392 
ME. A. CAYLET OX THE COYIC OP PIYE-POIYTIC 
or reducing by the equation of the curve, 
= (1 - + (2 Z - 32 l^Yyz + 6 ■ 
And the coefficient of 2Q is 
+ 2Z%^ +z^)+ ; 
or reducing by the equation of the curve, 
And we have 
2/=18^(l + 8r)^yz® 
+ 3^y2^((l - 32^^)^’^ + 6^yz^) 
+ 2Y+Q Ixhjz + Zfoffz^ -~y"z% -2Ix^ - 8^Vj/2: + ?/V) • 
Reducing the expressions of « and 2/, we find for the coefficients (a, i, c,f, y, J>). 
*..+10ia>+40«VyV+(6+120«=)*yz’-10/aY2‘--lfr-% 
2y= — 4Za;‘"— 40iVyz+(5 — 120i’V'3/V + 40Z*‘/z’+8hr-y z — 2i/ . , 
which givL the completely developed form of the equation of the five-pointic come. 
44 f ffivestigate L coordinates of the point of simple intersection of the cuhro and 
the five-pointic conic as follows : the equations of the two curves aie 
X®+Y®+Z'+6ZXYZ =0, 
(«,5,o,/,.9VUX,Y,Z)> = 0; 
or if we write a 
a = l, A— c, 
y=6^XY, B=2(^X+/Y), 
^ ^ + Y®, C = + 27iXA + 
then the two equations are +§ =0 
az*+bz+c=o, 
and the result of the elimination of Z will be 
(aZH yZ. + yZ2+ ^) = 0, 
where Z,, Z, are the roots of the equation AZ^+BZ-f C=0 ; that is, ue hare 
C® 
+ ay C(B-^-2AC) 
+ aB(-B®+2ABC) 
+/ CA^ 
-y^ BA^ 
A® 
