Proof
Apply XI.17 to the side faces and VI.1 to the parallel base-pairs;
the volume is proportional to one varying side at constant
cross-section.
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Depends on (3)
- VI.1Proposition VI.1Triangles and parallelograms which are under the same height are to one another as their bases.
- XI.17Proposition XI.17If two straight lines be cut by parallel planes, they will be cut in the same ratios.
- XI.24Proposition XI.24If a solid be contained by parallel planes, the opposite planes in it are equal and similar parallelograms.
Required by (dependents) (3)
- XI.28Proposition XI.28If a parallelepipedal solid be cut by a plane through the diagonals of the opposite planes, the solid will be bisected…
- XI.31Proposition XI.31Parallelepipedal solids which are on equal bases and of the same height are equal to one another.
- XI.32Proposition XI.32Parallelepipedal solids which are of the same height are to one another as their bases.
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