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Proposition: 1.10: Bisecting a Segment

(Proposition 10 from Book 1 of Euclid's “Elements”)

To cut a given finite straight line in half.

• Let $AB$ be the given finite straight line.
• So it is required to cut the finite straight line $AB$ in half.

Modern Formulation

It is possible to bisect an arbitrary segment; that is, it is possible to locate the midpoint of a segment.

Table of Contents

Proofs: 1

Mentioned in:

Corollaries: 1
Problems: 2
Proofs: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Propositions: 18 19 20
Sections: 21

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

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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"