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 :
 * $\tuple {c^2, c d, d^2}$

is a geometric sequence.

From :
 * $\tuple {a, m, b}$

is a geometric sequence for some $m$.

We have that $a$ is a square number.

From :
 * $b$ is a square number.