Proof
By XII.7 a prism is three equal pyramids; by XI.33 similar
parallelepipeds (and hence prisms) are in the triplicate ratio of
edges; transfer to pyramids by XII.5.
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Depends on (3)
- XI.33Proposition XI.33Similar parallelepipedal solids are to one another in the triplicate ratio of their corresponding sides.
- XII.5Proposition XII.5Pyramids which are of the same height and have triangular bases are to one another as their bases.
- XII.7Proposition XII.7Any prism which has a triangular base is divided into three pyramids equal to one another which have triangular bases.
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