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Vorlesungen über Neuere Geometrie. - [THE INNOVATION OF THE AXIOMATIC METHOD]
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).
Mathematik am Ursprung. Gesammelte Abhandlungen über Grundfragen der Mathematik.
Leipzig, Felix Meiner, 1927. Orig. printed wrappers. Frontwrapper loose. Small loss to top of backstrip. (4),149 pp. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on frontwrapper.
First edition of this collection of 7 of Pasch's most importent work on axiomatics and geometry.""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 ""Grundlagen 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).
Vorlesungen über Neuere Geometrie. Zweite Auflage. Mit einem Anhang: Die Grundlegung der Geometrie in historischer Entwicklung. Mit ingesamt 115 Abbildungen.
Berlin, Julius Springer, 1926. Orig. full cloth. Stamps on titlepage. X,275 pp. Internally clean and fine. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on front free endpaper.
Pasch's classic work from 1882 is here published together with Dehn's historical paper.
