Skip to Content

WESSEL, CASPAR. - THE FIRST SYSTEMATICAL THREATMENT OF COMPLEX NUMBERS.

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...

Herman H. J. Lynge & Søn A/S
lyn58364
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).
Address:
Silkegade 11
DK-1113 Copenhagen
Denmark
Phone:
CVR/VAT:
DK 16 89 50 16

Recently Added From Herman H. J. Lynge & Søn A/S

Anmärkiningar Om biåsestenen. (In:
More Photos
BERGIUS, PETER JONAS
Herman H. J. Lynge & Søn A/S
lyn62692
(Stockholm, 1777). 8vo. As extracted from "Kungl. Svenska vetenskapsakademiens handlingar", uncut unopened. Fine and clean. Pp. 304-309.
Medicinische und philosophische Schrifften von…
More Photos
ALBERTI, MICHAEL.
Herman H. J. Lynge & Søn A/S
lyn62695
Halle im Magdeburgischen, Hendel, 1721. 8vo. In contemporary full calf with four raise bands and richly gilt spine. Traces from old paper-label to upper part of spine. Leather on spine cracked, spine-ends slightly chipped. Internally nice and clean. (14), 620, (28) pp. First collected edition of Alberti’s essays. Alberti (1682–1757), professor of medicine and philosophy at Halle and later rector of the university, was a leading disciple of Georg Ernst Stahl who considered the soul as having control on the body. Therapies involved dealing with the internal senses and feelings.
More info
O Capital. (i.e. Portuguese:
More Photos
MARX, CARLOS [KARL] (+) GABRIELLE DEVILLE (+) [Translator:] ALBANO DE MORAES.
Herman H. J. Lynge & Søn A/S
lyn62679
Lisboa, De Francisco Luiz Goncalves, 1912. 8vo. In the original red printed cloth-binding with black and white lettering. Spine with loss of the white lettering. Paper-label pasted on to lower inner margin of front board. Very light wear to extremities, Internally very fine and clean. 240 pp. The exceedingly scarce first Portuguese edition of the most important abridged version of Marx's Capital ever to have appeared, published fifty-six years before the first full Portuguese (but published in Brazil) translation and whole sixy-two years before the first full translation published in Portugal. Curiously, two translations of the present work were made 1912 but the present translation seems to have priority (see Bastien, "Readings and Translations of Karl Marx in Portugal"). After the 1933 rise of Salazar's dictatorial Estado Novo regime, suppression of the relatively newly founded Communist party grew. Members were arrested, tortured, and executed and many were sent to the Tarrafal concentration camp in the Cape Verde Islands. Communist literature suffered an equally repressive fate, hence the rarity of the present work. Marxism and especially Marxist writing caught on comparatively late in Portugal: "As for the Socialist Party - supposed to be the main expression of Marxism -, it revealed itself unable to stimulate effective theoretical and doctrinal efforts. Its existence was an example of ambiguity and inconsequence. Its political programme went on mixing Marxian elements, associationist tradition and positivist thinking. Its strategy balanced continuously between an alliance with republican politicians and the maintenance of political autonomy. Its tatics balanced between electoral abstencionism and an involvement in election processes, that never led it to a relevant position in parliament. Even its international relations showed a lasting ambiguity: it had been created according to the instructions of the Marxist majority at the Hague Congress, when most of its members tended to support political abstencionism. When the formation of the Second lnternacional was taking place in Paris in 1889 Portuguese socialists tried to join the Marxist congress, after being present at the possibilist congress. In 1920 they decided to join the Third lnternacional (what was not accomplished), at the same time that an internal reformist turn was taking place." (Bastien, "Readings and Translations of Karl Marx in Portugal"). "The epitome, here translated, was published in Paris, in 1883, by Gabriel Deville, possibly the most brilliant writer among the French Marxians. It is the most successful attempt yet made to popularize Marx's scientific economics. It is by no means free from difficulties, for the subject is essentially a complex and difficult subject, but there are no difficulties that reasonable attention and patience will not enable the average reader to overcome. There is no attempt at originality. The very words in most cases are Marx's own words, and Capital is followed so closely that the first twenty-five chapters correspond in subject and treatment with the first twenty-five chapters of Capital. Chapter XXVI corresponds in the main with Chapter XXVI of Capital, but also contains portions of chapter XXX. The last three chapters-XXVII, XXVIII, and XXIX-correspond to the last three chapters-XXXI, XXXII, and XXXIII-of Capital." (ROBERT RIVES LA MONTE, Intruductory Note to the 1899 English translation). Capital de Marx also had a Portuguese edition at this time, or better, two different editions, both in 1912, but only in translation of the survey of Book I published in France by Gabriel Deville in 1883 (Marx, 1912a and Marx, 1912b). This version omitted material dealt with in at least four chapters of the original text and was not particularly appreciated by Engels. It was a simplified text, aimed at supporting the training of socialist militants and that made it possible for them to have access, indirect, to the work of Marx. The other summaries and anthologies of Capital, which, with a purpose similar to that of Deville, circulated in Europe during this period or ignored in Portugal, as was the case with Carlo Cafiero, or were only occasionally mentioned, as was the case with Paul Lafargue and Karl Kautsky, in its French versions. OCLC list two copies, both in the US.
More info
His Pokhodzhennia vydiv cherez pryrodnyi dobir,…
More Photos
DARWIN, CHARLES.
Herman H. J. Lynge & Søn A/S
lyn62681
(Kharkiv), Derzhavne medychne vyd-vo (State Medical Publishing House), 1936. 8vo. In publisher's original grey cloth binding with black lettering to spine with Darwin's portrait embossed on front board. Wear to extremities, corner bumped and light spoling to back board. Inner hinges split and first 3 leaves partly detached. Last 20 ff. slighly creased due to dampstain, otherwise internally a nice and clean copy. 674 pp. + frontispiece, portrait of Darwin and 1 plate with genealogical tree. The exceedingly rare first Ukranian translation of Darwin's landmark 'Origin of Species'. OCLC only list two copies (Library of Congress and The Huntington Library, USA) Freeman F797.
More info
Om Krigen med England. Med Tanker om samme…
More Photos
BOYE, JOHANNES.
Herman H. J. Lynge & Søn A/S
lyn62687
Fridericia, S. Elmenhoff, 1809. 8vo. In nice recent marbled paper covered boards with leather title-label with gilt lettering to spine. Ex-libris (Bent W. Dahlstrøm) to verso of front board. A nice and clean copy. 40 pp. Biblioteca Danica III, 572.
Regras methódicas para se aprender a escreuer o…
More Photos
VENTURA DA SILVA, JOAQUIM JOSE.
Herman H. J. Lynge & Søn A/S
lyn62100
Lisboa, Officina de Simão Thaddeo Ferreira, 1803. Folio-oblong (365 x 255 mm). In contemporary half calf. Wear to extremies, upper part of spine with loss of leather. Ex-libris pasted on to pasted down front end-paper. With, primarily marginal, brownspotting throughout. Dampstain to inner margin and upper outer margin of last 10 ff. 32 ff. Rare first edition of the most celebrated Portuguese treatise on calligraphy. Joaquim José Ventura da Silva (1777–1849), regarded as one of Portugal’s finest calligraphers and teachers of writing, composed this methodological guide to handwriting in which he combines a historical survey of scripts used in Portugal with practical instruction for teaching and learning penmanship.Ventura da Silva is reffered to by Innocencio (Diccionario Bibliographico) as "one of the best Portuguese Calligraphers". A second edition was published in 1819, a third in 1841, and a facsimile was published in Porto in 1899.
More info