Proposition: 1.36: Parallelograms on Equal Bases and on the Same Parallels

Euclid's Formulation

Parallelograms which are on equal bases and between the same parallels are equal to one another.


Modern Formulation

Parallelograms (\(\boxdot{ADCB}\) , \(\boxdot{EHGF}\)) on equal bases (\(\overline{BC}\), \(\overline{FG}\)) and standing between the same parallels (\(\overline{AH}\), \(\overline{BG}\)) are equal in area.

Proofs: 1

Proofs: 1 2 3 4 5

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"