‎Mathématiques‎

‎PINSKY, MARK A.‎

‎Partial Differential Equations and Boundary-Value Problems with Applications. Third Edition.‎

‎Boston, Mass., McGraw-Hill, (1998). Orig. wrappers. XIV,526 pp.‎

书商的参考编号 : 40505

‎FERRARO, V.C.A.‎

‎Electromagnetic Theory.‎

‎London, Athlone Press, 1956. Orig. full cloth. Dustjacket with small tears at spine ends. VIII,555 pp.‎

书商的参考编号 : 40509

‎HUSSERL, EDMUND.‎

‎Logische Untersuchungen [Mischungsauflage]. 2 Bde. Erster Band: Prolegomena zur reinen Logik. Dritte unveränderte Auflage. Zweiter Band. 1. Teil: Untersuchungen zur Phänomenologie und Theorie der Erkenntnis. Dritte unveränderte Auflage. Zweiter Band. ...‎

‎Halle, Niemeyer, 1922 (Vol.1 and vol. 2, I) - 1921 (Vol 2, II). Royal 8vo. Bound in three original uniform black half cloth bindings w. gilt titles to spines. Capitals a bit worn and inner front hinges a bit weak. Internally nice and clean. XXII, 257, (1) XI, (1), 508" XIII, (1), 244 pp.‎

‎A mixed set made up of the third and second edition (Dritte + Zweite Auflage) of Husserl's main work, one of the most important philosophical works of the 20th century. The ""Logical Investigations"" fundamentally changed philosophy and invoked the new philosophical era of the 20th century, -with this work Husserl founds phenomenology. Together with Heidegger's ""Sein und Zeit"" this must be considered the most important work of modern philosophy. The work was originally published 1900-1901, and the first edition is very difficult to come by. The second edition, is enlarged and revised, and the third collates exactly as the second. None of those two are common either.Husserl opens this fundamental work by attacking psychologism, and he then introduces his brand new philosophical method, which he had still by then not fully developed, but which came to influence all philosophy ever since -Phenomenology! Husserl himself calls this a ""Work of Breakthrough"" (see his preface to the second edition).In short, psychologism taught that logic itself was not an independent discipline, but a part of psychology, and it is this notion that Husserl gives its final blow in his logical investigations, -far more definitely than Frege had tried to some years earlier. Husserl now establishes a philosophy that asks the question of the essence of the matter of perception as opposed to the form of perception, as well as the meaning of the difference between formal or pure and material laws, truths and determinations, -all based on his strong interest in the relationship between the formalities of arithmetic and of logic. The work is the starting point for mereology, the formal first order theory of wholes and their parts. Mereology is both an application of predicate logic and a branch of formal ontology.Husserl is now famous as the father of phenomenology, and he decisively influenced the likes of Heidegger, Sartre, Carnap, Merleau-Ponty, Levinas, Ricoeur, Derrida etc. etc.‎

书商的参考编号 : 40584

‎"KLEIN, FELIX.‎

‎Vergleichende Betrachtungen über neuere geometrische Forschungen. - [THE ERLANGER PROGRAMM IMPROVED]‎

‎Leipzig, B.G. Teubner, 1893. 8vo. Orig. printed wrappers (no backstrip) to Heft 1, 43. Bd. of ""Mathematische Annalen"", the whole issue pp. IV,144. Klein's paper: pp.63-100. Frontwrapper repaired with the same kind of paper and without loss of letters. The sewing somewhat loose. Frontwrapper loose.‎

‎This is the second printing of Klein's famous ""Erlanger Programm"" having Klein's own improvements.For over two millennia geometry had been the study of theorems which could be proved from Euclid's axioms. However, in the beginning of the 19th century it was proved that there exist other geometries than that of Euclid. Motivated by the emergence of the new geometries of Bolyai, Lobachevsky, and Riemann, Klein proposed to define a geometry, not by a set of axioms, but instead in terms of the transformations that leave it invariant" according to Klein, a geometric structure consists of a space together with a particular group of transformations of the space. A valid theorem in that particular geometry is one that holds under this group of transformations. This controversial idea did not only give a more systematic way of classifying the different geometries, but also gave birth to new geometric structures such as manifolds. The Erlanger Programm was translated into six languages in the following two decades, and it has had an immense influence on geometry up to and throughout the 20th century.‎

书商的参考编号 : 40593

‎"JACOBI, CARL G.J.‎

‎Collection of 4 Memoirs: 1. De formatione et proprietatibus Determinantium. 2. De determinantibus functionalibus. 3. De functionibus alternantibus earumque divisione per productum e differentiis elementorum conflatum. - 4. Zum combinatorischen Analysis. - [INTRODUCING ""DETERMINANTS"" AND ""JACOBIANS""]‎

‎Berlin, G. Reimer, 1841. 4to. Without wrappers as Heft 4 in ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 22, heft 4. Titlepage to Heft 4. and pp. 285-380 +(2) pp. and 1 engraved plate. Jacobis papers: 1. pp. 285-318, 2. pp. 319,359, 3. pp. 360-371 and 4. pp. 372-374.‎

‎First printing of 2 importent and influential papers by Jacobi. In 1841 ""Carl Jacobi (1804-1851) develops the theory of determinants, including mention of the ""functional determinant"" or ""Jacobian"" in his paper ""De formatione et proprietatibus Determinantium"" (the first paper offered here). Later in the same year hepublishes a further development specifically of the theory of acobians in the memoir ""De determinantibus functionalibus"" (the second paper offered here). He shows for instance,that the Jacobian of a set of n functions in n variables is identically zero if and only if the functions are mutually dependent. Although functional determinants had been used earlier, they are later named after Jacobi due to his extensive development of their properties."" (Claire L. Parkinson in Breakthroughs).‎

书商的参考编号 : 40627

‎JULIA, GASTON.‎

‎Cours de Géometrie.‎

‎Paris, Gauthier-Villars, 1941. Royal8vo. Orig. printed wrappers. Uncut. VIII,508 pp.‎

书商的参考编号 : 40675

‎"ROBINS, BENJAMIN & LEONARD (LEONHARD).‎

‎Nouveaux Principes D'Artillerie..., commentés par Leonard Euler, traduits de L'Allemand, avec Notes, Par M. Lombard. - [WITH ROYAL PROVENANCE]‎

‎Dijon & Paris, L.N. Frantin & Jombert, 1783. Bound in fine contemp. full calf, raised bands and richly gilt compartments. Titlelabel with gilt lettering. A stamp on htitle and titlepage. (4),XIV,538,X,(1) pp. and 2 folded engraved plates. Internally clean and fine, printed on good paper.‎

‎First French edition of Robin's & Eulers work together. Robins' work New Principles of Gunnery was first issued in French in 1771 and Eulers work came together with Robins' work in the German translation of 1745. Euler's work is called ""Eulers erläuterte Artillerie.""""An inquiry from the King about the best work on artillery moved Euler to translate into German Benjamin Robin's ""New Principles on Gunnery"". Euler added his own supplements on ballistics, which were five times longer than the original text. These supplements occupy an important place in the history of ballistics..."" (DSB). - Poggendorff I:689.‎

书商的参考编号 : 40712

‎BASRI, SAUL A.‎

‎A Deductive Theory of Space and Time.‎

‎Amsterdam, North-Holland, 1966. Orig. boards. XI,163 pp.‎

书商的参考编号 : 40727

‎HERMES, HANS.‎

‎Einführung in die Verbandstheorie. Mit 24 Abbildungen.‎

‎Berlin, Springer-Verlag, 1955. Orig. full cloth. VI,164 pp.‎

‎First edition.‎

书商的参考编号 : 40729

‎"BOLZANO, BERNARD.‎

‎Versuch einer objectiven Begründung der Lehre von den drei Dimensionen des Raumes. (Aus dem Abhandlungen der k. böhm. Gesellschaft der Wissenschaften (V Folge, Bd. 3).) - [BOLZANO'S FIRST WORK ON SPACE AND TIME]‎

‎Prag [Prague], 1843. 4to. Uncut in the original printed light pink wrappers, with a dicreet new black cloth back-strip. A bit of brownspotting and minor chipping to edges pf wrappers, but overall a very nice copy of this fairly fragile publication. 15, (1) pp.‎

‎The very rare first edition, off-print (separately paginated), of this important treatise on space and time, which constitutes an important part of Bolzano's philosophical-logical theory. The present paper constitutes the first public formulation of these controversial ideas on time and space, with which Bolzano sets out to establish a foundation of mathematics which is non-empirical. By uniting mathematics and philosophy and applying both to the question of space and time, Bolzano here brings both sciences to a higher level of completeness, acknowledging that his theories depart from the those of Hegel, Kant, Schelling, etc. As always, Bolzano grabs the essence of the question and the terms that he is treating and retraces the concepts that must be used, establishing their original inner connection. In the present paper, the question of space, time, and thought are treated in order to establish the precise and full nature of space, a theme which Bolzano had apparently been working on for many years but previously only discussed with a very small number of intimate acquaintances, and now publishes on for the first time. The concept of space plays an important rôle in Bolzano's ontology and is closely linked to his mathematical and philosophical logic, in which the ""space-position"" plays a part in the demarcation of that which is purely mathematical and logical. Furthermore, for Bolzano, truth is constituted by true propositions (which state things as they are), and his canonical form of all propositions entails that ""[a] proposition is true iff the object has the property (the attribute) which belongs to the subject of the proposition. Moreover, empirical propositions must contain determinations of space and time. Without these determinations, the sentence ""It is snowing"" has no truth value, it is just a propositional form which does not correspond to a complete proposition"" ""in order to be true, [such propositions] require the addition of such specifications as to time (and often place as well), 'It is snowing today, in this place'"" (SEP).‎

书商的参考编号 : 41020

‎"KLEIN, FELIX.‎

‎Ueber die sogenannte Nicht-Euklidische Geometrie (+) Ueber die sogenannte Nicht-Euklidische Geometrie. (Zweiter Aufsatz). - [TWO MAIN WORKS ON NON-EUCLIDEAN GEOMETRY]‎

‎Leipzig, B.G.Teubner, 1871 u. 1873. Bound in 2 later full cloth. Small stamp on foot of titlepages.In. ""Mathematische Annalen. In Verbindung mit C. Neumann begründet durch Rudolf Friedrich Alfred Clebsch"", IV. und VI. Band. (4),637 pp. a. (4),642 pp., 6 plates. Klein's papers: pp. 573-625 a. pp. 112-145. Both volumes offered.‎

‎First edition of these 2 papers which unifies the Euclidean and Non-Euclidean geometries, by reducing the differences to expressions of the ""distance function"", and introducing the concepts ""parabolic"", ""elliptic"" and ""hyperbolic"" for the geometries of Euclid, Riemann and of Lobatschewski, Gauss and Bolyai. He further eliminates Euclid's parallel-axiom from projective geometry, as he shows that the quality of being parallel, is not invariant under projections.Klein build his work on Cayley's ""distant measure"" saying, that ""Metrical properties are not properties of the figure per se but of the figure in relation to the absolute."" This is Cayley's idea of the general projective determination of metrics. The place of the metric concept in projective geometry and the greater generality of the latter were described by Cayley as ""Metrical geometry is part of projective geometry."" Cayley's idea was taken over by Felix Klein....It seemed to him to be possible to subsume the non-Euclidean geometries, hyperbolic and double elliptic geometry, under projective geometry by exploring Cayley's idea. He gave a sketch of his thoughts in a paper of 1871, and then developed them in two papers (the papers offered here).Klein was the first to recognize that we do not need surfaces to obtain models of non-Euclidean geometries....The import which gradually emerged from Klein's contributions was that projective geometry is really logically independent of Euclidean geometry....By making apparent the basic role of projective geometry Klein paved the way for an axiomatic development which could start with projective geometry and derive the several metric geometries from it.""(Morris Kline).The offred volumes cntains other importen mathematical papers by f.i. by Klebsch, Lipschitz, Neumann, Noether, Thomae, Gordan, Lie, Du Bois-Raymond, Cantor (Über trigonometrische Reihen),etc.(Sommerville: Bibliography of Non-Euclidean Geometry p. 45 a. 49.)‎

书商的参考编号 : 41204

‎"WEYL, HERMANN.‎

‎Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen. - [FIRST DESCRIPTION OF ESSENTIAL SPECTRUM]‎

‎Leipzig, B.G. Teubner, 1910. 8vo. Without wrappers. Extracted from ""Mathematische Annalen. Begründet 1868 durch Alfred Clebsch und Carl Neumann. 68. Band"". Pp. 220-69.‎

‎First printing of Weyl's important paper in which he created the topic of essential spectrum.In mathematics, the essential spectrum is a certain subset of its spectrum, defined by a condition of the type that says, ""fails badly to be invertible"".‎

书商的参考编号 : 49486

‎"FATOU, PIERRE.‎

‎Séries trigonométriques et séries de Taylor. - [FIRST APPEARANCE OF THE FATOU SET]‎

‎Berlin, Stockholm, Paris, F. & G. Beijer, 1906. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 30, 1906. Entire volume offered. Stamp to title page, otherwise a fine and clean copy. Pp. 355-400. [Entire volume: 6, 410 pp].‎

‎First appearance of Fatou's seminal Ph.D. thesis in which he presented his famous Fatou theorem, which state that a bounded analytic function in the unit disc has radial limits almost everywhere on the unit circle. This theorem was at the origin of a large body of research in 20th-century mathematics under the name of bounded analytic functions. Fatou set is the 'regular' appearance of the chaotic Julia set and both if these initiated what was to be known as ""complex dynamics"" which eventually resulted in the Mandelbrot set.Fatou's thesis also include the first application of the Lebesgue integral to concrete problems of analysis, mainly to the study of analytic and harmonic functions in the unit disc. He furthermore studied for the first time the Poisson integral of an arbitrary measure on the unit circle and also made a major contribution to finding a solution to the related question of whether conformal mapping of Jordan regions onto the open disc can be extended continuously to the boundary.""He contributed important results on the Taylor series, the theory of the Lebesgue integral, and the iteration of rational functions of a complex variable. When studying the circle of convergence of the Taylor series, several points of view are possible: (1) one can look for criteria of convergence or divergence of the series itself on the circumference" (2) one can consider the limit values of the circle of the analytic function represented by the series and try to determine where these limit values are finite or infinite, as well as the properties of the functions of the argument represented by the real and imaginary parts of the series when these functions are well defined" (3) one can consider what points on the circumference, singular in the Weierstrass sense, also determine the analytic extension of the series. The link between these problems led Fatou to formulate a fundamental theorem in the theory of the Lebesgue integral."" (DSB).‎

书商的参考编号 : 49610

‎"POINCARÉ, H.‎

‎Remarques sur les intégrales irrégulières deséquations linéaires.‎

‎Berlin, G. Reimer, 1887. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 10, 1887. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 310-12. [Entire volume: (4), 397 pp].‎

‎First printing of Poincaré's reply to Thomé's critique of an earlier paper by Poincaré. In his reply Poincaré ""seems to have created a theory of asymptotic expansions where previously there had only been ad hoc techniques, and to have opened the door for the return into rigorous mathematics of divergent series."" (Bottazzini, Hidden Harmony).‎

书商的参考编号 : 49613

‎"POINCARÉ, H.‎

‎Sur la méthode horistique de Gyldén. - [POINCARÉ ON GYLDÉN'S HORISTIC METHODS]‎

‎Berlin, G. Reimer, 1905, 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 29, 1905. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 235-72. [Entire volume: (4), 433 pp].‎

‎First printing of Poincaré's final and most extensive paper on Gyldén's horistic methods.‎

书商的参考编号 : 49615

‎"TCHEBYCHEFF, P. [CHEBYSHEV] [TCHEBYCHEV].‎

‎Sur deux théorèmes relatifs aux probabilités. - [THE FOUNDATION FOR THE APPLICATION OF PROBABILITY THEORY TO STATISTICS]‎

‎Berlin, Stockholm, Paris, Almqvist & Wiksell, 1890. 4to. As extracted from ""Acta Mathematica"", Vol, 14, 1890. No backstrip. A fine and clean copy. Pp. 305-15.‎

‎First translation of Chebyshev's landmark paper (first published in Journal of the The St. Petersburg Academy in 1887) in which he laid the foundation for the application of probability theory to statistics, generalizing the theorems of Moivre and Laplace. It also generalized the theory of integral beta function. This led him to find an algorithm for finding an optimal solution in a system of linear equations with an approximate solution is known.""In the 1860's Chebyshev returned to the theory of probability. One of the reasons for this new interest was, perhaps, his course of lectures on the subject started in 1860. He devoted only two articles to the theory of probability, but they are of great value and designate the beginning of a new period in the development of this field. In the article of 1866 Chebyshev suggested a very wide generalization of the law of large numbers. In 1887 he published (without extensive démonstration) a corresponding generalization of the central limit theorem of Moivre and Laplace."" (DSB).""Chebyshev and many of his students were often cold and skepticall towrads various important achievements in Western European mathematics. In the two-hundred-year development period in probability theory its main achievements were the limiting theorems: the law of large number and the de Moivre-Laplace theorem. But the confines of applicability of these theorems and their further refinements and generalizations were not satisfactory. The second basic problem that occupied Chebyshev's attention was the central limit theorem. However, only in 1887 in the Proceedings of the Academy of Sciences was Chebyshev's paper devoted to this subject published."" (Maistrov, Probability and Mathematical Statistics, P. 202).‎

书商的参考编号 : 49619

‎"POINCARÉ, H.‎

‎Sur une Forme nouvelle des Équations du Probleme des trois Corps (+) Sur les rapports de l'analyse pure et de la physique mathématique.‎

‎Berlin, Uppsala & Stockholm, Paris, Almqvist & Wiksell, 1897. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 21, 1897. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 83-97"" Pp. 331-341.[Entire volume: (6), 376 pp + 4 plates].‎

‎First printing of this paper in which Poincaré arrives at a new theorem about canonical transformation, and in his later ""Methodes Nouvelles"", he proved this theorem using a variiational principle of mechanics, known today as the Hamilton principle.Also included is the first printing of Poincaré's principal address at the first International Congress of Mathematicians held in Zürich in 1897.‎

书商的参考编号 : 49621

‎"TETENS, JOHANN NICOLAI. - PROBABILITY IN VOTING.‎

‎Om Fleerheden af collective Stemmer, og Probabiliteten af samme.‎

‎(Kiøbenhavn, Johan Rudolph Thiele, 1799). 4to. Without wrappers. In: ""Nye Samling af det Kongelige Danske Videnskabernes Selskabs Skrifter."" Vol. V. Pp. 116-143.‎

‎First printing of a remarkable paper, probably being the first to give a mathematical treatment of the probability distribution of votes in the cases where voting - yes or no - selects itself into undergroups also voting yes or no and thus relating the result to the primary voting.The author, called ""The German Hume"" is well known for his work ""Einleitung zur Berechnung der Leibrenten und Anwartschaften"", which is a landmark work in actuarial science.‎

书商的参考编号 : 49633

‎"HILBERT, D. (+) H. POINCARÉ.‎

‎Über die Theorie der relativ-Abel'schen Zahlkörper [Hilbert] (+) Sur les fonctions abéliennes [Poincaré].‎

‎Berlin, Stockholm, Paris, Beijer, 1902. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol. 26, 1802. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 99-132" Pp. 48-98. [Entire volume: (4), 400 pp.].‎

‎First printing of these two important papers on the theory of quadratic number fields.‎

书商的参考编号 : 49641

‎"PAINLEVÉ, PAUL.‎

‎Sur les équations différentielles du second ordre et d'ordre supérieur dont l'intégrale générale est uniforme. - [PAINLEVÉ TRANSCENDENTALS]‎

‎Berlin, Stockholm, Paris, Beijer, 1902. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 25, 1902. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 1-86.[Entire volume: (4), 383 pp].‎

‎First appearance of Painlevé's important paper in which he introduced some of his transcendents, now know as ""Painlevé transcendents"".Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvable in terms of elementary functions. ""In old problems in which the difficulties seemed insurmountable, Painlevé defined new transcendentals for singular points of differential equations of a higher order than the first. In particular he determined every equation of the second order and first degree whose critical points are fixed. The results of these studies are applicable to the equations of analytical mechanics which admit rational or algebraic first integrals with respect to the velocities. Proving, in the words of Hadamard’s éloge, that ""continuing [the work of] Henri Poincaré was not beyond human capacity,"" Painlevé extended the known results concerning the n-body problem. He also corrected certain accepted results in problems of friction and of the conditions of certain equilibriums when the force function does not pass through a maximum.""Paul Painlevé later became the French prime minister.‎

书商的参考编号 : 49643

‎"HILBERT, DAVID.‎

‎Ein Beitrag zur Theorie des Legendre'schen Polynoms. - [HILBERT MATRIX]‎

‎Berlin, Stockholm, Paris, Almqvist & Wiksell, 1894. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 18, 1894. Entire volume offered. Stamps to title page and light wear to extremities, otherwise a fine and clean copy. Pp. 155-59.[Entire volume: (4), 421, (2) pp].‎

‎First printing of Hilbert's paper in which he introduced The Hilbert Matrix. In linear algebra, a Hilbert matrix is a square matrix with entries being the unit fractions. The Hilbert matrix is symmetric and positive definite and is also totally positive (meaning the determinant of every submatrix is positive). The Hilbert matrix is an example of a Hankel matrix.‎

书商的参考编号 : 49646

‎"PINCHERLE, SALVATORE.‎

‎Sur la géneration de systèmes récurrents au moyen d'une équation linéaire différentielle.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892-93]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16. First leaf detached, otherwise fine and clean. pp. 341-363.‎

‎First printing of Italian mathematician Pincherle's paper on linear differential equations.Salvatore Pincherle (1853 -1936) was an Italian mathematician. He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: ""Unione Matematica Italiana""), and was president of the Third International Congress of Mathematicians. The Pincherle derivative is named after him.‎

书商的参考编号 : 49648

‎"VOLTERRA, VITO.‎

‎Sur les vibrations lumineuses dans les milieux biréfringents.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 153-215.‎

‎First printing of Volterra's paper on the vibrations of light in a birefringence media.‎

书商的参考编号 : 49650

‎"LEBESGUE, H. (HENRI LÉON) - REVOLUTIONIZING THE CALCULUS.‎

‎Sur une généralisation de l'intégrale dérfinie. Note de H. Lebesgue, présentée par M. Picard. (Séance du Lundi 29 Avril 1901).‎

‎(Paris, Gauthier-Villars), 1901). 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 132, No 17. pp. (1013-) 1080. (Entire issue offered). Lebesgue's paper: pp. 1025-1028. Clean and fine.‎

‎First printing of Lebesgue's seminal paper on the calculus, which generalized the Riemann integral.""Building on the work of others, including that of Emile Borel and Camille Jordan, Lebesgue formulated the theory of measure in 1901 and in his famous paper Sur une generalisation de l'integrale definie, which appeared in the Comptes Rendus on 29 April 1901 (the paper offered), he gave the definition of the Lebesgue integral that generalises the notion of the Riemann integral by extending the concept of the area below a curve to include many discontinuous functions. This generalisation of the Riemann integral revolutionised the integral calculus. Up to the end of the 19th century, mathematical analysis was limited to continuous functions, based largely on the Riemann method of integration. There is a problem here, namely that a function which is not Riemann integrable may be represented as a uniformly bounded series of Riemann integrable functions. What made the new definition important was that Lebesgue was able to recognise in it an analytic tool capable of dealing with - and to a large extent overcoming - the numerous theoretical difficulties that had arisen in connection with Riemann's theory of integration.""‎

书商的参考编号 : 49675

‎(WOLFF, CHRISTIAN).‎

‎Vollständiges Mathematisches Lexicon, Darinnen alle Kunst=Wörter und Sachen, welche in der erwegenden und ausübenden Mathesi vor zu kommen pflegen...Überall aber zur Historie der Mathematischen Wissenschaften dienliche Nachrichten eingestreuet...(1.-)...‎

‎Leipzig, Gleditschen, 1734-42. 8vo. 2 cont. hcalf. Gilt backs. Backs rubbed, especially volume 2, which have been exposed to some damp, loosening the plates and some quires, but not dampstained. 2 engraved frontispieces. (6),(69o),(4)(6),543,140,(10) pp. and 46 engraved plates (36+10). Some light browning to inner margins in volume 2. Stamps on title-pages.‎

‎Largest edition of Wolff's well-known encyclopedia in which are treated all aspects of the mathematical sciences, pure as well as technical, the calculus, stereometrie, astronomy, hydrostatics, architecture etc. etc.‎

书商的参考编号 : 49682