Proposition: Prop. 12.08: Volumes of Similar Tetrahedra are in Cubed Ratio of Corresponding Sides
Similar pyramids which also have triangular bases are in the cubed ratio of their corresponding sides.
* Let there be similar, and similarly laid out, pyramids whose bases are triangles $ABC$ and $DEF$, and apexes the points $G$ and $H$ (respectively).
* I say that pyramid $ABCG$ has to pyramid $DEFH$ the cubed ratio of that $BC$ (has) to $EF$.
(not yet contributed)
Table of Contents
Proofs: 1 Corollaries: 1
Proofs: 1 2
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016