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‎"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).‎

Ссылка продавца : 44972

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‎"GORDAN, P.,‎

‎Ueber einen Satz von Hilbert. - [COINING ""HILBERT'S THEOREM""]‎

‎Leipzig, B.G. Teubner, 1893. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Herausgegeben von A. Clebsch und C. Neumann. 42. Band. 1. Heft."" Entire issue offered. Library-stamp to verso of title page. A fine and clean copy. [Gordan:] Pp. 132-42. [Entire issue: IV, 152 pp.].‎

‎First printing of Gordan' paper on Hilbert's (basic) theorem, in which Godan coined the term ""Hilbert's Theorem"".‎

Ссылка продавца : 44983

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‎"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.‎

Ссылка продавца : 45029

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‎"CLEBSCH. [RUDOLF FRIEDRICH ALFRED].‎

‎Ueber den Zusammenhang einer Classe von Flächenabbildungen mit der Zweitheilung der Abel'schen Functionen (+) Ueber die Bewegung eines Körpers in einer Flüssigkeit (+) Ueber die Bedeutung einer simultanen Invariante einer binären quadratischen und ein...‎

‎Leipzig, B.G. Teubner, 1871. 8vo. Bound in black full cloth with gilt lettering to spine. In ""Mathematische Annalen. Herausgegeben von A. Clebsch und C. Neumann. 3. Band, 1871"". Entire issue offered. Two library labels pasted on to pasted down front free end-paper and small blue library stamp to verso of title page. Small write bar-code pasted on to top left corner of front board. A fine and clean copy. [Clebsch:] Pp. 45-75" Pp. 238-262 Pp. 263-264" Pp. 265-267. [Entire issue: IV, 632 pp.].‎

‎First printing of four important paper by the influential German mathematician. ""In 1868 Gordan had already proved the precursory theorem on the finiteness of binary invariants. The theory of binary invariants thus being more complete, Clebsch published a book on this part of the theory (1872), giving a summary of the results obtained [In the offered papers]"". (DSB). In 1868 he and his friend Carl Neumann, son of Franz Neumann, founded the Mathematische Annalen.‎

Ссылка продавца : 45059

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‎"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.‎

Ссылка продавца : 45060

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‎"MOORE, ELIAKIM HASTINGS.‎

‎Concerning Transcendentally Transcendental Functions.‎

‎Leipzig, B.G. Teubner, 1896. 8vo. In ""Mathematische Annalen, 48. Band, 1-2 Heft, 1896"". In the original printed wrappers, without backstrips. Wrappers with a few nicks and some brownspotting to front wrapper and title page. Library stamp to verso of title page. [Moore:] Pp. 49-74. [Entire issue: IV, 240 pp. + 1 folded plate].‎

‎First printing of Moore probe of the theory of functions produced a clarified treatment of transcendentally transcendental functions.""Rigor and generalization characterized the mathe-matical research of Moore. His research fell principally into the areas of (1) geometry" (2) algebra, groups, and number theory (3) the theory of functions" and (4) integral equations and general analysis. Among these he emphasized the second and fourth areas. In geometry he examined the postulational foundations of Hilbert, as well as the earlier works of Pasch and Peano. He skillfully analyzed the independence of the axioms of Hilbert and formulated a system of axioms for n-dimensional geometry, using points only as undefined elements instead of the points, lines, and planes of Hilbert in the three-dimensional case. During his investigation of the theory of abstract groups, he stated and proved for the first time the important theorem that every finite field is a Galois field (1893). He also discovered that every finite group G of linear transformations on n variables has a Hermitian invariant (1896-1898). His probe of the theory of functions produced a clarified treatment of transcendentally transcendental functions and a proof of Goursat’s extension of the Cauchy integral theorem for a function without the assumption of the continuity of the derivative."" (DSB).‎

Ссылка продавца : 45061

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‎"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)‎

Ссылка продавца : 45091

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‎"CLEBSCH, RUDOLF FRIEDRICH ALFRED.‎

‎Ueber die simultane Integration linearer partieller Differentialgleichungen. - [FROBENIUS THEOREM]‎

‎Berlin, Georg Reimer, 1866. 4to. In ""Journal für die reine und angewandte Mathematik, 65. Band, 3 Heft, 1866"". In the original printed wrappers, without backstrip. Front wrapper with a brown mark to top left corner, otherwise fine and clean. [Clebsch:] Pp. 257-268. [Entire issue: Pp. 189-292, (2)].‎

‎First printing of Clebsch's paper in which the Frobenius theorem was introduced.Despite being named after Ferdinand Georg Frobenius, the theorem was first proven by Alfred Clebsch and Feodor Deahna. Deahna was the first to establish the sufficient conditions for the theorem, and Clebsch developed the necessary conditions. Frobenius is responsible for applying the theorem to Pfaffian systems, thus paving the way for its usage in differential topology.""German mathematician whose work on algebraic geometry was considered the first and most fundamental work in that branch of mathematics. Clebsch also developed a brilliant interpretation of some of Georg Riemann's work on function theory and investigated some aspects of algebraic geometry using approaches that differed from convention, focusing on algebraic interpretations rather than geometrical ones. Clebsch also founded an important journal, Mathematische Annalen before his premature death at the age of 39."" (Schlager, Science and Its Times, P. 267)The issue also contain:Cayley, Sur un cas particulier de la surface du quatrieme ordre avec seize points singuliers, P. 284-290.‎

Ссылка продавца : 45094

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‎"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

Ссылка продавца : 45095

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‎"JACOBI, C.G.J.‎

‎De resolutione aequationum per series infinitas.‎

‎(Berlin, G. Reimer, 1830). 4to. No wrappers. Extracted from""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 6. Band"". No backstrip. A fine and clean copy. [Jacobi:] pp. 257-286. [Entire issue: Pp. 215-310 + 1 folded plate.].‎

‎First printing of Jacobi's paper on infinit series. ""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."" (DSB)‎

Ссылка продавца : 45096

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‎"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)‎

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‎"MINDING. [ERNST FERDINAND ADOLF].‎

‎Ueber die Biegung gewisser Flächen.‎

‎Berlin, G. Reimer, 1838. 4to. In ""Journal für die reine und angewandte Mathematik, 18. Band, 4 Heft, 1838"". In the original printed wrappers, without backstrip. Fine and clean. [Minding:] Pp. 297-302. [Entire issue: Pp. 281-376, (2) + 1 folded plate.].‎

‎First printing of Minding's first work on the deformation of general ruled surfaces into ruled surfaces and showed that any ruled surface can be developed on another whose direction vectors form a circular cone. This was subject in which he was to make his most important discoveries. ""Minding's most important discoveries were in the dilierential geometry of surfaces"" in these works he brilliantly continued the researches of Gauss, which had been published in 1828. In his first paper (1830), which dealt with the isoperimetric problem of determining on a given surface the shortest closed curve surrounding a given area (on the plane it is the circumference of a circle), he introduced the concept of geodesic curvature. It was independently discovered in 1848 by O. Bonnet, and it was he who named it geodesic curvature. Minding soon proved, as did Bonnet after him, the invariance of the geodesic curvature under bending of the surface. Neither of them knew that the same results had been presented in an earlier, unpublished paper of Gauss's (1825)."" (DSB).‎

Ссылка продавца : 45099

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‎"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.‎

Ссылка продавца : 45101

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‎"OTTO, J.C.F.‎

‎Mathematische Theorie des Ricoschettschusses.‎

‎Berlin, Jonqs Verlagsbuchhandlung, 1833. Contemp. hcalf, gilt spine. Stamps on titlepage and front free endpaper.X,145,(1) pp. and 1 folded engraved plate. With ""Tafel"" I-IV (= pp.61-146). A few brownspots.‎

Ссылка продавца : 45110

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‎"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.‎

Ссылка продавца : 45114

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‎"CAYLEY, (ARTHUR).‎

‎A Memoir on Prepotentials. Received April 8, - Read June 10, 1875.‎

‎(London, Taylor and Francis, 1876). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1875 - Part II. Pp. 675-774. Clean and fine.‎

‎First printing of Cayley's importent paper on multiple integrals in which he gives the formula for the potential of certain heterogenous ellipsoids. Clifford called it ""a contribution of great value to the most importent branch of mathematical physics.""‎

Ссылка продавца : 45117

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‎"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

Ссылка продавца : 45118

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‎"CAYLEY, (ARTHUR)‎

‎On the Double Tangents of a Plane Curve. Received March 17, - Read April 14, 1859.‎

‎(London, Taylor and Francis, 1859). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1859 - Vol. 149 - Part I. Pp. 193-212. Clean and fine.‎

‎First printing of the paper in which Cayley gives a solution to the problem of double tangents.‎

Ссылка продавца : 45119

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‎RAUER, HEINZ.‎

‎Wahrscheinlichkeitstheorie und Grundzüge der Masstheorie.‎

‎Bln., 1968. orig. cloth. 342 pp.‎

Ссылка продавца : 4512

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‎"CAYLEY, (ARTHUR)‎

‎On the Analytical Theory of the Conic. Received May 8, - Read May 15, 1862.‎

‎(London, Taylor and Francis, 1862). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1862 - Vol. 152 - Part I. Pp. 639-662. Clean and fine.‎

‎First printing of an importent paper in analytical geometry.‎

Ссылка продавца : 45121

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‎"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.‎

Ссылка продавца : 45122

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‎"EULER, LEONHARD - ON COMPOUND OBJECT-GLASSES.‎

‎Sur les Avantages des Verres Objectifs composés de deux Verres simples. (On the advantages of telescopic glasses built with two lenses)‎

‎(Berlin, Haude et Spener, 1769). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", Année 1762, tome XVIII, pp. 249-264 and 1 engraved plate.‎

‎First printing. In the paper Euler states the mathematical theory for compund object-glasses of different capabilities.Enestroem: E. 381.‎

Ссылка продавца : 45124

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‎"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.‎

Ссылка продавца : 45126

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‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Modular-Functionen und der Modular-Integrale, Allgemeiner Charakter der Potenzial-Functionen (+) Theorie der Modular-Functionen und der Modular-Integrale.‎

‎Berlin, G. Reimer, 1838. 4to. In ""Journal für die reine und angewandte Mathematik, 18. Band, 1-2 Heft, 1838"". Both issues in the original printed wrappers, without backstrip. Fine and clean. [Gudermann, 1 heft:] Pp. 1-54. [Gudermann, 2 heft:] Pp. 142-175. [Entire issue, heft 1: IV, 100, (2) pp. 2 Heft: 101-188, (2) pp. + 2 plates, one of them detached.].‎

‎First printing of Gudermann's two papers on modular functions and modular integrals, ideas which anticipated his 1844-book.""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).‎

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‎"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).‎

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‎"SLONIMSKI, CH. Z. [CHAIM ZELIG SLONIMSKI], [HAYYIM SELIG].‎

‎Allgemeine Bemerkungen über Rechenmaschinen, und Prospectus eines neu erfundenen Rechen-Instrument (+) Eine allgemeine Formel für die gesammte jüdische Kalenderberechnung. - [FIRST RUSSIAN CALCULATOR]‎

‎Berlin, G. Reimer, 1844. 4to. In ""Journal für die reine und angewandte Mathematik, 28 Band, 2. Heft, 1844"". In the original printed wrappers, without backstrip. Fine and clean. [Slonimskyi:] Pp. 179-183"" Pp. 184-190. [Entire issue: Pp. 97-192, (2) + 1 plate.].‎

‎First printing of Slonimsky's paper on the design of his calculator or multiplying device, probably the earliest Russian contribution to designing a calculator. ""In the middle of the last century, the mathematician Zinovy (Zelig) J. Slonimsky (1810-1904) invented a simple multiplication device to implement one of the theorems, which he had proven. The device could multiply every number of permitted length (i.e. the length permitted by the device-design) by every simple number. In other words, the device was something like a mechanical multiplication table. Later, the Slonimsky theorem was used for another simple multiplication device, namely for the calculating bars designed by Jofe. Both devices are interesting as examples of technical implementations of complicated mathematical ideas rather than as mechanical innovations."" (Trogemann, Computing in Russia, P. 29).‎

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‎"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).‎

Ссылка продавца : 45145

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‎FRAENKEL, ADOLF.‎

‎Zehn Vorlesungen über die Grundlegung der Mengenlehre. Gehalten in Kiel auf Einladung der Kant-Gesellschaft, ortsgruppe Kiel, vom 8.-10. Juni 1925.‎

‎Leipzig u. Berlin, B.G. Teubner, 1927. Small 8vo. Orig. full cloth. X,182 pp.‎

Ссылка продавца : 45155

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‎"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)‎

Ссылка продавца : 45201

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‎"HILBERT, DAVID.‎

‎Zur Variationsrechnung. - [HILBERT'S 23RD PROBLEM]‎

‎Leipzig, B. G. Teubner, 1906. 8vo. In the original printed wrappers, without backstrip. In ""Mathematische Annalen, 62. Band., 3. Heft., 1906."". A fine and clean copy. Pp. 351-370. [Entire issue: Pp. 329-448.].‎

‎First printing of Hibert's important paper in which he addressed a number of topics in the Calculus of Variations and thereby extended the ideas given in his account of the 23rd problem. In contrast with Hilbert's other 22 problems, his 23rd is not so much a specific ""problem"" as an encouragement towards further development of the calculus of variations. His work in the present paper led to a modern definition of the field.‎

Ссылка продавца : 45202

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‎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.‎

Ссылка продавца : 45208

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‎"ROLLE, (MICHEL).‎

‎De L'Evanouissement des Quantitez inconnues dans la geometrie analytique.‎

‎(Paris, Jean Boudot, 1711). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1709"". Pp. 419-461.‎

‎First printing of one of Rolle's main papers on analytical geometry. Rolle was perhaps the first to use the term ""analytical geometry"" in print in the sense of the term used today. ""By analytic geometry Rolle understood research of one or the other of two types: in the one, geometric questions are transformed into problems of algebra, and in the other, one is occupied only with the graphical solutions of these problems. That is his view was thoroughly Cartesian.""(Boyer ""History of Analytic geometry"", pp. 155.‎

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‎"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).‎

Ссылка продавца : 45235

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‎NESBIT,A.‎

‎A Treatise on practical Mensuration, in eight Parts. Ninth Edition, corrected and greatly improved.‎

‎York, Longman, Orme, Brown..., 1838. Contemp. full motteled calf. Hinges weakening, but sill holding.XXIV,448 pp. Many textfigs.‎

Ссылка продавца : 45241

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‎"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.‎

Ссылка продавца : 45261

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‎KROYMANN, F.‎

‎Almeennyttig Regne=Bog. Oversadt af det Tydske.‎

‎Altona, 1802. 8vo. Indbundet i samtidigt hellæderbind med 4 ophøjede bind og messingspænde. False løse og revne i bogblok mellem p 336 og p 337. Ellers pænt eksemplar. 400 p.‎

Ссылка продавца : 45262

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‎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.‎

Ссылка продавца : 45264

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‎EULER, LEONHARD.‎

‎Vollständige Anleitung zur Integralrechnung. Aus dem Lateinischen ind Deutsche übersetz von Joseph Salomon. 4 Bde. - [A LANDMARK TEXTBOOK ON THE INTEGRAL CALCULUS]‎

‎Wien, Carl Gerold, 1828-30. 8vo. Bound in 4 contemp. marbled boards, titlelabels with gilt lettering. A few scratches to hinges and spine ends. Very small loos to 2 titlelabels. Light wear to top of spine on volume 4. Corners a bit bumped. 2 small paperlabels pasted to lower part of spines. A small stamp to foot of titlepages. VIII,439IV,424VIII,439"VI,520 pp. and 3 folded engraved plates.‎

‎First German edition (a translation from the Latin ""Institutiones Calculi Integralis"", 1768-70) of this landmark work on the integral calculus, being the most complete and accurate work on the subject at the time. It ""contained not only a full summary of everything then known on this subject, but also the Beta and Gamma functions and other original investigations"" (Cajori). The work exhibits Euler's numerous discoveries in the theory of both ordinary and partial differential equations, which were especially useful in mechanics.""(Euler) presents methods of definite and indefinite integration, having invented many of the methods himself, such as the use of an ""Euler substitution"" for rationalizing particular irrational differentials. His treatment is near exhaustive for integrals expressive as elementary functions. He also develops the theory of ordinart and partial differential equations and presents many properties of the beta and gamma function Eulerian integrals introduced by Euler earlier.""(Parkinson ""Breakthroughs"" 1768 M).Enestroem E 342, E 385, E 385 (The Latin edition). - Poggendorff I, 690.‎

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‎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.‎

Ссылка продавца : 45268

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‎"BERNOULLI, JOANNES [JOHANN].‎

‎Barometrum novum communi multo accuratius. - [BERNOULLI'S BAROMETER]‎

‎Leipzig, Grosse & Gleditsch, 1716. 4to. In: ""Acta Eruditorum Anno MDCCXVI"". 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. 10-14 + one engraved plate. [Entire volume: (2), 567, (39) pp. + four engraved plates.].‎

‎First Latin printing of Bernoulli's paper on the luminous barometer created by mercurial phosphorus. The phenomenon was first observed by French astronomer Jean Picard in 1675, but the practical use of the phenomenon was popularized by Bernoulli who made the first horizontal or rectangular barometer. Bernoulli's study of the subject had profound influence on the English scientist Francis Hauksbee who became of seminal importance to the development of electricity and electrostatic repulsion.The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

Ссылка продавца : 45319

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‎"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)‎

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‎"KEES, F. K. [FRIEDRICH KÖES].‎

‎Ratio Complanandi Superficies Curvas Corporum quorumlibet Geometricorum.‎

‎Leipzig, Grosse & Gleditsch, 1729. 4to. In: ""Actorum Eruditorum Supplementa Tomus IX"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two 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. 45-50. [Entire volume: (2), 509, (24), + two engraved plates.].‎

‎First publication of perhaps the first attempt to create a formula describing curvature or curved surfaces, thus making it one of the most important Danish contributions to mathematical history. The result is given in a double-integral.Euler established the theory of surfaces in his 'Recherches sur la courbure des surfaces', 1767. Gauss later took a fundamentally different approach to the study of surfaces"" in contrast to Euler he represented the points of a surface in terms of two external parameters. Gauss then derived his own notions of the fundamental quantities of surfaces, e.g. arc length, angle between curves, and curvature.Niels Nielsen ""Matematikeni Danmark 1528-1800"", Koës No. 9. Observator i Berlin, privatdocent i Kiel, underviste artilleriofficererne i Rendsborg, blev 1721 ordinær professor i matematik ved Kiels Universitet.(Pihl, Københavns Universitet 1479-1979, Bind XII, P. 146)‎

Ссылка продавца : 45324

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‎WOLFF, CHRISTIAN.‎

‎Elementa Matheseos Universae. Editio Nova priori multo auctior et correctior.Tomus I-II (von 5).(I. Qui Commentationem de Method Mathematica, Arithmeticam, Geometriam, Trigonometriam Planam, et Analysin tam Finitorum, quam Infinitorum, comlectitur. - ...‎

‎Halæ Magdeburgicæ, 1730-33. 4to. 2 contemp. full calf. Wear to the gilt lettering on spines. Spine ends worn. Part of leather at upper compartment on vol. one, gone. Some wear to spines. Engraved portrait of Wolff. First titlepage in red/black. (22),678(8),506 pp. and 61 (31 + 30) folded engraved plates.‎

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‎EUCLID (EUKLID) OF ALEXANDRIA.‎

‎Euclidis elementorum sex libri priores. Magnam partem novis demonstrationibus adornati. Opera & Studio Henrici Coetsii.‎

‎Lugdunum Batavorum (Leiden), Danielem à Gaesbeek, 1691. Small8vo. Contemp. full vellum. Spine gone and frontcover detached. Some soiling to covers. Wood-cut printers device on titlepage. (24),468 pp. and many diagrams in the text. A few scattered brownspots and a few quires with light browning.‎

‎First edition of Heinrich Coetsius' translation of the six first books of Euclid.Riccardi 1691, 7 - Max Steck p. 109, 1691.‎

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‎"CLAIRAUT, (ALEXIS CLAUDE de).‎

‎Indledning til Geometrien. Öfversat ifrån Fransyska Språket.‎

‎Stockholm, Lars Salvius, 1744. Samtidigt hldrbd. Øverste rygfelt med bortslid af noget af skindet. Uden forreste friblad. (14),190,22 pp. samt 14 kobberstukne plancher.‎

‎First Swedish edition of Clairaut's renowned elementary geometry ""Élémens de géométrie"", 1741.Clairaut’s Élémens de géométrie is linked to the more liberal school. He wanted geometry to be rediscovered by beginners and therefore put together, for himself and for them, a very optimistic history of mathematical thought that reflected the concepts of his contemporaries Diderot and Rousseau. (DSB).""I intended to go back to what might have given rise to geometry"" and I attempted to develop its principles by a method natural enough so that one might assume it to be the same as that of geometry’s first inventors, attempting only to avoid any false steps that they might have had to take"" [Élémens de géométrie, preface].‎

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‎"ACKERMANN, WILHELM.‎

‎Zum Hilbertschen Aufbau der reellen Zahlen. - [THE ACKERMANN FUNCTION - THE FIRST TOTAL COMPUTABLE FUNCTION]‎

‎Berlin, Julius Springer, 1928. 8vo. Without wrappers as extracted from ""Mathematische Annalen, 99. Band. 1928"". Pasted on backstrip in marbled paper. Internally fine and clean. Pp. 118-33‎

‎First printing of Ackermann's seminal paper in which the famous and exceedingly influential ""Ackermann Function"" was presented for the first time: ""One of the most important functions in computer science"". (Darling, The universal book of mathematics, p. 6)After Ackermann had published his function many mathematicians modified it and altered it to suit various purposes so that today ""the Ackermann function"" may refer to any of numerous variants of the original function.‎

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‎"RAILLIER DES OURMES. - THE MATHEMATICS OF THE MAGIC CUBE.‎

‎Mëmoire sur les Quarrés Magiques.‎

‎(Paris, L'Imprimerie Royale, 1763). 4to. No wrappers.Extract from ""Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome IV. Pp. 196-246 a. many textfigs. A very faint dampstain to outer margin.‎

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‎"BOSSUT, (CHARLES).‎

‎Recherches de Dynamique.‎

‎(Paris, Imprimerie Royale, 1760). 4to. Extract from ""Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome III. Pp. 473-500 a. 3 folded engraved plates.‎

‎First printing of one of Busset's major papers on mathematical physics.""Bossut was one of a very few whom d’Alembert took as students, and as such he was admitted as a correspondant to the Académie des Sciences on 12 May 1753" subsequently, he rose to géométre, mécanicien, and mathématicien. In 1761, 1762, and 1765 he won or shared prizes given by the Academy for memoirs on mechanics applied to the operation of ships and on the resistance of the ether in planetary motions. He won additional prizes for his mechanics memoirs from the academies of Lyons and Toulouse, and was elected to the scientific academies of Bologna, Turin, and St. Petersburg. In 1775 he participated with d’Alembert and Condorcet in a well known series of experiments on fluid resistance. Never more than a minor mathematician or physicist, Bossut is nevertheless one of the important figures in the history of physics and engineering education. (DSB).‎

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‎"BOSSUT, (CHARLES)‎

‎Usages de la Differentiation des Parametres, pour la Solution de plusieurs Problèmes de laa méthode inverse des Tangentes.‎

‎(Paris, Imprimerie Royale, 1755). 4to. Extract from ""Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome II. Pp. 435-451 a. 1 folded engraved plate.‎

‎First printing of Busset's first mathematical paper.""Bossut was one of a very few whom d’Alembert took as students, and as such he was admitted as a correspondant to the Académie des Sciences on 12 May 1753" subsequently, he rose to géométre, mécanicien, and mathématicien. In 1761, 1762, and 1765 he won or shared prizes given by the Academy for memoirs on mechanics applied to the operation of ships and on the resistance of the ether in planetary motions. He won additional prizes for his mechanics memoirs from the academies of Lyons and Toulouse, and was elected to the scientific academies of Bologna, Turin, and St. Petersburg. In 1775 he participated with d’Alembert and Condorcet in a well known series of experiments on fluid resistance. Never more than a minor mathematician or physicist, Bossut is nevertheless one of the important figures in the history of physics and engineering education. (DSB).‎

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‎"(TSCHIRNHAUS, EHRENFRIED W. von.). - THE ""TSCHIRNHAUS TRANSFORMATION""‎

‎Aufrendi omnes terminos intermedios ex data aequatione.‎

‎Leipzig, Grosse & Gleditsch, 1683. 4to. Without wrappers. In: ""Acta Eruditorum Anno MDCLXXXIII"", No. V (May issue). Pp.177-224 (entire issue offered). Tschirnhaus' paper: pp. 204-207. Some browning as usual. With titlepage to the volume 1683. Titlepage with a stamp and a faint dampstain.‎

‎First edition of Tschirnhaus' ""Tschirnhaus Tranformation"".Tschirnhaus work intensively on finding a general method for solving equations of higher of higher degree. ""His transformations constituted the most promising contribution to the solution of equations during the seventeenth century"" but his elimination of the second and third coefficients by means of such transformation was far from adequate for the solution of the quintic.(Boyer. A History of Mathematics, 1968, 472 p.).Tschirnhaus (1651-1708) , a Saxon nobleman, had as wide interest as acquaintances: He studied in Leyden, served in the Dutch army, visited England and Paris several times. He set up a glassworks in Italy and is said to have introduced Porcelain to Europe. He wrote about philosophy and mathematics and was a close friend of Leibniz.""In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683. It may be defined conveniently by means of field theory, as the transformation on minimal polynomials implied by a different choice of primitive element. This is the most general transformation of an irreducible polynomial that takes a root to some rational function applied to that root.""(Wikipedia).Parkinson ""Breakthroughs 1683 M.‎

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