‎JEU DE CARTES‎
‎FRACTIONS‎

‎Mémoire sur quelques Propriétés remarquable des Quantités transcendentes circulaires et logarithmiques. - [LAMBERT'S CONTINUED FRACTIONS AND IRRATIONALITY OF ""N""]‎

‎(Berlin, Haue et Spener, 1768). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XVII, pp. 265-322 and 1 folded engraved plate.‎

‎First edition, journal issue. ""One of Lambert's most famous results is the proof of the irrationality of ""N"" and e. It was based on the continued fractions, and two such fractions still bear his name.""(DSB).""Euler's work on continued fractions was used by Johann Heinrich Lambert.....to prove that if x is a rational number (not 0), then ex and tan x cannot be rational. He thereby proved not only that ex for positive integral x is irrational, but that all rational numbers have irrational natural (base e) logarithms.From the result of tan x, it follows tha, since tan (n/4)= 1, that neither n/4 nor n can be rational.Lambert actually proved the convergencee ofthe continued fraction expansion for tan x. (Morris Kline). - Struik, A Source Book, Chapter V, No 17).‎

‎Recherches sur les fractions continues.‎

‎(Paris, Gauthier-Villars), 1894. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 118, No 25. Pp. (1371-) 1442. (Entire issue offered). Le Chatelier's paper: pp. 1401-1411.‎

‎First printing of the milestone paper in which Stieltjes introduced the ""Stieltjes Integral"". He is often called ""the father of the analytic theory of continued fractions"" for his work in this area. ""On 18 June 1894 he published Recherches sur les fractions continues in Comptes Rendus de l'Académie des Sciences. A fuller version of this work appeared in the Annales de la Faculté des Sciences de Toulouse."" The integral which he introduced here while solving the moment problem, that is, given the moments of all orders of a body, find the distribution of its mass."".... a mathematical milestone. The work represents the first general treatment of continued fractions as part of complex analytic function theory"" previously, only special cases had been considered."" (Encyclopaedia Britannica).Parkinson ""Breakthroughs"" 1894 M. ‎

‎V.Ya. Spekorobogatko: The theory of branching chain fractions and its applicat‎

‎V.Ya. Spekorobogatko: The theory of branching chain fractions and its application in computational mathematics. In Russian /Skorobogatko V.Ya. Teoriya vetvyashchikhsya tsepnykh drobey i ee primenenie v vychislitelnoy matematike. M. Science 1983. 312s. We have thousands of titles and often several copies of each title may be available. Please feel free to contact us for a detailed description of the copies available. SKUalba93f671fc51d2234.‎

‎Social Democratic Fractions of the First and Second State Duma: Minutes of Frac‎

‎Social Democratic Fractions of the First and Second State Duma: Minutes of Fractional Meetings and Materials. 1906-1907 In Russian /Sotsial-demokraticheskie fraktsii I i II Gosudarstvennykh dum: protokoly fraktsionnykh zasedaniy i materialy. 1906-1907 gg. M. ROSSPEN 2020g. 1087chu. We have thousands of titles and often several copies of each title may be available. Please feel free to contact us for a detailed description of the copies available. SKUalb29c97075d9dbf0b3.‎

‎Helfman E.G., Wolfengout Y.U. et al. Decimal fractions in the Moomin House. In‎

‎Helfman E.G., Wolfengout Y.U. et al. Decimal fractions in the Moomin House. In Russian /Gelfman E.G., Volfengaut Yu.Yu. i dr. Desyatichnye drobi v Mumi-dome. A textbook on mathematics for the 5th grade. Bad design by S. Kazachkova based on drawings by Tove Jansson. Tomsk. Publishing House of Tomsk University. 1991. 190 p. We have thousands of titles and often several copies of each title may be available. Please feel free to contact us for a detailed description of the copies available. SKUalb354d03baca374e57.‎