DEDEKIND, Richard (1831-1916) - photo 1
DEDEKIND, Richard (1831-1916) - photo 2
DEDEKIND, Richard (1831-1916) - photo 3

DEDEKIND, Richard (1831-1916)

Lot 182
10.07.2024 10:30UTC +00:00
Classic
Sold
£ 7 560
AuctioneerCHRISTIE'S
Event locationUnited Kingdom, London
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ID 1249847
Lot 182 | DEDEKIND, Richard (1831-1916)
Estimate value
£ 4 000 – 6 000
DEDEKIND, Richard (1831-1916)
Stetigkeit und irrationale Zahlen. Braunschweig: Friedrich Vieweg, 1872.
A fine copy of the first edition in publisher’s wrappers of one of the most important works in mathematics, Dedekind’s arithmetic definition of the essence of continuity and the exact formulation of the concept of the irrational number. ‘This short work marks a significant epoch in the movement known as the arithmetization of analysis, that is, the replacement of intuitive geometric notions by concepts described in precise words’ (Landmark Writings, p. 553). Dedekind’s arithmetical foundation for the theory of real numbers ‘explained the real numbers as “cuts” in the realm of rational numbers. He arrived at concepts of outstanding significance for the analysis of number through the theory of order. The property of the real numbers, conceived by him as an ordered continuum, with the conceptual aid of the cut that goes along with this, permitted tracing back the real numbers to the rational numbers … With his publication of 1872, Dedekind had become one of the leading representatives of a new epoch in basic research, along with Weierstrass and Georg Cantor. This was the continuation of work by Cauchy, Gauss, and Bolzano in systematically eliminating the lack of clarity in basic concepts by methods of demonstration on a higher level of rigor. Dedekind’s and Weierstrass’ definition of the basic arithmetic concepts, as well as Georg Cantor’s theory of sets, introduced the modern development, which stands “completely under the sign of number,” as David Hilbert expressed it’ (DSB).

The contents leaf gives a pagination as though the text starts from p.1, but in fact the half-title is p.1 with the text itself starting on p.9. This suggests an intention to re-paginate at some point in the print run, but this does not seem to have occurred.

DSB 4, pp.1-5; I. Grattan-Guinness (ed.), Landmark Writings in Western Mathematics 1640-1940, Chapter 43. Parkinson, ‘Breakthroughs’, p. 415; Honeyman 840. We have not been able to trace any record of a copy selling at auction since the Honeyman copy in 1979 (RBH).

Octavo (225 x 142mm). Half-title, pp. 31, [1], 4pp. publisher’s ads bound in at end. Original printed orange publisher’s wrappers (two very short expertly repaired tears to lower wrapper affecting one letter only, foot of spine with expert repair, otherwise in fine condition); contained in a modern paper-covered case.
Place of origin:Western Europe, Germany, Europe
Auction house category:Books and manuscripts, Printed books
Address of auction CHRISTIE'S
8 King Street, St. James's
SW1Y 6QT London
United Kingdom
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10.07.2024 – 10.07.2024
Phone +44 (0)20 7839 9060
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