944 Extenfion of Cardan’s Rule to the 
qx — r. in the fecond cafe of it, in which r is lefs than 
idSd or — is lefs than — , and which therefore cannot be 
refolved by cardan’s rule. 
.1 will, however, fubjoin one more example to the 
fame purpofe,; which fhall be that of the equation x l - 
63^=162, which both Dr. wallis and Mr. de moivre 
have refolved by extradting what they call the impoffi- 
hle cube-roots of the impoffible binomial quantities 
81+ </ — 2700 and 8 1 — v^— 2 7 00 . Now this equation 
may be refolved by the foregoing expreffion e* x the 
feries -a + — - —fi + frf - See. in the manner fol- 
gee 243^ ofoie 
lowing. 
EXAMPLE 4. 
.47. 'Let it be required to find the root of the equation 
A 3 - 6 '2 ) X— l 62, 
'Here q is = 63; r is = 162; — , or- e, is =.8i; - or 
2 4 
ee, is = 65:61 ; -f js = 215 and E is - 9261, which is- 
greater than 656 1, or Therefore this equation can- 
not be refolved by cardan’s rule, but may by the infi- 
nite fedes 4*|*+=- ** fat cafe that fe- 
.rics is a converging one. 
;Now, 
