Numbers whose Product is Square are Similar Plane Numbers

Theorem

 * If two numbers by multiplying one another make a square, they are similar plane numbers.

Proof
Let $a$ and $b$ be natural numbers such that $a b$ is square.

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

We have that $a b$ and $a^2$ are both square.

By Square Numbers are Similar Plane Numbers they are similar plane numbers.

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

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

The result follows from.