and Infinite Series. 447 
134. But in Art. 61, the fame root was found to be 
— 1 — \/6, hence we obtain the fums of thefe firffc two 
particular feries ; and by the addition and fubtradtion of 
thefe two arife the other two following them, namely, 
i -f a/ 6 H- -^5 -f a/ 2 -f v' 5 — \/ 2 ^ 2 . 5 • 8 . 2 Z 
4 rs 
1 - 
■3 .6 .9. 12. $ 
4 
- &C, 
I 4- ^6 — -f a/ 2 — — V2 __ 2 . 2 2 . $ . 8 . I I' . 14 . 2* n. 
~ : 4^5 ' _ * 3 * 6 v 5 2 ' 3.6.9.12.15. 18. 7 s 
, + ^ = i + 
2 . 2 
2.5.8. 
2.5.8.11.14.2" 
^ 5 
3.6.5“ 3.6.9. 12. 5 4 3.6.9.12 .45 . 18 . 5 6 
- &c. 
-8cc. 
2 . 2 
^5 4- 1/2 + >^5 ^ _ 
2^5 “ 3 • ^ • 5 
2 . 5 . 8 . 2 2 
3 . 6 4 9 . 1 2 . 5 4 
And the laft but one of thefe equations agrees with one 
found in Art. 1 1 2. . 
135. Ex. 3. Alfo in the equation x z - 1 zx — 9, we 
have i b- 9, and v 7 V + c z = 4 ; confequently Z> = 4. and 
= 4 3 - b * 1 = 64 - i? = -t|i, which being greater than 
> or f, 4 this cafe ’ ' * J " J " ’ ’ " " 5 * 
s to the fecond clafs of ~feries, 
or thatof.the leaf: roots. Now here- x = vV+^- v 7 c-b — 
v 7 \ - i> », „ *. <U * . \ ” 
✓175+9 
1 7 i -..2 = 1 1*114378 - ^2-1 14378 - 
. P.t? . £ “ , 0 
^*23 ^$$1.9 - 1*2834930 = *9481669 ~ the root of 
the equation x 3 - $y{b z - . a* = %b ..or x 3 + .x = 9. 
And the terms of the two feries being found as in Art. 
113, namely, a + c +e + &c. = *3405 1, and b + d + f -+ 
&c. = ’03071, alfo being = we fhall have 
