Product of Similar Plane Numbers is Square

Theorem

 * If two similar plane numbers by multiplying one another make some number, the product will be square.

Proof
Let $a$ and $b$ be similar plane numbers.

From :
 * $a : b = a^2 : a b$

From there exists one mean proportional between $a$ and $b$.

From there exists one mean proportional between $a^2$ and $a b$.

From it follows that $a b$ is square.