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.
![fig45e](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book01/fig45e.png?raw=true)
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
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References
Adapted from CC BY-SA 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"