Proposition: 7.26: Product of Coprime Pairs is Coprime
(Proposition 26 from Book 7 of Euclid's “Elements”)
If two numbers are both prime to each of two numbers then the (numbers) created from (multiplying) them will also be prime to one another.
Modern Formulation
Let $A$ and $C,$ $B$ and $C,$ $A$ and $D,$ $B$ and $D$ be coprime. Then $AB$ is coprime to $CD.$
Table of Contents
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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