Second Cafe of the Cubick Equation x z —qx=r. 945 
Now, lince ‘C is = 9261, and ” is = 6561, we fhall 
have^-j, or ss, =2700, which is lefs than 6561, 
or ee, in the proportion of 100 to 243. Confequent- 
ly the feries 2 + — - — 8tc. and the produ6t 
of that feries multiplied into e' 1 , or the feries e" J x 
2 + — - — 3 i- + ±±L _ gcc. will converge. Therefore 
gee 243^ 6361^ 0 
the equation x 5 - 63# = 162 may be refolved by it as 
follows. 
48. Since ss is = 2700, and-, or ee, is =6561, we 
4 
iltall havej = gg = ~ =.411,522, and ± = .169,350, 
-and b = . o 6 9 , 6 9 1 , and confequently A”’ . * 2 . 2 . - = 
•° 9 I , 449 , and ^ = --;l 9, ”° = 1 S7 g =»oi3>938 > and 
2 43 r 
308 /’ 308 X . 069,691 __ 21 . 464,828 
'‘6561^ 
6561 
20.5 4 ^ 308 / 
6361 
= .003,271. Therefore 2 + 
„ ■ , . 0 - See. is = 2 + .091,449,- .0x3,938, + 
gee 2 43^ 036 1£ ^ 
.003, 271 - 8cc. = 2.094, 720, - .013, 938 - &c. = 
2.080,782, - &c. And e*, or v^fi?, is = = 
4.326,749. Therefore e* x the feries 2 + 
2 or - 
— + 
9^ 24 3 e 4 
308 / 
6361^ 
- &c. is = 4.326, 749 x 2.080, 782, - &c. = 
9.003,021 - &c ; that is, the root of the propofed e- 
quation „r 3 — 63^= 162 is = 9.003,021, - Sec. or fome- 
what lefs than 9.003,021 ; which is true to three places 
Vol. LX.VIII. 6 B of 
