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Proposition: Prop. 13.16: Construction of Regular Icosahedron within Given Sphere

(Proposition 16 from Book 13 of Euclid's “Elements”)

To construct an icosahedron, and to enclose (it) in a sphere, like the aforementioned figures, and to show that the side of the icosahedron is that irrational (straight line) called minor. fig16ae

fig16e

Modern Formulation

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Table of Contents

Proofs: 1 Corollaries: 1

Mentioned in:

Proofs: 1
Propositions: 2

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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