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Proposition: Prop. 13.14: Construction of Regular Octahedron within Given Sphere

(Proposition 14 from Book 13 of Euclid's “Elements”)

To construct an octahedron, and to enclose (it) in a (given) sphere, like in the preceding (proposition), and to show that the square on the diameter of the sphere is double the (square) on the side of the octahedron.

fig14e

Modern Formulation

(not yet contributed)

Notes

If the radius of the sphere is unity then the side of octahedron is $\sqrt{2}$.

Table of Contents

Proofs: 1

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Proofs: 1

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References

Adapted from (subject to copyright, with kind permission)

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

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016