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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Proofs: 1

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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",, 2016