- For let the medial (straight line) $BC$, which is commensurable in square only with $AB$, and which makes with $AB$ the rational (rectangle contained) by $AB$ and $BC$, have been subtracted from the medial (straight line) $AB$ [Prop. 10.27].
- I say that the remainder $AC$ is an irrational (straight line).
- Let it be called the first apotome of a medial (straight line).

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

\[\delta^{1/4} - \delta^{3/4},\]

for some positive rational number \(\delta\). See also [Prop. 10.37].

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