230 A Conjeclure concerning 
y 3 + 3 yyz -v 3 yzz +z 2 -qxy+z=r, 
oi ' }*+ %yz*y + z + z i -qxy+z=r. 
Now in this equation, the terms 3 yzx[y+z and qxy+z 
have contrary ligns. Confequently, if they can be fup- 
pofed to be equal to each other, they will deftroy each other, 
and the equation will be thereby reduced to the following 
fhort one,_y 3 +.s 3 =r; that is, if 3 yz and q can be fuppofed 
to be equal to each other, or if yz can be fuppofed to be 
equal to |, the equation will be reduced to the fhort 
equation y s +z l ~r. And, if in this fhort equation we 
fubllitute, inftead of z , its value (derived from the 
fame luppofition of the equality of 3 yz and q ) the equa- 
tion thence refulting will be + and by multi- 
plying both lides by_y 3 , it will be_y 6 + ^ = ry l \ and, by 
fubtradting _y 6 from both lides, it will be ry^—y^— q —\ 
which, though it rifes to the lixth power of y, is evi- 
dently of the form of a quadratic equation, and confe- 
quently may be refolved in the fame manner as a qua- 
dratic equation, fo far as to find the value of y 3 , or the 
cube of the rootj/; after which it will be pollible to find 
the value of y itfelf by the mere extraction of the cube 
root ; and, laftly, from the relation of y to x (contained 
in the two fuppofitions, that_y+£ is equal to x, and that 
3 yz 
