Lemma: Lem. 10.021: Medial is Irrational

(Lemma to Proposition 21 from Book 10 of Euclid's “Elements”)

If there are two straight lines then as the first is to the second, so the (square) on the first (is) to the (rectangle contained) by the two straight lines. * Let $FE$ and $EG$ be two straight lines. * I say that as $FE$ is to $EG$, so the (square) on $FE$ (is) to the (rectangle contained) by $FE$ and $EG$.


Modern Formulation

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Proofs: 1

Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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Adapted from (subject to copyright, with kind permission)

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