Lemma: Lem. 13.13: Construction of Regular Tetrahedron within Given Sphere
(Lemma to Proposition 13 from Book 13 of Euclid's “Elements”)
It must be shown that as $AB$ is to $BC$, so the (square) on $AD$ (is) to the (square) on $DC$.
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Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"