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Proposition: 1.46: Construction of a Square on a Given Segment

(Proposition 46 from Book 1 of Euclid's “Elements”)

To describe a square on a given straight line.

• Let $AB$ be the given straight line.
• So it is required to describe a square on the straight line $AB$.

Modern Formulation

Given an arbitrary segment \(\overline{AB}\), it is possible to construct a square on that segment.

Table of Contents

Proofs: 1 Corollaries: 1

Mentioned in:

Proofs: 1 2 3 4 5 6 7 8 9 10 11
Sections: 12

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

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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"