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18.

Prove that, if r be either semi-axis of the curve repre

sented by the equation

ua2 + vß3 + wy2 + Qu′ By + 2v′ ya + 2w′ aß = 0,

the values of r will be the roots of the equation

a2

+

b

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{u+% (au'—bv'—cw')}r2—as cos A {v + (bv' ́-cw' — au')}r" —bscos B

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ça

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{w + 2 (cw' — au'′ – bv') } r2 – cs cos C

ab

0,

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