188 THE ROYAL SOCIETY OF CANADA 
ap Aa + (u — x) €o+ ves 
NARS ICV 
ind Q = SatHeto—Wes 
Ns Th oma 
As A” lies on BC and also on FG, 
if ind A” =xe+(1—x)e; 
then will {xeo+)1—x)es} {a+ (u—m)eo+ves} {ert wee t+ (v —m)es} =0 
: nos 1—-x|=0 

À pr-my 
NUE y—n 
m 
x= 
m—n 
ind A” = 2-75 
m—n 
Similarly it may be shown that 
Se ee, ere ee 
n—l l—m 
ind 0” = 8, ind PY = SSO nd Qe 
5 Care v—¢ p—x 
ind E” = 
Mmyp—nx)e+ { u(my —nx) +mx(n—y) }e+{v(mp—nx) —np(m—x) }es 
(A+u+y—m) (mp—nx)+(m—n) (m—x)} 
ind F” = 
(GmbH) —lo(n—) a tu(né Het {né — 1x) +ny(l—¢) }es 
(A+ut+try—n) (np—lp)+(n—l) (n—v)o 
ind G” = 
{A(x — me) +16(m—x) a+ { u(x — mo) —mx(l—$) }e+v(Ix —mo)es 
(A+utv—l) (x—m¢)+(—m) — (ld)x 
Also A”B” and O’P” intersect at R 
. if ind R=xind A”+(1—x)ind B’, 
 x(me —nes) us (1—x) (nes — le) 
m—n n—l 
t Aen hea er Oh = 
