Proposition: Prop. 9.16: Two Co-prime Integers have no Third Integer Proportional

Euclid's Formulation

If two numbers are prime to one another then as the first is to the second, so the second (will) not (be) to some other (number). * For let the two numbers $A$ and $B$ be prime to one another. * I say that as $A$ is to $B$, so $B$ is not to some other (number).


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!



Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016