Proposition XII.7 — Any prism which has a triangular base is divided into three …

Proof

Cut the prism by two planes through opposite edge-pairs; the three resulting pyramids share a common apex and have congruent base triangles, so by XII.5 they have equal volume.

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Depends on (2)

XI.39Proposition XI.39If there be two prisms of equal height, and one have a parallelogram as base and the other a triangle, and if the…
XII.5Proposition XII.5Pyramids which are of the same height and have triangular bases are to one another as their bases.

Required by (dependents) (2)

XII.8Proposition XII.8Similar pyramids which have triangular bases are in the triplicate ratio of their corresponding sides.
XII.10Proposition XII.10Any cone is a third part of the cylinder which has the same base with it and equal height.

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