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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

Thank you to the contributors under CC BY-SA 4.0!

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@Calahan

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References

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"