— 
78 PROCEEDINGS OF SECTION A. 
Hence as O (a,Poyo) moves on the Steiner ellipse, the 
generating point WY of the directrix will move on the 
conic 
sec A sec B sec C 
ee 0, 
p "y 
a 
a conic to be afterwards referred to as the secant-conic,. 
and it may be at once verified that the focus 
F (ay sin *A, By sin ?.B, y) sin? C) will trace out the 
circum-circle of the triangle of reference. 
The line joining O and D has for equation 
* cos A sin (B — C) + Bai atte’ 2 A) 
Ao Bo 
+. cos Csin (A — B) = 0; 
0 
this line passes through the point P,, whose coordinates. 
are 
cosec 2A cosec 2B cosec 2C 
sin(B — C) sm(C — A)’ sin(A — B) 
The line joining O and F has for equation 
* sin A sin (B— C) + p sin B sin (C — A) 
ao Bo 
- Y sin (Cin A — B) =o 
- Yo 
and passes through the fixed point P, whose coordinates 
are 
cosec * A cosec *B cosec > C 
sin(B — Cy) sin (C— AY. sin (A — BY 
The line joining F and D has for equation 
cot A sin (B— C) + ping Were mes 
do Bo 
+ ~ cot Csn(A — B)=0 
Yo 
and passes through the fixed point P3 whose coordinates 
are ; 
sec A sec B sec C 
sin (B — C)’ sn (C —- A)’ sin (A —B) 
