438 Dr. hutton on Cubic Equations 
j j R A rrain 
+ -3333663 
- *0020413 
- *0020413 
*33*325° 
•6626500 
^3 
s/ 1 21 
log. 7*8212844. 
0*2385606 
- 0*6942618 
the latter feries ± *2320508 - - *‘3655830; 
\ the firft — 2*2320508 
middle root = — 2*4641016 
leaft root = — 2-0000000 
119. But, by Art. 64, the 3 roots are - 2 and 
1 — v/ 1 2 ; hence 
!_+ 3 V/ 3 _ t , 2 . 5 . 8 . 2 4 , 2 . 5 . 8 . II . 14. 2 6 
Vn 3.6.11* 3. 6 . 9 » 12 . 1.1 4 3 ^6 . 9 . 12 . 15 . 18 . 1 1 6 
ai = l- + *• *• 8 ‘ . » * . » 4 .. - See. 
120. And in this manner the roots of cubic equations 
may always be found by thefe feries ; and then by com- 
paring them with the roots of the fame equations, as 
found by other methods, we fhall obtain as many feries 
as we pleafe, whofe fums will be given. 
121. Hence 
