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Lemma: Lem. 12.04: Proportion of Sizes of Tetrahedra divided into Two Similar Tetrahedra and Two Equal Prisms

(Lemma to Proposition 4 from Book 12 of Euclid's “Elements”)

And one may show, as follows, that as triangle $LOC$ is to triangle $RVF$, so the prism whose base (is) triangle $LOC$, and opposite (plane) $PMN$, (is) to the prism whose base (is) [triangle] $RVF$, and opposite (plane) $STU$.

Modern Formulation

Table of Contents

Proofs: 1

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References

Adapted from (subject to copyright, with kind permission)

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