42 a Dr. button on Cubic Equations 
i 15/ 2 2 .5. s „ 
namely, T ^2 or — = 1 - — 6 - &c. = 
L + J*r£ . + - 2 ' 5,8, Ir — <kc. we obtain the 4 following 
3 3.6-9 3.6.9.12.15 T & 
feries : • . - ^ ' r : r , . J . . 
V3 + + 1 — T _ 2 - S ■ 8 __ __a . 5. 8 . n ,_i4 . 1 7 .20 
4^2 ~ 3.6.9.12 3 . 6 . 9 . 12 . 15 . 18 . 21 . 24 
V3 + ^ 4 ~* _ L + 2 • 5 ; 8 • 1 1 2. 5 . 8. 11 . 14. 17 . 20. 23 
• 41^2 ” 3 3 . 6 . 9 . 12 . 15 + 3.6.9. 12 . 15. 18.21 .24.27 * 
V3-^4 + i £_ , 2.5.8. 11.14 . a ,„ 
4^2 3-6 + 3.6.9. 12. 15. 18 ° t * 
Vj-jTj. - i _ _ 2.5. __ 2.5. 8. 11 .14.17 _ 
4^2 — — 3.6.9 3 . 6 . 9 . 12 . 15 . 18 . 21 
• - - ' 
89. It'alfo appears, that the feries 
• .1 4 - -l- ^ 8 :- rr ...grc 
3 3-6 3.6.9 3.6.9.12 3.6.9.12.15 * 
is the reciprocal of the feries . I •- 
I + i _ » + JLli- - -illli- + JiLhiL. fee. 
3- 3.6 3.6.9 3.6.9.12-- 3.6.9, I2.+5 
where the figns of the former feries are found by 
changing the figns of every other pair of terms' in the 
latter ; namely, omitting the firft term, change the figns 
^ ‘ vV ' Ci ' t * ' 
of the 2d and 3d terms, then palling over the 4th and 
5th terms, change the figns of fhe’bth and 7th; and fb 
on. For, by Art 86. the former of thefe feries is equal to 
-p — *, and, by Art, 72. the latter is equal to ty’ii 
v 2 
90. Let 
