Definition:Duplicate Ratio

Definition
Let $a, b, c$ be magnitudes such that:
 * $a : b = b : c$

Then $a$ has the duplicate ratio to $c$ of the ratio it has to $b$.

That is:
 * $a : c$ is the duplicate ratio of $a : b$.

From definition of ratio:

That is:
 * $a : c = \paren {a : b}^2$