I read this book most because of the author David Hilbert, the second reason is I just finish reading Euclid’s Elements, David Hilbert is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries, to help me build a solid grounding in the modern development of geometry
The translator of this book (from German to English) is Edgar J. Townsend:
In 1900, Edgar J. Townsend returned from advanced studies in Germany and became director of the mathematics department at the University of Illinois. He promptly arranged for the university to extend its collection of German geometric models and introduced a graduate program in mathematics.
E. J. Townsend mentioned at the preface:
The material contained in the following translation was given in substance by Professor Hilbert as a course of lectures on euclidean geometry at the University of Göttingen during the winter semester of 1898–1899. The results of his investigation were re-arranged and put into the form in which they appear here as a memorial address published in connection with the celebration at the unveiling of the Gauss-Weber monument at Göttingen, in June, 1899. In the French edition, which appeared soon after, Professor Hilbert made some additions, particularly in the concluding remarks, where he gave an account of the results of a recent investigation made by Dr. Dehn. These additions have been incorporated in the following translation.
Dr. Dehn’s important work is, I don’t have the follow version of this book named David Hilbert’s Lectures on the Foundations of Geometry, 1891–1902:I hope to have change to glance the follow version one day
Dehn gave an example of a non-Legendrian geometry where the angle sum of a triangle is greater than 180 degrees, and a semi-Euclidean geometry where there is a triangle with an angle sum of 180 degrees but Euclid’s parallel postulate fails. In Dehn’s geometries the Archimedean axiom does not hold.
This book reorganized the structure of Euclid’s Elements and categorized all the axioms into five groups, talk about the completeness, compatibility and independence, give audience a really deep insight at Euclidean geometry
