‎Mathematics‎

‎"HERMANN, GRETE.‎

‎Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. - [THE FOUNDATION OF COMPUTER ALGEBRA]‎

‎(Berlin, Julius Springer, 1926). 8vo. Without wrappers. Extracted from ""Mathematische Annalen. Begründet 1868 durch Alfred Clebsch und Carl Neumann. 95. Band"". Pp. 735-788.‎

‎"HERMANNUS, JACOBUS [HERMANN, JAKOB].‎

‎De nova accelerationis lege, qua gravia versus terram seruntur, suppositis Motu siurno terrae et vi gravitatis constanti.‎

‎Leipzig, Grosse & Gleditsch, 1709. 4to. In: ""Acta Eruditorum Anno MDCCIX"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 404-11. [Entire volume: Pp. (2), 547, (45) + eleven engraved plates.].‎

‎"HERMITE, C.‎

‎Note sur la réduction des fonctions homogénes á coefficients entiers et á deux indéterminées.‎

‎Berlin, G. Reimer, 1848. 4to. In ""Journal für die reine und angewandte Mathematik, 1848. Band, 4 Heft"". In the original printed wrappers, without backstrip. Fine and clean. [Hermite:] Pp. 357-364. [Entire volume: Pp. 275-364 + 3 folded plate.].‎

‎"HERMITE, CHARLES (+) JACOBI.‎

‎Extraits de deux lettres de M. Charles Hermite a M. Jacobi. - [THE VERY FIRST RESEARCH BY HERMITE]‎

‎Berlin, G. Reimer, 1846. 4to. In the original wrappers, without backstrip. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 32. Band, 1846"". Entire issue offered.‎

‎"HERMITE, CHARLES.‎

‎Sur quelques consequences arithmetiques des formules de la theorie des fonctions elliptiques.‎

‎Berlin, Stockholm, Paris, Beijer, 1885. 4to. With the original wrappers in ""Acta Mathematica, 5:4. Band]. No backstrip. Fine and clean. Pp. 297-330. [Entire issue: Pp. 297-408, 83-123 + 2 folded plates.].‎

‎"HERMITE, CHARLES. - INTRODUCING ""HERMITE-FUNCTIONS"" - ""HERMITE POLYNOMIALS""‎

‎Sur un nouveasu développement en série des fonctions. (2 Parts).‎

‎(Paris, Mallet-Bachelier), 1864. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 58, No 2 and No. 6. Pp. (93-) 140 a. pp. (261-) 296. (2 entire issues offered). hermite's paper: pp. 93-100 a. pp. 266-273.‎

‎First appearance of a famous paper in which Hermite introduced ""Hermite-functions"", solving differential equations over infinite intervals.""The Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series" in combinatorics, as an example of an Appell sequence, obeying the umbral calculus in numerical analysis as Gaussian quadrature in finite element methods as Shape Functions for beams" and in physics, where they give rise to the eigenstates of the quantum harmonic oscillator. They are also used in systems theory in connection with nonlinear operations on Gaussian noise. They are named after Charles Hermite (1864) (the paper offered) although they were studied earlier by Laplace (1810) and Chebyshev (1859).""(Wikipedia).‎

Bookseller reference : 48185

‎"HERMITE, CHARLES. - INTRODUCING HERMETIAN MATRICES.‎

‎Remarques sur un théoerème de M. Cauchy.‎

‎(Paris: Gauthier-Villars), 1855. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences"", Vol 41, No 6. Pp. (161-) 228. (Entire issue offered). Hermite's paper: pp. 181-183. Light marginal browning.‎

‎First apperance of the paper in which Hermite introduced the so-called Hermetian Matrix, which later should be of great importence for Quantum Mechanics.‎

Bookseller reference : 47893

‎"HERMITE, CHARLES. - SOLVING THE QUINTIC EQUATION.‎

‎Sur la résolution de l’équation du cinquième degré. (On the Solution of the Equation of the Fifth Degree).‎

‎(Paris, Mallet-Bachelier), 1858. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 46, No 11. Pp. (503-) 546 (entire issue offered). Hermite's paper: pp. 508-515.‎

‎First apperance of Hermite's famous paper in which he, by the application of elliptic functions, provided the first solution to the general equation of the fifth degree, the quintic equation.Hermite was a major figure in the development of the theory of algebraic forms, the arithmetical theory of quadratic forms, and the theories of elliptic and Abelian functions. He first studied the representation of integers in what are now called Hermitian forms. His famous solution of the general quintic equation appeared in Sur la résolution de l’équation du cinquième degré (1858"" ""On the Solution of the Equation of the Fifth Degree""). (Encyclopedia Britannica).Parkinson ""Breakthroughs"" 1858 M.‎

Bookseller reference : 47568

‎"HERMITE, CHARLES. - THE THEORY OF TRANSFORMATIONS.‎

‎Sur la théorie de la transformation des fonctions abéliennes. ( I,II,III a. IV,V,VI). 2 papers.‎

‎(Paris: Gauthier-Villars), 1855. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences"", Vol 40, No 5 + 6. Pp. (205-) 260 a. pp. (261-) 324. (2 entire issue offered). Hermite's paper's: pp. 249-256 a. 304-309.‎

‎First printing of Hermite's importent paper in which he created the theory of transformations.""Another topic on which Hermite worked and made important contributions was the theory of quadratic forms. This led him to study invariant theory and he found a reciprocity law relating to binary forms. With his understanding of quadratic forms and invariant theory he created a theory of transformations in 1855. His results on this topic provided connections between number theory, theta functions, and the transformations of abelian functions.""""Hermite’s 1855 results became basic for the transformation theory of Abelian functions as well as for Camille Jordan’s theory of ""Abelian"" groups. They also led to Herrnite’s own theory of the fifth-degree equation and of the modular equations of elliptic functions.""(DSB).‎

Bookseller reference : 49133

‎"HERSCHEL, J. F. W.‎

‎Description of a Machine for resolving by Inspection certain important Forms of Transcendental Equations. [Read May 7, 1832].‎

‎London, Taylor and Francis, 1833. 4to. As extracted, in ""Transactions of the Cambridge Philosophical Society"", volume 4. Fine and clean. Pp. (425)-440 + 1 plates.‎

‎First appearance of Herschel's paper on transcendental equations.‎

Bookseller reference : 54760

‎"HEYTING, (AREND).‎

‎Mathematische Grundlagenforschung Intuitionismus. Beweistheorie.‎

‎Berlin, Julius Springer, 1934. Bound with orig. wrappers in contemp. full cloth. Gilt lettering to spine. IV,73,(1) pp. A mint copy. (Issued in the series ""Ergebnisse der Mathematik und ihrer Grenzgebiete...Dritter Band.""‎

‎First edition. Heyting studied under Brouwer and became the leading figure of the 'Intutionistic School' in Logic and Mathematics. His work on Intuitionism and Proof Theory - the item offered - is a concise and well written survey in which the viewpoints of intuitionism and formalism are clearly described and contrasted. (A.S. Troelstra).‎

Bookseller reference : 40410

‎"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.‎

Bookseller reference : 49641

‎"HILBERT, DAVID.‎

‎Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem). Dem Andenken an Hermann Minkowski Gewidmet. - [Hilbert-Kamke problem]‎

‎Leipzig, B. G. Teubner, 1909. 8vo. Bound in contemporary half calf with gilt lettering to spine. In ""Mathematische Annalen"", 67 band. 1909. Bookplates to pasted down front free end-paper and library stamp to verso of title page. Top half of spine is detached. Bookblock, however, still firmly attached. Fine and clean. Pp. 281-300. [Entire volume: IV, 575 pp.].‎

‎First printing of a groundbreaking work in Number Theory. Edward Waring (1734-98) stated, in his ""Meditationes Algebraicae"" (1770), the theorem known now as ""Waring's Theorem"", that every integer is either a cube or the sum of at most nine cubes"" also every integer is either a fourth power of the sum of at most 19 fourth powers. He conjectured also that every positive integer can be expressed as the sum of at most r kth powers, the r depending on k. These theoremes were not proven by him, but by David Hilbert in the paper offered.Hilbert proves that for every integer n, there exists an integer m such that every integer is the sum of m nth powers. This expands upon the hypotheis of Edward Waring that each positive integer is a sum of 9 cubes (n=3, m=9) and of 19 fourth powers (n= 4, m=19).This issue also contains F. Hausdorff's ""Zur Hilbertschen Lösung des Waringschen Problems"", pp. 301-305.(Se Kline p. 609).‎

Bookseller reference : 47248

‎"HILBERT, DAVID.‎

‎Die logischen Grundlagen der Mathematik. - [IMPORTENT HILBERT-PAPER ON METAMATHEMATICS]‎

‎Berlin, Julius Springer, 1923. Later full cloth. In: ""Mathematische Annalen begründet durch Alfred Clebsch und Carl Neumann."", 88. Bd. (4),312 pp. Hilbert's paper: pp. 151-165. The whole volume offered.‎

‎First edition as a continuation of his paper from 1922 ""Neubegründung der Mathematik. Erste Mitteilung"".""This articlee, delivered as a lecture to the deutsche Naturforscher Gesellschaft in Leipzig, September 1922, is a sequel to (neubegründung...), and brings Hilbert's proof theory to maturity. Hilbert here introduces several technical refinements and clarification to his theory. Specifically: (i) he improves the formal system by adding a special sign for formal negation...(ii) he refines his account of the distinction between formal language and the metalanguage....(iii) he outlines a consistency proof for an elementary, quantifier-free formal system of number-theory. (iv) he begins to extend his proof theory to analysis and set theory....sketches a strategy for proving the consistency of a version of Zermel's axiom of choice for real numbers...(etc. etc). (William Ewald in from Kant to Hilbert, vol. II, pp.1134-35).‎

Bookseller reference : 41351

‎"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.‎

Bookseller reference : 49646

‎"HILBERT, DAVID.‎

‎Grundlagen der Geometrie. Zweite, durch Zusätze vermehrte und mit fünf Anhängen versehene Auflage. Mit zahlreichen in den Text gedruckten Abbildungen.‎

‎Leipzig, B.G. Teubner, 1903. Lex8vo. Orig. full cloth. Very slightly rubbed, a few tiny stains on covers. Small stamp on titlepage.V,175 pp. + Publishers announcements (2) pp.‎

‎Scarce second edition of a work which went through 15 editions in 100 years as one of the most influential mathematical publications of the 20th century. ""The development of Hilberts Grundlagen der Geometrie was not finished with the first edition. The complete content was continously revised, especially during his lifetime. He considered new results, gave hints in articles and improved his own formulations."" (Michael Toepell in Landmarks Writings in Western Mathematics). This second edition is nearly 2 times larger than the first edition, expanded with 5 supplements (Anhänge).‎

Bookseller reference : 38687

‎"HILBERT, DAVID.‎

‎Hermann Minkowski. - [HILBERT'S OBITUARY OVER MINKOWKI]‎

‎Leipzig, B.G. Teubner, 1910. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 68. Band. 4. Heft."" Entire issue offered. Internally very fine and clean. [Hilbert:] Pp. 445-71. [Entire issue: Pp. 445-572].‎

‎First printing of Hilbert's obituary over Minkowki. They had a life long friendship.""Minkowski was born of German parents who returned to Germany and settled in Königsberg [now Kaliningrad, R.S.F.S.R.] when the boy was eight years old. His older brother Oskar became a famous pathologist. Except for three semesters at the University of Berlin, he received his higher education at Köningsberg, where he became a lifelong friend of both Hilbert, who was a fellow student, and the slightly older Hurwitz, who was beginning his professorial career. Hilbert’s education at Königsberg and his close friendship with Hermann Minkowski both stimulated his interest in physics."" (DSB).‎

Bookseller reference : 44530

‎"HILBERT, DAVID.‎

‎Hermann Minkowski. - [HILBERT'S OBITUARY OVER MINKOWKI]‎

‎Leipzig, B.G. Teubner, 1910. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 68. Band. 4. Heft."" Entire issue offered. Internally very fine and clean. [Hilbert:] Pp. 445-71. [Entire issue: Pp. 445-572].‎

‎"HILBERT, DAVID.‎

‎Neue Begründung der Bolyai-Lobatschefskyschen Geometrie.. - [A]‎

‎Leipzig, B.G. Teubner, 1903. Orig. printed wrappers, no backstrip. In: ""Mathematische Annalen begründet durch Alfred Clebsch und Carl Neumann."", 57. Bd., 2 Heft. Pp. 137-264. The whole issue offered (Heft 2). Hilbert's paper:pp. 137-150 a. 7 textfigs.‎

‎First edition and first printing of Hilbert's importent proof of the possibility of the non-euclidean parallel-construction, in which he showes that only with the aid of ruler and compass it is possible to draw with the samer instruments, the common perpendicular to two lines which are not parallel and do not meet each other (the non-intersecting lines), the common parallel to the two lines which bound an angle"" and the line which is perpendicular to one of the bounding lines of an acute angle and parallel to the other, and how these constructions can be carried out. (Bonola: Non-Euclidean Geometry). The paper was reprinted in the second edition of his ""Grundlagen der Geometrie"" as Appendix III. (Sommerville: 1903 p. 196).‎

Bookseller reference : 41352

‎"HILBERT, DAVID.‎

‎The Foundations of Geometry. Authorized translation by E.J. Townsend.‎

‎Chicago, Open Court, 1902. Small 8vo. Orig. full red cloth, gilt. A rather faint dampstain along first hinge on frontcover, otherwise fine. VII,143 pp.‎

‎First English edition of Hilbert's ""Grundlagen der Geometrie"" from 1899, one of the most influential publications in 2oth Century mathematics.Throughout the 19th century geometry was developed far beyond our intuitive conception of space" hyperbolic geometry was discovered by Gauss, Bolyai, and Lobachevsky and elliptic geometry by Riemann. However, Euclidean and non-Euclidean geometry still involved an intuitive idea about the concepts 'point', 'line', 'lies on', 'between', etc. In his 'Grundlagen' Hilbert set out to give a strictly formal formulation of geometry were points, lines, planes are nothing more than abstract symbols and concepts as 'lies on' are simply algebraic relations between these symbols. Through his method Hilbert could analyse independence and completeness of the axioms for geometry and he presented a new smaller set of axioms for Euclidean geometry. It can not be said that the 'Grundlagen' contains new and surprising discoveries, its importance lies in the great influence which Hilbert's method had on all fields of mathematics, and even other sciences as physics, chemistry, and biology. The 'Grundlagen' initiated a whole new paradigm shift and eventually evolved mathematics, throughout the 20th century, into a network of axiomatic formal systems.‎

Bookseller reference : 35061

‎"HILBERT, DAVID.‎

‎The Foundations of Geometry. Authorized translation by E.J. Townsend.‎

‎Chicago, Open Court, 1902. Small 8vo. Orig. full red cloth, gilt. A rather faint dampstain along first hinge on frontcover, otherwise fine. VII,143 pp.‎

‎"HILBERT, DAVID.‎

‎Ueber binäre Formen mit vorgeschriebener Discriminante.‎

‎Leipzig, B. G. Teubner, 1888. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 31., 1888. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Very fine and clean. Pp. 482-492. [Entire volume: IV, 606 pp.].‎

‎First printing of Hilbert's paper on binary forms.‎

Bookseller reference : 47133

‎"HILBERT, DAVID.‎

‎Ueber den Dirichlet'schen biquadratischen Zahlenkörper. - [THE THEORY OF QUADRATIC NUMBER FIELDS]‎

‎Leipzig, B. G. Teubner, 1894. 8vo. Bound with the original wrappers in contemporary half calf. In ""Mathematische Annalen"", Volume 45., 1894. Entire volume offered. Library label to upper part of spine. Extremities with wear, internally very fine and clean. Pp. 309-340. [Entire volume: IV, 599 pp.].‎

‎First printing of Hilbert's influential paper on the theory of quadratic number fields. Hilbert's work enabled mathematicians to attack successfully the theory of quadratic forms with any number of variables and with any algebraic numerical coefficients. This lead in particular to the interesting problem: to solve a given quadratic equation with algebraic numerical coefficients in any number of variables by integral or fractional numbers belonging to the algebraic realm of rationality determined by the coefficients.The present volume contain several other papers by influential contemporary mathematicians.‎

Bookseller reference : 47138

‎"HILBERT, DAVID.‎

‎Ueber die Darstellung definiter Formen als Summen von Formenquadraten.‎

‎Leipzig, B.G. Teubner, 1888. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. XXXII. [32] Band. 3. Heft."" Entire issue offered. [Hilbert:] Pp. 342-50. [Entire issue: Pp. 309-456].‎

‎First publication of Hilbert's fundamental and exceedingly important paper on real algebraic geometry. ""In 1888, David Hilbert published an influential paper [the present] which became fundamental for real algebraic geometry, and which remains an inspiring source for research even today."" (Pfister & Scheiderer). David Hilbert, one of the most influential mathematicians of the 19th and early 20th centuries, is probably best known for the ""Hilbert Problems"" - a list of twenty-three problems in mathematics all unsolved at the time, and several of them were very exceedingly influential for 20th century mathematics.He is regarded as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.""Hermann Weyl described his teacher Hilbert's style: ""It is as if you were on a swift walk through a sunny open landscape" you look freely around, demarcation lines and connecting roads are pointed out to you, before you must brace yourself to climb the hill" then the path goes straight up."" (Princeton Companion to Mathematics).‎

Bookseller reference : 44427

‎"HILBERT, DAVID.‎

‎Ueber die Darstellung definiter Formen als Summen von Formenquadraten.‎

‎Leipzig, B.G. Teubner, 1888. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. XXXII. [32] Band. 3. Heft."" Entire issue offered. [Hilbert:] Pp. 342-50. [Entire issue: Pp. 309-456].‎