1898 - 99 .] Mr E. J. Hanson on a Set of Quadrics. 
357 
FG'H" or AB'C" so that as in § 6 the eliminant reduces to either 
FG'H" A or AB'C" A'. 
8. An interesting special case is that of the equations 
fx 2 + ayz - hzx - gxy = 0 
gif - hyz + bzx - fxy = 0 
hz 2 — gyz —fzx + cxy — 0 
( 7 ) 
associated with Sylvester’s classical elimination problem. 
To adapt the preceding results to this case we must replace 
a, b\ c',f, g, h,f, g, g", h" 
respectively by 
/» 9> h a , -K -g, \ -f, -g, -/, c. 
Making this change and denoting by A, B, etc., the co-factors of 
a , b, etc., in 8 where 
3 = 
the determinant (3) or (4) becomes 
aA 
bB. 
cG 
aK 
6B 
cF 
aGc 
b¥ 
cC 
and is therefore equal to abcS 2 . Hence restoring the literal portion 
of the factor omitted in § 6 the eliminant of (7) is abcfgJiB 2 . 
9. Again by making the substitution of the preceding section 
the determinant (6) becomes 
( 8 ) 
a 
. • • / 
-g -h 
. 
a -h f 
-g 
g 
-h b 
-f 
. & -/ 
g -h 
h -f c 
-g 
-g 
h 
c -f 
afg afh bgh bgf chf 
ing rows 1, 2, 3, 4, 5, 6 by 
ehg S - Qfgh 
fg, ¥, g\fg, ¥, 
