Classical Geometry (eBook)

I. E. LEONARD, PHD, is Lecturer in the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. The author of over fifteen journal articles, his areas of research interest include real analysis and discrete mathematics. J. E. LEWIS, PHD, is Professor Emeritus in the Department of Mathematical Sciences at the University of Alberta, Canada. He was the recipient of the Faculty of Science Award for Excellence in Teaching in 2004. A. C. F. LIU, PHD, is Professor in the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. He has authored over thirty journal articles. G. W. TOKARSKY, MSC, is Faculty Lecturer in the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. His areas of research interest include polygonal billiards and symbolic logic.

Preface v

Part I Euclidean Geometry

1 Congruency 3

2 Concurrency 41

3 Similarity 59

4 Theorems of Ceva and Menelaus 95

5 Area 133

6 Miscellaneous Topics 159

Part II Transformational Geometry

7 The Euclidean Transformations or Isometries 207

8 The Algebra of Isometries 235

9 The Product of Direct Isometries 255

10 Symmetry and Groups 271

11 Homotheties 289

12 Tessellations 313

Part III Inversive And Projective Geometries

13 Introduction to Inversive Geometry 339

14 Reciprocation and the Extended Plane 375

15 Cross Ratios 411

16 Introduction to Projective Geometry 435

Bibliography 466

Index 471

"The book is an extremely valuable compendium of
elementary constructions of Euclidean geometry. The text,
especially the proofs, is clearly structured and move forward in
simple steps, and thus are at the one hand very suitable for a
beginner in geometry and at the other hand exemplary for a teacher
of geometry." (Zentralblatt MATH, 1 October
2014)