Proposition: Prop. 13.13: Construction of Regular Tetrahedron within Given Sphere
(Proposition 13 from Book 13 of Euclid's “Elements”)
To construct a (regular) pyramid (i.e., a tetrahedron), and to enclose (it) in a given sphere, and to show that the square on the diameter of the sphere is one and a half times the (square) on the side of the pyramid.
Modern Formulation
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Notes
If the radius of the sphere is unity then the side of the pyramid (i.e., tetrahedron) is \[\sqrt{\frac 83}.\]
Table of Contents
Proofs: 1
 Lemma: Lem. 13.13: Construction of Regular Tetrahedron within Given Sphere
Mentioned in:
Proofs: 1
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016