Prism on Triangular Base divided into Three Equal Tetrahedra/Porism
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Porism to Prism on Triangular Base divided into Three Equal Tetrahedra
In the words of Euclid:
- From this it is manifest that any pyramid is a third part of a prism which has the same base with it and equal height.
(The Elements: Book $\text{XII}$: Proposition $7$ : Porism)
Proof
Apparent from the construction.
$\blacksquare$
Historical Note
This proof is Proposition $7$ of Book $\text{XII}$ of Euclid's The Elements.
Sources
- 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 3 (2nd ed.) ... (previous) ... (next): Book $\text{XII}$. Propositions