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The Reception of Ancient Indian Mathematics by Western Historians

  • Albrecht Heeffer
Chapter

Summary

While there has been an awareness of ancient Indian mathematics in the West since the sixteenth century, historians discussed the Indian mathematical tradition only after the publication of the first translations by Colebrooke in 1817. Its reception cannot be comprehended without accounting for the way that new European mathematics was shaped by Renaissance humanist writings. We sketch this background and show with one case study on algebraic solutions to a linear problem, how the understanding and appreciation of Indian mathematics was deeply influenced by the humanist prejudice that all higher intellectual culture, in particular all science, had risen from Greek soil.

Keywords

Sixteenth Century Latin Translation Greek Text Greek Mathematic Hindu Tradition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Borst, Arno: Das mittelalterliche Zahlenkampfspiel. Supplemente zuden Sitzungsberichten der Heidelberger Akademie der Wissenschaften, Philosophisch-historische Klasse, Vol. 5, Carl Winter Universitätsverlag, Heidelberg (1986).Google Scholar
  2. 2.
    Boyer, Carl: History of the Calculus and Its Conceptual Development. Dover Publications, New York (1959).Google Scholar
  3. 3.
    Busard, H. L. L. (ed.), Nemore, Jordanus de: De Elementis Arithmetice Artis. AMedieval Treatise on Number Theory (2 Vols.) Franz Steiner Verlag, Stuttgart (1991).Google Scholar
  4. 4.
    Cajori, Florian: A History of Mathematics. The Macmillan Company, New York (1893) (2nd ed. The Macmillan Company, New York, 1919).Google Scholar
  5. 5.
    Cantor, Moritz: Vorlesungen über Geschichte der Mathematik(4Vols., 1880–1908), Vol. I (1880); Von den ältesten Zeiten bis zum Jahre 1200 n. Chr., Vol.II (1892); Von 1200–1668, (2nd ed. Teubner: Leipzig, 1894, 1900).Google Scholar
  6. 6.
    Clark, Walter Eugene (ed.): The Āryabhaṭịya of Āryabhaṭa: An Ancient Indian Work on Mathematics and Astronomy. University of Chicago Press, Chicago (1930).Google Scholar
  7. 7.
    Colebrooke, Henry Thomas: Algebra with Arithmetic and Mensuration from the Sanskrit of Brahmagupta and Bhāskara. John Murray, London (1817) (Sandig Reprint Verlag, Vaduz, Lichtenstein 2001).Google Scholar
  8. 8.
    Cossali, Pietro: Origine, trasporto in Italia, primi progressi in essa dell’algebra. Storia critica di nuove disquisizioni analitiche e metafisiche arricchita (2 Vols.) Parma (1797–1799).Google Scholar
  9. 9.
    Curtze, Maximilian (ed.): Der Briefwechsel Regiomontan’s mit Giovanni Bianchini, Jacob von Speier und Christian Roder. Urkunden zur Geschichte der Mathematik im Mittelalter und der Renaissance 1, Abhandlungen zur Geschichte der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen begründet von Moritz Cantor, 12, 185–336 (1902).Google Scholar
  10. 10.
    Flegg, Graham: Numbers, Their History and Their Meaning. Andre Deutsch, London (1983).Google Scholar
  11. 11.
    Folkerts, Menso: Die älteste mathematische Aufgabensammlung in lateinischer Spräche, Die Alkuin zugeschriebenen Propositiones ad Acuendos Iuvenes. Denkschriften der Österreichischen Akademie der Wissenschaften Mathematische naturwissenschaftliche Klasse, 116(6), 13–80 (1978).Google Scholar
  12. 12.
    Friedlein, Godofredus (ed.): Boetii De institutione arithmetica libri duo. Teubner, Leipzig (1867).Google Scholar
  13. 13.
    Hankel, Herman: Zur Geschichte der Mathematik in Alterthum und Mittelalter. Teubner, Leipzig (1874).Google Scholar
  14. 14.
    Heath, Sir Thomas Little: A History of Greek Mathematics (2 Vols.) Oxford University Press, Oxford (1921) (reprint Dover publications, New York, 1981).Google Scholar
  15. 15.
    Heeffer, Albrecht: The Tacit Appropriation of Hindu Algebra in Renaissance Practical Arithmetic. Gaṇita Bhārāṭi 29, 1–2, 1–60 (2007).Google Scholar
  16. 16.
    Heeffer, Albrecht: A Conceptual Analysis of Early Arabic Algebra, in T. Street, S. Rahman and H. Tahiri (eds.) Arabic Logic and Epistemology. Kluwer 89–128 (2008).Google Scholar
  17. 17.
    Høyrup, Jens: In Measure, Number and Weight, Studies in Mathematics and Culture. State University of New York Press, Albany (1993).Google Scholar
  18. 18.
    Høyrup, Jens: A New Art in Ancient Clothes. Itineraries chosen between scholasticism and baroque in order to make algebra appear legitimate, and their impact on the substance of the discipline, Physis, 35 (1), 11–50 (1998).Google Scholar
  19. 19.
    Hutton, Charles: Mathematical and Philosophical Dictionary. J. Johnson and G.G. and J. Robinson, London (1795) (2 Vols.) (reprint Georg Olms, Heidelberg, 1973).Google Scholar
  20. 20.
    L’Huillier, Ghislaine: Le quadripartitum numerorum de Jean de Murs, introduction et édition critique. Mémoires et documents publiés par la sociéte ́de l’Ecole des chartes, 32, Droz, Geneva (1990).Google Scholar
  21. 21.
    Kaplan, Robert: The Nothing That Is: A Natural History of Zero. Oxford University Press, Oxford (2001).Google Scholar
  22. 22.
    Kaye, George Rusby: The Bakhshālī Manuscript. A Study in Mediaeval Mathematics (3 parts in 2 Vols.) Vol 1: Archaeological Survey of India, Kolkata (1927); Vol 2, Delhi (1933) (Reprint, Cosmo Publications, New Delhi, 1981).Google Scholar
  23. 23.
    Kern, Hendrik: The Āryabhaṭīya, With the Commentary Bhaṭadīpikā of Paramādīçvara, Brill, Leiden (1875).Google Scholar
  24. 24.
    Klein, Jacob: Die griechische Logistik und die Entstehung der Algebra. Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Berlin, 1934–1936. English translation: Greek Mathematical Thought and the Origin of Algebra. MIT Press, Boston Ma. (1968).Google Scholar
  25. 25.
    Nesselmann, Georg Heinrich Ferdinand: Versuch einer kritischen Geschichte der Algebra. Vol 1. Die Algebra der Griechen, Berlin (1842) (Reprinted, Minerva, Frankfurt, 1969).Google Scholar
  26. 26.
    Pistelli, Ermenegildo (ed.): Iamblichus Nichomachi arithmeticam introductionem liber, Teubner, Leipzig (1884) (reprinted, Teubner, Leipzig, 1975).Google Scholar
  27. 27.
    Regiomontanus, Johannes: Continentur in hoc libro. Rvdimenta astronomica alfragani. Item Albategni vs alstronomvs peritissimvs de motv stellarvm, ex obseruationibus tum proprijs, tum Ptolomaei, omnia cũ demonstratiõibus Geometricis and Additionibus Ioannis de Regiomonte. Item Oratio introductoria in omnes scientias Mathematicas Ioannis de Regiomonte, Patauij habita, cum Alfraganum publice praelegeret. Eivsdem utilissima introductio in elementa Euclidis, Johann Petreius, Nürnberg (1537).Google Scholar
  28. 28.
    Robbins, Frank Egleston, Karpinski, Louis Charles: Introduction to Arithmetic: Nicomachus of Gerasa; translated into English by Martin Luther D’Ooge, Macmillan, New York (1926).Google Scholar
  29. 29.
    Rodet, Léon: [L’]algèbre d’Al-Khârizmi et les méthodes indienne et grecque, Imprémerie nationale, Paris (1878).Google Scholar
  30. 30.
    Rodet, Léon: Leçons de calcul d’Āryabhaṭa, Journal Asiatique, 13 (7), 393–434 (1879).Google Scholar
  31. 31.
    Rose, Paul: The Italian Renaissance of Mathematics. Droz, Geneva (1975).Google Scholar
  32. 32.
    Shukla, Kripa Shankar, Sarma, K. V. (transl. and eds.): Āryabhaṭīya of Āryabhaṭa. Indian National Science Academy, New Delhi, India (1976).Google Scholar
  33. 33.
    Singmaster, David: Problems to Sharpen the Young. An Annotated Translation of ‘Propositiones ad Acuendos Juvenes’ The Oldest Mathematical Problem Collection in Latin Attributed to Alcuin of York. Translated by John Hadley, annotated by David Singmaster and John Hadley. Mathematical Gazette, 76 (475), 102–126 (1992) (extended and revised version, copy from the author).Google Scholar
  34. 34.
    Smith, David Eugene: History of Mathematics (2 Vols.) Ginn and Company, Boston, 1923, 1925 (Dover edition 1958, 2 Vols.).MATHGoogle Scholar
  35. 35.
    Tannery, Paul: Pour l’histoire de la science Hellène, Gauthier-Villars, Paris, (1920) (reprint of the second ed. by Jacques Gabay, Sceaux, 1990).Google Scholar
  36. 36.
    Tennulius, Samuel: In Nicomachi Geraseni Arithmeticam introductionem, et De fato / Jamblichus Chalcidensis; in Lat. serm. conversus, not. ill. à Sam. Tennulio, acc. Joach. Camerarii Explicatio in duos libros Nicomachi, Arnhem (1668).Google Scholar
  37. 37.
    Thibaut, George; Dvivedin, Mahamahopadhyaya Sudhākara: The Panchasiddhantika. The Astronomical Work of Varāhamihira. Benares (1889).Google Scholar
  38. 38.
    Thibaut, George, Astronomie: Astrologie und Mathematik, in G. Bühler (ed., later F. Kielhorn), Grundriss der Indo-Arischen Philologie und Alterumskunde, Vol. 3 (9), Tübner, Strasbourg.Google Scholar
  39. 39.
    Tropfke, Johannes: Geschichte der Elementar-Mathematik in systematischer Darstellung mit besonderer Berücksichtigung der Fachwörter. 3rd ed. (1930–40), Vol. I (1930), Rechnen, Vol. II. (1933), Allgemeine Arithmetik, Vol. III (1937), Proportionen, Gleichungen, Vol. IV (1940), Ebene Geometrie, Walter de Gruyter, Leipzig.Google Scholar
  40. 40.
    Tropfke, Johannes: Geschichte der Elementar-Mathematik in systematischer Darstellung mit besonderer Berücksichtigung der Fachwörter, Vol. I, Arithmetik und Algebra. Revised by Kurt Vogel, Karin Reich and Helmuth Gericke, Walter de Gruyter, Berlin (1980).Google Scholar
  41. 41.
    Waerden, Bartel Leendert van der: Science Awakening. Kluwer, Dortrecht (1954) (5th ed. 1988).CrossRefGoogle Scholar
  42. 42.
    Ver Eecke, Paul: Diophante d’Alexandrie. Les six livres arithmétiques et le livre des nombres polygones. Œuvres traduites pour la première fois du Grec en Français. Avec une introduction et des notes par Paul Ver Eecke. Ouvrage publié sous les auspices de la Fondation universitaire de Belgique. Brughes, Desclée, De Bouwer et Cie. (1926).Google Scholar
  43. 43.
    Wallis, John: A Treatise of Algebra Both Theoretical and Practical. Printed by John Playford for Richard Davis, London (1685).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Center for Logic and Philosophy of ScienceGhent UniversityGhentBelgium

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