94° 
Exlenjion of Cardan’s Rule to the 
or j. Therefore this equation cannot be refold- 
ed by cardan’s rule, but may by the feries <4 
2 + 
+— - 
lOi' 
308/ 
6561/ 
See. in cafe that feries is a con- 
gee 243 r 
verging one, 
- -• 3 
Now, lince — is-— and - is = we fhall have ss, 
7 2 7. .zf - 4 36^ 
or 
1 
2 7 
36-27 
_ __ 9 - 
27 . 4' 27 36 27x36 27x36 3*36* 
than r, or ee, in the proportion of 1 to 3. Confe- 
which is lefs 
quently the feries a + 
24s 
gee 
2. or 
243^ 
+ 
308./ 
6561/ 
- &c. and the fe- 
. 1 2SS 
ries ejx 3;*— 
gee- 
2 or 
308/ 
fee, will converge.- There- 
243 * 4 - 6561/ 
fore the equation x^-x-^ may be refolyed by the means 
of it as follows. 
42. Since ss is h-, and-, or^, is 
“ 3 X 36’ • ’ ’ 
36 V. 
we lliall 
have T = l =.333,333, and $ = i = .111,111, and 4 =3 
h = .o 3 7,037^and confe, quently g.= 
20 X.III,III 2.222,222 
2 7 
2 or 
*43 
= .009,144, 
.074,074. and !(j( . , 4J 
"TO*- Therefore 
656: 
2SS 20S$ 
2 + T + 
308/ 
,4^ ■ 656 re® - &c * iS = 2 + *O74,074 -.0O9,I44 -h 
.001, 738 = 2.075, 812-. 009, 144= 2.066,668. And: 
s/'e is = V^fT = -4 t = -4 — Therefore <4 x the feries 
■© v 7 6 1.817,121 
- 4 ~ 8CC. is = — X 2.066,668 = 
* 050 ir 1.8,17,121 7 
1. 13733; 
2JJ 20J 4 
2 -f — * — 
gee z^e 
