Definition: Def. 10.15: Fifth Apotome
(Definition 15 from Book 10 of Euclid's “Elements”)
And if the attached (straight line is commensurable), a fifth (apotome).
Modern Formulation
The fifth apotome is a straight line whose length is \[\alpha\,(\sqrt{1+\beta}1),\]
where \(\alpha,\beta\) denote positive rational numbers.
Mentioned in:
Proofs: 1 2 3 4 5 6 7
Propositions: 8 9 10 11
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016