Definition: Def. 10.06: Second Binomial
And if the lesser term is commensurable in length with the rational (straight line previously) laid out then let (the whole straight line) be called a second binomial (straight line).
The second binomial is a straight line whose length is
where \(\alpha,\beta\) denote positive rational numbers.
Proofs: 1 2 3 4 5 6 7 8
Propositions: 9 10 11
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