Les principes fondamentaux de la Géométrie

‎Paris: Gauthier-Villars, 1900 4to (28 cm), 114 pp. Bound before: Klein, Felix. Sur la Géométrie dite non Euclidienne. Off-print from Mathematische Annalen, Vol. IV, 1871. 62 pp. Bound before: Riemann, B.; Dedekind, R. Sur les hypothèses qui servent de fondement à la Géométrie. Off-print from Annali di Matematica Pura ed Applicata, Vol. 1869. 18 pp. Cont. leather-backed marbled boards, gilt-lettered spine with raised bands, marbled end-papers (binding rubbed, back hinge cracked at top, bookplate on the front paste-down, tear to front free end-paper, pencil number on half-title and small circular stamp on title of the first work, number stamped on P. 5, some pencil notes). Three very important and rare mathematical works. "Les principes fondamentaux de la Géométrie"refers to the French translation of a mathematical work called "Grundlagen der Geometrie" by David Hilbert. Published in 1899, "Grundlagen der Geometrie" is a significant mathematical treatise that presents an axiomatic approach to Euclidean geometry. Hilbert formulated a set of precise axioms from which the entire Euclidean geometry could be derived logically. These axioms served as the foundation for the rigorous study of geometry and provided a framework for understanding geometric concepts. "Sur la Géométrie dite non Euclidienne" translates to "On the Geometry Called Non-Euclidean". It is a work by Felix Klein, a German mathematician, published in 1871. Klein explores the foundations and implications of non-Euclidean geometry. "Sur les hypothèses qui servent de fondement à la Géométrie" ("Über die Hypothesen welche der Geometrie zu Grunde liegen") was a lecture delivered by Bernhard Riemann on 10 June 1854 on the occasion of his admission to the philosophical faculty of Göttingen and published posthumously by Richard Dedekind in 1867. This is Riemann's famous Habiltationsvortrag, in which he introduced the notions of a manifold, Riemannian metric, and curvature tensor. Riemann's ideas in this work laid the foundation for the modern understanding of geometry and its applications in physics, especially in the theory of general relativity. His work had a significant impact on the development of differential geometry and its broader implications in mathematics and theoretical physics.