Foundations of Geometry

This classic work by David Hilbert summarizes the advances in 19th century geometry that saw the field migrate from being concerned primarily with describing physical space to an axiomatic basis where as he described it to Otto Blumenthal, 'one must be able to say, "tables, chairs, beer-mugs," in place of "points, lines, planes."This edition has been reset with all new diagrams that replace the poor quality scans found in most editions of this work. Hilbert begins with 20 axioms divided into five groups and from these constructs not only the conventional Euclidean geometry, but a variety of other geometries that make use of certain axioms while rejecting others. The final chapter shows deep connections between axiomatic geometry and number theory that recall the origins of number theory in ancient Greece and Babylon. Though not intended as a textbook, the exacting mechanisms by which Hilbert constructs various geometries form an excellent example of mathematical thinking.