Proposition: 1.38: Triangles of Equal Area II
(Proposition 38 from Book 1 of Euclid's “Elements”)
Triangles which are on equal bases and between the same parallels are equal to one another.
* Let $ABC$ and $DEF$ be triangles on the equal bases $BC$ and $EF$, and between the same parallels $BF$ and $AD$.
* I say that triangle $ABC$ is equal to triangle $DEF$.
Triangles which stand on equal bases and in the same parallels are equal in area.
Table of Contents
Proofs: 1 2 3 4
Adapted from CC BY-SA 3.0 Sources:
- Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
- Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"