Proposition: Prop. 9.23: Sum of Odd Number of Odd Numbers is Odd

Euclid's Formulation

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


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2

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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