‎Mathematics‎

‎"GROTHENDIECK, A.‎

‎On the de Rham Cohomology of Algebraic Varieties. - [THE FOUNDATION OF CRYSTALLINE COHOMOLOGY]‎

‎[Paris, Presses Universitaires de France, 1966]. 4to. In the original stapled blank blue printed wrappers. Offprint from ""Institut des Hautes Études Scientifiques. Publications Mathématiques"" No. 29. Light wear to extrimities, otherwise fine and clean. Pp. 95-103, (1).‎

‎"GUDERMANN, CHR.‎

‎De curva quarti ordinis sphaerica, de Circulari scalena.‎

‎Berlin, G. Reimer, 1852. 4to. In the original printed wrappers, without back strip. In ""Journal für die reine und angewandte Mathematik"", 43. band, Heft 2, 1852. Entire second heft offered. Fine and clean. Pp. 93-113. [Entire volume: Pp. 93-184 + 3 plates.].‎

‎"GUDERMANN, CHRISTOPH.‎

‎Beweis des im zweiten Bande dieses Journals Seite 190. von Herrn Steiner aufgestellten Lehrsatzes No. 27. und Ableitung anderer ebenso einfacher Relationen.‎

‎(Berlin, G. Reimer, 1832) 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 8. Band, 1832"", without backstrip. Fine and clean. pp. 160-68.‎

‎"GUDERMANN, CHRISTOPH.‎

‎Potential oder zyklisch-hyperbolische Funktionen I - II.‎

‎(Berlin, G. Reimer, 1832) 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 8. Band, 1832"", without backstrip. Fine and clean. pp. 64-116" " Pp. 194-212.‎

‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Modular-Functionen und der Modular-Integrale, Allgemeiner Charakter der Potenzial-Functionen (+) Theorie der Modular-Functionen und der Modular-Integrale.‎

‎Berlin, G. Reimer, 1838. 4to. In ""Journal für die reine und angewandte Mathematik, 18. Band, 1-2 Heft, 1838"". Both issues in the original printed wrappers, without backstrip. Fine and clean. [Gudermann, 1 heft:] Pp. 1-54. [Gudermann, 2 heft:] Pp. 142-175. [Entire issue, heft 1: IV, 100, (2) pp. 2 Heft: 101-188, (2) pp. + 2 plates, one of them detached.].‎

‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Modular-Functionen und der Modular-Integrale, Allgemeiner Charakter der Potenzial-Functionen (+) Theorie der Modular-Functionen und der Modular-Integrale.‎

‎Berlin, G. Reimer, 1838. 4to. In ""Journal für die reine und angewandte Mathematik, 18. Band, 1-2 Heft, 1838"". Both issues in the original printed wrappers, without backstrip. Fine and clean. [Gudermann, 1 heft:] Pp. 1-54. [Gudermann, 2 heft:] Pp. 142-175. [Entire issue, heft 1: IV, 100, (2) pp. 2 Heft: 101-188, (2) pp. + 2 plates, one of them detached.].‎

‎First printing of Gudermann's two papers on modular functions and modular integrals, ideas which anticipated his 1844-book.""Gudermann devoted much more attention to the theory of special functions. After the earlier works of Leonhard Euler, John Landen, and A. M. Legendre (Gauss's results were still in manuscript), Niels Abel's studies on elliptical functions, published mostly in A. L. Crelle's Journal für reine und angewandte Mathematik, represented an important divide in treating this area. In 1829 Carl Jacobi's book Fundamenta nova theoriae functionum ellipticarum was published. At the time Gudermann was one of the first mathematicians to expand on these results. Beginning with volume 6 (1830) of Crelle's Journal, he published a series of papers which he later summarized in two books: Theorie der Potenzialoder cyklisch-hyperbolischen Functionen (1833) and Theorie der Modular-Functionen und der Modular-Integrale (1844), which were to have had a sequel which was never written."" (DSB).‎

Bookseller reference : 45138

‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Potenzial- oder der cyklisch- hyperbolischen Functionen. - [GUDERMANNIAN FUNCTION]‎

‎Berlin, G. Reimer, 1830. 4to. In ""Journal für die reine und angewandte Mathematik, 6. Band, 1 Heft, 1830"". In the original printed wrappers, without backstrip. Fine and clean. [Gudermann:] Pp. 1-39. [Entire issue: Pp. 106 pp. + 1 folded plate. ].‎

‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Potenzial- oder der cyklisch- hyperbolischen Functionen. - [GUDERMANNIAN FUNCTION]‎

‎Berlin, G. Reimer, 1830. 4to. In ""Journal für die reine und angewandte Mathematik, 6. Band, 1 Heft, 1830"". In the original printed wrappers, without backstrip. Fine and clean. [Gudermann:] Pp. 1-39. [Entire issue: Pp. 106 pp. + 1 folded plate. ].‎

‎First printing of Gudermann extensive and important paper on hyperbolic functions. During 1830ies Gudermann focused his work on these functions and published extensive on the subject, the present paper being the first. It was later coined the Gudermannian function.The function was introduced by Johann Heinrich Lambert in the 1760s at the same time as the hyperbolic functions. He called it the ""transcendent angle,"" and it went by various names until 1862 when Cayley suggested it be given its current name as a tribute to Gudermann's work in the 1830ies on the theory of special functions. The present paper together with two later published papers were collected in Theorie der potenzial- oder cyklisch-hyperbolischen functionen (1833), a book which expounded sinh and cosh to a wide audience.The issue also contain a paper by the famous Norwegian mathematician Niels Henrik Abel.""Gudermann devoted much more attention to the theory of special functions. After the earlier works of Leonhard Euler, John Landen, and A. M. Legendre (Gauss's results were still in manuscript), Niels Abel's studies on elliptical functions, published mostly in A. L. Crelle's Journal für reine und angewandte Mathematik, represented an important divide in treating this area. In 1829 Carl Jacobi's book Fundamenta nova theoriae functionum ellipticarum was published. At the time Gudermann was one of the first mathematicians to expand on these results. Beginning with volume 6 (1830) of Crelle's Journal, he published a series of papers which he later summarized in two books: Theorie der Potenzialoder cyklisch-hyperbolischen Functionen (1833) and Theorie der Modular-Functionen und der Modular-Integrale (1844), which were to have had a sequel which was never written."" (DSB).Gudermann is known today for being the teacher of Karl Weierstrass, who took Gudermann's course in elliptic functions in 1839, the first to be taught in any institute. Weierstrass was greatly influenced by this course, which marked the direction of his own research.‎

Bookseller reference : 45101

‎"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.‎

‎"GYLDÉN, HUGO.‎

‎Nouvelle recherches sur les séries employées dans les théories des planétes.‎

‎Berlin, Stockholm, Paris, Beijer, 1893. 4to. Without wrappers (but with titlepage and table of contents), as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 17 pp. (4), 168.‎

‎"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.‎

‎Ein Spezialfall des Entscheidungsproblems der theoretischen Logik. - [INCOMPLETENESS FROM THE STANDPOINT OF FIRST-ORDER LOGIC]‎

‎Leipzig & Berlin, B.G. Teubner, 1932. 8vo. A mint copy, in the original wrappers, still contained in the original plastic protection. In ""Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling, herausgegeben von Karl Manger, Heft 2"". Pp. 27-28. [Entire volume: 38 pp].‎

‎"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].‎

‎"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.‎

‎"HARNACK, A.‎

‎Ueber die Vieltheiligkeit der ebenen algebraischen Curven. - [ANTICIPATION OF HILBERT'S SIXTEENTH PROBLEM]‎

‎Leipzig, B. G. Teubner, 1876. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 10., 1876. 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.189-198. [Entire volume: IV, 592 pp.].‎

‎First printing of Harnack's Curve Theorem which formed the background for Hilbert's sixteenth problem. In real algebraic geometry, Harnack's curve theorem, named after Axel Harnack, describes the possible numbers ofconnected components that an algebraic curve can have, in terms of the degree of the curve.Hilbert's sixteenth problem was posed as the ""Problem of the topology of algebraic curves and surfaces"", he presented his problem as follows: ""The upper bound of closed and separate branches of an algebraic curve of degree n was decided by Harnack (the present paper)"" from this arises the further question as of the relative positions of the branches in the plane.As of the curves of degree 6, I have - admittedly in a rather elaborate way - convinced myself that the 11 branches, that they can have according to Harnack, never all can be separate, rather there must exist one branch, which have another branch running in its interior and nine branches running in its exterior, or opposite. It seems to me that a thorough investigation of the relative positions of the upper bound for separate branches is of great interest, and similarly the corresponding investigation of the number, shape and position of the sheets of an algebraic surface in space - it is not yet even known, how many sheets a surface of degree 4 in three-dimensional space can maximally have."" (Rohn, Flächen vierter Ordnung, Preissschriften der Fürstlich Jablonowskischen Gesellschaft, Leipzig 1886).Hilbert had investigated the M-curves of degree 6, and found that the 11 components always were grouped in a certain way. His challenge to the mathematical community now was to completely investigate the possible configurations of the components of the M-curves.Furthermore he requested a generalization of Harnack's Theorem to algebraic surfaces and a similar investigation of surfaces with the maximum number of components.The problem is still unsolved today.‎

Bookseller reference : 47129

‎"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.‎

Bookseller reference : 44828

‎"HAUSDORFF, F. [FELIX].‎

‎Grundzüge einer Theorie der geordneten Mengen. - [THE GENERALIZATION OF CANTOR'S CONTINUUM HYPOTHESIS]‎

‎Leipzig, B. G. Teubner, 1908. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet 1908 durch Alfred Clebsch und Carl Neumann. 65. Band. 4. Heft."" Entire issue offered. Wrappers with a few nicks, internally fine and clean. [Hausdorff:] Pp. 435-505. [Entire issue: Pp. 433-575].‎

‎First printing of Hausdorff important paper in which a generalization of Cantor's Continuum Hypothesis was presented for the first time. This is equivalent to what is now called the Generalized Continuum Hypothesis.The continuum hypothesis is a hypothesis, put forth by Georg Cantor in 1877, about the possible sizes of infinite sets. It states: ""There is no set whose cardinality is strictly between that of the integers and that of the real numbers.""Felix Hausdorff is considered to be one of the founders of modern topology and he contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis.‎

Bookseller reference : 44768

‎"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).‎

Bookseller reference : 42736

‎"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"")‎

Bookseller reference : 40482

‎"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.‎

‎First printing of Heine's doctoral dissertation. ""Heine in his doctoral dissertation determined the potential (steady-state temperature) nor merely for the interior of an ellipsoid of revolution when the value when the potential is given at the surface, but also for the exterior for such an ellipsoid anf for the shell between confocal ellipsoids of revolution."" (Morris Kline).‎

Bookseller reference : 40443

‎"HEISENBERG, W. [WERNER].‎

‎Über quantentheoretische Kinematik und Mechanik.‎

‎(Berlin, Julius Springer, 1926). 8vo. Without wrappers. Extracted from ""Mathematische Annalen. Begründet 1868 durch Alfred Clebsch und Carl Neumann. 95. Band"". Pp. 683-704.‎

‎First printing. This paper was written as a mathematical exposition of the Three-Man-Paper 'Zur Quantenmechanik II' by Born, Jordan, and Heisenberg from the same year.‎

Bookseller reference : 44772

‎"HELMERT, F.R.‎

‎Die Ausgleichungsrechnung nach der Methode der Kleinsten Quadrate mit Anwendungen auf die Geodäsie und die Theorie der Messinstrumente.‎

‎Leipzig, B.G. Teubner, 1872. Cont. hcalf. Gilt back, slightly rubbed. XI,348 pp.‎

‎"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.‎

Bookseller reference : 47146

‎"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.‎

‎"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.‎