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.
* Let $A$ and $B$ be two numbers.
* And let $A$ make $C$ (by) multiplying $B$, and let $B$ make $D$ (by) multiplying $A$.
* I say that $C$ is equal to $D$.
see multiplication of natural numbers is commutative.
Table of Contents
Proofs: 1 2 3 4 5
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016