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GRIFFITHS (H. B.).-
Surfaces.
P., Cedic, 1977, in 8° broché, 180 pages ; nombreuses figures.
Reference : 66550
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5 book(s) with the same title
Mémoire sur la théorie générale des surfaces courbes.
Draguignan, 30 Mai 1876.
Manuscrit autographe de ce texte important publié dans le "Journal de mathématiques pures et appliquées" (le "Journal de Liouville") en 1891. Le présent manuscrit, proprement calligraphié, semble être celui communiqué par Ribaucour au "Journal de Liouville" pour sa publication. On note cependant plusieurs différences entre le texte manuscrit et l'imprimé, qui sont : - une équation a été écrite d'une manière très différente et a été rayée (p. 41 du manuscrit). - dans l'imprimé se trouve une note de bas de page qui ne figure pas dans le manuscrit (p. 102). - un paragraphe a été supprimé dans l'imprimé (p. 114, 116). - des différences importantes de notations utilisées dans les équations (p. 105, 112, 113,114 ...) La première page du manuscrit porte : "Mémoire du Journal de Liouville avec les notations de M. G. Darboux" et le premier plat de la reliure, en lettres dorées : "Mémoire sur les surfaces applicables". On joint le tiré à part de cet article, broché (défraichi), sous couverture imprimée. Paris, Gauthier-Villars, 1890. In-4 de 108 pp., 219-270 pp. Polytechnicien et Ingénieur des Ponts et Chaussées, Albert Ribaucour (1845-1893) s'est illustré par ses recherches en géométrie différentielle. On joint : - RIBAUCOUR. Etude des élassoïdes ou surfaces à courbure moyenne nulle. In-4 de (2), VI, (2), 236 pp. [Extrait des Mémoires couronnés et mémoires des savants étrangers. Académie royale des sciences, des lettres et des beaux-arts de Belgique, T. XLIV, 1881]. Demi-basane verte à coins de l'époque. /// grand in-4 de 120 pp. Demi-basane verte à coins. (Reliure de l'époque.) //// Autograph manuscript of this important text published in the Journal de mathématiques pures et appliquées (the Journal de Liouville) in 1891. This neatly written manuscript appears to be the one submitted by Ribaucour to the Journal de Liouville for publication. However, there are several differences between the manuscript and the printed text, which are: - one equation has been written in a very different way and has been crossed out (p. 41 of the manuscript). - in the printed text there is a footnote that does not appear in the manuscript (p. 102). - a paragraph has been deleted in the printed version (pp. 114, 116). - significant differences in the notation used in the equations (pp. 105, 112, 113, 114, etc.). The first page of the manuscript reads: Mémoire du Journal de Liouville avec les notations de M. G. Darboux (Memoir from the Journal de Liouville with notes by M. G. Darboux) and the front cover of the binding reads, in gold lettering: Mémoire sur les surfaces applicables (Memoir on applicable surfaces). A separate copy of this article is included, sewn with a printed cover (with few damage). Paris, Gauthier-Villars, 1890. In-4, 108 pp., 219-270 pp. A graduate of the Ecole Polytechnique and a civil engineer, Albert Ribaucour (1845-1893) was renowned for his research in differential geometry. "Ribaucour's mathemetical work - to which he dedicated himself especially under the influence of Mannheim - belonged to his spare time, expect for a short period during 1873 and 1874, when he was répétiteur in geometry at the Ecole Polytechnique. His main field was differential geometry, and his work was distinguished enough to earn him the prix Dalmont in 1877 and a posthumous prix, Petit d'Ormoy in 1895, awarded by the Paris Academy. His most elaborate work was a study of minimal surfaces, 'Etude des élassoides ou surfaces à courbure moyenne nulle', presented to the Belgian Academy of Sciences in 1880. In the work he explained his method called perimorphie, which utilized a moving trihedron on a surface. The approach to minimal surfaces was to consider them as the envelope of the middle planes of isotropic congruences; this approach led Ribaucour to a wealth of results. Many of Ribaucour's papers deal with congruences of circle and spheres. Special attention was devoted to those system of circle that are orthogonal to a family of surfaces. Such systems form systemes cycliques, and it is sufficient for the circles to be orthogonal to more than two surfaces for them to be orthogonal to a family. Ribaucours research thus led him to envelopes of spheres, to triply orthogonal system, cyclides, and surfaces of constant curvature". Stuick, DSB 11, 398. With : - - RIBAUCOUR. Etude des élassoïdes ou surfaces à courbure moyenne nulle. In-4 de (2), VI, (2), 236 pp. [Extrait des Mémoires couronnés et mémoires des savants étrangers. Académie royale des sciences, des lettres et des beaux-arts de Belgique, T. XLIV, 1881]. Contemporary green half-basane with corners. /// PLUS DE PHOTOS SUR WWW.LATUDE.NET
Disquisitiones generales circa superficies curvas. (General Investigations of Curved Surfaces). - [FOUNDATION OF MODERN GEOMETRY]
Göttingen, Dieterich, 1828. Small 4to. Extracted from: 'Commentationes Societatis Regiae Scientiarum Gottingensis', Volume 6, pp.99-146. 4to. Modern half morocco with gilt spine lettering. Fine and clean throughout.
First edition of the work which inspired one of the greatest breakthroughs in geometry since Euclid.Euler established the theory of surfaces in his 'Recherches sur la courbure des surfaces', 1767. But Euler's treatment of surfaces is not invariant under a natural notion of isometry with his notion of curvature, for example, the plane and cylinder have different curvatures, although one surface can be bent into the other without stretching or contracting. Such two surfaces are locally alike and one would naturally demand that geometry on these two isometric surfaces are the same. Another way of viewing this is to say that geometry on the surface depends on the geometry of the particular space, in which the surface is embedded.In this work Gauss took a fundamentally different approach to the study of surfaces" in contrast to Euler he represented the points of a surface in terms of two external parameters. Gauss then derived his own notions of the fundamental quantities of surfaces, e.g. arc length, angle between curves, and curvature. The Gauss curvature is related to the Euler curvature, but possesses a fundamentally different property, namely that it is intrinsic, e.g. isometric surfaces have the same curvature at all points. Or, in other words: Geometry (in Gauss' notion) on the surface is independent of the particular geometry of the ambient space. This remarkable result is known as Gauss' ""theorema egregium"". With this work Gauss established a whole new (and more proper) theory of surfaces. In the paper Gauss derived several important theorems about the length, area, and angles of figures on surfaces. But the ""theorema egregium"" has deep roots in the foundation of geometry and was to initiate one of the greatest breakthroughs in geometry since Euclid. To Bernhard Riemann (a student of Gauss) this result suggested that a surface could be regarded as a space in itself with its own geometry, having its own notion of distance, angles, etc. independent of the geometry of some other space containing the surface. This idea became the corner stone of Riemann's famous 'Ueber die Hypothesen, welche der Geometrie zu Grunde liegen', 1867.Norman 880.
"MONGE, (GASPARD). - THE GENERAL REPRESENTATION OF DEVELOPABLE SURFACES.
Reference : 44972
(1780)
Mémoire sur les Fonctions Arbitraires continues ou discontinues, qui entrent dans les Intégrales des Équations aux Différences finies. (1774) (+) Mémoire sur les Propriétés de plusieur Genres de Surfaces Courbes, particulièrement sur celles des Surfac...
(Paris, Moutard, Panckoucke, 1780). 4to. Extract from ""Mémoires fe Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome IX. Pp. 345-381 a. 2 folded engraved plates. And pp. 382-440 a. 3 folded engraved plates. Clean and fine.
First printing of two importent papers by Monge in differential functions and infinitesimal geometry, - in the first he discussed the nature of the arbitrary functions involved in the integrals of, finite difference equations. He also considered the, equation of vibrating strings, a topic he later investigated more fully. In the second memoir Monge returned to infinitesimal geometry. Working on the theory of developable surfaces outlined by Euler in 1772, he applied it to the problem, of shadows and penumbrae and treated several, problems concerning ruled surfaces. ""It is in this paper that he gives a general representation of developable surfaces...""(Morris Kline ""Mathematical Thoughts from Ancient to Modern Times"", p. 567).
Traité de géométrie analytique A TROIS DIMENSIONS. Lignes et surfaces du premier et du second ordre. Théorie générale des surfaces. Courbes gauches et surfaces développables. Familles de surfaces. Traduit de l'anglais par O. Chemin -- PREMIERE EDITION FRANCAISE -- BEL EXEMPLAIRE -- 3 TOMES reliés en un volume (COMPLETE SET)
P., Gauthier-Villars, 1882/1891, 3 TOMES reliés en 1 volume in 8, demi-chagrin marron, dos orné de fers et filets dorés (reliure de l'époque), T.1 : 17pp., 336pp., T.2 : 10pp., 295pp., T.3 : 8pp., 220pp.
---- PREMIERE EDITION FRANCAISE ---- BEL EXEMPLAIRE ---- "When Salmon joined the staff of Trinity College in 1841, its mathematical school was already internationally known... There was a strong bias toward synthetic geometry in the school, and it was in this field that Salmon began his research work, although he shortly became interested in the algebraic theories... He played an important part in the applications of the theory of invariants and covariants of algebraic forms to the geometry of curves and surfaces... His chief fame as a mathematician, however rests on the series of textbooks that appeared between 1848 and 1862. These four treatises on conic sections, higher plane curves, modern algebra, and the geometry of three dimensions not only gave a comprehensive treatment of their respective fields but also were written with a clarity of expression and an elegance of style that made them models of what textbook should be... They remained for many years the standard advanced textbooks in their respective subjects". (DSB XII pp. 86/87)**4646/8342/N6AR-8343/N7AR
Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal -- BEL EXEMPLAIRE -- 4 VOLUMES (COMPLETE SET)
P., Gauthier-Villars, 1894/1946, 4 VOLUMES grand in 8, bochés, couvertures imprimées, T.1 (1941) : 6pp., (1), 618pp., T.2 (1915) : (4), 579pp., T.3 (1894) : 8pp., 512pp., T.4 (1946) : (4), 554pp.
---- BEL EXEMPLAIRE du cours donné par G. Darboux à la Sorbonne ---- "In 1878, Darboux became suppléant of Chasles at the Sorbonne and two years later succeeded Chasles in the chair of higher geometry which he held until his death... He was primarily a geometer but had the ability to use both analytic and synthetic methods, notably in the theory of differential equations... Darboux's approach to geometry is fully displayed in his four-volume Leçons sur la théorie générale des surfaces based on his lectures at the Sorbonne. This collection of elegant essays on the application of analysis to curves and surfaces is held together by the author's deep understanding of the connections of various branches of mathematics. There are many applications and excursions into differential equations and dynamics. Among the subjects covered are that applicability and deformation of surfaces, the differential equation of Laplace and its applications and the study of geodesics and of minimal surfaces. Typical is the use of the moving trihedral... ". (DSB III pp. 559/560) - Cajori p. 315 **1515/M7AR-5950/N3/N7AR-1518/CAV.E5-1506/CAV.E5
