Second Cafe of the Cubick Equation x i —qx=r. 927 
x % -qx-r in that cafe of it which falls under cardan’s 
rule, or in which r is greater than —f or — is greater 
than — . 
27 
30. I now proceed to confider the problem which is 
the principal object of this paper, which is to fhew how 
from the feries e \ x {2 - 2 " — — - 3 ° a f 6 — ' See, we may 
3 9« 243 j 4 6561/ J 
derive another feries, differing from it only in the figns 
of fome of the terms, by which the equation x l — qx — r 
may be I'efolved in that other cafe of it which does not 
come under cardan’s rule, and in which r is lefs than 
Hfil or — is lefs than — : and this without anv mention 
3^3 4 27 
of either impoffible or negative quantities. 
PROBLEM. 
¥0 refolve , by means of an infinite feries derived from the 
infinite feries e \ x ^ the fe- 
cond cafe of the cubick equation x 3 -qx-r, in which r is 
lefs than or — is lefs than — . 
3^3 4 27 
SOLUTION. 
31. We have feen that in the firfl: cafe of the e- 
equation x^-qx-r, in which — is greater than the pro- 
dudf 
