A problem on the approximation of n-roots based on the Viète’s work

Referencias bibliográficas

• F. Acerbi, B. Vitrac, Metrica. Héron d’Alexandrie. Introduction, texte critique, traduction française et notes de commentaire. Pisa-Roma: Fabrizio Serra Editore, 2014.
• Archimedes, The works of Archimedes. Reprint of the 1897 edition and the 1912 supplement, edited by T. L. Heath. Mineola, NY: Dover Publications, Inc., 2002.
• Aristarco de Samos, Sobre los tamaños y las distancias del Sol y la Luna, 2.a Ed. Introducción, traducción y notas de Ma. Rosa Massa-Esteve,Cádiz: Editorial UCA, Servicio de Publicaciones de la Universidad deCádiz, 2017.
• M. Bartolozzi, R. Franci, La regola dei segni dall’enunciato di R. Descartes (1637) alla dimostrazione di C.F. Gauss (1828), Archive for History of Exact Sciences 45 (1993), 335–374.
• J. Barrow-Green, J. Gray, R. Wilson, The History of Mathematics: a source-based approach. Volume I. Providence, Rhode Island: MAA Press, 2019.
• T. J. Bromwich, The methods used by Archimedes for approximating to square roots, The Mathematical Gazette 14 (1928), 253–257.
• F. Cajori, A history of the arithmetical methods of approximation to the roots of numerical equations of the unknown quantity, Colorado College Publication, General Series Ns. 51-52. Science Series Vol. XII (1910), 171-287.
• J.-L. Chabert, É. Barbin, M. Guillemot, A. Michel-Pajus, J. Borowczyk, A. Djebbar, J.-C. Martzloff, A History of Algorithms. From the Pebble to the Microchip. Berlin: Springer, 1999.
• K. Chemla, Guo Suchun, Les neuf chapitres. Le Classique mathématique de la Chine ancienne et ses commentaires. Paris: Dunod, 2004.
• B. Datta, The science of the Sulba. A study in Early Hindu Geometry. Calcutta: Calcutta University Press, 1932.
• T.F. De Lagny, Methodes nouvelles pour l’extraction et l’approximation des racines, Séconde edition, Paris: Jean Cusson, 1692.
• A. De Morgan, Notices of the progress of the problem of evolution, in The Companion to the Almanac [of the Society for the Diffusion of Useful Knowledge]; or Year-Book of General Information for 1839. London: Charles Knight, 1839, pp. 34–52.
• R. Descartes, Discours de la Méthode pour bien conduire sa raison, et chercher la vérité dans les sciences. Plus la Dioptrique, les Météores et la Géométrie, qui sont des essais de cette Méthode, Leiden: Imprimerie de Jan Marie, 1637.
• D. Fowler, E. Robson, Square root approximations in Old Babylonian Mathematics: YBC 7289 in context, Historia Mathematica 25 (1998), 366-378.
• A. Gasull, Los babilonios y Newton, Gaceta de la Real Sociedad Matemática Española 25 (2022), No. 3, 488.
• T.L. Heath, The thirteen books of Euclid’s Elements translated from the text of Heiberg with introduction and commentary. Three Volumes. Cambridge: University Press, 1908; second edition: University Press, Cambridge, 1925. Reprint: Dover Publ., New York, 1956
• B. Hughes, Fibonacci’s De Practica Geometriae. New York: SpringerVerlag, 2008.
• V. Katz, C. Tzanakis (Eds.), Recent developments on introducing a historical dimension in mathematics, Washington D.C. : The Mathematical Association of America, 2011.
• G.W. Leibniz, Sämtliche Schriften und Briefe. Reihe 7: Mathematische Schriften. Band 1: 1672–1676. Geometrie-Zahlentheorie-Algebra (I.Teil), edited by E. Knobloch, W.S. Contro. Berlin: Akademie-Verlag,1990.
• J.-C. Martzloff, A History of Chinese Mathematics. Berlin: SpringerVerlag, 2006.
• M.R. Massa-Esteve, The Algebraization of Mathematics: Using Original Sources for Learning Mathematics, Teaching Innovations 33(1) (2020), 21-35.
• A. Mellado Romero, La influencia del Cursus Mathematicus de Hérigone en la algebrización de la matemática, Doctoral Dissertation, Universidad de Murcia, 2022.
• M.A. Nordgaard, A Historical Survey of Algebraic Methods of Approximating the Roots of Numerical Higher Equations Up to the Year 1819, Teachers College, Colombia University, New York, 1922.
• F. Ritter, François Viète, inventeur de l’Algèbre moderne (1540-1603). Notice sur sa vie et son oeuvre, Dépot de la Revue Occidentale, París, 1895.
• E. Robson, Three Old Babylonian methods for dealing with Pythagorean triangles, Journal of Cuneiform Studies 9 (1997), 51-72.
• F. Romero Vallhonesta, I si fem un zoom i mirem la recta numèrica? In C. Ferragud, M.R. Massa Esteve (eds.), Actes de la XIX Jornada sobre la Història de la Ciència i l’Ensenyament. Barcelona: SHCT-IEC, 2023. Pp. 101-107.
• L.E. Sigler, Fibonacci’s Liber Abaci. A Translation into Modern English of Leonardo Pisano’s Book of Calculation. New York : Springer, 2003.
• J. Stedall, From Cardano’s Great Art to Lagrange’s reflections: filling a gap in the history of algebra. Zurich: European Mathematical Society, 2011.
• H. Suter, Über das Rechenbuch das Ali-ben Ahmed el-Nasawi, Bibliotheca Mathematica 7 (1906/1907), 113–119.
• I. Thomas (Transl.), Selections illustrating the history of Greek mathematics, 2 vls. Volume I, from Thales to Euclid / Volume II, from Aristarchus to Pappus. Cambridge, MA: Harvard University Press, 1957.
• F. Viète, De numerosa potestatum ad exegesim resolutione. Ex Opere restitutae mathematicae analyseos, seu, algebra nova Francisci Vietae, edited by Marino Ghetaldi, Paris, 1600.
• F. Viète, Francisci Vietae Opera mathematica, edited by F. van Schooten, Leiden, 1646.
• F. Viète, The analytic art, nine studies in algebra, geometry and trigonometry from the Opus Restitutae Mathematicae Analyseos, seu Algebrâ Novâ, Translated from the Latin and with an introduction by T. Richard Witmer. Mineola, NY : Dover Publications Inc., 2006.
• X.S. Wang, A simple proof of Descartes’ rule of signs, American Mathematical Monthly 111 (2004), 525–526.