Commentary on Proposition VIII.24

Back to Proposition VIII.24.

[Folio 0386 | p. 380]

If $a : b = c^2 : d^2$, and $a$ is a square, then $b$ is also a square. For $c^2, d^2$ have one mean proportional $cd$. [VIII. 18]

Therefore $a, b$, which are in the same ratio, have one mean proportional. [VIII. 8]

And, since $a$ is square, $b$ must also be a square. [VIII. 22]