Proposition: Prop. 8.24: If Ratio of Square to Number is as between Two Squares then Number is Square
(Proposition 24 from Book 8 of Euclid's “Elements”)
If two numbers have to one another the ratio which a square number (has) to a(nother) square number, and the first is square, then the second will also be square.
* For let two numbers, $A$ and $B$, have to one another the ratio which the square number $C$ (has) to the square number $D$.
* And let $A$ be square.
* I say that $B$ is also square.
Modern Formulation
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Table of Contents
Proofs: 1
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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