Proof
The 3D analogue of VI.20: scaling each of the three edges by ratio
multiplies the volume by . Apply VI.20 to two faces and
XI.32 to extrude.
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Depends on (3)
- VI.20Proposition VI.20Similar polygons are divided into similar triangles, equal in multitude and in the same ratio as the wholes; and the…
- XI.32Proposition XI.32Parallelepipedal solids which are of the same height are to one another as their bases.
- V.10Definition V.10When four magnitudes are continuously proportional, the first is said to have to the fourth the triplicate ratio of…
Required by (dependents) (3)
- XI.34Proposition XI.34In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those parallelepipedal…
- XI.37Proposition XI.37If four straight lines be proportional, the similar and similarly described parallelepipedal solids upon them will also…
- XII.8Proposition XII.8Similar pyramids which have triangular bases are in the triplicate ratio of their corresponding sides.
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