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"WESSEL, CASPAR. - THE FIRST SYSTEMATICAL THREATMENT OF COMPLEX NUMBERS.
Reference : 58364
(1797)
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 d...
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).
Om Directionens analytiske Betegning, et forsøg, anvendt fornemmelig til plane og sphæriske Polygoners Opløsning. - [THE FIRST SYSTEMATICAL THREATMENT OF COMPLEX NUMBERS]
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).
Den Nord=Østlige Fierdedeel af Siælland under det kongl: Videnskabernes Societets Direction ved rigtig Landmaaling optaget og ved trigonometriske samt astronomiske Operationer prövet. Reduceret og tegnet Aar 1768 af Caspar Wessel.
(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.
Den Sydvestlige Fierdedeel af Siælland under det Kongl: Videnskabernes Societets Direction ved rigtig Landmaaling optaget og ved trigonometriske samt astronomiske Operationer prövet. Tegnet af C. Wessel.
(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.
Kort over Siælland og Møen med tilgrænsende Kyster af Skaane, Falster, Laaland, Langeland, Thorsinge, Fyen, Samsöe og Jylland under det Kongl. Videnskabernes Selskabs Direction ved rigtig Landmaaling optaget og ved trigonometriske samt astronomiske Op...
(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.
Den syd østlige Fierdedeel af Siælland under det Kongl: Videnskabernes Societets Direction ved rigtig Landmaaling optaget og ved trigonometriske samt astronomiske Operationer prövet. Tegnet af C. Wessel. Aar 1770.
(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.
