Second-Cafe of the Cubick 'Equation x l —qx~r, 937 
half — , or than — , though lefs than — . And the nearer 
2 f 54 7 0 27 
^approaches to the greater will be the fwiftnefs with 
which this feries will converge. 
37. 1 will now add a few examples of the refolution 
of -cubicle equations of the aforefaid form, x i —qx=.r i in 
the fecond cafe of thofe equations, in which r is lefs 
than ildfl or - is lefs than — , by means of the infinite 
3V3 7 .4 n 7 
feries x 1 2 + — — — - + — &c. found in Art. 3 5 , 
j gee 243^ 6561^. 
in order to confirm the truth of the reafonings by w;hieh 
.that feries was obtained. 
? v 
EX A1PLE 
; o 
33 / Let it he required to refolve the equation x r - $ox~ 1 a« 
by means of the faid inf nite feries. 
ilb 
Here q is = 50 ; r is = 1 20 
- or e, is = 60; ", or 
1 ■ . V . ; .. ; .4 
^ # * t I2C,QOO 
ee, is =3600; q * is = 1 25,000; and ~ is — — — 
4629.629,629,629, &c. which isvgreater than- 360 Oi, 
or — . Therefore this equation cannot be refolved by 
cardan’s rule, but may by the exprelfion e s x the se- 
ries zri - — — iff- + 3 . ° - 8 ' -. — See. provided, that feries con- 
verges. Now, fince — is = 4629. 629, 629, 629, &tc. 
2 7 . 
* Vol. LXVIIL 6 A and 
