The
Vses
of
these
which
are
knowne
without
seeing
the
Sunne
,
are
30.
of
the
said
Index
or
Table
,
as
followeth
,
viz.
the
2.
9.
10.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
23.
24.
25.
26.
27.
28.
29.
30.
32.
33.
35.
37.
38.
39.
40.
41.
and
42.
of
which
13.
of
them
will
be
showne
onely
by
knowing
the
day
of
the
Month
,
viz.
the
18.
33.
21.
19.
25.
24.
35.
2.
38.
37.
20.
41.
and
42.
as
followeth
.
The
day
of
the
Month
knowne
to
finde
.
-
1.
The
houre
of
Sunne
rising
,
setting
,
and
length
of
the
day
.
-
2.
The
Sunnes
difference
of
Ascention
.
-
3.
The
Sunnes
Declination
.
-
4.
What
dayes
are
alike
in
length
,
and
what
day
the
Sunne
rising
in
the
one
,
shall
be
the
Sunne
setting
in
the
other
.
-
5.
The
Sunnes
place
,
or
degree
in
the
Eclipticke
.
-
6.
The
Sunnes
right
Ascention
,
and
oblique
Ascention
.
-
7.
The
houre
,
and
Altitude
of
the
Sunnes
comming
East
,
or
West
.
-
8.
The
distance
of
the
Sunnes
rising
,
or
setting
,
from
the
East
,
or
West
.
-
9.
The
height
,
or
depression
of
the
Sunne
in
the
Meridian
here
,
or
for
any
Latitude
.
-
10.
The
time
of
day
breake
,
and
end
of
twylight
.
-
11.
The
inequality
of
time
,
betweene
day
breake
,
and
Sunne
rising
.
-
12.
The
houre
,
and
Altitude
of
the
Sunnes
comming
upon
any
declining
wall
.
-
13.
At
what
houre
,
and
Altitude
,
the
Sun
must
have
to
be
opposite
or
perpendicular
,
to
a
declining
wall
.
First
,
to
finde
the
time
of
Sunne
Pro.
1
rising
,
or
setting
,
and
length
of
the
day
,
for
any
day
of
the
yeere
.
Seeke
the
day
of
the
Month
in
the
Kalender
,
Constru
¦
ctio
.
1
and
the
houre
line
that
meeteth
therewith
,
sheweth
the
time
of
Sunne
rising
,
or
setting
.
So
if
the
day
of
the
Month
were
the
13.
Exam.
of
October
,
the
parallell
that
meeteth
therewith
is
the
houre
,
viz.
7.
of
the
clocke
,
at
which
time
the
Sun
riseth
:
the
same
houre
is
noted
also
with
5.
which
is
the
time
of
Sun
setting
that
day
,
this
doubled
makes
10.
the
length
of
the
day
required
.
Secondly
,
to
finde
the
difference
Pro.
2
of
Ascention
,
for
any
day
of
the
yeere
.
Marke
what
Meridian
meeteth
with
the
day
Constru
¦
ctio
.
2
of
the
Month
in
the
Kalender
:
as
suppose
the
day
to
be
the
former
13.
of
October
,
which
is
the
houre
line
of
7.
and
5.
(
as
before
)
and
account
the
Numbers
of
Meridians
to
the
houre
of
6.
so
have
you
15.
gr.
or
an
houre
,
which
is
the
difference
of
Ascention
for
the
13.
day
of
October
required
.
Pro.
3
Thirdly
,
to
finde
the
Sunnes
declination
for
any
day
.
Constru
¦
ctio
.
3
Marke
what
parallell
of
Declination
meeteth
with
the
day
of
the
Month
in
the
Kalender
,
and
account
how
many
degrees
it
is
from
the
Equinoctiall
,
so
have
you
the
Sunnes
Declination
for
that
day
.
Exam.
So
if
the
day
were
the
last
of
August
,
the
parallell
that
meeteth
therewith
is
the
5th
.
from
the
Equator
,
and
somuch
is
the
Sunnes
declination
,
that
day
,
viz.
5.
gr.
.
North
declination
.
Pro.
4
Fourthly
,
to
finde
what
dayes
in
the
yeare
are
alike
in
length
,
and
what
day
the
Sunne
rising
in
the
one
,
shall
be
the
Sunne
setting
in
the
other
.
Constru
¦
ctio
.
4
For
the
first
,
note
that
the
dayes
betweene
the
10th
of
December
and
the
11th
.
of
Iune
,
are
dayes
of
Increase
,
and
the
rest
are
dayes
of
Decrease
.
Now
right
against
any
day
of
decrease
in
the
Kalender
,
is
the
day
of
increase
,
which
dayes
are
equall
one
to
the
other
.
Exam.
So
the
19.
day
of
May
,
is
against
the
4.
of
Iuly
,
at
which
time
the
Sunne
riseth
and
setteth
alike
without
sensible
error
,
viz.
4.
of
the
clocke
,
and
therefore
those
dayes
are
of
equall
length
,
and
so
of
others
.
For
the
second
,
to
finde
what
day
the
sunne
rising
in
the
one
,
shall
be
the
sunne
setting
in
the
other
.
Admit
the
day
to
be
the
18th
.
of
February
and
according
to
the
first
pro.
finde
the
time
of
Sunne
rising
,
which
is
at
40.
m.
after
6.
Exam.
of
the
clocke
Constru
¦
ctio
.
5
for
that
day
,
and
the
setting
20.
m
,
after
5.
then
marke
what
day
of
the
Month
the
houre
line
of
20
m
,
after
5.
in
the
forenoone
,
meeteth
with
the
Kalender
,
which
will
be
the
23.
of
August
,
so
the
18th
.
day
of
February
the
Sun
did
set
at
the
same
houre
that
it
did
rise
,
the
23.
day
of
August
.
Fiftly
,
to
finde
the
sunnes
place
,
or
Pro.
5
degree
,
for
any
day
of
the
yeere
.
Note
where
the
parallel
of
the
day
of
the
Month
crosseth
the
Eclipticke
,
that
is
the
Sunnes
Constru
¦
ctio
.
6
place
.
So
the
former
parallell
of
the
13th
.
of
October
meeteth
with
the
Eclipticke
in
the
beginning
of
♏
,
and
♓
,
but
which
of
these
is
the
Sunnes
place
,
the
quarter
of
the
yeare
may
easily
tell
you
,
viz.
♏
which
is
the
Sunnes
place
or
the
degree
in
the
Eclipticke
for
that
day
.
Pro.
6
Sixtly
,
to
finde
the
Sunnes
right
ascention
,
and
oblique
ascention
at
any
time
.
Constru
¦
ctio
.
7
Consider
what
Meridean
meeteth
with
the
Sunnes
place
in
the
Eclipticke
for
the
day
given
,
and
marke
the
number
of
Meridians
in
the
Equator
(
for
the
Meridians
are
numbred
in
the
Equator
,
as
is
sayd
before
in
the
description
)
so
have
you
the
Sunnes
right
Ascention
:
but
here
note
that
the
degrees
in
the
Eclipticke
are
numbred
forward
and
backeward
in
the
Eclipticke
unto
360.
gr.
upon
this
Instrument
:
so
are
the
right
Ascentions
of
those
degrees
also
numbred
forward
and
backward
in
the
Aequator
:
for
the
right
ascention
of
any
degree
in
the
Eclipticke
,
is
that
degree
of
the
Aequator
which
is
opposite
unto
it
,
(
the
succession
of
the
signes
considered
)
so
if
the
Sun
were
in
the
beginning
of
♏
,
the
right
Ascention
is
neere
208.
degrees
,
for
the
Meridian
that
passeth
by
the
beginning
of
♏
,
is
accounted
in
the
Equator
from
♈
,
and
is
within
6.
m
,
of
28.
gr.
Now
the
right
Ascention
of
♋
,
is
90.
gr.
and
the
beginning
the
of
♎
,
is
180.
gr.
and
from
the
beginning
of
♎
,
to
the
beginning
♏
,
is
within
6.
m
,
of
28.
gr.
as
before
,
all
is
which
put
together
makes
neere
208.
gr.
the
right
Ascention
of
the
Sun
the
13th
.
day
of
October
.
To
find
the
Sunnes
Oblique
Ascention
at
any
time
.
Note
that
the
difference
of
Ascention
,
is
the
Constru
¦
ctio
.
8
difference
alwayes
betweene
the
right
Ascention
of
the
Sun
,
and
the
oblique
Ascention
thereof
:
therfore
the
right
Ascention
known
by
the
last
direction
,
&
the
difference
of
Ascention
by
the
second
direction
,
the
oblique
Ascention
is
easily
had
,
by
Addition
,
or
substraction
thus
.
If
the
Sun
be
in
a
Southerne
signe
then
the
oblique
Ascention
,
is
greater
then
the
right
Ascention
,
by
so
much
as
the
difference
of
Ascention
comes
to
:
but
if
the
Sun
be
in
a
Northerne
signe
,
the
oblique
Ascention
is
so
much
lesse
:
which
difference
of
Ascention
as
before
by
the
2
Pro:
for
the
said
13th
.
of
October
was
15.
gr.
this
ad
unto
the
right
Ascention
of
the
beginning
of
♏
,
viz.
208.
gr.
makes
223.
gr.
the
Suns
oblique
Ascention
for
the
beginning
of
♏
,
on
the
13th
.
day
of
October
;
but
if
the
Sun
had
beene
in
the
beginning
of
♉
,
the
oblique
ascention
would
have
beene
onely
neere
13.
gr.
viz.
12.
gr.
54.
m.
Seventhly
,
to
find
the
suns
Altitude
,
Pro.
7
and
houre
of
the
suns
comming
East
,
or
West
,
any
day
of
the
yeare
above
the
Horizon
.
Here
note
that
this
Proposition
holds
in
use
Constru
¦
ctio
.
9
onely
for
that
time
of
the
Suns
being
in
the
Northerne
signes
that
is
from
the
10th
.
of
March
to
the
13th
.
of
September
:
therefore
lay
the
Index
to
the
East
,
or
Aequinoctiall
point
noted
with
E.
or
40.
&
50.
in
the
Limbe
:
so
have
you
instantly
at
once
without
farther
rectification
both
the
Altitude
and
houre
of
the
Suns
comming
East
or
West
,
above
the
Horizon
for
all
or
any
of
the
dayes
above
specified
:
so
the
parallel
of
any
day
of
the
Moneth
meeting
with
the
edge
of
the
Index
gives
the
Suns
Altitude
in
the
Index
,
and
the
Meridian
meeting
therewith
shewes
the
houre
.
Exam.
So
if
it
were
the
second
of
May
,
or
the
22.
of
Iuly
,
the
parallel
belonging
to
those
daies
meetes
with
the
Index
neere
about
,
23.
gr.
17.
m
,
and
there
also
meetes
with
that
point
,
the
houre
line
of
7
,
and
5.
which
sheweth
that
when
the
Sun
is
23.
gr.
17.
m
,
high
either
upon
the
second
of
May
or
the
22.
of
Iuly
;
then
the
Sun
will
be
due
East
or
West
,
and
that
will
happen
to
be
at
7
of
the
clocke
in
the
forenoone
,
and
5.
of
the
clocke
in
the
afternoone
.
Pro.
8
Eightly
,
to
find
the
distance
of
the
suns
rising
,
or
setting
,
any
day
of
the
yeare
,
from
the
East
,
or
West
,
called
the
suns
Amplitude
.
Constru
¦
ctio
.
12
Lay
the
Index
to
the
day
of
the
Moneth
,
for
the
time
given
,
&
the
edge
of
it
in
the
Limbe
of
the
Instrument
shall
shew
the
Amplitude
required
.
So
if
the
day
were
the
13th
.
Exam.
of
October
the
number
of
degrees
from
the
points
of
East
,
noted
with
40.
50.
unto
the
Index
is
18.
gr.
40.
m.
which
is
the
Suns
Amplitude
for
the
given
day
,
viz.
the
13th
.
day
of
October
.
Ninthly
,
to
know
the
suns
Meridionall
Pro.
9
Altitude
,
or
the
suns
depression
under
the
Horizon
,
at
Midnight
here
,
or
in
any
Latitude
,
for
any
day
in
the
yeare
.
Lay
the
Index
unto
the
houre
of
12
,
and
where
Constru
¦
ctio
.
11
the
parallel
of
the
day
of
the
Moneth
meeteth
that
therewith
shal
be
the
Suns
Meridionall
Altitude
.
So
if
it
were
the
13th
.
day
of
October
,
as
before
,
Exam.
the
parallell
,
for
that
day
is
11.
gr.
and
a
halfe
from
the
Equator
South
:
this
crosseth
the
Index
in
27.
gr.
which
is
the
Sunnes
Meridionall
Altitude
that
day
.
Now
for
the
Sunnes
depression
at
midnight
,
here
is
to
be
noted
,
that
any
degree
of
the
Eclipticke
is
at
any
time
so
much
below
the
Horizon
,
as
his
opposite
degree
in
the
Eclipticke
,
is
above
the
Horizon
at
the
same
time
.
Constru
¦
ctio
.
12
Therefore
where
the
contrary
parallell
of
the
Sunne
viz.
11.
gr.
and
a
halfe
North
,
meeteth
with
the
Index
in
the
houre
of
12.
that
shall
bee
the
Sunnes
Meridionall
depression
at
midnight
,
the
said
13th
.
day
of
October
.
Pro.
10
Tenthly
,
to
finde
the
time
of
day-breake
,
and
end
of
twy-light
,
with
the
Position
of
the
sunne
under
the
Horizon
for
any
time
.
This
proposition
,
hath
reference
to
the
Sunnes
depression
under
the
Horizon
,
for
it
is
said
to
bee
day
breake
or
twi-light
to
end
,
when
the
Sun
is
,
18.
gr.
under
the
Horizon
:
therefore
the
Construction
in
this
will
be
thus
.
Constru
¦
ctio
.
13
Account
18.
gr.
on
the
Index
then
move
the
Index
untill
that
degree
meete
with
the
Contrarie
parallel
of
Declination
for
the
day
given
,
so
the
Meridian
or
Houre-line
that
meeteth
therewith
shall
bee
the
houre
of
day
breake
required
.
Exam.
So
if
the
day
were
the
10.
of
Aprill
,
the
parallel
of
Declination
for
that
day
is
North
II.
gr.
and
a
halfe
which
I
seeke
out
one
the
other
side
of
the
Aequator
viz.
II.
gr.
and
a
halfe
South
Declination
,
and
Marke
where
the
18th
.
gr.
of
the
Index
meeteth
therewith
,
for
there
also
is
the
houre
of
day
breake
viz.
with
in
20.
m.
of
3.
in
the
Morning
,
and
20.
m.
past
9.
for
the
end
of
twi-light
the
sayd
10th
.
of
Aprill
,
also
the
Index
in
the
Horizon
at
that
Instant
sheweth
the
position
of
the
Sun
under
the
Horizon
viz.
neere
48
gr.
10.
m.
to
the
North
of
the
East
:
but
if
the
day
had
beene
the
13th
of
October
the
houre
of
daybreake
had
beene
2
minuts
before
5.
and
twi-light
would
have
ended
2.
m.
after
7.
Eleventhly
,
to
finde
the
inequallitie
Pro.
11
of
time
,
betweene
day
breake
and
Sun
rising
,
for
any
day
of
the
yeare
assigned
.
By
the
first
Construction
,
for
the
dayes
given
Constructio
.
14
finde
the
time
of
Sun
rising
,
and
by
the
former
13th
Construction
the
houre
and
time
of
day
breake
belonging
to
those
dayes
:
then
compare
the
time
betweene
the
Sun
rising
,
and
day
breake
of
the
one
,
with
that
of
the
other
,
so
the
difference
of
those
two
,
shall
bee
the
difference
of
time
required
.
Example
.
|
|
|
H.
M.
|
|
H.
M.
|
|
So
on
the
tenth
of
|
March
the
|
Sun
rising
is
at
|
6.
00
|
The
time
betweene
day
breake
and
Sun
rising
is
.
|
2.
0
|
the
difference
is
,
12.
m.
|
day
breake
is
at
|
4.
00
|
Docemb
.
the
|
Sun
rising
it
at
|
8.
12
|
2.
12
|
day
breake
,
is
at
|
6.
00
|
the
difference
is
.
1.
ho.
22.
m.
|
May
the
|
Sun
rising
is
at
|
4.
11
|
3.
34
|
day
breake
,
at
|
12
,
37
|
So
the
difference
of
time
betweene
day
breake
and
Sunne
rising
the
10th
of
December
is
neere
a
quarter
of
an
houre
longer
then
that
of
the
10th
of
March
;
but
more
then
an
houre
and
halfe
longer
betweene
day
breake
,
and
Sun
rising
the
10th
of
May
,
then
the
10th
of
March
.
Pro.
12
Twelfely
to
finde
the
houre
,
and
Altitude
of
the
sunnes
comming
upon
a
Declining
wall
any
day
of
the
yeare
.
☞
Seeing
the
declinations
of
Plaines
,
or
Walls
,
are
accounted
from
the
points
of
East
or
West
in
the
Horizon
,
as
the
sunnes
Amplitude
is
the
numbering
of
them
therefore
shall
bee
alike
,
in
the
Limbe
of
the
Instrument
.
Now
admit
the
Declination
of
a
Plaine
or
Wall
,
to
be
22.
gr.
the
opperation
Constru
¦
ctio
.
15
would
be
thus
.
The
Index
being
set
thereto
,
you
may
instantly
see
at
what
houre
the
Sunne
will
come
upon
the
Plaine
,
for
any
day
in
the
yeare
;
for
where
the
parallell
of
the
day
of
the
Moneth
crosseth
the
Index
amongst
the
houre-lines
,
(
which
Index
represents
the
Plaine
)
that
is
the
houre
of
the
Suns
comming
upon
the
Plaine
and
the
degrees
in
the
Index
gives
the
Sunnes
Altitude
.
Examp.
So
if
the
Sunne
were
in
the
Tropicke
of
♋
the
Tropicke
meeteth
with
the
Index
almost
within
5
m.
of
9
in
the
Morning
,
and
at
that
time
the
Sunne
commeth
upon
the
Plaine
,
and
there
the
Tropicke
cuts
also
the
Index
in
45.
gr.
.
40.
m.
which
is
the
suns
Altitude
at
that
time
that
the
Sun
wil
glance
or
begin
to
shine
upon
the
Plaine
.
As
for
the
time
of
the
suns
continuance
on
the
Plaine
(
as
is
specified
in
the
Index
or
Table
)
account
the
Declination
,
on
the
other
side
of
the
East
point
,
and
lay
the
Index
thereto
,
so
the
edge
of
it
in
the
Tropicke
of
♋
,
will
point
out
at
what
houre
the
Sun
goes
of
the
Plaine
viz.
at
6.
of
the
clock
&
38.
m
,
neere
,
if
the
declination
were
West
,
(
as
here
it
is
supposed
)
which
added
to
the
time
of
the
suns
comming
on
the
Plaine
,
makes
9.
houres
33.
m
,
&
so
long
the
sun
shines
on
the
Plaine
.
Thirteenthly
,
to
finde
at
what
Pro.
13
houre
,
and
Altitude
the
sun
must
have
to
be
opposite
,
or
perpendicular
to
a
declining
Plaine
,
any
day
in
the
yeere
.
Let
a
Plaine
decline
from
the
East
point
towards
the
South
22.
Example
.
gr.
account
this
in
the
Limbe
Constru
¦
ctio
.
16
from
the
houre
of
12.
and
lay
the
Index
thereto
,
so
the
parallell
that
crosseth
the
Index
,
doth
shew
the
Sunnes
Altitude
,
and
the
Meridian
meeting
therewith
,
gives
the
houre
,
at
which
time
the
Sun
will
be
opposite
to
the
Plaine
;
so
have
you
at
one
instant
for
every
day
in
the
yeare
,
at
what
houre
and
Altitude
,
the
Sunne
will
bee
opposite
to
the
Plaine
.
|
gr
.
m.
|
As
admit
the
dayes
were
these
.
|
Decem.
|
the
tenth
,
the
Suns
place
at
which
time
is
in
|
♑
|
and
the
houre
of
the
Suns
being
opposite
to
the
plaine
,
that
day
would
be
at
|
40-m
past
.
1
|
and
the
Suns
Altitude
at
that
time
would
be
,
|
12.12
|
March
.
|
♈
|
14
m.
past
.
1.
|
36.25
|
Iune
|
♋
|
48
m.
past
12
|
60.45
|
Thus
touching
the
resolution
of
the
former
13
uses
of
the
aforesaid
Table
,
or
Index
which
had
reference
only
to
the
knowledge
of
the
day
of
the
Month
,
there
are
13.
other
uses
of
the
foresaid
Index
,
or
Table
viz.
the
10.
12.
32.
39.
40.
23.
17.
16.
26.
27.
28.
29.
30.
Which
have
no
dependance
upon
the
sight
of
the
Sun
,
of
which
the
6
first
are
resolued
,
only
by
knowing
the
day
of
the
Month
,
and
the
other
7.
are
as
followeth
.
viz
by
knowing
the
day
of
the
Month
to
finde
.
-
1.
At
what
houre
the
shadow
of
an
Altitude
is
equall
,
double
,
triple
,
&c.
unto
it
.
-
2.
At
any
houre
and
Altitude
of
the
Sun
,
or
Azimuth
,
what
proportion
shadowes
have
to
their
bodies
.
-
3.
The
houre
of
the
day
agreeable
to
any
Altitude
,
or
Azimuth
.
-
4.
The
Suns
depression
and
Azimuth
at
any
houre
of
the
night
Assigned
.
-
5.
The
houre
of
the
day
to
our
Antipodes
,
by
suposing
the
Suns
Depression
under
the
Horizon
.
-
6.
At
what
houre
in
any
day
the
Suns
Azimuth
and
Altitude
will
be
equall
,
and
how
much
the
Altitude
and
Azimuth
will
be
.
To
finde
.
-
7.
What
number
of
dayes
will
make
the
day
an
houre
longer
,
or
shorter
at
any
time
.
-
8.
Th●
inequallitie
of
time
in
equall
moneths
,
or
equall
number
of
dayes
.
-
9.
The
degree
of
the
Aequator
in
the
Horizon
,
by
supposing
any
degree
of
the
Eclipticke
in
the
Horizon
.
-
10.
The
degree
of
the
Eclipticke
in
the
Horizon
by
supposing
the
degree
of
the
Equator
in
the
Horizon
.
-
11.
The
degree
of
Medium
Coeli
,
or
the
degree
of
the
Eclipticke
in
the
Meridian
,
by
supposing
the
degree
of
the
Eclipticke
in
the
Horizon
,
vel
contra
.
-
12.
The
Horoscope
,
or
the
degree
ascendant
,
or
descend●nt
,
and
the
Nonagessima
degree
at
any
houre
.
-
13.
What
Angle
the
Eclipticke
makes
with
the
Horizon
,
or
the
Altitude
of
the
Nonagessima
degree
,
&
what
Azimuth
it
is
in
at
any
houre
.
First
,
to
finde
the
Proportion
of
Pro.
14
shadowes
to
their
Altitudes
at
any
time
.
As
if
it
were
required
the
20
of
Aprill
,
Declaratio
.
at
what
houre
of
the
day
,
and
how
high
the
Sun
must
be
either
in
the
forenoone
or
afternoone
,
that
the
shadow
of
a
man
or
any
Altitude
,
shall
be
equall
unto
his
height
double
,
triple
,
quadruple
Quintuple
&c.
Constru
¦
ctio
.
17
Lay
the
Index
unto
the
numbers
in
the
line
of
shadowes
viz.
to
1.
2.
3.
4.
5.
&c.
and
wheresoever
any
of
those
divisions
in
the
line
of
shadowes
meete
with
the
Index
amongst
the
degrees
;
there
it
sheweth
what
height
the
Sun
must
have
,
to
make
the
shadowes
equall
,
double
,
triple
&c.
to
the
Altitude
.
Exam.
So
laying
the
Index
upon
1
in
the
line
of
shadowes
,
it
meeteth
with
45.
gr.
in
the
Index
:
&
so
high
the
Sun
must
be
to
make
the
shadow
of
a
man
or
any
thing
equall
to
his
height
upon
an
Horizontall
plaine
:
then
move
the
Index
to
and
fro
,
untill
the
said
45.
gr.
in
the
Index
meete
with
the
parallel
of
the
day
Month
,
viz
the
20.
of
April
,
so
the
houre
line
that
meeteth
therewith
,
is
the
houre
of
the
day
that
the
shadow
of
a
Man
:
or
other
Altitudes
,
will
be
equall
to
his
heigth
or
Altitude
,
viz
neere
10.
of
the
Clocke
in
the
forenoone
,
or
2.
of
the
Clocke
,
in
the
afternoone
.
|
|
|
|
|
forenoone
.
|
afternoone
.
|
|
|
|
gr
.
m.
|
|
ho.
m.
|
ho.
m.
|
And
according
to
the
same
directions
when
shadows
are
|
Double
.
|
The
Altitude
would
be
.
|
26.
33
|
and
the
houre
the
said
20.
of
Aprill
would
be
,
|
7.
37
|
4.
23
|
Triple
.
|
18.
26
|
6.
43
|
5.
17
|
Quadruple
.
|
14.
2
|
6.
16
|
5.
44
|
Quintuple
.
|
11.
19
|
5.
58
|
6.
02
|
Sextuple
.
|
9.
27
|
5.
46
|
6.
14
|
Septuple
.
|
8.
7
|
5.
37
|
6.
23
|
Octuple
.
|
7.
7
|
5.
31
|
6.
29
|
N●nocuple
.
|
6.
20
|
5.
25
|
6.
35
|
Decuple
.
|
5.
43
|
5.
21
|
6.
39
|
Vigecuple
.
|
2.
51
|
5.
2
|
6.
58
|
Secondly
,
to
finde
what
proportion
Pro.
15
shadowes
have
to
their
bodies
at
any
houre
in
the
day
,
Azimuth
,
or
Altitude
of
the
Sun
asigned
.
If
the
houre
be
knowne
,
or
supposed
,
move
the
Constru
¦
ctio
.
18
Index
until
it
meete
with
the
houre
in
the
parallel
of
the
day
of
the
Month
,
so
the
intersection
of
that
parallel
with
the
Index
is
the
suns
Altitude
,
and
the
edge
of
the
Index
,
in
the
Limbe
,
wil
shew
the
Suns
Azimuth
,
then
move
the
Index
until
the
degree
of
Altitude
intersect
the
line
of
shadowes
,
so
shall
you
have
the
proportion
of
shadowes
,
to
their
bodies
required
.
So
if
on
the
11th
.
of
Aprill
at
,
7.
Exam.
of
the
Clocke
in
the
forenoone
,
(
if
the
Sun
shine
,
)
it
were
required
what
proportion
the
shadow
of
a
man
shall
beare
to
his
height
,
or
the
shadow
of
an
Altitude
to
the
Altitude
,
the
parallel
that
belongeth
to
the
given
day
is
neere
12.
gr.
Marke
where
this
parallel
meeteth
with
the
given
houre
of
7.
and
bring
the
Index
to
it
;
so
have
you
the
Suns
height
at
that
houre
viz
18.
gr.
26.
m
,
and
the
edge
of
the
Index
in
the
Limbe
of
the
Instrument
,
shall
give
the
Azimuth
viz
4.
gr.
from
the
East
:
then
move
the
Index
,
untill
the
degree
of
the
Suns
Altitude
viz
18.
gr.
26.
m
,
meete
with
the
line
of
shadowes
which
will
be
in
3
,
which
sheweth
that
at
7.
of
the
Clock
in
the
forenone
the
said
11th
.
of
Aprill
,
the
shadow
of
a
man
,
or
the
shadow
of
an
Altitude
,
shall
be
Triple
to
his
height
:
the
like
will
be
at
5.
of
the
Clocke
in
the
afternoone
,
for
equall
distances
of
the
Sun
from
the
Meridian
the
same
day
,
without
sensible
error
,
will
give
equall
Altitudes
of
the
sun
,
and
equall
Altitude
of
the
sun
doth
produce
equall
shadowes
upon
Horizontall
Plaines
Constru
¦
ctio
.
19
Secondly
,
if
the
Position
or
Azimuth
of
the
Sun
be
knowne
or
supposed
,
which
admit
4
gr.
from
the
East
towards
the
South
.
Lay
the
Index
unto
it
in
the
limbe
,
&
marke
what
degree
in
the
Index
the
parallel
meeteth
with
,
which
is
with
18.
gr.
26.
m
,
so
have
you
the
suns
Altitude
in
the
Index
:
then
move
the
Index
until
the
degree
meete
with
the
Line
of
shadowes
;
so
have
you
the
proportion
of
shadowes
required
at
that
instant
,
viz
Triple
as
before
.
Constru
¦
ctio
.
20
Thirdly
,
if
the
Suns
height
be
knowne
or
supposed
,
which
admit
18.
gr.
26.
m
,
account
it
in
the
Index
,
and
moove
the
Index
until
that
degree
meete
with
the
line
of
shadowes
;
so
where
it
intersecteth
the
line
of
the
shadowes
,
there
you
have
the
proportion
of
shadowes
to
their
bodies
at
that
instant
of
time
required
,
which
will
be
triple
as
before
;
so
the
10th
.
of
Aprill
if
the
houre
be
7.
or
the
Altitude
18.
g.
26.
m
,
or
the
Azimuth
4.
gr.
from
the
East
toward
the
South
,
the
proportion
of
shadowes
to
their
bodies
will
be
Triple
.
Thirdly
to
finde
the
houre
of
the
Pro.
16
day
agreeable
to
any
Altitude
or
Azimuth
,
for
any
day
of
the
yeare
Proposed
.
For
the
first
account
the
Suns
Altitude
in
the
Constru
¦
ctio
.
21
Index
,
and
move
it
to
and
fro
untill
that
degree
meete
with
the
parallel
of
the
day
of
the
Month
:
so
the
Meridian
that
passeth
by
that
point
,
shal
be
the
houre
required
.
Thus
if
the
day
were
the
tenth
of
March
,
Exam.
the
Sun
being
that
day
in
the
Aequinoctial
,
&
the
Altitude
supposed
to
be
32.
gr.
37.
m
,
this
I
seeke
out
upon
the
Index
and
move
the
Index
till
that
degree
meete
with
the
Aequator
;
so
the
Meridian
or
houre
Circle
that
passeth
thereby
is
the
houre
viz.
10.
of
the
Clocke
in
the
forenoone
or
2.
of
the
Clocke
in
the
afternoone
,
and
if
you
move
the
Index
softly
along
as
the
degrees
of
the
Suns
Altitude
in
the
Index
intersect
the
Aequator
(
and
so
of
any
parallel
:
)
so
the
Meridian
that
meeteth
therewith
is
the
houre
of
the
day
agreeable
to
that
Altitude
.
For
the
second
,
to
finde
the
houre
Constru
¦
ctio
.
22
of
the
day
agreeable
to
any
Azimuth
.
As
suppose
it
were
36.
gr.
35.
m
,
Exam.
from
the
South
.
Move
the
Index
in
the
Limbe
unto
this
Azimuth
known
or
supposed
;
so
where
the
Index
crosseth
the
parallel
for
the
day
given
,
there
the
Meridian
that
meeteth
therewith
,
shewes
the
houre
of
the
day
viz
10.
of
the
Clocke
in
the
forenoone
or
2
in
the
afternoone
as
before
.
And
if
you
move
the
Index
softly
along
,
as
the
Index
passeth
by
any
Azimuth
in
the
Limbe
:
so
the
edge
of
the
Index
shall
intersect
the
parallel
of
declination
for
the
day
of
the
Month
,
in
the
houre
of
the
day
agreeable
to
that
Azimuth
:
by
which
proposition
and
the
last
,
Glasses
may
be
easily
placed
to
burne
according
to
the
Suns
Azimuth
,
or
houre
assigned
.
Pro.
17
Fourthly
,
to
finde
the
suns
depression
,
&
position
under
the
Horizon
,
at
any
houre
of
the
night
,
with
the
houre
of
the
day
to
our
Antipodes
,
by
supposing
the
sun
any
number
of
degrees
under
the
Horizon
.
Constru
¦
ctio
.
23
By
the
11th
Construction
it
is
said
that
any
degree
of
the
Eclipticke
,
is
asmuch
belowe
the
Horizon
at
any
time
,
as
his
opposite
degree
is
above
the
Horizon
at
the
same
time
:
therefore
if
the
Index
be
layed
to
the
like
parallel
,
on
the
contrary
side
of
the
Aequator
,
that
meeteth
with
the
given
houre
the
intersection
in
the
Index
shall
shew
you
the
degree
of
the
Suns
depression
under
the
Horizon
at
that
houre
.
So
if
at
10
of
the
Clocke
at
night
the
said
13th
of
October
it
were
required
to
finde
the
Suns
depression
under
the
Horizon
,
Exam.
consider
the
declination
,
or
the
suns
parallel
for
that
day
,
which
is
11.
gr.
and
a
halfe
South
,
which
declination
I
seeke
in
the
other
side
of
the
Aequator
,
and
marke
where
it
meeteth
with
the
houre
of
10.
unto
which
I
lay
the
Index
,
so
the
edge
thereof
in
the
Limbe
sheweth
the
suns
Azimuth
to
be
nere
42
gr.
30.
m
,
from
the
South
,
and
the
parallels
intersection
that
meeteth
with
the
Index
,
gives
the
Suns
depression
,
viz.
neere
43.
gr.
and
so
much
is
the
Sun
below
the
Horizon
,
and
in
that
position
the
13th
of
October
at
10.
of
the
Clocke
at
night
.
But
if
it
were
required
at
what
houre
of
the
Night
the
Sun
would
touch
the
verticall
Circle
of
East
and
West
under
the
Horizon
.
Lay
the
Index
to
the
point
of
East
and
marke
Constru
¦
ctio
.
24
where
about
the
Contrary
palle●
meeteth
with
the
Index
,
for
there
you
have
both
the
houre
and
the
degree
of
the
suns
depression
.
So
the
day
being
as
before
the
13th
of
October
,
Exam.
&
the
declination
south
11.
gr.
and
a
halfe
,
this
account
among●●
the
North
declinations
&
it
meeteth
with
the
Index
in
38
m
,
past
6.
the
houre
of
the
Suns
being
West
,
and
with
all
the
suns
depression
,
at
the
same
time
is
neere
14.
gr.
and
50.
m.
Pro.
18
Fiftly
,
to
finde
the
houre
of
the
day
to
our
Antipodes
,
by
supposing
the
suns
depression
under
the
Horizon
.
Constru
¦
ctio
.
25
Consider
the
declination
for
the
day
,
and
move
the
Index
to
and
fro
untill
the
degree
of
the
suns
depression
in
the
Index
,
meeteth
with
the
like
parallel
or
the
other
side
of
the
Aequator
,
so
the
houre
that
meeteth
therwith
is
the
houre
of
the
day
to
our
Antipodes
.
Exam.
So
if
on
the
20th
.
of
Aprill
,
we
should
suppose
the
sun
to
be
13.
gr.
under
the
Horizon
,
&
desire
to
know
the
houre
to
our
Antipodes
,
the
parallel
of
declention
for
that
day
is
15.
gr.
North
,
Now
in
the
Index
account
13.
degrees
and
move
it
to
and
fro
untill
the
said
thirteenth
degree
in
the
Index
meete
with
the
15th
.
parallel
of
South
declination
,
so
the
Meridian
that
meeteth
therewith
is
the
houre
of
the
day
to
our
Antipodes
,
within
2
m
,
of
9.
at
night
.
Pro.
19
Sixtly
,
to
finde
at
what
houre
in
any
day
,
the
suns
Azimuch
and
Altitude
will
be
equall
,
and
how
much
the
Altitude
and
Azimuth
will
be
.
Construction
.
Move
the
Index
,
to
&
fro
untill
the
edge
of
the
Index
meete
with
the
parallel
belonging
to
that
day
,
in
the
same
Number
of
degrees
that
the
end
of
the
Index
in
the
Limbe
from
the
point
of
East
doth
;
so
have
you
the
degree
of
the
Suns
Azimuth
,
and
Altitude
equall
the
one
to
the
other
,
and
the
Meridian
meeting
with
the
Index
in
the
parallel
of
the
given
day
,
sheweth
at
what
houre
that
Azimuth
,
and
Altitude
will
be
equall
.
So
admit
the
sun
to
be
in
the
Tropicke
of
♋
,
Exam
the
Index
being
moved
to
and
fro
untill
there
be
like
degrees
in
the
Index
,
and
in
the
Limbe
,
which
will
be
neere
16.
gr.
45.
m
,
and
there
the
houre
that
meeteth
therewith
is
12.
m
,
after
6.
in
the
forenoon
,
at
which
houre
the
eleventh
of
Iune
,
the
Suns
Azimuth
,
and
Altitude
,
will
be
equall
viz.
neere
16.
gr.
45.
m
,
as
before
.
Seventhly
,
to
finde
what
number
Pro.
20
of
dayes
any
time
of
the
yeare
,
will
make
the
day
an
houre
longer
or
shorter
.
Account
7.
gr.
and
a
halfe
amongst
the
Meridians
Construc
¦
tio
.
27
from
the
given
day
in
the
Kallender
,
and
note
the
day
of
the
Month
against
it
,
then
number
the
dayes
betweene
that
day
and
the
given
day
,
and
you
haue
the
answer
.
So
if
the
day
were
the
last
of
February
,
Exam.
or
the
first
of
March
,
consider
the
Suns
setting
that
day
by
the
Instrument
,
which
is
40.
m
,
past
5.
this
doubled
makes
the
length
of
the
day
,
11.
houres
20.
m
,
then
from
the
last
of
February
account
7.
gr.
and
a
halfe
and
it
will
point
out
the
fifteenth
of
March
at
which
time
the
Sun
seteth
at
10.
m
,
past
6
which
doubled
makes
12
houres
20.
m
,
so
the
fifteenth
of
March
,
the
length
of
the
day
is
an
houre
longer
then
it
was
the
first
of
March
;
and
the
difference
of
time
only
but
15.
dayes
,
but
if
the
number
of
daies
were
accounted
to
or
from
the
Suns
entring
into
the
Tropicall
points
,
it
will
be
more
then
35.
dayes
before
the
day
will
be
an
houre
longer
or
shorter
.
Exam.
So
if
from
the
tenth
of
Iune
we
should
account
7.
gr.
and
a
halfe
amongst
the
Meridians
from
that
Meridian
that
meeteth
with
the
tenth
of
Iune
,
it
would
fall
out
at
the
16th
.
day
of
Iuly
,
at
which
time
the
day
will
be
an
houre
shorter
then
it
was
the
tenth
of
Iune
,
and
the
intervall
of
time
more
then
twise
as
much
as
the
former
viz.
39.
dayes
.
Pro.
21
Eightly
,
to
finde
the
inequalitie
of
time
,
in
equall
Mounthes
or
equall
number
of
dayes
.
This
proposition
at
the
first
seemes
as
a
Paradox
,
yet
by
this
Instrument
may
easily
be
resolued
,
and
so
consequently
from
Mathematicall
principles
demonstrated
,
not
onely
the
inequalitie
of
equall
Months
,
but
also
the
inequalitie
of
Naturall
dayes
.
Now
a
day
naturall
according
to
the
generall
definition
is
one
revolution
of
the
Aequator
or
primum
mobile
,
that
is
from
sun
rising
to
sun
rising
:
or
it
is
the
time
wherein
the
sun
passeth
by
the
Meridian
,
and
commeth
to
the
Meridian
againe
,
commonly
taken
for
24.
houres
:
but
be
cause
that
in
that
intervale
of
time
the
sun
passing
from
the
Meridian
and
commeth
to
the
Meridian
againe
,
the
Sun
moves
according
to
his
Naturall
motion
(
secundum
antiquiorum
traditionem
)
neere
a
degree
more
or
lesse
;
therefore
the
Naturall
day
shall
be
some
what
longer
or
shorter
then
24.
houres
,
viz.
by
so
much
as
the
difference
of
right
ascention
of
that
degree
of
the
Eclipticke
comes
to
that
the
sun
is
in
,
and
seeing
the
degrees
of
the
Eclipticke
amongst
themselues
have
not
the
same
difference
of
right
Ascention
that
the
other
degrees
have
,
(
notwithstanding
the
degrees
of
the
Eclipticke
amongst
themselves
being
equall
the
one
to
the
other
)
the
suns
motion
ender
those
degrees
being
sometimes
quicker
,
and
sometimes
slower
,
it
will
necessarily
follow
that
the
sun
will
move
more
or
lesse
untill
the
sun
can
touch
the
Meridian
,
which
is
the
limit
or
tearme
of
the
suns
diurnall
revolution
as
before
:
this
difference
and
inequalitie
of
time
in
naturall
dayes
may
by
calculation
be
given
from
day
to
day
,
but
because
it
is
so
insensible
little
in
a
day
,
hardly
by
an
Instrument
of
this
nature
can
be
seene
,
but
by
a
number
of
dayes
,
compared
with
another
number
of
dayes
it
will
evidently
appeare
.
So
,
Exam.
if
it
were
required
how
much
the
Month
of
December
is
longer
then
the
Month
of
March
,
in
the
first
of
which
months
the
suns
motion
is
quicker
,
being
about
the
Perigeum
then
at
other
Constru
¦
ctio
.
28
times
,
now
both
of
which
months
have
equal
number
of
dayes
,
viz.
31.
Finde
the
right
ascention
for
the
|
beginning
and
ending
|
of
Mar.
viz.
|
350.0
.
|
the
difer
.
of
right
ascention
for
the
Month
of
Mar.
is
|
29.30
.
|
the
difference
betweene
these
is
5.
gr.
|
19.
30.
|
beginning
and
ending
|
of
Dece
.
viz.
|
257.
¾
|
the
difer
.
of
right
ascention
for
the
Month
of
Dece
.
is
|
34.
30.
|
292.
¼
.
|
which
5.
gr.
being
conuerted
into
time
by
allowing
4
minits
to
a
degree
makes
about
20.
m
,
and
so
much
is
the
Month
of
December
longer
then
the
Month
of
March
,
notwithstanding
both
of
these
Months
containing
equall
number
of
dayes
.
Pro.
22
Ninthly
,
to
finde
the
degree
of
the
Aequator
in
the
Horizon
,
by
suppossing
the
degree
of
the
Eclipticke
in
the
Horizon
.
Notatio
.
If
the
degree
given
be
in
the
Northerne
part
of
the
Ecliptike
,
the
oblique
Ascention
is
lesse
then
the
Constru
¦
ctio
.
29
right
Ascention
vel
contra
.
Get
therefore
first
the
right
Ascention
of
the
point
given
by
the
sixt
Pro.
and
the
difference
of
Ascention
by
the
2.
Pro.
for
that
taken
from
the
right
Ascention
gives
the
degree
of
the
Aequinoctiall
in
the
Horizon
,
but
if
the
given
degree
had
beene
in
a
Southren
signe
,
the
difference
of
Ascention
must
be
added
to
the
right
Ascention
,
so
have
you
the
degree
of
the
Aequator
in
the
Horizon
.
Tenthly
,
to
finde
the
degree
of
Pro.
23
the
Eclipticke
in
the
Horizon
by
supposing
the
degree
of
the
Aequator
in
the
Horizon
.
This
is
but
the
Conuerse
of
the
former
,
onely
Constru
¦
ctio
.
30
consider
the
correspondent
quarters
of
the
Aequinoctiall
to
these
of
the
Eclipticke
.
Eleventhly
,
to
finde
the
degree
of
Pro.
24
Medium
Coeli
,
or
the
degree
of
the
Eclipticke
in
the
Meridian
,
by
supp
sing
any
degree
of
the
Eclipticke
in
the
Horizon
.
Seeke
the
degree
of
the
Aequator
in
the
Horizon
,
Constru
¦
ctio
.
31
by
the
22.
Pro.
subtract
,
90.
from
it
(
if
the
Number
be
too
little
adde
a
whole
Circle
to
it
)
then
the
degree
of
the
Eclipticke
opposite
to
the
remainder
,
is
the
Answer
,
but
note
that
if
the
remainder
be
betweene
270.
and
360.
the
opposite
point
belongs
to
the
last
Quarter
of
the
Ecliptike
,
if
the
remainder
be
betweene
180.
and
270.
then
it
respects
the
3
quarter
of
the
Eclipticke
,
if
the
remainder
be
betweene
90.
and
180.
it
hath
reference
to
the
second
Quarter
.
&c.
But
if
the
degree
of
the
Eclipticke
in
the
Horizon
were
required
by
knowing
the
degree
of
the
in
Eclipticke
the
Meridian
.
This
,
is
onely
but
the
converse
of
the
former
,
&
Constru
¦
ctio
.
23
is
thus
performed
first
,
seek
the
right
Ascention
of
the
given
degree
of
Medium
Coeli
,
&
adde
thereto
90.
gr.
by
accounting
it
from
the
former
right
Ascention
,
&
note
the
suns
place
opposit
therto
for
the
difference
of
Ascention
of
this
last
degree
being
subtracted
from
the
former
degree
of
the
Aequator
in
the
Horizon
,
if
it
be
a
degree
of
the
Southren
signes
(
otherwise
Adde
)
gives
the
degree
of
the
Eclipticke
in
the
Horizon
demanded
.
Twelfthly
,
to
finde
the
Horoscope
Pro.
25
or
the
degree
Ascendant
,
or
descendant
and
the
Nonagessima
degree
at
any
houre
.
First
,
note
the
right
Ascention
for
the
day
given
Constru
¦
ctio
,
33
according
to
the
6.
Pro.
which
is
the
degree
of
the
Aequator
in
the
Meridian
,
at
12.
of
the
Clocke
,
unto
which
degree
adde
90.
so
have
you
the
degree
of
the
Aequator
in
the
Horizon
at
12.
of
the
Clocke
.
Then
consider
how
many
houres
the
given
houres
wants
of
12.
or
is
past
12.
which
conuerted
into
measure
and
accounted
Eastward
,
or
Westward
,
according
to
the
houre
given
from
the
former
points
of
the
Aequator
in
the
Horizon
at
12.
will
give
the
degree
of
the
Aequator
in
the
Horizon
at
the
houre
proposed
,
then
by
the
23.
Pro.
I
seeke
out
the
degree
of
the
Eclipticke
in
the
Horizon
answerable
to
the
degree
of
the
Aequator
so
have
you
the
degree
Ascendant
,
from
which
account
90.
gr.
or
3
signes
,
so
have
you
the
degree
of
the
Nonagessima
point
in
the
Horizon
,
but
if
you
reckon
6.
signes
from
the
Ascendant
,
you
have
the
desendant
degree
of
the
Eclipticke
in
the
West
of
the
Horizon
.
Pro.
26
Thirteenthly
,
to
finde
what
Angle
the
Eclipticke
makes
with
the
Horizon
,
or
the
Altitude
of
the
Nonagessima
degree
of
the
Eclipticke
,
above
the
Horizon
,
and
what
Azimuth
it
is
in
at
any
houre
.
According
to
the
last
Pro.
finde
the
degree
Constru
¦
ctio
.
34
Ascendant
,
and
the
Nonagessima
degree
,
then
by
the
24.
Pro.
finde
what
degree
of
the
Eclipticke
is
in
the
Meridian
,
Answerable
to
the
degree
of
the
Eclipticke
in
the
Horizon
,
so
shall
you
know
on
which
side
of
the
Meridian
the
Nonagessima
degree
is
,
&
how
far
from
the
Meridian
,
then
if
that
Index
be
layed
upon
the
houre
of
12
,
where
the
parallel
of
the
Nonagessima
degree
crosseth
it
,
that
should
be
the
height
of
it
,
if
it
were
in
the
Meridian
;
account
therfore
from
the
Meridian
or
houre
of
12.
in
the
Aequator
,
the
number
of
degrees
betweene
the
Nonagessima
degree
,
and
the
degree
of
the
Eclipticke
in
the
Meridian
,
&
marke
where
that
Meridian
meeteth
with
the
parallel
of
the
of
the
Nonagessima
degree
,
lay
the
Index
thereto
,
so
have
you
the
Altitude
of
the
Nonagessima
degree
in
the
Index
,
and
the
Azimuth
in
the
Horizon
,
or
Limbe
of
the
Instrument
.
There
are
yet
the
48.
49.
50.
9.
13.
14.
and
15th
.
uses
of
the
said
Index
or
Table
,
which
haue
no
relation
to
the
suns
sight
or
observation
in
there
operation
,
and
resolutions
,
and
should
have
followed
these
26.
uses
that
have
beene
delivered
:
but
I
referre
them
to
the
end
of
this
Tractat
;
as
for
these
uses
of
the
Instrument
which
depend
upon
the
Suns
sight
,
or
observation
they
are
these
13.
following
viz.
the
1.
31.
4.
6.
36.
7.
22.
3.
5.
34.
11.
43.
and
8th
.
viz.
to
shew
-
1.
The
Sun
,
or
starres
Altitude
above
the
Horizon
at
any
time
.
-
2.
The
houre
of
the
day
,
and
Azimuth
of
the
sun
.
-
3.
The
Meridian
Line
upon
any
appearance
of
the
Sun
.
-
4.
The
sit
of
a
building
,
or
costing
of
a
place
.
-
5.
The
Suns
Azimuth
,
and
houre
without
Observation
.
-
6.
The
variation
of
the
Needle
.
-
7.
The
Latitude
of
a
place
,
or
height
of
the
Pole
above
the
Horizon
.
-
8.
The
Suns
Azimuth
,
and
Altitude
at
any
houre
.
-
9.
The
vncertainetie
of
time
,
by
noting
the
shadow
of
things
.
-
10.
The
Quarter
of
the
yeare
and
day
of
the
Month
,
with
the
houre
,
Azimuth
,
and
the
Meridian
line
.
-
11.
Instantly
the
houre
of
the
day
,
the
Azimuth
,
and
Altitude
of
the
Sun
:
with
the
Meridionall
line
,
without
observation
or
sight
of
the
Sun
,
by
knowing
the
Proportion
betweene
the
length
of
a
shadow
upon
a
Horizontal
Plaine
,
and
that
which
did
cast
the
shadow
.
-
12.
The
Declination
of
a
Wall
,
by
seeing
the
Sun
beginning
to
shine
thereon
or
going
from
it
.
-
13.
The
Declination
of
a
Wall
,
the
Sun
shining
thereon
.
First
,
how
to
obserue
the
Sun
,
or
Pro.
27
starres
Altitude
above
the
Horizon
at
any
time
.
Lift
up
the
edge
of
the
Instrument
to
the
eye
,
Constru
¦
ctio
.
35
so
that
the
sight
which
is
at
the
Limbe
or
Circumference
of
the
Quadrant
be
next
the
eye
,
and
the
Index
to
hang
perpendicular
and
to
play
easily
by
the
side
therof
:
then
move
the
Quadrant
up
and
downe
untill
you
may
through
both
sights
see
the
Center
or
midle
of
the
Sun
,
or
starre
:
so
the
Index
in
the
Limbe
shall
fall
upon
the
degrees
of
the
Sun
or
starres
Altitude
above
the
Horizon
at
that
time
.
Or
without
looking
at
the
sun
,
the
Altitude
thereof
may
be
thus
found
:
hould
the
Quadrant
Constru
¦
ctio
.
36
that
the
Index
may
hang
perpendicular
,
or
be
verticall
as
before
,
then
move
about
the
Instrument
untill
the
edge
of
it
be
opposite
to
the
body
of
the
Sun
.
Now
supposing
the
Instrument
to
hang
thus
upon
his
Center
,
softly
lift
up
the
edge
thereof
which
is
towards
the
Sun
,
untill
you
see
the
beames
of
the
sun
passe
through
both
sights
,
then
the
Index
in
the
Limbe
shall
give
the
suns
Altitude
as
before
.
Pro.
28
Secondly
,
how
to
finde
the
houre
of
the
day
,
and
Azimuth
of
the
Sun
,
upon
any
appearance
of
the
Sunne
.
Constru
¦
ctio
.
37
By
the
last
Pro.
obserue
or
take
the
suns
Altitude
and
account
it
on
the
Index
,
then
seeke
for
the
parallel
of
the
day
of
the
Month
for
the
day
present
,
&
move
the
Index
untill
that
degree
of
Altitude
in
the
edge
of
the
Index
meete
with
the
parallel
of
the
day
,
so
the
Meridian
that
meeteth
with
that
degree
of
Altitude
in
the
Index
,
shall
be
the
houre
of
the
day
required
,
&
the
edge
of
the
Index
in
the
Limbe
of
the
Instrument
,
shall
likewise
shew
the
Suns
Azimuth
belonging
to
that
houre
.
So
if
upon
the
last
of
August
the
Suns
Altitude
in
the
forenoone
should
be
obserued
and
found
to
be
30.
Exam.
gr.
&
a
halfe
,
seeke
this
Altitude
out
upon
the
Index
&
move
the
Index
untill
the
degree
of
Altitude
meete
with
the
parallel
for
the
day
of
the
Month
given
,
viz.
the
fift
parallel
from
the
Aequator
Northward
so
the
houreline
that
meeteth
also
with
the
30.
gr.
&
a
halfe
in
the
Index
,
is
the
houre
viz.
neere
9.
&
that
shall
be
the
houre
of
the
day
at
that
instant
,
&
the
edge
of
the
Index
in
the
Limbe
cutteth
neere
35.
gr.
and
30.
m
,
from
the
point
of
East
,
towards
the
South
,
and
so
much
is
the
Suns
Azimuth
at
that
time
.
Thirdly
,
how
to
finde
the
Meridian
Pro.
29
line
,
and
the
true
points
of
North
,
&
South
,
East
,
and
West
upon
any
appearance
of
the
Sunne
.
According
to
the
27.
Pro.
first
obserue
the
Constru
¦
ctio
.
38
Suns
Altitude
above
the
Horizon
,
and
by
the
last
Construction
finde
the
Suns
Azimuth
agreeable
to
that
Altitude
:
let
the
Index
and
rest
at
that
degree
,
and
erect
the
prependicular
at
the
end
of
the
Index
,
then
houlding
the
plaine
or
face
of
the
Quadrant
parallel
to
the
Horizon
,
move
the
Instrument
Circular
,
untill
the
shadow
of
the
said
perpendicular
fall
by
the
side
of
the
Index
,
and
so
the
houerline
of
12
,
or
the
edge
of
the
Instrument
which
is
parallel
unto
it
(
which
is
the
North
and
south
edge
of
the
Instrument
)
shall
represent
the
Meridian
line
,
and
pointeth
out
the
North
and
South
in
the
Horizon
of
the
world
by
the
termes
thereof
,
and
the
other
straight
edge
of
the
Instrument
which
is
perpendicular
unto
that
edge
is
the
(
East
and
West
edge
of
the
Instrument
)
and
denoteth
or
sheweth
the
line
of
East
,
and
West
in
the
Horizon
,
of
the
world
.
But
this
may
be
more
accurately
done
if
you
place
the
backe
of
the
Instrument
downe
upon
an
Horizontall
plaine
,
and
the
edge
of
the
Index
being
at
the
degree
of
the
suns
Azimuth
observed
,
and
the
perpendicular
erected
at
the
end
of
the
Index
as
before
:
then
moving
the
Instrument
as
it
so
lyeth
untill
the
shadow
of
the
perpendicular
fall
by
the
side
of
the
Index
,
so
the
Meridian
of
the
Instrument
,
shall
be
in
the
Meridian
of
the
World
,
and
every
point
and
degree
in
the
Limbe
of
the
Instrument
shall
point
out
,
and
be
opposite
,
and
represent
his
like
degree
in
the
Horizon
of
the
world
.
Constru
¦
ctio
.
39
But
here
note
that
this
Construction
serves
only
but
for
the
forenoone
observation
;
for
if
the
practice
be
in
the
afternone
,
the
way
to
finde
the
Meridian
line
may
be
thus
.
Having
found
the
suns
Azimuth
as
before
,
lay
the
Index
upon
the
houre
line
of
12.
and
erect
the
perpendicular
at
the
end
thereof
,
and
move
the
Instrument
about
Circular
,
untill
the
shadow
of
the
said
perpendicular
fall
by
the
side
of
the
Index
:
for
then
if
the
edge
of
the
Index
be
moved
unto
the
suns
Azimuth
before
known
,
the
edge
of
the
Index
shall
represent
the
Meridian
line
,
&
90.
gr.
farther
shall
be
the
point
of
East
,
and
the
Center
of
the
Instrument
the
point
of
West
,
therefore
if
upon
the
plaine
that
the
Instrument
lies
upon
,
you
make
a
marke
at
the
edge
of
the
Index
which
is
in
the
Meridian
as
before
,
and
another
marke
right
under
the
Center
and
so
place
the
North
and
South
edge
of
the
Instrument
unto
these
two
points
:
then
every
degree
in
the
Horizon
.
or
Limbe
of
the
Instrument
,
shall
point
out
as
before
his
opposite
or
●ike
degree
in
the
Horizon
of
the
world
.
Fourthly
,
how
to
finde
the
sit
Pro.
30
of
a
Building
,
or
Costing
of
a
place
.
By
the
last
Pro.
finde
out
or
draw
the
Meridian
Constru
¦
ctio
40
line
,
.
and
place
the
North
and
South
edge
of
the
Instrument
unto
it
:
if
the
Building
or
Place
ly
in
the
Easterne
semicircle
of
the
world
(
but
if
it
ly
in
the
Westerne
semicircle
,
then
let
the
East
&
West
edge
of
the
Instrument
be
placed
upon
the
Meridian
line
)
so
the
eye
being
over
the
Center
of
the
Instrument
,
and
behoulding
the
place
,
let
the
Index
be
moved
untill
it
be
also
with
the
visual
line
observed
by
the
eye
,
that
is
opposite
to
the
place
,
so
the
edge
of
the
Index
,
from
the
Cardinall
points
of
the
Instrument
in
the
Limbe
,
viz.
from
the
East
or
West
,
North
or
South
,
shall
shew
the
bearing
of
that
place
from
you
,
in
respect
of
the
Cardinall
points
of
the
world
in
the
Horizon
:
but
if
two
sights
be
placed
at
the
Index
(
which
is
according
to
the
description
thereof
)
then
may
you
observe
the
place
through
the
sights
of
the
Index
by
leting
the
Instrument
rest
,
and
moving
the
Index
to
and
fro
untill
you
see
the
obiect
,
so
the
edge
of
the
Index
in
the
limbe
,
shall
point
out
the
bearing
or
Position
of
the
place
from
you
in
degrees
from
the
East
,
West
,
North
,
or
South
,
&
accounting
11.
gr.
and
¼
as
often
as
you
can
in
those
degrees
,
observed
:
you
have
the
point
of
the
Compasse
which
the
place
,
or
obiect
beares
from
you
.
Pro.
31
Fiftly
,
to
finde
the
suns
Azimuth
,
and
houre
without
observation
.
The
Meridian
line
being
drawne
first
upon
a
Constru
¦
ctio
.
41
plaine
according
to
the
former
directions
,
consider
if
it
be
in
the
forenoone
or
afternoone
;
if
in
the
forenoone
,
then
let
the
North
,
and
South
edge
of
the
Instrument
be
placed
unto
the
Meridian
line
,
but
if
it
be
in
the
afternoone
,
then
set
the
edge
of
East
,
&
West
of
the
Instrument
,
unto
the
Meridian
line
,
and
let
the
Instrument
rest
there
,
then
erect
the
perpendicular
at
the
end
of
the
Index
,
&
move
the
Index
about
untill
the
shadow
of
the
perpendicular
fall
by
the
side
of
the
Index
,
so
the
edge
of
the
Index
will
amongst
the
degrees
in
the
Limbe
shew
the
Suns
Azimuth
at
that
time
,
and
where
the
edge
of
the
Index
meeteth
with
the
parallel
of
the
day
of
the
Month
,
that
is
the
houre
of
the
day
at
that
time
.
But
if
the
Axis
be
rectified
then
there
is
no
neede
of
a
Meridian
line
to
be
drawne
,
for
this
Instrument
will
with
great
facilitie
finde
out
his
owne
Meridian
,
by
moving
it
to
and
fro
untill
the
shadow
of
the
perpendicular
which
is
ouer
the
Center
of
the
Instrument
,
intersect
the
same
houre
in
the
Parallel
of
the
day
of
the
Moneth
,
that
the
Axis
doth
amongst
the
Common
houres
▪
so
that
houre
shall
be
the
houre
of
the
day
for
that
instant
,
and
the
shadow
of
the
said
perpendicular
,
cutting
the
Limbe
,
or
extended
unto
it
,
doth
there
shew
the
Suns
Azimuth
,
and
so
the
Meridian
of
the
Instrument
at
that
position
,
shal
be
in
the
Meridian
of
the
world
required
.
Sixtly
,
to
finde
the
variation
Pro.
32
of
the
needle
.
By
the
twentie
nineth
Pro.
vpon
an
even
Plaine
parallel
to
the
Horizon
draw
the
Meridian
line
,
&
Constru
¦
ctio
.
42
place
the
North
&
South
line
of
the
Card
directly
over
the
said
Meridian
line
,
so
the
Number
of
degrees
that
the
Needle
cutteth
in
the
Card
from
the
North
and
South
line
of
the
Card
,
that
shall
be
the
variation
of
the
Needle
required
;
otherwise
it
may
be
found
thus
:
Neere
unto
the
Center
of
the
Index
,
upon
the
Index
may
a
small
Brosse
pinne
be
so
placed
that
it
may
be
erected
perpendicular
to
the
Center
of
the
Instrument
and
halfe
an
inch
above
it
.
Let
a
Needle
by
placed
upon
this
pinne
,
then
lay
the
East
,
and
West
edge
of
the
Instrument
to
the
Meridian
line
,
&
when
the
Needle
resteth
,
move
the
Index
,
untill
the
edge
of
it
be
directly
under
the
Needle
so
the
edge
of
the
Index
;
in
the
Limbe
of
the
Instrument
,
shall
point
out
or
shew
the
Needles
variation
required
.
Pro.
33
Seventhly
,
to
finde
the
Latitude
of
a
place
,
or
the
Poles
hight
above
the
Horizon
.
Constru
¦
ctio
.
43
First
,
draw
the
Meridian
line
upon
some
plaine
by
helpe
of
the
38.
Construction
,
then
erect
the
prependicular
at
the
end
of
the
Index
,
and
place
the
North
and
South
edge
of
the
Instrument
,
to
the
Meridian
line
so
drawne
upon
the
plaine
,
and
move
also
the
Index
untill
the
edge
thereof
touch
the
houre
of
12.
let
the
Instrument
rest
at
this
position
,
then
marke
diligently
about
noone
or
12.
of
the
Clocke
when
the
shadow
of
the
perpendicular
doth
fall
by
the
edge
of
the
Index
,
for
then
the
sun
is
in
the
Meridian
,
at
which
time
according
to
the
27.
Pro.
obserue
or
take
the
suns
height
(
which
is
his
Meridian
Altitude
,
for
that
day
)
and
by
the
3.
Pro.
finde
the
Suns
declination
agreeable
to
that
day
,
and
adde
it
to
the
Suns
Meridionall
Altitude
observe
(
if
it
be
South
declination
,
otherwise
subtract
it
from
the
former
Meridionall
Altitude
,
)
so
have
you
the
height
of
the
Aequinoctial
above
the
Horizon
,
that
taken
from
90.
gives
the
depression
of
the
South
Pole
under
the
Horizon
,
which
is
alwayes
equall
to
the
elevation
of
the
North
Pole
above
the
Horizon
.
So
if
upon
the
tenth
of
Aprill
,
Exam.
the
Meridian
Altitude
should
be
found
to
be
50.
gr.
the
Declination
belonging
to
that
day
by
the
3.
Pro.
is
11.
gr.
and
a
halfe
North
,
which
being
subtracted
(
according
to
the
former
directions
)
leaves
38.
gr.
30.
m
,
the
height
of
the
Aequinoctiall
above
the
Horizon
:
&
that
taken
from
90.
leaves
51.
gr.
30.
m
the
depression
of
the
South
Pole
under
the
Horizon
:
or
the
elevation
of
the
North
Pole
above
the
Horizon
,
for
the
height
of
the
Aequinoctiall
knowne
,
the
Complement
thereof
is
alwayes
the
Latitude
of
the
place
,
or
height
of
the
Pole
:
and
here
note
generally
that
the
height
of
the
Pole
and
Aequinoctiall
together
,
doe
alwayes
make
a
Quadrant
or
90.
gr.
therefore
the
height
of
one
of
them
being
knowne
,
the
height
of
the
other
is
also
knowne
,
and
further
here
note
that
if
the
sun
have
North
Declination
,
the
sun
is
so
much
higher
then
the
Aequinoctiall
at
none
that
day
,
by
so
much
as
his
Declination
,
cometh
to
,
but
if
the
Sun
have
South
Declination
,
then
the
Sun
is
lower
then
the
Aequinoctiall
that
day
at
noone
,
by
so
much
as
his
Declination
cometh
to
,
by
which
you
may
easily
gether
when
to
adde
,
or
subtract
the
suns
Declination
to
,
or
from
the
suns
Meridianall
Altitude
to
get
the
height
of
Aequator
,
which
knowne
the
Poles
height
cannot
be
unknowne
.
Pro.
34
Eightly
,
to
finde
the
suns
Azimuth
and
Altitude
for
any
houre
.
Constru
¦
ctio
.
44
Marke
where
the
parallel
for
the
day
of
the
Month
meeteth
with
the
given
houre
,
and
bring
the
edge
of
the
Index
thereto
,
so
the
degree
that
the
edge
of
the
Index
cutteth
in
the
Limbe
of
the
Instrument
that
shal
be
the
Suns
Azimuth
,
and
the
degree
that
the
houre
cutteth
in
the
Index
,
that
shall
be
the
Suns
Altitude
required
.
So
,
if
upon
the
tenth
of
December
at
nine
of
the
Clocke
in
the
Morning
,
Exam.
the
Suns
Azimuth
and
Altitude
were
required
,
marke
first
where
the
Tropick
of
Capricorne
(
which
is
the
parallel
,
for
that
day
given
)
meeteth
with
the
given
houre
of
nine
,
and
bring
the
Index
thereto
,
so
the
edge
of
it
in
the
Limbe
pointeth
out
neere
40.
gr.
and
a
halfe
,
&
so
much
is
the
Suns
Azimuth
,
from
the
South
,
at
nine
of
the
Clocke
in
the
forenoone
,
the
said
tenth
of
December
,
and
the
houre
line
meeting
with
the
Index
,
sheweth
neere
5.
gr.
25.
m.
so
much
is
the
suns
Altitude
at
that
time
;
now
if
you
move
the
Index
softly
along
,
as
the
edge
of
it
passeth
by
any
houre
for
any
day
of
the
yeare
,
so
the
edge
of
the
Index
in
the
Limbe
of
the
Instrument
sheweth
the
suns
Azimuth
,
and
the
intersection
of
the
parallel
with
the
Index
shall
shew
the
Suns
Altitude
belonging
to
that
houre
.
Ninthly
,
to
shew
the
uncertaintie
Pro.
35
of
time
,
by
noting
the
shadow
of
things
.
It
is
usually
noted
by
some
,
that
when
the
shadow
of
the
edge
of
a
Window
,
Dore
,
Wall
,
or
such
like
,
shall
touch
such
or
such
markes
,
that
it
shall
be
then
such
,
or
such
an
houre
of
the
day
,
and
so
constantly
to
hould
for
all
the
yeare
,
this
obseruation
is
farre
from
truth
,
and
the
principalls
of
Astronomie
(
and
may
be
easily
contradicted
by
such
which
have
but
indifferent
judgement
in
the
Nature
of
shadowes
,
and
the
Suns
passages
by
the
Meridians
and
verticall
Circles
of
the
Heavens
,
for
by
how
much
greater
the
propinquitie
of
the
Suns
approchment
is
unto
the
Zenith
,
or
verticall
point
,
by
so
much
the
more
shall
the
houre
or
time
be
various
in
one
and
the
same
Azimuth
.
So
in
the
last
Pro.
the
Azimuth
of
the
Sun
the
tenth
of
December
,
at
nine
of
the
Clocke
in
the
forenoone
,
was
found
to
be
40.
gr.
and
a
halfe
,
Exam
and
the
Suns
distance
from
the
Zenith
,
at
that
time
was
neere
84.
gr.
35.
m
,
Now
admitte
the
Suns
distance
from
the
Zenith
the
tenth
of
Iune
were
but
32.
gr.
35.
m
,
the
Sunne
being
in
the
same
Azimuth
,
the
houre
would
be
halfe
an
houre
past
10.
For
the
Index
being
layed
to
the
houre
of
9.
in
the
Tropicke
of
♑
.
(
which
is
the
Suns
parallel
,
for
the
said
tenth
of
December
,
)
and
it
cutteth
the
Constru
¦
ctio
.
45
parallels
of
the
Suns
Motion
in
the
inequalitie
of
time
,
and
so
the
complement
of
the
former
32.
gr
35.
m
,
in
the
Index
,
meeteth
with
the
Tropicke
of
♋
,
(
which
is
the
Suns
parallel
for
the
tenth
of
Iune
)
in
halfe
an
houre
past
10.
so
that
it
evidently
appeares
,
that
the
shadow
of
a
perpendicular
thing
on
the
tenth
of
December
,
denoting
the
houre
of
the
day
to
be
9.
of
the
Clocke
,
the
same
shadow
the
tenth
of
Iune
,
shall
represent
halfe
an
houre
past
10.
so
the
error
shall
be
an
houre
and
a
halfe
:
but
if
you
move
the
Index
unto
the
houre
of
9.
belonging
to
the
tenth
of
Iune
,
the
Index
shall
point
you
out
in
the
Limbe
neere
68.
gr.
of
Azimuth
for
that
houre
,
which
at
9.
of
the
Clocke
the
tenth
of
December
,
was
but
40.
gr.
&
an
halfe
,
so
the
difference
of
Azimuth
in
one
and
the
same
houre
,
shall
be
27.
gr.
and
a
halfe
,
&
the
time
as
before
,
an
houre
and
a
halfe
:
which
differences
are
sufficient
to
confirme
the
point
.
Tenthly
,
to
finde
the
Quarter
of
Pro.
36
the
yeare
,
and
day
of
the
month
,
if
it
were
forgotten
.
Constru
¦
ctio
.
46
At
any
appearance
of
the
Sun
by
the
27.
Pro.
take
the
Suns
Altitude
,
then
place
the
North
and
South
edge
of
the
Instrument
unto
the
Meridian
line
formerly
,
drawne
(
if
in
the
forenoone
)
otherwise
place
the
East
,
and
West
,
edge
of
Instrument
to
the
Meridian-line
,
and
erect
the
prependicular
at
the
end
of
the
Index
,
then
moove
the
Index
to
and
fro
untill
the
shadow
of
the
prependicular
fall
by
the
side
of
the
Index
,
so
the
parallel
that
meeteth
with
the
degree
of
the
Suns
obserued
Altitude
,
in
the
edge
of
the
Index
,
parallel
in
the
Kalender
that
shall
shew
the
day
of
the
Month
required
.
So
if
,
Exam.
upon
a
certaine
day
in
the
yeare
the
suns
Altitude
were
observed
and
found
to
be
36.
gr.
having
placed
the
edge
of
the
Instrument
to
the
Meridian
line
,
and
rectified
the
Index
,
then
move
the
Index
,
untill
the
shadow
of
the
prependicular
fall
by
the
edge
of
the
Instrument
,
let
the
Instrument
rest
at
this
position
,
and
account
the
former
36.
gr.
upon
the
Index
,
which
degree
meeteth
with
the
houre
in
the
Aequator
,
and
also
that
intersecteth
the
Kalender
,
in
the
tenth
of
March
,
&
the
thirteenth
of
September
,
but
which
of
these
dayes
is
the
day
of
the
Month
,
the
next
dayes
obseruation
of
the
Sun
upon
the
same
houre
will
helpe
you
,
for
if
the
suns
Altitude
besound
to
be
greater
then
the
day
of
the
month
inquired
after
it
was
the
tenth
of
(
March
,
because
the
sun
from
the
tenth
of
December
unto
the
eleventh
of
Iune
,
doth
every
day
at
one
&
the
same
houre
,
ascend
,
)
but
if
the
Suns
Altitude
be
found
to
be
lesse
then
the
former
dayes
observation
specified
was
,
then
the
day
required
,
was
the
thirteenth
of
September
,
because
that
from
the
eleventh
of
Iune
,
unto
the
tenth
of
December
,
the
suns
Altitude
every
day
doth
sensibly
diminish
at
one
and
the
same
houre
.
☞
But
here
is
to
be
noted
that
if
there
be
no
Meridionall
line
,
then
the
prependicular
over
the
Constru
¦
ctio
.
47
Center
and
the
Axis
of
the
Index
being
erected
,
place
downe
the
backe
of
the
Instrument
upon
an
Horizontall
plaine
,
and
move
the
Instrument
to
and
fro
,
untill
the
shadow
of
the
Axis
meete
with
the
same
houre
below
the
Tropicke
,
amongst
the
common
houres
,
that
the
shadow
of
the
prependicular
over
the
Center
of
the
Instrument
meeteth
with
on
the
face
of
the
Instrument
,
for
then
the
parallel
that
crosseth
or
meeteth
with
the
shadow
of
the
prependicular
,
and
the
houre
,
will
in
the
Kalender
shew
the
day
of
the
Month
required
,
and
so
then
the
Meridian
of
the
Instrument
shall
be
in
the
Meridian
of
the
world
,
and
every
point
or
degree
in
the
Horizon
of
the
Instrument
,
it
shall
point
out
his
like
,
or
opposite
degree
in
the
Horizon
of
the
world
.
Constru
¦
ctio
,
48
Or
otherwise
it
may
be
done
thus
,
take
the
Suns
Altitude
,
then
immediatly
by
some
Watch
,
clock
,
or
Sun-dyall
,
learne
the
houre
of
the
day
,
and
move
the
Index
to
and
fro
,
untill
the
Suns
Altitude
in
the
Index
,
meete
with
the
former
houre
,
so
the
parallel
that
meeteth
therewith
,
shall
shew
the
day
of
the
Month
in
the
Kalender
required
,
then
having
the
day
of
the
Month
,
you
have
the
Quarter
of
the
yeare
,
for
from
the
tenth
of
March
unto
the
eleventh
of
Iune
,
is
the
Spring
quarter
,
from
the
eleventh
of
Iune
,
to
the
thirteenth
of
September
,
is
the
Summer
quarter
,
from
the
thirteenth
of
September
,
to
the
tenth
of
December
is
the
Autummuall
quarter
,
and
from
the
tenth
of
December
,
unto
the
tenth
of
March
,
is
the
Winter
Quarter
.
Eleuenthly
,
to
finde
the
houre
of
Pro.
37
the
day
,
the
Azimuth
and
Altitude
of
the
Sun
,
with
the
Meridionall
line
without
obseruation
,
or
sight
of
the
sun
,
by
knowing
the
proportion
betweene
the
length
of
a
shadow
upon
a
Horizontal
Plaine
,
and
that
which
cast
the
shadow
.
First
,
let
the
thing
that
casteth
the
shadow
,
or
Constru
¦
ctio
.
59
something
equall
in
length
unto
it
,
be
divided
into
ten
equall
parts
,
and
each
of
those
parts
subdived
into
ten
other
equall
parts
,
(
which
thing
so
divided
shal
represent
a
common
scale
,
)
then
measure
the
shadow
with
the
scale
,
and
marke
how
often
the
shadow
is
longer
then
the
scale
,
and
the
Decimall
part
if
there
be
any
,
so
have
you
the
proportion
betweene
the
shadow
,
and
that
which
did
cast
the
shadow
,
and
then
is
it
resolved
accor
-
to
the
conuerse
of
the
fifteenth
Pro.
,
mathematical diagram
Exam.
Admit
some
one
:
upon
the
12.
of
February
,
or
on
the
ninth
of
October
,
houlding
a
staffe
prependicular
as
A
B
,
or
supposing
it
to
be
part
of
the
Coyne
of
a
House
,
or
edge
of
a
Window
or
such
like
should
cast
a
shadow
,
as
B
,
C
,
which
being
noted
,
or
drawne
and
having
divided
the
staffe
,
or
thing
as
before
,
and
should
then
measure
the
shadow
,
as
B
,
C
,
by
the
said
staffe
or
scale
,
and
finde
it
to
be
contained
therein
three
times
,
and
6
,
parts
or
6
,
decimals
,
the
porportion
of
the
Gnomon
,
or
scale
,
A
B
,
to
the
shadow
B
C
,
would
be
as
1
to
3.
and
6/10.
Construc
¦
tio
.
50
Move
therefore
the
Index
to
and
fro
,
untill
the
edge
of
it
meere
with
3.
and
6/10
,
in
the
line
of
shadowes
;
so
have
you
the
degree
of
the
Suns
Altitude
at
that
instant
in
the
Index
,
viz.
15.
gr.
and
½
then
seeke
out
the
parallel
for
the
12.
of
February
,
or
the
ninth
of
October
(
the
day
given
)
which
is
neere
the
tenth
degree
from
the
Aequator
South
,
move
the
Index
,
until
the
former
15.
gr.
.
and
½
in
the
Index
,
meeteth
with
the
said
parallel
for
the
day
,
so
have
you
the
houre
belonging
to
that
time
,
which
will
be
neere
42
m
,
past
8.
in
the
Morning
,
or
18.
m
,
past
3
in
the
after
noone
,
and
the
edge
of
the
Index
in
the
Limbe
of
the
Instrument
sheweth
the
suns
Azimuth
also
at
that
instant
,
viz
,
neere
39.
gr.
12.
m
,
from
the
East
toward
the
South
.
Now
for
the
Meridionall
line
,
this
may
be
done
Constru
¦
ctio
.
51
at
any
time
after
,
if
the
Azimuth
be
not
forgotten
:
for
if
the
Center
of
the
Instrument
be
layed
downe
upon
any
part
of
the
shadow
B
C
,
and
so
the
Instrument
to
be
mooved
upon
his
Center
untill
the
said
shadow
B
C
,
formerly
drawne
,
cut
the
edge
of
the
Limbe
,
in
the
aforesaid
Azimuth
of
39.
gr.
30.
m
,
then
the
Meridian
of
the
Instrument
shall
be
in
the
Meridian
of
the
world
,
and
if
that
shadow
were
from
a
Window
,
or
Building
,
the
position
of
the
Instrument
,
shall
denote
the
position
of
the
Window
or
Building
.
Twelfthly
,
to
finde
the
Declination
Pro.
38
of
a
Wall
;
by
seeing
the
sun
beginning
to
shine
thereon
,
or
going
from
it
.
By
the
27.
Pro.
take
the
height
of
the
Sun
,
and
Constru
¦
ctio
.
52
by
the
28.
Pro.
finde
the
Suns
Azimuth
for
the
Altitude
,
so
the
Azimuth
thus
found
shall
be
the
declination
of
the
Plaine
required
:
for
the
declination
of
any
perpendicular
Plaine
,
is
accounted
from
the
points
of
East
,
West
,
North
or
South
,
in
the
Horizon
,
as
the
Suns
Azimuth
is
:
therefore
whatsoever
Plaine
is
in
the
plaine
of
any
virticall
Circle
,
that
Plaine
is
as
far
from
any
of
the
Cardinal
points
of
the
Horizon
,
as
the
sun
is
at
that
time
,
&
so
the
Sun
,
being
in
that
virticall
Circle
,
shall
necessarily
glance
upon
the
Plaine
:
and
therefore
looke
what
the
Suns
Azimuth
is
at
that
instant
,
such
shall
be
the
Declination
of
the
Plaine
required
.
Thirteenthly
,
to
finde
the
Declination
Pro.
39
of
a
Plaine
,
upon
any
appearance
of
the
Sunne
.
mathematical diagram
Thus
for
the
Construction
of
the
aforesaid
13.
uses
which
did
depend
upon
the
suns
observation
,
the
48.
49.
50.
9.
13.
14.
and
15th
.
uses
of
the
Index
or
Table
against
Page
the
first
,
should
have
followed
;
but
before
I
speake
of
them
it
will
not
be
inconvenient
that
I
apply
the
Instrument
unto
the
resolution
of
the
44.
45.
46.
&
47.
uses
of
the
aforesaid
Index
or
Table
,
which
have
reference
to
night
observation
,
upon
such
Starres
which
are
,
or
may
be
placed
on
the
face
of
the
Instrument
,
betweene
the
two
Tropickes
,
or
under
the
Tropicke
of
Cancer
,
according
to
there
Declinations
,
and
right
Ascentions
:
which
are
these
following
.
The
names
of
the
Stars
|
Decli
.
|
Rec
:
|
The
names
of
the
stars
|
Decli
.
|
Rec.
|
G.
M.
|
H.
M.
|
G.M.
|
G.M.
|
H.
M
|
G.
M.
|
Ex.
Alae
Pegasi
|
13.9
.
N.
|
23.54
.
|
1.
30.
|
Co●
Hydrae
.
|
7.5
.
A
|
9.
10.
|
42.45
.
|
pri.
♈
.
|
●1
.
40
.
N.
|
1.46
.
|
26.
30.
|
Cor
Leonis
.
|
13.45
.
B.
|
9.
48.
|
33.00
.
|
Oculus
.
♉
.
|
15.42
.
N.
|
4.15
.
|
63.45
.
|
Cauda
♌
.
|
16.38
.
B
|
11.30
|
7.26
.
|
pri
singuli
.
Ori.
|
0.
17.
S.
|
5.
13.
|
78.15
.
|
Spica
.
♍
.
|
9.
●0
.
M.
|
13.
5.
|
16.15
.
|
Canis
maior
.
|
16
.
1●
S.
|
6.
30.
|
82.15
.
|
Arcturus
.
|
21.10
.
B.
|
14.
0.
|
29.
30.
|
Canis
minor
.
|
6.
9.
N.
|
7.20
.
|
70.00
.
|
Aquila
.
|
8.
00.
S.
|
19.32
|
66.45
.
|
Much
may
be
said
upon
the
uses
of
these
starres
,
but
for
brevitie
I
onely
delivere
these
foure
examples
following
.
1.
First
,
for
any
night
of
the
yeare
,
to
find
at
what
houre
,
and
Altitude
any
of
the
said
starres
will
be
in
the
Meridian
,
(
that
so
they
may
be
known
.
)
2.
To
know
at
any
day
,
at
what
houre
any
of
these
starres
riseth
,
or
setteth
,
with
their
time
of
continuance
above
the
Horizon
,
and
in
what
part
of
the
Hemispheare
,
they
may
be
seene
with
their
Azimuth
,
and
Altitude
at
any
houre
.
3.
Thirdly
,
to
finde
in
any
night
at
what
part
of
the
Horizon
,
any
of
the
aforesaid
starres
riseth
,
or
setteth
,
and
at
what
houre
,
and
Altitude
they
will
be
due
East
,
or
West
.
4.
Fourthly
,
upon
the
sight
or
apparance
of
any
of
the
said
Starres
,
to
finde
the
Azimuth
thereof
:
and
the
houre
of
the
night
.
Pro.
40
First
in
any
night
,
to
finde
at
what
houre
and
Altitude
,
any
of
the
aforesaid
starres
will
be
in
the
Meridian
.
Constru
¦
ctio
.
54
By
the
sixth
Pro:
finde
the
Suns
rigth
Ascention
for
the
day
given
,
which
conuerted
into
time
by
allowing
for
every
15.
degrees
an
houre
,
and
for
every
degree
4.
m
,
then
substract
this
right
Ascention
of
the
Sun
,
from
the
starres
right
Ascention
,
so
the
remainder
or
difference
of
time
,
shall
shew
how
many
houres
the
starres
shall
come
later
to
the
Meridian
then
the
Sun
:
but
if
the
subtraction
cannot
be
made
,
then
adde
24.
houres
to
it
&
you
have
the
Answere
,
Exam.
so
,
if
upon
the
sixth
of
February
,
it
were
required
to
find
at
what
houre
any
of
the
aforesaid
starres
will
be
in
the
Meridian
,
or
due
South
,
first
therefore
by
the
said
sixth
Pro.
I
find
the
suns
right
Ascention
for
the
day
given
viz
,
330.
gr.
which
containes
three
nineties
or
270.
each
90.
gr.
being
six
houres
,
and
so
the
whole
270.
gr.
makes
18.
houres
,
and
the
other
60.
gr.
at
15.
gr.
to
an
houre
makes
4.
houres
more
all
which
put
together
makes
22.
houres
:
so
the
right
Ascention
of
the
Sun
the
sixth
of
February
,
is
neere
330.
gr.
as
before
,
or
22.
houres
|
|
H.
M.
|
|
H.
M.
|
|
Which
22.
houres
taken
from
the
right
ascention
of
the
aforesaid
Stars
,
viz.
from
.
|
Ex.
Ala
Pegasi
.
|
23.54
.
|
there
remaines
.
|
1.
54.
P.
|
the
time
of
the
starres
being
in
the
Meridian
.
|
Pri.
♈
.
|
1.
46.
|
3.
46.
P.
|
Oculus
.
♉
.
|
4.
15.
|
6.
15.
P.
|
Orion
singu.
1.
|
5.
13.
|
7.
13.
P.
|
Canis
Maior
|
6.
30.
|
8.
30.
P.
|
Canis
Minor
.
|
7.
20.
|
9.
20.
P.
|
Cor
Hidra
.
|
9.
10.
|
11.
10.
P.
|
Cor
Leonis
.
|
9.
48.
|
11.
48.
P.
|
Cauda
.
♌
.
|
11.40
.
|
1.
40.
A.
|
Spica
verginis
.
|
13.05
.
|
2.
05.
A.
|
Arcturus
|
14.00
.
|
4.
00.
A.
|
Aquila
.
|
19.32
.
|
9.
32.
A.
|
For
seeing
that
22.
houres
the
Sunnes
right
Ascention
,
is
greater
then
the
right
Ascention
of
any
of
the
starres
afore
specified
,
substract
this
22
,
houres
from
24.
houres
,
rest
2.
houres
,
which
added
to
the
right
Ascention
of
each
Starre
before
delivered
,
you
have
the
houre
of
the
Stars
coming
to
the
Meridian
:
hence
you
may
gather
which
of
those
starres
,
are
out
of
observation
for
that
time
,
viz.
Alae
Pegasi
,
Pri.
♈
,
and
Aquila
,
which
come
to
the
Meridian
in
the
day
time
:
but
if
the
day
given
had
been
the
26th
of
Iuly
,
the
right
Ascention
of
the
Sunne
,
that
day
is
neere
135.
gr.
or
9.
houres
.
|
|
H.M.
|
|
H.M.
|
|
which
9.
houres
taken
from
the
right
Ascention
of
the
aforesaid
starrs
viz
,
from
.
|
Ex.
Alae
Pegasi
.
|
23.
54.
|
leaves
.
|
2.
54.
A.
|
the
time
of
the
stars
comming
to
the
Meridian
.
|
Pri.
♈
.
|
1.
46.
|
04.46
.
A.
|
Oculus
♉
.
|
4.
15.
|
07.
15.
A.
|
Orion
Singu
.
|
1.
5.
31.
|
08.
13.
A.
|
Caenis
Maior
.
|
6.
30.
|
09.30
.
A.
|
Canis
Minor
.
|
7.
20.
|
10.
20.
A.
|
Cor
hidra
.
|
9.
10.
|
00.10
.
P.
|
Cor
Leonis
.
|
9.
48.
|
00.48
.
P.
|
Cauda
.
♌
.
|
11.
40.
|
02.40
.
P.
|
Spica
vergenis
.
|
13.5
.
|
04.
05.
P.
|
Acturus
.
|
14.
00.
|
05.
●0
P.
|
Aquila
.
|
19.32
.
|
10.32
.
P
|
For
the
right
Ascention
of
the
Sun
being
but
9.
houres
take
it
from
the
right
ascention
of
Cor.
hidra
which
is
9.
houres
10.
m
,
rest
10.
m
,
which
sheweth
that
Cor.
Hydra
comes
to
the
Meridian
10.
m
,
later
then
the
Sun
that
day
,
that
is
,
10.
m
,
after
12
and
so
the
rest
,
whose
rightascention
is
greater
then
the
Suns
.
But
for
these
starres
,
whose
right
Ascention
is
lesse
then
the
said
9.
houres
,
subtract
this
9
houre
from
24.
houres
,
rest
15.
houre
(
or
rather
subtract
it
from
12.
rest
3.
houres
)
this
adde
unto
the
right
ascention
of
any
of
the
aforesaid
starres
,
as
suppose
Canis
Minor
makes
22.
houres
20.
m
,
which
sheweth
that
Canis
minor
,
wil
come
to
the
Meridian
.
22.
houres
20
,
m
,
later
that
day
then
the
sun
:
therefore
this
,
22.
houres
and
20.
m
,
being
considered
according
to
an
hourly
account
sheweth
,
that
Canis
Minor
will
come
to
the
Meridian
at
10.
of
the
clocke
and
20.
m
:
of
the
next
day
(
the
right
ascention
of
the
Internall
of
time
being
neglected
)
or
for
brevitie
adde
the
aforesaid
3.
houres
unto
the
right
ascention
of
these
Starres
,
whose
right
ascentions
are
lesser
then
the
Suns
,
so
have
you
the
Meridionall
houre
required
.
Hence
may
be
gathered
that
Alae
Pegasi
,
Pri.
♈
and
Aquila
,
are
onely
for
observation
that
night
,
the
other
starres
are
out
of
observation
,
and
will
come
to
the
Meridian
,
in
the
day
time
.
Lastly
,
to
finde
the
Meridionall
Altitude
of
any
of
these
starres
,
lay
the
edge
of
the
Index
unto
the
houre
line
,
of
12
,
so
the
parallel
of
the
starres
declination
that
crosseth
the
edge
of
the
Index
,
shall
there
shew
you
in
the
Index
,
the
Meridionall
Altitude
of
the
starre
required
.
Pro.
41
Secondly
,
to
know
at
any
day
,
at
what
houre
any
of
the
starres
(
inscribed
on
the
Instrument
)
riseth
or
setteth
,
with
their
time
of
continuance
above
the
Horizon
,
&
in
what
part
of
the
hemispheare
,
they
may
be
seene
,
with
their
Azimuth
,
and
Altitude
at
any
houre
.
Constru
¦
ctio
.
55
By
the
last
direction
finde
the
houre
of
the
stars
being
in
the
Meridian
,
then
marke
what
houre
the
parallel
of
the
declination
of
any
starre
intersecteth
the
Horizon
or
Kalender
,
so
have
you
the
houre
or
time
of
the
starres
rising
or
setting
,
and
the
number
of
houres
,
from
that
point
of
the
stars
rising
in
the
Horizon
,
unto
the
Meridian
being
doubled
,
gives
the
countinuance
of
the
starres
above
the
Horizon
,
required
.
So
if
upon
the
6th
.
of
February
,
it
were
demanded
at
what
houre
Oculus
♉
.
Exam.
would
ascend
,
&
how
long
it
would
continue
above
the
Horizon
.
By
the
last
proposition
,
get
the
houre
of
the
starres
being
in
the
Meridian
,
which
is
at
6.
of
the
Clocke
and
15.
minuts
at
night
,
and
marke
the
Number
of
houres
betweene
the
Meridian
,
and
that
point
where
the
parallel
of
Oculus
♉
,
meeteth
with
the
Kalender
,
which
is
7.
houres
24
,
minuts
,
this
doubled
makes
14.
houres
48.
m
,
and
so
long
will
Oculus
♉
,
be
above
the
Horizon
.
But
if
from
the
said
7
,
houres
and
24.
m
,
the
said
6
,
houres
15.
m
,
be
taken
,
there
will
rest
1.
houre
9.
m
,
and
so
much
before
12.
of
the
clocke
at
noone
,
doth
Oculus
♉
rise
,
that
is
51.
m
,
after
10
,
of
the
Clocke
,
and
so
consequently
if
the
said
7.
houres
and
24.
m
,
be
added
unto
the
houre
of
the
starres
being
in
the
Meridian
,
viz.
6.
of
the
Clocke
and
15.
m
,
as
before
,
the
said
starre
will
set
at
39.
m
,
past
1
,
in
the
Morning
.
Lastly
,
if
at
any
houre
betweene
the
rising
of
the
starre
,
and
the
setting
thereof
,
it
be
required
at
what
Position
and
Altitude
the
starre
is
in
.
It
is
thus
done
.
Account
to
the
given
houre
,
from
the
houre
of
the
starre
rising
,
setting
,
or
being
in
the
Meridian
,
Constru
¦
ctio
.
56
(
in
the
parallel
of
the
starres
declination
)
and
lay
the
Index
thereto
,
so
the
edge
of
it
in
the
Limbe
of
the
Instrument
,
shall
shew
the
starres
Azimuth
or
Position
,
and
where
the
parallel
of
the
starres
Declination
crosseth
the
edge
of
the
Index
,
that
shall
be
the
starres
Altitude
,
at
that
houre
.
So
if
on
the
said
6th
.
of
February
,
at
11.
Exam.
of
the
Clocke
at
night
,
it
were
required
in
what
Position
,
or
Azimuth
Oculus
♉
,
was
in
,
and
also
how
high
above
the
Horizon
:
I
make
,
or
suppose
the
houre
of
12.
to
be
the
aforesaid
6.
of
the
Clocke
and
15.
m
,
(
for
at
that
houre
as
before
Oculus
♉
was
in
the
Mridian
)
and
from
thence
in
the
stars
parallel
of
Declination
,
I
account
untill
I
come
unto
11.
of
the
Clocke
,
viz.
that
is
4.
houres
,
and
45.
m
,
from
12.
and
lay
the
Index
thereto
,
so
the
edge
of
the
Index
in
the
Limbe
,
pointeth
out
4.
gr:
24.
m
,
and
so
farre
Oculus
♉
,
is
distant
from
the
West
at
11.
of
the
Clocke
at
night
,
and
the
parallel
of
the
starres
Declination
meeteth
with
the
Index
in
24.
gr
,
neere
,
which
is
the
starres
Altitude
,
at
that
houre
required
.
Pro.
42
Thirdly
,
to
find
in
any
night
of
the
yeare
,
in
what
part
of
the
Horizon
any
of
the
starres
on
the
instrument
riseth
or
setteth
,
and
at
what
houre
,
and
Altitude
a
starre
will
be
due
East
,
or
West
.
Constru
¦
ctio
.
57
For
the
first
,
Marke
where
the
parallel
of
the
starres
declination
crosseth
the
Horizon
,
or
Kalender
,
Lay
the
edge
of
the
Index
hereto
,
so
the
number
of
degrees
betweene
the
edge
of
the
Index
,
and
the
point
of
East
or
West
,
upon
the
limbe
of
the
Instrument
,
sheweth
the
distance
of
the
starres
rising
from
the
East
or
West
.
So
if
it
were
required
in
what
part
of
the
Horizon
Oculus
♉
riseth
,
Exam.
marke
where
the
parallel
of
the
stars
Declination
crosseth
the
Horizon
,
and
lay
the
edge
of
the
Index
thereto
,
so
it
cutteth
the
Limbe
of
the
Instrument
from
the
East
neere
26.
gr.
and
so
farre
Oculus
♉
,
riseth
from
the
East
towards
the
North.
For
the
second
to
finde
the
time
of
a
starres
coming
East
,
or
west
.
By
the
40th
.
Pro.
consider
at
what
houre
the
star
Constru
¦
ctio
.
58
is
in
the
Meridian
,
then
lay
the
edge
of
the
Index
to
the
point
of
East
and
West
,
and
account
in
the
parallel
of
the
stars
Declination
the
number
of
houres
betweene
the
edge
of
the
Index
,
and
the
houre
of
12.
which
being
taken
from
the
houre
of
the
stars
being
in
the
Meridian
,
gives
the
houre
of
the
stars
coming
East
,
but
added
unto
the
houre
of
the
stars
being
in
the
Meridian
,
shewes
the
houre
of
the
stars
being
West
.
So
if
it
were
demaunded
at
what
houre
,
Exam.
upon
the
6th
.
of
February
,
Cor
♌
,
would
be
due
East
or
West
,
and
what
Altitude
the
starre
should
then
have
.
First
,
lay
the
edge
of
the
Index
,
to
the
point
of
East
and
West
,
&
wheresoever
the
parallel
of
the
starres
declination
crosseth
the
edge
of
the
Index
that
shall
be
the
starres
Altitude
,
viz.
neere
17.
gr
45.
m
,
then
account
the
number
of
houres
in
the
parallel
of
the
starres
Declination
betweene
the
edge
of
the
Index
,
and
the
houre
of
12.
which
is
neere
5.
houres
and
12.
m
,
which
taken
from
the
houre
of
the
starres
being
in
the
Meridian
,
)
which
by
the
40th
.
Pro.
was
at
11.
of
the
clocke
&
48.
m
,
at
night
)
rests
6
houres
,
and
36.
m
:
but
if
the
said
5.
houres
and
12.
m
,
be
added
unto
the
said
11.
houres
and
48.
m
,
it
makes
17.
houres
,
from
which
12.
being
taken
leaves
5
,
houres
.
So
upon
the
6th
.
of
February
,
Cor
♌
shall
be
due
East
,
at
36.
m
,
past
6
,
at
night
,
and
due
West
,
at
5
,
of
the
Clocke
in
the
Morning
,
and
the
Stars
Altitude
,
being
either
East
or
West
,
is
neere
17.
gr.
45.
m
,
as
was
required
.
Pro.
43
Fourthly
,
upon
the
sight
or
appearance
of
any
of
the
aforesaid
stars
,
to
finde
the
Azimuth
thereof
,
and
the
houre
of
the
night
.
By
the
40th
.
Pro.
for
the
day
given
finde
the
Constru
¦
ctio
.
59
houre
of
the
starres
coming
to
the
Merid●●
then
by
the
27.
Pro.
take
the
starres
heigh●
〈◊〉
account
that
height
in
the
Index
,
the●
〈…〉
Index
untill
the
degree
of
the
starre●
〈…〉
the
Index
,
meete
with
the
parall●
〈…〉
Declination
,
so
the
edge
of
the
〈…〉
sheweth
the
starres
Azimuth
,
and
the
Meridian
that
meeteth
with
the
degree
of
the
Altitude
,
in
the
Index
shall
shew
you
the
houre
that
the
starre
wants
to
be
in
the
Meridian
,
or
is
past
the
Meridian
,
which
added
,
or
subtracted
from
the
houre
of
the
starres
being
in
the
Meridian
,
gives
the
houre
of
the
night
required
.
So
if
the
day
were
the
26th
.
of
Iuly
,
Exam.
and
if
Aquila
,
should
be
observed
to
be
on
the
West
of
the
Meridian
,
29.
gr.
20.
m
,
high
above
the
Horizon
,
this
I
seeke
out
upon
the
Index
,
and
move
the
Index
to
and
fro
untill
the
said
,
29.
gr.
20.
m
,
meete
with
the
parallel
of
Declination
,
of
Aquila
,
so
the
edge
of
the
Index
,
in
the
Limbe
doth
point
out
the
starres
Azimuth
from
the
South
,
viz.
63.
gr.
12.
m
,
and
the
Meridian
that
meeteth
with
the
aforesaid
degree
of
Altitude
,
is
the
time
of
the
starres
distance
from
the
Meridian
,
viz.
neere
3.
houres
and
28.
m
,
this
added
unto
the
houre
of
Aquilas
being
in
the
Meridian
,
which
by
the
40th
.
Pro.
was
at
10.
of
the
Clocke
&
32.
m
,
at
night
,
makes
14.
houres
,
or
2
of
the
Clocke
,
in
the
Morning
,
so
if
Aquila
were
observed
the
26th
.
of
Iuly
,
to
be
29.
gr.
20.
m
,
high
to
the
West
of
the
Meridian
,
then
the
Position
or
Azimuth
of
that
starre
from
the
Meridian
,
was
63.
gr.
12.
m
,
and
the
houre
at
that
instant
,
was
at
2.
of
the
Clocke
in
the
Morning
.
Thus
touching
the
resolution
of
the
aforesaid
44.
45.
46.
and
47th
.
Pro.
of
the
aforesaid
Index
or
Table
,
which
did
belong
to
Astronomicall
obseruations
,
the
last
uses
now
follow
,
viz.
48.
49.
50.
9.
13.
14.
and
15th
.
uses
of
the
Index
or
Table
,
which
are
onely
proper
to
Geometricall
Practices
,
viz.
to
shew
-
1.
How
to
measure
the
Quantitie
of
an
Angle
,
or
to
take
the
distance
of
two
Starres
.
-
2.
How
to
measure
distances
and
bredthes
.
-
3.
How
to
take
the
Circuit
of
a
figure
,
or
the
surueigh
of
a
Place
.
-
4.
The
inclination
of
a
Plaine
,
or
to
Place
a
Plaine
Horizontall
.
-
5.
Whether
an
Altitude
be
in
the
Point
of
libration
,
or
above
,
or
below
the
levell
of
the
eye
,
and
how
much
.
-
6.
How
much
the
hight
of
an
Altitude
is
above
the
eye
,
which
is
accessable
,
or
in
accessable
.
-
7.
How
to
measure
any
Part
of
an
Altitude
,
which
is
not
approachable
.
First
,
how
to
obserue
or
finde
the
Pro.
44
measure
of
an
Angle
,
or
take
the
distance
of
two
starres
by
the
Instrument
.
Let
the
Istrument
be
placed
upon
some
Rest
,
Constru
¦
ctio
.
60
which
may
be
so
accommodated
that
the
Instrument
,
may
be
elevated
,
depressed
,
or
be
placed
Horizontall
,
as
occasion
requires
,
then
erect
the
sights
of
the
Index
,
&
place
the
edge
of
the
Index
upon
the
houre
line
of
12.
the
Index
so
placed
looke
through
the
sights
thereof
and
moving
the
Instrument
upon
his
Rest
to
and
fro
,
untill
you
see
the
marke
or
Starre
,
that
makes
the
Angle
or
distance
required
.
Then
screw
fast
the
Instrument
to
the
socket
,
and
move
about
the
Index
,
untill
through
the
sights
thereof
you
see
the
other
marke
or
star
,
so
the
number
of
degrees
betweene
the
edge
of
the
Index
and
the
houre
of
12.
in
the
Limbe
of
the
Instrument
shall
be
the
measure
of
the
Angle
,
or
distance
of
the
two
Stars
sought
for
.
Let
E
and
D
be
two
markes
or
Starres
,
Exam.
and
let
the
Angle
E
A
D
,
or
distance
E
D
,
be
required
.
The
Instrument
,
A
B
M
,
being
placed
upon
his
Rest
G
H
I
K
,
obserue
one
of
the
markes
or
starres
as
D
,
through
the
sights
(
admit
A
B
,
)
so
the
visuall
line
shall
be
A
B
D
,
then
having
made
fast
the
Instrument
,
move
the
Index
A
B
,
untill
through
the
sights
of
it
you
see
the
other
marke
or
starre
,
E
,
which
suppose
to
be
in
the
visuall
line
,
A
C
E
,
so
the
Arke
of
the
Limbe
of
the
Instrument
B
C
,
shall
be
the
distance
betweene
the
two
Stars
,
ED
,
or
the
measure
of
the
Angle
E
A
D
,
Corollarie
.
required
.
Now
Infinit
are
the
uses
of
knowing
the
Quantitie
of
Angles
,
in
the
Copious
and
vast
Body
of
Mathematicall
Practices
,
therefore
from
the
multitude
of
Examples
that
might
be
raised
upon
them
,
or
extracted
from
them
,
I
will
onely
instance
for
brevitie
,
upon
these
two
plaine
,
and
ordinary
ones
following
.
mathematical diagram
Secondly
,
how
to
measure
distances
,
Pro.
45
and
Breadths
.
Let
G
F
L
H
,
Exam.
represent
part
of
the
Perimeter
of
a
Fort
,
and
let
it
be
required
,
that
standing
at
some
convenient
place
without
Musket
shot
,
as
admit
at
Y
,
the
distance
betweene
the
points
of
the
Bulwarke
viz.
F
&
L
,
as
also
the
measure
of
the
face
of
either
of
the
Bulwarks
viz.
F
E
,
or
M
L
,
with
the
length
of
the
Cortaine
D
N
,
and
all
the
distances
from
Y
,
viz.
Y
F
,
Y
E
,
Y
M
,
and
Y
L
,
were
required
.
Or
suppose
O
P
Q
R
,
were
4
places
,
whose
severall
●istances
the
one
from
the
other
as
from
O
to
P
,
then
from
P
to
Q
,
and
from
Q
to
R
,
&
also
the
several
distances
from
Y
viz.
Y
O
,
Y
P
,
Y
Q
and
Y
R
,
were
demanded
.
The
Construction
and
resolution
upon
either
of
these
is
alike
,
therefore
Constru
¦
ctio
.
61
we
will
instance
upon
the
latter
.
Place
the
Instrument
upon
his
Rest
,
at
Y
,
and
the
edge
of
the
Index
,
upon
the
houre
of
12.
then
looking
through
the
sights
of
the
Index
,
upon
some
marke
taken
at
pleasure
in
the
field
,
which
,
admit
to
be
S
,
then
observe
the
first
marke
R
,
so
have
you
the
Angle
S
Y
R
,
which
suppose
52.
gr.
30.
m
,
then
looke
to
Q
,
so
have
you
the
Angle
SYQ
,
which
let
be
63.
gr.
15.
m.
then
looke
to
P
,
so
ha●e
you
the
Angle
SYP
,
admit
to
be
74.
gr.
15.
m
,
and
lastly
looke
to
O
,
so
have
you
the
Angle
S
Y
O
,
123.
gr.
15.
m
:
for
these
Angles
are
taken
with
great
facillitie
,
when
once
the
Instrument
is
rectified
as
in
the
first
direction
is
specified
,
for
you
neede
not
but
move
the
Index
,
Circular
from
obiect
to
obiect
,
so
the
Arkes
of
the
Limbe
of
the
Instrument
as
before
,
from
the
houre
of
12
,
unto
the
edge
of
the
Index
,
shall
shew
the
measure
of
the
seuerall
Angles
observed
.
Thus
at
Y
,
place
up
a
Marke
,
and
in
the
visuall
line
,
Y
S
,
and
measure
a
certaine
distance
at
pleasure
,
as
admit
to
S
,
and
suppose
it
were
found
to
be
900.
foote
(
or
300.
yardes
)
then
placing
the
Instrument
at
S
,
upon
his
Rest
,
and
laying
the
edge
of
the
Index
to
the
houre
of
12.
I
move
the
Instrument
about
,
untill
through
the
sights
of
the
Index
I
may
see
the
marke
which
was
set
up
at
my
,
last
station
,
then
make
fast
the
Instrument
,
and
observe
O
,
so
have
you
the
Angle
Y
S
O
,
which
suppose
to
be
26.
gr.
50.
m
,
then
looke
to
P
,
so
have
you
the
Angle
Y
S
P
,
which
let
be
55.
gr.
50.
m
,
then
looke
to
Q
,
so
have
you
the
Angle
Y
S
Q
,
which
admit
to
be
60.
gr.
15.
m
,
lastly
observe
R
,
so
have
you
the
Angle
Y
S
R
,
87.
gr.
In
like
maner
may
you
observe
the
Angles
at
the
Fort
from
the
stations
Y
,
and
S
,
formerly
specified
all
which
observations
may
be
placed
downe
in
Tables
,
as
here
under
appeares
,
which
may
be
called
the
Tables
of
observed
Angles
.
mathematical diagrams
|
Ang:
G.
M.
|
Distances
|
Ang:
G.M.
|
Distances
.
|
Y.
S.
900.
|
R
Y
S.
52.
30
|
S
R.
1099.
5
|
S
Y
L.
55.
45.
|
S
L.
1071.
0
|
Q
Y
S.
63.
15
|
S
Q.
963.
6
|
S
Y
M.
68.
15
|
S
M.
1182.
2
|
P
Y
S.
74.
15
|
S
P.
1132.
2
|
S
Y
E.
89.
10.
|
S
E.
1364.
4
|
O
Y
S.
123.
50
|
S
O.
1526.
1
|
S
Y
F.
104.00
|
S
F.
1459.
5
|
Y
S
O.
26.
50.
|
Y
O.
829.
2
|
Y
S
F.
39.
15.
|
Y
F.
971.
6
|
Y
S
P.
55.
50.
|
Y
P.
973.
2
|
Y
S
E.
49.
35.
|
Y
E.
1039.
2
|
Y
S
Q.
60.
15.
|
Y
Q.
937.
0
|
Y
S
M.
66.
45.
|
Y
M.
1169.
4
|
Y
S
R.
87.
00.
|
Y
R.
1384.
|
Y
S
L.
79.
30.
|
Y
L.
1268.
2
|
Now
touching
the
resolution
of
the
point
,
there
is
a
triple
way
of
operation
,
viz.
either
Arithmeticall
,
Instrumentall
,
or
Geometricall
,
each
of
which
being
sufficiently
facill
,
to
such
which
are
versed
in
the
documents
of
Mathematicall
Practices
,
but
the
later
because
it
is
more
vulgar
,
and
easiest
to
be
apprehended
,
I
will
instance
here
upon
:
which
is
that
part
of
Geometrie
,
commonly
called
Pretraction
,
a
thing
so
common
that
almost
every
one
that
hath
any
entrance
in
Geometrie
,
can
performe
it
according
to
the
ordinary
way
they
are
instructed
in
.
But
to
facilitate
that
kind
of
practice
,
I
aduise
such
as
affect
this
kinde
of
Practice
to
use
the
Protracter
,
which
I
use
,
which
is
a
plaine
then
sector
,
having
a
smal
hole
at
the
Center
,
whose
two
legges
from
the
Center
are
made
with
a
sharpe
edge
,
but
so
that
they
lie
flat
upon
the
Paper
,
&
each
of
them
to
be
divided
into
100
or
1000
diuisions
with
a
Quadrantall
Arke
or
more
divided
and
fastned
also
at
the
end
of
one
of
the
leggs
,
but
so
that
the
Quadrantall
,
Arke
have
also
an
edge
to
lie
flat
upon
the
Paper
,
and
to
slide
in
at
the
other
leg
,
so
shall
it
be
accommodated
and
made
a
fit
,
&
apt
Instrument
to
finde
the
Quantitie
of
Angles
,
in
a
Plot
,
or
to
protract
Angles
,
for
service
,
as
followeth
.
So
to
search
out
the
distance
of
O
P
Q
R
,
Exam.
the
one
from
the
other
,
or
all
the
distances
from
Y
as
was
required
:
by
the
helpe
of
the
former
Angles
of
observations
and
Protracter
,
it
may
be
done
thus
.
mathematical diagram
Thirdly
,
how
to
take
the
Circuite
Pro.
46
of
a
figure
,
or
the
surueigh
of
a
Place
.
Let
ABCD
,
Exam.
be
a
plaine
to
be
raised
as
Fortifiers
have
it
,
or
a
field
to
be
ploted
as
surveyers
account
it
,
or
a
Figure
whose
Perimeter
is
required
,
as
Geometritians
treate
of
it
.
The
Plaine
Table
,
Notatio
.
may
be
held
best
for
this
service
,
as
such
would
have
it
,
whose
learning
is
altogether
versed
therein
.
But
any
Instrument
shall
be
able
to
doe
this
Service
,
that
can
but
accuratly
take
or
measure
any
Angle
,
(
not
that
we
reject
that
,
but
make
use
of
this
for
the
present
)
and
therefore
in
this
action
,
it
were
no
losse
of
time
to
make
a
preambulation
about
the
field
,
to
view
the
severall
windings
and
turnings
thereof
,
and
what
Angles
with
greatest
Conveniency
,
and
expedition
are
to
be
observed
,
and
what
might
be
omitted
,
and
at
the
Angles
of
consequence
there
to
set
up
some
marke
,
and
upon
those
Angles
to
fabricate
the
whole
worke
:
for
here
especially
is
to
be
noted
,
that
the
more
Angles
that
are
obserued
in
any
practise
,
by
way
of
Circumscribing
a
Field
,
or
Campaigne
,
the
greater
,
and
more
evident
shall
the
error
be
in
the
Conclusion
.
mathematical diagram
So
in
the
Figure
A
B
C
D
,
Exam.
there
is
eleven
Angles
and
as
many
sides
,
now
if
at
every
Angle
,
an
observation
should
be
made
,
it
would
be
more
.
subiect
to
error
(
as
before
)
then
if
lesse
Angles
were
observed
,
therfore
in
this
Diagramme
fewer
Angles
of
observation
may
be
fully
sufficient
to
raise
that
Plaine
,
Take
the
Plot
of
the
Field
,
or
give
the
Perimeter
of
that
Figure
,
Therefore
suppose
the
noted
Angles
of
Consequence
to
be
,
A
,
B
,
C
,
D
,
Q
,
the
worke
may
be
then
thus
.
Place
the
Instrument
,
upon
his
rest
at
A
,
and
obserue
the
Angle
Q
AB
,
which
suppose
32.
gr.
10
m
,
then
measure
Q
A
,
with
a
Decimall
Chaine
(
or
such
like
,
)
which
suppose
to
be
5.
Chaines
,
note
this
in
a
peece
of
paper
,
then
take
the
Instrument
up
,
and
measure
the
line
,
A
B
,
but
first
onely
A
E
,
which
suppose
to
be
11.
Chaines
and
60
Linkes
,
which
is
written
down
thus
.
11.
60.
Then
measure
the
distance
from
E
to
the
Angle
F
,
which
admit
to
be
2.
20
,
Lastly
,
go
one
with
the
measure
A
B
,
which
suppose
to
be
15.
00
,
the
Angle
of
obseruation
,
and
measures
thus
taken
may
be
noted
downe
one
against
another
,
as
in
the
Table
following
,
then
place
the
Instrument
Constru
¦
ctio
.
63
upon
his
rest
at
B
,
and
obserue
the
Angle
:
ABC
,
which
note
downe
also
and
measure
the
distance
,
B
G
,
and
G
H
,
and
then
going
on
with
G
B
,
to
G
I
,
and
marke
and
measure
B
I
,
and
then
measure
also
I
K
,
and
so
goe
on
with
B
C
,
which
measures
are
all
placed
down
as
appeares
in
the
Table
of
Angles
and
measures
following
:
In
like
matter
performe
the
rest
of
the
worke
untill
you
come
to
Q
,
and
so
all
the
Angles
and
measures
will
be
according
to
the
Table
here
under
specified
.
The
Table
of
Angles
.
|
The
Table
of
measures
.
|
G.M.
|
5.
00.
|
32.10
.
|
11.
60.
|
|
2.20
.
|
|
15.
00.
|
80.10
.
|
6.
00.
|
1.00
.
|
9.
20.
|
2.00
.
|
16.
40.
|
79.30
.
|
6.
90.
|
1.
29.
|
8.
00.
|
74.
45.
|
3.
70.
|
1.
15.
|
5.
40.
|
mathematical diagram
But
it
had
beene
fully
sufficient
(
by
helpe
of
this
Protractor
)
to
have
plotted
the
aforesaid
Plaine
,
by
knowing
the
former
Measures
,
and
two
Angles
of
obseruation
only
.
Pro.
47
Fourthly
,
how
to
finde
the
Inclination
of
a
Plaine
,
or
to
Elevate
a
Plaine
unto
an
Angle
assigned
,
and
to
Place
a
Plaine
Horizontall
.
Constru
¦
ctio
.
65
For
the
first
,
Set
the
East
and
West
,
edge
of
the
Instrument
unto
the
Plaine
,
then
if
the
edge
of
the
Index
in
the
Limbe
of
the
Instrument
,
cut
the
point
of
East
or
West
,
the
Plaine
is
verticall
,
and
doth
not
Incline
,
but
if
the
Index
fall
from
the
points
,
looke
how
many
degrees
it
is
from
the
points
of
East
or
West
in
the
Limbe
of
the
Instrument
so
much
is
that
Inclination
of
the
Plaine
.
For
the
Second
,
to
Elevate
a
Plaine
,
to
an
Angle
assigned
.
This
is
onely
the
same
with
the
former
,
but
may
be
applyed
to
severall
uses
,
as
to
trie
the
mount
,
or
to
mount
a
Peece
of
Ordinance
at
any
Randon
:
or
to
place
Burning
glasses
(
or
others
)
at
severall
Angles
,
to
receive
each
others
Reflexon
,
and
that
the
point
of
concurse
,
or
inflammation
in
such
Glasses
may
be
in
the
Radius
or
beame
of
the
Sunne
,
or
that
the
point
of
inflamation
,
the
representative
Image
,
or
the
extensive
Elumination
may
be
proiected
to
a
point
assigned
.
For
the
Third
,
to
rectifie
a
Plaine
Horizontall
.
Constru
¦
ctio
.
66
Place
the
North
and
South
edge
of
the
Instrument
,
unto
the
under
face
of
the
Plaine
,
and
then
marke
if
the
edge
of
the
Index
,
cut
the
points
of
East
or
West
in
the
Limbe
of
the
Instrument
,
for
then
the
Plaine
is
Horizontall
,
but
if
it
swarne
from
that
point
,
then
it
is
not
Horizontal
,
but
the
Plaine
is
to
be
raised
,
or
depressed
,
untill
by
severall
tryalls
in
sundry
parts
of
the
Plaine
,
you
see
the
edge
of
the
Index
fall
upon
the
points
of
East
or
West
,
for
then
shall
it
be
truly
Horizontall
:
Otherwise
you
may
rectifie
the
Plaine
Horizontall
,
by
operating
upon
the
upper
face
of
it
,
if
you
set
a
Cube
upon
the
plaine
,
and
then
placing
the
East
and
West
edge
of
the
Instrument
unto
the
side
of
the
Cube
,
for
then
the
obseruation
will
be
as
the
former
,
and
therefore
,
accommodated
&
concluded
accordingly
.
Pro.
48
Fiftly
,
to
finde
whether
an
Altitude
be
in
the
Point
of
libration
,
or
above
,
or
below
the
levell
of
the
eye
,
and
how
much
.
Declaration
.
Let
C
B
and
X
,
be
three
severall
obiects
,
and
let
their
severall
situations
be
required
.
Constru
¦
ctio
.
67
First
,
let
the
Instrument
hang
upon
a
rest
perpendicular
,
and
let
it
be
held
stedfast
that
the
Index
may
be
verticall
,
and
play
easily
by
the
side
of
the
Instrument
,
then
looking
through
the
sights
of
it
,
lift
the
Instrument
up
and
downe
,
untill
you
see
your
marke
,
which
suppose
first
C
,
and
admit
the
Index
should
cut
5.
in
the
line
of
shadowes
,
which
sheweth
that
C
,
is
higher
then
the
eye
by
the
5th
.
part
of
the
distance
of
the
bassis
of
the
obiect
,
from
the
eye
,
supposed
at
A.
Secondly
,
if
through
the
sights
of
the
Instrument
you
see
the
second
obiect
,
B
and
the
Index
falling
upon
no
part
in
the
line
of
shadowes
,
then
it
sheweth
that
the
point
B
,
is
levell
with
the
eye
,
for
if
in
any
observation
the
Index
fall
betweene
the
beginning
of
the
line
of
shadowes
,
(
which
is
neere
the
begining
of
December
)
and
the
sight
next
the
eye
,
it
argueth
that
the
obiect
is
higher
then
the
eye
,
but
if
the
Index
fall
beyond
the
beginning
of
the
line
of
shadowes
,
then
the
obiect
is
lower
then
the
eye
.
Thirdly
,
if
you
observe
the
obiect
X
,
(
the
Constru
¦
ctio
.
68
eye
being
at
A
,
)
then
if
in
observing
the
Marke
X
,
through
the
sights
of
the
Instrument
,
the
Index
shall
fall
beyond
the
beginning
of
the
line
of
shadowes
,
that
is
from
the
Kalender
number
the
degrees
,
in
the
Limbe
from
the
edge
of
the
Index
unto
that
point
,
and
account
the
same
backward
from
the
point
in
the
Limbe
that
is
opposit
to
the
beginning
of
the
line
of
shadowes
,
and
lay
the
edge
of
the
Index
unto
it
,
then
suppose
the
Index
,
in
the
line
of
shadowes
intersect
8.
which
sheweth
that
the
point
X
is
lower
then
the
levell
of
the
eye
,
by
the
eight
part
of
the
distance
from
you
to
the
marke
.
Now
if
the
distance
should
be
100.
foote
,
then
the
point
X
,
shall
be
below
the
Horizontall
line
,
or
line
of
levell
A
B
,
12.
foote
and
½
which
is
the
⅛
part
of
100.
the
distance
before
specified
.
Sixtly
,
how
to
finde
the
height
of
Pro.
49
an
Altitude
above
the
levell
of
of
the
eye
,
either
Accessible
,
or
inaccessible
.
Let
,
B
C
be
an
Altitude
and
the
eye
at
,
Declaratio
.
A
distant
from
the
Basis
of
B
,
100.
foote
.
If
through
the
sights
of
the
Instrument
the
summet
of
the
Altitude
B
C
,
viz.
C
,
be
seene
,
and
the
Index
falling
upon
5
,
in
the
line
of
shadowes
,
Constru
¦
ctio
.
69
it
argueth
the
Altitude
B
C
,
to
be
the
5th
.
part
of
the
distance
,
viz.
of
A.
B.
which
is
20.
foot
.
Or
let
the
Altitude
of
G
,
be
sought
out
,
whose
Basis
cannot
be
seene
Admit
,
the
first
station
be
made
at
A
and
seing
the
summet
of
the
Altitude
G
,
the
Index
should
cut
3
in
the
line
of
shadowes
,
it
Argueth
that
the
distance
to
the
Basis
of
the
Altitude
,
is
triple
to
the
Altitude
,
then
if
I
should
go
neerer
to
the
Altitude
,
viz.
at
D
,
and
should
obserue
the
summet
or
top
of
the
Altitude
G
,
and
that
the
Index
should
fall
upon
1.
in
the
line
of
shadowes
,
then
it
sheweth
that
the
distance
from
D
,
to
the
Basis
of
the
Altitude
is
equall
to
the
Altitude
.
Now
suppose
that
betweene
D
and
A
were
80.
foote
it
should
seeme
that
the
Altitude
obserued
should
be
40.
foote
,
for
if
at
D.
the
distance
to
the
Altitude
be
equall
to
the
Altitude
,
&
the
distance
from
A
,
to
the
Altitude
,
be
Triple
to
the
Altitude
,
then
the
distance
from
D
to
the
Altitude
is
the
⅓
of
the
distance
AR
,
&
so
AD
,
shall
be
double
to
DR
,
therefore
halfe
the
distance
AD
,
viz.
40.
foot
is
the
Altitude
required
.
Pro.
50
Seventhly
,
to
measure
any
part
of
an
Altitude
which
is
not
approachable
.
Declaratio
.
Let
G
H
,
a
part
of
an
Altitude
be
required
to
be
measured
.
First
,
search
out
the
height
G
R
,
as
before
40.
Constru
¦
ctio
.
70
foote
,
then
admit
standing
at
A
and
looking
to
H
,
through
the
sights
,
the
Index
should
cut
4
,
which
shewes
the
distance
from
A
,
to
be
Quadruple
to
the
Altitude
of
H
R
,
and
if
comming
neerer
the
Altitude
80.
foote
,
viz.
at
D
,
I
should
observe
H
againe
,
through
the
sights
of
the
Instrument
,
and
finde
the
Index
to
cut
1
,
and
⅓
,
in
the
line
of
the
shadowes
,
then
the
distance
from
D
,
to
the
Altitude
H
R
,
viz.
D
R
,
should
containe
the
Altitude
H
R
,
once
,
and
a
third
part
of
the
Altitude
,
now
seeing
that
D
R
,
is
1
and
⅓
,
therefore
H
R
,
shall
be
1
,
but
the
observation
at
A
shewed
the
distance
from
A
,
to
the
Altitude
H
R
,
to
be
Quadruple
,
and
seeing
that
D
R
,
is
1
,
and
1
part
of
3
,
therefore
A
D
,
must
be
2
,
and
2
parts
of
3
,
which
makes
A
R
,
the
whole
distance
to
be
4
,
or
Quadruple
to
H
R
,
but
if
A
B
,
2
,
and
2
parts
be
80.
foote
then
D
R
,
being
1
,
and
1
,
part
shall
be
40
foote
,
and
if
D
R
,
1
,
and
⅓
,
be
40.
foote
,
then
H
R
,
(
which
was
1
should
be
but
30.
foote
,
&
so
consequently
H
R
,
)
taken
from
G
R
,
there
shall
remaine
G
H
,
10.
foote
,
the
measure
of
the
part
of
the
Altitude
required
.
In
like
manner
might
we
applie
the
Instrument
to
the
measuring
of
Bredths
and
distances
:
but
that
which
is
delivered
may
serue
for
the
present
,
and
as
fully
sufficient
for
the
Ingenious
.