Proposition: 7.04: Smaller Numbers are Dividing or not Dividing Larger Numbers

Euclid's Formulation

Any number is either part or parts of any (other) number, the lesser of the greater. * Let $A$ and $BC$ be two numbers, and let $BC$ be the lesser. * I say that $BC$ is either part or parts of $A$.

fig04e

Modern Formulation

For two positive integers $0 < a < b$ we have either $a\mid b\wedge a\neq b$ or $a\not\mid d.$

Notes

Proofs: 1

Proofs: 1


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

Github:
bookofproofs
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