Proof
A triangular prism is half a parallelogram prism on the same height
(by I.34 applied to the cross-sections); the area-doubling condition
makes the two prisms have equal volume.
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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.28Proposition XI.28If a parallelepipedal solid be cut by a plane through the diagonals of the opposite planes, the solid will be bisected…
- XI.32Proposition XI.32Parallelepipedal solids which are of the same height are to one another as their bases.
Required by (dependents) (2)
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