GEOMETRY OF AN AXIS OF HOMOLOGY (ee 
equation of the pair of tangents to S, from aPiyi 
becomes 
] 
i 1 
LF ERAS estas BeOS Bh ae ee 
ay (By: — Bry) * Bo Cyn = ria) * Yo (afi — au) 
These lines are mutually perpendicular if 
Cos A Cos B Cos C 
pres Be Toes ae Os 
ag Bo 
SF C Cos B 
a Bmn(— + + 
Bo 
Cos a Cos ei 1 
= =\= 0. 
a1 (3; iz Bo ai Yo 
Hence the ten of the director-cirele of Sj is 
Cos A 
2S By( + 
This may be reduced to the oe 
(By sin A + yasin B + asin C) 
ee C++) 
eae yia1 
> a? 
=e Cos B 
@) rs a8 
Yo 
Ea ee in 
a sin A * 3 sn B v Yo sin c) 
— (asind + PsinB + y sin C) 
a B Ue jeatt 
eo tan A + 2B, tan B ai Yo tan c) The 
showing that the radical axis of the director-circle 
of S§; and of the circum-circle of the triangle of reference 
is the axis of homology of 
(ay tan A, By tan B, yp tan C). 
The equation of the pair of tangents to S, from apBoyo 
takes the form 
dp a-ak 
a FOBe w? 1) Ge a + ae) rE 
§ 6. Given five points on a conic, to construct the 
conic. 
Take any three of the points ABC as a triangle of 
reference and let the axes of homology of the remaining 
points D, E with respect to this triangle intersect in O. 
