Second Cafe of the Cubick Equation x'-qx-r. 929 
reflectively, as in- the foregoing example we multiplied 
.0998 into -, and .009,950 into — , and .000,992 into 
, and found the products to be .022,117, .000,818, 
and .000,046 ; and 6thly, to fubtraCt all the products fo 
obtained from 2 the firft term of the feries. This is 
the common and the proper way of computing the feries 
a- — - — — — r - , 3 °~ -- 6 - Sec. when we want to make ufe 
gee 243^ 6561^ 
of it in practice. But it may alfo be computed in ano- 
ther manner, which may be defcribed as as follows. 
Inftead of infert the compound quantity — - q — it 
27 
felf, to which ss is equal, in all the terms of it. And 
it will be thereby converted into the following feries, to 
3 
2 
gee 
r *_ 
64 
grr 
(Z- 
jl}_ 
20 
rr 
_ ?l| 2 
308 
rr j 
4 
27) 
' 243 x 1 
4 
27I 
6561 e * 
4 27 
ife < 
IS : 
= 2, and confequently £ 4 : 
r 4 
~ 76 ’ 2 
rr 
f*\ . 
- 32 ° X 
rr 
_£> 
19712 
»r 
■U 
27 
243 ' 4 
"4 
27 1 
656 1 r 6 X 
4 27 
Q 3 rr q s 
&cc. or 2 x I — 
grr 4 27 
320 - 2 rrq 6 q 
243 r 4 X ^16 4x27 2.7x27 
l 9 7*2 
3'V 
+ 
3 rr q 
636 lr * 
&c. or (putting 
64 16x27 4x27x27 27x27x271 0 
the Greek letters #,€^,'8£c. for the numeral co-efficients 
s 
&c. re fpe 61 ively) 2 
243 
OJ 
rr 
..1Z. _ 
* 1 4 
27/ 
+ 
|r 4 % rrq h 
16 4X27' 27x27 
¥ol. LXVIIL 
7 
76 X I— 
3 ; Y 
■ + ■ 
3 rr ? 
64 16 x27 4x27x27 27x27x 27 " 
2 Z 
