76 PROCEEDINGS OF SECTION A. 
The axis of any point on the conic will pass through O, 
z.e., the generating point of any line through O will be a 
point on the required conic. 
Let LM be any line drawn through O cutting CB 
produced in a’ and construct a point a such that CaBd 
is a harmonic range; let LM meet AB produced in y’ 
and construct a point y.such that AyBy’ is a harmonic 
range. Let Adaand Cy intersect in #; then F isa point 
on the conic. 
§ 7. Let the equations of any two in-conics be 
Me ae B + wake O 
ei By Y1 
a, /B + /%=0 
ee dee | SA" Ye 
These conics may be regarded as the envelope of the 
axes of homology of points lying on the axes of homo- 
logy of a,B,y; and asBoyo respectively. Hence the 
fourth common tangent to these conics is the axis of the 
point of intersection of 
a) By Val 
ean: Y 
+7, +-—=0 
a Be Y2 : 
viz., of the aM 
aya: (Bry2 — Bayi), Bie (y1a2— y201), Yr72 (a182— a2f31), 
and the fourth common tangent 1s 
a 
Ms then (Bry = Boy) (3; i (y1a2 — a 
/ +. 5 ails = eee 
Tke* equations of the in-circle and ex-circles of the 
triangle of reference being written 
ee 
Oa 2A + 2b + 30> 
, 7 sec '— 
