386
A MEMOIR ON CUBIC SURFACES.
[412
50. And the coordinates of the 21 distinct lines are
(a)
(b)
<*) !
(/)
(9)
(h)
whence equations may be taken to be
l
0
0
0
- 1
1
(1)
X=0, Y+ IZ = 0
0
m
0
1
0
- 1
(3)
Y= 0, Z + mX = 0
0
0
n
- 1
1
0
(5)
Z = 0, X+ nY= 0
r 1
0
0
0
-1
1
(2)
o
II
N
T
+
N
o
II
N
0
m _1
0
1
0
-1
(4)
7 = 0, Z + m~ 1 X= 0
0
0
-1
1
0
(6)
Z = 0, X+ n~ l Y= 0
1
n
m
0
m
Jy
n
~Wy
(45)
X+ nY + mZ= 0, X + /3y\V=Q
n
1
l
l
ya
0
n
ya
(16)
Y+ lZ + nX = 0, Y + ya ]V = 0
m
l
1
l
a/3
m
ay3
0
(23)
Z + mX+ IY= 0, Z + a/3W=0
1
1
n
m
0
VI
a8
1
wa8
(46)
X+ n~ 1 Y + mZ = 0, X-a8IY=0
n
1
1
l
1
l{38
0
n
"y8S
(26)
Y+ l~ 1 Z + nX= 0, r-yS31F=0
1
m
l
1
l
y8
1
my8
0
(24)
Z +m" 1 A+ ¿7=0, y8JY=0
1
n
1
m
0
1
maS
n
a8
(35)
X+ nY + m~ 1 Z= 0, X-a8W=0
1
n
1
l
l
/38
0
1
n/38
(15)
o
II
OO
CQ-
1
KS
o'
II
H
1
§
+
N
+
m
1
7
1
1
ly8
m
7 8
0
(13)
Z + mX + T 1 7=0, Z- y 8W=0
1
1
n
1
m
0
1
m/3y
1
n(3y
(36)
X+ n~ l Y + vi~ l Z = 0, X + (3yW= 0
1
n
1
1
7
1
lya
0
1
nya
(25)
7 + l~ 1 Z+n~ 1 X= 0, 7+yaJF=0
1
m
1
7
1
1
la(3
1
mya
0
(14)
^ + w“ 1 X+ r i F=0, Z + a/3W=0
1
0
0
0
0
0
(12)
h
it
o
il
o
0
1
0
0
0
0
(34)
7 = 0, T7 = 0
0
0
1
0
0
0
(56)
N
ll
©
ll
o