Abstract
THIS book is a comprehensive survey of the present conditions of the foundations of geometry. In the first part, the author follows Klein's programme of Erlangen, and discusses the notions of congruence and invariance, using freely the theory of groups, and giving an analytical treatment of generalised vectors without, however, employing determinants. But algebra is scarcely sufficient for an adequate description of the implications of space: geometry is more than a combination of numbers. So, in the second part of the monograph, the author gives an exposition of geometry as an autonomous axiomatic construction, discussing single systems of axioms with their logical characteristics.
Vorlesungen über Grundlagen der Geometrie.
Von Prof. Kurt Reidemeister. (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mil besonderer Berücksichtigung der Anwendungsgebiete, herausgegeben von R. Courant, Band 32.) Pp. x + 147. (Berlin: Julius Springer, 1930.) 11 gold marks.
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G., T. Mathematics. Nature 128, 626 (1931). https://doi.org/10.1038/128626b0
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DOI: https://doi.org/10.1038/128626b0