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. * Let $ABCD$ and $EFGH$ be parallelograms which are on the equal bases $BC$ and $FG$, and (are) between the same parallels $AH$ and $BG$. * I say that the parallelogram $ABCD$ is equal to $EFGH$.


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"