228 A Conjecture concerning 
times, and thereby to preferve their difference y-z 
always of the fame magnitude, or equal to x, it is evident 
that the product or re£tangle yz will increafe conti- 
nually at the fame time from o ad infinitum , and confe* 
quently will pafs fucceffively through all degrees of 
magnitude, and therefore muft at one point of time 
during its increafe become equal to q -. 
And having thus found this fuppofition of the equa- 
lity of yz and - , or of 3 yz and q, to be always poffible, 
3 
whatever might be the magnitudes of q and r, our in- 
veftigator would juft ly confider his folution of the equa- 
tion x^+qx-r (which was founded on that fuppofition) 
as legitimate and compleat. And thus we fee in what 
manner it feems probable, that cardan’s rule for refold- 
ing the cubic equation a? 3 +yx=r may have been difco- 
vered. 
Of the equation x v -qx=r . 
Art. 5. In this fecond equation x z -qx=r, in which the 
fecond term qx is fubtra&ed from the firft, or marked 
with the fign -, it feems to have been natural for the 
perfon who invented thefe rules to fubftitute the fum as 
well as the difference of two other quantities,^ and z, in- 
ftead 
