500 
[371 
371. 
ON A FORMULA FOR THE INTERSECTIONS OF A LINE AND 
CONIC, AND ON AN INTEGRAL FORMULA CONNECTED 
THEREWITH. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. vn. (1866), pp. 1—6.] 
In a letter to me, dated 15 May, 1862, Mr Spottiswoode has extracted from an 
unpublished Memoir, and he has kindly permitted me to communicate, the following 
formula for the points of intersection of a line and conic; viz. if the equations of the 
line and conic are 
+ ny + K z = 0, 
and if 
(a, b, c, f g, hrfx, y, zj = 0 ; 
6°~ = 
V> 
£> v, K 
a, h, g 
h b, f 
L 9, f c 
or, what is the same thing, if 
0 2 = -(M, B, C, F, G, y, O 2 , 
where A = be — / 2 , &c. as usual; then the coordinates (x, y, z) of a point of intersection 
of the line and conic are found from the linear equations 
(gy-h£-0)x + (f V -b{X )y + (crj- ft )z = 0, 
9% )“> + №-/%- 0)y + (gZ-ci; )z = 0, 
(kg-ay )x + (bi;-hy )y + (fg-g v -0)z = 0,