165] A TRIANGLE CIRCUMSCRIBED ABOUT A CONIC. 
Hence the equation of the line joining the two simple points of intersection is 
33 
[165’ 
e points 
îe conic 
larmonic 
ied the 
simple 
r, Avhat 
ìe line 
or expanding and reducing 
X , 
y . 
z 
1 
1 
1 
Pa’ 
Qb’ 
Rc 
a 
b 
c 
P ’ 
Q ’ 
R 
P%x + Qrjy + RÇz = 0. 
The equation of the tangent to the conic at the common point of intersection is 
evidently 
Px + Qy+ Rz = 0. 
The last-mentioned lines, together with the harmonic lines (r), (s), viz. the lines 
ax + by + cz = 0, 
+ 
y z „ 
T+ - = o, 
b c 
may be considered as the sides of an inscribed quadrilateral; the equation of the conic 
must therefore be expressible in a form in which this is put in evidence; to do this, 
I first form the equation 
“ + ^H(s + ! + ;) = ^ +ÿ,+2!,_2 ( 1_ f!) 
yz - 
zx — 2 
which may also be written 
where 
ax + by + cz} +1 + ^ = x 2 + y 2 + & - 2\yz - 2yzx - 2vxy, 
and then putting 
an equation which gives 
x —ssr - 
lx = 
F+F-y* 
2& 
i; 2 + if— Ç 2 
2 fT 
A=p+^+^-2i7C-2gf-2|^, 
C. III. 
A = P 2 — 4 rjt, 
= Q 2 - 
= R 2 — 4 ¡¿7], 
5