Proposition: 7.16: Natural Number Multiplication is Commutative

(Proposition 16 from Book 7 of Euclid's “Elements”)

If two numbers multiplying one another make some (numbers) then the (numbers) generated from them will be equal to one another.

fig16e

Modern Formulation

see multiplication of natural numbers is commutative.

Proofs: 1

Proofs: 1 2 3 4 5


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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