Second Cafe of the Cuhick Equation x*-qx=r. 931 
that is equal to x, it is impoffible that the faid remainder 
(which is produced by that fubftitution) fhould be accu- 
rately equal to the whole value of r. 
32. By the help of this obfervation We may from the 
foregoing feries 2- — - - See. which, be- 
ing multiplied into e }, or the cube-root of , exprefles 
the value of x in the equation x^—qx = r, in the firft cafe 
of that equation, when ’-C is greater than q — , deduce ano- 
ther feries refembling the former in the compofition of 
its terms, but differing from it in the figns to be prefixed 
to fome of them, that will likewife (if multiplied into 
e j, or the cube-root of r - j exprefs the value of x in the 
fecond cafe of the fame equation, in which r ~ is lefs than 
and which cannot be refolved by cardan’s rules* 
This may be done as follows* 
33 . If in this fecond cafe of the equation x^—qx-V 
we fubtradt — from , and call the remainder ss (as we 
before put ss for the oppofite difference - — J and then 
raife the powers of ss, to wit, s\ /, /, s 10 , and alfo 
? 4 
the correfpondent powers of its value to wit, 
