Proposition Replicated
Proposition XII.5
Pyramids which are of the same height and have triangular bases are to one another as their bases.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XII.5
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
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Depends on (3)
- X.1Proposition X.1Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and…
- XII.3Proposition XII.3Any pyramid which has a triangular base is divided into two pyramids equal and similar to one another, similar to the…
- XII.4Proposition XII.4If there be two pyramids of the same height which have triangular bases, and each of them be divided into two pyramids…
Required by (dependents) (4)
- XII.6Proposition XII.6Pyramids which are of the same height and have polygonal bases are to one another as the bases.
- XII.7Proposition XII.7Any prism which has a triangular base is divided into three pyramids equal to one another which have triangular bases.
- XII.8Proposition XII.8Similar pyramids which have triangular bases are in the triplicate ratio of their corresponding sides.
- XII.9Proposition XII.9In equal pyramids which have triangular bases the bases are reciprocally proportional to the heights; and those…
Discussion
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