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Proposition: 1.03: Cutting a Segment at a Given Size

(Proposition 3 from Book 1 of Euclid's “Elements”)

For two given unequal straight lines, to cut off from the greater a straight line equal to the lesser. * Let $AB$ and $C$ be the two given unequal straight lines, of which let the greater be $AB$. * So it is required to cut off a straight line equal to the lesser $C$ from the greater $AB$.

Modern Formulation

Given two arbitrary segments in the plane, which are not congruent, it is possible to cut the segment with bigger length such that one of its two subsegments is congruent to the smaller segment.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Sections: 30

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"