‎Mathématiques‎

‎"EULER, LEONHARD.‎

‎Recherches sur le Mouvement de Rotation des Corps celestes (Studies on the rotational movement of celestial bodie). (And the same author:) Solution d'une Question curieuse qui ne paroit soumise a aucune Analyse. (Solutions of a curious question which ... - [RECREATIONAL MATHEMATICS]‎

‎(Berlin, aud et Spener, 1766). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XV, pp. 265-309 a. 2 engraved plates., pp. 310-337.‎

‎"EULER, LEONHARD.‎

‎Recherches sur les plus Grand et plus Petits qui se trouvent dans les Actions des Forces.‎

‎(Berlin, Haude et Spener, 1750). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome IV, pp. 149-188 and 2 folded engraved plates..‎

‎"EULER, LEONHARD.‎

‎Solution d'une Question tres difficile dansl le Calcul des Probabilités.‎

‎(Berlin, Haude et Spener, 1771). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome XXV, pp. 285-302. Fine and clean.‎

‎"EULER, LEONHARD.‎

‎Sur la Probabilité des Séquences dans la Lotterie Génoise (On the Probability of Sequences in the genoise Lottery). - [THE GENOISE LOTTERY]‎

‎(Berlin, Haude et Spener, 1767). 4to. Without wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXI, pp. 191-230.‎

‎"EULER, LEONHARD.‎

‎Sur quelques Proprietés des Sections Coniques, qui conviennent à une infinité d'autres Lignes Courbes. Traduit du Latin.‎

‎(Berlin, Haude et Spener, 1746). 4to. No wrappers, as issued in ""Memoires de l'Academie Royale des Sciences et Belles-Lettres"" Tome I, pp.71-98.‎

‎"EULER, LEONHARD.‎

‎Sur une Contradiction apparente dans la Doctrine des Lignes courbes (On an apparent contradiction in the theory of curves) + (continuation:) Demonstration sur le Nombre des Points, ou deux Lignes des Ordres quelques peuvent se couper (A proof concerni...‎

‎(Berlin, Haude et Spener, 1750). 4to. No wrappers, as issued in ""Mémoires de L'Academie Royale des Sciences et Belles-Lettres"", tome IV, pp. (219)-233 and (234)-248.‎

‎"EULER, LEONHARD.‎

‎Variae Demonstrationes Geometriae. (Various geometric demonstrations).‎

‎(Petropoli (St. Petersbourg), 1750). 4to. Uncut, without wrappers. Extracted from ""Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tom. I. ad Annum 1747 et 1748. Pp. 49-66 a. 1 engraved plate. Clean and fine.‎

‎"EULER, LEONHARD. - THE GAME PHARON.‎

‎3 works by Euler: Nouvelle Méthode d'Éliminer les Quantités inconnues des Equations. - Recherches sur les Microscopes a´Trois Verres et les Moyens de les Perfectionner. - Sur L'Avantage du Banquier au Jeu du Pharaon.‎

‎(Berlin, Haude et Spener, 1766). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", tome XX, pp. 91-164 (91-116"117-143"144-164). 1 engraved plate ( belonging to ""Microscope..."")‎

‎3 first editions by Euler in algebra, in optics and in the theory of chance - in this last paper he discusses the so-called St. Petersburg paradox, the Game Pharon.‎

书商的参考编号 : 31081

‎"EULER, LEONHARD. - HYDRAULIC TURBINES.‎

‎Application de la Machine Hydraulique de M. Segner à toutes sortes D'Ouvrages et de ses Avantages sur les autres Machines hydrauliques dont on se sert ordinairement. (The application of Mr. Segner's hydrological machine to all sorts of work and its ...‎

‎(Berlin: Haude & Spener, 1753). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome VII. Pp. 271-304 and 2 folded engraved plates.‎

‎"EULER, LEONHARD. - INTRODUCING ""THE EULER CONSTANT"" AND ""THE FUNCTION NOTATION""‎

‎De Linea celerrimi descensus in Medio qvocunqve resistente. (On the curve of fastest descent in whatever resistent medium). (+) De progressionibus harmonicis observationes. (On harmonic progressions). (+) De infinitis curvis iusdem generis seu methodu...‎

‎(Petropoli, St. Petersburg, Typis Academiae, 1740). 4to. No wrappers. In: ""Classes Prima continens Mathematica. Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tomus VII ad Annum 1735, &..... Euler's papers: pp. 135-149, 150-161, 174-183 a. 184-200 and 2 engraved plates. Clean and fine.‎

‎First printing of 4 importent early papers by Euler. Enestroem: E42, E43, E44 a. E45.E42: This is Euler's second paper on the ""Brachistochrone problem"".E43. Here Euler introduces THE EULER CONSTANT. ""The Euler-Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma.""E44: ""This is an extensive paper that develops a method for finding a family of curves arising from the constant of integration of dz = Pdx, which is treated as the second variable"" the rudiments of partial differentiation are presented, and there is an extensive survey of homogeneous functions centred around what is now know as Euler's Theorem for such functions. The origins of this paper would seem to be Proposition 15 of Vol. 2 of the Mechanica, relating to families of tautochronous curves, where an integration relying on Euler's Theorem is required."" (Ian Bruce).E45: Here Euler introduces the FUNCTION NOTATION f(x). ""This is an equally extensive paper that continues the development of methods for finding a family of curves arising from the constant of integration of dz = Pdx, which is treated as the second variable. A method is developed for finding the modular equation for the first order equation that is extended to cover a number of cases"" this in turn is extended to second and higher orders. The method involves finding suitable functions to integrate, starting from a part of the modular equation that is integrable, so that the whole equation is of this form. This paper is noteworthy in addition as it seems to be the first in which the function notation, albeit in a slightly different form from the modern meaning, is introduce. I have not been able to check all the equations at this stage.""(Ian Bruce).This section also contains DANIEL BERNOULLI: Demonstrationes theorematum svorum de oscillationibus corporum filo flexili connexorum et catenae verticaliter suspensae. Pp. 162-173.‎

书商的参考编号 : 50926

‎"EULER, LEONHARD. - THE EULER-FERMAT THEOREM PROVED.‎

‎De Superficie Conorum Scalenorum, aliorumqve corporum conicorum. (On the surface of scalene cones and of other conic bodies). (+) Theoremata circa divisores numerorum. (Theorems on divisors of numbers). (2 papers by Euler).‎

‎(Petropoli (St. Petersbourg), 1750). 4to. Uncut, without wrappers. Extracted from ""Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tom. I. ad Annum 1747 et 1748. Pp. 3-19 a. 1 engraved plate., and pp. 20-48.‎

‎"EULER, LEONHARD. - THE GAME PHARON.‎

‎3 works by Euler: Nouvelle Méthode d'Éliminer les Quantités inconnues des Equations. - Recherches sur les Microscopes a´Trois Verres et les Moyens de les Perfectionner. - Sur L'Avantage du Banquier au Jeu du Pharaon.‎

‎(Berlin, Haude et Spener, 1766). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", tome XX, pp. 91-164 (91-116" 117-143 "144-164). 1 engraved plate ( belonging to ""Microscope..."")‎

‎"EULER, LEONHARD. - THE KOENIG-MAUPERTUIS CONTROVERSY.‎

‎Examen de la dissertation de M. le Professeur Koenig, inseree dans les actes de Leipzig, pour le mois de mars 1751. (Examination of the dissertation of Professor Koenig inserted into the Acts of Leipzig for the month of March 1751) (+) Essay d'une D...‎

‎(Berlin, Haude et Spener, 1753). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome VII, Année 1751. Pp. 221-245 and pp. 246-254 a. 1 engraved plate.‎

‎First editions. The first paper concerns the Argument over the principle of least action, relating to the famous controversy - and one of the ugliest scientific controversies - between Koenig and Maupertuis. ""In 1751 a sensational new argument began when S. König published some critical remarks on Maupertuis’s principle of least action (1744) and cited a letter of Leibniz in which the principle was, in König’s opinion, formulated more precisely. Submitting to Maupertuis, the Berlin Academy rose to defend him and demanded that the original of Leibniz’ letter (a copy had been sent to König from Switzerland) be presented. When it became clear that the original could not be found, Euler published, with the approval of the Academy, ""Exposé concernant l’examen de la lettre de M. de Leibnitz"" (1752), where, among other things, he declared the letter a fake. The conflict grew critical when later in the same year Voltaire published his Diatribe du docteur Akakia, médecin du pape, defending König and making laughingstocks of both Maupertuis and Euler.""(DSB) - Enestrom No. 199.The second paper - Enestrom No. 200.‎

书商的参考编号 : 49695

‎"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.‎

书商的参考编号 : 45126

‎"FABER, G.‎

‎Über stetige Funktionen. (In ""Mathematische Annalen. 66. Band. 1909""). - [FIRST PUBLICATION OF THE 'HIERARCHICAL BASIS' WITHIN MATHEMATICS]‎

‎Berlin, Julius Springer, 1909. 8vo. Bound with the original wrappers in black full cloth. A small white barcode pasted on to top left corner of front board. Library stamp pasted on the pasted down front free end-paper and stamp to verso of title page. A very nice and clean copy. [Faber:] Pp. 81-94. [Entire issue: IV, 575, (1) pp.].‎

‎First printing of Faber's important paper in which he introduces the 'hierarchical basis' and uses it for the representation of functions. Faber was building on the idea of Archimedes who computed approximately using a hierarchy of polygonal approximations of a circle. In the 1980s Faber's idea became an important ingredient for the efficient solution of partial differential equations.The issue contain the following papers of interest:Weyl, H. Singuläre Integralgleichungen. Pp. 273-324.Weyl, H & F. Jerosch. Über die Konvergenz von Reihen, die nach periodischen Funktionen fortschreiten. Pp. 67-80.And many other papers by contemporary mathematicians.‎

书商的参考编号 : 44834

‎"FARR, WILLIAM. - THE USE OF SCHEUTZ'S THIRD DIFFERENTIAL ENGINE.‎

‎On the Construction of Life-Tables, illustrated by a New Life-Table of the Healthy Districts of England. Received March 17, - Read April 7, 1859.‎

‎(London, Taylor and Francis, 1859). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1859 - Vol. 149 - Part II. With the titlepage to Part II. Pp. 837-878, 1 folded engraved plate, tables in the text. The plate slightly browned. It includes 1 typeset by the Scheutz calculator.Clean and fine.‎

‎First appearance of a pioneer paper in statistical calculations of life-expectations., containing THE VERY FIRST APPLICATION OF A DIFFERENCE ENGINE TO MEDICAL STATISTICS.""Farr's preliminary report (the paper offered), describing the use of the Scheutz Engine no. 3 to prepare life tables, was published 5 years before his ""English Life Table"". Farr, a pioneer in the quantitative study of morbidity and mortality, was chief statistician of the General Register Office, Englands central statistical office. Influenced by Babbage, he had long been interested in the use of a calculating machine, such as Babbage's Difference Engine to compute life tables"" see page 854 of the present report, in which Farr refers to his 1843 letter on the subject to the registrar-general. Farr had seen and tested the machine's predecessor, the Scheutz Engine No. 2, when it was on display in London. It was at Farr's recommandation that the British government authorized in 1857 the sum of Pound 1200 for the Scheutz Engine no. 3 to be constructed by the firm Bryan Donkin, a manufacturer of machines for the color printing of bank notes and stamps....Farr's printing report, received by the Royal Society on March 17 of that year, was written while Scheutz Engine no. 3 was still ""in the course of construction by Messr. Donkin"" (p. 854). The reports table B1, ""Life-Table of Healthy English Districts"", made from stereotype plates produced by the calculator, represents the very first application of a difference engine to medical studies.""(Hook and Norman, Origins of Cyperspace, No. 77.). - Garrison & Morton: 1700.1.‎

书商的参考编号 : 43002

‎"FATOU, PIERRE.‎

‎Séries trigonométriques et séries de Taylor. - [FIRST APPEARANCE OF THE FATOU SET]‎

‎Berlin, Stockholm, Paris, F. & G. Beijer, 1906. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 30, 1906. Entire volume offered. Stamp to title page, otherwise a fine and clean copy. Pp. 355-400. [Entire volume: 6, 410 pp].‎

‎First appearance of Fatou's seminal Ph.D. thesis in which he presented his famous Fatou theorem, which state that a bounded analytic function in the unit disc has radial limits almost everywhere on the unit circle. This theorem was at the origin of a large body of research in 20th-century mathematics under the name of bounded analytic functions. Fatou set is the 'regular' appearance of the chaotic Julia set and both if these initiated what was to be known as ""complex dynamics"" which eventually resulted in the Mandelbrot set.Fatou's thesis also include the first application of the Lebesgue integral to concrete problems of analysis, mainly to the study of analytic and harmonic functions in the unit disc. He furthermore studied for the first time the Poisson integral of an arbitrary measure on the unit circle and also made a major contribution to finding a solution to the related question of whether conformal mapping of Jordan regions onto the open disc can be extended continuously to the boundary.""He contributed important results on the Taylor series, the theory of the Lebesgue integral, and the iteration of rational functions of a complex variable. When studying the circle of convergence of the Taylor series, several points of view are possible: (1) one can look for criteria of convergence or divergence of the series itself on the circumference" (2) one can consider the limit values of the circle of the analytic function represented by the series and try to determine where these limit values are finite or infinite, as well as the properties of the functions of the argument represented by the real and imaginary parts of the series when these functions are well defined" (3) one can consider what points on the circumference, singular in the Weierstrass sense, also determine the analytic extension of the series. The link between these problems led Fatou to formulate a fundamental theorem in the theory of the Lebesgue integral."" (DSB).‎

书商的参考编号 : 49610

‎"FECHNER, G.TH.‎

‎Ueber den Ausgangswerth der kleinsten Abweichungssumme, dessen Bestimmung, Verwendung und Verallgemeinerung.‎

‎Leipzig, S. Hirzel, 1874. Small 4to. Orig. printed wrappers. (4),76 pp. Offprint from ""Des XI. Bandes d. Abh. d. math.-phys. Classe d. Königl. Sächsischen Gesells. d. Wissensch. No. I"" A few pencil underlinings, otherwise fine and clean.‎

‎First edition in the scarce offprint. Fechner is known as the founder of psychophysics, his theory of psycho-physical paralellism, as the first universal indeterminist and by the so-called ""Fecnner-Weber Law"". - Freud said:""I was always open to the Ideas of Fechner and have followed that thinker upon many importent points."" (Freud, 1925 p. 86).‎

书商的参考编号 : 28831

‎"FISHER, R.A. and WISHART, J.‎

‎The Derivation of the Pattern Formulae of Two-Way Partitions from those of Simpler Patterns. [Received 28 November, 1930. - Read 11 December, 1930]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 33]. - [COINING ""CUMULANTS""]‎

‎London, Hodgson & Son, 1932. Royal 8vo. Entire volumes 33+34 of ""Proceedings of the London Mathematical Society. Second Series"" bound together in a very nice contemporary blue full cloth binding with gilt lettering and gilt ex-libris (""Belford College. Univ. London"") to spine. Very minor bumping to extremities. Binding tight and in excellent, very nice, clean, and fresh condition in- as well as ex-ternally. Small circle-stamp to pasted-down front free end-paper and to title-page of volume 33 (""Bedford College for Women""). Discreet library-markings to upper margin of pasted-down front free end-paper. Pp. 195-208. [Entire volumes: (´Vol. 33, 1932:) (4), 563, (1) pp." " (vol. 34, 1932:) (6), 562 pp.].‎

‎"FISHER, RONALD.‎

‎The Analysis of Variance with Various Binomial Transformations.‎

‎(No place, Oxford University Press, 1954). 8vo. Stapled. Extracted from ""Biometrika"", 1954. before being bound. Presumingly serving the purpose of an offprint. A very fine a clean copy, near mint. Pp. 130, (1), 131-139.‎

‎"FLORIJN, JACOB.‎

‎Verhandeling over het Sommeren en Interpoleren van arithmetische Serien.‎

‎Amsterdam, Hengst en Zoon, 1816. 4to. No wrappers as issued. (4),68 pp. Offprint from ""Koninklijk Nederlandsch Institut van Wetenschappen, Letterkune...""‎

‎"FOURIER, (JEAN BAPTISTE JOSEPH).‎

‎Analyse des Équations Déterminées. Premiere Partie (Livre Premiere- Deuxieme, all published). - [FOURIER'S THEORY OF EQUATIONS]‎

‎Paris, Firmin Didot Frères, (1830) 1831. 4to. Contemp. hcalf. Richly gilt spine. A paperlabel pasted on top of spine. (4),XXIV,258 pp. and 1 folded engraved plate. A few minor brownspots. A fine, wide-margined copy.‎

‎"FOURIER, (JEAN BAPTISTE JOSEPH). - TOWARDS THE ANALYTICAL THEORY OF HEAT.‎

‎7 Papers on Radiant Heat: 1. Théorie de la chaleur (Extrait) - 2. Note sur la Chaleur rayonnante. - 3. Sur la Théorie-Physique de la Chaleur rayonnante. - 4. Extrait d'un Mémoire sur la Refroidissement séculaire du globe terrestre. - 5. Remarques géné... - [THE GREEN-HOUSE EFFECT]‎

‎(Paris, Crochard, 1816, 1817,1817,1820, 1824, 1824, 1825). Without wrappers as issued in: ""Annales de Chimie et de Physique, Par MM. Gay-Lussac et Arago."". Vol. 3, pp. 350-375. - Vol. 4, pp. 128-145. - Vol. 6, pp. 259-303. - Vol. 13, pp. 418-38. - Vol. 27, pp. 136-167. - Vol. 27, pp. 236-281. - Vol. 28, pp. 337-365.‎

‎"FREDHOLM, IVAR.‎

‎Sur les équations de l'équilibre d'un corps solide élastique. - [FREDHOLM'S DOCTORAL DISSERTATION]‎

‎Berlin, Stockholm, Paris, Almqvist & Wiksell, 1900. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 23, 1900. Entire volume offered. Stamps to title page and wear to extremities, otherwise a fine and clean copy. Pp. 1-42.[Entire volume: (4), 416 pp].‎

‎"FREDHOLM, IVAR.‎

‎Sur les équations de l'équilibre d'un corps solide élastique. - [FREDHOLM'S DOCTORAL DISSERTATION]‎

‎Berlin, Stockholm, Paris, Almqvist & Wiksell, 1900. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 23, 1900. Entire volume offered. Stamps to title page and wear to extremities, otherwise a fine and clean copy. Pp. 1-42.[Entire volume: (4), 416 pp].‎

‎First appearance of Fredholm's doctoral thesis (finish in 1898 but not published till 1900) and his first major work in partial differential equations. His doctoral dissertation involved a study of partial differential equations, the study of which was motivated by an equilibrium problem in elasticity. He solved his operator equation in the particular cases which arise in the study of the physical problem in his thesis (and in the paper which appeared in 1900 based on that thesis)""Fredholm's first major work was in partial differential equations. His doctoral thesis, written in 1898 and published in 1900, involved the study of the equation-written in Fredholm's own operator notation. [...] This equation is significant because it occurs in the study of deformation of anisotropic media (such as crystals) subjected to interior or exterior forces. Initially, Fredholm solved only the particular equations associated with the physical problem"" in 1908 he completed this work by finding the fundamental solution to the general elliptical partial differential equations with constant coefficients."" (DSB).‎

书商的参考编号 : 49773