ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 393 
ai 3- $8 as 38 
Bs Si 9 2 cs i al 0 a ei 508 
0+ : a 8 Thee gee 
2 tee i = 7 1-2) 
or, say, 
Das, Bee eee ain 1 nye a 
If we denote the first portion of the eliminant, viz. (0 +0’) A, by A, and the second 
portion by —B, and the alternative forms of these by A’ and — B’, we can thus express 
the eliminant in four different ways, viz. 
ea CN apy MKB AY BS 
(48) Using the cyclical substitution on the right-hand member of the immediately 
preceding identity, we see that we can put in place of it 
| 19 ie yO, 47’ 48 44" 
| =e set 9 at we Ss 
22 | 7 ; 4— | + So) sore 5 : 1-5 
| 39 33 69 66’ 
| mss aa 9 ae eae 
| 0 i 9 6 1 O+ 5 3 5 
Di 28’ 29/ 59 55’ 
ak Ea nae Sat 8 Pi es 
3 tne as q 4 
But the determinants here are those occurring in the left-hand member: consequently 
we deduce 
c 
aN OAT 
(49) Returning to § 46, and noting that A, has two columns in common with A,, 
and that the result of the cyclical substitution on A, is simply to change this pair of 
columns into another pair of A,, the third column remaining all the while unaltered, we 
see that 
(0+0)A, — D4A, 
