Lemma: Lem. 12.02: Areas of Circles are as Squares on Diameters
(Lemma to Proposition 2 from Book 12 of Euclid's “Elements”)
So, I say that, area $S$ being greater than circle $EFGH$, as area $S$ is to circle $ABCD$, so circle $EFGH$ (is) to some area less than circle $ABCD$.
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Table of Contents
Proofs: 1 2 3 4
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"