Geometry: Euclid and beyond. (English) Zbl 0954.51001

Undergraduate Texts in Mathematics. Berlin: Springer. xi, 526 p. (2000).
The author takes Euclid’s Elements (Books I-IV, VI and XI–XIII) as starting point for a study of geometry from a modern mathematical perspective.
The textbook is divided into the following eight major Chapters. Euclid’s geometry, Hilbert’s axioms, Geometry over fields, Segment arithmetic, Area, Construction problems and field extensions, Non-Euclidean geometry, Polyhedra.
Also included are complete proofs and the exercises at the end of each of 47 sections. The Appendices offer: Statements of the most frequently quoted results from Euclid’s Elements, Notes to every section, List of axioms, References to further study, Index of Euclid’s propositions and complete Index of notions.
These Appendices together with 550 Figures and twenty plates, 4 in color easily “navigate” through the whole text which is a useful source of material for those who teach geometry.


51-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry