Proposition Replicated

Proposition XII.3

Any pyramid which has a triangular base is divided into two pyramids equal and similar to one another, similar to the whole, and having triangular bases, and into two equal prisms; and the two prisms are greater than the half of the whole pyramid.

type · theoreticalevidence · argumentextracted by · author

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

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 (3)

I.10 I.34 XI.39

PropositionProposition XII.3

Outgoing (2)

XII.4 XII.5

Full neighborhood

Depends on (3)

I.10Proposition I.10To bisect a given finite straight line.
I.34Proposition I.34In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas.
XI.39Proposition XI.39If there be two prisms of equal height, and one have a parallelogram as base and the other a triangle, and if the…

Required by (dependents) (2)

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

Discussion

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