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Proposition: Prop. 9.32: Power of Two is Even-Times Even Only

(Proposition 32 from Book 9 of Euclid's “Elements”)

Each of the numbers (which is continually) doubled, (starting) from a dyad, is an even-times-even (number) only.

• For let any multitude of numbers whatsoever, $B$, $C$, $D$, have been (continually) doubled, (starting) from the dyad $A$.
• I say that $B$, $C$, $D$ are even-times-even (numbers) only.

Modern Formulation

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Table of Contents

Proofs: 1

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References

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", https://proofwiki.org/wiki/Main_Page, 2016