946 Extenfon of Cardan’s Rule to the 
of figures, the error being in the fourth place of fi- 
gures, or the third place of decimal fractions, where 
there ought to be a cypher inftead of a 3, becaufe the 
accurate value of x in this equation is 9, as will appear 
upon trial : for, if x be taken = 9, we fhall have x s — 
729, and 63^=567, and confequently x z -6^x (=729 
-56 7>=i6a. 
SCHOLIUM. 
49. This refolution of the equation x^-G^x-iGz 
anfwers to Dr. wallis’s refolution of it by extracting 
the cube-roots of the impoffible binomial quantities 
8i+v / —2700 and 81— —2700, inafmuch as both re- 
solutions are originally derived from cardan’s rule. 
But the difference between them is, that the method 
here delivered is intelligible in every ft ep of it, whereas 
Dr. wallis’s method treats of impoffible quantities, or 
quantities of which no clear idea can be formed, in the 
whole ccurfe of the procefs, though it concludes with 
a refult that is intelligible, by means of the equality of 
the impoffible members of the two ultimate quantities 
l + lv^-3 and f — ■!•</— 3 (whofe fum is equal to the 
value of a), and the contrariety of the figns + and — , 
which are prefixed to them. The doctor’s method of 
finding \ + j \/ - 3 and \ — - 3 to be the cube-roots 
of 
a 
