‎Mathématiques‎

‎"GYLDÉN, HUGO.‎

‎Untersuchungen über die Convergenz der Reihen, welche zur Darstellung der Coordinaten der Planaten angewendet.‎

‎Berlin, Stockholm, Paris, Beijer, 1887. 4to. With the original wrappers in ""Acta Mathematica, 9:3. Band]. No backstrip. Fine and clean. Pp. 185-294. [Entire issue: Pp. 185-320]‎

‎"GÖDEL, KURT.‎

‎Über Vollständigkeit und Widerspruchsfreiheit (+) Eine Eigenschaft der Realisierungen des Aussagenkalküls.‎

‎Leipzig & Berlin, B.G. Teubner, 1932. 8vo. In the original wrappers. In ""Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling, herausgegeben von Karl Menger, Heft 3"". A near mint copy, Pp. 12-13"" Pp. 20-21. [Entire volume: 26 pp].‎

‎First printing of these two important papers both closely related to Gödel landmark paper Über formal unentscheidbare Sätze"". Here Gödel applies the extensions of the incompleteness theorems to a wider class of formal systems : ""is already the more modern first-order Peano arithmetic, the system in which Godel in his abstract described his incompleteness results. The passage [in the present paper] envisages the introduction of higher-type variables, which would have the effect of re-establishing the system P, but as one proceeds to higher and higher types, that ""all the [unprovable] propositions constructed are expressible in Z (hence are number-theoretic propositions)"" is an important point about incompleteness. The last sentence of the [1932] passage is Godel's first remark on set theory of substance, and significantly, his example of an ""axiom of cardinality"" to take the place of type extensions is essentially the one that both Abraham Fraenkel [1922] and Thoralf Skolem [1923] had pointed out as unprovable in Ernst Zermelo's [1908] axiomatization of set theory and used by them to motivate the axiom of Replacement. "" (Kanamori, Gödel and Set Theory). ""By invitation, in October 1929 Gödel began at tending Menger's mathematics colloquium, which was modeled on the Vienna Circle. There in May 1930 he presented his dissertation results, which he had discussed with Alfred Tarski three months ear lier, during the latter's visit to Vienna. From 1932 to 1936 he published numerous short articles in the proceedings of that colloquium (including his only collaborative work) and was coeditor of seven of its volumes. Gödel attended the colloquium quite regularly and participated actively in many discus sions, confining his comments to brief remarks that were always stated with the greatest precision."" (DSB)‎

Riferimento per il libraio : 49345

‎"GÖDEL, KURT.‎

‎Über Vollständigkeit und Widerspruchsfreiheit (+) Eine Eigenschaft der Realisierungen des Aussagenkalküls.‎

‎Leipzig & Berlin, B.G. Teubner, 1932. 8vo. In the original wrappers. In ""Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling, herausgegeben von Karl Menger, Heft 3"". A near mint copy, Pp. 12-13" " Pp. 20-21. [Entire volume: 26 pp].‎

‎"HARTREE, DOUGLAS R.‎

‎The ENIAC, an Electronic Computing Machine. - [""FIRST PAPER ON AN ELECTRONIC DIGITAL COMPUTER PUBLISHED IN A LARGE-CIRCULATION""]‎

‎London, Macmillan & Co., 1946. 8vo. Without wrappers. Extracted from ""Nature. No. 4015, Saturday, October 12, 1946, Vol. 158"". A fine and clean copy. [Hartree:] Pp. 500-6. [Entire offered issue: Pp. 495-528].‎

‎First printing of this ""first paper on an electronic digital computer published in a large-circulation international scientific journal."" (OOC).The ENIAC was the first general-purpose electronic computer. It was a Turing-complete [computationally universal] digital computer capable of being reprogrammed to solve a full range of computing problems.""Hartree, a British mathematician, first learned of ENIAC [Electronic Numerical Integrator And Computer] in 1945, when he saw the as-yet uncompleted machine during a visit to the Moore School. In 1946 he returned to the Moore School as a participant in the Moore School lectures, advising on nonmilitary uses of ENIAC"" during this time he became the first Englishman to work with the machine. He was the first to bring news of ENIAC to Great Britain, publishing the above article in Nature shourtly after his return from the United States. Although he himself invented no new calculating devices, Hartree's promotion of electronic digital calculating methods in scientific computation helped to stimulate the development of more powerful computers like Cambridge University's EDSAC."" (OOC).The ENIAC was compared to today's standard rather large: It was 100 feet long, 10 feet high, and 3 deep and contained 18,000 vacuum tubes, about 70,000 resistors, 10,000 capacitors, and 6,000 switches. It consumed 140 kilowatts of power, so much power that, when operated, the lights in a nearby town dimmed.See: Hook & Norman. Origins of Cyberspace 648.‎

Riferimento per il libraio : 44828

‎"HADAMARD, JACQUES.‎

‎Theorie des équations aux dérivées partielles linéaires hyperboliques et du probléme de Cauchy.‎

‎(Berlin, Stockholm, Paris, Almqvist & Wiksell, 1907). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler"", Bd. 31, pp. 333-380.‎

‎"HARTREE, DOUGLAS R.‎

‎The ENIAC, an Electronic Computing Machine. - [""FIRST PAPER ON AN ELECTRONIC DIGITAL COMPUTER PUBLISHED IN A LARGE-CIRCULATION""]‎

‎London, Macmillan & Co., 1946. 8vo. Without wrappers. Extracted from ""Nature. No. 4015, Saturday, October 12, 1946, Vol. 158"". A fine and clean copy. [Hartree:] Pp. 500-6. [Entire offered issue: Pp. 495-528].‎

‎"HEINE, E.‎

‎Anwendungen der Kugelfunctionen und verwandten Functionen. Zweite umgearbeitete und vermehrte Auflage.‎

‎Berlin, G. Reimer, 1881. Lex8vo. Near contemp. full cloth. Gilt lettering to spine. A small nick to upper part of spine at fronthinge. XII,380 pp. Fine and clean.‎

‎Scarce second enlarged edition. of volume 2 (Angewandten Functionen). ""His greatest work, Handbuch der Kugelfunctionen was first published in 1861. The second edition (1878-81) of Heine's book was still a standard compendium on spherical functions well into the 1930's if one considers the frequency with which it was quoted"" that this edition has never been reprinted, however,belies this impression."" (DSB). (Heine's ""Handbuch der Kugelfunctionen, Theorie und Anwendungen, zweiter Band"")‎

Riferimento per il libraio : 40482

‎"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.‎

Riferimento per il libraio : 54760

‎"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.‎

‎First publication of Hermann's seminal paper (her doctoral thesis) which founded computer algebra. It first established the existence of algorithms - including complexity bounds - for many of the basic problems of abstract algebra, such as ideal membership for polynomial rings. Hermann's algorithm for primary decomposition is still in use today. The paper anticipates the birth of computer algebra by 39 years.""[The paper] is an intriguing example of ideas before their time. While computational aspects of mathematics were more fashionable before the abstractions of the twentieth century took hold, mathematicians of that time certainly knew nothing of computers nor of today's idea of what an algorithm is. The significance of the paper can be found on the first page, where we find (in translation):The claim that a computation can be found in finitely many steps will mean here that an upper bound for the number of necessary operations for the computation can be specified. Thus it is not enough, for example, to suggest a procedure, for which it can be proved theoretically that it can be executed in finitely many operations, if no upper bound for the number of operations is known. The fact that the author requires an upper bound suggests that there must exist an actual procedure or algorithm for doing computations. We see in this paper the first examples of procedures (with upper bounds given) for a variety of computations in multivariate polynomial ideals. Thus we have here a paper anticipating by 39 years the birth of computer algebra"". (ACM SIGSAM Bulletin, Volume 32. 1998).Not in Hook & Norman.‎

Riferimento per il libraio : 44771

‎"HEAWOOD, P. J.‎

‎Map-colour theorem. [Received 27 January, 1947. - Read 20 February, 1947.] [In: Proceedings of the London Mathematical Society. Second Series. Volume 51].‎

‎London, Hodgson & Son, 1950. Royal 8vo. Volume 51 of ""Proceedings of the London Mathematical Society. Second Series"" Bound with all the six original front-wrappers for all six parts of the volume (bound in at rear) in a very nice contemporary blue full cloth binding with gilt lettering and gilt ex-libris (""Belford College. Univ. London"") to spine. Minor bumping to extremities. Binding tight, and in excellent, very nice, clean, and fresh condition, in- as well as ex-ternally. Small circle-stamp to title-page (""Bedford College for Women""). Discrete library-markings and book-plate stating that the book was presented to the Library of Bedford College by ""Professor H. Simpson./ 1949-50"" to pasted-down front free end-paper. Library-label tipped in at front free end-paper. Pp. 161-175. [Entire volume: (4), 483 pp.].‎

‎First edition of one of the last articles by a key figure in Map-colour theory. Percy John Heawood, proved in 1890 that Alfred Kempe's Four-colour theorem was flawed and established his own five-colour theory. ""Heawood was, however, able to salvage an important idea, that of Kempe chains, from Kempe's proof. Using Kempe's work, Heawood was able to prove that every map is 5-colorable."" (Hilton, Mathematical vistas: from a room with many windows, 2002, p. 148 ). ""It is not known how Heawood became aware of the Four-Color problem. However, his life's work in mathematics was centered on it. After his first paper, 1890, he published seven more papers on the same subject, the last in 1949 at the age of 88."", his biographer Gabor Dirac wrote. (Fritsch, Rudolf. The four color theorem: history, topological foundations, and idea of proof, 1998, 24 p).‎

Riferimento per il libraio : 42736

‎"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.].‎

‎First printing.Charles Hermite (1822-1901), French mathematician, made significant contributions to pure mathematics, and especially to number theory and algebra. In 1858 he solved the equation of the fifth degree by elliptic functions, and in 1873 he proved that e (the base of natural logarithms) is transcendental. The legacy of his work can be shown in the large number of mathematical terms which bear the adjective 'Hermitian'.‎

Riferimento per il libraio : 46404

‎"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.].‎

‎First printing of Hermite's paper on the arithmetical consequences of the theory of elliptic functions. Charles Hermite (1822-1901), French mathematician, made significant contributions to pure mathematics, and especially to number theory and algebra. In 1858 he solved the equation of the fifth degree by elliptic functions, and in 1873 he proved that e (the base of natural logarithms) is transcendental. The legacy of his work can be shown in the large number of mathematical terms which bear the adjective 'Hermitian'. The present issue also contain the following paper:Fiedler, W.: Über die Durchdringung gleichseitiger Rotationshyperboloide von parallelen Axen (mit zwei Tafeln).‎

Riferimento per il libraio : 45905

‎"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).‎

Riferimento per il libraio : 48185

‎"HELMHOLTZ, HERMANN von. - HELMHOLTZ RESONANCE.‎

‎Theorie der Luftschwingungen in Röhren mit offenen Enden.‎

‎Berlin, Georg Reimer, 1860. 4to. Hcalf, but spine gone and covers loose. In: ""Journal für die reine und angewandte Mathematik Crelle/Borchardt"", 57. Band. IV,375,(1) pp. (Entire volume offered). Helmholtz' paper: pp. (1-) 72. A small brownspot to page one.‎

‎First printing of Helmholtz' groundbreaking work on the aerial vibrations in tubes. Together with his work on Vortex Motion (Ueber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen) from 1858 it ""must be reckoned among the most brilliant of Helmholtz's mathematical achievements, only rivalled, and perhaps surpassed, by the work of the last ten years of his life.""(Leo Koenigsberger, p. 180 ff).The paper was reprinted in Ostwald's Klassiker Nr. 80.The volume contains further importent papers by Clebsch, C. neumann, Borchardt, Cayley, Hesse, Hermite, Kronecker, Kummer etc.‎

Riferimento per il libraio : 47154

‎"HELMHOLTZ, HERMANN von. - A SEMINAL PAPER ON HYDRODYNAMICS.‎

‎Ueber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen,‎

‎Berlin, Georg Reimer, 1858. 4to. Extracted from ""Journal für die reine und angewandte Mathematik Crelle/Borchardt"", 55. Band, 1. Heft.: 3. Pp. 25-55 and with titlepage to volume 55. A bit of browning to outer corners of titlepage.‎

‎Firsi printing of Helmholtz' seminal paper on the hydrodynamics of vortex motion, which is the first detailled analysis of fluid motion not constrained to being irrotational - being his most importent contribution to mathematical physics. The paper was the direct inspiration for J.J. Thomson's ""vortex atom"" (See Pais ""Inward Bound"", pp. 176 ff).""In 1857, in a work of genius that proved him to be a mathematician of first rank 'On the Integrals of the Hydrodynamic Equations which express Vortex-motion' (the paper offered), he gave the solution of some extremely difficult hydrodynamical problems. He rejected the earlier hypotheses, and followed up the analogies between the motion of fluids and the electromagnetic action of electrical currents, which were of such much importence for his subsequent work on the Theory of Electricity and Magnetism.""Leo Koenigsberger, p. 167 ff.)""In 1858 Helmholtz published his seminal memoir ""Ueber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen,"" important for both its physical results and its mathematical methods. His motivations for taking up this new research interest remain unclear. One motive seems, however, to have been his interest in frictional phenomena, carried over from his interest in energetics"" another was his growing awareness of the power of Green’s theorem.""(DSB).Parkinson ""Breakthroughs"", 1858 P.‎

Riferimento per il libraio : 47146

‎"HEAWOOD, P. J.‎

‎Map-colour theorem. [Received 27 January, 1947. - Read 20 February, 1947.] [In: Proceedings of the London Mathematical Society. Second Series. Volume 51].‎

‎London, Hodgson & Son, 1950. Royal 8vo. Volume 51 of ""Proceedings of the London Mathematical Society. Second Series"" Bound with all the six original front-wrappers for all six parts of the volume (bound in at rear) in a very nice contemporary blue full cloth binding with gilt lettering and gilt ex-libris (""Belford College. Univ. London"") to spine. Minor bumping to extremities. Binding tight, and in excellent, very nice, clean, and fresh condition, in- as well as ex-ternally. Small circle-stamp to title-page (""Bedford College for Women""). Discrete library-markings and book-plate stating that the book was presented to the Library of Bedford College by ""Professor H. Simpson./ 1949-50"" to pasted-down front free end-paper. Library-label tipped in at front free end-paper. Pp. 161-175. [Entire volume: (4), 483 pp.].‎

‎"HEINE, EDUARD.‎

‎Ueber einige Aufgaben, welche auf partielle Differentialgleichungen führen‎

‎Berlin, G.Reimer, 1843. 4to. Without wrappers as extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. XXVI, Heft 3, Titlepage to ""Heft"" 3 present. PP. 185-216.‎

‎"HELE - SHAW, H.S. - THE ANALOGUE CALCULATING MACHINE.‎

‎The Theory of Continous Calculating Machines and of a Mechanism of this class on a New Principle. Received and Read June 19, 1884.‎

‎London, Harrison and Sons, 1886. 4to. No wrappers as extracted from ""Philosophical Transactions"", 1885. Vol. 176 - Part II, Pp. 367-402 a. 34 textillustr.‎

‎"HELMHOLTZ, HERMANN von. - A SEMINAL PAPER ON HYDRODYNAMICS.‎

‎Ueber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen‎

‎Berlin, Georg Reimer, 1858. 4to. Extracted from ""Journal für die reine und angewandte Mathematik Crelle/Borchardt"", 55. Band, 1. Heft.: 3. Pp. 25-55 and with titlepage to volume 55. A bit of browning to outer corners of titlepage.‎

‎"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.‎

‎"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.‎

‎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.‎

‎"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.‎

‎"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.‎