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2020-08-12 09:42:21
PEANO, GUISEPPE
Arithmetices Principia Nova Methodo Exposita
Turin: Bocca Brothers, 1889. First edition. EXTREMELY RARE FIRST EDITION IN ORIGINAL WRAPPERS OF PEANO'S MOST IMPORTANT WORK, CONTAINING THE "PEANO AXIOMS" FOR THE NATURAL NUMBERS; OF SEMINAL IMPORTANCE IN MATHEMATICS AND MATHEMATICAL LOGIC. "Peano's most important contribution to the development of the theory and practice of the axiomatic method was his system of axioms for the arithmetic of the natural numbers... On the basis of his axiomatization, Peano constructed the entire theory of natural numbers. In particular, he showed how the elementary theorems of arithmetic can be obtained from his axioms" (Styazhkin, History of Mathematical Logic from Leibniz to Peano, 1969, pp. 278-9). With "the publication of Arithmetices principia, nova methodo exposita, Peano not only improved his logical symbolism but also used his new method to achieve important new results in mathematics; this short booklet contains Peano's first statement of his famous postulates for the natural numbers, perhaps the best known of all his creations. His research was done independently of the work of Dedekind, who the previous year had published an analysis of the natural numbers, which was essentially that of Peano but without the clarity of Peano... Arithmetices principia made important innovations in logical notation, such as Î for set membership and a new notation for universal quantification. Indeed, much of Peano's notation found its way, either directly or in a somewhat modified form, into mid-twentieth-century logic" (DSB). "Written in Latin, this small book was Peano's first attempt at an axiom … [Click Below for Full Description]
Bookseller: The Manhattan Rare Book Company [USA]

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