◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--9-number-theory-applications / Proposition: Prop. 9.34: Number neither whose Half is Odd nor Power of Two is both Even-Times Even and Even-Times Odd

Proposition: Prop. 9.34: Number neither whose Half is Odd nor Power of Two is both Even-Times Even and Even-Times Odd

Euclid's Formulation

If a number is neither (one) of the (numbers) doubled from a dyad, nor has an odd half, then it is (both) an even-times-even and an even-times-odd (number).

• For let the number $A$ neither be (one) of the (numbers) doubled from a dyad, nor let it have an odd half.
• I say that $A$ is (both) an even-times-even and an even-times-odd (number).

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

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

Github:

non-Github:

@Fitzpatrick

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