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 $\overline{AB}$.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3
Sections: 4
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"