434 Dr. hutton on Cubic Equations 
hi. Then for the other roots, by multiplying the 
terms a, b, c, &c. of the former by &c. we have 
« — j a 
7 
= 11 C ~ 
IS c 
■« ='H* = 
33,33333 
1931 
6 
» = = *0049383 
^ = IT D = 97 
- '0049480 
+ *3335270 
- *0049480 
*3285790 - - - log. 1*5166398 
V6 — ^ 
i, 923°956 
the fecond feries ± *27525513 - - 1-4397354 
1 the greateft root + 1*72474487 
middle root 2*00000000 
leaft root 1*44948974 
1 1 2. But, by Art. 61, thefe 3 roots were found to 
be 2 and — 1 ± 6 ; which being compared with the fe- 
ries belonging to this cafe, we find 
1 1 _ T . . 2 • 2 , 1 • s . 3 • 11 • 14. ** 
2^5 3.6.25 3.6.9.I2.25 1 3 . 6 . 9 . 12 . 15 . iB . 25 J 
V 6-2 , , I 2.5.2 2. C. 8. II. 2* o 
2 5 = — 7-2 ; 4- — 7-2 i — 8cc. 
4 v ° 3 3.6.9.25 3.6.9.12.15.25 
1 13. Ex. 7. In the equation x z - 1 2 at = 9, we have 
a — - 4, b — I, and r 1 = h — 64 = — ^ 5 , which being 
negative, and- greater than < 7 , we fhall have 3 real roots 
by the feries in Art. 98. 
3 
Now 
