Wessel caspar (7 Ergebnisse)

First edition. The First Calculus of Vectors. First edition, journal issue, of the first work to propose a geometric representation of complex numbers. "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. Despite its lack of influence upon the development of mathematics, Wessel's publication was remarkable in many ways: he was not a professional mathematician; Norway and Denmark were not mathematically productive or stimulating at that time; he was not a member of the Royal Danish Academy (he had been helped and encouraged by J. N. Tetens, councillor of state and president of the science section of the Academy); and yet his exposition was, in some respects, superior to and more modern in spirit than Argand's. 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 . Wessel's initial formulation was remarkably clear, direct, concise, and modern. It is regrettable that it was not appreciated for nearly a century and hence did not have the influence it merited" (DSB). We have never seen an offprint of this paper, and it is probable that none exists. Not on RBH. "To have a short title for Wessel's On the Analytical Representation of Direction. An Attempt Applied Chiefly to Solving Plane and Spherical Polygons, I call it his Attempt. He opened this by giving the impression that it was born of a wish to find expressions for line segments from which their lengths and directions can be determined and to find a way of calculating with such expressions. This wish seems very natural for a surveyor who had solved an endless number of problems concerning triangles. Wessel added, however, another motivation: he had been seeking a method whereby he could avoid 'the impossible operations'. He also stated that this had paradoxically shown that the possible sometimes has to be sought by 'impossible means'. He did not explain what he meant by 'impossible operations', but it is likely that he thought of extracting the square root of -1, and generally operations with impossible, i.e., complex numbers. If this is the case, it appears that complex numbers were also a source of inspiration for Wessel. "Irrespective of whether Wessel originally started with complex numbers or with line segments, he structured his Attempt as a pursuit of algebraic operations for directed line segments. This idea might be seen as an extension of what Descartes did in La géométrie, namely to show how the operations +, -, ?, :, and ? can be interpreted for traditional line segments. Wessel did not refer to Descartes, but he spent more than a page arguing that it is allowed to conceive of the algebraic operations in a broader sense so that they can be applied to an extended field of quantities . "Wessel's line segments were defined by their directions.…

Kiøbenhavn, Johan Rudolph Thiele, (1797) 1799. 4to. Recently bound in a nice pastiche-binding of brown half calf with five raised bands and gilt red leather title-label to elaborately gilt spine. Vellum corners and marbled paper over boards. Published in: "Nye Samling af det Kongelige Danske Videnskabernes Selskabs Skrifter." Vol. V. A very nice copy. Pp.469-518 + 3 folded engraved plates. First edition of this seminal publication in which Wessel presents the first systematical treatment of the theory of complex numbers and furthermore being 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).…

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).…

(København, 1771). (59 x 69 cm.). Kobberstukket kort over Sydøstsjælland fra Køge Bugt til den nordlige del af Møn. Opdelt i 24 sektioner og opsat på lærred således, at det ved foldning let kunne medbringes. Enkelte svage brunpletter. Det første videnskabelige kort over Sydøstsjælland, som en del af Wessels berømte Sjællands-kvartet. Da kortet udkom var det den mest præcise kortprojektion overhovedet, idet Wessel anvendte sin opdagelse vedrørende de komplekse tal.- Bibl. Dan.II,603.…

(København), 1772. 57x69 cm. Kobberstukket kort over Sydvestsjælland med Store Bælt, Nordlangeland og Østfyn i samtidig håndkolorereing (kystlinjerne og signaturerne). Det første videnskabelige kort over Sydvestsjælland, som en del af Wessels berømte Sjællands-kvartet. Da kortet udkom var det den mest præcise kortprojektion overhovedet, idet Wessel anvendte sin opdagelse vedrørende de komplekse tal. Sjælden i koloreret stand.…

(København), 1777. 62x68 cm. Kobberstukket kort opdelt i 24 sektioner og opsat på lærred, foldet i en samtidig kassette. Originaltrykket af Videnskabernes selskabs general-kort over Sjælland m.v., som blev til efter Wessel havde tegnet sine 4 delkort over Sjælland (1768-72) og Skanke havde fuldført sit detailkort over Mön, Falster og Lolland (1776). General-kortet er, ligesom Wessels detailkort, en milepæl i kartografien, idet Wessel anvendte sin opdagelse vedrørende de komplekse tal til denne projektion.…

(København), 1771. (59 x 69 cm.). Kobberstukket kort over Nordøstsjælland. Opdelt i 24 sektioner og opsat på lærred således, at det ved foldning let kunne medbringes. Det første videnskabelige kort over Nordøstsjælland, som den første udgvne del af Wessels berømte Sjællands-kvartet udgivet af Videnskabernes Selskab. Da kortet udkom var det den mest præcise kortprojektion overhovedet, idet Wessel anvendte sin opdagelse vedrørende de komplekse tal. Dette kort er det første og mest eftertragtede af Videnskabernes Selskabs opmåling af Danmark.Bibl.Danica II,603. - Bramsen p. 146, gengivet.…