Proposition: Prop. 8.14: Number divides Number iff Square divides Square
(Proposition 14 from Book 8 of Euclid's “Elements”)
If a square (number) measures a(nother) square (number) then the side (of the former) will also measure the side (of the latter). And if the side (of a square number) measures the side (of another square number) then the (former) square (number) will also measure the (latter) square (number) .
 Let $A$ and $B$ be square numbers, and let $C$ and $D$ be their sides (respectively).
 And let $A$ measure $B$.
 I say that $C$ also measures $D$.
 So, again, let $C$ measure $D$.
 I say that $A$ also measures $B$.
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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