Proposition: 1.44: Construction of Parallelograms II

(Proposition 44 from Book 1 of Euclid's “Elements”)

To apply a parallelogram equal to a given triangle to a given straight line in a given rectilinear angle.


Modern Formulation

Given an arbitrary triangle (\(\triangle{C}\)), an arbitrary angle (\(\angle{D}\)), and an arbitrary segment (\(\overline{AB}\)), it is possible to construct a parallelogram (\(\boxdot{FGBE}\)) equal in area to the triangle $\triangle{C}$ which contains the given angle $\angle {D}=\angle{GBE}$ and has a side $\overline{GB}$ equal in length to the given segment $\overline{AB}$.

Proofs: 1

Proofs: 1 2 3
Sections: 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"