Definition: Def. 10.10: Sixth Binomial

(Definition 10 from Book 10 of Euclid's “Elements”)

And if neither (term is commensurable), a sixth (binomial straight line).

Modern Formulation

The sixth binomial is a straight line whose length is \[\sqrt{\alpha}+\sqrt{\beta},\] where \(\alpha,\beta\) denote positive rational numbers.

Proofs: 1 2 3 4 5 6 7 8
Propositions: 9 10 11

Thank you to the contributors under CC BY-SA 4.0!



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",, 2016