪
so
is
the
totall
sine
to
the
sine
of
the
Arke
.
As
the
sine
of
the
parralell
is
to
the
sine
giuen
:
so
is
the
Tangent
of
the
parralell
to
the
sine
of
the
Arke
sought
.
As
the
totall
sine
is
to
the
sine
giuen
;
so
is
the
Secant
of
parralell
to
the
sine
of
the
Arke
sought
.
As
the
Tangent
of
the
complement
is
to
the
sine
giuen
:
so
is
the
Tangent
thereof
to
the
sine
of
the
Arke
sought
.
Out
of
the
Logarithme
of
the
sine
giuen
,
●●ke
the
Logarithme
of
the
complement
of
L●●i
:
the
rest
is
the
Logarithme
of
the
sine
.
By
Instrument
let
the
distance
of
the
signe
giuen
be
taken
from
the
Centor
and
fitted
in
the
sine
of
the
complement
of
Latitude
;
8
To
finde
how
many
miles
on
Earth
or
Sea
serueth
to
a
minute
of
time
in
the
Heauen
,
in
any
parralell
of
Latitude
.
AS
the
totall
sine
is
to
15.
mile
,
which
serueth
a
minute
of
time
vnder
the
equator
:
so
is
the
sine
of
the
complement
of
Latitude
to
the
number
sought
.
As
the
Tangent
of
the
Lati●●●e
is
to
the
miles
in
the
equator
:
so
is
the
sine
of
the
Latitude
to
the
miles
sought
.
As
the
Secant
of
the
Latitude
is
to
the
miles
in
a
minute
at
the
equator
:
so
is
the
totall
sine
to
the
miles
in
a
minute
of
that
parralell
.
As
the
Secant
of
the
complement
of
Latitude
,
is
to
the
miles
in
the
equator
:
so
is
the
Tangent
thereof
to
the
miles
in
a
minute
of
that
parralell
.
Add
the
Logarithme
of
the
15.
miles
,
to
the
Logarithme
of
the
complement
of
Latitude
,
the
summe
is
the
Logarithme
of
the
miles
in
that
parralell
.
By
the
Instrument
or
Sector
,
take
15.
the
miles
that
serue
in
the
equator
to
a
minute
of
time
out
of
the
equall
parts
,
and
fit
it
ouer
in
the
totall
sines
:
then
the
distance
ouer
in
the
sine
of
the
complement
of
Latitude
applied
to
the
equall
parts
,
sheweth
the
miles
to
a
minute
in
that
parralell
.
This
chapter
ha●
shewed
how
to
finde
the
leagues
run
in
any
course
,
or
the
Ships
way
,
and
to
finde
the
difference
of
Longitude
,
with
things
thereto
pertaining
,
the
next
sheweh
.
Chapter
the
9.
9
To
finde
the
course
the
way
and
difference
of
Latitude
giuen
.
AS
the
miles
in
way
(
or
run
)
is
to
the
totall
sine
:
so
is
the
miles
in
difference
of
Latitude
to
the
course
(
or
run
)
his
sine
from
〈…〉
As
the
miles
in
difference
of
latit.
to
the
totall
sine
,
so
the
miles
in
way
to
the
seca
.
of
course
from
meridian
.
As
the
difference
of
latitude
to
the
way
,
so
the
totall
sine
to
the
secant
of
course
from
meridian
.
Square
both
difference
of
latitude
and
way
,
then
subtract
the
lesser
out
of
the
greater
,
out
of
the
remainder
,
Let
the
logarithme
of
way
be
taken
out
of
the
logarithme
of
difference
of
latitude
,
the
remainder
is
logarithme
of
course
from
paralell
.
Take
the
equall
parts
in
way
,
and
fit
over
in
the
totall
sine
,
then
take
the
difference
of
latitude
,
and
fit
over
in
equall
sines
,
giues
the
course
from
paralell
.
10.
To
find
the
course
,
the
way
,
and
longitude
given
.
AS
the
way
to
the
totall
sine
,
so
the
longitude
to
course
from
the
meridian
.
As
the
longitude
to
the
totall
sine
,
so
the
way
to
the
secant
of
course
from
paralell
.
As
the
longitude
to
the
way
,
so
the
totall
sine
to
the
secant
of
course
from
paralell
.
Square
both
longitude
and
way
,
then
subtract
the
lesser
out
of
the
greater
,
out
of
the
remainder
extract
the
square
roote
,
Let
the
logarithme
of
way
be
taken
out
of
the
logarithme
of
difference
of
longitude
,
the
remainder
is
logarithme
of
course
from
the
meridian
.
Let
the
equall
parts
in
way
be
fitted
over
in
the
totall
sine
,
then
the
long●fitted
over
in
equall
sines
,
gives
the
course
from
the
meridian
.
11.
To
find
the
course
,
the
longitude
and
latitude
g●uen
.
AS
the
½
of
the
2
sides
added
,
is
to
the
difference
of
each
side
,
so
the
tangent
of
½
the
2
unknowne
angles
,
to
the
tangent
of
an
arke
,
which
being
added
to
,
or
taken
from
½
the
2
vnknowne
angles
,
gives
the
course
.
Take
the
logarithme
of
the
greater
side
,
out
of
the
logarithme
of
the
lesser
,
the
remainder
is
logarithme
of
the
angle
opposite
to
the
lesser
side
.
Open
the
sector
to
a
rectangle
,
and
take
the
longitude
and
latitude
,
and
fit
them
on
2
sides
from
the
center
;
and
from
those
2
extensions
take
the
distance
with
a
paire
of
compasses
,
and
fit
it
over
in
the
totall
sine
;
Then
take
the
longitude
,
and
fit
over
in
equall
sines
,
gives
the
course
from
the
meridian
,
but
the
latitude
so
fitted
giues
the
course
from
paralell
.
12.
To
find
the
latitude
,
the
course
and
way
giuen
.
AS
the
totall
sine
to
the
way
,
so
the
sine
of
course
from
paralell
to
the
latitude
sought
.
As
the
secant
of
course
from
paralell
to
the
way
,
so
the
tangent
of
the
same
to
the
difference
of
latitude
.
As
the
secant
of
course
from
the
meridian
,
to
the
way
,
so
the
totall
sine
to
the
difference
of
latitude
.
As
the
tangent
of
course
from
the
meridian
,
to
the
way
,
so
the
sine
of
the
same
course
to
the
difference
of
latitude
.
Adde
the
logarithme
of
way
to
the
logarithme
of
course
from
paralell
,
the
totall
is
the
logarithme
of
difference
of
latitude
.
Take
the
miles
in
way
,
and
fit
over
in
the
totall
sine
,
then
the
distance
over
in
the
sine
of
course
from
paralell
,
giues
the
miles
in
difference
of
latitude
.
I
haue
shewed
already
,
chap.
7.
how
the
distance
from
Paramont
hill
was
found
;
And
as
I
conceiue
,
it
is
easie
to
finde
the
distance
of
places
,
if
you
doe
but
know
the
vse
of
my
Table
of
sines
,
tangents
and
secants
,
proviso
,
note
that
the
3
angles
of
any
right-lined
triangle
is
equall
to
2
rectangles
or
180
degrees
.
For
commonly
at
sea
,
you
must
obserue
the
land
,
shore
,
or
whatsoever
it
is
you
would
know
the
distance
from
,
what
angle
it
maketh
with
your
course
;
as
admit
40
degrees
,
then
reckon
your
ships
way
,
suppose
1000
fathome
,
and
then
observe
againe
,
let
your
second
angle
be
100
degrees
,
then
adde
100
deg
:
&
40
degr
:
which
subtract
from
180
degr
:
remainder
40
degr
:
for
the
third
angle
;
then
haue
you
3
angles
and
one
side
given
,
by
which
meanes
the
other
2
sides
are
easily
had
,
and
consequently
the
distance
.
Now
if
the
young
beginner
be
troubled
to
finde
the
sine
of
an
angle
,
so
big
as
100
degr
:
let
him
note
what
the
Table
saith
;
subtract
90
degr
:
from
100
degr
:
the
remainder
10
degr
:
subtract
from
90
degr
:
rests
So
degr
:
or
subtract
100
degr
:
from
180
degr
:
rests
80
degr
:
whose
sine
in
my
table
is
985
;
the
other
two
angles
being
40
degr
:
and
40
degr
:
their
sines
are
643
and
643
,
and
the
distance
1000
fathome
:
Now
to
fetch
the
distance
from
shore
say
,
as
643
the
sine
of
40
degr
:
at
c
,
found
as
before
,
to
1000
fathome
,
the
distance
from
a
to
b
,
the
a
places
of
observation
,
so
984
the
sine
of
80
degr
:
in
the
lesser
quadrant
,
or
100
degr
:
in
the
great
,
(
which
is
all
one
)
to
the
distance
from
a
to
c
1531
●6●/61●
fathome
.
Another
example
.
996
sine
of
84
degr
:
50.
985
sine
of
80
de.
262
sine
of
15
d:
10.
Let
your
first
observation
be
at
b
80
degr
:
the
second
at
d
84
degr
:
50
,
and
by
your
reckoning
the
distance
254
fathome
;
now
it
is
easy
by
the
former
rule
to
find
the
angle
at
c
15
degr
:
10
:
then
say
if
262
giue
254
,
what
giues
985
,
facit
c
d
954
110/●●●
:
And
as
262
to
254
,
so
996
to
the
distance
b
c.
So
that
it
is
all
one
whether
the
angles
be
right
,
or
obtuce
,
or
acute
,
if
they
be
all
acute
,
there
is
no
more
to
doe
but
take
the
sines
out
of
my
table
as
in
the
figure
K
,
and
no
more
,
if
one
be
a
rectangle
,
then
the
other
2
are
acute
,
but
if
an
angle
be
obtuce
,
as
in
the
figure
L
,
the
angle
at
b
100
degr
:
doe
by
that
angle
whatsoever
it
be
,
as
in
the
first
example
;
here
because
the
angles
at
a
and
c
are
equall
,
therefore
the
distance
from
b
to
c
is
1000
fathome
.
But
by
the
second
example
,
it
is
but
965
77/●●●
,
therefore
the
angle
at
d
was
not
truly
taken
;
for
what
965
77/●●●
is
in
proportion
to
1000
,
so
is
the
angle
at
d
to
the
true
angle
:
which
must
needs
be
more
then
84
degr
:
50
,
and
the
angle
at
c
lesse
then
15
degr
:
10
and
consequently
the
side
c
d
is
more
then
954
120/●●●
.
And
further
you
may
note
,
if
you
have
observed
so
well
that
the
angles
be
truly
taken
,
then
have
you
not
reckoned
your
ships
way
truly
;
and
so
you
may
see
that
one
of
these
doth
correct
the
other
,
as
in
the
end
of
the
7
chapter
.
And
you
may
fetch
a
distance
by
Geometricall
protraction
,
as
in
chap.
4.
suppose
you
would
know
the
distance
from
c
and
b
to
f
,
in
the
figure
m
,
first
having
drawne
the
angle
b
e
f
,
then
reckon
your
ships
way
from
●
to
b
●00
fathome
,
and
having
laid
downe
so
much
by
your
scale
and
compasses
,
(
see
pag.
12
)
you
shall
obserue
to
lay
the
line
●
b
right
in
the
course
your
ship
went
,
with
b
next
your
eye
,
and
e
towards
the
place
of
your
first
observation
;
then
from
b
draw
another
line
to
f
,
and
that
line
will
intersect
with
the
line
a
f
at
f
,
and
then
you
may
measure
the
distance
;
as
in
this
example
b
f
is
100
fathom
,
and
e
f
is
140
fathom
.
The
next
thing
that
will
trouble
the
young
beginner
,
is
the
propositions
in
these
8
and
9
chapters
,
which
are
most
easily
performed
,
because
the
demonstration
is
so
plaine
.
First
therfore
as
in
all
plain
triangles
,
the
sides
are
in
proportion
one
to
another
,
as
the
subtences
of
the
angles
opposite
,
or
as
the
sines
of
the
angles
opposite
to
those
sides
.
Example
in
the
inscribed
triangle
:
A
the
angle
at
b
is
in
proportion
to
the
side
c
d
or
arke
c
g
d
,
as
the
angle
c
to
the
side
b
d
,
or
arke
b
d
e
,
and
so
is
the
angle
d
to
the
side
b
c
,
or
arke
b
f
c.
So
note
that
in
all
rectangled
right-lined
triangles
,
the
two
containing
sides
of
the
rectangle
stand
perpendicular
one
upon
the
end
of
another
:
Therefore
if
you
put
the
least
side
for
radius
or
totall
sine
,
as
in
the
figure
b
,
the
other
side
will
be
the
tangent
,
and
the
subtending
side
of
the
rectangle
will
be
the
secant
;
or
if
you
put
the
greater
side
for
radius
,
the
least
will
be
the
tangent
,
and
the
subtence
the
secant
,
or
you
may
put
the
subtence
for
radius
,
as
in
the
figure
c
is
done
.
It
is
manifest
then
that
any
side
may
be
put
for
the
totall
sine
:
First
,
if
you
put
the
subtending
side
for
radius
,
as
in
the
figure
d
,
let
a
b
be
part
of
a
meridian
,
and
a
c
part
of
a
paralell
;
then
is
the
angle
at
b
the
course
from
the
meridian
,
and
the
angle
at
c
is
the
course
from
paralell
.
Then
if
the
difference
of
latitude
a
b
,
and
course
,
that
is
the
angle
at
b
or
c
be
given
,
you
may
finde
the
leagues
runne
,
or
distance
b
c
,
as
in
the
first
resolution
Arithmeticall
.
Or
if
you
put
the
longer
side
a
b
for
radius
,
then
say
as
the
totall
sine
a
b
to
the
difference
of
latitude
a
b
,
so
the
secant
b
c
of
course
,
b
from
the
meridian
,
to
the
distance
b
c
;
if
you
put
the
least
side
for
radius
,
say
as
the
tangent
a
b
of
course
c
from
paralell
,
to
a
b
the
difference
of
latitude
,
so
b
c
the
secant
of
the
same
course
,
to
b
c
the
distance
.
Let
this
su●●ice
for
the
first
proposition
chap.
8.
But
if
you
demaund
the
difference
of
longitude
,
the
latitude
and
course
being
given
,
you
may
doe
it
by
the
first
or
second
example
Arithmeticall
in
this
chapter
.
page
29
;
or
if
you
put
the
longer
side
b
c
for
radius
,
say
,
as
the
course
c
to
a
b
,
so
the
course
b
to
a
c
the
longitude
:
but
if
you
put
the
side
a
b
for
radius
,
say
,
as
the
totall
sine
to
the
difference
of
latitude
,
so
the
tangent
a
c
to
the
difference
of
longitude
:
if
the
least
side
be
put
for
radius
,
say
,
as
the
tangent
a
b
to
the
difference
of
latitude
,
so
the
totall
sine
to
the
difference
of
longitude
.
And
this
sufficeth
for
the
Geometricall
demonstrotion
of
the
third
proposition
,
chap.
8.
And
now
you
see
how
the
proportionall
numbers
doe
arise
,
it
is
easie
to
take
them
out
of
the
Table
,
and
worke
them
Arithmetically
;
and
what
is
said
of
these
propositions
may
be
said
of
all
the
rest
by
the
very
same
reason
;
except
the
second
proposition
chap.
8
,
and
the
11
proposition
in
this
chapter
page
27
:
the
first
of
these
is
done
as
in
Earlid
1.47
.
or
thus
Arithmetically
.
Let
the
line
a
be
3
leagues
of
longitude
and
the
line
b
4
leagues
of
latitude
,
first
multiply
3
〈◊〉
3
,
it
is
9
,
and
4
into
4
is
16
,
which
added
is
25
,
the
square
roote
is
5
,
for
5
times
5
is
25
,
and
this
is
equall
to
the
line
c
,
the
shippes
way
.
The
Geometricall
demonstration
is
this
,
set
the
line
a
perpendicular
vpon
the
line
b
,
as
in
the
figure
f
,
then
draw
the
line
c
,
and
it
is
5
the
shippes
way
.
There
is
another
way
of
demonstration
,
by
adding
the
sides
of
the
squares
into
one
;
also
if
the
way
and
longitude
had
beene
given
,
to
subtract
the
one
out
of
the
other
Geometrically
,
the
remainder
is
the
difference
of
latitude
:
if
the
way
and
latitude
had
beene
given
,
then
the
side
of
the
remainder
is
the
difference
of
longitude
,
Euclid
1.47
.
theor
.
33.
6.31
.
theor
.
21.
The
next
should
be
of
the
11
proposition
,
but
I
suppose
he
that
understands
that
is
more
than
an
ignorant
man
,
therefore
whosoever
will
learne
that
,
with
the
extraction
of
the
square
and
cube
roote
,
or
any
thing
else
that
is
in
my
booke
,
or
any
of
those
things
that
I
have
set
out
in
any
of
my
bills
;
let
them
come
to
my
dwelling
,
and
I
will
satisfie
their
demaund
so
farre
forth
as
God
shall
inable
mee
:
where
youth
may
bee
taught
,
dieted
and
lodged
for
reasonable
consideration
.
CHAP.
X.
Of
the
motion
of
the
Moone
,
and
comming
into
the
Harbour
.
I
Might
here
have
added
many
and
manifold
propositions
,
and
chiefly
those
which
doe
concerne
the
great
circle
distance
betweene
any
two
places
howsoever
scituate
;
but
I
will
first
see
thy
kinde
acceptance
of
this
:
which
if
you
receive
thankfully
,
I
shall
be
ready
to
shew
thee
many
more
to
thy
great
satisfaction
,
with
the
Geometricall
demonstration
,
which
I
have
gathered
into
a
booke
in
Folio
.
And
now
I
will
finish
this
worke
with
the
Moones
motion
;
supposing
you
are
come
in
sight
of
your
wished
port
in
safety
:
which
I
doe
heartily
wish
to
all
honest
Seamen
of
my
Country
,
that
travell
the
seas
to
good
ends
.
And
admit
you
are
in
a
strange
coast
,
you
may
the
better
come
to
finde
the
time
of
a
full
sea
,
at
a
spring
tide
,
to
bring
your
good
shippe
over
a
barre
or
shole
:
so
I
shall
end
my
worke
where
Mr.
Addison
began
his
:
then
having
read
this
,
you
may
reade
his
which
is
hereto
joyned
;
giving
you
to
understand
,
if
you
learne
well
these
propositions
of
mine
,
they
will
make
even
the
hardest
things
in
his
booke
easy
for
thy
understanding
.
Let
the
full
sea
at
your
place
of
being
be
at
a
S
Moone
on
the
day
of
conjunction
as
at
a
,
and
the
Sunne
going
in
4
degrees
,
as
from
a
to
c
,
the
Moone
removing
in
the
meane
time
48
degrees
from
the
Sunne
,
as
to
d
,
doth
make
3
houres
12
minutes
after
noone
for
the
time
of
high
water
;
and
in
16
dayes
more
the
Sunne
going
from
c
to
e
,
that
is
●0
degrees
from
a
:
in
the
meane
time
the
Moone
going
from
d
to
f
,
that
is
260
degrees
from
a
,
which
maketh
17
houres
20
minutes
,
then
substract
12
houres
0
minutes
from
17
houres
20
minutes
,
the
remainder
5
houres
20
minutes
;
out
of
which
take
1
houre
20
minutes
for
the
time
of
the
Sunnes
motion
in
20
dayes
,
remainder
4
a
clocke
for
the
true
time
of
full
sea
the
Moone
being
20
dayes
olde
;
if
you
perceive
not
the
reason
hereof
inquire
futher
,
and
so
you
may
examine
the
truth
hereof
.
Therefore
to
the
ignorant
and
honest
Seaman
I
say
,
joyne
these
things
in
practise
with
those
things
thy
Master
doth
teach
thee
at
sea
:
And
to
those
things
you
learne
at
sea
by
experience
joyne
the
practise
of
the
things
taught
in
this
booke
,
and
you
shall
be
able
in
short
time
,
through
Gods
grace
,
no
doubt
,
to
take
charge
thy selfe
to
thy
great
commendations
.
To
conclude
,
you
may
doe
most
of
the
things
taught
in
this
booke
as
afore
spoken
of
chapter
the
4
,
with
rular
and
compasses
;
which
if
you
practise
and
make
your selfe
able
to
performe
,
(
wishing
to
every
good
man
that
is
willing
to
follow
these
rules
,
that
I
were
at
his
elbow
to
make
him
a
more
plaine
demonstration
)
he
shall
be
able
in
a
short
time
,
to
doe
such
service
,
which
without
those
will
not
be
performed
in
ten
times
so
much
time
.
And
so
I
pray
thee
to
accept
of
this
my
labour
,
for
unto
such
as
are
ignorant
and
honest
,
that
would
learne
,
onely
doe
I
write
this
booke
:
And
be
sure
to
reade
it
all
before
you
judge
,
so
shall
you
see
that
such
a
thing
there
is
,
then
reade
it
over
againe
,
and
you
shall
see
what
manne●
of
thing
it
is
,
so
you
may
judge
of
the
good
will
of
the
Authour
,
and
reade
it
over
the
third
time
to
thy
singular
profit
.
As
in
Ecclesiasticus
chapter
the
22.
verse
●3
,
it
i●
〈◊〉
neighbour
,
so
I
say
to
thee
of
thy
friend
to
Navigation
;
〈◊〉
Be
faithfull
to
him
in
his
poverty
,
that
you
may
rejoyce
with
him
in
his
prosperity
,
abide
stedfast
with
him
in
the
time
of
his
trouble
,
that
you
may
be
heire
with
him
in
(
this
his
little
book
)
his
heritage
:
for
a
meane
estate
is
not
alwayes
to
be
contemned
,
nor
the
rich
that
is
foolish
to
be
had
in
admiration
.
Now
I
besech
Almighty
God
of
his
mercy
in
Christ
Iesus
,
that
wee
may
so
profit
in
Christs
schoole
,
that
wee
may
bee
able
thereby
to
passe
the
waves
of
this
sea
of
glasse
,
that
we
may
all
arrive
at
the
haven
of
eternall
happinesse
.
Amen
.
FINIS
.