Proposition Replicated

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.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XII.4

Euclid's Elements, encoded as an rrxiv paper

Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT

Neighborhood at a glance

Incoming (2)

VI.1 XII.3

PropositionProposition XII.4

Outgoing (1)

XII.5

Full neighborhood

Depends on (2)

VI.1Proposition VI.1Triangles and parallelograms which are under the same height are to one another as their bases.
XII.3Proposition XII.3Any pyramid which has a triangular base is divided into two pyramids equal and similar to one another, similar to the…

Required by (dependents) (1)

XII.5Proposition XII.5Pyramids which are of the same height and have triangular bases are to one another as their bases.

Discussion

No replications, contradictions, or comments registered yet for this claim.