# Definition:Geometric Mean/Mean Proportional/General Definition

## 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.