42. 8 
Dr. hutton on Cubic Equations 
That is, x = 7 is ■= 2 J/— x ; 1 -A 
7 7 V 2 3 . 6 . 
2 . 37 
2.3.8.37^ 
Z r ~l 
9I 3.6.9.12.91^ 
10 1. The other two roots are imaginary, and in 
Art. 56 they were found to be = but by means 
of the feries in Art. 68, they are here found to be 
~7 <V -3 
'I 2 . Cc 
— + - — 
3 3 • 6 .96 
— + &CC. 
a . ; . 8 . 37‘ 
. 5 . 8 . 11 . 14. 37' 
Confequently we obtain thefe following fums ; 
_ 7 _ 3/ y _ x _ 2 • 37’' 
2 V51 3 . 6 . 91 
1 3/2 i! 
r;v 2’- 
3 . 6 . 9 . 12: . 9 I 4 3 . 6 *9 . 12 . 13 . 18 . 91' 
See. 
A + 2 • $ • 37 
3 3.6.9.91 
+ 
2 . 5.8 . 11 . 37 
8cc, 
57 V 2" 3 3.6.9.91" 3 . 6 . 9 . 1.2 ^ 13 . 91“" 
102. Ex. 2. I11 the equation x 3 + 30 At = 117? we 
have a - \p - to, b - {q ~ - 7 L - 58^, and A = A + 
<z 3 — III)*, which being poiitive, and greater than b z y 
the proper feries for this is that in Art. 91, namely* 
.5.8. n£ 4 
2 b I 2 , tl) 
X — -57 X l + 7 1 "T - — 7— 
j / c - 3 3- 6 -9‘ 3.6.9.12.15, 
+ &c, 
Now l -~ — 
* 133 
= ’7738308. Hence 
A a 
