Proposition: 1.45: Construction of Parallelograms III
(Proposition 45 from Book 1 of Euclid's “Elements”)
To construct a parallelogram equal to a given rectilinear figure in a given rectilinear angle.
Modern Formulation
Given an arbitrary convex quadrilateral $ABCD$ and an arbitrary angle (\(\angle{E}\)), it is possible to construct a parallelogram $FKML$ equal in area to the given \(n\)sided figure $ABCD,$ which contains an angle $\angle{FKM}$ equal to the given angle $\angle{E}.$
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3
Sections: 4
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Calahan
 @Casey
 @Fitzpatrick
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"