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Proposition: Prop. 13.15: Construction of Cube within Given Sphere

(Proposition 15 from Book 13 of Euclid's “Elements”)

To construct a cube, and to enclose (it) in a sphere, like in the (case of the) pyramid, and to show that the square on the diameter of the sphere is three times the (square) on the side of the cube.

Modern Formulation

(not yet contributed)

Notes

If the radius of the sphere is unity then the side of the cube is \[\sqrt{\frac 43}.\]

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2
Propositions: 3

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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