Axiomatic Approach to Geometry

Francis Borceux is Professor of mathematics at the University of Louvain since many years. He has developed research in algebra and essentially taught geometry, number theory and algebra courses and he has been dean of the Faculty of Sciences of his University and chairman of the Mathematical Committee of the Belgian National Scientific Research Foundation.

From the book reviews: "The axiomatic approach to geometry accounts for much of its history and controversies, and this book beautifully discusses various aspects of this. ... I thoroughly enjoyed this book, and highly recommend it for instructors who are preparing courses in this material or who just want a great reference on their shelves. ... There are exercises and problems appearing at the end of each chapter ... . Any decent college library should own this book ... ." (Mark Hunacek, MAA Reviews, January, 2014) "This book is eminently suitable for prospective teachers and their docents. The reader benefits from the author's long experience in lecturing geometry. The text is presented with contemporary mathematical rigor and free of strenuous historical sources ... . This wonderful book offers a deep insight into the beginning of geometric science 35 centuries before, into its further synthetic development through the ages, and into its culmination with Hilbert." (Rolf Riesinger, zbMATH, Vol. 1298, 2014)

• Introduction.- Preface.- 1.The Prehellenic Antiquity.- 2.Some Pioneers of Greek Geometry.- 3.Euclid’s Elements.- 4.Some Masters of Greek Geometry.- 5.Post-Hellenic Euclidean Geometry.- 6.Projective Geometry.- 7.Non-Euclidean Geometry.- 8.Hilbert’s Axiomatics of the Plane.- Appendices: A. Constructibily.- B. The Three Classical Problems.- C. Regular Polygons.- Index.- Bibliography.​