Beschreibung
First edition, rare. "Calcolo Geometrico, G. Peano's first publication in mathematical logic, is a model of expository writing, with a significant impact on 20th century mathematics" (Kannenberg). It may be regarded (in part) as a preliminary version of his more famous work Arithmetices Principia, published in the following year. "Peano's first publication in logic was a twenty-page preliminary section on the operations of deductive logic in Calcolo Geometrico secondo l'Ausdehnungslehre di H. Grassmann (1888)" (DSB). "Peano had [in Calcolo Geometrico] used the logic of Boole and Schröder in mathematical investigations and introduced into it a number of innovations that marked a definite advance upon the work of his predecessors: for instance, the use of different signs for logical and mathematical operations, and a distinction between categorical and conditional propositions that was to lead him to quantification theory" (van Heijenoort, p. 83). The remainder of the work is a development of Hermann Grassmann's Ausdehnungslehre, first published in 1844, which had introduced a novel algebra of geometrical quantities which pre-figures modern vector algebra. Peano's exposition is not only a model of clarity, in contrast to Grassmann's which was notoriously obscure, but he also followed a more axiomatic style than had Grassmann. "In Chapter IX, with the innocent-sounding title 'Transformations of a linear system,' one finds the crown jewel of the book: Peano's axiom system for a vector space, the first-ever presentation of a set of such axioms. The very wording of the axioms (which Peano calls 'definitions') has a remarkably modern ring, almost like a modern introduction to linear algebra. Peano also presents the basic calculus of set operations, introducing the notation for 'intersection,' 'union,' and 'element of,' many years before it was accepted" (Kannenberg). COPAC lists copies at BL, Cambridge, Oxford and Mathematical Association only; no copies listed on ABPC/RBH. Kannenberg, Introduction to the English translation, Geometric Calculus - According to the Ausdehnungslehre of H. Grassmann, 2000; Van Heijenoort: From Frege to Gödel. A Source Book in Mathematical Logic, 1879-1931. 8vo, pp. x, [ii], 170, [2] (light browning, a few marginal notations in pencil). Contemporary half-cloth, paper label on spine (a little rubbed, label chipped). Bestandsnummer des Verkäufers ABE-1633015770216
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