Proposition: 1.42: Construction of Parallelograms I
(Proposition 42 from Book 1 of Euclid's “Elements”)
To construct a parallelogram equal to a given triangle in a given rectilinear angle.
* Let $ABC$ be the given triangle, and $D$ the given rectilinear angle.
* So it is required to construct a parallelogram equal to triangle $ABC$ in the rectilinear angle $D$.
Modern Formulation
Given an arbitrary acute angle (\(D\)) and an arbitrary triangle (\(\triangle{ABC}\)), it is possible to construct a parallelogram equal in area to the triangle, which also contains the given angle (\(D=\angle{FEC}\))
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2
Sections: 3
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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"