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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)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

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