Definition:Separation of Ratio

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Definition

Let $R = a : b$ be a ratio.

Then the separation of $R$ is the ratio $a - b : b$.


In the words of Euclid:

Separation of a ratio means taking the excess by which the antecedent exceeds the consequent in relation to the consequent by itself.

(The Elements: Book $\text{V}$: Definition $15$)