Proposition XII.13 — If a cylinder be cut by a plane which is parallel to its opp…

Proof

Parallel cross-sections give equal circles (XI.16 implies parallel diameters); the volume scales linearly with axial length by XII.11.

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Depends on (2)

XI.16Proposition XI.16If two parallel planes be cut by any plane, their common sections are parallel.
XII.11Proposition XII.11Cones and cylinders which are of the same height are to one another as their bases.

Required by (dependents) (1)

XII.14Proposition XII.14Cones and cylinders which are on equal bases are to one another as their heights.

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