Euclid:Proposition/XII/17/Porism

Proposition

In the words of Euclid:

But if in another sphere also a polyhedral solid be inscribed similar to the solid in the sphere $BCDE$, the polyhedral solid in the sphere $BCDE$ has to the polyhedral solid in the other sphere the ratio triplicate of that which the diameter of the sphere $BCDE$ has to the diameter of the other sphere.

(The Elements: Book $\text{XII}$: )


Sources

  • 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 3 (2nd ed.) ... (previous) ... (next): Book $\text{XII}$. Propositions
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