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Titel: Disquisitiones arithmeticae.
Verlag: Leipzig, G. Fleischer, 1801
8vo (220 x 135 mm), pp [i-v] vi-xviii 668 [8, errata]; B7, G4, K3, Ff7 and Tt6 are cancels as usual; a few gatherings with some light foxing, mostly marginal, as usual; title and preliminary leaves a little more, faint dampstain to lower margins of the final few gatherings, a remarkably fine, fresh, large, entirely uncut and partially unopened copy in contemporary marbled calf-backed blue speckled boards, red morocco label. £40,000First edition, a fine uncut copy, of the work that 'begins a new epoch in mathematics' (PMM). Published when Gauss was just twenty-four, Disquisitiones arithmeticae revolutionised number theory. It is one of the most influential mathematical books ever published.In this work Gauss 'introduces, among other things, the concept of congruence, whereby a set of elements is separated into disjoint classes by means of an equivalence relation. Gauss develops the congruence concept in the book's first sections and then uses it to unify and extend the work of his predecessors on arithmetical divisibility and to create a coherent theory of quadratic forms, including a proof of the law of quadratic reciprocity, called by Gauss the theorema aureum or "gem of arithmetic." He also generalizes his earlier work on constructing the regular polygon of 17 sides, presenting a universal criterion for determining which regular n-sided polygons can be constructed only with straight-edge and compass and which cannot. Finally, he includes a rigorous proof of the long-known Fundamental Theorem of Arithmetic that any positive integer can be uniquely (except for order) expressed as a product of primes' (Parkinson Breakthroughs).Provenance: 8 contemporary folded manuscript inserts of detailed mathematical calculations in Latin and Spanish (for pages 44, 56, 58, 59, 60, 64, 65, and 78)Dibner 114; Evans 11; Horblit 38; Norman 878; Parkinson p 238; PMM 257. Buchnummer des Verkäufers 3971
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