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
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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