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](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book07/fig04e.png?raw=true)
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
Table of Contents
Proofs: 1
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Proofs: 1
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References
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