Geometry Revisited.

Front cover -- Copyright Page -- Preface -- Contents -- 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-turn -- 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 -- 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.

Back Cover.

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 Morley's 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.