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 $DEF$.


Modern Formulation

Triangles which stand on equal bases and in the same parallels are equal in area.

Proofs: 1

Proofs: 1 2 3 4

Thank you to the contributors under CC BY-SA 4.0!



Adapted from CC BY-SA 3.0 Sources:

  1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

  1. Casey, John: "The First Six Books of the Elements of Euclid"

Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"