412] 
A MEMOIR ON CUBIC SURFACES. 
445 
Section XVIII = 12 - B, - 20,. 
Article Nos. 18Ö to 189. Equation WXZ + F 2 (X + Z) = 0. 
186. The diagram of the lines and planes are 
Planes are 
Y= 0 
0 
A=0 
01 
Z = 0 
02 
X + Z=0 
34 
w=o 
04 
B.-2G,. 
Ol\ H“ 1 
X 
H-» 
to 1 II 
1x6= 6 
1x4= 4 
2x8 = 16 
1 X 16 = 16 
• 
• 
Plane through the three axes. 
2x12 = 24 
• ■ 
Biplanes. 
lx 3= 3 
• 
* * 
Plane touching along edge and con 
taining the mere line. 
lx 2= 2 
5 45 
• 
* * 
Plane touching along axis through 
the two cnicnodes and containing 
the mere line. 
Mere line, being 
also a trans 
versal. 
Edge of the binode. 
Axis through the 
two cnicnodes. 
Axes, each through 
the binode and 
a cnicnode. 
where the equations of the lines and planes are shown in the margins. 
187. The mere line is facultative; the edge is also facultative counting twice (this 
will appear from the discussion of the reciprocal surface): b' = p'=3, t'= 1.