Proposition: Prop. 12.05: Sizes of Tetrahedra of Same Height are as Bases

Euclid's Formulation

Pyramids which are of the same height, and have triangular bases, are to one another as their bases. * Let there be pyramids of the same height whose bases (are) the triangles $ABC$ and $DEF$, and apexes the points $G$ and $H$ (respectively). * I say that as base $ABC$ is to base $DEF$, so pyramid $ABCG$ (is) to pyramid $DEFH$.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2

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Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016