‎Mathematics‎

‎"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

‎"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.‎

‎"HILBERT, DAVID. - WARING'S PROBLEM SOLVED.‎

‎Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl nter Potenzen (Waringische Problem).‎

‎Leipzig, B.G. Teubner, 1909. Orig. printed wrappers. No backstrip. In. ""Mathematische Annalen. Hrsg. von Felix Klein, Walther v. Dyck, David Hilbert, Otto Rosenthal"", 67. Bd., 3. Heft. Pp. 281-432 (=3. Heft). Hilbert's paper: pp. 281-300.‎

‎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 : 41656

‎"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.‎

‎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

‎"HINTIKKA, JAAKKO.‎

‎Knowledge and Belief. An Introduction to the Logic of the two Notions. - [FOUNDING CONTEMPORARY EPISTEMIC LOGIC]‎

‎Ithaca, New York, Cornell University Press, (1962). 8vo. Orig. full blue cloth w. blue lettering to spine and front board. Very minor bumping to capitals and minor bleaching to small part of lower spine. Original blue dust-jacket w. red lettering. Spine faded and some minor brownspotting. Stamp to title-page ( Weston College Library Weston, Mass.) and stamped library-number and date to verso of title-page. An excellent, internally near mint, copy in an unusually fine dust-jacket. Not price-clipped. X, 179 pp.‎

‎The uncommon first edition, first issue of Hintikka's seminal main work, which also constitutes the main work of contemporary epistemic logic.The Finnish born philosopher and logician, Jaakko Hintikka (born 1929), Professor of Philosophy at the University of Boston, is generally accepted as the founder of formal epistemic logic and of game semantics for logic. He has contributed seminally to the fields of philosophical and mathematical logic, philosophy of mathematics and science, language theory and epistemology. Independently of Evert Willem Beth he discovered the semantic tableau, and he is famous for his work on game semantics and logical quantifiers. In 2005 Hintakka was awarded the Schock Prize in logic and philosophy, the philosophical equivalent to the Nobel prize, ""for his pioneering contributions to the logical analysis of modal concepts, IN PARTICULAR THE CONCEPTS OF KNOWLEDGE AND BELIEF "". The first edition of this seminal work, which has founded contemporary epistemic logic, is very difficult to find. The work was reprinted three times between 1962 and 1969, but after that the work was only printed again in 2005.""In 1962 Jaakko Hintikka published ""Knowledge and Belief: An Introduction to the Logic of the Two Notions"" with Cornell University Press. Almost every paper or a book on epistemic and doxastic logic that has appeared since then has referred to this seminal work. Although many philosophers working in logic, epistemology, game-theory, economics, computer science and linguistics mention the book, it is very likely that most have never literally had their hands on it, much less owned a copy. After a fourth printing in 1969, Knowledge and Belief went out of print and as many of us have found to our dismay, it has become increasingly difficult to find used copies at our local shops or online. It is our pleasure to provide the interdisciplinary community with this reprint edition of Knowledge and Belief."" (Abstract of the re-issue edition, Prepared by Vincent F. Hendricks & John Symons, King's College Publications, 2005).In this breakthrough work, Hintikka sets out to understand and explain the logical behavior of the two fundamental epistemological notions, Knowledge and belief. ""The word ""logic"" which occurs in the subtitle of this work is to be taken seriously. My first aim is to formulate and to defend explicit criteria of consistency for certain sets of statements - criteria which, it is hoped, will be comparable with the criteria of consistency studied in the established branches of logic. What the statements in question are like is also indicated in the title [...]"" (Chapter One, Prolegomena, p.3).""Knowledge and Belief"" has been extremely influential from the time of its appearance and continues to be so to this day, also due to the fact that epistemic logic has greatly influenced the fields of game theory, artificial intelligence and distributed computing.‎

Bookseller reference : 36630

‎"HINTIKKA, JAAKKO.‎

‎Knowledge and Belief. An Introduction to the Logic of the two Notions.‎

‎Ithaca, New York, Cornell University Press, (1964). 8vo. Orig. full blue cloth w. blue lettering to spine and front board. Original blue dust-jacket w. red lettering. An excellent, near mint copy in an astonishingly fine dust-jacket, not price-clipped. Old owner's name to front free end-paper. Internally very nice and clean. A very good copy. X, 179 pp.‎

‎First edition, second printing of Hintikka's seminal main work, which also constitutes the main work of contemporary epistemic logic.The Finnish born philosopher and logician, Jaakko Hintikka (born 1929), Professor of Philosophy at the University of Boston, is generally accepted as the founder of formal epistemic logic and of game semantics for logic. He has contributed seminally to the fields of philosophical and mathematical logic, philosophy of mathematics and science, language theory and epistemology. Independently of Evert Willem Beth he discovered the semantic tableau, and he is famous for his work on game semantics and logical quantifiers. In 2005 Hintakka was awarded the Schock Prize in logic and philosophy, the philosophical equivalent to the Nobel prize, ""for his pioneering contributions to the logical analysis of modal concepts, IN PARTICULAR THE CONCEPTS OF KNOWLEDGE AND BELIEF "". The first edition of this seminal work, which has founded contemporary epistemic logic, appeared in 1962 and is very difficult to find. The work was reprinted three times between 1962 and 1969, but after that the work was only printed again in 2005. The second issue appeared in 1964 and the third in 1967.""In 1962 Jaakko Hintikka published ""Knowledge and Belief: An Introduction to the Logic of the Two Notions"" with Cornell University Press. Almost every paper or a book on epistemic and doxastic logic that has appeared since then has referred to this seminal work. Although many philosophers working in logic, epistemology, game-theory, economics, computer science and linguistics mention the book, it is very likely that most have never literally had their hands on it, much less owned a copy. After a fourth printing in 1969, Knowledge and Belief went out of print and as many of us have found to our dismay, it has become increasingly difficult to find used copies at our local shops or online. It is our pleasure to provide the interdisciplinary community with this reprint edition of Knowledge and Belief."" (Abstract of the re-issue edition, Prepared by Vincent F. Hendricks & John Symons, King's College Publications, 2005).In this breakthrough work, Hintikka sets out to understand and explain the logical behavior of the two fundamental epistemological notions, Knowledge and belief. ""The word ""logic"" which occurs in the subtitle of this work is to be taken seriously. My first aim is to formulate and to defend explicit criteria of consistency for certain sets of statements - criteria which, it is hoped, will be comparable with the criteria of consistency studied in the established branches of logic. What the statements in question are like is also indicated in the title [...]"" (Chapter One, Prolegomena, p.3).""Knowledge and Belief"" has been extremely influential from the time of its appearance and continues to be so to this day, also due to the fact that epistemic logic has greatly influenced the fields of game theory, artificial intelligence and distributed computing.‎

Bookseller reference : 36632

‎"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

‎"HILL, G. W.‎

‎On the Part of the Motion of Lunar Perigee Which is a Function of the Mean Motions of the Sum and Moon. - [THE HILL DETERMINANT]‎

‎Berlin, Stockholm, Paris, Beijer, 1886. 4to. Bound with the original printed wrappers in contemporary half calf. In ""Acta Mathematica Hrsg. von G. Mittag-Leffler."", Bd. 8. Entires issue offered. Fine and clean. Pp. 1-36 [Entire volume: (4), 392 pp.].‎

‎Second printing (with some additions) of Hill's important paper in he introduced the the Hill Determinant or Hill's Equations""The memoir of 1877 entitled On the Part of the Motion of the Lunar Perigee Which Is a Function of the Mean Motions of the Sun and Moon contains the incontrovertible evidence of Hill’s mathematical genius. He was led to a differential equation, now called Hill’s equation, that is equivalent to an infinite number of algebraic linear equations. Hill showed how to develop the infianite determinant corresponding to these equations.""‎

Bookseller reference : 50827

‎"HILBERT, DAVID.‎

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

‎Chicago, Open Court, 1902. Small 8vo. Orig. full red cloth. Wear to topof spine. Old owners name on title-page. VII,143 pp., textfigs. Clean and fine.‎

‎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 : 59043

‎"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 Endlichkeit des Invariantensystems für binäre grundformen (+) Ueber Büschel von binären Formen mit vorgeschriebener Functionaldeterminante. - [""WITHOUT DOUBT THIS IS THE MOST IMPORTANT WORK ON GENERAL ALGEBRA""]‎

‎Leipzig, B.G. Teubner, 1888. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet 1888 durch Rudolf Friedrich Alfred Clebsch. XXXIII.[33] Band. 2. Heft."" Entire issue offered. Internally very fine and clean. [Hilbert:] Pp. 223-6"" Pp.227-36 [Entire issue: Pp. 161-316].‎

‎First printing of Hilbert's exceedingly important and groundbreaking paper in which he proved his famous Basis Theorem that is, if every ideal in a ring R has a finite basis, so does every ideal in the polynomial ring R[x]. Hilbert had thus connected the theory of invariants to the fields of algebraic functions and algebraic varieties. When Felix Klein read the paper he wrote ""I do not doubt that this is the most important work on general algebra that the Mathematische Annalen has ever published.""Hilbert submitted a paper proving the finite basis theorem to Mathematische Annalen. However Gordan was the expert on invariant theory for the journal and he found Hilbert's revolutionary approach difficult to appreciate. He refereed the paper and sent his comments to Klein:""The problem lies not with the form ... but rather much deeper. Hilbert has scorned to present his thoughts following formal rules, he thinks it suffices that no one contradict his proof ... he is content to think that the importance and correctness of his propositions suffice. ... for a comprehensive work for the Annalen this is insufficient.""Gordan rejected the article. His - now famous - comment was: Das ist nicht Mathematik. Das ist Theologie. (i.e. This is not Mathematics. This is Theology).However, Hilbert had learnt through his friend Hurwitz about Gordan's letter to Klein and Hilbert wrote himself to Klein in forceful terms:""... I am not prepared to alter or delete anything, and regarding this paper, I say with all modesty, that this is my last word so long as no definite and irrefutable objection against my reasoning is raised.""At the time Klein received these two letters from Hilbert and Gordan, Hilbert was an assistant lecturer while Gordan was the recognised leading world expert on invariant theory and also a close friend of Klein's. However Klein recognised the importance of Hilbert's work and assured him that it would appear in the Annalen without any changes whatsoever, as indeed it did. Hilbert expanded on his methods in a later paper, again submitted to the Mathematische Annalen [1893] and Klein,after reading the manuscript, wrote to Hilbert saying:-I do not doubt that this is the most important work on general algebra that the Annalen has ever published.Later, after the usefulness of Hilbert's method was universally recognized, Gordan himself said: ""I have convinced myself that even theology has its merits"".(Klein. Development of mathematics in the 19th century. P. 311).Sometimes Hilbert's first publication of the Basis Theorem is referred to as being published in the paper ""Zur Theorie der algebraischen Gebilde"" in Göottinger Nachrichten in 1888. This, however, was published in December 1888 and the present issue was published in March.‎

Bookseller reference : 44430

‎"HILBERT, DAVID.‎

‎Ueber die reellen Züge algebraischer Curven.‎

‎Leipzig, B.G. Teubner, 1891. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 38. Band. 1. Heft."".(Entire issue offered). Titlepage to Bd. 38. IV,160 pp. a. 1 folded plate. Hilbert's paper: pp. 115-138.‎

‎First apperance of an importent paper on algebraic geometry.The issue contains also Felix Klein ""Ueber Normierung der linearen Differentialgleichungen zweiter Ordnung"", pp. 144-152.‎

Bookseller reference : 45868

‎"HILBERT, DAVID. - HABILITATIONS THESIS.‎

‎Ueber einen allgemeinen Gesichtspunkt für invariantentheorietische Untersuchungen im binären Formengebiete.‎

‎Leipzig, B.G. Teubner, 1887. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 28. Band. 3. Heft."". (Entire issue offered). Pp. 309-456. Hilbert's paper: pp. 381-446.‎

‎This is Hilbert's ""Habilitationsschrift"", a fundamental work on algebraic invariants.‎

Bookseller reference : 45870

‎"HILBERT, DAVID.‎

‎Ueber die Darstellung definiter Formen als Summen von Formenquadraten.‎

‎Leipzig, B.G. Teubner, 1888. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 32., 1888. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of verso of title page. Very fine and clean. Pp. 342-350. [Entire volume: Pp. IV-600.]‎

‎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). The volume contain several other papers by influential contemporary mathematicians such as Felix Klein, Hurwitz, Lie, Lilienthal and Peano.‎

Bookseller reference : 47123