72 PROCEEDINGS OF SECTION A. 
ON THE GEOMETRY OF AN AXIS OF 
. HOMOLOGY. 
By Eveuyn G. Hoae, M.A. 
- . o . 
§1. Given a triangle ABC’ and a point O whose 
triimear coordinates are apoyo, the equation of its axis 
of homology with reference to the triangle is 
y 
La 0 
i) Bo Yo 
The axis of homology of any point (a/B’y’) on Z will 
be 
B 
a Y 
af + p’ = / == (peo cee veelesiois we (1) 
subject to the relation 
/ / / 
py erage een: 
a Po - Yo : 
The envelope of (1) is the in-conic 
ie ee ei), 
A * 0 Yo 
a conic having double contact with the conic 
Y Ao Bo Yo 
95 ae ae ee 
2 3 Y ’ 
a 
along the line L = 0. 
The coordinates of the intersection of Z and Sy, are 
(ao, W3o5 w*7o) (aos w[3o5 Wyo), Where w is one of the 
imaginary cube-roots of unity. 
§2. Let dO, BO, CO, meet the axis of homology of 
O in A,B,C, respectively ; the coordinates of Ay ByCy 
are respectively 
(== Beaty, Bo, Yo) (ao, =a 21355 Yo) (ao; Bo erie 270) 
and the axes of homology of Ay By Cy are respectively 
~ 
to 
| 
| 
|| 
bo| 
2 
ae 
| 
| 
(=) 
S 
2 
Ke) 
