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Bibliography BIBLIOGRAPHY Abel, Niels Henrik “Untersuchungen über die Reihe: m m · (m − 1) m · (m − 1) · (m − 2) 1 + .x+ .x2 + .x3 +··· u.s.w., ” 1 1 · 2 1 · 2 · 3 Journal für die reine und angewandte Mathematik, 1 (1826) 311–339. Pages 311– 315 are reproduced with English translation in Stedall, Mathematics emerging, pp. 516–524. Translation of an extract in Birkhoff, A source book in classical analysis, pp. 68–70; reprinted in Calinger, Classics of mathematics, pp. 594–596. French version: “Recherches sur la série m m(m − 1) m(m − 1)(m − 2) 1 + x + x2 + x3 +···” 1 1 · 2 1 · 2 · 3 in Œuvres complètes de Niels Henrik Abel, 2nd. ed., Vol. 1, Contenant les mémoirs publiés par Abel, pp. 219–250. Œuvres complètes de Niels Henrik Abel. Nouvelle édition publiée aux frais de l’état norvégien par MM. L. Sylow et S. Lie, 2 vols., Grøndahl & Søn, Christiania, Norway, 1881, 1965; facsimile reproduction by Éditions Jacques Gabay, Sceaux, 1992. Agnesi, Maria Gaetana Instituzioni analitiche ad uso della gioventù italiana, 4 vols., Nella Regia-Ducal Corte, Milan, 1748. English translation as Analytical institutions, in four books: originally written in Italian, by Donna Maria Gaetana Agnesi, Professor of the Mathematicks and Philosophy in the University of Bologna. Translated into English by the late Rev. John Colson, M.A. F.R.S. and Lucasian Professor of the Math- ematicks in the University of Cambridge. Now first printed, from the translators manuscript, under the inspection of the Rev. John Hellins, B.D. F.R.S. and vicar of Potter’s-Pury, in Northhamptonshire, Taylor and Wilks, Chancery-Lane, London, 1801 (Colson changed Agnesi’s differential notation to fluxonial notation). Al-Masudi, Ali Muruj al-Zahab wa al-Maadin al-Jawahir, originally written in 947, revised 956. Edited by Charles Pellat, 7 vols., Publications de l’Université Libanaise, Section des Études Historiques, Beirut, 1965–1979. English translation of volume 1 by Aloys Sprenger as El-Masudi’s historical encyclopaedia entitled “Meadows of gold and mines of gems,” Oriental Translation Fund of Great Britain and Ireland, London, 1841. Al-Tusi, Mohammed Kitab shakl al-qatta; facsimile reproduction of the Arabic version and French translation as Traité du quadrilatère attribué a Nassiruddin-el Toussy by Alexandros Carathéodory, Typographie et Litographie Osmanié, Constantinople, 1891. E.A. González-Velasco, Journey through Mathematics: Creative Episodes in Its History, 412 DOI 10.1007/978-0-387-92154-9, © Springer Science+Business Media, LLC 2011 Bibliography 413 d’Alembert, Jean le Rond “Addition au mémoire sur la courbe que forme une corde tenduë, mise en vibra- tion,” Histoire de l’Académie Royale des Sciences et des Belles-Lettres de Berlin, 6 (1750, pub. 1752) 355–360. Encyclopédie, ou Dictionnaire raisonné des sciences, des arts et des métiers, par une société de gens de lettres. Mis en ordre et publié par M. Diderot, ... & quant à la partie mathématique, par M. d’Alembert, ..., 17 volumes, Briasson, David l’aîné, Le Breton, Durand, Paris, 1751–1765, and 18 additional volumes in later years. “Recherches sur la courbe que forme une corde tenduë mise en vibration,” His- toire de l’Académie Royale des Sciences et des Belles-Lettres de Berlin, 3 (1747) 214–219 (pages 214–217 are reproduced with translation in Stedall, Mathematics emerging, pp. 265–271), and “Suite des recherches,” 3 (1747) 220–249. Archimedes of Syracuse The quadrature of the parabola, in Heath The works of Archimedes with The method of Archimedes, pp. 233–252. The sand-reckoner, in Heath, The works of Archimedes with The method of Archimedes, pp. 221–232; reprinted in Hawking, God created the integers. The mathematical breakthroughs that changed history, pp. 200–208; selections also reprinted in Calinger, Classics of mathematics, pp. 147–151. Argand, Robert Essai sur une manière de représenter les quantités imaginaires, dans les con- structions géométriques, privately printed, Paris, 1806. Second edition with a pref- ace by Guillaume-Jules Hoüel, Gauthier-Villars, Paris, 1874; reproduced by Albert Blanchard, Paris, 1971. Articles 3 to 7 reproduced with translation in Stedall, Mathe- matics emerging, pp. 462–467. Translated into English by Arthur Sherburne Hardy as Imaginary quantities: Their geometrical interpretation, D. Van Nostrand, New York, 1881. “Philosophie mathématique. Essay sur une manière de représenter les quantités imaginaires dans les constructions géométriques,” Annales de mathématiques pures et apliquées, 4 (1813–1814) 133–147. Aristarchos of Samos Aqirsqvot’ peq`i lecehxm ja`i aporsgls’ xm gkot‘ ja`i rekmgy. The complete text in Greek with an English translation entitled On the sizes and distances of the sun and moon can be seen in Heath, Aristarchus of Samos, the ancient Copernicus, pp. 352–411. Aryabhata The Aryabhatiya, translated into English with notes by William Eugene Clark as The Aryabhatiya of Aryabhata. An ancient Indian work on mathematics and astronomy, The University of Chicago Press, Chicago, Illinois, 1930. Critical edition in Sanskrit with English translation and notes by Kripa Shankar Shukla and K. 414 Bibliography Venkateswara Sarma, Aryabhatiya of Aryabhata, Indian National Science Academy, New Delhi, 1976. Bardi, Jason Socrates The calculus wars. Newton, Leibniz, and the greatest mathematical clash of all time, Thunder’s Mouth Press, New York, 2006. Baron, Margaret E. The origins of the infinitesimal calculus, Pergamon Press, Oxford, 1969; reprin- ted by Dover Publications, New York, 1987, 2004. Barrow, Isaac Lectiones geometricæ; in quibus (præsertim) generalia curvarum linearum symp- tomata declarantur, William Godbid, London 1670; 2nd. ed. 1674; first translated into English by Edmund Stone as Geometrical lectures: explaining the generation, nature and properties of curve lines. Read in the University of Cambridge by Isaac Barrow; translated from the Latin edition, revised, corrected and amended by the late Sir Isaac Newton, Printed for S. Austen, London, 1735; second edition of 1674 reprinted by Georg Olms Verlag, Hildesheim · New York, 1976. Abridged transla- tion with notes, deductions, proofs omitted by Barrow, and further examples of his method by Child as The geometrical lectures of Isaac Barrow. Bateman, Harry “The correspondence of Brook Taylor,” Bibliotheca Mathematica, (3) 7 (1906– 1907) 367–371. Bhaskara Mahabhaskariya, edited and translated by Kripa Shankar Shukla, Lucknow Uni- versity, Lucknow, 1960. Beaugrand, Jean de “De la manière de trouver les tangentes des lignes courbes par l’algèbre et des imperfections de celle du S. des C[artes];” reproduced in Œuvres de Fermat,V, Supplément, 1922, pp. 102–113. Bell, Eric Temple Men of mathematics, Simon and Schuster, NewYork, 1937; reprinted by Touch- stone Books, New York, 1986. Berggren, J. Lennart Episodes in the mathematics of medieval Islam, Springer-Verlag, 1986, 2003. “Mathematics in medieval Islam,” in Katz, ed., The mathematics of Egypt, Meso- potamia, China, India, and Islam. Berkeley, George The analyst; or, a discourse addressed to an infidel mathematician. Wherein it is examined whether the object principles, and inferences of the modern analysis are more distinctly conceived, or more evidently deduced, than religious mysteries and points of faith, Jacob Tonson, London, 1734; reproduced in pp. 63–102 of Vol. 4 Bibliography 415 of The works of George Berkeley Bishop of Cloyne, ed. by Arthur Aston Luce and Thomas Edmund Jessop, 9 volumes, Thomas Nelson and Sons, Ltd., London, 1951, 1964. Reprinted by Kessinger Publishing Company, Kila, Montana, 2004; reprinted by Nabu Press, Berlin, 2010. Bernoulli, Daniel “Lettre de Monsieur Daniel Bernoulli, de l’Académie Royale des Sciences, à M. Clairaut de la même Académie, au sujet des nouvelles découvertes faites sur la vibrations des cordes tendues,” Journal des Sçavans, (March 1758) 157–166. “Réflexions et éclaircissements sur les nouvelles vibrations des cordes exposées dans les mémoires de l’Académie de 1747 et 1748,” Histoire de l’Académie Royale des Sciences et des Belles-Lettres de Berlin, 9 (1753) 147–172 and 173–195. Bernoulli, Jakob “Analysis problematis antehac propositi,” Acta Eruditorum, 9 (1690) 217–219 = Jacobi Bernoulli, Basileensis, Opera, Tomus primus, N°. XXXIX, pp. 421–426. Jacobi Bernoulli, Basileensis, Opera, Gabriel and Philibert Cramer, Geneva, 1744; reprinted by Birkhäuser Verlag, 1968. Tractatus de seriebus infinitis earumque summa finita, et usu in quadraturis spatiorum & rectificationibus curvarum, in pp. 241–306 of Ars conjectandi, opus posthumum. Accedit Tractatus de seriebus infinitis, et epistola Gallicè scripta de ludo pilæ reticularis, Impensis Thurnisiorum, Fratrum, Basel, 1713; reprinted by Culture et Civilisation, Brussels, 1968. The Tractatus can also be seen in Jacobi Bernoulli, Basileensis, Opera, 1744. Parts I and II are in Tomus primus with the titles Positiones arithmeticæ [Positionum arithmeticarum] de seriebus infinitis, earumque summa finita, N°. XXXV, pp. 375–402, and N°. LIV, 517–542. Parts III to V are in Tomus secundus with the title Positionum de seriebus infinitis, earumque usu in quadraturis spatiorum & rectificationibus curvarum (there is a slight variation in the title of Part III), N°. LXXIV, pp. 745–767, N°. XC, pp. 849–867, and N°. CI, pp. 955–975. Bernoulli, Johann “Additamentum effectionis omnium quadraturarum & rectificationum curvarum per seriem quandam generalissimam,” Acta Eruditorum, 13 (November 1694) 437– 441 = Opera omnia, Vol. I, N°. XXI, pp. 125–128. Der Briefwechsel von Johann Bernoulli, Otto Spiess, ed., Birkhäuser
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