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) $STU$.
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Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"