‎Mathematics‎

‎"CLEBSCH, A.‎

‎Ueber das Pfaffsche Problem.‎

‎Berlin, G. Reimer, 1862. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 60. Band, 1862""., without backstrip. Fine and clean. [Clebsch:] Pp. 193-251.‎

‎First printing of Clebsche's important paper on Pfaff invariants.""German mathematician whose work on algebraic geometry was considered the first and most fundamental work in that branch of mathematics. Clebsch also developed a brilliant interpretation of some of Georg Riemann's work on function theory and investigated some aspects of algebraic geometry using approaches that differed from convention, focusing on algebraic interpretations rather than geometrical ones. Clebsch also founded an important journal, Mathematische Annalen before his premature death at the age of 39."" (Schlager, Science and Its Times, P. 267)‎

Bookseller reference : 48048

‎"CLEBSCH, A.‎

‎Ueber symbolische Darstellung algebraischer Formen. - [SEMINAL CONTRIBUTION TO THE SYMBOLIC METHOD IN INVARIANT THEORY]‎

‎Berlin, G. Reimer, 1861. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 59. Band, 1861"". Without backstrip. Fine and clean. [Clebsch:] Pp. 1-62.‎

‎First printing of Clebsch's early and founding paper on the symbolic method in invariant theory. The Symbolic method is based on treating the form as if it were a power of a degree one form, which corresponds to embedding a symmetric power of a vector space into the symmetric elements of a tensor product of copies of it.""Clebsch completed the symbolic calculus for forms and invariants created by Aronhold, and henceforth one spoke of the Clebsch-Aronhold symbolic notation. Clebsch’s own contributions in this field of algebraic geometry include the following. With the help of suitable eliminations he determined a surface of order 11n - 24 intersecting a given surface of order n in points where there is a tangent that touches the surface at more than three coinciding points. For a given cubic surface he calculated the tenth-degree equation on the resolution of which the determination of the Sylvester pentahedron of that surface depends. For a plane quartic curve Clebsch found a remarkable invariant that, when it vanishes, makes it possible to write the curve equation as a sum of five fourth-degree powers. At the end of his life Clebsch inaugurated the notion of a ""connex,"" a geometrical object in the plane obtained by setting a form containing both point and line coordinates equal to zero."" (DSB)‎

Bookseller reference : 48050

‎"CHRISTOFFEL, E. B.‎

‎Über die Gaußsche Quadratur und eine Verallgemainerung derselben.‎

‎Berlin, G. Reimer, 1858. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 55. Band, 1858""., without backstrip. Fine and clean. [Christoffel:] Pp. 61-82.‎

‎First printing.‎

Bookseller reference : 48064

‎"SIEBECK.‎

‎Ueber die graphische Darstellung imaginärer Functionen.‎

‎Berlin, G. Reimer, 1858. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 55. Band, 1858""., without backstrip. Fine and clean. [Siebeck:] Pp. 221-253" [Steiner)] Pp. 356-378.‎

Bookseller reference : 48066

‎EUCLID (EUKLID) OF ALEXANDRIA.‎

‎De Sex Första jämte Ellofte och Tolfte Böckerna af Euclidis Elementa, eller grundeliga Indledning til geometrien, til Riksens Ungdoms Tjenst opå Svenska Språket utgifna af Mårten Stroemer.‎

‎Upsala, Johan Edman, 1774. Lille 8vo. Samtidigt hldrbd. med ophøjede binf på ryggen. Rygtitel. Ryg noget slidt, mest ved kapitæler. (18),429,(1) pp., talrige textfigurer. Brugsspor. Et bladhjørne bortrevet. Nogle samtidige notater og tilskrifter.‎

‎De første 6 bøger blev oversat for første gang på svensk i 1744 (også af Mårten Stroemer), mens udgaven her er den første svenske oversættelse, som også omfatter 11. og 12. Bog.Riccardi: 1774-2 - Steck: V29.‎

Bookseller reference : 48172

‎"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

‎HILBERT, D. und S. COHN-VOSSEN.‎

‎Anschauliche Geometrie. Mit 330 Abbildungen.‎

‎Berlin, Julius Springer, 1932. Orig. full cloth. Small stamp to foot of titlepage. VIII,310 pp., textillustr. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on front free endpaper. Internally fine and clean.‎

‎First edition.‎

Bookseller reference : 48245

‎BOREL, ÈMILE.‎

‎Lecons sur les Séries Divergentes.‎

‎Paris, Gauthier-Villars, 1901. Lex8vo. Uncut in orig. printed wrappers. Small stamp on foot of titlepage. VIII,182,(2) pp. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on frontwrapper. Internally fine and clean.‎

‎First edition.‎

Bookseller reference : 48247

‎MATHEMATICAL TREATISES - DOMENICO CHELINI, NICOLA TRUDI, FRANCESCO SIACCI, DOMENICO AMANZIO, NICODEMO JADANZA, GIOVANNI DE BERARDINIS.‎

‎Sulla Composizione Geometrica de' sistemi di rette di Aree e di Punti. (Chelini, Bologna 1870) - Teori delle Equazioni Differenziali lineari. (Trudi, Napoli 1876) - Della Rotazione dei Corpi liberi. Memoria Prima. (Siacci, Napoli 1877) - Sulla Svilu...‎

‎Bologna, Torino, Napoli, 1870, 1876, 1877, 1877, 1882, 1884. Folio. Bound in one nice hvellum. All 6 memoirs in offprints. De Bernardinis' memoir inscribed from the author. 51 - (2),71 - (4),30 - (2),32 - 33 - 23 pp.‎

Bookseller reference : 48320

‎PASCAL, E.‎

‎Repertorium der höheren Mathematik. Zweite, völlig umgearbeitete Auflage. Hrsg. von P. Epstein und H.E. Timerding. 2 Bde. (1. Analysis Erste Hälfte . - 2. Geometrie. Grundlagen und ebene geometrie).‎

‎Leipzig u. Berlin, B.G. Teubner, 1910. Orig. hcloth and orig. full cloth. XV,527XVI,534 pp.‎

Bookseller reference : 48332

‎DURÈGE, H.‎

‎Theorie der Elliptischen Functionen. Versuch einer elementaren Darstellung. In fünfter Auflage neu bearbeitet.‎

‎Leipzig, Teubner, 1887. Orig. full cloth. Small stamp to titlepage. VIII,436 pp. Clean and fine.‎

Bookseller reference : 48334

‎DZIOBEK, O.‎

‎Lehrbuch der Analytischen Geometrie. Erster Theil: Analytische geometrie der Ebene. Zweite verbesserte Aufl.‎

‎Braunschweig, A. Graff, 1909. Orig. full cloth. VIII,358 pp.‎

Bookseller reference : 48336

‎SALMON-FIEDLER.‎

‎Analytische Geometrie des Raumes. Unter Mitwirkung von Alexander Brill. Neu herausgegeben von Karl Kommerell. Erster Theil Die Elemente und die Throeie der Flächen zweiter Ordnung. Erste - Zweite Lieferung. Fünfte Auflage.‎

‎Leipzig, Berlin, B.G. teubner, 1922-23. Bound in one nice hcalf. Spine gilt with gilt lettering. VI,X,612 pp., 1 plate and textillustr. Clean and fine.‎

Bookseller reference : 48341

‎HESSE, OTTO.‎

‎Vorlesungen aus der Analytischen Geometrie der geraden Linie, des Punktes und der Kreises in der Ebene. Vierte Auflage revidiert und ergänzt von S. Gundelfinger.‎

‎Leipzig, B.G. Teubner, 1906. Orig. full cloth. VIII,252 pp.‎

Bookseller reference : 48343

‎GARABEDIAN, P.R.‎

‎Partial Differential Equations.‎

‎New York, Wiley & Sons, (1964). Orig. boards. XII,671 pp. Clean and fine.‎

Bookseller reference : 48345

‎KLAUA, DIETER.‎

‎Allgemeine Mengenlehre. Ein Fundament der Mathematik. I-II. Zweite, erweiterte Auflage. 2 Bde.‎

‎Berlin, Akademie-Verlag, 1970-69. 2 orig. full cloth. X,379VIII,364 pp. Clean and fine.‎

Bookseller reference : 48348

‎SINGER, IVAN.‎

‎Best Approximation in Normal Linear Spaces by Elements of Linear Subspaces.‎

‎Bucharest, Berlin, Publ. House of the Academy, Springer, 1970. Royal8vo. Orig. full cloth. 409 pp. Clean and fine.‎

Bookseller reference : 48353

‎BJÖRLING, C.F.E.‎

‎Elementerna af Algebraiska Analysen och Differential-Kalkylen efter Cauchy, bertrand, Todhunter m.fl. 1.-2. Delen.‎

‎Upsala, Esaias Edquist, (1866-67). Et samtidigt hldrbd. Rygforgyldning of skindtitel. (14),291 pp. samt 2 foldeplancher. Lidt fugtskjold på foden af den ene planche.‎

Bookseller reference : 48355

‎DUSCHEK, ADALBERT.‎

‎Vorlesungen über höhere Mathematik. 2 Bde.‎

‎Wien, Springer=Verlag, 1949-50. 2 orig. full cloth. X,395VI,386 pp., textfigs. Clean and fine.‎

Bookseller reference : 48357

‎GNEDENKO, B.V. and A.N. KOLMOGOROV.‎

‎Grenzverteilungen von Summen unabhängiger Zufallsgrössen. Wissenschaftlichen Bearbeitung der deutsche Ausgabe (von) Josef Heinhold.‎

‎Berlin, Akademie-Verlag, 1959. Orig. full cloth. VIII,279 pp. Clean and fine.‎

Bookseller reference : 48361

‎KATZNELSON, YITZHAK.‎

‎An introduction to harmonic analysis.‎

‎New York, John Wiley, (1968). Orig. full cloth. XIII,264 pp. Clean and fine.‎

Bookseller reference : 48364

‎HEWITT, EDWIN and KENNETH A. ROSS.‎

‎Abstract Harmonic Analysis. Vol. I: Structure of Topological Groups, Integration Theory, Group Representations.‎

‎Berlin, Göttingen, Heidelberg, Springer-Verlag, 1963. Orig. full cloth. VIII,547 pp. Clean and fine.‎

Bookseller reference : 48367

‎"CHURCH, ALONZO (+) ALAN TURING (+) EMIL POST.‎

‎[Church:] A note on the Entscheidungsproblem (+) Correction to A note on the Entscheidungsproblem (+) Review of ""A. M. Turing. On Computable numbers, with an application to the Entscheidungsproblem"" (+) [Post:] Finite combinatory processes-formulation... - [LANDMARK VOLUME IN THE HISTORY OF LOGIC]‎

‎[No place], The Association for Symbolic Logic, 1936 & 1937. Royal8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 1 & 2 bound together. Barcode label pasted on to back board. Small library stamp to lower part of 16 pages. A very fine copy. [Church:] Pp. 40-1" Pp. 101-2. [Post:] Pp. 103-5. [Turing:] Pp. 153-163" 164. [Entire volume: (4), 218, (2), IV, 188 pp.]‎

‎First edition of this collection of seminal papers within mathematical logic, all constituting some of the most important contributions mathematical logic and computional mathematics. A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) CORRECTION TO A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) REVIEW OF ""A. M. TURING. ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM"":First publication of Church's seminal paper in which he proved the solution to David Hilbert's ""Entscheidungsproblem"" from 1928, namely that it is impossible to decide algorithmically whether statements within arithmetic are true or false. In showing that there is no general algorithm for determining whether or not a given statement is true or false, he not only solved Hilbert's ""Entscheidungsproblem"" but also laid the foundation for modern computer logic. This conclusion is now known as Church's Theorem or the Church-Turing Theorem (not to be mistaken with the Church-Turing Thesis). The present paper anticipates Turing's famous ""On Computable Numbers"" by a few months. ""Church's paper, submitted on April 15, 1936, was the first to contain a demonstration that David Hilbert's 'Entscheidungsproblem' - i.e., the question as to whether there exists in mathematics a definite method of guaranteeing the truth or falsity of any mathematical statement - was unsolvable. Church did so by devising the 'lambda-calculus', [...] Church had earlier shown the existence of an unsolvable problem of elementary number theory, but his 1936 paper was the first to put his findings into the exact form of an answer to Hilbert's 'Entscheidungsproblem'. Church's paper bears on the question of what is computable, a problem addressed more directly by Alan Turing in his paper 'On computable numbers' published a few months later. The notion of an 'effective' or 'mechanical' computation in logic and mathematics became known as the Church-Turing thesis."" (Hook & Norman: Origins of Cyberspace, 250) Church coined in his review of Turing's paper the phrase 'Turing machine'.FINITE COMBINATORY PROCESSES-FORMULATION I: The Polish-American mathematician Emil Post made notable contributions to the theory of recursive functions. In the 1930s, independently of Turing, Post came up with the concept of a logic automaton similar to a Turing machine, which he described in the present paper (received on October 7, 1936). Post's paper was intended to fill a conceptual gap in Alonzo Church's paper on 'An unsolvable problem of elementary number theory'. Church had answered in the negative Hilbert's 'Entscheidungsproblem' but failed to provide the assertion that any such definitive method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be one written in the form of instructions to mind-less worker operating on an infinite line of 'boxes' (equivalent to the Turing machines 'tape'). The range of instructions proposed by Post corresponds exactly to those performed by a Turing machine, and Church, who edited the Journal of Symbolic Logic, felt it necessary to insert an editorial note referring to Turing's ""shortly forthcoming"" paper on computable numbers, and asserting that ""the present article ... although bearing a later date, was written entirely independently of Turing's"". (Hook & Norman: Origins of Cyberspace, 356).COMPUTABILITY AND LAMBDA-DEFINABILITY (+) THE Ø-FUNCTION IN LAMBDA-K-CONVERSION: The volume also contains Turing's influential ""Computability and lambda-definability"" in which he proved that computable functions ""are identical with the lambda-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene"". (Hook & Norman: Origins of Cyberspace, 395).‎

Bookseller reference : 48376

‎"KRIPKE, SAUL A.‎

‎A Completeness Theorem in Modal Logic. - [KRIPKE MODELS FOR MODAL LOGIC]‎

‎(No place), The Association for Symbolic Logic, 1959. Lev8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 24. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. A very fine copy. Pp. (1) - 14. [Entire volume: VI, 374 pp.).‎

‎The seminal first printing of Kripke's debut article, which provided the basis for his logic and for the model theory for modal logic in general. The work constitutes the very beginning of Kripke Semantics (often called possible world semantics). Kripke's works in general are rare in fist editions. Many of them remain unpublished and are only known in privately circulated manuscripts.The American philosopher Saul A. Kripke (born 1940) is an exceedingly important logician and philosopher of language and one of the most powerful and influential thinkers of analytic and Anglo-American philosophy. He is considered the greatest living philosopher and perhaps the greatest since Wittgenstein. In 2001 he was awarded the Schock Prize in Logic and Philosophy, which is considered the philosopical equivalent of the Nobel Prize.Kripke, who grew up in Omaha in a religious Jewish family, was somewhat of a prodigy child. During grammar school he got intimately acquainted with and mastered to perfection algebra, geometry and calculus, and very early on he took up philosophy, which later became his career. Still a teenager, in high school, he wrote a work that was to change the face of philosophical logic forever, namely the groundbreaking paper ""A Completeness Theorem for Modal Logic"", which was printed a few years later, in 1959, in the Journal of Symbolic Logic, while he was in his first year at Harvard University. This seminal debut work proposed what later came to be known as Kripke models for modal logic. The story goes that the paper earned a letter from the department of mathematics urging Kripke to apply for a job there, to which he is said to have written an answer explaining ""My mother said that I should finish high school and go to college first.""In 1962 he graduated from Harvard University, where he remained until 1968, first as a member of the Harvard Society of Fellows and then as a lecturer. During these years he developed the logical theories founded in the ""Completeness Theorem"" further and made seminal contributions to the field of logic and semantics. Kripke Semantics is a formal semantics for non-classical logic systems that Kripke began developing in his teenage years, first published something on in 1959 (the present work) and further developed in the 60'ies and. The development of Kripke Semantics was no less than a breakthrough in the making of non-classical logics, of which no model theory existed before Kripke's. With this work, Kripke laid the foundation for proving completeness theorems for modal logic, and for identifying the weakest normal modal logic, which is now named K after him.‎

Bookseller reference : 48378

‎"TURING, M. (+) H. A. NEWMAN.‎

‎A Formal Theorem in Church's Theory of Types (+) Practical forms of type theory‎

‎(No place), The Association for Symbolic Logic, 1942, 1943 &1948. Lev8vo. Bound in two uniform red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 7, 8 [Bound together] & 13.. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. Minor scratches to extremities of volume 13. A fine set. Pp. 28-33" Pp. 80-94. [Entire volumes: IV, 164 pp." IV, 236 pp.).‎

‎First printing of the two important - but often overlooked - papers by Turing which provide ""information about Turing's thoughts on the logical foundations of mathematics which is not to be found elsewhere in his writings"". (Copeland, The Essential Turing, P. 206).‎

Bookseller reference : 48381