‎Mathematics‎

‎"SCHOENFLIES, ARTHUR MORITZ.‎

‎Beiträge zur Theorie der Punktmengen I-I (+) Beiträge zur Theorie der Punktmengen II (+) Beiträge zur Theorie der Punktmengen III. - [SCHOEFLIES FAMOUS STUDIES IN TOPOLOGY]‎

‎Leipzig, B.G. Teubner, 1904, 1906. 8vo. In ""Mathematische Annalen, 58. Band, 1904" 59. Band, 1904" 62. Band, 2. Heft, 1906"". 58. Band and 62. Band in the original printed wrappers, without backstrips. Date written with pencil to both front wrappers. 59. Band bound in half cloth with the original wrappers, with wear to spines. All three issue internally very fine and clean. Pp: 195-234" Pp. 129-160" Pp.286-328.‎

‎First printing of this influential series of papers by Schoenflies, his ""fundamental researches into the topological aspects of point set theory"" (Anderson. Who gave you the epsilon? P. 144).""The greater part of Schoenflies' original contributions to topology is contained in three papers [The offered] and is devoted to plane topology. He proved the topological invariance of the dimension of the square, and he invented the notions and theorems that are connected with the characterization of the simple closed curve in the plane by its dividing the plane into two domains of which it is the everywhere attainable boundary. There are numerous gaps and wrong statements in this part of Schoenflies' work, and these errors led L. Brouwer to some of his startling discoveries."" (DSB).‎

Bookseller reference : 44917

‎"DEDEKIND, VON R.‎

‎Ueber Gruppen, deren sämmtliche Theiler Normaltheiler sind. - [FIRST PRINTING OF DEDEKIND GROUP / HAMILTONIAN GROUP]‎

‎Leipzig, B.G. Teubner, 1897. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. 48. Band. 4. Heft."" Entire issue offered. Minor soiling to back wrapper, internally fine and clean. [Dedekind:] Pp. 548-61. [Entire issue: 433-606, (2) pp.].‎

‎First printing of Dedekind groups, named named after Richard Dedekind, who investigated them in proving a form of the above structure theorem (for finite groups). He named the non-abelian ones after William Rowan Hamilton, the discoverer of quaternions.In group theory, a Dedekind group is a group G such that every subgroup of G is normal. All abelian groups are Dedekind groups. A non-abelian Dedekind group is called a Hamiltonian group‎

Bookseller reference : 44919

‎"TINSEAU (D'AMONDANS, CHARLES de).‎

‎Sur quelques Propriètés des Solides renfermés par des Surfaces composées de Lignes droites.‎

‎(Paris, Moutard, Panckoucke, 1780). 4to. Extract from ""Mémoires fe Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome IX. Pp. 625-642 and 2 folded engraved plates.‎

‎First appearance of an importent papwer in the history of analytic geometry.""Two of the three memoirs that constitute Tinseau’s oeuvre deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface, contact curves of circumscribed cones or cylinders, various surfaces attached to a space curve, the determination of the osculatory plane at a point of a space curve, problems of quadrature and cubature involving ruled surfaces, the study of the properties of certain special ruled surfaces (particularly conoids), and various results in the analytic geometry of space. In these two papers the equation of the tangent plane at a point of a surface was first worked out in detail (the equation had been known since Parent), methods of descriptive geometry were used in determining the perpendicular common to two straight lines in space, and the Pythagorean theorem was generalized to space (the square of a plane area is equal to the sum of the squares of the projections of this area on mutually perpendicular planes). (DSB). Although Tinseau published very little, his papers are of great interest as additions to Monge’s earliest works. Indeed, Tinseau appears to have been Monge’s first disciple.‎

Bookseller reference : 44932

‎"ZERMELO, ERNST FRIEDRICH FERDINAND.‎

‎Beweis, dass jede Menge wohlgeordnet werden kann. (Aus einem an Herrn Hilbert gerichteten Briefe). - [INTRODUCING BOTH ""THE AXIOM OF CHOICE"" AND ""THE WELL-ORDERING THEOREM""]‎

‎Leipzig, B.G. Teubner, 1904. 8vo. Bound in half cloth with five raised bands and gilt lettering to spine. In ""Mathematische Annalen. Begründet 1868 durch von A. Clebsch und C. Neumann. 59. Band."" Small bar-code pasted on to top left corner of front wrapper. Two library labels pasted on to pasted down front free end-paper and a small stamp to verso of title page. Pp. 514-16.‎

‎First appearence of this fundamental paper in metamathematics and mathematical logic in which he introduced both ""The Axiom of Choice"" and ""his sensational proof of the well-ordering theorem"" (DSB). By this paper Zermelo contributed decisively to the development of set-theory. Zermelo took up the problem, left over by Cantor, of what to do about the comparison of sets that are not well-ordered. ""In 1904 (the paper offered) he proved....that every set can be well-ordered. To make the proof he had to use what is now known as the axiom of choice (Zermelo's axiom), which states that given any collection of nonempty, disjoined sets, it is possible to choose one member from each set and so make up a new set. The axiom of choce, the well-ordering theorem, and the fact that any two sets may be compared as to size, are equivalent principles.""(Morris Kline). A controversy arose around ""The axiom of Choice"", from Bertrand Russell, Tarski, Frege, Hilbert, Brouwer and others, mainly, and of course importent, over how to interpret the words ""choose"" and ""exists"".The issue also contain the following papers of interest:David Hilbert. Über das dirichletsche prinzip. Pp. 161-186.Lie, Sophus. Drei Kapitel aus dem unvollendeten zweiten Bande der Geometrie der Berührungstransformationen. Pp. 193-313.Schoenflies, A. Beitrage zur Theorie der Punktmengen II, Pp. 129-160.‎

Bookseller reference : 44952

‎"MONGE, (GASPARD). - THE GENERAL REPRESENTATION OF DEVELOPABLE SURFACES.‎

‎Mémoire sur les Fonctions Arbitraires continues ou discontinues, qui entrent dans les Intégrales des Équations aux Différences finies. (1774) (+) Mémoire sur les Propriétés de plusieur Genres de Surfaces Courbes, particulièrement sur celles des Surfac...‎

‎(Paris, Moutard, Panckoucke, 1780). 4to. Extract from ""Mémoires fe Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome IX. Pp. 345-381 a. 2 folded engraved plates. And pp. 382-440 a. 3 folded engraved plates. Clean and fine.‎

‎First printing of two importent papers by Monge in differential functions and infinitesimal geometry, - in the first he discussed the nature of the arbitrary functions involved in the integrals of, finite difference equations. He also considered the, equation of vibrating strings, a topic he later investigated more fully. In the second memoir Monge returned to infinitesimal geometry. Working on the theory of developable surfaces outlined by Euler in 1772, he applied it to the problem, of shadows and penumbrae and treated several, problems concerning ruled surfaces. ""It is in this paper that he gives a general representation of developable surfaces...""(Morris Kline ""Mathematical Thoughts from Ancient to Modern Times"", p. 567).‎

Bookseller reference : 44972

‎"BASEDOW, JOHANN BERNHARD. - MATHEMATICS IN THE EDUCATIONAL REFORM.‎

‎Bewiesene Grundsätze der reinen Mathematik. 2 Bde. (1. Bd. Zahlenkunst und Algebra, zur elementarischen Bibliothek. 2. bd. Geometrie und Etwas von dem Unendlichen).‎

‎Leipzig, Siegfried Lebrecht Crusius, 1774. Bound in 2 very fine contemp. full calf, raised bands, richly gilt spines. Title-and tomelabels in leather on spines with gilt lettering., gilt border on all covers. Blindtooled decorations on covers in Cambridge-style, ""mirror-binding"". Edges gilt. Stamp on foot of titlepages. (22),312"(16),296 pp. and 11 folded engraved plates. Light browning to some quires and to top of titles, otherwise fine.‎

‎Scarce first edition of the famous German educators mathematical textbook, - his suggestion to how mathematics should be taught in his educational reform. Basedow’s views were based on the writings of men such as John Amos Comenius, John Locke, and Jean-Jacques Rousseau. His practical teaching methods were more expansive in their implications for education than those of any of his immediate predecessors in the field, and by the early 19th century they had become a fundamental force in Germany’s public school systems.Basedow blev i 1753 ansat af J.H.E. Bernstorff ved Sorø Akademi som professor i moral og de skønne videnskaber. Her kom han bl.a. i forbindelse med den danske oplysningsforfatter og Sorø-professor Jens Schielderup Sneedorff, hvis værker han oversatte til tysk. Sneedorff blev selv inspirereret af Basedows pædagogiske idéer.‎

Bookseller reference : 45029

‎"HILBERT, DAVID.‎

‎Über den Begriff der Klasse von Differentialgleichungen.‎

‎Leipzig, B.G. Teubner, 1912. 8vo. Bound in half cloth with the original wrappers. Marbled boards. In ""Mathematische Annalen. Herausgegeben von A. Clebsch und C. Neumann. 73. Band, Heft 1-4, 1912"". Black leather title label to spine with gilt lettering. Library label pasted on to top of spine and library stamp to title page. Light writing in pencil to front wrapper. [Hilbert:] Pp. 95-108. [Entire issue: IV, (2), 599, (1)].‎

‎First printing of Hilbert's paper on on the concept of the class of differential equations.The issue contain many other papers by contemporary mathematicians.‎

Bookseller reference : 45060

‎"BOOLE, GEORGE.‎

‎Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order (+) On certain theorems in the calculus of variations (+) On the integration of linear differential equatio... - [FIRST PAPERS BY BOOLE]‎

‎Cambridge, Macmillan, Barclay, and Macmillan, 1840-1846. 8vo. Bound in recent brown full cloth with gilt letting to spine. In ""The Cambridge Mathematical Journal, Vol. 1-2, Second edition"". Light writing in pencil to title page and very light miscolouring to borders of pages, otherwise a fine and clean copy. VI, 311, (1), VIII, (2), II, 284 pp. + folded plates.‎

‎First printing of four early papers by the influential British mathematician and philosopher. As the inventor of Boolean logic-the basis of modern digital computer logic-Boole is regarded in hindsight as a founder of the field of computer science. His earliest published paper was the ""Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order."" Printed in the Cambridge Mathematical Journal in February 1840 (Volume 2, no. 8, pp. 64-73), and it led to a friendship between Boole and D.F. Gregory, the editor of the journal, which lasted until the death of the latter in 1844.In 1840 he began to contribute to the recently founded Cambridge Mathematical Journal and also to the Royal Society, which awarded him a Royal Medal in 1844 for his papers on operators in analysis"" he was elected a fellow of the Royal Society in 1857.""In papers in the Cambridge Mathematical Journal in 1841 and 1843 [The present], Boole dealt with linear transformations. The algebraic fact had been partly perceived by Lagrange and by Gauss, but Boole's argument drew attention to the (relative) invariance of the discrimiant ab - h2, and also to the absolute invariants of the transformation. This was the starting point of the theory of invariants, so rapidly and extensively developed in the second half of the nineteenth century."" (DSB)‎

Bookseller reference : 45091

‎"JACOBI, C.G.J.‎

‎De functionibus ellipticis commentatio. - [ELLIPTIC FUNCTIONS]‎

‎(Berlin, G. Reimer, 1829). 4to. No wrappers. Extracted from""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 4. Band"". No backstrip. A fine and clean copy. [Jacobi:] pp. 371-390. [Entire issue: Pp. 311-422 + 1 folded plate].‎

‎First printing of a key memoir in the establishment of ""Elliptic Functions"". The acknowledged founders of the theory of ""Elliptic Functions"" are Abel and Jacobi. Both had arrived at the key idea of working with inverse functions of the elliptic integrals, an idea Abel had since 1823. Jacoby next gave proof of the results he had published in 1827 ( a paper published in ""Astronomische Nachrichten"" in several articles in Crelle's Journal for the years 1828-30, -the offered paper is one of these.""The most celebrated results of his research were those in elliptic functions, published in 1829, which brought him the praise of Legendre.""(Boyer). The offred paper was incorporated in Jcobi's main work ""Fundamenta nova theoriae functionum ellipticarum"", published 1829. Selvom‎

Bookseller reference : 45095

‎"CAYLEY, ARTHUR.‎

‎Sur quelques propriétés des déterminants gauches.‎

‎Berlin, Georg Reimer, 1846. 4to. In ""Journal für die reine und angewandte Mathematik, 32. Band, 2 Heft, 1846"". In the original printed wrappers, without backstrip. Front wrapper with a brown mark to top left corner, otherwise fine and clean. [Cayley:] Pp. 119-23. [Entire issue: Pp. 93-180, (2)].‎

‎First printing of Cayley's paper on Rotation matrix or skew-symmetric matrix (a square matrix A whose transpose is also its negative).""By 1846 Cayley had made use of four dimensions in the enunciation of specifically synthetic geometrical theorems, suggesting methods later developed by Veronese (C. M. P., I, no. 50 [1846], 317-328). Long afterward Cayley laid down in general terms, without symbolism, the elements of the subject of ""hyperspace"" (cf his use of the terms ""hyperelliptic theta functions,"" ""hyperdetermtnant,"" and so on) in his ""Memoir on Abstract Geometry"" (C. M. P., VI, no. 413 [1870], 456-469), showing that he was conscious of the metaphysical issues raised by his ideas in the minds of his followers but that as a mathematician he was no more their slave then than when remarking in his paper of 1846 (published in French): ""We may in effect argue as follows, without having recourse to any metaphysical idea as to the possibility of space of four dimensions (all this may be translated into purely analytic language)."""" (DSB)‎

Bookseller reference : 45097

‎"GUDERMANN, CHRISTOPH.‎

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

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

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

Bookseller reference : 45101

‎"BUÉE, (ADRIEN). - INFLUENTIAL WORK ON IMAGINARY NUMBERS.‎

‎Mémoire sur les Quantités imaginaires. Communicated by William Morgan. Read June 20, 1805.‎

‎(London, W. Bulmer and Co., 1806). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1803 - Part I. Pp. 23-88 a. 1 folded engraved plate.‎

‎First printing of Buée's memoir on imaginary numbers, an influential work containing original ideas. He shows how imaginary numbers can be represented geometrically.‎

Bookseller reference : 45114

‎"CAYLEY, (ARTHUR)‎

‎A Memoir on the Theory of Reciprocal Surfaces. Received November 12, 1868, - Read January 14, 1869.‎

‎(London, Taylor and Francis, 1870). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1869 - Vol. 159 - Part I. Pp. 201-229. Clean and fine.‎

‎First printing of the paper which ""contains some extensions of dr. Salmon's theory of Reciprocal Surfaces‎

Bookseller reference : 45118

‎RAUER, HEINZ.‎

‎Wahrscheinlichkeitstheorie und Grundzüge der Masstheorie.‎

‎Bln., 1968. orig. cloth. 342 pp.‎

Bookseller reference : 4512

‎"CAYLEY, (ARTHUR)‎

‎On the Curves which satisfy given Conditions. Received April 18, - Read May 2, 1867. (+) Second Memoir on the Curves...(2 Papers).‎

‎(London, Taylor and Francis, 1869). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1868 - Vol. 158. Pp. 75-143 a. pp. 145-172. Clean and fine.‎

‎First printings on 2 influential memoirs on the analytical geometry of curves.‎

Bookseller reference : 45122

‎"EULER, LEONHARD. - THE OPTICAL THEORY OF COMPOUND LENSES FOR TELESCOPES AND MICROSCOPES.‎

‎Régles générales pour la Construction des telescopes et de Microscopes, de quelque nombre de Verres qu'ils soient composés. (Rules for the construction of telescopes and microscopes).‎

‎(Berlin, Haude et Spener, 1759). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", Année 1757, tome XIII, pp. a. 1 engraved plate.‎

‎First printing of an importent paper in which Euler shows how to manufacture catoptrical telescopes and microscopes in accordance with general rules and founded on his own experiments. - The calculation concerning light ray aberrations, brought about due to the sphericty of the glass, is a masterpiece of analysis of the highest order and he also incorporates the mathematical theory of achromatic combination of lenses, which was first realized by Dollond in the same year, 1757.‎

Bookseller reference : 45126

‎"JACOBI, C. G. J.‎

‎Auflösungen und Beweise einer Reihe von Aufgaben und Lehrsätzen der ebenen Geometrie (+) Beweis eines geometrischen Satzes.‎

‎Berlin, G. Reimer, 1846. 4to. In ""Journal für die reine und angewandte Mathematik, 31 Band, 2. Heft, 1846"". In the original printed wrappers, without backstrip. Fine and clean. [Jacobi:] Pp. 93-110"" Pp. 178-180. [Entire issue: Pp. 93-180, (2) + 2 plates.].‎

‎First printing of two papers by Jacobi on geometry.""Most of Jacobi's fundamental research articles in the theory of elliptic functions, mathematical analysis, number theory, geometry, and me-chanics were published in Crelle's Journal fue die reine and angewandte Mathematik. With an average of three articles per volume, Jacobi was one of its most active contributors and quickly helped to establish its international fame. Yet his tireless occupation with research did not impair his teaching. On the contrary- never satisfied to lecture along trodden paths, Jacobi presented the substance of his own investigations to his students. He would lecture up to eight or ten hours a week on his favorite subject, the theory of elliptic functions, thus demanding the utmost from his listeners. He also inaugurated what was then a complete novelty in mathematics-research seminars-assembling the more advanced students and attracting his nearest colleagues."" (DSB).‎

Bookseller reference : 45143

‎"PONCELET, J. V. [JEAN-VICTOR].‎

‎Application de la méthode des moyennes à la transformation, au calcul numériques et à la détermination des limites du reste des séries.‎

‎Berlin, G. Reimer, 1835. 4to. In ""Journal für die reine und angewandte Mathematik, 13 Band, 1. Heft, 1835"". In the original printed wrappers, without backstrip. Fine and clean. [Poncelet:] 54 pp. [Entire issue: pp. IV, 54 pp.].‎

‎First printing of this extensive paper by the French mathematician on number theory and infinite series. ""Poncelet's years of study led to his personal belief that geometry could be founded on a series of fundamental principles as general as those on which algebra was based. He carried this belief forward by suggesting that since every straight line and plane extend to a point of infinity, then any new points on a line would be the same for specific parallel lines (or planes). At this time in mathematical history, it was accepted that all infinite elements of space were supposed to lie on the infinite plane of space, known as the projective plane.Early on, Poncelet's colleagues were extremely reluctant to accept his ideas and resulting theories. However, as time went on, several prominent German mathematicians not only accepted them but contributed to the emerging new science. Among those who recognized Poncelet's breakthrough in the field were Karl Georg Christian von Staudt, Felix Klein, Georg Cantor, Richard Dedekind, and Moritz Pasch. They were later joined by Otto Stolz of Austria who made his own contributions to the field.He died on December 22, 1867, in Paris without the recognition he deserved for his brilliant contributions to the world of numbers. His Treatise on the Projective Properties of Figures (1822) is still regarded as the pioneer work in the field."" (Schlager, Science and its Times, P. 261).‎

Bookseller reference : 45145

‎"GORDAN. [PAUL ALBERT].‎

‎Die Simultanen Systeme binärer Formen. - [GORDAN ON BINARY FORMS]‎

‎Leipzig, B. G. Teubner, 1870. 8vo. Bound with the original wrappers in black full cloth with gilt lettering to spine. In ""Mathematische Annalen, 2. band, 1870"". Entire issue offered. Two library labels pasted on to pasted down front free end-paper and library stamt to verso of title page. [Gordan:] Pp. 227-280. [Entire issue: IV, 649, (1), pp.].‎

‎First printing of Gordan's important paper in which he proved that any finite system of binary forms of arbitrary degree had a complete system of invariants. These archievement earned Gordan the name ""King of invariant theory"". (Kolmogorov, Mathematics of the 19th century, p. 85).Paul Gordan, German mathematician, was a major contributor to the field of invariant theory. He collaborated with Rudolf Clebsch on both invariant theory and algebraic geometry, and also developed proofs demonstrating that the numbers e and ? are transcendent numbers, numbers that are not the root of any algebraic equation with rational coefficients. A strict mathematical logician, Gordan commented that David Hilbert's less formal approach to mathematics was ""not mathematics, it is theology."" (Schlager, Science and Its Times, P. 269)‎

Bookseller reference : 45201

‎FRAENKEL, ADOLF.‎

‎Einleitung in Die Mengenlehre.‎

‎Berlin, Julius Springer, 1928. 8vo. Bound with the original orange wrappers in full cloth with leather title label to spine. Previous owner's name written to front wrapper. Some miscolouring to extremities and occasional underlining in text. XIII, (1), 424, (2) pp.‎

Bookseller reference : 45208

‎"SAURIN, JOSEPH.‎

‎Solution et Analyses de quelques Problêmes appatenans aux nouvelles Méthodes. (+) Solution Generale du Probleme, ou parmi une infinité de Courbes semblables décrites sur un Plan vertical, & aiant un même axe & un même point d'origine, il s'agit de...‎

‎(Paris, Jean Boudot, 1711). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1709"". Pp. 26-35 a. 1 folded engraved plate. + pp. 257-266 a. 1 folded engraved plate.‎

‎First printing of two historical papers in the development of the diffrential calculus.""Saurin’s two papers (1709) on curves of quickest descent represent a solution of a problem first posed by Jakob I Bernoulli - to find which of the infinitely many cycloids linking a given point as origin to a given line is the curve of quickest descent from the point to the line - and then an extension of the problem to any family of similar curves. Saurin followed the differential methods of Johann I Bernoulli, although he studiously avoided taking a position in the brothers’famous quarrel.""(DSB).‎

Bookseller reference : 45235

‎"CLEBSCH, A. [RUDOLF FRIEDRICH ALFRED].‎

‎Ueber die ebene Abbildung der geradlinigen Flächen vierter Ordnung, welche eine Doppelcurve dritten Grades besitzen.‎

‎Leipzig, B.G. Teubner, 1870. 8vo. In ""Mathematische Annalen, 2. Band, 3. Heft, 1870"". In the original printed wrappers, without backstrips. Back wrappers with a few nicks. [Clebsch:] Pp. 504-13. [Entire issue: 385-514 pp].‎

‎First printing.‎

Bookseller reference : 45261

‎MULCAHY, JOHN.‎

‎Principles of Modern Geometry, with Numerous Applications to Plane and Spherical Figures and an Appendix, Containing Questions for Exercise. Intended Chiefly for the Use of Junior Students.‎

‎Dublin, Hodges and Smith, 1852. 8vo. In the original publisher's embossed full cloth with gilt lettering to spine. Some wear and soiling to extremities. Hindges weak. Lacking front free end paper. Internally fine. VII, (1), 227 pp.‎

Bookseller reference : 45264

‎KÖNIG, FRANZ.‎

‎Die leichteste Art den Kindern das rechnen auf eine angenehme Weise beizubringen, auch zum Selbstunterrichte für Erwachsene anwendbar, welche im Rechnen noch keinen oder keinen gründlichen Unterricht erhalten haben. (2 Theile).‎

‎Prag, Johann Gottfried Calve, 1815. Uncut in orig. marbled boards. Spine with nicks in the thin paper. Handwritten paperlabel to spine. (6),VI,249,(4)176,(1) pp. A few small brownspots. Internally fine and clean.‎

Bookseller reference : 45268

‎"BERNOULLI, JOANNES [JOHANN].‎

‎Responsio ad nonneminis provocationem eiusque solutio quaestionis ipsi ad eodem proposititae de invenienda linea curva, quam describit proiectile in medio resistente (+) Problema Analyticum, quod omnibus Geometris non-Anglis proposuit. - [THE FINAL SOLUTION TO THE BALLISTIC CURVE]‎

‎Leipzig, Grosse & Gleditsch, 1719. 4to. In: ""Acta Eruditorum Anno MDCCXIX"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 256-270. [Entire volume: (4), 539, four engraved plates.].‎

‎First printing of Bernoulli's exceedingly important paper in which he presented the final (and correct) solution to the ballistic curve. Newton had also occupied himself with the problem but had only solved the law of resistance. In 1718, English mathematician Keill had given Bernoulli the following challenge: ""Find the curve which a projectile describes through the air on the simplest hypothesis of uniform gravity and density in the medium, the resistance varying as the square of the velocity"". The challenge was more an attempt to humiliate Bernoulli, since it was supposed to be unsolvable, than it was an attempt to advance mathematics. ""It was therefore natural the Bernoulli, when he published his solution of Keill's problem and an account of his conduct, should dwell at greater length upon his triumph over the English mathematician than upon his very considerable achievement in mathematics."" (Hall, Ballistics in the seventeenth century, Pp. 155).""Bernoulli's criticism of Taylor's Methodus incrementorum was simultaneously an attack upon the method of fluxions, for in 1713 Bernoulli had become involved in the priority dispute between Leibniz and Newton. Following publication of the Royal Society's Commercium epistolicum in 1712, Leibniz had no choice but to present his case in public. He released-without naming names-a letter by Bernoulli (dated 7 June 1713) in which Newton was charged with errors stemming from a misinterpretation of the higher differential. Thereupon Newton's followers raised complicated analytical problems, such as the determination of trajectories and the problem of finding the ballistic curve, which Newton had solved only for the law of resistance R = av (R = resistance, a = constant, v = velocity). Bernoulli solved this problem (AE, 1719) for the general case (R = avn), thus demonstrating the superiority of Leibniz' differential calculus."" (DSB)‎

Bookseller reference : 45321