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Arithmetices Principia Nova Methodo Exposita. Turin: Bocca Brothers, 1889.
Details
PEANO, Guiseppe (1858-1932)
Arithmetices Principia Nova Methodo Exposita. Turin: Bocca Brothers, 1889.
Extremely rare first edition in the original printed wrappers, of Peano's most important work, containing the first statement of the famous Peano axioms for the natural numbers, and which remains of seminal importance to 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 ? 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). No copies listed on ABPC/RBH.
Octavo (240 x 159mm). Pp. [xvi], 20 (some very minor damp staining). Original printed wrappers, unopened and uncut (corners and lower margin slightly chipped, backstrip slightly defective and repaired, covers lightly stained).
Arithmetices Principia Nova Methodo Exposita. Turin: Bocca Brothers, 1889.
Extremely rare first edition in the original printed wrappers, of Peano's most important work, containing the first statement of the famous Peano axioms for the natural numbers, and which remains of seminal importance to 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 ? 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). No copies listed on ABPC/RBH.
Octavo (240 x 159mm). Pp. [xvi], 20 (some very minor damp staining). Original printed wrappers, unopened and uncut (corners and lower margin slightly chipped, backstrip slightly defective and repaired, covers lightly stained).
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