Proposition: 7.21: Co-prime Numbers form Fraction in Lowest Terms
Euclid's Formulation
Numbers prime to one another are the least of those (numbers) having the same ratio as them.
![fig21e](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book07/fig21e.png?raw=true)
Modern Formulation
If $\frac{A}{B}$ is a reduced fraction, i.e. $A$ and $B$ are co-prime, then from all pairs of numbers having the same ration, $A$ and $B$ are the smallest.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9 10 11
Propositions: 12
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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