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 $CD$.

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