Proposition: Prop. 9.22: Sum of Even Number of Odd Numbers is Even

(Proposition 22 from Book 9 of Euclid's “Elements”)

If any multitude whatsoever of odd numbers is added together, and the multitude of them is even, then the whole will be even. * For let any even multitude whatsoever of odd numbers, $AB$, $BC$, $CD$, $DE$, lie together. * I say that the whole, $AE$, is even.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1

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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