- For let the medial (straight line) $CB$, which is commensurable in square only with the whole, $AB$, and which contains with the whole, $AB$, the medial (rectangle contained) by $AB$ and $BC$, have been subtracted from the medial (straight line) $AB$ [Prop. 10.28].
- I say that the remainder $AC$ is an irrational (straight line).
- Let it be called a second apotome of a medial (straight line).

A second apotome of a medial (straight line) is a straight line whose length is expressible as

\[\alpha^{1/4}-\frac{\sqrt{\beta}}{\alpha^{1/4}},\]

where $\alpha$ and $\beta$ are positive rational numbers. See also [Prop. 10.38].

Proofs: 1

Proofs: 1 2 3 4

Propositions: 5 6

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

**Prime.mover and others**: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016