THE INNOVATION OF THE AXIOMATIC METHOD

PASCH, MORITZ.

Vorlesungen über Neuere Geometrie.

Leipzig, B.G. Teubner, 1882. Contemp. hcloth. IV,201,(1) pp., textfigs. At end inserted "Anfangsgründe der beschreibende Geometrie nebst einem Anhang über Kartenprojection. Ein Leitfaden beim Unterricht an höheren Lehranstalten von Wilhelm Mink." Orig. printed wrappers. 47 pp. textfigs. Internally fine and clean.

Scarce first edition of this groundbreaking work. "The work on non-Euclidean geometry had brought the realization that geometries are man-made constructions bearing upon physical space but not necessarely exact idealization of it. This fact implied that several major changes had to be incorporated in any axiomatic approach to geometry. These were recognized and stressed by Moritz Pasch (1843-1930), who was the first to make major contributions to the foundations of geometry. His "Vorlesungen über neuere Geometrie", (the offered item) is a groundbreaking work." (Morris Kline).
"Pasch initiated the axiomatic method, although the foundational developments of his time were against this point of view. Thus Cantor's striking discoveries were based, from an axiomatic point of view, on nothing...As late as 1903 Frege poked fun of at the axiomatic method as presented in Hilbert's "rundlagen der Geometrie....particularly Peano continued Pasch's work. In 1889 Peano published both his exposition of geometry, following Pasch, and his treatment of number...Pasch played a crucial role in the innovation of the axiomatic methode. This method, with contributions from logic and algebra, is a central feature of twentieth-century mathematics." (DSB). - Sommerville "Bibliography of Non-Euclidean Geometry", p. 67 (1882).

Order-nr.: 39290