Full text: The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., sadlerian professor of pure mathematics in the University of Cambridge (Vol. 6)

412] 
A MEMOIR ON CUBIC SURFACES. 
403 
Section V = 12 — jB 4 . 
Article Nos. 85 to 94. Equation WXZ + (X + Z)(Y> - ctX> - bZ*) = 0. 
85. The diagram of the lines and planes is 
Lines. 
bd bO h-» 
V=12-£ 4 . 
12 
1'2' 
11' 
12' 
21' 
22' 
11'. 22' 
12'. 21' 
2x12 = 24 
lx 3= 3 
4 x 4 = 16 
86. The planes are 
Biplanes containing 
rays 1, 2 and 1', 2' 
respectively. 
Plane touching along 
edge and contain 
ing the transversal. 
Biradial planes each 
containing a ray 
of the one and a 
ray of the other 
biplane. 
Planes each through 
the transversal. 
z = o, 
[12] 
Z =0, 
[l'2 r \ 
X + Z= 0, 
[0] 
-XVa+Y-ZVb = 0, 
[HI 
XVâ+ Y — Z Vb = 0, 
[121 
-XVa+Y+ZVb = 0, 
[211 
XVa+Y+ZVb = 0, 
[221 
Vrí(X + Z)+ W = 0, 
[ir.221 
— 2 Vab (X + Z)+ W = 0, 
[12'. 21']. 
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