59] ON THE THEORY OE ELIMINATION. 373 
equations, however, which are not independent, but are connected by 
a"of V + b'Y V + cV W + l"yz V + m"zx V + n"xy V 
— (a'x 2 W + b'y- W + dz 2 W + I'yz W + m'zx W + n'xy W) = 0, 
ax 2 W + by- W + cz 2 W + lyz W + mzx W + nxy W 
- (a"a? U + b"f- U + c"z 2 U + l”yz U + m"zx U + n"xy U) = 0, 
a'x 1 U + b'y 2 U + d z 1 U + I’yz U + m'zx U + n'xy TJ 
— (ax 2 V + by 2 V + cz 2 V + lyzV + mzxV + nxyV) = 0. 
Arranging these coefficients in the required form, we have the following value of V. 
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