Proposition: 7.01: Sufficient Condition for Coprimality
Euclid's Formulation
Two unequal numbers (being) laid down, and the lesser being continually subtracted, in turn, from the greater, if the remainder never measures the (number) preceding it, until a unit remains, then the original numbers will be prime to one another.
 For two [unequal] [numbers]bookofproofs$2315, $AB$ and $CD$, the lesser being continually subtracted, in turn, from the greater, let the remainder never measure the (number) preceding it, until a unit remains.
 I say that $AB$ and $CD$ are prime to one another  that is to say, that a unit alone measures (both) $AB$ and $CD$.
Modern Formulation
See coprime numbers.
Table of Contents
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References
Bibliography
 Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition
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