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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)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2

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References

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", https://proofwiki.org/wiki/Main_Page, 2016