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.
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Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"