278 Wilder'' s Algebraic Solution, 



regard to 1 a a^,) to y^ — 3p^/+a;3-{-— » the function we 



parted from. 

 We may further observe the function, 



^^-ir+^' 



becomes, when the 



denominator is a factor of the numerator, independently of a?, 



(^/ ^ + 3zy^ +(3z2 — 3p)y + 



x^ — 



{x'^-^y^ -\-Szy^ -\-{Sz'' — Sp)y-\-z^ - SpzY+{y-\-z){x^ - {y^+ 



4 

 z^ —SpzY 



)i 1 



hence, when z=0, we have the following equations, 



3p=-b, 



{x^-\-p^y=c, 



{x^ — cy -\-y{x^ — cY-\-p=^0 ; from which y is known. 

 {y^ -\-py-\-q)^ — x^ 

 The function jy — Tl) ' ^^ proper to reduce 



cubics ; for if we make 



y34.ay+6 ~=^'+^^'+^^+^- and determine A, 

 B, and C, so that the denominator is a factor of the numer- 

 ator, we shall have, 



A=3p, . 



B+«=3g + 3pS 



C-f A«4-&=6p^+^% 



"Qa+kh = 3q^-\-3p^q, 



Qa-\-m = Spq\ 



06=^=5 -f-a;2 ; or 



