226 
A Conjecture concerning 
are, both of them, affirmative) the terms of the new 
equation, arifing from i'uch fubftitution, would all of 
them be likewife affirmative; and confequently none of 
them, though they fhould happen to be exactly equal to 
each other, could exterminate each other, and thereby 
render the new equation more Ample than the old one, 
which was the only view with which the fubftitution 
would have been made. He would, therefore, fuppofe 
x to be equal to y-z; and by fubftituting this quantity 
inftead of x in the original equation x 3 +qx=r > he would 
transform that equation into the following one, to wit, 
Now in this equation it is evident, that the terms 
3 yz xy-z and q xy—z have contrary figns ; and therefore, 
if their co-efficients ^yz and q can be fuppofed to be 
equal to each other, thofe terms will mutually deftroy 
each other, and the equation will be reduced to the fol- 
lowing fhort one, y l -z' i -r. And if in this equation we 
fubftitute, inftead of z, its value derived from the 
fame fuppofition of the equality of q and 3j yz, the equa- 
3 
tion will be y 3 — A— — r\ and, by multiplying; both ildes 
rifes to the lixth power of the unknown quantity y, is 
y^~ 3yyz+ o,yzz-z^+qy-q z = r, 
3r 
4 
evidently 
