278 Wilder’s Algebraic Solution. 
; 3 
regardtol a a?,)toy® — spy +0? 455 the function we 
parted from. 
We may further es the function, 
—+5, 
becomes, when the 
(»—; a +042) Se 3) + 
Eee LIS is a factor of i numerator, independently of 2, 
_ Yi t3zy? eos —3p)y+ 
(x?-(y? +-3zy? +(327—3p)y +2? — sp: )* ae -(y°+ 
4 
z°.—3pz)* 
demas 2 ree 
S2y? +(3z? — Sp)y+z* — spz)* +p 
hence, when z=0, we have the following equations, 
3p b, 
(=°-+p*)*=e, 
(x img taletcad! peels from which y is known. 
y? +pytq)*—«* 
The oe y? -bay-+b 
cubics; for if we make 
ety ays Ay +By-+-C, and determine A, 
B, and C, Sao the denominator is a factor of the numert- 
ator, we shall have, 
» is also proper to reduce 
Ch=q? +x? or 
