◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--3-circles / Section: Book 03: Fundamentals of Plane Geometry Involving Circles

Section: Book 03: Fundamentals of Plane Geometry Involving Circles

In the 3rd Book, Euclid continues with the development of plane geometry, focusing on the theory of circles. This book contains some basic insights about the plane geometry of circles. For instance:

• Prop. 3.02 identifies the circle as a convex figure.
• If two circles cut each other, then they do not have the same center (Prop. 3.05).
• If two circles touch another, then the straight line through their centers goes also through the point, at which they touch another (Prop. 3.11 and Prop. 3.12).
• The central angle is the double size of the inscribed angle (Prop. 3.20).
• The inscribed angles joining the ends of the same arc are equal (Prop. 3.21).
• The intersecting chord theorem (Prop. 3.35).
• The tangent secant theorem (Prop. 3.36 and Prop. 3.37).

Moreover, this book contains the following compass and ruler constructions:

• Finding the center of a given circle (Prop. 3.01),
• Construction of a tangent to a given circle (Prop. 3.17),
• Construction of a circle from its segment (Prop. 3.25),
• Bisection of an arc (Prop. 3.30),
• Construction of an arbitrary circular segment (Prop. 3.33 and Prop. 3.34).

Table of Contents

1. Subsection: Definitions from Book 3
2. Subsection: Propositions from Book 3

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

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@Calahan

@Casey

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"