50 
MR. H. M. TAYLOR OX A SPECIAL FORM OF THE 
which may be written 
abydk^jjL^ ■ 
- {aa.h/3 + aoicy + aadS + b/Scy + b^dS + cydB 
— CM — 6/3 — cy — dB “hi) “h ct/BcB = 0. 
§ 7. Next we will find the equations of the lines 18 and 19, which meet the lines 
1 , 5 , 8 , 12 . 
Any line intersecting' 1 and 12 is represented by equations of the form 
X — oT = Xy 
r. - dT 
vz 
(18) or (19). 
Since this line intersects (5), whose equations are 
y — 6T = 0 
u = 0 
the equations 
— x + {a/b + X) y = 0 
d/b y vz = 0 
ux + {ft — 1/6) y yz = 0 
are simultaneously true. 
Hence 
— 1 
a 
X “h ct/6 
djb 
ft-^lb 
V 
y 
= 0 . 
Ag’ain, because this line intersects (8), whose equations are 
the equations 
r _ cT = 0 
X — 0 
Xy fi- ajc z 
{v “h d/c) z — u 
ftu + (r - ^ h) 2= + Sr 
0 
0 
0 
are simultaneously true. 
Hence 
ft 
ajc 
V “h djc — 
y — I /c 
1 = 0. 
7 - 
8 
