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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)

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

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016