# Definition:Geometric Mean/Mean Proportional/General Definition

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## Definition

In the language of Euclid, the terms of a (finite) geometric progression of positive integers between (and not including) the first and last terms are called **mean proportionals**.

## Historical Note

This extension of the definition of a mean proportional is never made specifically in Euclid's *The Elements*, but introduced without definition in Between two Cubes exist two Mean Proportionals.

In the words of Euclid:

*To three given straight lines to find a fourth proportional.*

(*The Elements*: Book $\text{VI}$: Proposition $12$)