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Proposition·Untested·2605.00009

Proposition XII.4

If there be two pyramids of the same height which have triangular bases, and each of them be divided into two pyramids equal to one another and similar to the whole, and into two equal prisms, then, as the base of the one pyramid is to the base of the other pyramid, so will all the prisms in the one pyramid be to all the prisms in the other pyramid.

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Proof

Each iteration of XII.3 doubles the number of prisms; by proportionality of bases (VI.1) the prism-sums maintain the same ratio as the original bases.

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Depends on (2)

Required by (dependents) (1)

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