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Arthur
Hopton
AT
LONDON
,
Nicholas
Okes
Simon
Waterson
,
Topographical
glasse
,
Topographicall
glasse
.
1
de
Officiis
:
Quae
nihil
alienum
vendicat
,
quae
cuilibet
dat
,
quod
suum
est
,
quae
negligit
propriam
vtilitatem
,
vt
seruet
communem
aequitatem
;
Et
secundum
ipsum
,
prima
iusticia
in
Deum
,
secunda
in
patriam
,
tertia
in
parentes
,
quarta
in
omnes
.
cuilibet
dare
quod
suum
est
,
A
particulari
ad
generale
,
non
est
tenenda
ratio
:
Alphonsus
,
Aristarchu●
,
Archimides
,
Pauls
Church
.
Clauis
Mathematica
Circular
Scale
B
A
,
L
O
,
A
B
L
O
A
B
,
A
B
,
L
O
Aqua
vitae
Isosceles
Tryangle
Geodeticall
Staffe
,
Mathematicall
Staffe
,
5.
10.
15.
B
C
B
C
Orthogonium
Isosceles
,
A
B
,
A
C
,
A
B
A
C
C
A
C
D
C
B
,
C
B
,
O
N
,
C
O
,
C
P
,
C
Q
,
C
R
,
C
S
,
C
T
,
C
V
,
80.
70.
60.
50.
40.
30.
20.
C
B
,
C
B
B
F
:
B
D
,
B.
F
:
A
Z
:
A
B
,
A
A
,
A
S
A
B
:
A
R
,
A
Q
,
A
L
L
,
A
P
P
,
A
Z
A
R
A
T
,
A
Q
A
Y
,
A
L
L
A
D
,
A
B
A
C
D
E
D
F
E
D
D
F
,
C
B
,
C
B
,
C
F
C
H
,
C
I
C
K
,
C
L
C
M
,
C
N
C
O
,
C
P
C
Q
,
C
R
,
C
S
,
B
D
,
B
D
A
B
A
C
A
B
D
E
4.
H.
F.
w
A
R
Q
M
Q
N
A
B
I
L
O
Aqua
vitae
P
P
G.
M
N
N
Is
the
legs
closed
with
the
Graduator
therein
,
which
beeing
thrust
home
should
be
put
all
into
the
hollow
staffe
.
commodissimum
,
Tyronibusque
facillimum
:
Per
de
hospity
Sancts
Clementis
societate
conditum
&
editum
.
Is
the
Graduation
of
the
equall
diuisions
,
which
must
be
put
times
vpon
this
instrument
,
one
vpon
the
one
side
of
the
Graduator
,
and
twise
on
each
leg
,
as
in
the
Are
chorde
deuisions
,
and
are
placed
times
vpon
this
Instrument
,
once
on
the
Graduator
,
as
in
the
Proposition
,
and
once
on
each
leg
vpon
the
lower
side
outwards
,
as
in
the
Proposition
,
and
as
they
be
placed
in
the
figure
Are
degrees
of
a
circle
from
proiected
vpon
the
right
leg
Are
parts
of
the
Geometricall
quadrant
placed
one
by
one
,
on
one
of
the
sides
of
the
Graduator
,
as
in
the
Are
parts
of
the
placed
also
on
the
one
of
the
sides
of
the
graduator
,
as
in
the
These
things
so
ordered
,
you
must
place
of
thrée
Tables
insuing
vpon
the
outer
side
of
the
hollow
staffe
,
which
will
serue
you
for
many
pleasant
and
necessarie
vses
;
and
if
your
Staffe
be
too
small
to
hold
the
Table
of
the
Sunnes
altitude
,
as
he
may
if
you
make
the
legges
very
small
(
as
the
vse
is
being
in
brasse
or
siluer
)
then
may
you
omitte
to
stamp
the
minutes
on
the
right
hand
,
each
row
putting
one
degrée
more
vnto
the
degrées
,
if
the
minutes
answering
thereunto
much
excéede
and
so
may
you
place
the
Table
on
the
smallest
Staffe
that
is
.
Iohn
Tomson
for
the
number
of
Timber
measure
,
and
therefore
I
aptly
call
him
In
the
foote
of
this
staffe
,
there
must
be
a
steele
picke
,
and
in
the
top
,
two
péeces
of
Brasse
,
with
a
screw
hole
therein
for
the
center
pin
,
to
fasten
the
center
of
the
instrument
therunto
,
that
on
of
these
screw
péeces
,
must
stand
in
the
top
of
the
staffe
,
the
other
in
the
side
,
as
neare
to
the
top
as
you
can
,
the
first
serueth
to
take
angles
of
latitude
,
that
which
is
in
the
side
serueth
to
place
the
legges
to
take
Angles
of
altitude
,
as
will
appeare
in
the
second
Booke
.
Propo
.
B
C
B
C
,
O
P
,
M
N
,
I
K
I
A
C
B
R
C
R
B
R
A
,
A
C
A
B
,
B
A
C.
4.
Prop
.
4.
Prop
.
5.
10.
15.
20.
Of
the
equall
diuisions
.
5.
10.
15.
20.
Geodaesia
est
ars
,
quae
propositae
magnitudinis
quantitatem
nota
quadam
mensura
inuenit
.
Terrae
distributio
,
Terrarum
partitio
:
Orthogonium
,
Amblygonium
,
vis
namque
optica
e
duobus
oculis
in
vnum
conducta
,
firmius
collimat
.
manus
quietae
,
2.
3.
4.
Theodilitus
&c
,
18.
20.
Pearch
.
Day-worke
.
A
Pian
P.
Ryff
.
mensurae
minores
,
mensurae
maiores
,
1
Granum
hordeaceum
,
2
Digitus
,
3
Vncia
seu
pollex
,
1.
½
Apian
3.
4
Palmus
minor
,
5
Spithama
,
P.
R.
alii
dicunt
,
palmus
maior
,
6
Pes
,
7
Cubitus
seu
sesquipes
,
8
Gradus
siue
gressus
,
Apian
2
passus
simplex
.
9
Passus
,
Passus
Geometricus
,
10
Orgya
,
mensurae
maiores
.
11
Pertica
siue
virga
,
12
Stadium
,
13
Leuca
,
14
Miliare
Italicum
:
15
Miliare
Germanicum
,
16
Miliare
Germanicummagnum
,
17
Miliare
Germanicum
commune
,
32.
stadia
.
Spanish
league
3.
Italian
:
Longitude
,
Latitude
,
Altitude
,
Manus
quietae
,
9.
&
10.
C
A
B
A
C
,
A
B
:
C
A
B
,
D
E
,
videl
.
57.
C
A
M
,
A
M
,
C
A
M
,
104.
visa
versa
Another
Example
.
Oculus
Tauri
,
and
Canis
Maior
;
46.
¼
Cornelius
Gemma
Casiopaeia
,
Vrsa
maior
,
Ara
,
pars
equina
Centauri
.
A
B
C
,
B
C
A
,
C
B
,
C
A
B
,
A
B
A
C
B
A
C
C
B
C
A
,
A
C
B
,
A
C
A
C
B
,
A
B
A
C
B
,
Two
Angles
knowne
,
being
scituate
at
the
ends
of
a
line
knowne
,
to
find
the
quantitie
of
the
3.
Angle
,
and
the
other
two
sides
vnknowne
.
A
B
A
B
C
B
C
K
M
,
K
M
,
K
R
K
C
R
B
C
A
,
N
A
B
B
C
27
.
½
C
,
26
.
⅕
N
,
videl
.
N
M
M
N.
A
B
C
F
,
M
N
,
N
O
:
C
A
A
B
C
B
A
B
57.
Two
knowne
angles
of
a
Tryangle
,
being
scituate
,
the
one
at
the
end
of
a
line
knowne
,
and
the
other
opposite
to
the
said
line
,
to
finde
the
other
angle
and
two
lines
vnknowne
.
C
D
P
C
B
R
C
P
,
30.
C
D
,
F
A
R
One
angle
,
and
two
sides
of
a
Tryangle
beeing
knowne
,
which
containe
the
angle
knowne
,
to
finde
the
other
two
angles
,
and
third
side
vnknowne
.
C
A
C
B
,
A
B
,
A
B
C
,
C
A.
Si
Triangula
sunt
aequiangula
seu
similia
,
cruribus
homologis
propertionalia
,
&
contra
.
A
B
D
F
,
C
E
,
B
E
,
B
E
G
A
,
C
A
,
H
G
,
E
A
,
B
A
A
B
E
D
E
F
D
A.
viz.
E
F.
D
,
viz.
K
I
D
G
S
O
,
K
M
H
I
,
F
G
,
S
O
A
C
,
S
O
A
C
K
M
H
I
,
S
O
C
A
,
B
A
,
K
S
D
O
A
B
C
,
A
B
,
A
C
C
B
C
A
B
,
A
B
46.
C
A
40.
C
B
43.
A
C
A
C
B
,
E
C
A
;
C
A
A
C
:
A
C
C
E
24.
B
F
B
C
,
B
G
B
C
,
C
E
,
B
A
B
C
,
D
B
,
B
A
30.
B
C
60.
D
B
11.
A
note
for
another
working
by
the
staffe
then
before
.
B
F
,
B
R
P
C
D
,
R
A
F
:
C
D
,
C
D
B
F
A
C
/
15
C
F
/
25
,
R
B
/
30
B
F
/
50
,
A
C
/
15
R
B
/
30
,
C
F
/
25
B
F
/
50
To
worke
in
maner
of
the
Sector
by
the
Geodeticall
staffe
.
C
A
B.
A
N
P
N
A
B
,
N
P
A
P
A
N
,
A
G
,
A
C
F
,
A
B
,
A
B
,
A
G
,
C
D
,
A
B
,
A
G
To
apply
it
Geodetically
.
In
ciuill
affaires
.
E.
19.
Debent nihilominus ipsi numeri , in vsum practicum eo modo reuocari , vt ignotus & optatus numerus quartum possideat ordinem : Orontius lib . 3. cap . 4. De Arith . Parct . ac ipse primus , ré & nomine conueniat cum ipso tertio , secundus autem cum acquisito quarto .
The
Proposition
.
Two
Angles
knowne
,
and
scituate
at
the
ends
of
a
line
knowne
,
to
finde
the
quantitie
of
the
third
angle
,
&
the
other
two
sides
vnknowne
,
in
any
Tryangle
.
C
B
A
,
B
C
A
,
C
B
B
A
,
C
A
,
C
B
A
,
C
B
B
A
,
C
A
,
55.
viz.
A
C
B
,
C
B
,
27
.
½
C
B
A
,
27
.
½
A
C
B
,
27.
½
.
A
C
B
The
Proposition
.
Two
angles
of
a
Tryangle
beeing
knowne
,
whereof
the
one
is
scituate
at
the
end
of
a
line
knowne
,
and
the
other
opposite
to
the
said
line
knowne
,
to
finde
the
third
angle
,
and
other
two
lines
vnknowne
.
F
B
F
R
:
3.
viz.
R
F
B
,
R
B
F
F
R
B
R
B
F
R
F
B
F
R
B
:
R
F
B
F
R
B
,
F
R
B
,
viz.
60.
B
R
B
F
,
viz.
50.
F
R
,
R
B
B
F.
The
Proposition
.
An
angle
knowne
,
and
two
lines
knowne
,
containing
the
said
knowne
angle
,
to
finde
the
other
two
angles
vnknowne
,
and
the
third
line
.
C
A
B
C
,
B
A
,
C
B
A
C
B
B
A
C
A
,
viz.
55.
viz.
C
B
A
B
C
A
The
Proposition
.
Two
lines
and
one
angle
being
giuen
,
so
that
the
one
line
is
the
side
of
the
angle
knowne
,
and
the
other
doth
subtend
the
said
angle
,
yet
to
finde
the
third
line
,
and
the
other
two
angle
vnknowne
.
C
B
A
,
B
C
,
viz.
40.
C
A
viz.
55.
A
B
,
49.
A
B
C
,
79.
B
C
A
60
:
C
B
A
C
A
C
B
40.
B
A
,
49.
A
C
:
A
K
C
,
A
D
C
,
23.
K
D
,
D
Z
P
,
F
P
Z
:
D
,
23.
Y
P
:
D
P
N
Z
D
P
N
P
,
C
D
A
C
:
C
D
N
Z
,
N
P
,
D
P
D
K
C
A
N
Z
D
P
144.
A
C
The
Geometricall
ground
.
Si
Triangula
sunt
aequiangula
seu
similia
,
cruribus
homologis
proportionalia
,
&
contra
.
A
C
D
D
P
N
A
C
D
D
P
N
D
P
A
C
,
A
C
C
D
,
D
P
P
N
:
N
P
N
D
,
C
D
A
C
:
N
P
P
D
,
D
C
C
A
,
N
P
D
C
,
P
D
C
A.
N
Z
P
D
,
D
K
C
A
,
N
Z
D
K
,
P
D
C
A.
The
end
of
the
second
Booke
of
the
Geodeticall
Staffe
.
Orontius
.
Chap.
4.
D
B
E
F
Orontius
Chap.
5.
A
B
:
A
C
,
D
C
E
,
C
D
,
C
E
,
A
C
A
F
,
A
B
A
C
,
A
C
A
F
2.
A
B
A
F
The
Geometicall
demonstration
hereupon
.
B
C
F
,
B
C
F
C
B
F
,
B
F
C
A
C
F
,
C
F
A
A
C
F
,
C
A
F
C
B
F
B
F
C
,
A
C
F
C
F
A
,
B
F
C
,
C
B
A
A
C
F
,
B
C
A
C
A
F
:
A
C
B
C
F
A
:
A
B
C
A
C
F
,
quare
&
quae
circum
aequales
angulos
laterae
proportionalia
:
A
C
A
F
A
B
A
C
,
C
D
D
E
,
B
F
A
B
;
F
B
,
Orontius
Chap.
8.
F
G
,
G
I
,
H
I
:
F
G
G
I
I
G
G
F
G
I
F
G
,
G
I
F
G
A
K
L
,
G
L
,
G
F.
G
N
,
M
N
,
G
N
G
N
G
F
:
viz.
10.
S
G
Vmbra
recta
,
Vmbra
versa
,
1
½
,
Orontius
.
Chap.
9.
F
G
,
F
N
G
,
N
G
F
G
:
N
G
F
G
G
I
;
F
G
:
G
I
G
F
Orontius
.
Chap.
12.
F
G
,
B
A
viz.
4.
D
O
,
I
L
,
F
G
H
K
,
D
L
B
I
;
viz.
Z
:
B
H
,
B
K
,
D
Y
B
R
Gemma
Frisius
.
Chap.
8.
Gemma
Frisius
in
his
Booke
called
Vsus
Annuli
Astronomici
,
teacheth
this
way
for
such
that
be
ignorant
in
Arithmeticke
.
9.
Vmbrae
rectae
vmbrae
rectae
,
8.
vmbrae
versae
,
6.
vmbrae
versae
,
3.
vmbrae
versae
;
Orontius
Chap.
10.
C
D
A
C
,
B
F
A
H
,
E
G
,
A
E
:
E
G
A
E
B
H
A
B
A
B
B
H
A
B
I
K
A
I
,
L
B
A
B
:
I
K
A
I
A
B
B
L
A
B
B
L
A
B
B
L
A
C
D
,
A
B
H
A
C
K
,
A
B
L
,
A
C
C
D
A
C
D
,
A
B
B
E
:
A
E
E
G
,
A
B
B
H
:
A
I
I
K
,
A
B
B
L
,
Relatiuarelatiuis
singulorum
triangulorum
,
comparando
latera
.
Orontius
Chap.
10.
A
B
D
E
:
C
D
D
E
,
C
B
B
A
:
C
D
D
E
:
C
B
B
A
,
C
B
C
A
A
F
,
A
B
,
F
G
,
G
C
,
G
B
A
B
A
C
F
:
C
F
G
,
viz.
4●
.
C
F
G
C
G
F
F
C
G
A
C
B
,
Per
sextam
secundae
partis
perspectiuae
communis
,
at
que
decimam
12
&
13.
perspectiuae
Vitellionis
.
C
F
G
,
viz.
45.
A
C
B
,
viz.
45.
B
C
viz.
6.
viz.
6.
C
B
viz.
6.
B
A
C
,
A
B
D
E
,
D
C
,
B
C
:
C
D
D
E
,
B
C
B
A
:
D
E
D
C
,
A
B
B
C
:
Hypsometricall
Scale
:
Orontius
,
Chap.
3.
F
A
E
A
E
E
F
A
E
E
F
4.
A
E
E
F
Orontius
.
Chap.
3.
B
E
,
E
F
,
E
H
,
E
K
,
E
F
;
E
F
A
E
A
E
,
E
F
;
E
H
,
A
E
,
E
H
,
B
G
A
E
E
H
A
E
A
E
;
E
H.
A
E
E
H
E
K
,
E
K
A
E
A
E
E
K
,
D
I
E
K
A
E
A
L
E
K
Orontius
,
Chap.
8.
Because
the
working
of
this
Chapter
is
but
vice
versa
to
the
former
,
we
will
therefore
turne
the
figure
thereof
vpside
downe
,
and
so
make
him
serue
our
purpose
.
A
K
,
A
F
,
A
H
,
A
E
:
B
C
,
C
D
:
C
D
,
A
K
:
A
E
E
K
,
D
I
A
E
E
K
A
E
E
G
E
F
:
A
E
E
F.
A
E
E
F
A
E
,
E
F.
A
E
,
E
H
:
A
E
E
H.
B
G
E
A
E
F
A
E
,
E
F
:
A
E
E
F
Orontius
,
Chap.
II
.
E
F
D
H
,
20
H
:
20
D
K
,
K
:
60
G
I
,
E
F
Orontius
.
Chap.
13.
A
E
,
G
F
:
F
A
G
:
A
D
H
I
:
A
I
A
F
F
G.
A
H
I
,
A
F
G
,
A
H
I
A
G
F
,
A
I
H
A
F
G
,
A
I
A
H
,
A
F
F
G
F
A
,
A
E
E
F
A
E
E
F
A
F
A
E
F.
E
F
6
:
A
F
:
H
I
A
D
,
A
I
,
I
H
:
A
F
F
G
:
F
G
A
F
Orontius
,
Chap.
13.
R
E
O
Z
O
P
,
R
O
L
:
O
L
E
F
O
F
L
E
:
E
F
O
L
L
R
L
E
,
O
L
L
R
,
Orontius
,
Chap.
13.
E
F
E
F
:
A
F
E
,
E
F.
A
B
E
F
A
E
6
Orontius
,
Chap.
15.
P
R
,
S
R
:
S
R
S
H
S
G
,
S
H
G
H
S
G
G
H
S
H
S
H
:
S
H
G
H
,
S
R
,
R
P.
S
G
H
,
S
P
R
S
H
G
S
R
F
,
S
H
H
G
,
S
R
R
P
,
S
H
H
G
S
H
S
R
R
P
S
R
R
P
Orontius
,
Chap.
15.
A
L
A
E
,
E
L
,
E
A
;
To
performe
the
same
by
the
staffe
other
waies
.
L
E
L
E
L
A
:
Orontius
.
Chap.
16.
B
E
F
G
,
B
G
,
E
F
B
G
:
A
C
,
E
B
B
G
,
E
F
;
E
B
,
B
H
Eu
.
lib
.
Ra
.
li
.
B
E
F
G
,
A
G
;
A
B
,
B
G.
F
B
E
B
E
;
E
B
B
G.
B
E
B
E
,
G
B
:
Orontius
,
Chap.
16.
E
B
G
F
:
A
B
B
G
:
E
B
:
E
B
B
G
,
E
B
B
G
E
F
:
Orontius
,
Chap.
17.
F
,
EE
,
FF
,
F
,
FF
D
F
F
,
EE
,
F
,
FF
F
,
GG
,
9
GG
,
EE
Iacobs
Staffe
For
with
my
staffe
came
I
ouer
this
Iorden
:
Esse
omnium
reliquorum
geodaeticorum
instrumentorum
commodissimum
,
P.
Ramus
M
O
,
M
N
:
R
.
S.T.V.W.O
:
N
B
,
M
O
;
N
10
10
20
M
N
M
O
,
M
N
To
worke
by
the
scale
.
M
O
N
B
,
M
N
,
M
N
,
N
B
,
M
O.
M
N
,
M
N
,
O
B
,
The
ruler
made
,
you
shall
worke
the
golden
rule
thereby
thus
.
B
A
C
;
To
worke
the
golden
rule
.
A
C
A
B
,
A
C
,
E
G
D
F
,
E
G
A
B
,
A
G
,
G
D
D
F
D
E
F
D
K
I
:
I
K
,
Ra
.
lib
.
&
Ra
.
viz
,
E
G
,
F.
D.
12
,
20
,
5
,
48
,
48
,
20
,
12
,
5
,
48
,
20
,
The
numbers
proposed
20-30-8
reduced
to
reuersed
proportion
,
20-8-30
reduced
to
direct
proportion
,
8.20
,
30.
Ans.
75.
Proposition
Bac
.
Iac
.
Si
visus
sit
ab
indicis
recti
in
metam
longitudinis
:
9
P.
7.
21
,
P.
vt
tunc
erit
segmentum
indicis
ad
segmentum
Transuersais
,
sic
mensoris
altitudo
ad
quaesitam
longitudinem
.
The
Proposition
for
my
staffe
.
As
the
equall
parts
included
on
the
left
legge
,
betwixt
the
site
and
the
center
,
are
to
the
parts
on
the
right
leg
included
betwixt
the
file
and
the
center
,
so
is
the
length
to
the
height
,
and
contrarie
.
Nec
quidquaminterest
,
siue
longitudo
sit
in
subiecto
plano
,
siue
in
ascensu
descenuve
montis
,
sursum
deorsumve
collimando
:
dummo
do
index
in
lineam
longitudinis
sit
rectus
.
Proposition
Bac
.
Iac
.
Sivisus
sit
ab
initio
Indicis
paralleli
in
metam
longitudinis
:
vt
erit
segmentum
transuresarii
ad
segmentum
Indicis
,
fic
data
sen
cognita
altitudo
ad
longitudinem
.
The
proposition
for
my
staffe
.
As
the
included
parts
vpon
the
right
leg
are
to
the
parts
included
vpon
the
left
legge
,
so
is
the
giuen
altitude
to
the
longitude
desired
.
Propositio
Bacu
.
Iac
.
Si
visus
sit
ab
initio
transuer
sarii
par
alleli
,
in
met
am
longitudinis
,
per
terminum
Indicis
recti
ad
metam
in
alto
propositam
:
vt
erit
in
Indice
differentia
maioris
segmenti
ad
minus
,
sic
differentia
inter
priman
&
secundam
stationem
ad
longitudinem
quaesitam
The
Proposition
for
my
staffe
.
Propositio
Bac
.
Iac
.
Si
visus
sit
ab
initio
Transuersarii
rectiterminum
altitudinis
,
per
terminum
indicis
paralleli
in
metam
altitudinis
:
vt
erit
segmentum
Transuersarii
ad
segmentum
indicis
,
sic
longitudo
data
ad
altitudinem
.
For
the
Geodeticall
Staffe
,
Prop
.
Propositio
,
Bac
.
Iac
.
Sivisus
sit
ab
initio
indicis
paralleli
in
metam
profunditatis
:
vt
erit
segmentum
Transuersarii
ad
segmentum
indicis
,
sic
data
longitude
ad
profunditatem
.
For
the
Geodeticall
staffe
.
24
,
2
/
4
Propositio
Bac
.
Iac
.
Si
visus
sit
ab
initio
indicis
recti
in
terminum
altitudinis
:
vt
erit
segmentum
indicis
ad
segmentum
Transuersarri
,
sic
data
longitudo
ad
altitudinem
.
The
Geodeticall
staffe
.
Sivisus
sit
ab
initio
Indicis
,
per
pinnas
seudioptras
Transuersarii
&
cursoris
,
in
terminos
notae
partis
:
vt
erit
interuallum
pinnaerum
ad
reliquum
supereminentis
Transuersarii
,
sic
notae
desuper
altitudinis
pars
adreliquam
.
The
Geodeticall
staffe
.
22
,
½
Propositio
,
Bac
.
●ac
.
Sivisus
sit
ab
initio
Indicis
recti
in
terminum
altitudinis
,
vt
erit
in
In
dice
differentia
segmenti
ad
differentiam
distantiae
(
primae
videl
.
ac
secundae
stationis
)
sic
segmentum
Transuersarit
ad
altitudinem
.
For
the
Geodeticall
Staffe
.
30
,
44.
Proposition
Bac
.
Iac
.
Si
visus
sit
ab
initio
Indicis
recti
,
per
pinnas
Transuersarii
,
in
terminos
latitudinis
:
vt
erit
Indice
differentia
segmentorum
(
per
duplicē
distantiam
facta
)
ad
differentiam
ipsam
stationum
seu
distantiarum
,
sic
interuallum
primarum
Trausuersarii
ad
latitudinem
quaesitam
.
A
B
A
B
,
A
I
B
,
B
I
C
:
C
I
D
,
D
I
K
,
K
I
E
,
30
E
I
F
,
20
F
I
G
,
9
G
I
H
72
H
I
A
,
51
The
quantitie
of
the
angles
of
position
or
station
.
I
C
,
7
¾
I
D
,
19
I
K
,
12
½
I
E
28
I
F
25
I
G
14
I
H
,
The
quantitie
of
each
angle
of
station
.
A
B
:
A
B
;
M
A
N
:
N
A
O
;
o
A
P
,
P
A
Q
,
A
,
M
A
,
N
A
,
O
A
,
P
A
,
Q
A
,
R
A
,
S
A
,
T
A
,
V
A
:
9
¼
A
N
,
7
¾
A
O
,
12
½
A
H
A
I
,
25
,
A
K
14
,
A
L
21
C
A
D
:
viz.
57
D
A
E
,
4.5
,
6
,
7
,
E
A
F
:
F
A
G
,
G
A
H
,
H
A
I
,
I
A
K
,
K
A
G
:
A
B
D
,
33
D
B
E
E
B
F
,
F
B
G
,
G
B
H
,
H
B
I
,
I
B
K
,
K
B
A
,
A
B
A
F
G
I
K
:
A
C
E
,
E
C
F
,
F
C
G
,
G
C
H
,
H
C
I
,
I
C
K
,
K
C
A
,
A
B
,
C
D
,
L
O
Q
R
,
L
D
M
,
M
D
N
,
N
D
O
,
O
D
P
,
P
D
Q
,
Q
D
R
,
R
D
S
,
S
D
L
,
M
D
,
N
D
,
O
D
,
P
D
,
2
,
3
,
4
,
T
,
V
,
w
,
X
,
Y
,
Z
,
L
,
C
D
T
V
21
V
w
A
B
C
D
E
F
G
H
,
A
I
B
,
39
B
G
C
,
67
The
quantitie
of
each
angle
of
station
.
I
,
viz.
27
A
B
,
B
C
,
C
D
,
D
E
,
E
F
,
F
G
,
G
H
,
H
A
;
The
quantitie
of
each
angle
of
station
,
with
sides
subtending
the
said
angles
.
A
,
I
,
27
M
A
,
A
I
,
A
M
M
A
N
,
N
A
O
,
A
B
,
20¼
A
M
,
A
O
,
A
P
,
A
G
,
R
A
,
A
S
,
A
T
,
A
V
,
M
A
:
A
B
C
D
E
,
A
,
B
,
B
H
,
A
B
,
35
,
I
B
H.
A
B
C
,
I
B
H
,
viz.
145
:
Si
duae
rectae
inter
secantur
,
aequant
angulos
verticales
inter
se
,
5
,
P.
8
,
&
omnes
quatuor
rectis
.
I
B
H
A
B
C
viz.
35
A
B
C
,
Si
recta
oblique
insistit
rectae
,
5
,
P
8
,
anguli
deinceps
positi
duobus
rectis
aequentur
,
&
contra
.
H
E
E
F
,
I
C
E
D
,
E
H
F
G
:
E
l
,
●
H
E
F
G.
G
F
E
,
G
A
B
,
A
B
A
B
C
,
B
C
C
D
E
,
D
E
,
G
A
,
G
,
B
,
A
G
A
B
A
B
A
B
A
B
C
,
G
A
A
G
F
G
,
A
G
,
F
G
G
F
E
,
F
G
A
G
,
A
B
,
Ra
,
lib
,
Lu
,
lib
,
A
C
C
B
:
C
B
,
A
C
,
B
C
A
C
,
Cathetum
B
C
A
B
A
C
,
A
B
,
B
E.
A
B
,
Vide
lib
,
A
B
,
A
B
:
A
C
,
A
B
,
C
B
A
,
Eu
,
lib
,
A
B
,
B
D
,
A
B
,
C
D
A
B
,
To
worke
by
the
new
quadrant
.
D
C
A
B
,
A
K
,
A
K.
A
K
,
F
G
,
A
K
,
F
G
,
A
K
,
F
G
,
To
open
the
legges
vnto
any
angle
assigned
.
3
:
180
1
In
omni
triangulo
tres
anguli
simul
sumpti
,
sunt
duobus
rectis
aquales
.
Euc
.
lib
.
1.
P.
32.
Ram
.
lib
.
6.
P.
9.
2
Cuiuscunque
triangulaeti
latera
sunt
binario
pluratriangulis
,
è
quibus
constat
.
Ram
.
lib
.
10.
Pr●
.
1.
cons
.
1.
The
end
of
the
first
part
of
the
art
of
Geodetia
.
Ignorant
in
the
termes
,
and
ignorant
also
in
the
Art.
of
a
new
Table
.
47
ferè
,
Of
an
Orthogonium
,
Isosceles
.
Proposition
.
1.
B
A
C
,
A
C
A
B
D
C
:
B
A
C
,
A
B
C
B
C
D.
A
C
A
F
A
C
,
A
F
10
A
B
20
,
A
B
E
F
,
A
B
C
,
B
E
G
,
F
C
G
,
Of
an
orthogonium
Scalenum
.
Proposition
.
2.
26.
E.
1.
A
B
,
A
C
A
B
A
C
40
:
20
A
B
A
C
,
A
B
B
C
,
A
B
C
,
H
I
,
10
,
A
C
400
,
E
H
20
,
A
C
A
B
20
,
To
measure
an
oxigonium
Isopleuron
.
Proposition
.
1.
A
B
⅓
8
/
1
,
AE
,
3
,
A
C
,
B
A
E
,
9
,
viz.
15
,
A
B
B
E
E
C
A
C
,
3
B
D
C
E
,
A
B
C.
A
B
B
C
11
7
/
21
D
C
D
A
,
A
E
C
D
A
B
C
L
O
,
M
P
,
P
N
,
L
Q
,
N
O
,
L
,
M
,
A
B
C
,
A
B
A
C
8
,
B
C
10
:
To
performe
the
same
Proposition
otherwise
.
Of
an
Ambly
gonium
,
and
to
measure
the
Area
thereof
.
Proposition
2.
Of
an
Amblygonium
Scalenum
.
Proposition
3.
Proposition
1.
To
find
the
perpendicular
of
an
Isophiron
oxigonium
.
B
E
5
Proposition
2.
To
finde
the
perpendicular
in
an
Isosceles
Oxigonium
.
B
D
B
C
,
A
B
A
C
,
B
D
;
B
D
A
B
,
A
D
Proposition
3.
To
finde
the
perpendicular
of
any
Oxigonium
Scalenium
.
Oxigonium
Scalenum
L
M
N
,
L
M
6
½
L
N
7
½
M
N
L
M
:
6
½
L
N
7
½
56
:
L
M
6
½
,
L
N
7
½
17
½
,
M
O
,
viz.
6.
L
M
L
M
4
½
;
N
O
:
4
½
,
L
N
,
Prodosition
4.
To
finde
the
perpendicular
in
any
Ambligonium
Isosceles
.
A
B
C
,
A
B
A
C
B
D
8
:
Proposition
5.
To
find
the
perpendicular
in
any
Amblygonium
Scalenum
.
L
M
N
,
L
M
20
,
L
N
34
,
M
N
42
,
L
M
400
,
L
N
1156
,
M
N
1764
:
—
1764
,
M
O
,
L
O
,
16
:
Proposition
1.
Of
a
quadrate
or
square
.
aequilater
parallelogram
,
A
C
20
A
B
C
D
,
B
C
,
A
C
Proposition
2.
Of
an
Oblonge
.
A
B
20
A
C
40
,
A
B
C
D.
B
C
,
A
C
40
,
B
A
20
,
Proposition
3.
To
measure
a
Rombus
.
Parallelogram
,
aequilater
,
32.
Ra
.
A
B
C
D
A
F
,
B
C
,
B
C
;
A
C
12
,
D
E
8
,
D
E
;
A
C
D
A
B
C
A
D
C
,
A
C
,
E
D
,
A
C
H
G
,
A
B
C
D
;
Ambligonium
Isosceles
,
B
D
Ambligonium
Isosceles
A
E
B
D
G
I
,
A
B
C
D
Orthogonium
Scalenum
,
A
E
E
D
A
E
D
G
,
Proposition
4.
To
measure
a
Romboides
.
A
B
C
D
B
F
B
C
,
B
C
G
F
,
A
B
C
D.
A
C
,
Ambligonium
Scalenum
:
D
E
Ambligonium
Scalenum
A
C
D
,
A
C
Proposition
5.
To
measure
a
Trapezium
Isosceles
.
Quadrilater
Triangular
,
Orthogonium
Trapezium
,
Ambligonium
Trapezium
.
Isosceles
Trapezium
,
Trapezia
A
B
C
D
,
A
B
C
D
,
B
C
A
D
:
B
C
A
D
10
,
10
4
F
E
16
,
A
B
C
D
Proposition
6.
An
Orthogonium
Trapezium
.
Orthogonium
Trapezium
F
G
H
E
,
F
G
6
E
H
18
,
E
K
12
,
F
E
5
;
F
I
K
E
,
F
G
H
E
,
G
I
L
L
K
H.
Proposition
7.
An
Ambligonium
Trapezium
.
Trapeziums
A
D
C
D
Diagonall
A
D
,
A
D
Proposition
8.
To
find
the
perpendicular
in
an
Isosceles
Trapezium
:
Isosceles
Trapezia
A
B
C
D
,
A
B
10
A
C
4
,
A
D
16
;
A
C
A
D
Proposition
1.
To
measure
a
Regular
Poligonium
.
Si fiat planus è perpendiculari à centro in latus , & dimidio p●ri●etri , factus est area multanguli or dinati : Oron cap . 8. lib . 2. De R● & prac . Geomet . Ra . l. 19. P. 1.
The
plaine
number
made
of
the
perpendicular
,
drawne
from
the
center
vnto
the
side
,
and
of
halfe
the
perimeter
,
is
the
content
of
a
multangled
ordinate
figure
.
poligonium
A
B
C
D
,
B
C
,
D
E
:
D
E
F
A
,
polygonium
pentagon
,
Proposition
2.
To
find
the
center
of
a
polygonium
hauing
an
odde
side
.
B
C
;
Proposition
3.
To
finde
the
center
of
any
polygonium
containing
equall
sides
.
D
E
F
H
G
M
K
;
5
⅖
,
93
⅗
Hexagon
Poligonium
.
Proposition
4.
Of
irregular
Polygoniums
,
called
irregular
figures
.
The
plaine
number
made
of
the
radius
and
halfe
the
circumference
,
is
the
content
of
a
circle
.
160
,
40
,
●24
,
L
O
16
M
N
42
,
M
N
21
L
O
16
,
L
M
N
,
L
O
M
M
N
L
O
M
N
:
L
M
N.
A
D.
Proposition
1.
For
a
square
.
A
B
C
D
A
B
viz.
2
Proposition
2.
For
an
Oblonge
.
A
B
D
C
A
B
20
A
C
40
,
A
B
D
C
;
B
C
,
Proposition
3.
For
a
Rombus
.
A
B
C
D
,
B
D
16
A
C
12
:
B
D
,
A
C
:
A
B
C
D
:
Proposition
4.
For
a
Romboides
.
Vide
prop.
A
C
,
Proposition
5.
A
Generall
Rule
.
Poligonium
Pentagon
,
A
D
G
B
C
H
:
B
C
:
D
B
C
H
Proposition
6.
To
measure
all
kind
of
land
without
taking
the
plot
.
A
B
F
E
D
,
Topographicall
Glasse
,
&c.
Proposition
7.
To
find
where
the
perpendicular
in
any
tryangle
fals
vpon
the
base
,
without
Arithmeticke
,
in
the
open
field
.
A
B
C
D
C
D
A
B
Topographicall
Glasse
C
D
,
viz.
200
:
Trapezia
A
B
C
E
,
D
E
C
,
B
E
A
C
C
A
B.
A
B
D.
Place
this
Table
betwéene
folio
A
B
C
:
C
B
C
D
A
,
C
B
,
A
B
30
,
40
,
50
,
ADmit
you
haue
a
parallelogram
which
conteins
.
perches
,
&
that
with
a
parallele
to
one
of
the
endes
,
I
would
cut
off
acres
first
therfore
by
some
Rules
before
published
,
find
the
length
of
one
of
the
longer
parallele
sides
which
let
be
roode
;
thē
I
multiply
for
so
many
roods
are
there
in
Acres
the
whole
Area
,
which
yeldeth
.
which
deuide
by
.
the
number
of
perches
conteined
in
the
whole
area
,
which
yeeldeth
in
the
Quotient
foote
,
and
so
much
must
you
measure
from
the
end
in
both
the
longer
parallele
sides
,
&
where
that
number
ends
,
in
each
side
make
two
markes
direct
from
one
of
which
vnto
the
other
draw
a
line
which
shal
cut
of
iust
acres
:
&
this
rule
is
general
for
al
quadrangle
péeces
of
ground
whose
sides
&
ends
be
parallell
be
the
figure
a
Rombus
,
an
oblong
&c.
other
wayes
you
may
find
(
which
I
omit
)
to
separat
other
regulare
figures
,
&
the
rather
because
there
shal
a
Table
of
purpose
insue
,
and
may
be
perfourmed
Instrumentally
also
.
And
heere
note
when
you
haue
any
péece
of
ground
how
irregular
soeuer
or
of
what
regular
fashion
soeuer
,
as
circle
,
&c.
you
may
reduce
the
same
in
to
a
square
or
such
like
figure
as
is
*
taught
,
&
so
spéedely
measure
the
same
,
or
deuide
it
into
what
kinde
or
how
many
partes
you
wil
,
as
you
be
taught
in
the
Cap.
of
this
Booke
.
4
/
11
4
/
21
¼
½
¾
,
Another
Example
.
M.
Digges
The
ground
.
viz.
1728
1
⅔
,
16
64
/
65
,
16
64
/
65
16
⅘
A
B
A
C
B
60
B
16
E
G
I
,
F
E
;
E
G
,
viz.
E
F
,
G
H
I
H
E.
E
F
,
E
F
,
C
A
viz.
60
A
D
B.
E
G
,
C
D
,
F
G
M
:
F
G
,
H
F
,
E
G
,
F
E
F
H
,
G
F
A
D
C
30
A
C
D
,
E
G
,
K
G
L
;
H
I
F
H
E
,
G
F
,
G
H
,
F
G
D
A
58
C
A.
A
C
B
,
C
O
O
C
A
C
B
,
A
B
,
F
E
A
F
E
,
viz.
30
A
F
B
,
viz.
●8
F
E
B
,
A
E
B
,
viz.
45
E
F
,
I
F
H
,
L
F
I
,
L
E
M
,
F
B
,
N
E
M
,
F
A
,
A
B
,
viz.
40
F
B
,
F
A
,
E
B
,
E
A
,
10
,
20
,
40
,
8
,
10
,
16
,
20
,
30
,
A
B
C
C
B
3
Prop
.
45
C
B
C
E
E
B
,
Metamorphosis
1.
Eucl
.
l.
12.
p.
2.
Ram
.
l.
15.
p.
2
.
&l
.
19.
p.
2.
Cons
.
1.2
.
&
3.
To
reduce
a
Circle
into
an
Oblonge
.
A
B
,
5
½
●
5
½
:
A
B
,
B
C
,
B
C
A
B
;
A
B
,
B
C
,
A
R
B
N
,
E
I
5
½
,
5
½
B
E
,
3
½
E
B
E
G
:
E
G
F
B
,
H
E
I
E
,
E
F
K
H
,
E
I
E
H
;
E
G
E
B
;
E
P
A
B
,
Metamorphosis
2.
To
reduce
the
Sector
of
any
circle
into
an
Oblonge
.
N
E
B
L
E
B
M
,
E
B
,
B
O.
E
P
E
H
E
B
,
E
P
Q
H
,
R
E
B.
Metamorphosis
3.
To
reduce
a
Lunular
into
asquare
.
A
B
C
D
,
A
B
,
viz.
E
C
F
B
,
Metamorphosis
4.
To
reduce
an
Oblonge
into
a
square
.
A
B
A
G
;
viz.
A
E
F
G
A
B
C
D
,
G
B
B
D
B
D
A
G
,
B
D
A
G
A
B
B
D
G
B
,
A
G
K
I
K
G
,
A
I
;
K
L
;
K
N
M
L
,
K
I
H
G
,
K
L
,
Metamorphosis
5.
The
one
side
of
an
Oblonge
,
and
the
side
of
a
square
being
giuen
,
to
find
the
other
side
of
the
Oblonge
,
that
is
,
to
reduce
a
square
into
an
Oblonge
,
to
containe
the
iust
height
of
the
Oblonge
proposed
.
A
B
B
D
D
A
,
A
F
A
E
;
D
E
Metamorphosis
6.
To
reduce
a
square
into
an
Oblonge
,
not
regarding
the
height
of
the
Oblonge
.
A
G
G
B
,
A
G
:
A
B
,
B
G
B
D
A
B
D
C
A
E
F
G
,
Metamorphosis
7.
To
reduce
a
tryangle
into
a
square
,
and
to
find
the
meane
proportion
betwixt
the
perpendicular
and
the
base
of
any
tryangle
.
A
B
C
:
B
C
A
D
D
C
:
A
D
B
C
,
B
E
,
D
F
B
E
,
A
F
F
H
I
A
:
D
H
D
H
I
G
,
A
B
C
?
Metamorphosis
8.
To
reduce
any
irregular
or
multanguled
figure
into
one
square
.
A
B
C
D
E
F
,
A
E
F
H
,
A
D
E
,
I
A
C
D
,
A
B
C
:
L
M
L
N
;
Hipothenusall
M
N
,
M
N
,
M
L
,
L
N
,
Euc
.
lib
.
1.
Prop
.
47.48
.
&
6.
Prop
.
31.
Ra
.
l.
12.
Prop
.
5.
M
N
,
M
N
O
:
O
M
F
E
O
M
,
M
P
,
P
O
,
P
O
R
G
,
A
B
C
D
E
F
:
320
,
viz.
80
,
281
,
600
,
Metamorphosis
9.
To
performe
the
last
Metamorphosis
in
strumentally
.
G
10
H
14
17
13
/
60
M
N
;
17
13
/
60
I
12
M
O.
P
O
,
Metamorphosis
10.
To
performe
the
last
Metamorphosis
Arithmetically
.
viz.
GH
I
K
,
H
196
,
17
13
/
60
,
289
169
/
600
433
169
/
3000
,
P
O.
Proposition
1.
To
cut
a
line
by
extreme
and
meane
proportion
.
C
D
,
C
D
,
C
H.
C
D
C
D
H
D
C
H
H
D
,
C
H
,
C
D
C
H
Proposition
2.
Two
numbers
being
giuen
,
to
find
two
lines
which
shall
haue
such
proportion
one
to
the
other
,
as
the
numbers
giuen
haue
.
Sirectam triangulo est parallela basi , secat crura proportionaliter , Ra . l. 6. p. 9. & contra , Eucl . l. 1. Prop . 32.
D.
Hood
C
D
:
C
E
;
Viz
.
C
D
C
E
,
Proposition
3.
A
line
being
giuen
,
and
a
proportion
assigned
,
to
lay
downe
a
line
,
which
shall
be
to
the
line
giuen
in
suchproportion
as
was
assigned
.
C
E
,
C
E
,
C
E
C
D
,
C
E
,
Proposition
4.
Two
lines
being
giuen
,
to
find
what
proportion
the
one
hath
to
the
other
.
Art
of
Goedetia
C
D
C
E
C
D
C
E
C
D
C
E
,
Proposition
5.
To
denide
a
line
into
any
number
of
equall
parts
proposed
.
B
E
B
E
,
B
C
,
B
E
F
E
,
Proposition
6.
A
line
being
giuen
to
deliuer
any
part
thereof
.
A
E
A
E
A
E
A
B
,
A
E
:
A
D
,
Or
thus
Arithmetically
.
A
E
A
G
,
A
E
,
Proposition
1.
Two
figures
or
two
peeces
of
ground
being
giuen
,
to
finde
what
proportion
the
one
hath
to
the
other
.
Proposition
2.
Any
chord
of
a
circle
being
giuen
,
to
find
the
diameter
of
a
circle
,
to
which
the
inscription
of
the
chorde
shall
answer
.
B
C
B
C
G
H.
Proposition
3.
E
G
F
,
E
D
E
D
E
F
D
E
D
E
S
Q
,
D
I
,
E
I
G
L.
E
H
M.
Proposition
4.
Proposition
5.
The
chord
of
any
circle
being
giuen
,
to
find
what
proportion
it
beareth
to
the
circumference
.
B
A
vide
E
I
:
R
S
,
R
S
E
I.
Proposition
6.
To
find
a
right
line
equal
to
any
assigned
arke
of
a
circle
.
Proposition
1.
A
circle
being
giuen
,
and
a
proportion
assigned
,
to
deliuer
a
circle
answering
to
the
Symmetry
thereof
,
and
the
proportion
assigned
.
A
B
;
A
B
,
C
D
:
F
F
,
E
G
F
:
D
G
,
D
G
Problema
.
2.
A
greater
tryangle
being
giuen
,
and
a
proportion
assigned
,
to
make
a
tryangle
lesser
and
like
the
greater
,
according
to
the
proportion
assigned
.
D
L
F
,
D
F
,
D
C
;
C
D
,
B
A
;
E
F
,
D
G
F
D
,
F
K
:
D
L
,
K
M.
K
M
F
D
L
F
,
Problema
3.
A
lesser
tryangle
being
giuen
,
and
a
proportion
assigned
,
to
make
a
greater
like
and
proportionall
.
visu
verso
D
G
E
I
D
D
G
K
H
D
I.
E
H
D
E
I
D
,
Problema
4.
To
performe
the
second
prob
.
by
drawing
parallel
lines
about
the
tryangle
.
B
C
D
,
Euc
.
l.
4.
prop.
5.
Ra
.
l.
17.
pro
.
5
,
B
C
D
:
A
B
,
A
B
P
Q
R
S
:
P
Q
R
S
G
E
,
E
G
G
H
E
,
M
H
,
F
H
M
A
B
,
A
C
A
D
,
A
K
,
A
L
;
I
K
,
K
L
,
L
I
,
B
C
,
C
D
,
D
B
,
I
K
L
B
C
D
,
I
K
L
B
C
D
,
Ra
.
l.
4.
prop.
15.
Cons
.
1.
Problema
5.
To
performe
the
third
proposition
,
by
drawing
parallel
lines
about
the
figure
.
I
K
L
,
A
I
A
,
K
,
A
L
A
I
,
M
E
;
A
I
,
B
E
,
B
E
B
N
E
,
M
A
M
N
,
A
I
,
A
K
,
A
L
,
B
C
,
C
D
,
D
E
,
I
K
,
K
L
,
L
I
,
B
C
D
I
K
L
,
Problema
.
6.
A
greater
tryangulate
figure
,
or
peece
of
ground
being
giuen
,
and
a
proportion
assigned
,
to
deuide
the
lesser
,
so
that
he
shal
be
like
vnto
the
greater
,
and
keepe
the
proportion
assigned
.
A
w
X
Y
Z
,
&c.
A
X
,
A
Y
,
A
Z
,
A
w
,
A
w
,
A
w
,
A
F
:
w
X
F
E
,
X
Y
E
D
;
D
C
Y
Z
,
C
B
Z
&
.
A
B
C
D
E
E
,
A
w
X
Y
Z
&
,
Problema
7.
A
lesser
tryangulate
being
giuen
and
a
proportion
assigned
,
to
deliuer
a
greater
,
like
and
proportionall
to
the
lesser
.
cap
.
p.
A
F
,
A
w
w
X
,
X
Y
,
Y
Z
,
Z
,
&c.
F
E
,
E
D
,
D
C
,
C
B
,
A
w
X
Y
Z
,
&c.
Problema
8.
A
field
of
tryangulates
being
giuen
,
to
inscribe
a
tryangulate
with
parallel
sides
according
vnto
the
proportion
assigned
.
F
F
G
G
,
Z
Y
X
w
,
A
FF
,
A
GG
,
A
A
Z
,
A
w
,
A
w
A
w
,
A
F.
w
X
,
F
E
,
X
Y
,
E
D
,
HH
II
,
B
C
D
E
F
,
FF
GG
,
Z
Y
X
w
,
parts
like
to
the
parts
of
a
figure
giuen
,
and
in
like
manner
situate
,
be
placed
vpon
a
terme
giuen
,
there
shall
be
placed
vpon
the
fame
terme
a
figure
,
like
to
the
figure
giuen
,
&
in
like
manner
situate
.
Ra
.
L.
4.
P.
14.
Cons
.
4.
Like
figures
be
figures
equianguled
proportionall
in
the
feete
of
the
equall
angles
.
Ra
.
l.
&
pro
.
as
before
.
Problema
9.
Any
kind
of
figure
being
giuen
,
and
a
proportion
assigned
,
to
make
a
figure
which
shall
haue
his
sides
to
the
sides
of
the
figure
giuen
,
in
such
,
proportion
as
was
required
.
A
B
C
D
E
,
A
C
,
A
C
,
A
F
;
A
D
,
A
G
;
A
E
,
A
B
,
A
H
,
A
I.
A
A
,
A
K
;
K
I
,
A
I
,
I
F
,
F
G
,
G
H
H
K.
A
F
G
H
K
I
A
I
F
G
H
A
B
C
D
E
,
Or
thus
otherwise
.
Problema
10.
To
deuide
or
cut
off
any
number
of
acres
from
any
parallelogram
,
be
it
square
,
Rombus
,
&c.
by
aright
line
drawne
from
a
corner
to
the
opposite
side
.
Problema
11.
The
King
granted
a
peece
of
wast
ground
vnto
eight
men
,
vpon
condition
that
fiue
of
them
shall
occupy
their
portions
together
:
yet
to
be
seuered
from
the
parts
of
the
other
three
,
which
also
occupie
their
three
parts
together
.
I
demaund
how
it
shall
be
performed
.
A
B
C
D
:
A
D
,
E
D
:
E
F
D
C
A
B.
A
E
F
B
E
F
C
D
E
C
F
,
A
B
F
E
,
A
B
C
D
E
F
G
H
I
,
A
C
,
C
E
,
A
E
C
E
,
A
C
E
,
C
E
,
K
13
M
33
D
11
M
D
C
M
L
,
56
C
E
M
33
M
D
;
A
E
I.
N.
William
Ashbe
A
B
Another
Example
.
William
Cocke●
Seruises
proper
vnto
each
tenant
in
the
Manor
,
and
where
Heriots
be
due
,
&c.
Note
the
Demesnes
with
the
site
of
the
Manor
house
,
&c.
being
faire
and
in
good
reparations
conteines
500.
acres
,
220
of
errable
,
of
pasture
150
,
of
medow
130
,
left
vnplatted
.
Also
the
Tenants
claime
paughnage
for
foure
pence
a
swine
in
the
common
wood
.
William
Cocke
Willam
Cocke
Pated
for
,
William
Cocke
Robert
Dodde
,
(
HH
)
(
HH
)
Grounds
naturally
good
,
bring
forth
Artificiall
good
grounds
,
are
Signes
of
fertill
grounds
,
and
such
as
be
rich
,
are
Signes
of
barren
,
leane
and
vnfruitfull
ground
.
Signes
of
bad
ground
,
are
.
Bad
grounds
naturally
yeeld
The
yearely
growth
of
trees
is
knowne
Topographicall
Glasse
.
Inpratis
40
acr
.
in
pasturis
80
ac
.
&c.
per
annum
:
Almanacke
1608
,
per
.
annum
per
annum
Geodeticall
Staffe
,
Art
of
Geodetia
18
,
12
,
Theodelitus
Geodetical
½
⅓
Art
of
Geodetia
,
Ra
.
l.
1.
p.
6.
Ra
.
l.
2.
p.
2.
Eucl
.
l.
13.
p.
3.
Ra
.
l.
2.
p.
7.
ibid
.
p.
8.
Eu
.
35.
p.
11.
Ra
.
l.
3.
p.
3.
Ra
.
ibid
.
p.
4.
R.
l.
4.
p.
5.
Eu
.
l.
1.
def
.
11.
Eu
.
ibid
.
Def
.
12.
Of
a
figure
.
Ra
.
l.
4.
p.
1.
Euc
.
l.
1.
p.
14.
13.
Ra
.
l.
6.
p.
7.
Eu
.
l.
6.
p.
2.
Eu
.
l.
1.
p.
32.
Eu
.
l.
1.
p.
5.
&
6.
Ra
.
l.
6.
p.
10.
Cons
.
3.
Eu
.
l.
1.
p.
19.
&
18.
Eu
.
l.
6.
p.
1.
90
,
50
Axioma
1.
In
plaine
rectangled
tryangles
,
any
one
of
the
three
sides
may
be
put
for
the
radius
,
A
B
C
,
A
B
,
B
C
,
A
B
C
;
A
C
A
B
C.
A
C
B
C
B
A
C
,
A
B
,
B
C
A
C
A
B
C
,
A
B
Consectary
1.
Therefore
in
plaine
right
angled
tryangles
A
B
C
,
B
59
B
59
,
40
Which
is
to
say
.
A
B
4
B
C
A
B
/
100000
B
C
/
505029
A
B
/
24
feete
A
C
12
12671
/
100000
A
B
/
115861
B
C
/
58513
A
B
/
24
feet
B
C
12
17986
/
115861
Or
to
conclude
:
A
B
/
198008
B
C
/
100000
A
B
/
24
feet
B
C
12
23902
/
198008
A
B
24
A
C
A
B
/
100000
A
C
/
86310
A
B
/
24
feet
A
C
20
71444
/
100000
A
B
/
115861
A
C
/
100000
A
B
/
24
feete
A
C
20
82776
/
115861
Or
to
conclude
.
A
B
/
198008
A
C
/
170901
A
B
24
A
C
141465
/
198008
A
C
20
71444
/
100000
B
C
A
C
/
86310
B
C
/
505027
A
C
20
71444
/
100000
B
C
12
16418
/
86●10
A
C
/
100000
B
C
/
58523
A
C
20
71444
/
100000
B
C
12
12071
/
100000
Or
to
conclude
.
A
C
/
170901
B
C
/
100000
A
C
20
71444
/
100000
B
C
12
26636
/
170901
Consectarie
2.
By
the
giuing
of
two
sides
which
soeuer
they
be
,
both
the
acure
angles
are
obtained
by
a
double
proportion
,
according
to
the
side
that
you
appoint
for
the
radius
.
A
B
C
,
A
B
B
C
,
A
B
/
5
Feet
B
C
/
3
feete
,
A
B
/
100000
B
C
/
59995
B
A
C
,
A
B
C.
B
C
/
3
Feet
A
B
/
5
Feet
,
B
C
/
100000
A
B
/
166679
A
B
C
,
A
B
C
,
A
C
4
B
C
3
A
C
/
4
feete
B
C
/
3
feet
B
C
/
100000
B
C
/
74991
B
A
C
,
B
C
/
3
feete
A
C
/
4
feete
B
C
/
100000
A
C
/
133549
A
B
C
,
Axioma
2.
In
all
kind
of
plaine
tryangles
A
B
C.
A
B
A
B
C
,
A
B
,
A
C
B
;
B
C
B
A
C
,
A
C
B
:
A
C
A
B
C
,
A
C
,
A
B
C.
A
B
B
C
,
A
C
B
,
B
A
C
,
Consectarie
1.
Therefore
the
angles
being
giuen
,
the
proportion
of
the
side●
be
also
found
.
And
by
the
consequence
A
B
C
,
A
20
C
60
B
99
A
B
86935
A
C
B
,
60
B
C
34475
B
A
C
,
20
A
C
98642
A
B
C
,
99
A
B
34
B
C
A
C
,
A
B
/
869●5
B
C
/
34475●
A
B
/
34
feete
B
C
13
42660
/
●6935
In
like
manner
.
A
B
/
869●5
A
C
/
98642●
A
B
/
34
feet
A
C
38
●9324
/
89985
Veltranspositis
terminis
intermediis
.
A
C
B
/
8663●
A
B
/
34
feete
,
B
A
C
/
●4475
B
C
13
42
/
8●
A
C
B
/
8693●
A
B
/
34
et
A
B
C
/
98642
A
C
38
50
/
●●
Consectarie
2.
Two
sides
of
a
tryangle
being
giuen
,
with
an
angle
opposite
to
one
of
the
said
sides
,
to
find
the
other
side
,
and
the
other
two
angles
opposite
to
the
two
sides
.
A
B
C
,
A
B
34
B
C
13
42660
/
86935
A
C
B
A
B
A
B
C
A
C
,
A
C
B
60
A
B
B
C
13
41669
/
86935
A
B
A
C
B
86935
B
C
B
A
C
34475.
Veltransposi●is
terminis
intermedii●●
AB
/
34
feete
A
C
B
/
86●35
B
C
,
13
42000
/
86935
B
A
C
/
34475
B
A
C
A
B
,
A
C
●0
B
C
10
B
A
C
29
A
B
C
B
C
10
A
C
20
B
C
B
A
C
49974
A
C
A
B
C
,
A
C
A
D
C
88
A
B
C
91
Axioma
III
.
In
all
kind
of
plaine
tryangles
.
A
B
C
,
B
C
,
A
C
A
B
C
,
D
A
E
E
A
C
A
B
C
,
B
A
C
,
D
A
C
;
D
A
F
,
F
A
C
,
D
A
E
D
A
F
,
E
A
C
,
F
A
C
,
F
A
E.
D
C
,
D
A
E
D
G
,
E
A
C
C
H
;
F
N
F
K
,
F
E
:
G
D
P
,
C
P
H
,
P
D
G
D
,
P
C
C
H
,
4.
P.
6.
Eucl
.
A
C
A
B
C
,
B
C
B
A
C
,
D
P
P
C
,
A
C
D
C
A
C
B
C
,
D
P
P
C
,
A
C
B
C
:
N
P
A
C
B
C
D
P
P
C
N
P
O
P.
A
K
L
F
E
M
A
D
N
O
P
C
,
D
C
K
M
,
D
C
N
P
K
M
L
E
O
C
O
P
F
M
,
F
E
Or
with
more
ease
.
N
P
,
F
M
,
F
E
K
M
L
E
,
F
M
,
F
E.
Consectarium
.
Therefore
in
plaine
oblique
angled
tryangles
,
two
sides
being
giuen
with
the
angle
comprehended
by
the
same
,
the
other
two
angles
are
also
found
.
A
B
C
,
A
C
5
,
B
C
3
A
C
B
40
A
B
C
B
A
C
Therefore
I
say
,
Axioma
V.
In
all
kind
of
plaine
tryangles
,
A
B
C
,
A
C
,
B
C
,
A
C
,
C
D
E
F
,
A
C
A
B
B
D
A
B
A
C
,
A
C
A
D
E
B
A
B
A
C
,
A
E
A
C
1.
P.
37
C
B
,
B
D
,
E
B
B
F.
F
G
,
A
G
A
B
C
,
B
C
,
B
G
B
C
,
A
B
20
A
C
13
Therefore
I
conclude
,
BC
/
21
Feet
BD
/
3●
Feet
BE
/
7
Feet
BF
/
11
Feet
,
B
C
21
F
C
,
10
F
G
,
G
C
G
C
G
B
16
A
Manuduction
or
the
vse
of
the
former
Axiomes
.
A
B
C
,
D
A
E
,
B
C
B
E
1
P.
29
,
A
B
C
D
A
E
:
In
plaine
obliquangled
tryangles
.
30
P.
But
the
three
former
differences
may
be
resolued
by
the
first
Axioma
,
if
so
that
from
any
vnknowne
angle
vpon
the
fide
opposite
thereto
,
a
perpendicular
be
let
fall
,
happening
within
or
without
the
tryangle
,
according
as
the
case
shall
require
,
&
thereby
the
obliquangled
tryangle
is
conuerted
into
two
tryangles
;
whether
the
perpendicular
fall
within
or
without
the
tryangles
A
B
A
C
B
,
B
C
,
B
A
C
,
A
B
B
C
To
the
same
effect
you
may
say
by
the
first
Axioma
:
A
B
B
D
,
B
A
D
,
A
B
B
D
E
B
D
B
C
D
B
C
B
C
D
B
D
B
C
A
B
C
B
A
B
A
C
B
,
B
C
B
A
C
After
the
same
manner
may
you
say
.
B
C
B
D
B
C
D
,
B
C
B
D
B
D
A
B
B
D
A
B
A
B
D
,
B
A
D
,
B
A
D
D
B
C
,
A
B
C
:
A
B
A
C
,
A
B
C
,
A
C
B
To
the
same
effect
may
you
say
by
the
first
Axioma
:
A
B
B
D
B
A
D
,
A
B
D
B
A
B
A
D
A
B
D
,
A
B
,
A
D
A
C
,
D
C
D
C
B
D
:
D
C
,
B
D
D
C
B
,
B
A
C
,
A
B
C.
B
C
,
1.
Axiom
.
D
C
D
C
B
,
D
C
,
B
C.
Thus
farre
of
the
dimension
of
tryangles
by
sines
,
tangents
,
and
secants
,
which
I
haue
for
the
most
part
drawne
from
the
doctrine
of
Bartholo
.
Pitiscus
Grunbergens
.
a
forraine
moderne
writer
,
hoping
you
will
take
pleasure
in
the
application
thereof
to
the
singular
vse
of
the
Geodeticall
staffe
.
By
this
Sinicall
doctrine
may
you
find
the
sides
,
diagonals
and
perpendiculars
in
any
figure
,
and
so
thereby
measure
fields
,
woods
,
countries
,
&c.
as
in
the
sixt
booke
.
Problema
1.
The
distance
of
any
Turret
,
&c.
being
giuen
,
to
finde
the
altitude
.
B
G
,
A
C
,
E
G
200
Topographicall
Glasse
,
C
A
B
29
A
B
C
60
AC
/
86892
A
B
C
60
/
200
deg
20
m
.
feete
B
C
/
4949●
B
A
C
29
A
C
/
200
feete
B
C
113
80204
/
86892
,
A
C
/
199000
B
C
/
56●62
B
A
C
29
A
C
/
200
feete
B
C
113
922
/
2000
Or
to
conclude
.
A
C
/
175556
A
B
C
60
B
C
/
109000
A
C
/
209
feete
B
C
113
162172
/
175556
But
vulgarly
.
B
C
56961
A
C
,
113
9●2
/
1000
B
C.
Probleme
2
;
The
distance
of
any
towre
being
giuen
,
to
find
the
hypotenusall
.
A
C
200
A
B
C
A
B
,
&c.
A
B
C
/
86892
60
deg
.
20
m
.
A
C
/
200
feete
A
C
B
/
1●●000
90
A
B
230
14340
/
86892
A
C
/
100000
A
B
/
11508●
B
A
C
,
29
A
C
/
200
feete
A
B
230
17
/
100
Therefore
compendiously
,
A
B
,
115085
A
C
,
200
230
17000
/
100000
230
17
/
100
A
B.
Probleme
3.
Any
part
of
the
distance
of
a
tower
being
giuen
,
to
find
the
rest
.
A
C
A
D
,
E
F
90
B
A
C
29
B
D
C
,
30
Prop
.
Chap.
1.
A
B
C
,
60
D
B
C
44
D
B
C
96568
,
A
B
C
175556
,
A
D
,
A
D
/
789●●
D
C
/
96568
A
D
/
90
feete
D
C
/
●2●●
feete
D
C
96568
A
D
90
A
D
,
78988
Probleme
IIII
.
Any
parte
of
a
distance
being
giuen
,
to
find
out
the
altitude
.
AD
/
78988
BC
/
100000
AD
/
90
feete
BC
/
114
feete
Probleme
V.
Any
parte
of
a
distance
being
giuen
,
to
find
the
hypothenufall
.
B
D
C
,
A
D
B
134
30
Pro
.
Chap.
2●
D
B
C
44
B
C
D
90
A
D
B
834
A
D
B
134
,
B
A
C
29
A
D
B
16
AD
/
28122
A
B
D
16
A
B
A
D
B
134
deg
.
/
71933
,
AD
/
90
feete
.
A
B
,
230
491
/
28122
A
B
D
/
28122
A
D
/
90
feete
,
●
D
B
/
71933
234
401
/
28122
Or
if
you
seeke
the
Hypothenufall
D
B
;
say
A
D
/
28122
B
D
29
deg
.
40
m
.
/
49495
A
D
/
90
feet
D
B
154
11274
/
28122
A
B
D
/
28122
A
D
/
90
feete
,
●
A
D
29
deg
40
m
.
/
49495
D
B
158
11274
/
28122
Probleme
6.
To
seeke
any
kind
of
distance
at
one
station
.
F
E
,
F
A
E
75
A
E
A
E
F
A
E
/
100000
F
A
E
75
deg
.
58
m
.
/
400086
,
A
E
/
4
feete
E
F
/
16
feete
Therefore
vulgarly
,
16
344
/
109000
F
E.
Q
H
B
Q
H
101
B
H
Q
67
Q
B
H
12
Q
B
H
12
deg
.
/
20791
Q
H
●
67
deg
.
/
92939
Q
H
/
4
feete
Q
B
17
1579
/
20791
H
B
:
H
B
Q
12
deg
.
/
20791
H
Q
B
102
deg
.
/
98162
Q
H
/
4
feete
H
B
18
18410
/
20791
H
B
,
Therefore
vulgarly
18
18410
/
20791
H
Q
C
,
Q
H
C
,
H
C
Q
,
Probleme
VII
.
To
seeke
the
distance
betwixt
any
two
townes
,
any
two
ships
vpon
the
seas
,
or
any
other
inaccessible
obiects
whatsoeuer
.
113
(
92200
As
for
the
purpose
:
A
D
/
2
A
C
/
3
●
D
/
4
D
F
/
6
,
A
C
,
C
D
,
A
B
2
,
D
F
;
viz
,
6
The
description
and
vse
of
the
Canon
or
Table
for
the
dimension
of
tryangles
,
by
sines
,
Tangents
,
and
secants
,
according
as
I
haue
newly
calculated
the
same
.
Radium
particularum
60,000,000,000
Radium
particularum
,
1,000,000,000,000,000
,
G
C
,
I
B
I
F
B
,
I
H
B.
B
C
,
B
G
D
E
,
B
C
D
B
G
D
,
B
E
D
B
C
B
G
,
B
E
,
B
E
D
,
B
G
D
,
B
C
D
B
C
,
B
F
B
K.
B
E.
B
F
viz.
B
K
E
A.
11
Sinus
versus
B
C
E
C
,
sinus
versus
B
G
,
G
F
,
13
Sinus
versus
maior
G
E
,
G
F
B
14
Sinus
versus
minor
E
C
B
C.
L
C
B
C.
A
L
B
C
:
18
Cordus
B
D
B
C
D.
Def
.
Circles
of
declination
be
counted
vpon
the
limbe
from
the
equinoctiall
towards
the
poles
.
Def
.
Circles
of
latitude
are
counted
from
the
Zodiacke
vpon
the
limbe
.
Def
.
Circles
of
altitude
and
depression
are
counted
from
the
Horizon
on
the
limbe
.
Def
.
Take
it
generall
that
all
parallell
lines
are
counted
on
the
limbe
from
that
great
circle
they
lye
parallell
vnto
towards
the
pole
thereof
.
Def
.
You
must
first
vnderstand
that
all
kind
of
ellipticall
lines
by
a
certaine
reducement
are
measured
by
chords
vpon
the
limbe
,
like
to
parallels
.
Def
.
Ameridian
is
a
great
circle
passing
by
the
poles
of
the
world
,
and
cutting
the
equinoctial
at
right
angles
expressed
by
chords
,
and
reduced
to
the
limbe
by
lines
paralell
to
the
of
clocke
meridian
.
Def
.
All
Azimuths
be
great
circles
passing
by
the
verticall
point
,
and
crossing
the
horizon
at
right
angles
,
expressed
by
chords
on
the
limbe
,
and
transferred
thereunto
by
lines
parallell
to
the
east
and
west
Azimuth
.
All
circles
of
longitude
be
great
circles
passing
by
the
poles
of
the
Zodiack
,
cutting
the
eclipticke
at
right
angles
,
measured
vpon
the
limbe
and
transferred
thereunts
by
lines
parallell
vnto
the
axtrée
of
the
eclipticke
.
Def
.
All
great
circles
be
meridians
,
circles
of
longitude
,
verticall
circles
,
Coluers
,
the
equinoctiall
,
ecliptake
,
&c.
Def
.
All
lesse
circles
be
parallels
.
Def
.
Generally
all
great
circles
crosse
one
the
other
vpon
the
center
,
and
all
other
lesse
circles
neuer
crosse
ouer
the
center
.
The
center
in
this
proiectment
doth
represent
the
equinoctiall
points
of
♈
&c
♎
,
the
circumference
,
the
meridian
,
or
of
clocke
line
,
but
in
some
conclusions
,
the
Solstitiall
Colure
.
Def
.
All
times
are
reckoned
from
of
the
clocke
at
noone
,
to
at
night
,
and
are
measured
in
the
parallell
of
the
sunne
(
and
so
do
Astronomers
count
it
in
their
.
Ephemerides
)
and
counted
from
the
axes
of
the
Equinoctiall
.
Def
.
One
degrée
of
the
Equinoctiall
containes
foure
minutes
of
time
,
and
degrées
one
houre
,
for
which
purpose
behold
the
insuing
table
.
A
B
C
D
E
A
F
B
D
,
G
H
,
C
E
,
G
C
H
E
,
A
D
,
G
C
G
H
C
D
,
A
B
A
F
G
H
,
G
L
,
G
L
G
I
L
,
F
A
I
M
,
I
O
,
H
P
H
P
,
H
P
H
F
P
F
K
30
F
A
K
R
,
H
P
G
L
,
A
B
C
D
E
B
D
E
C
B
D
;
A
B
C
D
E
B
D
F
C
B
G
,
L
D
23
G
L
H
P
,
B
H
50
A
B
C
D
E
B
D
B
D
C
E
,
B
D
F
K
,
L
M
,
N
O
,
23
B
D
,
B
Q
,
L
K
C
E
B
D
B
D
R
C
52
R
S
T
w
;
L
K
N
Q
,
64
42
/
60
25
11
/
62
B
C
D
E
B
D
F
K
Y
V
,
B
D
,
V
D
,
A
B
C
D
E
F
K
K
L
N
Q
O
M
,
A
K
N
Q
,
R
Z
N
Q
A
L
,
A
B
C
D
E
,
11
40
/
60
B
I
51
40
/
50
A
B
C
D
F
G
11
40
/
60
40
12
/
60
I
K
F
G
A
B
C
D
E
B
D
L
K
A
L
,
O
E
O
LL
.
O
C
viz.
27
54
/
60
180
viz.
120
57
49
/
6●
viz.
●7
122
21
/
60
Gem
.
Can
.
Cap.
Sagit
.
A
B
C
D
E
F
G
C
D
I
H
B
,
2●
/
60
F
G
I
H
,
B
E
,
13
46
/
60
52
20
/
60
29
47
/
60
viz
29
47
/
60
32
13
/
60
29
47
/
60
Taurus
,
viz.
271
47
/
60
Capella
,
Hircus
,
76
37
/
69
22
2
/
4
A
B
C
D
E
,
F
G
M
I
H
Q
F
P
,
M
I
,
v●z
22
76
●7
/
60
B
F
F
G
,
viz.
B
F
P
G
,
45
●
/
60
72
●1
/
●●
A
B
C
D
E
,
F
G
L
I
34
13
/
60
L
I
B
R
A
C
,
B
E
viz.
52
20
/
60
55
47
/
60
34
1●
/
60
52
20
/
60
A
B
C
D
E
,
F
G
O
P
H
I
O
P
H
I
Q
A
40
40
/
60
40
40
/
60
40
40
/
60
A
B
C
D
,
O
P
R
B
40
40
/
60
B
I
B
Q
R
A
,
O
P
H
A
Q
I
,
B
I
52
20
/
60
Imum
Coeli
B
D
C
E
,
B
C
L
I
R
,
R
16
,
8
7
56
/
60
L
T
B
C
,
L
I
F
G
A
V
A
B
C
E
D
,
C
D
F
G
H
I
I
N
Insula
Zirisaea
,
16
2
/
4
A
F
D
K
E
,
L
I
16
2
/
4
8
¼
C
B
B
E
viz.
52
Gemma
Frifius
,
16
●0
/
60
4
30
/
60
Insula
Zirisaea
A
B
C
E
D
,
C
D
O
P
H
I
O
H
The
degrees
of
the
Eclipticke
any
time
being
in
the
Meridian
,
is
called
Gradus
Medii
Coeli
,
with
some
,
Cor
Coeli
,
but
most
generall
,
Culmem
Coeli
,
thus
had
.
Vice
versa
,
A
B
C
E
D
,
C
D
B
E
H
I
F
G
11
40
/
60
;
I
K
I
H
,
46
12
/
90
;
11
8
/
60
;
11
8
/
60
;
A
B
B
A
C
:
A
C
A
B
C
E
D
,
H
I
F
P
F
G
B
E
60
,
4
A
B
C
E
D
,
H
I
F
G
11
40
/
60
;
F
G
A
E
C
D
F
G
F
C
:
C
B
A
F
,
A
I
A
K
30
,
A
L
45
,
A
M
60
,
A
N
75
,
A
F
90
:
12
5
/
60
24
43
/
60
38
37
/
60
54
3
/
60
71
28
/
60
1
,
2
,
3
,
A
B
C
D
F
G
H
,
F
G
H
E
:
E
H
F
G
H
F
,
F
A
,
F
S
:
viz.
12
5
/
60
H
K
,
E
K
K
R
24
43
/
60
L
E
H
24
43
/
60
E
L
Q
,
viz.
38
●7
/
60
H
E
M
38
37
/
60
E
M
M
A
N
A
,
54
3
/
60
,
71
28
/
60
E
N
E
O
,
F
E.
8
,
F
P
,
F
O
F
N
F
Q
,
11
,
2
10
,
3
9
,
4
I
E
H
:
I
E
H
,
H
E
,
F
G
H
I
,
I
H
I
H
9
10
/
60
19
●
/
60
K
K
,
31
2
/
60
46
33
/
60
5
,
66
A
B
C
D
A
B
,
E
F
,
A
F
B
:
E
F
A
F
,
9
10
/
60
F
E
G
,
E
G
F
H
19
●
/
60
,
D
F
I
31
2
/
60
F
K
46
12
/
60
F
L
60
F
A
90
F
E
M
,
E
F
C
H
,
C
D
M
E
E
M
11
,
10
A
B
C
D
viz.
53
E
F
G
H
:
G
I
,
E
F
F
E
G
E
F
K
L
:
M
N
,
K
L
,
O
P
,
P
Q
C
Q
R
,
Q
S
,
K
L
,
Q
R
K
L
,
Q
F
Q
R
45
K
L
S
F
V
w
O
Q
V
w
9
,
10
,
Q
O
Y
Z
,
P
Q
,
11
,
10
,
9
,
8
,
7
,
6
,
5
,
4
,
1.
2.
3.
4.
5.
6.
7.
8.
A
B
C
D
,
D
E
,
E
F
D
C
,
E
F
,
G
H
;
H
I
K
I
L
,
I
L
,
I
H
O
,
I
H
P
,
I
H
Q
,
I
H
R
,
I
H
S
;
I
L
E
F
A
F
,
E
F
Q
P
O
,
E
F
N
Z
O
;
B
D
C
I
G
,
M
N
Z
O
,
8.
9.
10.
1.
2.
3.
I
G
I
H
,
For
walles
declining
into
the
West
.
Otherwise
without
the
Sunne
.
A
B
C
,
D
B
,
B
E
E
D
:
A
C
37
F
G
,
I
D
:
E
D
,
D
I
I
K
,
M.
Blagraues
6
A
C
B
D
E
D
D
I
Mathematicall
Flowers
,
Insulae
Fortunatae
,
Britannia
,
Rhodus
,
Scilia
,
America
,
&c.
13
Peninsula
Cymbrica
Chersonesus
,
14
Isthmus
,
2
Peninsulaes
Peninsula
,
Isthmus
,
Bohemia
,
Saxonia
Amphiscij
,
Heteroscij
,
Periscij
,
Antaeci
,
Periaeci
16.
Amphiscij
,
17
Heteroscij
,
temperate
Zones
,
18
Periscij
,
19
Antaeci
paria
tempora
,
20
Periaeci
21
Antipodes
52
½
13
1
/
3
A
B
C
D
B
D
E
F
52
½
A
D
:
13
1
/
3
E
F
Edenburgh
,
Venice
,
Toletum
,
&c.
11
¼
S
E
G
H
,
C
I
N
S
,
S
w
N
,
F
C
A
N
,
A
N
,
45
N
w
,