Lemma: Lem. 11.23: Making a Square Area Equal to the Difference Of Areas of Two Other Incongruent Squares

(Lemma to Proposition 23 from Book 11 of Euclid's “Elements”)

And we can demonstrate, thusly, in which manner to take the (square) on \(OR\) equal to that (area) by which the (square) on \(AB\) is greater than the (square) on \(LO\).

Modern Formulation

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Proofs: 1

Proofs: 1

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Adapted from (subject to copyright, with kind permission)

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