1884 books for « klein w c »Edit

‎Zum Mehrkörperproblem der Quantentheorie (+) Über Wellen und Korpuskeln in der Quantenmechanik. - [JORDAN-KLEIN MATRICES]‎

‎Berlin, Julius Springer, 1927. 8vo. Entire volume 45 of ""Zeitschrift für Physik"" bound in contemporary half cloth with gilt title to spine. Library stamp to title-page. Corners and lower capital bumped, hinges a bit weak. An overall fine and clean copy. Pp. 751-765"" 766-775. [Entire volume: VII, (1), 910 pp.].‎

‎First publication of Jordan and Klein's influential paper (the first mentioned) which contributed to the close connection between quantum fields and quantum statistics, today known as Jordan-Klein matrices. ""Born, Heisenberg, and Jordan had indicated, and Dirac had demonstrated, the close connection between quantum fields and quantum statistics. Second quantization guarantees that photons obey Bose-Einstein statistics. What about other particles which obey Bose-Einstein statistics? The year 1927 was not over before Jordan and Klein addressed this question [in the present paper]."" (Pais, Inward bound. p. 338). ""Jordan and Klein found that ""one can quantize just as well the non-relativistic Schroedinger equation. In honor of these contributions the matrices have been named Jordan-Klein matrices."" (ibid. p. 339). ""Convinced that the many-body problem in quantum mechanics can be stated correctly only in the context of quantized matter waves (""repeated"" or ""second"" quantization. as it was called later by Léon Rosenfeld), Jordan started working out his ideas together with Wolfgang Pauli. Oskar Klein, and Eugene Wigner. During his stay in Copenhagen in the summer 1927 Jordan established, together with Klein, the first nonrelativistic formalism of second quantization for a system of interacting Bose particles."" (DSB).The second paper, ""Über Wellen und Korpuskeln in der Quantenmechanik"", ""contained several other formal and mathematical generalizations, but its main practical value is that, in the newly established theory of the 'quantized wave field', the fluctuations in the Bose case now satisfied all requirements following from Einstein's light-quantum treatment of 1924 and 1925."" (Mehra, The historical development of quantum theory, 2000, p. 231.‎

‎Weitere Untersuchungen über das Ikosaeder. - [FELIX KLEIN ON THE ICOSAHEDRON]‎

‎Leipzig, B.G. Teubner, 1877. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. XII. [12]. Band. 4. Heft."" Entire issue offered. Internally very fine and clean. [Klein:] Pp. 503-60. [Entire issue: Pp. pp. 433-576].‎

‎Frist printing of Klein's paper on the icosahedron.""A problem that greatly interested Klein was the solution of fifth-degree equations, for its treatment involved the simultaneous consideration of algebraic group theory, geometry, differential equations, and function theory. Hermite, Kronecker, and Brioschi had already employed transcendental methods in the solution of the general algebraic equation of the fifth degree. Klein succeeded in deriving the complete theory of this equation from a consideration of the icosahedron, one of the regular polyhedra known since antiquity. These bodies sometimes can be transformed into themselves through a finite group of rotations. The icosahedron in particular allows sixty such rotations into itself. If one circumscribes a sphere about a regular polyhedron and maps it onto a plane by stereographic projection, then to the group of rotations of the polyhedron into itself there corresponds a group of linear transformations of the plane into itself. Klein demonstrated that in this way all finite groups of linear transformations are obtained, if the so-called dihedral group is added. By a dihedron Klein meant a regular polygon with n sides, considered as rigid body of null volume."" (DSB VII, p. 400).The icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids.‎

‎Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac. - [KLEIN-NISHINA FORMULA]‎

‎Berlin, Springer, 1929. 8vo. Bound in contemporary half cloth with gilt lettering, In ""Zeitschrift für Physik"", Band 52, 1929. Entire issue offered. Two stamps to title page, otherwise fine. Pp. 853-68. [Entire volume: VIII, 894 pp].‎

‎First appearance of the important paper which constitutes one of the first results obtained from the study of quantum electrodynamics and ""played an important role in discussions of the applicable limits of quantum mechanics to studies of cosmic rays and nuclear physics."" (DSB).""In early 1928 Nishina returned to Copenhagen and worked with Oskar Klein. As a result of their cooperation, the Klein-Nishina formula was completed in October of the same year, before Nishina's return to Japan. In 1923 the quantum (particle) nature of X rays was discovered by Arthur Compton. Nishina had once made an experimental approach to this phenomena at the Cavendish Laboratory. The relation among the increased wavelength of the scattered X rays, the energy of recoiled electrons, and the scattering angle was accounted for by the quantum nature. In 1928 Nishina and Klein calculated the cross section and intensity of the Compton scattered radiation by the use of Dirac's new relativistic quantum mechanics of electrons. They succeeded in a complicated calculation by doing this separately and checking it together. (Nishina also brought this method of calculation with a team back to Japan.)Nishina and Klein searched for the solution of Dirac's wave equation in the case of a free electron (initially at rest) in the field of a plane electromagnetic wave."" (DSB).The Klein-Nishina was one of the first results obtained from the study of quantum electrodynamics. Consideration of relativistic and quantum mechanical effects allowed the development of an accurate equation for the scattering of radiation from a target electron. Before this derivation, the electron cross section had been classically derived by the British physicist and discoverer of the electron, J.J. Thomson. However, scattering experiments showed significant deviations from the results predicted by the Thomson cross section. Further scattering experiments agreed perfectly with the predictions of the Klein-Nishina formula.‎

‎Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac. - [KLEIN-NISHINA FORMULA]‎

‎Berlin, Springer, 1929. 8vo. Bound in contemporary half cloth with gilt lettering, In ""Zeitschrift für Physik"", Band 52, 1929. Entire volume offered. Two stamps to title page, otherwise fine. Pp. 853-68. [Entire volume: VIII, 894 pp].‎

‎First appearance of the important paper which constitutes one of the first results obtained from the study of quantum electrodynamics and ""played an important role in discussions of the applicable limits of quantum mechanics to studies of cosmic rays and nuclear physics."" (DSB).""In early 1928 Nishina returned to Copenhagen and worked with Oskar Klein. As a result of their cooperation, the Klein-Nishina formula was completed in October of the same year, before Nishina's return to Japan. In 1923 the quantum (particle) nature of X rays was discovered by Arthur Compton. Nishina had once made an experimental approach to this phenomena at the Cavendish Laboratory. The relation among the increased wavelength of the scattered X rays, the energy of recoiled electrons, and the scattering angle was accounted for by the quantum nature. In 1928 Nishina and Klein calculated the cross section and intensity of the Compton scattered radiation by the use of Dirac's new relativistic quantum mechanics of electrons. They succeeded in a complicated calculation by doing this separately and checking it together. (Nishina also brought this method of calculation with a team back to Japan.)Nishina and Klein searched for the solution of Dirac's wave equation in the case of a free electron (initially at rest) in the field of a plane electromagnetic wave."" (DSB).The Klein-Nishina was one of the first results obtained from the study of quantum electrodynamics. Consideration of relativistic and quantum mechanical effects allowed the development of an accurate equation for the scattering of radiation from a target electron. Before this derivation, the electron cross section had been classically derived by the British physicist and discoverer of the electron, J.J. Thomson. However, scattering experiments showed significant deviations from the results predicted by the Thomson cross section. Further scattering experiments agreed perfectly with the predictions of the Klein-Nishina formula.‎

‎Über die sogenannte Nicht-Euclidische Geometri. (Erster-) Zweiter Aufsatz. - [THE NON-EUCLIDEAN GEOMETRY OF KLEIN]‎

‎(Leipzig, B.F. Teubner, 1871 a. 1873). Without wrappers, (wrappers blank to Second Part) as published in ""Mathematische Annalen. Hrsg. von Felix Klein, Walter Dyck, Adolph Mayer."" Vol. IV, pp. 573-625 and vol. VI, pp. 112-145. Kept in a cloth-portfolio.‎

‎First edition. In these groundbreaking papers Klein established that if Euclidean geometry is consistent then non-Euclidean geometry is consistent as well and he introduces the adjectives ""parabolic"", ""elliptic"", and ""hyperbolic"" for the respective geometries of Georg Riemann, of Nicolai Lobachevsky, of C.F. Gauss and Janos Bolyai. ""Cayley's idea (that metrical geometry is part of projective geometry) was taken over by Felix Klein (1849-1925) and generalized so as to include the non-Euclidan geometries. Klein, a professor at Göttingen, was one of the lading mathematicians in Germany during the last part of the nineeeeteenth and first part of the twentieth century. During the years 1869-70 he larned the work of Lobatchevsky, Bolyai, von Staudt, and Cayley"" however, even in 1871he did not know Laguerre's result. It seemed to him to be posible to subsume the non-Euclidean geometries, hyperbolic, and double elliptic geometry, under projective geometry byexploiting Cayley's idea. He gave a sketch og his thoughts in a paper of 1871, and then developed them in two papers (1871 a. 1873, the ppers offered here). Klein was the first to obtain models of non-Euclidean geometries."" (Morris Kline). - Sommerville, Bibliography of Non-Euclidean Geometry p.45 (1871) and p. 49 (1873).‎

‎Zum Mehrkörperproblem der Quantentheorie (+) Über Wellen und Korpuskeln in der Quantenmechanik. - [JORDAN-KLEIN MATRICES]‎

‎Berlin, Julius Springer, 1927. 8vo. Entire volume 45 of ""Zeitschrift für Physik"" bound in a red-brown contemporary half cloth with gilt title to spine. Library stamp to title-page. Corners and lower capital bumped, hinges a bit weak. An overall fine and clean copy. Pp. 751-765"" 766-775. [Entire volume: VII, (1), 910 pp.].‎

‎First publication of Jordan and Klein's influential paper (the first mentioned) which contributed to the close connection between quantum fields and quantum statistics, today known as Jordan-Klein matrices. ""Born, Heisenberg, and Jordan had indicated, and Dirac had demonstrated, the close connection between quantum fields and quantum statistics. Second quantization guarantees that photons obey Bose-Einstein statistics. What about other particles which obey Bose-Einstein statistics? The year 1927 was not over before Jordan and Klein addressed this question [in the present paper]."" (Pais, Inward bound. p. 338).Jordan and Klein found that ""one can quantize just as well the non-relativistic Schroedinger equation. In honor of these contributions the matrices have been named Jordan-Klein matrices."" (ibid. p. 339). The second paper, ""Über Wellen und Korpuskeln in der Quantenmechanik"", ""contained several other formal and mathematical generalizations, but its main practical value is that, in the newly established theory of the 'quantized wave field', the fluctuations in the Bose case now satisfied all requirements following from Einstein's light-quantum treatment of 1924 and 1925."" (Mehra, The historical development of quantum theory, 2000, p. 231.‎

‎Sur les Fonctions Uniformes qui se reproduisent par des Substitutions Linéaires (+) [Klein's introduction to the present paper].‎

‎Leipzig, B.G. Teubner, 1882. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet 1882 durch Rudolf Friedrich Alfred Clebsch. XIX. [19] Band. 4. Heft."" Entire issue offered. [Poincaré:] Pp. 553-64. [Entire issue: Pp. 435-594].‎

‎First printing of Poincaré's paper on his comprehensive theory of complex-valued functions which remain invariant under the infinite, discontinuous group of linear transformations. In 1881 Poincaré had published a few short papers with some initial work on the topic, and in the 1881, Klein invited Poincaré to write a longer exposition of his results to Mathematische Annalen which became the present paper. This, however, turned out to be an invitation to at mathematical dispute:""Before the article went to press, Klein forewarned Poincaré that he had appended a note to it in which he registered his objections to the terminology employed therein. In particular, Klein disputed Poincaré's decision to name the important class of functions possessing a natural boundary circle after Fuch's, a leading exponent of the Berlin school. The importance he attached to this matter, however, went far beyond the bounds of conventional priority dispute. True, Klein was concerned that his own work received sufficient acclaim, but the overriding issue hinged on whether the mathematical community would regard the burgeoning research in this field as an outgrowth of Weierstrassian analysis or the Riemannian tradition."" Parshall. The Emergence of the American Mathematical Research Community. Pp. 184-5.The issue contains the following important contributions by seminal mathematicians:1. Klein, Felix. Ueber eindeutige Functionen mit linearen Transformationen in sich. Pp. 565-68.2. Picard, Emile. Sur un théorème relatif aux surfaces pour lesquelles les coordnnées d´un point quelconque s´experiment par des fonctions abéliennes de deux paramètres. Pp. 578-87.3. Cantor, Georg. Ueber ein neues und allgemeines Condensationsprincip der Singularitäten von Functionen. Pp. 588-94.‎

‎Zum Mehrkörperproblem der Quantentheorie (+) Über Wellen und Korpuskeln in der Quantenmechanik. - [JORDAN-KLEIN MATRICES]‎

‎Berlin, Julius Springer, 1927. 8vo. Entire volume 45 of ""Zeitschrift für Physik"" bound in a black contemporary half cloth with gilt lettering to spine. Library stamp to free front end-paper. An overall fine and clean copy. Pp. 751-765"" 766-775. [Entire volume: VII, (1), 910 pp.].‎

‎First publication of Jordan and Klein's influential paper (the first mentioned) which contributed to the close connection between quantum fields and quantum statistics, today known as Jordan-Klein matrices. ""Born, Heisenberg, and Jordan had indicated, and Dirac had demonstrated, the close connection between quantum fields and quantum statistics. Second quantization guarantees that photons obey Bose-Einstein statistics. What about other particles which obey Bose-Einstein statistics? The year 1927 was not over before Jordan and Klein addressed this question [in the present paper]."" (Pais, Inward bound. p. 338).Jordan and Klein found that ""one can quantize just as well the non-relativistic Schroedinger equation. In honor of these contributions the matrices have been named Jordan-Klein matrices."" (Ibid. p. 339). The second paper, ""Über Wellen und Korpuskeln in der Quantenmechanik"", ""contained several other formal and mathematical generalizations, but its main practical value is that, in the newly established theory of the 'quantized wave field', the fluctuations in the Bose case now satisfied all requirements following from Einstein's light-quantum treatment of 1924 and 1925."" (Mehra, The historical development of quantum theory, 2000, p. 231.‎

‎Ueber die sogenannte Nicht-Euklidische Geometrie (+) Ueber die sogenannte Nicht-Euklidische Geometrie. (Zweiter Aufsatz). - [TWO MAIN WORKS ON NON-EUCLIDEAN GEOMETRY]‎

‎Leipzig, B.G.Teubner, 1871 u. 1873. Bound in 2 later full cloth. Small stamp on foot of titlepages.In. ""Mathematische Annalen. In Verbindung mit C. Neumann begründet durch Rudolf Friedrich Alfred Clebsch"", IV. und VI. Band. (4),637 pp. a. (4),642 pp., 6 plates. Klein's papers: pp. 573-625 a. pp. 112-145. Both volumes offered.‎

‎First edition of these 2 papers which unifies the Euclidean and Non-Euclidean geometries, by reducing the differences to expressions of the ""distance function"", and introducing the concepts ""parabolic"", ""elliptic"" and ""hyperbolic"" for the geometries of Euclid, Riemann and of Lobatschewski, Gauss and Bolyai. He further eliminates Euclid's parallel-axiom from projective geometry, as he shows that the quality of being parallel, is not invariant under projections.Klein build his work on Cayley's ""distant measure"" saying, that ""Metrical properties are not properties of the figure per se but of the figure in relation to the absolute."" This is Cayley's idea of the general projective determination of metrics. The place of the metric concept in projective geometry and the greater generality of the latter were described by Cayley as ""Metrical geometry is part of projective geometry."" Cayley's idea was taken over by Felix Klein....It seemed to him to be possible to subsume the non-Euclidean geometries, hyperbolic and double elliptic geometry, under projective geometry by exploring Cayley's idea. He gave a sketch of his thoughts in a paper of 1871, and then developed them in two papers (the papers offered here).Klein was the first to recognize that we do not need surfaces to obtain models of non-Euclidean geometries....The import which gradually emerged from Klein's contributions was that projective geometry is really logically independent of Euclidean geometry....By making apparent the basic role of projective geometry Klein paved the way for an axiomatic development which could start with projective geometry and derive the several metric geometries from it.""(Morris Kline).The offred volumes cntains other importen mathematical papers by f.i. by Klebsch, Lipschitz, Neumann, Noether, Thomae, Gordan, Lie, Du Bois-Raymond, Cantor (Über trigonometrische Reihen),etc.(Sommerville: Bibliography of Non-Euclidean Geometry p. 45 a. 49.)‎

‎Zur Nicht-Euklidischen Geometrie (+) Ueber die Nullstellen der hypergeometrischen Reihe.‎

‎Leipzig, B.G. Teubner, 1890. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. XXXVII. [37]. Band. 4. Heft."" Entire issue offered. Internally very fine and clean. [Klein:] Pp. 544-72"" 573-90. [Entire issue: Pp. pp. 465-604].‎

‎First printing of Klein's important contribution to non-Euclidean geometry. Klein saw a fundamental unity in the subject of non-Euclidean geometry. Rather than a heterogeneous collection of abstruse mathematics, non-Euclidean geometry was in Klein's view a ""concrete discipline"".For over two millennia geometry had been the study of theorems which could be proved from Euclid's axioms. However, in the beginning of the 19th century it was proved that there exist other geometries than that of Euclid. Motivated by the emergence of the new geometries of Bolyai, Lobachevsky, and Riemann, Klein proposed to define a geometry, not by a set of axioms, but instead in terms of the transformations that leave it invariant" according to Klein, a geometric structure consists of a space together with a particular group of transformations of the space. A valid theorem in that particular geometry is one that holds under this group of transformations. This controversial idea did not only give a more systematic way of classifying the different geometries, but also gave birth to new geometric structures such as manifolds. Landmark Writtings in Western Mathematics 1640-1940, p.544-52.‎

‎Die Mechanik nach den Principien der Ausdehnungslehre. - [FELIX KLEIN ON THE ICOSAHEDRON]‎

‎Leipzig, B. G. Teubner, 1877. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 12., 1877. 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. Title page missing a small piece of paper to the right margin, not affecting text. Very fine and clean. Pp. 503-60. [Entire volume: IV, 576 pp.].‎

‎Frist printing of Klein's paper on the icosahedron.""A problem that greatly interested Klein was the solution of fifth-degree equations, for its treatment involved the simultaneous consideration of algebraic group theory, geometry, differential equations, and function theory. Hermite, Kronecker, and Brioschi had already employed transcendental methods in the solution of the general algebraic equation of the fifth degree. Klein succeeded in deriving the complete theory of this equation from a consideration of the icosahedron, one of the regular polyhedra known since antiquity. These bodies sometimes can be transformed into themselves through a finite group of rotations. The icosahedron in particular allows sixty such rotations into itself. If one circumscribes a sphere about a regular polyhedron and maps it onto a plane by stereographic projection, then to the group of rotations of the polyhedron into itself there corresponds a group of linear transformations of the plane into itself. Klein demonstrated that in this way all finite groups of linear transformations are obtained, if the so-called dihedral group is added. By a dihedron Klein meant a regular polygon with n sides, considered as rigid body of null volume."" (DSB VII, p. 400).The icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids.The volume contain many other papers by contemporary mathematicians. ‎

‎Vergleichende Betrachtungen über neuere geometrische Forschungen. - [THE ERLANGER PROGRAMM IMPROVED]‎

‎Leipzig, B.G. Teubner, 1893. 8vo. Orig. printed wrappers (no backstrip) to Heft 1, 43. Bd. of ""Mathematische Annalen"", the whole issue pp. IV,144. Klein's paper: pp.63-100. Frontwrapper repaired with the same kind of paper and without loss of letters. The sewing somewhat loose. Frontwrapper loose.‎

‎This is the second printing of Klein's famous ""Erlanger Programm"" having Klein's own improvements.For over two millennia geometry had been the study of theorems which could be proved from Euclid's axioms. However, in the beginning of the 19th century it was proved that there exist other geometries than that of Euclid. Motivated by the emergence of the new geometries of Bolyai, Lobachevsky, and Riemann, Klein proposed to define a geometry, not by a set of axioms, but instead in terms of the transformations that leave it invariant" according to Klein, a geometric structure consists of a space together with a particular group of transformations of the space. A valid theorem in that particular geometry is one that holds under this group of transformations. This controversial idea did not only give a more systematic way of classifying the different geometries, but also gave birth to new geometric structures such as manifolds. The Erlanger Programm was translated into six languages in the following two decades, and it has had an immense influence on geometry up to and throughout the 20th century.‎

‎Über Zusammenstösse zwischen Atomen und freien Elektronen (Klein & Rosseland) (+) Über die verschiedenen Arten des radioaktiven Zerfalls und die Möglichkeit ihrer Deutung aus der Kernstruktur (Meitner) (+) Präzisionsmessungen in der L-Serie der schwer... - [THE DISCOVERY OF COLLISIONS OF THE SECOND KIND]‎

‎Berlin, Julius Springer, 1921. 8vo. Entire volume 4 of ""Zeitschrift für Physik"" bound in contemporary black half cloth with gilt lettering to spine. Library stamp to title-page and traces of paper label pasted on to lower part of spine. Minor wear to extremities. A nice and clean copy. [Klein & Rosseland:] Pp. 46-51" [Meitner:] Pp. 146-56 [Coster:] Pp. 178-88" [Schrödinger:] Pp. 347-354. [Ladenburg:] Pp. 451-468. [Entire volume: IV, 476 pp.].‎

‎First printing of this collection of influential papers within 20th century physics. Klein and Rosseland's paper (ÜBER ZUSAMMENSTÖSE ZWISCHEN ATOMEN UND FREIEN ELEKTRONEN) created an entire new field of physics: Collisions of the second kind. Klein and Rosseland discovered that and electron in an excited state could jump to a lower state without radiation with the released energy being transferred to a free electron as kinetic energy. ""Franck and Hertz had shown how collisions between atoms and free electrons could cause excitation of the atoms, involving the transition of an electron from one stationary state to another of higher energy, the difference being equal to the loss of energy of the free electron. Klein and Rosseland considered the equation as how this would influence the thermal equilibrium between the atomic systems and free electron when Einstein's considerations of 1917 on the statistical equilibrium between blackbody radiation and atoms were used."" (Thorsen. The Penetration of Charged Particles Through Matter. P. 27.)Niels Bohr took a great interest in the paper and his correspondences reveal that he had great expectations regarding the utility of the concept of collisions of the second kind. Ladenburg's paper (DIE QUANTENTHEORETISCHE DEUTUNG DER ZAHL DER DISPERSIONSELEKTRONEN) is the first printing of the first step towards the formulation of a quantum-theoretic interpretation of dispersion (the Ladenburg-Equation). Ladenburg's results were later (1924) generalized by Kramers in his ""The Law of dispersion and Bohr's Theory of Spectra."".‎

‎Über die Auflösung der allgemeine Gleichungen fünften und sechsten Grades (+) Bericht über den Stand der Herausgabe von Gauss' Werken. Sechster Bericht.‎

‎Leipzig, B. G. Teubner, 1905. 8vo. In the original printed wrappers, without backstrip. In ""Mathematische Annalen, 61. Band, 1. Heft, 1905"". Fine and clean. [Klein:] Pp. 50-71"" Pp. 72-76. [Entire issue: IV, 160 pp].‎

‎First printing of Felix Klein's paper on how to solve fifth and sixth degree equations. Klein considered equations of degree > 4, and was especially interested in using transcendental methods to solve the general equation of the fifth degree. Building on the methods of Hermite and Kronecker, he produced similar results to those of Brioschi and went on to completely solve the problem by means of the icosahedral group. This work led him to write a series of papers on elliptic modular functions, the present paper being one of the last and concluding.As editor of Mathematische Annalen Felix Klein set himself the task of collecting previously unstudied material of Gauss. He organized a campaign to collect materials and enlisted experts in special fields to study them. From 1898 until 1922 he rallied support with fourteen reports, published under the title ""Bericht über den Stand der Herausgabe von Gauss' Werken,"". The present being the sixth. ‎

‎Über die Transformation der elliptischen Funktionen und die Auflösung der Gleichungen fünften Grades (+) Über die Transformation siebenter Ordnung der elliptischen Funktionen. - [FIRST MATHEMATICAL DESCRIPTION OF DESSIN D'ENFANT / DEDEKIND TESSELLATION]‎

‎Leipzig, B. G. Teubner, 1879. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 14., 1879. 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. 111-172"" Pp. 428-471. [Entire volume: Pp. (4), 576].‎

‎First printing of Felix Klein's two hugely influential papers in which he for the first time presented the first recognizable modern ""dessins d'enfants"". Klein called these diagrams Linienzüge (German, plural of Linienzug ""line-track"", also used as a term for polygon).Dedekind did in 1877 publish a paper in which part of the mathematical background for the ""dessins d'enfants"" was present. It was, however, Klein that fully explored, both mathematical and visual, its potential. ‎

‎Neue Untersuchungen im Gebiete der elliptischen Functionen.‎

‎Leipzig, B.G. Teubner, 1886. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. XXVI. [26]. Band. 3. Heft."" Entire issue offered. Internally very fine and clean. [Klein:] Pp. 455-464. [Entire issue: Pp. 309-464].‎

‎First printing of Klein's paper on elliptic functions. ""One of the leading mathematicians of his age, Klein made many stimulating and fruitful contributions to almost all branches of mathematics, including applied mathematics and mathematical physics. Moreover, his extensive activity contributed greatly to making Göttingen the chief center of the exact sciences in Germany. An opponent of one sided approaches, he possessed an extraordinary ability to discover quickly relationships between different areas of research and to exploit them fruitfully."" (DSB).‎

‎Dessin de C. Klein : Fleurs‎

‎ Dessin Reproduction en couleurs d'un dessin de C. Klein (22,2 x 39,5 cm), représentant des fleurs ; bords jaunis, quelques traces et une petite déchirure sans manque sur le dessin, par ailleurs assez bon état général. Livraison a domicile (La Poste) ou en Mondial Relay sur simple demande.‎

‎Ueber einen liniengeometrischen Satz (+) Zur Interpretation der complexen Elemente in der Geometrie (+) Eine Uebertragung des Pascal'schen Satzes auf Raumgeometrie (+) Ueber den allgemeinen Functionsbegriff und dessen Darstellung durch eine willkürli...‎

‎Leipzig, B. G. Teubner, 1883. 8vo. Bound with the original wrappers in contemporary half calf with gilt lettering to spine. In ""Mathematische Annalen"", Volume 22., 1883. Entire volume offered. Wear to extremities. Library label pasted on to top of spine. Small library stamp to lower part of verso of title page. Very fine and clean. VI, 592 pp.‎

‎First printing of Klein's papers on geometry.""One of the leading mathematicians of his age, Klein made many stimulating and fruitful contributions to almost all branches of mathematics, including applied mathematics and mathematical physics. Moreover, his extensive activity contributed greatly to making Göttingen the chief center of the exact sciences in Germany. An opponent of one sided approaches, he possessed an extraordinary ability to discover quickly relationships between different areas of research and to exploit them fruitfully."" (DSB).‎

‎Vergleichende Betrachtungen über neuere geometrische Forschungen. Programm zum Eintritt in die philosophische Facultät und den Senat der k. Friedrich-Alexanders-Universität. - [THE ERLANGER PROGRAMM]‎

‎Erlangen, Andreas Deichert, 1872. 8vo. (233x152mm). Uncut with the original printed front-wrapper (loose) - back-wrapper missing. Fine and clean throughout. 48 pp.‎

‎First edition of the ""Erlanger Programm"". For over two millennia geometry had been the study of theorems which could be proved from Euclid's axioms. However, in the beginning of the 19th century it was proved that there exist other geometries than that of Euclid. Motivated by the emergence of the new geometries of Bolyai, Lobachevsky, and Riemann, Klein proposed to define a geometry, not by a set of axioms, but instead in terms of the transformations that leave it invariant" according to Klein, a geometric structure consists of a space together with a particular group of transformations of the space. A valid theorem in that particular geometry is one that holds under this group of transformations. This controversial idea did not only give a more systematic way of classifying the different geometries, but also gave birth to new geometric structures such as manifolds. The Erlanger Programm was translated into six languages in the following two decades, and it has had an immense influence on geometry up to and throughout the 20th century. Scarce. Landmark Writtings in Western Mathematics 1640-1940, p.544-52.‎

‎Zur Theorie der Liniencomplexe des ersten und zweiten Grades (+) Die allgemeine lineare Transformation der Liniencoordinaten (+) Ueber die Abbildung der Complexflächen vierter Ordnung und vierter Classe. - [KLEIN ON LINE COMPLEXES]‎

‎Leipzig, B.G. Teubner, 1870. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Herausgegeben von A. Clebsch und C. Neumann. 11. Band. 2. Heft."" Entire issue offered. Minor loss to wrappers, internally fine and clean. [Neumann:] Pp. 182-186. [Entire issue: IV, 191, (1) pp.].‎

‎First printing of these three paper by Klein, in which he for the first time presented his much used theory regarding line complexes, algebraic geometry. ‎

‎Beweis für die Nichtauflösbarkeit der Ikosaedergleichung durch Wurzelzeichen.‎

‎Leipzig, B.G. Teubner, 1905. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. 61. Band. 3. Heft."" Entire issue offered. Internally very fine and clean. Pp. 369-371. [Entire issue: Pp. 289-452].‎

‎First printing of Klein's paper on the Icosahedron.""One of the leading mathematicians of his age, Klein made many stimulating and fruitful contributions to almost all branches of mathematics, including applied mathematics and mathematical physics. Moreover, his extensive activity contributed greatly to making Göttingen the chief center of the exact sciences in Germany. An opponent of one sided approaches, he possessed an extraordinary ability to discover quickly relationships between different areas of research and to exploit them fruitfully."" (DSB).‎

‎Ueber einen liniengeometrischen Satz (+) Zur Interpretation der complexen Elemente in der Geometrie (+) Eine Uebertragung des Pascal'schen Satzes auf Raumgeometrie (+) Ueber den allgemeinen Functionsbegriff und dessen Darstellung durch eine willkürlic...‎

‎Leipzig, B. G. Teubner, 1883. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 22., 1883. 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. VI, 592 pp.‎

‎First printing of Klein's papers on geometry.""One of the leading mathematicians of his age, Klein made many stimulating and fruitful contributions to almost all branches of mathematics, including applied mathematics and mathematical physics. Moreover, his extensive activity contributed greatly to making Göttingen the chief center of the exact sciences in Germany. An opponent of one sided approaches, he possessed an extraordinary ability to discover quickly relationships between different areas of research and to exploit them fruitfully."" (DSB).‎

‎Rome. ‎

‎Paris Editions du Seuil - Album Petite planète 3 1959 In-4 Cartonnage toilé éditeur Edition originale Dédicacé par l'auteur‎

‎EDITION ORIGINALE. Préface et textes de Pasolini, Belli, Klein,. 153 photographies de Klein, mises en page par le photographe. Sans la jaquette mais ENVOI AUTOGRAPHE signé de Klein, agrémenté d'un petit coeur " To Serge ROME SWEET ROME Klein Paris 13 Nov 08". Très bon Cartonnage toilé et jaquette illustrés éditeur 0‎

‎Gérard Klein (Le livre d'or de la science-fiction)‎

‎Presses Pocket Le livre d'or de la science-fiction Dos carré collé 1979 In-12 (10,5 x 17,5 cm), dos carré collé, 371 pages ; quelques marques d'usage sur les plats (coin corné au quatrième plat, légère pliure au premier plat), par ailleurs bon état. Livraison a domicile (La Poste) ou en Mondial Relay sur simple demande.‎

‎Das Gewitter und die dasselbe begleitende Erscheinungen. Ihre Eigenthümlichkeiten und Wirkungen sowie die Mittel sich vor den Verheerungen des Blitzes zu schützen.‎

‎Graz, 1871. Contemporary halfcalf. 150 pp., and 1 plate. Bound with Klein's ""Entwickelungsgeschichte des Kosmos nach dem gegenwärtigen Standpunkte der gesammten Naturwissenschaften"", Braunschweig, 1870. 170 pp.‎

‎Two first editions.‎