‎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.)‎

‎Ueber die Transformation elfter Ordnung der elliptischen Functionen. (i.e. ""On the eleventh order transformation of elliptic functions""). - [BELYI'S THEOREM]‎

‎Leipzig, B. G. Teubner, 1879. 8vo. In the original wrappers without backstrip. In ""Mathematische Annalen"", Volume 15, heft 3 + 4, 1879. Entire issue offered. Very fine and clean. Pp. 533-554. [Entire issue: 305-576 + 1 folded plate].‎

‎First printing of what later was to be known af Belyi's theorem or Belyi functions named after G. V. Belyi in 1979. Belyi functions and dessins d'enfants dates to the work of Felix Klein" he used them in this study an 11-fold cover of the complex projective line with monodromy group PSL.‎

‎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).‎

‎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.‎

‎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.‎

‎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.‎

‎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.‎

‎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. ‎

‎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 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).‎

‎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. ‎

‎Über hyperelliptische Sigmafunktionen.‎

‎Leipzig, B.G. Teubner, 1886. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 27., 1886. 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. 431-464 . [Entire volume: Pp. IV, 600.]‎

‎First printing of Klein's important work on hyperelliptic sigma functions.‎

‎PETIT VOYAGE DANS LE MONDE DES QUANTA‎

‎FLAMMARION. 2004. In-12. Broché. Bon état, Couv. convenable, Dos satisfaisant, Intérieur frais. 204 pages. . . . Classification Dewey : 510-Mathématiques‎

‎ Classification Dewey : 510-Mathématiques‎

‎Calculus: An Intuitive and Physical Approach‎

‎Dover Publications Inc 1998 in8. 1998. Broché.‎

6 Images

‎Bon état dos ridé intérieur propre ex-libris‎

‎Arithmétique pour calculateurs électroniques - les opérations dans les systèmes binaire,ternaire,octal,etc, dans les divers codes, le tout suivi d'exercices avec leurs solutions.‎

‎Chiron. 1963. In-8. Broché. Etat d'usage, Couv. légèrement passée, Dos satisfaisant, Intérieur acceptable. 176 pages - coins frottés.. . . . Classification Dewey : 372.7-Livre scolaire : mathématiques‎

‎ Classification Dewey : 372.7-Livre scolaire : mathématiques‎

‎Mais OUI vous comprenez la trigonométrie - 2e édition‎

‎Paul Legrain. 1963. In-8. Broché. Etat d'usage, Couv. légèrement passée, Dos plié, Intérieur acceptable. 230 pages - nombreux schémas en noir et blanc dans le texte. 2e plat légèrement plié.. . . . Classification Dewey : 510-Mathématiques‎

‎Dessins de R. Almeras. Classification Dewey : 510-Mathématiques‎

‎The Development of Logic.‎

‎Oxford, Clarendon Press, (1966). Orig. full cloth. VIII,762 pp. Clean and fine.‎

‎Mathematical Logic and the Foundations of Mathematics. An Introductory Survey.‎

‎London, D. van Nostrand, (1963). 8vo. Orig. full cloth. XIV,435 pp.‎

‎First edition.‎

‎Mathematical Logic and the Foundations of Mathematics. An Introductory Survey.‎

‎Ldn., N.Y., 1963. Orig. worn cloth. XIV, 435 pp.‎

‎Sur les maxima et les minima des intégrales doubles.‎

‎Berlin, Stockholm, Paris, Almqvist & Wiksell, 1892-3. 4to. As extracted from ""Acta Mathematica"", Vol, 16, 1892-3. No backstrip. A fine and clean copy. Pp. 65-140.‎

‎First printing of Kobb's paper in which he obtained the edge conditions for the double integral in parametric form.‎

‎Introduction to the Theory of Finite Automata. Translated from the Russian. Translation edited by J. C. Shepherdson.‎

‎Amsterdam, North-Holland Publ. Comp., 1965. 8vo. Orig. full cloth in orig. dust jacket. X,337 pp.‎

‎First English edition. Published in the series 'Studies in Logic and the Foundations of Mathematics', edited by L. E. J. Brouwer, A. Heyting, A. Robinson and P. Suppes.‎

‎Sur les déterminants infinis et les équations différentielles linéaires.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892-93]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16. Fine and clean. Pp. 217-295.‎

‎First printing of Koch's last paper relating to his doctoral thesis. Von Koch is known principally for his work in the theory of infinitely many linear equations and the study of the matrices derived from such infinite systems. He also did work in differential equations and in the theory of numbers. (DSB).‎

‎Sur une application des déterminants infinis à la théorie des équations différentielles linéaires (+) Sur les déterminants infinis et les équations différentielles linéaires.‎

‎[Berlin, Stockholm, Paris, Beijer, 1891 - 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 15 and 16. Fine and clean. Pp. 53-63" Pp. 217-295.‎

‎First printing of Koch's two paper which together constitute his doctoral thesis. Von Koch is known principally for his work in the theory of infinitely many linear equations and the study of the matrices derived from such infinite systems. He also did work in differential equations and in the theory of numbers. (DSB).‎

‎EXERCICES DE GEOMETRIE ANALYTIQUE ET DE GEOMETRIE SUPERIEURE, A L'USAGE DES CANDIDATS AUX ECOLES POLYTECHNIQUE ET NORMALE ET A L'AGREGATION, QUESTIONS ET SOLUTIONS, 1re PARTIE‎

‎Gauthier-Villars, Paris. 1886. In-8. Relié demi-cuir. Bon état, Couv. convenable, Dos à nerfs, Intérieur acceptable. 347 pages. Auteur, titre, fleurons, roulettes et filets dorés sur le dos. Etiquette de code sur le dos. Tampon et annotation d'institution religieuse en page de titre. Dos frotté. Signature en page de garde.. . . . Classification Dewey : 372.7-Livre scolaire : mathématiques‎

‎Cercle et systèmes de cercles. Ellipse, hyperbole, parabole (équations réduites). Courbes d'ordre supérieur... Classification Dewey : 372.7-Livre scolaire : mathématiques‎