Second Cafe of the Cubick Equation x i -qx=r. 925 
Here q is = 300, and r is = 2108. Therefore 
0 3^3 
2 X 300 X a/ TOO 2 X I OO X V 200 2 XIOOXIO -/3 
IS = ^ — 0 — 22 2 = 2 X IOO 
3X a/3 Vi A/3 
x.io = 20oo, which is lefs than 2108, or r. Therefore 
this equation comes under the cafe of cardan's rule, 
and confequently may be refolved by means of the infi- 
8cc. if that feries 
nite feries * 4 x (2-^- 
3 * gee 243^ 
308 i 6 
6361 e 6 
has been juftly derived from the third expreffion of the 
value of x given by cardan’s rule. 
26. Now, iince r is = 2108, , or e, will be= 1054, 
and b r , or ee , will be = 1,110,916. And, lince q is- 
= 300, - will be = 100, and or the cube of 1 , will 
3 3 
3 
be = 1 000,000 ; and confequently ss> will 
be (= 1, 1 10,916 — 1000,000) = 1 10,916. Therefore, 
the fraction — is = = .0998. Therefore ~ is 
ee 1,110,916 e A 
= .0998^ = .009,950, and h-is = .0998I 3 = .000,992 ; 
and — is=— x .0998 
gee g 
.1996 
022,177; and 
20 r 
2 4 j e< 
JS 
= — x .009,950 = - 199 ’ co ° - .000,818; and 308 -s i3=~- 
243 y?y o 24.3 6561/ 6561 
x .000,992 = = .000,046; and confequently. 
2 SS 20 5 4 
+ 
gee 243^ 6561* 
+ JSiil is = .02 2,1 77 + .000,8 1 8, + .000,046- 
, 2 ss 20 r 300 s 
-.023,041; and 2 - — - ^7“ 6sfri7 
308 , lis= 2-. 023,041 
