The
third
Proposition
.
A
Comet
,
or
the
Moone
appearing
,
to
find
the
Paralax
or
difference
of
aspect
thereof
,
and
thereby
the
distance
of
the
same
aboue
the
Centre
or
Circumference
of
the
Earth
.
Wh●●
Par●●●●
is
.
THe
Paralax
or
difference
of
Aspect
(
according
to
the
Astronomers
)
is
an
angle
,
made
of
the
concurrence
of
the
visual
lyne
,
directly
respecting
a
Coelestiall
luminary
;
and
of
the
lyne
of
the
true
mouing
;
which
proceedeth
from
the
Centre
of
the
Earth
,
passing
by
the
Centre
of
the
same
Luminarie
,
vnto
the
Firmament
;
The
semidiametre
of
the
Earth
,
beeing
the
sole
efficient
cause
of
such
Angles
.
Neyther
do
such
angles
happen
to
euery
of
the
coelestial
Luminaries
,
saue
onely
to
such
as
are
neerest
vnto
the
Earth
,
as
the
☽
☿
♀
and
☉
;
and
amongst
them
also
,
those
which
are
neerest
,
haue
most
sensible
paralax
,
or
difference
of
Aspect
:
as
the
figure
following
doth
plainely
demonstrate
.
diagram
wherein
A
representeth
the
Centre
of
the
Earth
,
A
B
the
Semidiametre
,
A
F
the
verticall
lyne
,
D
the
farthest
or
more
remote
Luminarie
,
yeelding
smallest
paralax
,
A
E
the
lyne
of
his
true
place
in
the
firmament
,
K
the
neerest
Luminary
,
yeelding
greatest
Paralax
,
A
I
the
lyne
of
the
true
place
thereof
,
B
G
the
visuall
lyne
,
the
Obseruor
being
in
B.
Whereby
it
appeareth
,
that
the
Angle
E
D
G
,
or
his
verticall
B
D
A
,
being
the
Paralax
of
the
more
remote
Luminary
,
is
lesse
then
the
angle
I
K
G
,
or
his
verticall
B
K
A
,
the
Paralax
of
the
neerer
Luminary
:
both
which
Paralaxes
,
are
caused
by
the
sensible
quantity
of
the
Semidiametre
of
the
Earth
,
beeing
compared
with
their
Orbs.
How
to
find
the
quantitie
of
the
Paralax
.
To
finde
the
quantitie
of
the
Paralax
of
the
Moone
,
or
Comet
,
for
any
hower
or
Meridian
giuen
,
during
the
appearance
thereof
aboue
the
Horizon
:
you
shall
with
the
Cosmodelite
(
the
Circle
thereof
being
inclyned
according
to
the
inclination
of
the
Equator
)
take
two
seuerall
Obseruations
(
hauing
some
space
of
tyme
betweene
)
:
at
each
of
which
,
seeing
the
said
Comet
or
Moone
through
the
sights
of
the
Index
,
you
must
carefully
note
the
degrees
intersered
therewith
,
in
the
Limbe
of
the
said
Circle
.
Then
comparing
the
quantity
of
the
arch
contayned
betweene
the
two
poyntes
(
at
the
seuerall
obseruations
)
intersected
in
the
said
Limb
,
with
the
arch
answering
to
the
space
of
tyme
betweene
the
two
obseruations
(
beeing
reduced
into
degrees
and
minutes
of
the
Equinoctiall
)
and
the
lesser
arch
substracted
from
the
greater
,
the
remaynder
is
the
Paralax
or
difference
of
aspect
sought
.
Although
some
perhaps
will
say
here
,
that
the
Planets
,
by
reason
of
their
excentricities
and
proper
mouings
,
do
vnequally
mooue
,
in
respect
of
the
Primum
Mobile
:
which
although
I
confesse
,
yet
I
say
,
that
in
the
space
of
tyme
,
spent
in
the
said
Obseruation
,
the
same
is
so
insensibly
small
,
as
that
it
were
absurd
to
make
any
scruple
thereof
.
Another
way
to
find
the
Paralax
.
First
seeke
,
out
of
the
Astronomicall
Tables
or
otherwise
,
the
true
place
,
in
the
Zodiack
,
of
the
Luminary
you
will
obserue
,
for
the
tyme
and
Meridian
assigned
;
then
examine
the
true
place
of
some
knowne
fixed
star
,
or
one
of
the
Superior
Planets
,
(
appearing
at
that
tyme
aboue
the
Horizon
giuen
)
:
thereby
obtayning
the
Angle
,
subtending
the
Arch
of
the
Distance
from
one
of
those
Luminaryes
to
the
other
:
Then
take
the
visuall
distance
(
by
some
exact
Mathematicall
Instrument
)
betweene
the
said
two
Luminaries
:
which
had
,
and
compared
with
the
former
so
calculated
,
the
difference
is
the
Paralax
of
the
said
lower
Planet
or
Luminary
,
for
that
instant
.
The
like
may
be
performed
by
the
Sun
,
at
his
rising
or
setting
,
beeing
neere
the
Horizon
,
and
hauing
some
Planet
or
notable
fixed
Star
nigh
vnto
him
.
And
here
you
may
note
,
that
the
Paralax
is
alwayes
greater
,
neere
the
Horizon
,
then
beeing
more
eleuated
:
As
also
that
the
superior
Planets
♄
℞
and
♂
scant
yeelde
any
sensible
Paralax
,
by
reason
of
the
small
quantitie
of
the
Earths
semidiametre
,
in
respect
of
their
Orbs.
To
finde
the
distance
of
any
Comet
or
Planet
aboue
the
Earth
.
diagram
diagram
Then
to
finde
how
farre
the
said
Luminarie
is
distant
from
the
Earth
(
hauing
described
the
proportionall
Tryangle
aforesaide
)
and
hauing
the
measure
of
one
of
the
sides
thereof
giuen
,
viz
,
the
Semidiametre
of
the
Earth
AK
,
which
according
to
most
writers
is
3436
4\11
myles
,
which
measure
I
find
to
be
6.
tymes
and
a
halfe
,
contained
in
the
side
KC
,
and
therefore
conclude
the
same
to
be
distant
from
the
Centre
of
the
Earth
,
21477
2/11
myles
;
and
from
the
surface
of
the
Earth
,
18041
1/11
myles
.
Thus
much
is
sufficient
,
for
the
finding
of
the
Paralax
,
and
distance
of
any
Coelestiall
body
(
hauing
Paralax
)
from
the
Centre
or
superficies
of
the
Earth
.
The
Eighth
Proposition
.
How
to
find
the
Longitude
Mechanically
,
&
to
describe
al
the
notable
places
in
a
Region
or
Country
,
on
a
Map
or
Plat
,
according
to
theyr
true
situations
and
distances
one
from
another
.
TO
performe
this
Proposition
,
there
must
bee
first
prouided
a
kynd
of
Horse-litter
(
lyke
to
the
figure
following
)
hauing
one
wheele
,
of
such
greatnesse
,
as
(
the
horses
trauayling
,
with
the
same
)
it
may
lightlie
trample
on
the
face
of
the
Earth
,
and
easilie
turne
about
,
alwayes
answering
,
in
his
motion
,
the
swiftnesse
or
slownesse
of
the
horses
pasing
.
This
wheele
must
also
mooue
or
turn
about
other
wheels
,
so
framed
,
as
that
with
an
Index
,
it
may
(
after
the
ordinary
manner
of
common
watches
)
expresse
when
the
said
great
wheele
(
so
trampling
)
shall
haue
iustly
measured
a
certain
number
of
pases
,
pearches
,
or
furlongs
,
and
theyr
parts
;
in
such
sorte
,
as
that
the
Obseruator
(
in
the
Hoslitter
)
may
readily
find
at
any
tyme
by
the
same
,
how
many
pases
,
pearches
,
or
furlongs
,
the
saide
Horselitter
shall
haue
passed
ouer
.
There
must
bee
also
a
perfect
Marine
Compasse
,
or
else
a
large
magneticall
Needle
and
Fly
,
hanged
in
the
same
manner
,
with
circles
of
brasse
which
I
hold
better
and
more
exact
,
by
reason
it
is
not
so
ponderous
,
vpon
the
poynt
of
the
Pinne
;
and
therefore
must
of
necessity
be
more
quick
and
ready
to
shew
the
true
respectiue
poynt
.
All
which
,
beeing
fitly
placed
in
the
saide
Litter
,
and
he
being
seated
therein
;
when
the
horses
begin
to
make
way
,
let
him
note
in
his
Maryne
Compasse
iustly
,
vpon
what
poynt
of
the
Compasse
or
parts
,
they
make
theyr
direct
coutse
:
Or
if
hee
shall
vse
the
Needle
and
Flye
afore
mentioned
,
then
let
him
obserue
what
poynt
,
or
degree
,
the
South
poynt
of
the
Needle
shall
cut
(
in
the
Lymbe
of
the
said
Flye
)
,
vntill
hee
come
to
the
next
turning
or
angle
;
which
must
bee
diligently
set
downe
in
a
paper
or
Table
,
at
euery
angle
,
together
with
the
number
of
Pases
,
Pearches
,
or
Furlongs
found
(
from
one
angle
to
the
next
)
by
the
said
Index
:
alwayes
distinguishing
each
angle
,
with
the
measured
Quantitie
betweene
that
and
the
last
before
,
with
seueral
characters
or
Alphabeticall
notes
;
to
auoyde
the
mistaking
of
them
,
one
for
another
.
Thus
much
carefully
performed
,
and
the
notes
of
the
seuerall
direct
courses
from
Angle
to
angle
,
with
the
measured
quantity
between
each
angle
exactly
set
down
;
there
is
no
more
to
be
don
abroad
,
but
hee
may
then
,
in
his
chayre
at
home
,
draw
with
a
protractor
(
diuided
in
al
poynts
answerable
to
the
diuisions
of
the
Marine
Compasse
,
or
to
the
Flye
vnder
the
Needle
)
by
the
notes
aforenamed
,
the
whole
way
,
with
euery
angle
or
turning
,
and
all
things
and
places
of
note
,
as
Riuers
,
houses
,
gates
,
paths
,
styles
,
trees
,
&
such
lyke
,
by
or
through
which
the
said
Litter
passed
.
diagram
diagram
The
practise
and
vse
of
the
Protractor
followeth
.
Hauing
the
notes
of
the
true
distance
from
Angle
to
Angle
,
and
how
they
beare
and
are
situate
one
from
another
,
draw
on
the
Parchement
or
paper
,
whereon
the
Plat
shall
be
drawne
,
certaine
obscure
straite
lyned
Paralelles
ouer
the
whole
face
thereof
;
each
,
two
inches
or
thereabouts
,
distant
one
from
an
other
.
Then
begin
at
such
a
place
,
as
that
the
Parchement
or
Paper
may
each
way
be
able
to
receiue
the
whole
description
(
which
reason
will
shew
)
,
and
place
the
Protractor
(
by
meanes
of
the
diuisions
engraued
on
the
ends
of
the
long
square
thereof
)
vpon
,
or
paralell
to
,
one
of
the
descrybed
obscure
pararelles
:
then
seeke
in
the
Lymbe
for
the
poynt
of
the
Compasse
,
or
degree
,
by
which
the
second
Angle
is
noted
to
bear
or
be
situate
from
the
first
:
there
make
a
prick
,
and
drawe
an
infinite
obsceure
lyne
,
from
the
Centre
of
the
Protractor
,
through
the
said
prick
;
Then
open
a
paire
of
Compasses
,
to
the
proportion
of
a
Scale
(
answerable
to
the
distance
noted
,
from
the
first
Angle
to
the
second
)
and
set
one
foote
in
the
poynt
,
where
the
Centre
of
the
Protractor
was
,
and
with
the
other
foote
(
the
Compasses
vnaltered
)
note
a
prick
in
the
saide
obscure
lyne
;
which
will
there
represent
the
true
place
,
distance
and
situation
,
of
the
second
angle
from
the
first
.
Then
,
placing
the
Centre
of
the
Protractor
vpon
the
last
described
prick
,
do
in
al
things
as
before
,
both
for
the
poynt
of
the
Compasse
or
degree
,
and
for
the
distance
also
,
and
consequently
the
lyke
for
all
the
other
angles
,
vntill
they
bee
all
described
in
the
same
,
according
to
theyr
true
distance
,
situations
,
wayes
,
&
turnings
,
and
by
which
the
Horselitter
passed
,
and
for
which
the
saide
notes
were
so
taken
.
Note
,
that
if
there
should
bee
betweene
any
two
of
the
angles
some
small
crookednesse
or
bending
,
the
forme
thereof
may
be
well
represented
on
rue
paper
of
notes
,
the
same
beeing
present
to
the
Obseruators
eye
.
Likewise
if
there
be
any
House
,
Gate
,
style
,
tree
,
or
any
other
thing
fit
to
be
noted
;
the
Obseruator
,
making
remembrances
in
his
said
notes
,
may
easily
with
his
Protractor
make
description
of
them
,
answerable
to
theyr
situations
and
distances
.
Then
,
hauing
the
true
Longitude
and
Latitude
of
anie
one
place
described
in
the
sayde
Plot
or
Mappe
,
it
cannot
bee
but
the
Longitudes
and
Latitudes
of
all
other
places
therein
will
offer
them selues
,
by
reason
of
theyr
knowne
situations
and
distances
.
Thus
haue
you
the
meanes
to
finde
the
Longitudes
mechanicallie
:
and
how
to
make
a
Mappe
or
Chart
of
any
Region
,
Countrey
,
Shiere
,
and
all
the
places
of
note
within
them
,
verie
exactlie
.
The
forme
of
the
Horselitter
.
It
will
bee
also
necessarie
to
place
a
scale
of
the
same
proportionall
euen
●arts
,
were
they
myles
,
Furlongs
or
pases
,
by
which
you
made
your
saide
Plot
or
Map
,
in
the
most
conuenient
spare
place
:
and
if
you
wil
also
,
a
Flye
containing
the
poynts
of
the
Compasse
duely
situate
will
not
be
impertinent
.
A
Corollary
.
Then
it
followeth
by
the
same
reason
,
vsing
only
a
Chayne-lyne
of
2.3
.
or
4.
pearch
length
,
in
the
stead
of
the
Horselitter
,
to
measure
the
distances
betweene
the
seuerall
angles
,
and
an
Instrumente
with
sights
(
as
the
Cosmodelite
herein
mentioned
,
or
such
〈…〉
a
perfect
:
Magneticall
needle
,
to
expresie
(
vpon
a
Flye
placed
vnderneath
the
same
)
the
degrees
or
poynts
of
the
Compasse
intersected
when
the
said
sights
shall
bee
directed
vnto
or
respect
the
seuerall
angles
,
euerally
;
with
which
and
the
quantity
of
pearches
,
conteyned
betweene
the
seuerall
angles
distinctly
noted
,
and
the
same
then
protracted
in
all
poynts
according
to
the
formen
instructions
,
you
may
truely
describe
any
field
,
Mannour
,
Park
,
forrest
wood
,
or
Fortification
,
in
a
Chart
,
Map
or
Plat
,
very
exactly
.
Corollarie
.
II.
Likewise
to
find
the
Longitude
of
any
place
at
Sea
,
mechanically
;
there
may
be
an
engine
made
&
ioyned
to
the
side
of
the
Ship
,
hauing
a
wheele
finned
(
lyke
the
wheel
of
a
water
mil
)
and
hanged
in
a
Channel
(
made
of
boards
)
with
Circles
lyke
the
marine
Compasse
,
to
the
end
it
may
alwayes
hang
leuell
in
the
said
Channell
,
and
so
moue
by
meanes
of
the
water
passing
through
the
same
;
it
being
both
at
the
entry
and
issue
narrow
,
and
wide
in
the
midst
to
withstand
the
billowes
and
waues
,
which
would
otherwise
hinder
the
proportionall
turning
of
the
said
wheel
:
which
may
also
with
an
Index
in
the
manner
of
that
of
the
Horselitter
,
expresse
how
much
the
Ship
shall
haue
made
way
,
from
the
time
of
setting
forth
,
alteration
of
the
course
,
or
from
watch
to
watch
:
which
together
with
true
notes
of
the
seuerall
courses
by
what
poynt
of
the
C̄opasse
the
Ship
hath
performed
her
way
,
and
in
all
things
(
in
this
practice
)
imitating
the
fore-taught
operations
for
the
Hoslitter
,
the
true
description
of
the
course
and
quantity
of
Leagues
,
with
the
angles
and
turnings
,
that
such
a
Ship
shall
make
,
from
time
to
time
in
a
whole
voyage
,
shal
by
these
means
be
truly
set
forth
and
kept
,
in
the
maner
of
a
Trauerse
.
And
at
any
time
applying
the
same
on
the
Sea
Chard
or
plat
,
the
Longitude
&
Latitude
of
any
place
in
the
same
will
be
presently
found
,
together
with
the
true
place
where
the
same
Ship
for
that
tyme
is
,
or
was
at
any
tyme
in
the
whole
voyage
;
and
how
farre
distant
from
any
Hauen
,
Iland
,
Sands
,
Rocks
,
or
dangers
described
in
the
said
Map
or
Seacard
.
Annotatio
.
How
the
Master
or
Pylot
at
Sea
may
,
with
any
Instrument
,
much
more
exactly
obserue
the
Coelestial
luminaries
,
then
the
ordinary
manner
can
admitte
.
I
Cannot
here
omit
,
though
in
digressing
manner
,
to
set
down
a
means
written
by
an
excellent
French
Author
,
(
from
whome
I
confesse
I
gathered
manie
flowers
to
decorate
this
small
posie
,
)
whereby
the
Seamen
may
,
notwithstanding
the
heauing
&
setting
of
the
Ship
,
with
much
more
exactnesse
obserue
,
with
their
Instrument
,
the
Sun
,
Stars
and
any
Coelestiall
Luminary
,
then
theyr
ordinary
and
vsuall
manner
can
permit
,
For
by
mine
owne
practise
I
continually
found
it
almost
impossible
(
in
a
calme
excepted
)
to
make
any
exact
obseruation
,
by
reason
of
the
violent
shaking
of
the
body
,
caused
by
the
continuall
agitation
of
the
Ship
.
First
then
in
some
conuenient
place
in
the
Shippe
,
there
must
be
two
small
p●●●es
of
Tymber
,
of
4.
feet
a
peece
in
length
,
set
vpright
4.
or
5.
feete
distant
one
from
another
,
to
support
,
at
the
vpper
ends
of
them
,
two
great
Iron
circles
hanged
like
the
brasse
circles
of
the
marine
Compasse
:
within
which
Circles
ther
may
be
a
seat
&
Table
so
placed
,
as
that
the
Obseruor
(
beeing
entered
therin
)
may
hang
steady
&
leauel
,
although
the
Ship
it selfe
do
heaue
and
set
,
and
shall
be
able
thereby
more
perfectly
to
obserue
any
Coelestiall
Luminary
with
exactnesse
.
And
the
whole
frame
may
be
so
made
,
that
it
may
be
taken
asunder
,
and
set
vp
and
down
at
pleasure
,
to
auoide
incombrance
.
The
making
of
the
Cosmodelite
,
an
excellent
Instrument
for
many
Mathematical
practises
in
Astronomy
,
Geometry
,
and
Cosmography
,
viz
,
for
the
finding
of
the
Longitude
of
any
place
;
To
take
any
Altitude
Latitude
or
distance
within
the
Angle
of
sight
;
To
make
a
Map
or
Plat
of
any
Country
,
Mannor
,
field
,
fortification
or
Towne
;
To
delineate
Sun
dialls
vpon
all
planes
giuen
,
with
great
facility
,
inuented
by
the
Author
.
WHether
you
will
haue
your
instrument
of
Brasse
or
fine
grained
Woode
,
you
must
frame
a
Circle
of
fiue
or
six
Inches
Diametre
at
the
least
,
within
the
Lymbe
of
which
,
you
may
describe
&
engraue
certain
Circles
one
within
another
,
(
for
seuerall
vses
)
:
one
of
which
Circles
shall
be
diuided
into
360.
equall
parts
or
degr●●s
,
which
shall
serue
for
astronomicall
and
〈◊〉
●eometricall
obseruations
;
another
of
the
said
circles
shall
be
diuided
into
24.
equall
parts
,
(
and
eache
of
them
again
into
subdiuisions
,
as
halves
&
quarters
)
which
shal
both
serue
of
it selfe
for
an
Equinoctial
Diall
,
being
inclyned
to
the
inclination
of
the
Aequator
;
and
also
most
readily
to
delineate
all
Sun
Dialls
,
Murall
and
Horizontall
,
as
in
the
Proposition
preceding
is
fully
taught
.
Then
shal
you
make
an
Index
of
the
length
of
the
whole
Circles
Diametre
,
whose
fiduciall
lyne
may
serue
for
each
seuerall
inscribed
Circle
,
and
erect
a
sight
neere
vnto
each
end
thereof
.
Then
also
make
a
Semicircle
about
three
inches
Diametre
,
leauing
some
part
more
then
a
Semicircle
aboue
the
Diametre
thereof
,
both
for
the
better
ioyning
the
same
vnder
the
Circle
,
which
must
be
done
directlie
vnder
one
o●
the
Diametres
,
and
for
the
better
scope
to
eleua●●
or
embase
the
same
;
The
lymbe
of
which
Se●●circle
you
shall
diuide
into
180.
equall
partes
or
degrees
,
viz
,
each
Quadrant
into
90.
There
must
be
also
a
peece
of
the
same
substance
so
framed
,
as
that
the
Semicircle
may
,
as
betweene
two
Cheekes
or
supporters
,
mooue
vp
and
downe
to
any
inclination
,
vpon
a
pin
which
must
passe
through
the
Centre
of
the
Semicircle
and
heads
of
the
said
Cheeks
or
supporters
,
and
must
haue
at
the
smaller
end
a
Nut
and
screw
to
locke
the
same
at
pleasure
;
&
the
saide
Cheeks
must
haue
a
fiduciall
edge
,
to
note
in
the
Lymbe
of
the
Semicircle
the
eleuation
and
inclination
of
the
great
C●●●e
,
when
occasion
shall
require
.
Furthermore
the
lower
end
of
the
Cheeks
must
bee
ioyned
to
the
staffe
(
which
must
support
the
whole
)
as
the
two
feete
of
a
payre
of
Compasses
,
or
rather
as
the
legs
of
the
Sector
or
Circumferental
Scale
are
ioyned
together
,
with
three
round
planes
to
make
one
ioynt
head
:
the
two
outmost
of
those
planes
we
wil
cal
Eares
,
&
do
differ
only
from
the
head
of
a
Sector
in
a
pinne
which
is
to
passe
through
the
Centre
carrying
a
double
Index
at
one
end
thereof
,
and
the
other
end
must
bee
fitted
to
a
screw
nut
,
to
locke
the
same
fast
when
you
please
:
also
the
middle
part
of
the
same
pin
must
be
square
;
yet
round
towards
each
end
,
fitted
to
the
three
holes
in
the
Centre
of
the
three
round
planes
,
the
hole
of
the
middle
plane
beeing
square
to
the
end
,
when
the
Instrument
is
inclyned
;
that
then
this
●quare
hole
may
,
by
reason
of
the
squarenesse
of
the
●iddle
of
the
Pin
,
carry
the
said
double
Index
with
it
proportionally
Circular
vpon
that
eare
whereon
it
mooues
:
whose
Lymbe
,
being
likewise
diuided
into
degrees
,
will
expresse
there
the
true
quantity
of
such
inclination
.
And
it
is
also
very
necessary
to
place
,
on
the
Centre
of
the
great
Circle
and
Index
thereof
(
after
the
vsuall
maner
)
a
box
with
a
perfect
Magneticall
needle
therein
,
and
a
fly
fixed
in
the
bottom
,
exactly
diuided
into
degrees
and
Rombes
,
hauing
the
variation
of
the
compasse
for
the
place
of
obseruation
alwayes
noted
therein
.
Thus
is
the
Cosmodelite
fitly
prepared
●o
performe
your
expectation
in
any
Mathematicall
obseruation
.
The
figures
of
each
part
,
before
mentioned
,
follow
heere
demonstrated
.
diagram
The
great
Circle
is
A
,
the
Index
thereof
C
,
and
the
sights
for
the
same
Index
K
K
:
the
Semicircle
is
B
,
which
is
to
be
ioyned
directly
vnder
the
Diametre
L
M.
The
peece
with
two
Cheeks
is
E
,
the
vpper
pin
and
screw
thereof
,
I
:
the
lower
end
of
the
same
peece
,
beeing
the
middle
plane
with
a
square
hole
at
the
Centre
,
D
;
the
other
two
planes
ioyned
to
the
Staffe
F
:
the
pinne
for
the
same
and
the
screwes
therof
are
G
&
H
:
the
box
with
a
Magnetical
needle
P
,
to
be
placed
on
the
Centre
and
Index
.
All
which
ioyned
together
is
represented
by
the
figure
at
N.
Here
could
I
further
adde
two
other
necessarie
parts
vnto
the
saide
Instrument
:
one
whereof
,
for
●●e
making
of
a
Chorographicall
description
,
on
a
●●●p
or
Plat
,
of
al
the
angles
in
sight
,
at
one
sole
sta●●●●
.
The
other
,
by
two
seuerall
stations
,
(
without
●●ng
the
respecting
lynes
by
degrees
,
poynts
of
〈◊〉
Compasse
,
or
parts
of
eyther
;
and
without
the
〈◊〉
of
Protractor
,
or
any
arithmeticall
notations
)
●●eally
to
describe
on
the
saide
Instrument
all
the
notable
places
,
which
at
these
two
stations
were
to
be
seene
:
according
to
their
true
distances
and
situations
,
each
from
other
.
All
which
and
many
other
,
if
I
shall
find
these
acceptable
,
I
wil
hereafter
eyther
generally
publish
,
or
particularly
explane
to
any
true
well
willer
of
these
practise
.
Also
I
might
heere
apply
the
vse
of
this
Instrument
to
measure
all
visuall
distances
within
the
Angle
of
sight
,
and
how
to
cary
a
Rowling
trench
vnder
Grounde
directly
vnto
any
place
appoynted
to
be
vndermined
with
infinite
other
necessary
conclusions
:
But
because
the
most
of
them
haue
beene
already
taught
how
to
be
performed
by
other
instruments
(
not
so
general
as
this
)
I
therefore
presume
,
the
ingenious
practiser
will
with
so
much
ease
apply
them
hereunto
as
it
might
seeme
superfluous
for
me
here
to
iterate
the
same
.
How
by
the
helpe
of
the
Cosmodelite
to
delineate
a
Sunne
Diall
,
on
any
Plane
giuen
,
with
great
facility
&
without
the
vse
of
Arithmetick
.
PLace
the
Cosmodelite
so
vpon
his
foote
,
as
that
it
may
be
neere
vnto
the
Plane
or
wall
whereon
you
desire
to
draw
your
Sun
Dial
,
being
se●
so
directly
vpright
,
by
the
helpe
of
a
Plummet
〈◊〉
otherwise
,
that
the
planes
of
the
Eares
thereof
be
〈◊〉
perpendicular
to
the
Horizon
:
that
done
,
locke
fa●●
the
saide
Eares
with
the
screw
and
nut
.
Then
by
the
Magneticall
needle
or
otherwyse
,
place
the
lyne
of
12
(
in
the
Instruments
great
Circle
)
directly
in
the
Meridian
lyne
of
that
place
:
and
(
by
the
Semicircle
and
degrees
thereof
)
embase
the
North
part
of
the
same
great
Circle
,
so
many
degrees
as
the
North
part
of
the
Aequinoctiall
is
embased
vnder
the
Horizon
,
and
so
shall
the
plane
of
the
great
Circle
be
found
to
be
in
the
true
plane
of
the
Aequator
of
the
world
,
which
it
heere
representeth
.
Thus
all
parts
of
the
Cosmodelite
being
fast
locked
,
it
is
readily
prepared
to
delineate
a
Sun
Diall
on
any
plane
,
against
which
it
is
placed
as
aboue
said
.
To
practise
this
Proposition
you
shall
first
(
the
Cosmodelite
placed
according
to
the
former
directions
)
fasten
in
the
Centre
of
the
great
Circle
,
a
threed
of
5.
or
six
foote
in
length
,
and
erect
the
same
perpendicular
to
the
plane
of
the
same
great
Circle
;
extending
it
so
farre
,
as
it
may
intersect
the
giuen
Plane
,
and
therein
note
a
poynt
or
prick
;
which
prick
shall
be
both
a
Centre
to
the
hower
lynes
,
&
also
the
poynt
from
which
the
Style
or
Ostens●r
for
the
same
Diall
must
proceede
:
and
the
same
lyne
,
so
erected
,
doth
also
well
demonstrate
vnto
you
the
verie
fiduciall
edge
of
the
Ostensor
or
style
:
These
things
performed
,
you
haue
now
no
more
to
doe
for
the
setting
●●rth
of
the
hower
pricks
in
the
said
Plane
,
but
to
〈◊〉
the
said
three●
straite
,
vpon
eache
of
the
hower
●es
engraued
on
the
Instrument
,
and
to
extend
●●e
same
forth
so
far
,
at
each
tyme
,
as
it
may
touch
●nd
make
so
many
seu●rall
pricks
as
there
will
fall
hower
lynes
(
in
that
maner
)
on
the
said
Plane
:
as
for
such
howers
whereon
the
threed
beeing
applyed
,
and
infinitely
extended
,
will
not
yet
any
where
intersect
the
said
Plane
,
it
is
certaine
that
those
howers
cannot
be
found
on
that
Plane
,
by
the
shadow
of
the
Sun
.
All
the
pricks
beeing
so
set
downe
,
on
the
Plane
,
that
will
fall
thereon
;
you
must
then
draw
a
straite
lyne
from
the
first
described
pricke
,
to
eache
of
the
other
pricks
,
and
those
shall
be
the
hower
lynes
,
for
the
same
Diall
,
truely
described
.
Then
an
Ostensor
or
Style
hauing
his
fiducial
edge
and
being
placed
according
to
the
former
instruction
,
and
the
figures
for
eache
hower
set
downe
at
the
end
of
each
of
them
,
to
distinguish
them
one
from
another
:
you
shall
so
haue
descrybed
an
exact
Sunne
Dyall
,
Perspectiuelie
.
Note
that
if
,
in
the
erecting
of
the
threed
perpendicular
to
the
plane
of
the
great
Circle
,
it
happen
to
bee
paralell
to
the
plane
(
on
which
you
haue
described
your
Sunne
dyall
as
aforesayde
)
and
so
will
no
where
intersect
the
same
plane
;
Then
must
the
Ostensor
or
Style
be
also
paralel
,
and
of
such
distance
from
the
plane
giuen
as
the
perpendicular
erected
threed
extended
is
.
Thus
may
you
by
the
helpe
of
the
Cosmodelite
delineate
a
Sunne
Diall
,
Direct
,
Inclyning
,
Declyning
,
or
Reclyning
,
on
any
Plane
,
or
H●rizon
giuen
.
Master
Robert
Smyth
his
intention
to
delineate
a
Sun
Dialll
on
any
Plane
in
any
one
Paralel
giuen
,
with
a
Instrument
of
sleight
charge
.
FIrst
draw
a
Quadrant
,
and
diuide
the
Arch
thereof
into
90.
equall
partes
or
degrees
,
and
extend
a
straite
lyne
from
the
Centre
or
square
angle
of
the
same
,
vnto
the
degree
in
the
arch
answering
the
Latitude
of
the
paralell
giuen
;
prolonlonging
the
same
lyne
,
beyond
the
Arch
or
lymbe
,
some
6.
or
8.
inches
,
or
more
or
lesse
at
pleasure
.
Also
extend
the
Base
lyne
of
the
Quadrant
as
farre
as
you
thinke
fit
(
for
the
bignesse
of
your
instrument
)
and
at
the
end
of
the
same
lyne
erect
a
perpendicular
which
may
intersect
the
first
extended
lyne
.
So
shall
the
sayde
perpendicular
,
the
Base
,
and
the
line
drawne
by
the
degree
of
Latitude
,
describe
vnto
you
a
rectangled
Tryangle
.
Then
drawe
a
Circle
(
whose
Dyametre
may
be
about
halfe
the
length
of
the
Base
lyne
of
the
Tryangle
aforesaide
)
and
diuide
the
Circumference
of
the
said
circle
into
24.
equall
partes
:
in
the
Centre
of
which
Circle
you
shall
fix
a
threed
of
4.
or
5.
feete
in
length
:
The
said
Tryangle
and
Circle
being
then
cut
out
of
some
thin
boord
of
fine
grained
woode
,
and
the
circle
let
on
,
vpon
the
side
of
the
Tryangle
which
subtendeth
the
square
angle
,
so
farre
as
that
the
centre
of
the
circle
may
touch
or
exactlie
ioyne
to
the
said
line
,
●nd
the
plane
of
the
circle
stand
square
to
the
said
●yne
,
and
the
diuisions
being
distinguished
Arithmetically
from
12.
to
12.
as
appeareth
in
the
figure
following
:
The
sayde
Instrument
is
readie
to
performe
the
promised
effecte
in
manner
following
.
diagram
The
vse
and
practise
of
the
said
Instrument
.
Place
and
fasten
your
Tryangle
vpon
or
neere
vnto
the
Plane
on
which
you
purpose
to
drawe
the
Sundiall
,
in
such
manner
as
that
the
syde
E
F
may
be
perpendicular
vnto
the
Horizon
,
and
the
lyne
E
A
directly
in
the
Meridian
lyne
of
the
place
:
so
shall
the
lyne
A
F
be
found
to
represent
the
Axis
of
the
world
;
and
the
circles
circumference
to
bee
exactly
in
the
Plane
of
the
Aequinoctiall
.
Then
haue
you
no
more
to
doe
,
but
apply
the
threed
on
so
many
of
the
24.
diuisions
seuerally
,
as
,
being
infinitely
extended
,
it
note
in
the
plane
giuen
,
so
many
touch
poynts
as
there
can
be
howers
found
by
the
Sunnes
shadow
vpon
the
saide
plane
:
And
drawing
straite
lynes
from
the
poynt
in
the
plane
,
(
which
the
lyne
A
F
of
the
Tryangle
respects
)
vnto
eache
of
the
saide
touch
poynts
,
such
lynes
shall
be
the
true
hower
lynes
to
expresse
the
exact
hower
of
the
day
,
by
the
shadowe
of
an
Ostensor
or
Style
;
which
must
bee
placed
to
carry
the
true
forme
of
the
said
lyne
A
F
of
the
same
Tryangle
vpon
the
said
plane
giuen
:
Applying
also
the
Arithmeticall
characters
,
correspondent
to
those
of
the
circle
,
vppon
the
hower
lynes
seuerallie
,
you
shall
so
haue
delineated
a
perfect
Sundiall
vpon
the
Plane
giuen
.
The
making
of
an
artificiall
Engine
,
whereby
with
a
small
strength
giuen
,
you
may
lift
vp
any
ponderous
weight
assigned
WHen
Hieron
(
King
of
Sicilia
)
had
builded
a
a
Ship
of
such
admirable
greatnesse
(
to
present
vnto
Ptolome
,
King
of
Aegypt
)
as
that
al
the
inhabitants
of
Syracusia
,
were
not
able
by
any
meanes
they
could
practice
,
to
launch
it
into
the
water
:
Archimedes
,
that
excellent
Mathematician
,
caused
this
engine
to
be
framed
;
whereby
the
King
himselfe
,
did
with
one
hand
lift
vp
the
sayde
mightie
vessell
from
the
Earth
,
and
set
it
into
the
Sea
:
which
although
many
,
aswell
Historiographers
,
as
others
,
haue
in
theyr
works
mentioned
;
yet
none
haue
hitherto
set
downe
the
perfect
framing
thereof
,
saue
only
the
learned
Besson
;
who
ha●●
thus
left
it
vnto
posterity
.
The
Tripaston
(
for
so
〈◊〉
nameth
it
)
may
be
composed
,
of
as
many
wheele
and
screwes
(
to
turne
those
wheeles
)
as
you
wi●●
but
of
fower
of
each
at
the
least
.
The
first
screw
must
haue
a
handle
to
turne
about
lyke
the
handle
of
a
handmyll
or
grynding
stone
;
and
so
fitted
,
as
being
turned
round
,
it
may
also
turne
the
first
wheele
,
by
meanes
of
the
oblique
swellings
of
the
same
screw
,
falling
betweene
the
Teeth
or
Cogs
of
the
saide
first
wheele
:
which
Teeth
must
be
so
many
in
number
as
may
be
proportionall
to
the
strength
you
would
multiplie
by
the
same
.
The
Axletree
of
the
first
wheele
must
haue
vpon
the
same
a
second
screw
,
which
may
in
like
manner
,
and
proportion
,
turne
a
second
wheele
,
and
that
second
a
thirde
;
which
third
a
fowerth
,
and
so
infinitely
at
pleasure
.
Now
if
the
first
screw
(
by
the
handle
)
be
turned
about
20.
tymes
,
to
the
turning
of
the
first
wheele
once
:
I
affirme
that
the
sayde
first
wheele
will
lift
vp
as
much
poyse
or
burthen
,
as
the
strength
of
20.
men
will
extend
vnto
,
hauing
a
cord
fastened
to
the
same
,
and
to
the
Axletree
of
the
saide
first
wheele
,
and
a
man
to
turne
about
the
first
screw
by
the
handle
thereof
.
The
second
wheele
hauing
the
lyke
proportion
in
motion
to
the
first
as
the
first
hath
to
the
handle
,
I
conclude
that
the
second
wheele
will
in
lyke
sort
rayse
vp
20
tymes
20
mens
strength
,
which
is
400
mens
strength
.
The
third
wheele
20
tymes
400
mens
strength
,
which
is
8000.
The
fowerth
20
tymes
8000
which
is
160000
mens
strength
,
and
so
foorth
infinitely
;
A
thing
which
to
many
will
seeme
incredible
:
but
who
so
will
duely
put
the
same
in
practice
shall
find
it
fully
able
to
performe
the
promised
effect
:
whereby
it
appeareth
that
it
was
not
without
reason
,
that
Archimedes
affirmed
that
he
could
moue
the
whole
Globe
of
the
Earth
out
of
her
place
,
if
he
had
any
firme
place
in
the
Ayre
,
that
could
support
his
said
Engine
;
and
therevpon
made
this
Probleme
,
Datum
pondus
datis
veribus
mouere
.
But
here
may
some
make
question
,
if
the
slowenesse
of
this
Engin
cannot
by
some
Artificiall
meanes
be
hastened
:
to
which
I
answere
it
may
,
by
taking
away
one
or
two
of
the
last
wheeles
screwes
and
Axis
,
and
in
their
places
so
vse
common
Pullies
,
whereof
Vitruuius
wryteth
in
his
tenth
booke
and
third
Chapter
:
which
Pappus
in
his
Annotations
vpon
the
Mechanicks
of
Archimedes
affirmeth
to
haue
also
infinite
force
,
with
great
celerity
.
Thus
much
may
suffice
for
the
framing
of
this
Engine
,
whose
benefite
may
be
extended
to
infinite
necessary
vses
:
Onely
I
will
here
demonstrate
in
the
figure
following
the
forme
of
the
said
Screwes
and
wheeles
.
diagram
diagram