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"RIEMANN, B. (BERNHARD). - RIEMANN-TOPOLOGY AND RIEMANN-SURFACES.
Reference : 47147
(1857)
Theorie der Abel'schen Functionen. (And 3 other memoirs by Riemann of 1857).
Berlin, Georg Reimer, 1857. 4to. Spine gone. Covers loose. In: ""Journal für die reine und angewandte Mathematik Crelle/Borchardt"", 54. Band. IV,388 pp. (Entire volume offered). Internally clean and fine. The memoir: pp. 115-155.
First appearance of these groundbreaking papers on Abelian functions and hypergeometric series, introducing the use of cross cuts to define the n-fold connectivity of a surface and extending many of the ideas from his dissertation of 1851 (Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse). ""His famous theory of Abelian functions"" the theory itself, ONE OF THE MOST NOTABLE MASTERWORKS OF MATHEMATICS.""(DSB)""While four importent papers repeat many of the ideas in his dissertation, they are primarely devoted to Abelian integrals and functions. The fourth paper is the one that gave the subject its major development (Theorie der Abel'schen Functionen). All four were difficilt to understand"" ""they were a book with seven seals"". Fortunately many fine mathematicians later elaborated on and explained the material.""(Kline ""Mathematical Thought from Ancient to Modern Times"", p. 663)""His courses in 1855-1856, in which, he expounded his now famous theory of Abelian functions, were attended by C. A. Bjerknes, Dedekind, and Ernst Schering"" the theory itself, one of the most notable masterworks of mathematics, was published in 1857."" DSB)Abelian functions were studied by Abel and Jacobi"" they are a generalization of elliptic functions. Building on the ideas introduced in his thesis, particularly that of a Riemann surface, Riemann developed a very powerful geometric theory that resolved a number of outstanding problems. This work established Riemann as an important mathematician, but it was not without controversy. Riemann made extensive use, without proof, of a variational principle called the Dirichlet principle. Weierstrass had his doubts about it, and after Riemann's death it fell into disrepute. This state of affairs eventually had fruitful consequences. Several mathematicians successfully found proofs of Riemann's results without using the Dirichlet principle, and the principle itself was given a rigorous proof in 1899 by Hilbert. The three other Riemann-papers (all in first edition) are: 1. ""Allgemeine Voraussetzungen und Hülfsmittel für die Untersuchung von Functionen unbeschränkt veränderlichen Grössen"", pp. 101-104. - 2. ""Lehrsätze aus der analysis situs für die Theorie der Integrale von zweigliedrigen vollständigen Differentialen"", pp. 105-110, with 4 textillustr. - 3. ""Bestimmung einer Function einer veränderlichen complexen Grösse durch Grenz- und Unstetigkeitsbedingungen."", pp. 111-114.The volume contains further importent mathematical papers by Dedekind, Cayley, Lipschitz, Clebsch.Parkinson ""Breakthroughs"" 1857 M.
Ueber die Identität der Schwingungen des Lichts mit den elektrischen Strömen. (And Riemann:) Ein Beitrag zur Elektrodynamik. (2 Papers). - [TWO MILESTONE PAPERS ON THE THEORY OF ELECTROMAGNETISM]
Leipzig, Johann Ambrosius Barth, 1867. Contemp. hcalf, raised bands, gilt spinewith gilt lettering. A few scratches to binding. In ""Annalen der Physik und Chemie. Hrsg.von Poggendorff"", Bd. 131. (Entire volume offered). (2),X,660 pp. and 5 engraved plates. Small stamps to verso of titlepage and to verso of plates. Clean and fine.
First German edition (which originally appeared the same year in Danish in ""Oversigt over det Kongelige Danske Viidenskabernes Selskabs Forhandlinger"") of Lorenz' paper, which contains his important studies on the electromagnetic theory of light in which he - less than two years after, but independently of, Maxwell - found that LIGHT MIGHT BE INTERPRETED AS ELECTROMAGNETIC WAVES, and that his equations lead to the CORRECT VALUE FOR THE VELOCITY OF LIGHT. AND: First appearance of RIEMANN'S important paper (issued posthumously) in which he introduces the concept of ""RETARDED POTENTIALS"". Riemann suggests that Poisson's equation be modified by introducing terms which, though too small to be appreciable in ordinary experiments, would be capable of accounting for the propagation of electrical effects through space with a finite velocity c. This, so far as it goes, is in agreement with the view now accepted as correct.""The procedure which Lorenz followed was that of which Riemann had suggested in 1858 (the present paper by Riemann, which was published for the first time in 1867), namely, to modify the accepted formula of electrodynamics by introducing terms which, though too small to be appreciable in ordinary laboratory experiments, would be capable of accounting for the propagation of electrical effects through space with a finite velocity...The (Lorenz-) equations are, however, the fundamental equations of Maxwell's theory"" and therefore the theory of L. Lorenz is practically equivalent to that of Maxwell, so far as concerns the propagation of electromagnetic disturbances through free aether.....he suggested that ALL LUMINOUS VIBRATIONS MIGHT BE CONSTITUTED BY ELECTRIC CURRENTS, and hence that there was 'no longer any reason for maintaining the hypothesis of an aether, since we can admit that space contains sufficient ponderable matter to enable the disturbance to be propagated"" (Edmund Whittaker in ""A History of the Theories of Aether and Electricity I"", p. 267-70).""Maxwell seems to have considered the great paper of L. Lorenz on retarded potentials (published simultaneously in 1867 with a paper written in 1858 by B. Riemann on the same theme) as insufficiently supportive of his vision of a dynamical theory of theelectromagnetic field, whereas the present attitude is that Riemann and Lorenz made important contributions to the Maxwellian view."" (Kirk T. McDonald in ""Maxwell's Objection to Lorenz' Retarded Potentials"").
Zur Theorie der Nobili'schen Farbenringe.
Leipzig, Johann Ambrosius Barth, 1855. Contemp. hcalf, raised bands, gilt spine. A few scratches to spine. Small stamps to verso of titlepages and verso of plates. In ""Annalen der Physik und Chemie. Hrsg. von J.C. Poggendorff"", Bd. 95. (Entire volume offered). (2),X,628 pp. and 6 engraved plates, partly folded. Riemann's paper: pp. 130-139. Clean and fine.
First appearance of an importent paper in mathematical physics, dealing with the foudations of electricity. Here Riemann uses semiconvergent (asymptotic) series, an approach which motivated the subsequent works of Weber and Henkel.
Revue d'Histoire des Sciences - Marie-José Durand sur John Locke - Hélène Gispert sur Darboux et Hoël - Mohammed Allal Sinaceur sur Dedekind et Bernhard Riemann - René Taton sur Pierre Costabel
Reference : 100498
(1990)
Revue d'Histoire des Sciences - Tome XLIII, n° 2/3 - Avril-septembre 1990 , (Genèse de l'algèbre symbolique en Angleterre : Une influence possible de John Locke - Principes de l'analyse chez Darboux et Hoël (1870-1880) - Dedekind et le programme de Riemann, suivi de la traduction de Analytische Untersuchungen zu Bernhard Riemann's Abhandlungen über die Hypothesen, welche der Geometrie zu Grunde Liegen - Pierre Costabel, 1913-1969)
Presses Universitaires de France - P.U.F. , Revue d'Histoire des Sciences Malicorne sur Sarthe, 72, Pays de la Loire, France 1990 Book condition, Etat : Bon broché, sous couverture imprimée éditeur blanche, titre en bleu et noir grand In-8 1 vol. - 239 pages
1ere édition, 1990 Contents, Chapitres : 1. Articles : Marie-José Durand : Genèse de l'algèbre symbolique en Angleterre : Une influence possible de John Locke - Hélène Gispert : Principes de l'analyse chez Darboux et Hoël (1870-1880) : Textes et contextes - Mohammed Allal Sinaceur : Dedekind et le programme de Riemann, suivi de la traduction de Analytische Untersuchungen zu Bernhard Riemann's Abhandlungen über die Hypothesen, welche der Geometrie zu Grunde Liegen, par R. Dedekind - René Taton : Pierre Costabel, 1913-1969, liste des publications de Pierre Costabel - 2. Documentation : Yehuda Rav : Georg Cantor, 1845-1918 par Walter Purkert et Hans-Joaquim Ilgauds - Jean-Paul Mathieu : Sur le théorème d'Ampère - Comptes rendus couverture à peine jaunie avec quelques rousseurs sinon très bon état, intérieur frais et propre - Paginé 129 à 368
On The Hypotheses which lie at the Bases of Geometry. (Translated by W.K. Clifford). (Ueber die Hypothesen, welche der Geometrie zu Grunde liegen).
London and New York, Macmillan and Co., 1873. 4to. Orig. full brown cloth, gilt spine, pictorial gilt frontcover. Near mint condition. Small embossed stamp at upper corner of title-page (David Dunlop ObservatoRy Library). In: ""Nature, a weekly illustrated Journal of Science."", Volume VIII, May 1873 to October 1873. XII,562 pp. (Entire volume offered). Riemann's paper: pp. 14-17 a. 36-37. Internally clean and fine, no traces of use.
First English translation of this milestone work on the foundations of geometry. It ""is one of the key work from which derives the modern study of differential geometry, and especially the study of manifolds of dimension greater than two. It was to prove central to the overthrow of Euclidean geometry as the source of geometrical ideas and to Einstein's general theory of relativity after 1915."" (Grattan-Guiness ""Landmark Writings in Western Mathematics 1640-1940).It is a translation of Riemann's famous Habilitationsvortrag held in 1854 (in secondary literature, it is often misidentified as his Habilitationsschift, but that was concerned with Fourier series and was delivered the year before). Riemann begins his lecture with a remark about a certain darkness that lies at the foundation of geometry. This darkness obscures the relations between that which geometry assumes, i.e. the notion of space and the first principles of constructions in space. In Riemann's oponion one must take another approach towards this problem than the usual axiomatic method used ever since Euclid. The approach taken by Riemann is to a large extent guided by Gauss's work on the intrinsic geometry of surfaces"" 'Disquisitiones generales circa superficies curvas', 1828. In this work Gauss showed that the curvature of a surface can be determined without reference to the ambient Euclidean space in which it lies, i.e. that the curvature is an intrinsic property of the surface. Based on this, Gauss showed several fundamental theorems about figures on the surface by referring only to the surface itself, i.e. indicating that the surface itself is a space with its own geometry, independent of the geometry of the ambient Euclidean space. Riemann argues that the true objects and properties of geometry are those which can be studied within the space itself, and he defines a general n-dimensional space in a similar manner to the parametric representation of a surface. Riemann believed that we know space only locally, he therefore bases his study of the geometry of such a general space (or manifold as they are known today) on the infinitesimal methods of calculus. This choice is a crucial departure from the classical axiomatic methods used by Euclid, Lobachevsky, and Bolyai. The notion of distance (or metric) on a manifold is a generalization of the usual Euclidean distance formula in n-dimensions. Particular choices of space and metric reveal both the hyperbolic geometries of Lobachevsky and Bolyai, and elliptic (or Riemannian) geometry. Riemann's approach to geometry is of paramount importance, this work ""did more to change our ideas about geometry and physical space than any work on the subject since Euclid's Elements."" (Landmark Writings in Western Mathematics, p.507). ""The importance of this treatise is not confined to pure mathematics. Without it, Einstein would not have been able to develop his general theory of relativity."" (Printing and the Mind of Man, p.177).
Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite. - [RIEMANN'S MOST IMPORTANT CONTRIBUTION TO MATHEMATICAL PHYSICS]
Göttingen: Verlag der Dieterichschen Buchhandlung, 1860. 4to. (263x211mm). Offprint from the eighth volume of the 'Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen'. Bound in recent attractive marbled boards. Paper title label on front board. 25,(1:blank) pp.
First edition, offprint issue. In this paper Riemann laid the foundations of the theory of propagation on nonlinear and linear waves governed by hyperbolic equations. The concepts introduced here - Riemann invariants, the Riemann initial value problem, jump conditions for nonlinear equations, the Riemann function for linear equations - are still the basic building blocks of the theory today.
Ueber das Verschwinden der (theta)- Functionen.
Berlin, Georg Reimer, 1866. 4to. In: ""Journal für die reine und angewandte Mathematik"", 65. Bd., Zweites Heft. With title to Zweites Heft (2) pp. and pp. 97-188,(2). Riemann's paper: pp. 161-172.
First printing of this paper issued just before Riemann's death. The paper is a follow-up of his paper ""Theorie der Abelschen Functionen"" issued in the same journal in 1854. - ""The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathematical physics.""
Beweis des Satzes, dass eine einwerthige mehr als 2nfach periodische Function von n Veränderlichen unmöglich ist.
Berlin, Georg Reimer, 1869. 4to. No wrappers. Extracted from""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 71, 1869, Fine and clean. Pp. 197-200. [Offered pages: Pp. 97-200.].
First printing of this posthumously published paper by Riemann.
