‎Mathématiques‎

‎"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.‎

Riferimento per il libraio : 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.‎

Riferimento per il libraio : 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.‎

Riferimento per il libraio : 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).‎

Riferimento per il libraio : 38704

‎RUTHERFORD, D.E.‎

‎Introduction to Lattice Theory.‎

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

Riferimento per il libraio : 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).‎

Riferimento per il libraio : 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.‎

Riferimento per il libraio : 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).‎

Riferimento per il libraio : 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.‎

Riferimento per il libraio : 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.‎

Riferimento per il libraio : 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).‎

Riferimento per il libraio : 38967

‎BIRCH, T.W.‎

‎Maps topographical and statistical.‎

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

Riferimento per il libraio : 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

Riferimento per il libraio : 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.‎

Riferimento per il libraio : 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.‎

Riferimento per il libraio : 39049

‎"EULER, LEONHARD.‎

‎Principes de la Trigonometrie Spherique tirés de la Méthode des plus Grands et plus Petits (Principles of spherical Trigonometry deduced from the Method of Maxima and Minima). (And same author:) Élémens de la Trigonometrie spheroidique tirés de la Met... - [EULER'S SPHERICAL GEOMETRY]‎

‎(Berlin, Haude et Spener, 1755). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome IX, pp. 223-257 and 1 folded engraved plate (a tear to plate, no loss), and pp. 258-293 and 1 folded engraved plate.‎

‎Both papers first edition. The modern form of trigonometry as well of all trigonometry are due to Euler. Whereas trigonometry before Euler was concerned with trigonomic Lines, Euler's trigonometry deals with trigonomic Function. - ""In the first paper Euler constructs spherical trigonometry as the intrinsic geometry of the surface of the sphere. He expresses the line element ds of the surface in terms of the longitude and latitude of a point, defines the great circles as curves that minimize the integral of the line element, and, in connection with with the determination of the minimum of a side of a spherical triangle, derives 10 equations of spherical geometry.. After the discovery that the shape of the earth is that of a spheroid, Euler, (in the second paper here offered) extended his methods to spheroids. He develops this subject in its entirety...and here deduced very many of the formulas of spherical geometry"" (Rosenfeld & Abramovich). - Enestrom: E:214 a. E: 215. - Another Paper by Euler is withbound: Examen d'une Controverse sur la Loi de Refraction de Rayon de differentes Couleurs par Rapport a la diversité des Milieux transparens par lesquels ils sont transmis."" pp. 294-320. (Enestrom: E 216.‎

Riferimento per il libraio : 39052

‎BRETSCHNEIDER, C.A.‎

‎Die Geometrie vor Euklides. Ein historischer Versuch.‎

‎Leipzig, H.G. Teubner, 1870. Modest contemp. hcloth. Stamp on titlepage. IV,184 pp., 1 folded lithographed plate. First and last leaves slightly brownspotted.‎

Riferimento per il libraio : 39076

‎"LAMBERT, JOHANN HEINRICH.‎

‎Observations Analytiques.‎

‎(Berlin, C.F. Voss, 1772. 4to. Without wrappers as extracted from ""Nouveaux Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Annee 1770, pp. 225-244 and 1 engraved plate.‎

‎First edtion. In this paper Lambert starts from a simple problem for a function of 2 variables x and y, then proceeds to expand the method to more difficult differentiations.‎

Riferimento per il libraio : 39084

‎"EULER, LEONHARD.‎

‎Recherches sur la Déclination de L'Aiguille aimantée. (And:) Corrections Nécessaires pour la Théorie de la Déclination. (And the same author:) Sur la Force de Colonnes.(Research concerning the declination of the magnetized needle - The necessary corre...‎

‎(Berlin, Haude et Spener, 1759-68). 4to. Without wrappers extracted from ""Mémoires de l'Academie Royale des Science et Belles-Lettres"", tome XIII, pp. 175-251 and 4 folded engraved plates, tome XXII, pp. 213-264 and 2 engraved plates., tome XIII, pp.and 1 folded engraved plate.‎

‎All 3 papers all in first edition. Euler's proposed theory of magnetic fields influenced both Faraday and Maxwell. Euler viewed the magnetic field as waves through the ether, jus like his theory of light was founded on the existence of the ether. - Enestrom E 237 + E 362 and E 238.‎

Riferimento per il libraio : 39097

‎"POINCARÉ, HENRI.‎

‎Sur L'Uniformisation des Fonctions Analytiques. - [THE UNIFORMIZATION PROBLEM SOLVED]‎

‎(Berlin, Stockholm, Paris, Almqvist & Wiksell, 1907). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler"", Bd. 31, pp. 1-63.‎

‎First edition. Clebsch and Riemann tried to solve the problem of the uniformization for curves. ""In 1882 Klein gave a general uniformization theorem, but the proof was not complete. In 1883 Poincaré announced his general uniformization theorem but he too had no complete proof. Both Klein and Poincaré continued to work hard to prove this theorem but no decisive result was obtained for twent-five years. In 1907 Poincare (in the offered paper) and Paul Koebe independently gave a proof of this uniformization theorem...With the theorem on uniformization now rigorously established an improved treatment of algebraic functions and their integrals has become possible."" (Morris Kline).‎

Riferimento per il libraio : 39130

‎"POINCARÉ, HENRI.‎

‎Sur les Intégrales irrégulieres des Equations linéaires. - [THE FORMAL THEORY OF ASYMPTOTIC SERIES]‎

‎(Berlin, Uppsala & Stockholm, Paris, 1886). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", Bd. 8, pp. 295-344.‎

‎First edition. ""The full recognition of the nature of those divergent series that are useful in the representation and calculation of functions and a formal definition of those series wer achieved by Poincaré and Stieltjes independently in 1886. Poincaré called these series asymptotic while Stieltjes continued to use the term semiconvergent. Poincaré took up the subject in order to further the solution of linear differential equations. Impressed by the usefulness of divergent series in astronomy, he sought to determine which were useful and why. he succededed in islolating and formulating the essential property...Poincaré applied his theory of asymptotic series to diffrential equations, and theree are many such uses in his treatise on celestical mechanics, 'Les Methodes nouvelles de la mechanique céleste"". (Morris Kline).‎

Riferimento per il libraio : 39132

‎"POINCARÉ, HENRI.‎

‎Sur une Forme nouvelle des Équations du Probleme des trois Corps. - [THE HAMILTON PRINCIPLE]‎

‎(Berlin, Uppsala & Stockholm, Paris, Almqvist & Wiksell, 1897). 4to. No wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", Bd. 21, pp. 83-97.‎

‎First edition. In this paper 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.‎

Riferimento per il libraio : 39134

‎"KLEIN, FELIX.‎

‎Über die sogenannte Nicht-Euclidische Geometri. (Erster-) Zweiter Aufsatz. - [THE NON-EUCLIDEAN GEOMETRY OF KLEIN]‎

‎(Leipzig, B.F. Teubner, 1871 a. 1873). Without wrappers, (wrappers blank to Second Part) as published in ""Mathematische Annalen. Hrsg. von Felix Klein, Walter Dyck, Adolph Mayer."" Vol. IV, pp. 573-625 and vol. VI, pp. 112-145. Kept in a cloth-portfolio.‎

‎First edition. In these groundbreaking papers Klein established that if Euclidean geometry is consistent then non-Euclidean geometry is consistent as well and he introduces the adjectives ""parabolic"", ""elliptic"", and ""hyperbolic"" for the respective geometries of Georg Riemann, of Nicolai Lobachevsky, of C.F. Gauss and Janos Bolyai. ""Cayley's idea (that metrical geometry is part of projective geometry) was taken over by Felix Klein (1849-1925) and generalized so as to include the non-Euclidan geometries. Klein, a professor at Göttingen, was one of the lading mathematicians in Germany during the last part of the nineeeeteenth and first part of the twentieth century. During the years 1869-70 he larned the work of Lobatchevsky, Bolyai, von Staudt, and Cayley"" however, even in 1871he did not know Laguerre's result. It seemed to him to be posible to subsume the non-Euclidean geometries, hyperbolic, and double elliptic geometry, under projective geometry byexploiting Cayley's idea. He gave a sketch og his thoughts in a paper of 1871, and then developed them in two papers (1871 a. 1873, the ppers offered here). Klein was the first to obtain models of non-Euclidean geometries."" (Morris Kline). - Sommerville, Bibliography of Non-Euclidean Geometry p.45 (1871) and p. 49 (1873).‎

Riferimento per il libraio : 39154

‎"WEIERSTRASS, KARL.‎

‎Über eine besondere Gattung von Minimalflecken.‎

‎Berlin, Königl. Akad. d. Wissenschaften, 1867. Orig. printed wrappers, uncut. In ""Monatsbericht der Königlich Preussischen Akademie der Wissenschaften zu Berlin"", August 1867, pp. 511-598. Weierstrass' paper: pp. 511-518.‎

‎First edition. Weierstrass is considered the most important German mathematician in the nineteenth-century after Gauss and Riemann.‎

Riferimento per il libraio : 39157

‎"HILBERT, DAVID.‎

‎Über ternäre definite Formen.‎

‎(Berlin, Stockholm, Paris, 1893). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", Vol. 17, pp. 169-197.‎

‎First edition. This importent paper constitutes Hilbert's own version of part of the solution of his ""Mathematische Probleme"" listed at the International mathematical Congress in Paris 1900 (as problem 17) on the ""Expression of definite forms by squares"". ""....But since as I have shown, not every definite form can be compounded by addition from squares of forms, the question arises - which I have answered affirmatively for ternary forms (the paper offered here)- whether every definite form may be expressed as a quotient of sums of squares of forms....""‎

Riferimento per il libraio : 39160