OF THE FIFTH DEGREE. law 
the quantities A, B, D, Ay, B,, D,, are known rational functions 
of po, ps3, etc. And 
(5? + D?) (At a D} oa) “(Be pe D2 ¢* 2) 
+ 4{AB (B? + D2) — A, By (B? + D? } 
{AB (42 — D? c2 z) — A; B, (A? — D?e? z)| = 0. (25) 
§12. To verify this result, the Gaussian equation in §8 may be used. 
Here 
a 6 sll? + 112 x 19 118 x 3 
SS co ( 56 oe ae 
Wey 114 3* x 72 x 114 + aes aaa a a 
= =| Grae 24 x 512 eine ole t aa 
Peeass 11" 
a 4x 516 
2x 7351 Cea xeLTs a x 414 
eee ie Oe AN ee se 
(ie 2 2 1 es 
_ 3x 31 x 116 
a 4 x 516 
118 118 
a eT 
117 11? x 109 
B= oF x 58 (— 53 + AA oA le t9 oS 31) = =e BT 
a 116 63 x 11? lige TT? x 19° x" 3t 
ete IN 5S CE 8 x 58 
117 »% 26 
= ~~) 
Therefore 
9 «x 1112 x 41 2 2 114 x 11029 
eo 8x! ey oe 
9 x 114 x 89 
ine hoa se 
111¢ x 40139 
2 2 
A ——Dice2= — = 
; : 210 Seyp* 
