Proposition XI.37 — If four straight lines be proportional, the similar and simi…

Proof

3D analogue of VI.22: similar parallelepipeds are in the triplicate ratio of edges; equality of triplicate ratios is equivalent to equality of edge ratios.

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Depends on (2)

VI.22Proposition VI.22If four straight lines be proportional, the rectilineal figures similar and similarly described upon them will also be…
XI.33Proposition XI.33Similar parallelepipedal solids are to one another in the triplicate ratio of their corresponding sides.

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