Corollary: Cor. 12.17: Construction of Polyhedron in Outer of Concentric Spheres

(related to Proposition: Prop. 12.17: Construction of Polyhedron in Outer of Concentric Spheres)

(Corollary to Proposition 17 from Book 12 of Euclid's “Elements”)

And, also, if a similar polyhedral solid to that in sphere $BCDE$ is inscribed in another sphere then the polyhedral solid in sphere $BCDE$ has to the polyhedral solid in the other sphere the cubed ratio that the diameter of sphere $BCDE$ has to the diameter of the other sphere.

fig17e

Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs
non-Github:
@Fitzpatrick


References

Adapted from (subject to copyright, with kind permission)

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