Proposition XII.17 — Given two spheres about the same centre, to inscribe in the …

Proof

3D analogue of XII.16: apply XII.16 in great-circle cross-sections, then triangulate the sphere using XI.27 to assemble a polyhedron strictly inside the larger sphere and outside the smaller.

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Depends on (2)

XI.27Proposition XI.27On a given straight line to construct a parallelepipedal solid similar and similarly situated to a given…
XII.16Proposition XII.16Given two circles about the same centre, to inscribe in the greater circle an equilateral polygon with an even number…

Required by (dependents) (1)

XII.18Proposition XII.18Spheres are to one another in the triplicate ratio of their respective diameters.

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