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Proposition: 3.01: Finding the Center of a given Circle

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

To find the center of a given circle.

• Let $ABC$ be the given circle.
• So it is required to find the center of circle $ABC$.
• Let some straight line $AB$ have been drawn through ($ABC$), at random, and let ($AB$) have been cut in half at point $D$ [Prop. 1.9].
• And let $DC$ have been drawn from $D$, at right angles to $AB$ [Prop. 1.11].
• And let ($CD$) have been drawn through to $E$.
• And let $CE$ have been cut in half at $F$ [Prop. 1.9].
• I say that (point) $F$ is the center of the [circle] $ABC$.

Modern Formulation

It is possible to locate the center of a circle.

Table of Contents

Proofs: 1 Corollaries: 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
Propositions: 29 30 31
Sections: 32

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"