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Research Article

Introducing differential calculus in Spain: The fluxion of the product and the quadrature of curves by Tomàs Cerdà

Bibliography

  • Manuscripts
  • Bramieri, Esteban, Tratado del Cálculo Diferencial, Madrid: Royal Academy of History, 1757-1760, Cortes 9/2816.
  • Cerdà, Tomàs, Tratado de Fluxiones, Madrid: Royal Academy of History, 1757-1759, Cortes 9/2792, 9/2812.
  • Cerdà, Tomàs, Carta a Simpson, Madrid: Royal Academy of History, 1758, Cortes 9/2792.
  • Rieger, Christian, Introducción fácil al algoritmo de las fluxiones, Madrid: Royal Academy of History, 1761-1765, Cortes 9/2792.
  • Wendlingen, Johannes, Elementos de Mathematicas, Tomo VIII: Análisis de los infinitos; Tomo IX: Cálculo Exponencial, Diferencio-diferencial y Aritmética de los infinitos, Madrid: Royal Academy of History, 1756-1761, Cortes 9/2812, 9/3811.
  • Printed Sources
  • Ausejo, Elena, Sánchez, Medrano, and Javier, Francisco, ‘Construyendo la Modernidad: Nuevos datos y enfoques sobre la introducción del cálculo infinitesimal en España (1717-1787)’, Llull, Universidad de Zaragoza, 33/71 (2010), 25–56.
  • Bails, Benet, Elementos de matemática, Madrid: D. Joachin Ibarra, 1779-1790.
  • Bair, Jacques, Błaszczyk, P, Ely, R, Henry, V, Kanovei, V, Katz, K U, Katz, M G, Kutateladze, S S, McGaffey, T, Reeder, P, and Schaps, D M, ‘Interpreting the infinitesimal mathematics of Leibniz and Euler’, Journal for General Philosophy of Science/Zeitschrift für Allgemeine Wissenschaftstheorie, 48/2 (2017), 195–238.
  • Bascelli, Tiziana, Bottazzi, E, Herzberg, F, Kanovei, V, Katz, K U, Katz, M G, Nowik, T, Sherry, D, and Shnider, S, ‘Fermat, Leibniz, and the gang: The true history of the concept of limit and shadow’, Notices of the American Mathematical Society, 61/8 (2014), 848–864. https://doi.org/10.1090/noti1149. arXiv:1407.0233 [math.HO].
  • Berenguer, Joaquim, Cerdà (1757-1759). Tratado de Fluxiones, Barcelona: Reial Acadèmia de Ciències i Arts de Barcelona (RACAB) with the support of the project HAR2013-44643-R (Ministerio de Economía y Competividad), and the project SGR (grup de recerca consolidat) HIS-STM (SGR 1410), 2015. https://ccuc.csuc.cat/search~S23*spi?/tTratado+de+Fluxiones/ttratado+de+fluxiones/1%2C2%2C2%2CB/frameset&FF=ttratado+de+fluxiones+++++1757+++++1759&1%2C1%2C/indexsort=-.
  • Berenguer, Joaquim, La recepció del càlcul diferencial a l’Espanya del segle XVIII. Tomàs Cerdà: introductor de la teoria de fluxions, 2016, PHD on History of Science guided by the doctor Mª Rosa Massa-Esteve, Universitat Autonòma de Barcelona. http://www.tdx.cat/handle/10803/367217, https://www.educacion.gob.es/teseo/mostrarRef.do?ref=1211406.
  • Berenguer, Joaquim, ‘Simpson i Cerdà: esborrant fronteres entre Leibniz i Newton’, Quaderns d’Història de l’Enginyeria, 16 (2018), 167–188.
  • Blake, Francis, An explanation of fluxions in a short essay on the theory, London: Printed for W. Innys, 1741.
  • Blanco Abellán, Mónica, ‘Thomas Simpson: weaving fluxions in 18th-century London’, Historia Mathematica, 41/1 (2013), 38–81.
  • Boistel, Guy, ‘L’observatoire des jésuites de Marseille sous la direction du père Esprit Pézenas (1728-1763)’, in Cahiers d’Histoire et de Philosophie des Sciences, 54. Lyon: SFHST/ENS-LSH, École Normale Supérieure de Lyon Editions, 2005, 27–45.
  • Bos, Henk J M, ‘Differentials, higher-order differentials and the derivative in the Leibnizian calculus’, Archive for History of Exact Sciences, 14/1 (1974), 1–90.
  • Bos, Henk J M, ‘Newton, Leibniz y la tradición leibniziana’, in Ivor Grattan Guiness (ed), Del cálculo a la teoria de conjuntos, 1630-1910. Una introducción histórica, Madrid: Alianza Editorial, S.A, 1980, 1984, 69–124, (Original title: ‘Newton, Leibniz and the Leibnizian tradition’, in Grattan Guiness, Ivor, From the Calculus to Set Theory, 1630-1910. An Introductory History, 1980, 49–93).
  • Bruneau, Olivier, Colin Maclaurin ou l’obstination mathématicienne d’un newtonien, Nancy: Presses Universitaires de Nancy, 2011.
  • Cajori, Florian, A history of the conceptions of limits and fluxions in great Britain, Chicago and London: The Open Court Publishing Company, 1919.
  • Cerdà, Tomàs, Liciones de Mathemática o Elementos Generales de Arithmética y Algebra para el uso de la clase, Barcelona: Francisco Surià, 1758.
  • Cerdà, Tomàs, Lecciones de mathematica o Elementos generales de Geometria para el uso de la clase, Barcelona: Francisco Surià, 1760.
  • Cerdà, Tomàs, Lección de Artilleria para el uso de la clase, Barcelona: Francisco Surià, 1764.
  • Child, J M, The early mathematical manuscripts of Leibniz, translated from the Latin texts published by Carl Immanuel Gerhardt with critical and historical notes, London, Chicago: The Open court publishing company, 1920.
  • Clarke, Frances Marguerite, Thomas Simpson and his times, submitted for the degree of Doctor of Philosophy in the Faculty of Philosophy, Columbia University, New York: Waverly Press, 1929.
  • Cuesta Dutari, Norberto, Historia de la Invención del Análisis Infinitesimal y de su introducción en España, Salamanca: Universidad de Salamanca, 1985.
  • Feingold, Mordechai, ‘Newton, Leibniz, and Barrow too: an attempt to a reinterpretation’, Isis, 84/2 (1993), 310–338.
  • Garma Pons, Santiago, ‘Producción matemática y cambios en el sistema productivo en la España de finales del siglo XVIII’, in Manuel Gutiérrez Esteve, Cid Martínez, Jesús Antonio and Antonio Carreira (ed), Homenaje a Julio Caro Baroja, Madrid: Centro de Investigaciones Sociológicas, 1978, 431–447.
  • Garma Pons, Santiago, ‘La Enseñanza de las Matemáticas’, in José Luís Peset Reig (ed), Historia de la Ciencia y de la Técnica en la Corona de Castilla. Salamanca: Junta de Castilla y León, IV, 2002, 311–346.
  • Gassiot Matas, Lluís, Tomas Cerdà i el seu Tratado de Astronomia, Barcelona: Centre d’estudis d’Història de les Ciències de la Universitat Autònoma de Barcelona, 1996.
  • Gerhardt, Karl Immanuel, Historia et origo calculi differentialis, Hannover: Hahn, 1846.
  • Grabiner, J V, ‘Was Newton’s calculus a dead end? The continental influence of Maclaurin’s Treatise of Fluxions’, American Mathematical Monthly, 104/5 (1997), 393–410.
  • Guicciardini, Niccolò, The development of Newtonian calculus in Britain 1700-1800, Cambridge: Cambridge University Press, 1989.
  • Guicciardini, Niccolò, ‘Three traditions in the calculus: Newton, Leibniz and Lagrange’, in Ivor Grattan Guiness (ed), Companion encyclopedia of the history and philosophy of the mathematical sciences. Baltimore and London: Johns Hopkins University Press, 1994, 308–317.
  • Guicciardini, Niccolò, Reading the Principia: the debate on Newton’s mathematical methods for natural philosophy from 1687 to 1736, Cambridge: Cambridge University Press, 1999.
  • Guicciardini, Niccolò, Isaac Newton on mathematical certainty and method, Cambridge, Massachusetts, London: The MIT Press, 2009.
  • Hodgson, James, The Doctrine of Fluxions, London: T. Wood, 1736.
  • Jullien, Vincent, ‘Explaining the sudden rise of methods of indivisibles’, in V. Jullien (ed), Seventeenth-century indivisibles revisited. Basel: Springer International Publishing Switzerland, 2015, 1–18.
  • Knobloch, Eberhard, ‘L'infini dans les mathématiques de Leibniz’, in L'infinito in Leibniz, Problemi e terminologia, Simposio Internazionale Roma, 6–8, November 1986, Roma: Edizioni dell' Ateneo, 1990, 33–51.
  • Knobloch, Eberhard, ‘Leibniz's rigorous foundation of infinitesimal geometry by means of riemannian sums’, Synthese, 133/1 (2002), 59–73.
  • Knobloch, Eberhard, ‘Beyond Cartesian limits: Leibniz's passage from algebraic to “transcendental” mathematics’, Historia Mathematica, 33/1 (2006), 113–131.
  • Knobloch, Eberhard, ‘Leibniz and the infinite’, Quaderns d’Història de l’Enginyeria, 16 (2018), 11–32.
  • Leibniz, Gottfried Wilhelm, ‘Nova methodus pro maximis et minimis, itemque tangentubus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus’, Acta Eruditorum, [Anno MDCLXXXIV], (1684), 467–473.
  • Leibniz, Gottfried Wilhelm, ‘Monitum de characteribus algebraicis’, Miscellanea Berolinensia. Berolini:Sumptibus Johan. Christ. Papenii, (1710), 155–160.
  • Leibniz, Gottfried Wilhelm, ‘Elementa. mss Elementa calculi novi pro differentiis … ’, in K. I. Gerhardt (ed), Historia et origo calculi differentialis, Hannover: Hahn, 1846, 32–38.
  • L’Hospital, Guillaume de, L’analyse des infiniments petits pour l’intelligence des lignes courbes, Paris: de l’Imprimirie Royale, 1696.
  • Maclaurin, Colin, The elements of the method of Fluxions, demonstrated after the manner of ancient geometricians, Edimburg: Printed by T. W. And T. Ruddimans, 1742.
  • Mahoney, Michael S, ‘The beginnings of algebraic thought in the seventeenth century’, in S. Gaukroger (ed), Descartes, philosophy, mathematics and physics. Totawa, NJ: The Harverster Press, Brighton (Sussex) and Barnes & Noble Books, 1980, 141–155.
  • Malet, Antoni, From indivisibles to infinitesimals, studies on seventeenth-century mathematizations of infinitly small quantities, Bellaterra: Universitat Autònoma de Barcelona. Servei de Publicacions, 1996.
  • Malet, Antoni, ‘The Origins of the Calculus in Seventeenth-Century England’, 2008, https://www.academia.edu/2494082/The_Origins_of_the_Calculus_in_Seventeenth-Century_England. Originally published in Italian translation as ‘L'emergenza del calcolo infinitesimale’. Also available in French translation as ‘L'émergence du calcul infinitésimal en Grande Bretagne’, in C. Bartocci, P. Odifreddi, eds. La mathématique I: les lieux et les temps (Paris: CNRS, 2009), 310–340.
  • Malet, Antoni, and Panza, Marco, ‘Newton on indivisibles’, in V. Jullien (ed), Seventeenth-century indivisibles revisited. Basel: Springer International Publishing Switzerland, 2015, 365–390.
  • Mancosu, Paolo, Philosophy of mathematics and mathematical practice in the seventeenth century, Oxford: Oxford Univ. Press, 1996.
  • Massa-Esteve, Maria Rosa, ‘The harmonic triangle in Mengoli’s and Leibniz’s works’, Quaderns d’Història de l’Enginyeria, 16 (2018), 233–258.
  • Massa-Esteve, Maria Rosa, ‘La Reial Acadèmia de Matemàtiques de Barcelona (1720-1803) Matemàtiques per a Enginyers’, Quaderns d’Història de l’Enginyeria, 14, 2014, 17–34.
  • Massa-Esteve, Maria Rosa, ‘The role of indivisibles in Mengoli’s quadratures’, in V. Jullien (ed), Seventeenth-century indivisibles revisited, Basel: Springer International Publishing Switzerland, 2015, 307–346.
  • Massa-Esteve, Maria Rosa, and Roca-Rosell, Antoni, ‘Contents and sources of practical geometry in Pedro Lucuce’s course at the Barcelona royal military academy of mathematics’, in Gianna Katsiompura (ed), Scientific cosmopolitanism and local Cultures: religions, ideologies, societies. proceedings of 5th international conference of the European society for the history of science, Athens: National Hellenic Research Foundation/Institute of Historical Research, 2014, 329–335.
  • Massa-Esteve, Maria Rosa, Roca-Rosell, Antoni, and Puig-Pla, Carles, ‘“Mixed” mathematics in engineering education in Spain. Pedro Lucuce’s course at the royal military academy of mathematics of Barcelona in the eighteenth century’, Engineering Studies, 3/3 (2011), 233–253.
  • Navarro Brotóns, Víctor, ‘Scientific activity in Spain and the role of the Jesuits (1680-1767)’, in Gian Paolo Brizzi and Roberto Greci (ed), Gesuiti e Università in Europa (secoli XVI-XVIII, Parma: Arti del Convegno di studi, 2003, 421–434.
  • Navarro Loidi, Juan, ‘Lección de Artillería by Tomás Cerdá and the Revolution of the Spanish Artillery during the 18th Century’, 3rd International Conference of the European Society for the History of Science (ICESHS), Vienna, 2008.
  • Navarro Loidi, Juan, ‘La incorporación del cálculo diferencial e integral al Colegio de Artillería de Segovia’, Llull, 36/78 (2013), 333–358.
  • Newton, Isaac, ‘Analysis by equations of an infinite number of terms’, in John Stewart (ed), Sir Isaac Newton’s two treatises: of the quadrature of curves, and analysis by equations of an infinite number of terms, explained: containing the treatises themselves, translated into English, with a large commentary … , London: J. Bettenham, at the expense of the Society for the Encouragement of Learning [etc], 1745, 1669, 344–479.
  • Newton, Isaac, The Mathematical Principles of Natural Philosophy, 1687, translated into English by Andrew Motte, New York, 1846. (Original title: Philosophiae naturalis Principia Mathematica. Imprimatur S. Pepys, Reg. Soc. Praeses. Londini).
  • Newton, Isaac, The method of Fluxions and infinite series with its application to the geometry of curve-lines. By the inventor Sir Isaac Newton. Translated from the Author’s Latin original not yet made publick. Consisting of annotations, illustrations and suplements by John Colson, M.A. and F.R.S, London: H. Woodfall, 1736.
  • Padilla y Arcos, Pedro, Curso militar de Mathematicas, sobre las partes de esas Ciencias, pertenecientes al Arte de la Guerra, Madrid: Antonio Marín, 1753–1756.
  • Probst, Siegmund, ‘The calculus’, in Maria Rosa Antognazza (ed), The Oxford Handbook of Leibniz, Oxford: Oxford University Press, 2018.
  • Schubring, G, Conflicts between generalization, rigor and intuition, New York: Springer, 2005.
  • Serfati, Michel, ‘On the “sum of all differences” and the origin of mathematics according to Leibniz: mathematical and philosophical aspects’, in D. Riesenfeld (ed), Perspectives on theory of controversies and the ethics of communication, Berlin: Berlin-Akademie, 2014, 68–80.
  • Simpson, Thomas, A new treatise of fluxions, London: Printed by Tho. Gardner, 1737.
  • Simpson, Thomas, The Doctrine and Application of Fluxions, London: J. Nourse, 1750.
  • Simpson, Thomas, Miscellaneous tracts on some curious and very interesting subjects, London: J. Nourse, 1757.
  • Stone, Edmund, The method of Fluxions both direct and inverse. The former being A translation from the celebrated Marquis De L’Hospital’s analyse des infiniments Petits: and the latter Supply’d by the translator, E. Stone, F.R.S, London: William Innys, 1730.
  • Taylor, Brook, Methodus Incrementorum Directa & Inversa, 1715, Impensis Gulielmi Innys ad Insignia Principis in Coemetrio D. Pauli, London, 1717.
  • Wendlingen, Johannes, Elementos de la Mathematica, Madrid: Joachin Ibarra, 1756–1761, (4V.).
  • Whiteside, Derek Thomas, The mathematical papers of Isaac Newton (Edited by D.T. Whiteside, et al., vol 8), Cambridge: Cambridge University Press, 1967–1981.
  • Wolff, Christian, Elementa Matheseos Universae, Genevae: apud Henricum-Albertum Gosse & socios, 1713–1715.

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