#942 · Algebra · Linear equations

Quadratic ratios from cyclic definitions

If $x = cy + b z, y = a z + c x, z = b x + a y$ , show that $\frac{x ^{2}}{1 - a ^{2}} = \frac{y ^{2}}{1 - b ^{2}} = \frac{z ^{2}}{1 - c ^{2}}$ .

~11 minProof · checked by AIcyclic equationsratios

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 18

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