Proposition: Prop. 8.16: Number does not divide Number iff Square does not divide Square
(Proposition 16 from Book 8 of Euclid's “Elements”)
If a square number does not measure a(nother) square number then the side (of the former) will not measure the side (of the latter) either. And if the side (of a square number) does not measure the side (of another square number) then the (former) square (number) will not measure the (latter) square (number) either.
 Let $A$ and $B$ be square numbers, and let $C$ and $D$ be their sides (respectively).
 And let $A$ not measure $B$.
 I say that $C$ does not measure $D$ either.
 So, again, let $C$ not measure $D$.
 I say that $A$ will not measure $B$ either.
Modern Formulation
(not yet contributed)
Table of Contents
Proofs: 1
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Fitzpatrick
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