GEOMETRY OF AN AXIS OF HOMOLOGY. 77 
and two others, the fourth common tangents to J, and 
I, Th, Tare 
Log = aa + (6 — c)(B — y) =0 
Inn = 6B + (ec — a/(y — a) =0 
In, = cy + (a — b)(a ~ B) = 0. 
These lines intersect in the points 
cos ae sin Ca cos B sin Bre A cos ¢ 
oe B >, 2 2 
sin C-8 cos z cos 2B sin A= B cos c 
2 9? Di 2 eo 
sin Bae cos A Sl Bi cos B cos oo 
2, go? oy a 6 
These points, the vertices of the triangle of reference, 
the centre of the in-circle and the point 
24 2B 20 
( cos =u GU =e GOs =) 
2 2 2 
all le on the conic 
pends — GC 3A See tA 3B 
sin — —— Cos — sin ——— COs — 
2 2 a: 2 2 
a B 
eae, | B G! 
sin Cob A= 0 
§ 8. The conic S; will be a parabola if 
1 1 ] 
aa, + bBo ae CY6 wth 
ie. if agBoyo lie on the Steiner eHipse, 
cosec Md cosec B_ cosec C 
egeemecn es =0. 
a p ue 
The equation of the directrix of the parabola being ARR E eS 
a p x 0, 
a, tan A a 3, tan B Si yocuatine. on 
the directrix may be regarded at the axis of homology 
of a point D, whose coordinates are (a) tan A, (3, tan B, 
Yo tan C) 
