(related to Proposition: Prop. 10.024: Rectangle Contained by Medial Straight Lines Commensurable in Length is Medial)

- For let the rectangle $AC$ be contained by the medial straight lines $AB$ and $BC$ (which are) commensurable in length.
- I say that $AC$ is medial.

- For let the square $AD$ have been described on $AB$.
- $AD$ is thus medial [see previous footnote].
- And since $AB$ is commensurable in length with $BC$, and $AB$ (is) equal to $BD$, $DB$ is thus also commensurable in length with $BC$.
- Hence, $DA$ is also commensurable with $AC$ [Prop. 6.1], [Prop. 10.11].
- And $DA$ (is) medial.
- Thus, $AC$ (is) also medial [Prop. 10.23 corr.] .
- (Which is) the very thing it was required to show.∎

**Fitzpatrick, Richard**: Euclid's "Elements of Geometry"