Corollary: Cor. 10.009: Commensurability of Squares

(related to Proposition: Prop. 10.009: Commensurability of Squares)

(Corollary to Proposition 9 from Book 10 of Euclid's “Elements”)

And it will be clear, from (what) has been demonstrated, that (straight lines) commensurable in length (are) always also (commensurable) in square, but (straight lines commensurable) in square (are) not always also (commensurable) in length.

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"