Proof
Analogue of XII.8 for cones / cylinders: by similarity the height
scales proportionally with the diameter; cube of the linear ratio
gives the volume ratio.
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Depends on (3)
- XII.8Proposition XII.8Similar pyramids which have triangular bases are in the triplicate ratio of their corresponding sides.
- XII.10Proposition XII.10Any cone is a third part of the cylinder which has the same base with it and equal height.
- XII.11Proposition XII.11Cones and cylinders which are of the same height are to one another as their bases.
Required by (dependents) (1)
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