‎Mathématiques‎

‎"QUINE, WILLARD ORMAN VAN.‎

‎A System of Logistic. - [MAGNIFICENT PRESENTATION-COPY]‎

‎Cambridge, Massachusetts, Harvard University Press, 1934. Original full red cloth with gilt line-borders to boards, original dust-jacket, somewhat worn, with a red label over the price and chips and nicks to extremities. Minor loss to corners of dust-jacket, and a large loss of upper part of spine of dust-jacket (ca. 6 x 2 cm), thus lacking the title to spine of dust-jacket, and leaving the cloth of the same part of the spine sunned and the gilding of the title on spine almost faded off. Some soiling to dust-jacket. Internally nice and clean. X, (2), 204 pp.‎

‎An excellent presentation copy of this scarce first edition of the great logician's first book, which is the published version of his doctoral thesis, hailed by Whitehead as a landmark in the history of symbolic logic.Inscribed by Quine ""To F. Gomes Cassidy, historian of/ languages, from Van Quine, manu-/ facturer of one. Mathematical/ truth is linguistic convention,/ and logic is the [four Chinese characters]"".Frederic Gomez Cassidy (1907-2000) was a great capacity within wold language scholarship and a close friend of Quine, whom he had known since school and been to Oberlin College with. He was a talented linguist specialized in Early English, Creoles, Lexicography, and American language, who is now primarily famous for his lately begun monumental project, the ""Dictionary of American Regional English"" (known as DARE). Cassisy was born in Jamaica to a Canadian father and a Jamaican mother and grew up hearing their varieties of standard British English as well as the Cleole variety of the Black majority. When Cassidy was eleven years old, the whole family moved to Ohio. ""Here the young Jamaican was introduced to yet another variety of English and was dismayed to learn that it was he who sounded ""funny."" But that distinction was to have a significant benefit. It piqued the curiosity of a classmate who sought to know and befriend the boy who looked, acted, and sounded so different. That classmate was Willard Van Orman (""Van"") Quine, later to become one of America's most distinguished philosophers. The friendship he and Fred began as boys was to last their lifetimes, nourished by shared experiences at Oberlin College, regular correspondence through the decades, and frequent summer hiking trips."" (Memorial Resolution of the Faculty of the University of Wisconsin-Madison on the Death of Professor Emeritus Frederic Gomes Cassidy). The time at Oberlin College was of specific joy to him, and it was here he came to explore his interest in languages, philosophy, and science. He obtained his BA in 1930 and his MA, also at Oberlin, in 1932, and in 1938 he was given his PhD from the University of Michigan. Quine graduated from Oberlin College in 1930. He then won a scholarship to study for his doctorate at Harvard University, where he wrote the important thesis that was to constitute his first book. Quine's supervisor at Harvard was Alfred North Whitehead, who has also written the Foreword to his first book and who introduced him to Bertrand Russell, who visited Harvard during this time. From then on, Quine kept an ongoing correspondence with Russell. Quine finished his doctorate in two years and was awarded his Ph.D. in philosophy from Harvard in 1932. After that he received a travelling fellowship, which he used to travel to Vienna, where he got acquainted with the members of the Vienna Circle. During his travels he also met Gödel and Ayer. In Warsaw he spent six weeks with Tarski, and in Prague he studied under Carnap, who greatly inspired him. After his year of travelling, he returned to Harvard, where he published the present version of his doctoral dissertation, his first book.""In this book Dr. Quine has effected an extension of the scope of Symbolic Logic. The advance is more than an improvement in symbols. It extends to fundamental notions. He has introduced a generality adequate to the complexity of the subject matter"" and the symbolism embodies the generality of its meaning. I have no hesitation in stating by belief that Dr. Quine's book constitutes a landmark in the history of the subject."" So Whitehead writes in his Foreword (p. (IX) ). The logic that Quine takes into consideration is that of Russel and Whitehead's ""Principia Mathematica"", and when Whitehead towards the end of the Foreword states that ""Dr. Quine does not touch upon the relationship of Logic to Metahysics. He keeps strictly within the boundaries of his subject. But - if in conclusion I may venture beyond these limits - the reformation of Logic has an essential reference to Metaphysics. For Logic prescribes the shapes of metaphysical thought"" (p. X), the metaphysics he is talking about is nominalism. For Russell and Whitehead, Quine's work represented an unusual illustration of their own logic.The work was also under much influence of the Polish logicians, and as Whitehead concludes in his Foreword, ""it is interesting to note the influence of of the work of Professor H. M. Scheffer, and of the great school of Polish mathematicians. There is continuity in the progress of ordered knowledge."" (P. X).‎

书商的参考编号 : 37638

‎EUCLID (EUKLID) OF ALEXANDRIA.‎

‎Euclidis Elementorum libri XV. Una cum scholiis antiqvis a Federico Commandino Urbinate in latinum conuersi. Ac nuper a multis mendis quibus antea scatebat vendicati....‎

‎Pisavri (Pesaro), Typis Flaminij Concordiæ, 1619. Folio. Contemp. hcalf. Fronthinge nearly broken, but still holding. Titlepage in red a. black. (8) of 10 leaves, lacking first leaf of the foreword and last leaf of Index. Text complete. 255 leaves with many figures in the text. First 16 leaves with some browning and foxing in lower right corners. 5 leaves mended, no loss of text and 8 with smaller repairs, no loss. A few annotations in margins in old hand.‎

‎Scarce second (expanded) edition of Federico Commandino's importent translation of the Elements. Commandino's first translation was published in 1572, and this translation was made use of by subsequent editors for centuries. The first Italian translation was also done from the Latin text of Commandino. - Riccardi 1619,2. - Max Steck: IV 19.‎

书商的参考编号 : 37801

‎PÓLYA, G. und G. SZEGÖ.‎

‎Aufgaben und Lehrsätze aus der Analysis. 2 Bde. (1. Reihen. Integralrechnung. Funktionentheorie - 2. Funktionentheorie. Nullstellen. Polynome. Determinanten. Zahlentheorie.‎

‎Berlin, Göttingen, Heidelberg. Springer-Verlag, (1954). 2 orig. full cloth. XVI,338X,407 pp.‎

书商的参考编号 : 37836

‎KOWALEWSKI, GERHARD.‎

‎Einführung in die Analytische Geometrie. Dritte, unveränderte Aufl.‎

‎Berlin, Walter de Gruyter, 1929. Orig. full cloth. A small tear at upper part of fronhinge. (8),360 pp., 112 textdiagrams. Clean and fine.‎

书商的参考编号 : 37842

‎CARNAP, RUDOLF.‎

‎Einführung in die symbolische Logik mit besonderer Berücksichtigung ihrer Anwendungen. Zweite neubearbeitete und erweiterte Auflage. Mit 5 Textabbildungen. - [MAX BLACK'S COPY]‎

‎Wien, Springer=Verlag, 1954. 8vo. Orig. grey cloth w. blue lettering, capitals a bit bumped" orig. white and black dust-jacket w. some soiling, and a bit of loss to upper capital. X, 209, (1), (2, -advertisements) pp.‎

‎Second issue of Carnap's important Introduction to Symbolic Logic with Applications, which constitutes a highly important introduction to this foundational science of the 20th century, Max Black's copy with his signature to front free end-paper.""Die symbolische Logik ist eine Grundlagenswissenschaft ersten Ranges geworden, deren Bedeutung heute vor allem in angelsächsischen Ländern eingeschätzt wird. Nach den Worten des Verfassers, der, aus dem ""Wiener Kreis"" kommend, selbst massgeblich an der Gestaltung dieser Wissenschaft mitgewirkt hat, ist die Symbolik eine unter genauen Regeln stehende Sprach, durch deren Verwendung die Formen des eigenen Denkens verschärft werden können..."" (Front flap).The British-American Max Black (1909-1988) was one of the leading analytic philosophers of the first half of the 20th century. He has contributed with important works within the fields of philosophy of language, mathematics and science as well as studies on and translations of Frege. He studied mathematics at Queens' College, Cambridge, where he met Russell, Wittgenstein, G. E. Moore, and Ramsey and developed a profound interest in the philosophy of mathematics.Rudolf Carnap (born 1891 in Ronsdorf, Germany, died 1970 in Santa Monica, California) was an immensely influential analytic philosopher, who has contributed decisively to the fields of logic, epistemology, semantics, philosophy of science, and philosophy of language. He was one of the leading figures of the Vienna Circle, and a prominent logical positivist. He studied philosophy, physics and mathematics at the universities of Berlin and Freiburg, and worked at the universities of Jena, Vienna and Prague until 1935, when he, due to the war, emigrated to the U.S., where he became an American citizen in 1941. In America he became professor of the University of Chicago. In Jena he was appointed Professor of Mathematics, though his main interest at that time was in physics.After the publication of his first work, Carnap's involvement with the Vienna Circle began to develop. He met Reichenbach in 1923 and was introduced to Moritz Schlick in Vienna, where he then moved to become assistant professor at the university. He soon became one of the leading members of the Vienna Circle, and in 1929 he, Neurath, and Hahn wrote the manifest of the Circle.This copy of Carnap's important introduction to this field so important for the analytic philosophers, unites two of the giants of the period. In his autobiography, Carnap writes ""I also had interesting discussions with some of the younger philosophers, among them Alfred Ayer, who had been in Vienna for some time when I was already in Prague, R.B. Braithwaite, and Max Black"" they were interested in recent ideas of the Vienna Circle, such as physicalism and logical syntax."" (In Schilpp, ""The Philosophy of Rudolf Carnap"", 1963, p.34).‎

书商的参考编号 : 37993

‎VON NEUMANN, JOHANN (JOHN).‎

‎Eine Axiomatisierung der Mengenlehre. [In: Journal für die reine und angewandte Mathematik, vol. 154, pp.219-240]. - [THE VON NEUMANN AXIOMS OF SET THEORY]‎

‎Berlin & Leipzig: Walter de Gruyter, 1925. Large 4to. (300x234mm). The entire volume 154 [(4),259,(1) pp.] offered here in original blank wrappers. Exceptionally fine.‎

‎First edition of von Nuemann's first significant publication, in which he introduced the concept of classes, and gave the first finite axiomatisation of set theory.‎

书商的参考编号 : 38042

‎HALL, A. RUPERT.‎

‎Philosophers at War. The Quarrel between Newton and Leibniz.‎

‎Cambridge, London etc., Cambridge University Press, (1980). Orig. full cloth with dustjacker. XIII,338 pp.‎

书商的参考编号 : 38162

‎"GAUSS, CARL FRIEDRICH. - THE METHOD OF LEAST SQUARES IN GERMAN.‎

‎Theorie der Bewegung der Himmelskörper welche in Kegelschnitten die Sonne umlaufen. Ins Deutsche übertragen von Carl Haase. Mit einem Anhange sowie mit einer photographisches Abbildung...Gauss-Medaille...Facsimile der Gauss'schen lateinischen und deut...‎

‎Hannover, Carl Meyer, 1865. 4to. Contemp. modest hcloth. 2 orig. photographs mounted as frontispiece (Gauss-medal). 279,72,(2) pp. 3 plates, 6 tables. Internally clean.‎

‎First German edition of this milestone in mathematical statistics, first published in Latin as ""Theoria motus corporum coelestium in sectinibus conicis solem ambientum. 1809."" - In this work Gauss revealed for the first time his method of least squares. On January 1, 1801, the Italian astronomer Giuseppe Piazzi discovered the planetoid Ceres, but could only observe it for few days before it was lost in the glare of the Sun until the end of the year. After so many months of not being observed it was not possible to calculate with existing methods at which position it should reappear. However Gauss, at an age of 24, astounded when he in December predicted the exact location at which Ceres again could be observed. Gauss did not reveal how he had calculated the orbit of Ceres. First in 1809 Gauss published his second book ""Theoria motus corporum coelestium in sectionibus conicis solem ambientium"" (the offered item) in which he revealed his new method of orbit calculation. In the first part he dealt with differential equations, conic sections and elliptic orbits, while in the second part, the main part of the work, he showed how to estimate and then to refine the estimation of a planet's orbit using a new method involving minimizing the sum of squared residuals, e.g., the method of least squares. He was able to prove the correctness of the method under the assumption of normally distributed errors. It is here that the Gaussian curve, expressing statistical distribution in probablility, makes its appearance. This work, along with the 'Discuisitiones', was the fruit of the triumphal decade in Gauss' life and established his reputation as a mathematical and scientific genius of the first order. Hald: History of Mathematical Statistics 1750-1930, pp.351-357.‎

书商的参考编号 : 38464

‎"GULDBERG, ALF.‎

‎Om integration af Differentialligninger af 2den orden.‎

‎Christiania, Jacob Dybwad, 1895. Uncut in orig. printed wrappers. Offprint from ""Christiania Videnskabs-Selskabs Forhandlinger 1895. No. 6"". 48 pp.‎

‎First edition. Offprint issue.‎

书商的参考编号 : 38572

‎STURM, (JOHANN CHRISTOPH).‎

‎Mathesis Compendiaria sive Tyrocinia Mathematica Tabulis. Matheseos Generalis. Arithmeticis. Algebraicis. Geometricis. Trigonometrica. Opticis. Architecturæ Militaris. Architecturæ Civilis. Chronologicis. Statica sive Mechanica. Horologiographica. Chi...‎

‎Leipzig & Coburg, Pauli Güntheri Pfotenhaueri, 1707. Bound to style in a fine later full calf., raised bands, gilt compartments and titlelabel. 69 pp., 19 full-page engraved illustrations and 2 half-page. 2 nicks to the right part of titlepage neathly repaired, no loss of text.‎

‎Fifth edition of Sturm's excellent illustrated work on the different branches of pure and applied mathematics, such as geometry, arithmetics, algebra, trigonometry, optics, statics, mechanics etc.‎

书商的参考编号 : 38637

‎"LEBESGUE, HENRI.‎

‎Lecons sur les Séries Trigonométriques.‎

‎Paris, Gauthier-Villars, 1906. Contemp. full cloth, gilt lettering on spine. (8),128 pp. A few faint brownspots in the margins of the first leaves, otherwise fine and clean.‎

‎First edition. Lebesgue is known for ""The Lebesgue Integral"" and his invention of measure, called ""The Lebesgue Measure"". The item offered is his second book.‎

书商的参考编号 : 38673

‎BOREL, ÉMILE.‎

‎Lecons sur les Fonctions de Variables Réelles et les Developppements en Séries de Polynomes. Avec des Notes par Paul Painleve et Henri Lebesque.‎

‎Paris, Gauthier-Villars, 1905. Royal8vo. Orig. printed wrappers. Backstrip with small tears. VIII,(1),160 pp.‎

‎First edition.‎

书商的参考编号 : 38681

‎FRECHET, MAURICE.‎

‎Méthode des fonctions arbitraires.Theorie des évenements en chaine dans le cas d'un nombre fini d'états possibles.‎

‎Paris, Gauthier-Villars, 1938. Royal8vo. Uncut in orig. printed wrappers. (24),315 pp.‎

‎First edition.‎

书商的参考编号 : 38688

‎"CARTAN, ÉLIE.‎

‎La Géométrie des espaces de Riemann.‎

‎Paris, Gauthier-Villars et Cie, 1925. Uncut in orig. printed wrappers. (Mémorial des Sciences Mathématiques...Fascicule IX). (4),60,(4) pp. Small tears to backstrip, no loss.‎

‎First edition. The modern theory of differential geometry grew up in the years following Einstein's introduction of his general theory of relativity, by the work of Elie Cartan (his Géométrie des espaces de Riemann) and Herman Weyl.""Cartan was one of the most profound mathematicians of the last hundred years, and his influence is still one of the most decisive in the development of modern mathematics...Cartan's contributions to differential geometry are no less impressive, and it may be said that he revitalized the whole subject, for the initial work of Riemann and Darboux was being lost in dreary computations and minor results...his guiding principle was a considerable extension of the method of ""moving frames"" of Darboux and Ribaucooour, to which he gave a tremendous flexibility and power, far beyond anything that had been done in classical differential geometry."" (Jean Dieudonne in DSB).‎

书商的参考编号 : 38704

‎RUTHERFORD, D.E.‎

‎Introduction to Lattice Theory.‎

‎Edinborgh a. London, Oliver & Boyd, (1965). Orig. boards with dustjacket. VIII,117 pp.‎

书商的参考编号 : 38743

‎GENOCCHI, ANGELO (recte GIUSEPPE PEANO).‎

‎Calcolo differenziale e principii di calcolo integrale, pubbicato con aggiunte dal Dr. Giuseppe Peano. - [A FOUNDATIONAL WORK OF THE SCIENCE OF INFINITESIMAL CALCULUS]‎

‎Torino, Fratelli Bocca, 1884. 8vo. Cont. full green cloth w. gilt title and ornamentation to spine. Minor occasional browning. A very nice and clean copy. XXXII, 333, (5, -index and errata) pp.‎

‎The scarce first edition of Peano's first major publication, his first book, the work that brought him international fame, and one of the most important calculus texts since the time of Euler and Cauchy.The present book, which has a somewhat strange history, contributing to its scarcity, is considered a constitutional work of the science of infinitesimal calculus. In 1899 it was translated into German, and in 1903 into Russian.The famous Italian mathematician, logical philosopher, pioneer of symbolic logic, and a founder of mathematical logic and set theory, Giuseppe Peano (1858 -1932), studied mathematics at the University of Turin, where he was employed just after graduating (1880), and where he stayed almost all of his life, devoting his life to mathematics. After having graduated with honours, he was employed to assist first Enrico D'Ovidio, and then the renowned Angelo Genocchi, who possessed the chair of Infinitesimal calculus. At this time, Genocchi's health was declining, and the teaching of the infinitesimal calculus course was handed over to Peano already in 1882. In 1880 Peano had published his first paper, and the following year he published another three" in 1884 he published his first book, the foundational ""Calculus and Principles of Integral Calculus"", which constitutes one of ""the most important works on the development of the general theory of functions since the work of the French mathematician Augustin-Louis Cauchy (1789-1857)"". (Encycl. Britt.)As is evident from the title-page, the work was based on Genocchi's lectures on calculus"" however, the book turned out to be much more than, and in fact something completely different from, that. Peano stands as the editor of the work, but in fact most of the book is written by Peano himself. Apparently, Genocchi had given his approval to the publication of an edited version of his lectures, but when he saw the final result, he regretted the fact that it had appeared under his name. Genocchi stated in a letter that ""... the volume contains important additions, some modifications, and various annotations, which are placed first. So that nothing will be attributed to me which is not mine, I must declare that I have had no part in the compilation of the aforementioned book and that everything is due to that outstanding young man Dr Giuseppe Peano ..."".Peano assumed full responsibility for the work and also recognised it as his own. He later saw the importance that this book has had on the development of the science of infinitesimal calculus. ""In 1915 he (Peano) printed a list of his writings, adding: ""My works refer especially to infinitesimal calculus, and they have not been entirely useless, seeing that, in the judgment of competent persons, they contributed to the constitution of this science as we have it today."" This ""judgment of competent persons"" refers in part to the ""Encyclopädie der mathematischen Wissenschaften"", in which Alfred Pringsheim lists two of Peano's books among nineteen important calculus texts since the time of Euler and Cauchy. The first of these books was Peano's first major publication and is something of an oddity in the history of mathematics, since the title page gives the author as Angelo Genocchi, not Peano: ""Angelo Genocchi, Calcolo differenziale e principia de calcolo integrale, publicato con aggiunte dal Dr. Guiseppe Peano."" The origin of the book is that Bocca Brothers wished to publish a calculus text based on Genocchi's lectures. Genocchi did not wish to write such a text but gave Peano permission to do so. After its publication Genocchi, thinking Peano lacked regard for him, publicly disclaimed all credit for the book, for which Peano then assumed full responsibility."" (D.S.B. X:441).Later the same year, after the publication of this his first major work, Peano became professor at the university of Turin. His first work now stands, not only as one of the founding texts of modern infinitesimal calculus, but also as a prime example of Peano's excellent style, which perfectly mixes simplicity and rigour. ""Beginning with a strict definition of real number, essentially that of Dedekind, he develops the calculus systematically, formulating every theorem with the greatest possible accuracy and precision, and strictly avoiding in the proofs any illegitimate appeal to intuitive properties of curves. When the customary enunciations of theorems are too loose, or conditions that need to be satisfied are not as a rule clearly stated, Peano often constructs counter-examples to show that assertions made in standard textbooks are incomplete or erroneous...."" (Kneebone, Mathematical Logic and Foundations of Mathematics, p. 142). Cellerino nr. 1. ""Prima edizione del primo libro di Peano che venne tradotto nel 1899 in tedesco e nel 1903 in russo. Pubblicato sotto il nome di Genocchi di cui Peano era assistente, il volume è in realtà interamente opera sua tanto che Genocchi lo disconobbe publicamente dando origine ad una breve polemice. Questa è l'opera che diede a Peano notorietà internazionale."" (Cellerino, Guiseppe Piano e la sua scuola. Catalogo monografico. Milano, 2004).‎

书商的参考编号 : 38779

‎"LAMBERT, JOHANN HEINRICH.‎

‎Abhandlung Von dem Gebrauche der Mittagslinie Beym Land=und Feldmessen.‎

‎(München, 1863). 4to. Bound in recent hcloth. Issued in ""Abhandlungen der Churfürstlichen Baierischen Akademie der Wissenschaften"", Bd. I, pp. (3-)54, and 1 folded engraved plate. Fine and clean.‎

‎First edition. - Poggendorff I:1357.‎

书商的参考编号 : 38812

‎"PEANO, GUISEPPE.‎

‎Applicazioni geometriche del calcolo infinitesimale. - [THE ""GEOMETRICAL CALCULUS""]‎

‎Torino, Bocca, 1887. Large 8vo. Cont. half vellum binding with gilt leather title-label to spine. Old library-mark rather crudely removed from back. Inner front hinge a bit weak. A bit of brownspotting. Library-stamp to title-page. XII, 334, (2) pp.‎

‎The rare first edition of the work in which Peano introduces the basic elements of geometric calculus and gives new definitions for the length of an arc and for the area of a curved surface.The famous Italian mathematician, logical philosopher, pioneer of symbolic logic, and a founder of mathematical logic and set theory, Giuseppe Peano (1858 -1932), studied mathematics at the University of Turin, where he was employed just after graduating (1880), and where he stayed almost all of his life, devoting his life to mathematics. After having graduated with honours, he was employed to assist first Enrico D'Ovidio, and then the renowned Angelo Genocchi, who possessed the chair of Infinitesimal calculus. In 1890 Peano became extraordinary professor, and in 1895 ordinary professor, of infinitesimal calculus at the Unversity of Turin. His important work ""Geometrical Applications of Infinitesimal Calculus"" is based on Peano's lectures on infinitesimal calculus and its application to geometry from 1885. In the important work he introduced his geometrical calculus and presented several new geometrical discoveries.""The treatise ""Applicazioni geometriche del calcolo infinitesimal"" (1887) was based on a course Peano began teaching at the University of Turin in 1885 and contains the beginnings of his ""geometrical calculus"" (here still influenced by Bellavitis' method of equipolences), new forms of remainders in quadrature formulas, new definitions of length of an arc of a curve and of area of a surface, the notion of a figure tangent to a curve, a determination of the error term in Simpson's formula, and the notion of the limit of a variable figure. There is also a discussion of the measure of a point set, of additive functions of sets, and of integration applied to sets. Peano here generalized the notion of measure that he had introduced in 1883."" (D.S.B. X:443).‎

书商的参考编号 : 38823

‎WEYL, HERMANN.‎

‎Mathematische Analyse des Raumproblems. Vorlesungen gehalten in Barcelona und Madrid. Mit 8 Abbildungen.‎

‎Berlin, Julius Springer, 1923. Orig. printed wrappers, uncut. Small nicks to backstrip. VII,117,(1) pp. Clean and fine.‎

‎First edition.‎

书商的参考编号 : 38942

‎"SHANNON, C.E.‎

‎Probability Error for Optimal Codes in a Gaussian Channel.‎

‎(New York), American Telephone and Telegraph Compagny, 1959. Orig. printed wrappers. A stamp on frontwrapper and first leaf. ""The Bell System Technical Journal"", Volume 38, Number 3, pp. 611-907. The Shannon paper: pp. 611-656.‎

‎First edition. ""A study is made of coding and decoding systems for a continous channel with an additive gaussian noise and subject to an average power limitation at the transmitter. Upper and lower bounds are found for the error probability in decoding with optimal codes and decoding systems. These bounds are close together for signaling rates near channel capacity and also for signaling rates near zero, but diverge in between. Curves exhibiting these bounds are given."" (Shannon p. 611). - Hook & Norman: 898.‎

书商的参考编号 : 38947

‎BOHR, HARALD.‎

‎Zur Theorie der Fast Periodischen Funktionen. I-III. (I. Eine Verallgemeinerung der Theorie der Fourierreihen - II. Zusammenhang der fastperiodischen Funktionen mit Funktionen von unendlich vielen Variabeln" gleichmässige Approximation durch trigonome... - [ALMOST PERIODIC FUNCTIONS]‎

‎(Berlin, Stockholm, 1924-25). 4to. Bound in one full fabrikoid. As issued in ""Acta Mathematica"", vols 45,46,47. - Pp. 29-127, pp. 102-214 - pp. 238-281. Clean and fine. A very small tear to the last two leaves repaired without loss.‎

‎First edition of Harald Bohr's main work. Harald Bohr was younger brother to Niels Bohr. ""The problem of which function may be represented by Dirichlet series led Bohr to his main achievement, the theory of almost periodic functions, on which the greater part of his later work is concentrated....Whereas hitherto in the theory of Dirichlet series one always worked withh frequencies forming a monotonic sequence, Bohr discovered that in order to obtain an answer to the problem one would have to consider series with quite arbitrary frequencies. The answer was obtained by introducing the notion of almost periocicity. The theory was published in three papers (the offered papers) in ""Acta Mathematica"", and numerous mathematicians joined in the work on its simplification and extension. Thus Weil and Wiener connected it with the classical theories of integral equations and Fourier integrals, and Bochner developed a summation method for Bohr-Fourier series gneralizing Fejér's theorem."" (Børge Jessen in DSB).‎

书商的参考编号 : 38967

‎BIRCH, T.W.‎

‎Maps topographical and statistical.‎

‎Oxford, Clarendon Press, (1960). Small 4to. Orig. full cloth. XIV,240 pp., textillustrations and plates.‎

书商的参考编号 : 38984

‎BURKHARDT, HEINRICH.‎

‎Funktionentheoretische Vorlesungen. 1,-2. Theil. (1. Einführung in die Theorie der Analytischen Functionen einer complexen Veränderlichen. - 2. Elliptische Funktionen).‎

‎Leipzig, Veit & Comp., 1897-99. Bound in one contemp. hcalf. Spine gilt. Slightly rubbed. XII,213,XVI,373 pp. Internally clean and fine‎

书商的参考编号 : 38993

‎"LA GRANGE (LAGRANGE), JOSEPH LOUIS. - MAXIMA AND MINIMA.‎

‎Sur les Courbes Tautochrones. (and ) Nouvelles Réflexions sur les Tautochrones. - [THE CALCULUS OF VARIATIONS]‎

‎(Berlin, Haude et Spener, 1767 and Berlin, Ch. Fr. Voss, 1774). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"" Tome XXI, pp. 364-380 and "" Nouveau Mémoires..."", pp. 97-122.‎

‎Both first edition in the journal form. Huygens proved Geometrically in 1659 that the tautochrone was a cycloid curve. This solution was later used to attack the problem of the Brachistochrone curve. Jacob Bernoulli solved the problem by using calculus in a paper from 1690, which for the first time used the term 'integral'. Both Lagrange and Euler loked for an analytical solution to the problem. Lagrange, in the papers offered here, developed a formal calculus based on the analogy between Newton's theorem and the successive differentiations of the product of two functions. He also communicated this to Eule in a letter written in Latin slightly before the Italian publication. In a letter to D'Alembert in 1769 Lagrange confirmed that this method of maxima and minima was the first fruit of his studies - he was only 19 when he divised it - and that he regarded it as his best work.A paper by Leonhard Euler:Éclaircissement plus détailles sur La generation et Propagation du Son et sur la Formation de L'Echo"" Berlin Academy Royale 1767"" in first edition withbound.‎

书商的参考编号 : 39044

‎"LA GRANGE (LAGRANGE), JOSEPH LOUIS.‎

‎Sur L'Integration des Equations à differences partielle du premier ordre. - [A MASTERPIECE OF ANALYSIS]‎

‎(Berlin, C.F. Voss, 1774). 4to. Uncut with wide margins, without wrappers as issued in ""Nouveaux Memoires de L'Academie Royales des Sciences et Belles- Lettres"", Année MDCCLXXII, pp. 353-372.‎

‎First edition of a work which is a breakthrough in the theory of ""First Order Partial Differential Equations"", generalizing the method of variation of parameters for solving differential equations. "" The oldest theory of integration of partial differential equations of the first order are due to Lagrange"" it is based on the fundamental fact that the most general solution of such differential equations can be calculated with the help of differentiations and eliminations if a complete integral of the differential equationn is known"" - ""This problem (of partial differential equations) had only been lightly touched on by Clairaut, Euler, d'Alembert, and Condorcet. Lagrange wrote: ""Finally I have just read a memoir that Mr de Laplace presented recently.....This reading aweakened old ideas that I had on the same subject and resulted in the following investigations...(which constitute) a new and complete theory."" Laplace wrote on 3 February 1778 that he considered Lagrange's essay ""a masterpiece of analysis, by the importence of the subject, by the beauty of method, and by the elegant manner in which it is represented."" (DSB). - Parkinson, Breakthroughs 1774 M.‎

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