Proposition: 7.21: Coprime 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.
* Let $A$ and $B$ be numbers prime to one another.
* I say that $A$ and $B$ are the least of those (numbers) having the same ratio as them.
Modern Formulation
If $\frac{A}{B}$ is a reduced fraction, i.e. $A$ and $B$ are coprime, 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 BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016