The Mathematical Intelligencer

, Volume 21, Issue 3, pp 38–47 | Cite as

What is ancient mathematics?

Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Aaboe and J. L. Berggren,Didactical and other remarks on some theorems of Archimedes and infinitesimals, Centaurus 38 (1996), 295–316.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    K. Andersen,Cavalieri’s method of indivisibles, Arch. Hist. Exact. Sci. 31 (1985), 291–367.MATHMathSciNetGoogle Scholar
  3. [3]
    T. Apostoi,Calculus, vol. I, 2nd Edition, John Wiley & Sons, New York, 1967.Google Scholar
  4. [4]
    I. Asimov,How did we Find out that the Earth is Round?, Walker &Co., New York 1972.Google Scholar
  5. [5]
    I. Asimov,Asimov’s new Guide to Science, Basic Books, New York 1984.[Google Scholar
  6. 6]
    Archimedes,The Works of Archimedes, edited in modern notation with introductory chapters by T.L. Heath. With a supplement,The method of Archimedes, recently discovered by Heiberg, Dover, New York, 1953. Reprinted (translation only) in [36].Google Scholar
  7. [7]
    Archimedes,Opera Omnia, IV vol., cum commentariis Eutocii, iterum edidit I.L Heiberg, corrigenda adiecit E.S. Stamatis, B.G. Teubner, Stuttgart, 1972.Google Scholar
  8. [8]
    Archimède,Oeuvres, 4 vol., texte établi et traduit par C. Mugler, Les Belles Lettres, Paris, 1970–72.Google Scholar
  9. [9]
    M. Balme and G. Lawall,Athenaze, An Introduction to Ancient Greek, 2 vols., Oxford University Press, New York, 1990.Google Scholar
  10. [10]
    A. Avron,On strict constructibility with a compass alone, J. Geometry 38 (1990), 12–15.CrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    ET. Bell,Men of Mathematics, Simon and Schuster, New York, 1937.MATHGoogle Scholar
  12. [12]
    L. Bers,Calculus, vol. I, Holt, Rinehart and Winston, New York, 1969.Google Scholar
  13. [13]
    L. Bieberbach (1886–1982),Theorie der geometrischen Konstruktionen, Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften, Mathematische Reihe, Band 13, Verlag Birkhäuser, Basel, 1952.Google Scholar
  14. [14]
    Cleomedes (circa 150 B.C.), DeMotu Circulari Corporum Caelestium, 2 vols., H. Ziegler, editor, Teubner, Leipzig 1891. See [32, p. 106] [43] [54, Vol. 2, p. 267].Google Scholar
  15. [15]
    H.S.M. Coxeter,Introduction to Geometry, John Wiley & Sons, New York, 1989.Google Scholar
  16. [16]
    H.T. Croft, K.J. Falconer, and R.K. Guy,Unsolved Problems in Geometry, Springer-Verlag, New York 1991.CrossRefMATHGoogle Scholar
  17. [17]
    P.J. Davis,The rise, fall, and possible transfiguration of triangle geometry: A mini history, Amer. Math. Monthly 102 (1995), 204–214.CrossRefMATHMathSciNetGoogle Scholar
  18. [18]
    E.J. Eijksterhuis,Archimedes, Princeton University Press, Princeton 1987Google Scholar
  19. [19]
    M. Djoric and L. Vanhecke,A Theorem of Archimedes about spheres and cylinders and two-point homogeneous spaces, Bull. Austral. Math. Soc. 43 (1991), 283–294.CrossRefMATHMathSciNetGoogle Scholar
  20. [20]
    U. Dudley,A budget of trisections, Springer-Verlag, New York, 1987.CrossRefMATHGoogle Scholar
  21. [21]
    C.H. Edwards,The Historical Development of the Calculus, Springer-Verlag, New York, 1979.CrossRefMATHGoogle Scholar
  22. [22]
    C.H. Edwards and D.E. Penney,Calculus and Analytic Geometry, second edition, Prentice Hall, Englewood Cliffs, NJ, 1988.Google Scholar
  23. [23]
    Euclid,The Thirteen Books of Euclid’s Elements, translated with introduction and commentary by T.L. Heath, Dover 1956.Google Scholar
  24. [24]
    D.H. Fowler,The Mathematics of Plato’s Academy: a New Reconstruction, Clarendon Press, Oxford 1990.Google Scholar
  25. [25]
    S.H. Gould,The Method of Archimedes, Amer. Math. Monthly 62 (1955), 473–476.CrossRefMATHMathSciNetGoogle Scholar
  26. [26]
    R.M. Green,Spherical Astronomy, Cambridge University Press, Cambridge 1985.Google Scholar
  27. [27]
    J. Hadamard (1865–1963),Leçons de géométrie élémentaire, 2 vols., A. Colin, Paris, 1937.Google Scholar
  28. [28]
    D. Hammett,The Maltese Falcon, Penguin, Middlesex, 1930.Google Scholar
  29. [29]
    E. Hayashi,A reconstruction of the proof of Proposition 11 in Archimedes method, Historia Sci. 3 (1994), 215–230.MATHMathSciNetGoogle Scholar
  30. [30]
    G.H. Hardy (1877–1947),A Mathematician’s Apology, Cambridge University Press, New York, 1985.Google Scholar
  31. [31]
    R. Hartshorne,A Companion to Euclid, a course of geometry based on Euclid’s Elements and its modern descendents, AMS, Berkeley Center for Pure and Applied Mathematics, 1997.Google Scholar
  32. [32]
    T. Heath,A History of Greek Mathematics, vol. II, Dover, New York, 1981.Google Scholar
  33. [33]
    I.L. Heiberg,Eine neue Archimedes-Handschrift, Hermes 42 (1907), p. 235.Google Scholar
  34. [34]
    H.L.F. von Helmholtz,Helmholtz treatise on physiological optics, translated from the 3d German ed., edited by J.P.C. Southall, Dover, New York, 1962.Google Scholar
  35. [35]
    D. Hughes-Hallett, A.M. Gleason, et al.,Calculus, John Wiley & Sons, New York, 1994. Second edition, 1998.Google Scholar
  36. [36]
    Great Books of the Western World, vol. 11, R.M. Hutchins, editor, Encyclopaedia Britannica, Inc., Chicago, 1952.Google Scholar
  37. [37]
    G. Johnson,The Big Question: Does the Universe Follow Mathematical Law? The New York Times, February 10, 1998.Google Scholar
  38. [38]
    F. Klein (1849–1925),Elementary Mathematics from an Advanced Viewpoint, 2 vols, Macmillan, New York, 1939.Google Scholar
  39. [39]
    W.R. Knorr,The evolution of the Euclidean elements, Synthese Historical Library 15, D. Reidel, Dordrecht-Boston, MA, 1975.Google Scholar
  40. [40]
    W.R. Knorr,Archimedes and the Spirals: The Heuristic Background, Historia Math. 5 (1978), 43–75.CrossRefMATHMathSciNetGoogle Scholar
  41. [41]
    W.R. Knorr,The Ancient Tradition of Geometric Problems, Birkhäuser, Boston, 1986.Google Scholar
  42. [42]
    W.R. Knorr,The method of indivisibles in ancient geometry, in “Vita mathematics” (Toronto, ON, 1992; Quebec City, PQ, 1992), 67–86, MAA Notes 40, Math. Assoc. America, Washington, DC, 1996.Google Scholar
  43. [43]
    K. Lasky, The Librarian who Measured the Earth, Little, Brown & Co., Boston 1994.Google Scholar
  44. [44]
    H. Lebesgue,Leçons sur les constructions géométriques, Gauthier- Villars, Paris, 1950. Reissued, Jacques Gabay, Paris, 1987.MATHGoogle Scholar
  45. [45]
    E. Moise,Elementary Geometry from an Advanced Viewpoint, Addison-Wesley, Reading, MA, 1974.Google Scholar
  46. [46]
    R. Netz, personal communication.Google Scholar
  47. [47]
    Nicomachus of Gerasa (circa 100 A.D.),Introduction to Arithmetic, translated by M.L D’Ooge, in [36]. See [54, Vol. 1, p. 101].Google Scholar
  48. [48]
    Pappus,La Collection Mathématique, traduit avec une introduction et notes par P. Ver Ecke, Desclée de Brouwer, Paris, 1933.Google Scholar
  49. [49]
    Plutarch,Lives, vol. 5, translated by B. Perrin, Loeb Classical Library 87, Harvard University Press, Cambridge, MA, 1917. Also, translated by John Dryden (1631–1700), http://www.oed.com/ plutarch.html.Google Scholar
  50. [50]
    A. Selberg,Collected Works, 2 vols, Springer Verlag, New York, 1989, 1991.Google Scholar
  51. [51]
    G.F. Simmons,Calculus with Analytic Geometry, McGraw Hill, New York, 1985.Google Scholar
  52. [52]
    H.M. Stark,On the “gap” in a theorem of Heegner, J. Number Theory 1 (1969), 16–27.CrossRefMATHMathSciNetGoogle Scholar
  53. [53]
    H. Swann,Commentary on rethinking rigor in calculus: The role of the mean value theorem, Amer. Math. Monthly 104 (1997), 241–245.CrossRefMATHMathSciNetGoogle Scholar
  54. [54]
    I. Thomas,Greek Mathematical Works, 2 vol., Loeb Classical Library 335, 362, Harvard University Press, Cambridge, MA, 1980.Google Scholar
  55. [55]
    G. Toussaint,A new look at Euclid’s second proposition, Math. Intelligencer15 (1993), 12–23.CrossRefMATHMathSciNetGoogle Scholar
  56. [56]
    I. Vardi,A classical reeducation, in preparation.Google Scholar
  57. [57]
    I. Vardi, APXIMHΔOΥΣ ΠEPI TΩN EΛIKΩN EΦOΔOΣ, in preparation.Google Scholar
  58. [58]
    B.L. van der Waerden,Science Awakening I, Scholar’s Bookshelf Press, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988.Google Scholar
  59. [59]
    A. Wiles,Modular elliptic curves and Fermat’s last theorem, Ann. of Math. 141 (1995), 443–551CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 1999

Authors and Affiliations

  1. 1.Bures-sur-YvetteFrance

Personalised recommendations