74 PROCEEDINGS OF SECTION A. 
The equation of the axis of the Symmedian point, 
Eee 
is satisfied by 
( — 2a, b,c) (a, — 2b, c) (a, b, — 2c). 
Let the lines joining the vertices of the triangle 4A BC 
to the Symmedian point meet the circum-circle of the 
triangle in A’B’C’; then the sides of the triangle 
A’ B’C’ touch the Brocard ellipse. For the coordinates 
of A’ B’C’ are respectively 
b 
(-$2<) (a, —5.¢) (a, »,— 5), 
and the equation of BC” is 
a 
REN ea 
Sea aes Gece 
c 
i.e., B’C’ is the axis of homology of (— 2a, 6, ¢), a point 
on the axis of homology of the Symmedian point. 
§.5. Since the axis of homology of any point on the 
conic 
AY Si. Bi ge TRE 
G2 pS ay 
passes through a,/3,y,, it follows that the axes of the 
two points in which Ju = 0 cuts this conic are the pair 
of tangents which may be drawn to the conic S, from 
aj 2171 
Let a’B’y’ be the coordinates of such a point of inter- 
section ; the axis of this point is 
a 
S++ 4=0 
In addition, 
a 
H 4h + Um 
/ / / 
ao Bo Yo 
Hence etl B B a a: as; — a3 
Cys Ai eh _ ‘ya; — : — 
a p’ 7 V1 ey en y V1 1 1 
and substituting in the last of the above relations, the 
