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.


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"