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Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morleys remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.

H. S. M. Coxeter, S. L. Greitzer

Preface

**Chapter 1 Points and Lines Connected with a Triangle **

1.1 The extended Law of Sines

1.2 Ceva´s theorem

1.3 Points of interest

1.4 The incircle and excircles

1.5 The Steiner-Lehmus theorem

1.6 The orthic triangle

1.7 The medial triangle and Euler line

1.8 The nine-point circle

1.9 Pedal triangles

**Chapter 2 Some Properties of Circles **

2.1 The power of a point with respect to a circle

2.2 The radical axis of two circles

2.3 Coaxal circles

2.4 More on the altitudes and orthocenter of a triangle

2.5 Simson lines

2.6 Ptolemy´s theorem and its extension

2.7 More on Simson lines

2.8 The Butterfly

2.9 Morley´s theorem

**Chapter 3 Collinearity and Concurrence **

3.1 Quadrangles; Varignon´s theorem

3.2 Cyclic quadrangles; Brahmagupta´s formula

3.3 Napoleon triangles

3.4 Menelaus´s theorem

3.5 Pappus´s theorem

3.6 Perspective triangles; Desargues´s theorem

3.7 Hexagons

3.8 Pascal´s theorem

3.9 Brianchon´s theorem

**Chapter 4 Transformations **

4.1 Translation

4.2 Rotation

4.3 Half-tum

4.4 Reflection

4.5 Fagnano´s problem

4.6 The three jug problem

4.7 Dilatation

4.8 Spiral similarity

4.9 A genealogy of transformations

**Chapter 5 An Introduction to Inversive Geometry **

5.1 Separation

5.2 Cross ratio

5.3 Inversion

5.4 The inversive plane

5.5 Orthogonality

5.6 Feuerbach´s theorem

5.7 Coaxal circles

5.8 Inversive distance

5.9 Hyperbolic functions

**Chapter 6 An Introduction to Projective Geometry **

6.1 Reciprocation

6.2 The polar circle of a triangle

6.3 Conics 138 6.4 Focus and directrix

6.5 The projective plane

6.6 Central conics

6.7 Stereographic and gnomonic projection

Hints and Answers to Exercises

References

Glossary

Index