180 THE ROYAL SOCIETY OF CANADA 
and —+—+-—= 
will be the line equation of P. 
VII. Given the triangle ABC and a coplanar point P, to locate 
the; polar of P with respect to ABC. 
Construct 
BC .AP=A’, CA. BP=B’ and AB. CP=C’, 
BC . B’C’=A’, CA. C’A’=B” and AB. A’B’=C’, 
then will A”, B”, C” be collinear on the polar of P. 
/ / / " " 
Let a, €2, 63, €'1, €, €’'3 €’1, €’2 

(AC!) _w 
(C'B) \ 
(BA')_»’ 
(AC) ow’ 
(CB) _ 
(B'A) » 
(G'A) J (A'B) _" (BC) _ 



(C’B) m (A’C) , (B’A) 
heal a 2 eee 
Na ew 
and = ule + ves Spe N'a + v'es 
y” + y! : x! + y! 
aad 3 = wees =xe+(1—x)e: 
m—l 
Sp NIED eh i ote 
m—-l N+ m—-l pity’  y'+v! 
ib cea 
m y’ 
and e”; be the indices of A, B, 
C; A’, B,C’, A" Band ts 
respectively, and let 
’ 
