Definition:Alternate Ratio

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Let $a : b$ and $c : d$ where $a : b$ denotes the ratio of $a$ to $b$.

Then the alternate ratio is defined as $a : c$ and $b : d$.

In the words of Euclid:

Alternate ratio means taking the antecedent in relation to the antecedent and the consequent in relation to the consequent.

(The Elements: Book $\text{V}$: Definition $12$)