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 $B$.

fig14e