Proposition XI.34 — In equal parallelepipedal solids the bases are reciprocally …

Proof

3D analogue of VI.14: by XI.32 the ratio of volumes is the compounded ratio of bases and heights; equal volumes force the compounded ratio to be unity, i.e.\ reciprocal proportion.

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Depends on (3)

VI.14Proposition VI.14In equal and equiangular parallelograms the sides about the equal angles are reciprocally proportional; and equiangular…
XI.32Proposition XI.32Parallelepipedal solids which are of the same height are to one another as their bases.
XI.33Proposition XI.33Similar parallelepipedal solids are to one another in the triplicate ratio of their corresponding sides.

Required by (dependents) (1)

XI.36Proposition XI.36If three straight lines be proportional, the parallelepipedal solid formed out of the three is equal to the…

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