Prism on Triangular Base divided into Three Equal Tetrahedra/Porism

From ProofWiki
Jump to navigation Jump to search

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