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Proposition: 1.23: Constructing an Angle Equal to an Arbitrary Rectilinear Angle

(Proposition 23 from Book 1 of Euclid's “Elements”)

To construct a rectilinear angle equal to a given rectilinear angle at a (given) point on a given straight line.

• Let $AB$ be the given straight line, $A$ the (given) point on it, and $DCE$ the given rectilinear angle.
• So it is required to construct a rectilinear angle equal to the given rectilinear angle $DCE$ at the (given) point $A$ on the given straight line $AB$.

Modern Formulation

It is possible to construct an angle $\angle{FAG}$ equal to an arbitrary angle $\angle{CDE}$ on an endpoint of a given segment $\overline{AB}.$

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
Sections: 19

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"