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Geometry Geometry Revisited by Coxeter

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 Mentor P: 18,071 Author: H. S. M. Coxeter, Samuel L. Greitzer Title: Geometry Revisited Amazon Link: http://www.amazon.com/Geometry-Revis.../dp/0883856190 Prerequisities: High-School mathematics Level: Undergrad Table of Contents:  Preface Points and Lines Connected with a Triangle The extended Law of Sines Ceva's theorem Points of interest The incircle and excircles The Steiner-Lehmus theorem The orthic triangle The medial triangle and Euler line The nine-point circle Pedal triangles Some Properties of Circles The power of a point with respect to a circle The radical axis of two circles Coaxal circles More on the altitudes and orthocenter of a triangle Simson lines Ptolemy's theorem and its extension More on Simson lines The Butterfly Morley's theorem Collinearity and Concurrence Quadrangles; Varignon's theorem Cyclic quadrangles; Brahmagupta's formula Napoleon triangles Menelaus's theorem Pappus's theorem Perspective triangles; Desargues's theorem Hexagons Pascal's theorem Brianchon's theorem Transformations Translation Rotation Half-turn Reflection Fagnano's problem The three jug problem Dilatation Spiral similarity A genealogy of transformations An Introduction to Inversive Geometry Separation Cross ratio Inversion The inversive plane Orthogonality Feuerbach's theorem Coaxal circles Inversive distance Hyperbolic functions An Introduction to Projective Geometry Reciprocation The polar circle of a triangle Conics Focus and directrix The projective plane Central conics Stereographic and gnomonic projection Hints and Answers to Exercises References Glossary Index