Extenfion of Cardan’s Rule) See. 9&3 ' 
comes impoffible, and the expreffion givenby cardan’s 
rule for the value of x (which is either 
V S NF 
r 
27 
\rr I3 \ r I 
4 ^ \ i ~2~~y 
-p. 
4 2 *>' 5 
VFVFl; 
involves in it the impoffible quantity — F, and there- 
fore is unintelligible and ufelefs: or, according to what 
appears to me a more correct way of fpeaking (who ne- 
ver could form any idea of a negative quantity, and ne- 
ver underftand by the fign - any thing more than the 
fubtraftion of a leffer quantity from a greater), the quan- 
tity - — — becomes itfelf impoffible, or the fuppolition 
that k is greater than (which is one of the founda- 
tions of cardan’s rule), is no longer time, and confe- 
quently the rule itfelf, which is built upon it, can no 
longer take place. 
2. Neverthelefs it is poffible, by the help of Sir Isaac 
newton’s binomial theorem, to extend this rule to this 
latter cafe, in which - is lefs than and which it is not 
of itfelf fitted to refolve; or, to fpeak with more accu- 
racy, it is poffible to derive from the expreffion of- the 
value of x given by cardan’s rule for the refolution o£> 
the equation x*-qx~r in the firft cafe, in which - is 
greater 
