x Contents 9.2.4. Planar families of spheres Dupin cyclides 340 9.3. M¨ obius geometry 341 9.3.1. Objects of M¨ obius geometry 341 9.3.2. Projective model of M¨ obius geometry 344 9.3.3. M¨ obius transformations 348 9.4. Laguerre geometry 350 9.5. Pl¨ ucker line geometry 353 9.6. Incidence theorems 357 9.6.1. Menelaus’ and Ceva’s theorems 357 9.6.2. Generalized Menelaus’ theorem 360 9.6.3. Desargues’ theorem 361 9.6.4. Quadrangular sets 362 9.6.5. Carnot’s and Pascal’s theorems 364 9.6.6. Brianchon’s theorem 366 9.6.7. Miquel’s theorem 367 Appendix. Solutions of Selected Exercises 369 A.1. Solutions of exercises to Chapter 2 369 A.2. Solutions of exercises to Chapter 3 376 A.3. Solutions of exercises to Chapter 4 377 A.4. Solutions of exercises to Chapter 6 381 Bibliography 385 Notation 399 Index 401

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