Definition: Def. 10.09: Fifth Binomial
And if the lesser (term is commensurable), a fifth (binomial straight line).
Modern Formulation
The fifth binomial 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 8
Propositions: 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