The Foundations of Geometry

David Hilbert, a renowned German mathematician of the nineteenth and twentieth centuries, contributed to many branches of the field, according to his biographers at the University of Saint Andrews, but, "his work in geometry had the greatest influence in that area after Euclid," they say. One of the ways that influence was manifested was by the set of axioms he published in 1899, first in German, under the title, "Grundlagen der Geometrie" ("The Foundations of Geometry" in English). It, and its continued updates, pioneered the way mathematics, particularly geometry, was taught and studied in the twentieth century by using the axiom system and the use of models to prove axioms. The book was based on a course of lectures he had just given at the University of Götttingen that studied the axioms of Euclidean geometry. It was immediately translated into French. The response that translation received from the mathematics community caused Hilbert to make some changes, changes which were incorporated into the English translation by E.J. Townsend which Hilbert authorized and which appeared in 1902. That means the first English edition is considered to be second edition over all. It gets even more complicated after that. Hilbert continued to revise his axioms throughout his lifetime so that there were, in all, seven editions before his death in 1943, and later mathematicians kept at it with new editions in German and other languages. However, this copy keeps things simple: It is what the publisher calls a "reprint edition" of the original 1902 translation, released by the same American publisher, The Open Court Publishing Company, in 1947. Our copy is, overall, in excellent condition for its age. Slight age tanning. The text block is pristine, and the book has no marks, folds, or tears. The binding is tight and square and none of the pages are loose or missing. The binding is red cloth with the title and author stamped in foil on the front cover and on the spine. The text on the front cover is still bright but that on the spine has faded. The spine also shows some bumping at the top and bottom. See our photos. Very good++.…