# Definition:Euclid's Definitions - Book V/17 - Ratio Ex Aequali

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## Definition

In the words of Euclid:

*A***ratio ex aequali**arises when, there being several magnitudes and another set equal to them in multitude which makes two and two are in the same proportion, as the first is to the last among the first magnitudes, so is the first to the last among the second magnitudes;

Or, in other words, it means taking the extreme terms by virtue of the removal of the intermediate terms.

(*The Elements*: Book $\text{V}$: Definition $17$)

## Sources

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 2*(2nd ed.) ... (previous) ... (next): Book $\text{V}$. Definitions