924 Extenjion of Cardan’s Rule to the 
VA c 'h j + \f 3 [e — s, or j — H r +\J 
— s, from which it 
was derived. However, that it may appear that this fe- 
ries will exhibit the root of the equation x 3 ~qx=r tru- 
ly, if we will take the neceffary pains of computing it, 
I will here fubjoin one example, and no more, of the 
refolution of a cubick equation of that form by means 
of it, having taken care to chufe fuch numbers for q 
and r as lhall make k be but little greater than ~ , and 
ccnfequently fhall give us only a fmall number for the 
fraction by the continual multiplication of which the 
terms of the feries are generated. 
An example of the refolutmi of a cubick equation of the 
aforef aid form, x 3 -qx=r, in the Jirjl cafe of it, in which 
r is greater than or is greater than by means 
of the expreffion <?' x the infinite feries 2 — - 
308J 6 
6$6ie* 
- <wc. obtained in Art. 23. 
25. Let it be required to refolve the equation x 3 —■ 
300# ■= 2108 by means of the infinite feries e> x 
[2-— — 2 RA - &x. obtained in Art. 23. by the 
4 gee 243^ 6561*° ' 
help of Sir isaac newton’s binomial theorem. 
Here 
