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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.

• Let $AB$ be the given straight line, $C$ the given triangle, and $D$ the given rectilinear angle.
• So it is required to apply a parallelogram equal to the given triangle $C$ to the given straight line $AB$ in an angle equal to (angle) $D$.

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

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

Github:

non-Github:

@Calahan

@Casey

@Fitzpatrick

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"