492] 
29 
2 = 0. 
[491 
the same torus may be 
; the axis 00'. 
5 through the axis, the 
conics, intersecting the 
mrface having as before 
illy situate intersections 
iregoing form, but it is 
of the torus here is 
2 
492. 
NOTE ON A SYSTEM OF ALGEBRAICAL EQUATIONS. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. xi. (1871), 
pp. 132, 133.] 
Consider the system of equations 
a + b(y -1- zf + cy"z 2 = 0, 
a + b (z + xf + cz 2 x 2 = 0, 
a + b (x 4- yf + cPy 1 = 0, 
which is a particular case of that belonging to the porism of the in-and-circumscribed 
triangle. We have y and z the roots of 
consequently 
a + bx- + 2u .bx + v?(b + cx 2 ) = 0 ; 
— 2 bx 
y+ z = 
b + coc 2 ’ 
a + bx 2 
or substituting in the equation between y and 2, this becomes 
(ac + 6 2 ) (a + 4<bx° + cx 4 ) = 0, 
so that if ac + b 2 is not = 0, we have 
a + M>x- + cx 4 =0,