If Ratio of Square to Number is as between Two Squares then Number is Square

Theorem
Let $a, b, c, d \in \Z$ be integers such that:
 * $\dfrac a b = \dfrac {c^2} {d^2}$

Let $a$ be a square number.

Then $b$ is also a square number.

Proof
From :
 * $\left({c^2, c d, d^2}\right)$

is a geometric progression.

From :
 * $\left({a, m, b}\right)$

is a geometric progression for some $m$.

We have that $a$ is a square number.

From :
 * $b$ is a square number.