102 ON A FORMULA OF ELIMINATION. [733 
contain each of them the factor ©x©.,, that is, V; they, in fact, each of them vanish 
if ©x = 0, and they also vanish if © 2 = 0; or, by a direct substitution, we have 
xz - f> = e s y B,®„ = - A<e,e„ 
(yi ^2/ 
XW-YZ= „ -(¿i-W^ + fl,)«!©.. =-^L 4 ©x© 2 (^ + ^), 
YW — Z 2 = „ — (<9x — 0 2 ) 2 ^ x (9 2 ©i© 2 , =-J. 4 ©x© 2 ^ 2 . 
Or, what is the same thing, these are = — AV, 2J5V, — (7 V, respectively; thus the 
first equation is 
{3A 2 c - 6ABb +(-AG + 4B 2 ) a} {245(2 - 34(7c + (7 2 a| 
— (— A 2 d + 34(76 — 2BOa) 2 = — A (A 3 d 2 + &c.), = — A V ; 
and similarly for the other two equations. The nodal curve is thus given by the 
twofold system X = 0, Y= 0, Z = 0, W = 0. 
The method may be extended to the case where, instead of the quadric equation 
{A, B, C][6, l) 2 = 0, we have an equation of any higher order, but the formulae are 
less simple.