Commentary on Proposition IX.1

Back to Proposition IX.1.

[Folio 0390 | p. 384]

The product of two similar plane numbers is a square.

Let $a$, $b$ be two similar plane numbers.

Now

$$a : b = a^2 : ab. \hfill \text{[VII. 17]}$$

And between $a$, $b$ there is one mean proportional. [VIII. 18]

Therefore between $a^2 : ab$ there is one mean proportional. [VIII. 8]

And $a^2$ is square; therefore $ab$ is square. [VIII. 22]