Product of Similar Plane Numbers is 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.