Proposition XI.28 — If a parallelepipedal solid be cut by a plane through the di…

Proof

The two pieces are mirror-image prisms with congruent base-triangles (by I.34); by XI.24 their volumes are equal.

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Depends on (3)

I.34Proposition I.34In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas.
XI.24Proposition XI.24If a solid be contained by parallel planes, the opposite planes in it are equal and similar parallelograms.
XI.25Proposition XI.25If a parallelepipedal solid be cut by a plane parallel to opposite planes, then, as the base is to the base, so will…

Required by (dependents) (2)

XI.29Proposition XI.29Parallelepipedal solids which are on the same base and of the same height, and in which the extremities of the sides…
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…

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