The Method of
96
Now
FLUXIO N
s,
of the Areas be added to, and fubtracted from,their fum before found, half the aggregate o. 1053605156578263 be the greater Area hd, will and half or the remainder will be the lefler Area AD. 0.0953101798043248 52.
53.
as
By the fame tables thofe Areas AD and hd will be obtain'd when AB and Ab are fuppos'd T ~, or CB=i.oi, and
=
alfo,
d>
if this difference
o.gg, if the numbers are but duly transferr'd to lower places, may be here feen. O O2OOOOOOOOOOOOOC0 O.O30ICOOOOOOOO3OO 66666666666 50020000 4000000
3^
28
Sum
o 020000(5667066(195
Sum
0.0001000050003333
=
AJ
AD.
==AD. 0^
fo putting 0.999, there will be obtain'd
= AD = =
and
A or
or
AB andA=-~o-> orCB=i.oor,
And
54.
and'
Ad= 0.0010005003335835,
o. 0009995003330835.
AF=
CA
AB
and i) putting 55. In the fame manner (if fe Areas will arife, o.2, or 0.02, or 0.002, the
and
A^=o.223 1435513 142097, and ADz=o. 1823215567939546, 0.0 19802 627296 1797, A</= 0.0202027073 175194, and AD o.ooi AW=o.oo2oo2 andAp
= =
From
56.
thefe Areas thus
found
it
will be eafy to derive others, f'
I
by addition and fubtradtion alone. the
fum of
the Areas 0.693
I
For
as
it
2.
\
into
is
-^
=
2,
to the Ratio's
47 I ^5599453 belonging
2
o 8 upon the parts of the Abfcifs 1.2 and 1.2 2, as is known. o.9,)will be the Area AFcPjS, C/3 being the fum 1.0986122886681097 of the Again, fince ^ into 2 3,
^|and
^-
(that
,
is,
infifting
=
=
Area's belonging to and 2, ^-|
Again, as Areas
will
c /3=5;
And
it
thus,
x 10 xo.98 -
is
be
and
~=
and 2
x5=
obtain'd
Area AFcT/3, C/3 being
10,
10x10=100,
7,
=499
=AF
;
and
lox
it is
plain,
i.i
and
=
<
10x100=1000,
= n,
x
and
that the Area
the compofition of the Areas found before,
3..
by a due addition of
AF^/3, 1.6093379124341004 when C/3 T/3, 2.3025850929940457
fince
=
5,
will be the
'
=when 10.
and
^5
'
I
.'
^)
and
AF^/3 may be found by when C/3 i oo i ooo
=
j
i
7>