Proposition: Prop. 10.089: Construction of Fifth Apotome
(Proposition 89 from Book 10 of Euclid's “Elements”)
To find a fifth apotome.
Modern Formulation
This proposition proves that the fifth apotome has length
\[\alpha\,(\sqrt{1+\beta}-1),\]
where \(\alpha,\beta\) denote positive rational numbers.
Notes
See also [Prop. 10.52].
Table of Contents
Proofs: 1
Mentioned in:
Propositions: 1
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References
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016