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Lynge & Søn

Om Directionens analytiske Betegning

Om Directionens analytiske Betegning, et forsøg, anvendt fornemmelig til plane og sphæriske Polygoners Opløsning. (Essai sur la représentation analytique de la direction, avec des applications, en particular à la détermination des polygones plans et des polygones sphériques).

WESSEL, CASPAR. - THE FIRST SYSTEMATICAL THREATMENT OF COMPLEX NUMBERS. Kiøbenhavn, Johan Rudolph Thiele, (1797) 1799. 4to. Uncut and unopened in original blue boards. Published in: "Nye Samling af det Kongelige Danske Videnskabernes Selskabs Skrifter." Vol. V. Wessel's paper: pp.469-518 and 3 folded engraved plates (the last plate inserted at p. 463). The whole volume V offered in its original binding. Engraved titlevignette. XII,670 pp., 15 engraved plates. 4 leaves with upper right corners gone, not affecting Wessel's paper. First edition of this important first systematical treatment of the theory of complex numbers and at the same time, the first work to add vectors in three-dimensional space."Wessel’s fame as a mathematician is based entirely on one paper, written in Danish and published in the Mémoires of the Royal Danish Academy, that established his priority in publication of the geometric representation of complex numbers. John Wallis had given a geometric representation of the complex roots of quadratic equations in 1685; Gauss had had the idea as early as 1799 but did not explicitly publish it until 1831. Robert Argand’s independent publication in 1806 must be credited as the source of this concept in modern mathematics because Wessel’s work remained essentially unknown until 1895, when its significance was pointed out by Christian Juel. The title of Wessel’s treatise calls it an "attempt" to give an analytic representation of both distance and direction that could be used to solve plane and spherical polygons. The connection of this goal with Wessel’s work as a surveyor and cartographer is obvious. The statement of the problem also suggests that Wessel should be credited with an early formulation of vector addition. In fact, Michael J. Crowe, in A History of Vector Analysis (University of Notre Dame Press, 1967), defines the first period in that history as that of a search for hypercomplex numbers to be used in space analysis and dates it from the time of Wessel, whom he calls the first to add vectors in three-dimensional space." (DSB).
method-draw-image (23)

Beqvem Skibs=Journal=Bog, (i Steentryk). Dens indretning og Brug.

BILLE, MICHAEL. Kjöbenhavn, Thieles Bogtrykkeri, 1837. 8vo. In later blue paper covered boards. Round title-label to upper part of front board. Upper part of spine missing the paper and front board partly detached. Stamp to title-page, otherwise internally fine. 20 pp. + 2 folded tables. The rare first edition of Bille's work on how to keep a logbook. Michael Johannes Petronius Bille was a Danish-Norwegian, and Prussian naval officer born 8 November 1769 in Stege on the Danish Island of Møn into a naval family which had produced and would produce Danish admirals.Over fifteen years he also served as a teacher of mathematics and astronomy at the Seekadettenakademiet (Dansk Søværnets Officersskole). From 1807-1811, he served as a captain stationed in Kristiansand in charge of the gunboat squadron (Roflotillen). In 1812-1813 he commanded a French warship in the Scheldt. From 1815 he served as pilot inspector in Helsingør until he entered Prussian service in 1820.In 1821 he began a very fruitful career as director of the Prussian Navigationsschule in Danzig. After three years he moved the school into a building that lay outside Danzig at the mouth of the Radaune River because the St. Jacob Church was inadequate. The school was then assigned to the war schooner Stralsund commanded by Longé. From 1825 the school also had the gunboat Danzig. Bille and the vessels were under the authority of the Ministry of War in Berlin. This may be seen as the beginning of the Prussian Navy.
Einige strittige Frage der Capitalstheorie. Drei Abhandlungen.

Einige strittige Frage der Capitalstheorie. Drei Abhandlungen.

BÖHM-BAWERK, EUGEN von - [OFF-PRINT - PRESENTATION-COPY] Wien & Leipzig, Wilheml Braumüller, 1900. 8vo. In contemporary half cloth with gilt lettering to spine. Endpapers brownspottet. Offprint from: "Zeitschrift für Volkswirtschaft, Socialpolitik und Verwaltung", Achter Band. 'Vom Verfasser' inscribed on upper right corner of title-page. With previous owner's dedication to pasted down front end-paper: "An H. Furuja (Oct. 1947) / Seiichi Tobata Leipzig August 1928", and to verso of front free end-paper: "Zugleich / S. S. 129-360 von Eugen von Böhm -Bawerk: Kleine / Abhandlungenåuber Kapital und Zins, hrsg von / Franz X. Weiss. 1926 Wien und Leipzig". A fine copy. (4), 127, (1) pp. Presentation copy of the rare offprint, and first separate edition, of this important contribution to the problems of capital theory in which Böhm-Bawerk elaborate and defend his theories presented in 'Positive Theory of Capital' (1889). Bohm-Bawerk's thoughts on capital and interest also exerted great influence on many American economists, in particularly Irving Fisher.The present copy was given by the author to an unknown recipient, then passed on to the Japanese economist Seiichi Tobata (1899 - 1983), Professor of agriculture and economics at Tokyo University, recipient of the 1968 Ramon Magsaysay Award for Public Service for his contributions to the modernization of Japanese agriculture, J. A. Schumpeter's 'Theorie der wirtschaftlichen Entwicklung', History of Economic Analysis and other works in Japan. Hiroshi Furuya (1920 - 1957, also spelled as Furuja), Professor of economics at Tokyo. He specialized in mathematical economics."The neoclassical part of his (Böhm-Bawerk's) argument, in particular his analysis of intertemporal consumer behaviour, was taken up by Irving Fisher (1907, 1930) and developed into a theory of interest which is based on the notion of time preference and the concept of investment opportunities' (in The New Palgrave, vol.1, p.257).Specifically in this work, Böhm-Bawerk posed a problem which had not been seen before in its full importance: the role of the rate of interest in the choice of an optimal method of production' (ibid, p.258)."As civil servant and economic theorist, Bohm-Bawerk was one of the most influential economists of his generation. A leading member of the Austrian School, he was one of the main propagators of neoclassical economic theory and did much to help it attain its dominance over classical economic theory. His name is primarily associated with the Austrian theory of capital and a particular theory of interest' (ibid, p.254)