Proofs and Contexts: the Debate between Bernoulli and Newton on the Mathematics of Central Force Motion

Chapter
Part of the Trends in the History of Science book series (TRENDSHISTORYSCIENCE)

Abstract

In this essay I analyze the solutions given by Isaac Newton and Johann Bernoulli to a well-posed mathematical problem known in the eighteenth century as the ‘inverse problem of central forces’. This work prompted polemical exchanges between two rival groups: the first, whose leader was Newton, was based in Oxford, Cambridge, and London; the second, whose leading representatives were Leibniz and Bernoulli, was scattered througout Europe, though centered in Basel and Paris.

Keywords

Polemical Exchange 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [Arnold 1990] Arnold, Vladimir I., Huygens and Barrow, Newton and Hooke: Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvents to Quasicrystals. Translated from the Russian by Eric J. F. Primrose. Basel, Boston, Berlin: Birkhäuser, 1990.Google Scholar
  2. [Bernoulli 1710] Bernoulli, Johann, “Extrait de la Réponse de M. Bernoulli à M. Herman, Datée de Basle le 7 Octobre 1710”. Mémoires de l’Académie des Sciences (1710): 521–33.Google Scholar
  3. [Bernoulli 1716] Bernoulli, Johann, “Epistola pro Eminente Mathematico, Dn. Johanne Bernoullio, Contra Quendam ex Anglia Antogonistam [sic] Scripta”. Acta Eruditorum (1716): 296–315.Google Scholar
  4. [Bertoloni Meli 1999] Bertoloni Meli, Domenico, “Caroline, Leibniz, and Clarke”. Journal of the History of Ideas 60 (1999): 469–86.Google Scholar
  5. [Bevir 1999] Bevir, Marc, The Logic of the History of Ideas. Cambridge: Cambridge University Press, 1999.Google Scholar
  6. [Bloor 1991] Bloor, David, Knowledge and Social Imagery. Chicago: The University of Chicago Press, 1991 (first ed. 1976).Google Scholar
  7. [Bos 2001] Bos, Henk J. M., Redefining Geometrical Exactness: Descartes’ Transformation of the Early Modern Concept of Construction. New York: Springer, 2001.Google Scholar
  8. [Brackenridge 1995] Brackenridge, Bruce, The Key to Newton’s Dynamics. Berkeley, Los Angeles, London: California University Press, 1995.Google Scholar
  9. [Brackenridge 2003] Brackenridge, Bruce, “Newton’s Easy Quadratures: ‘Omitted for the Sake of Brevity”’. Archive for History of Exact Sciences 57 (2003): 313–36.Google Scholar
  10. [Chandrasekhar 1995] Chandrasekhar, Subrahmanyan, Newton’s Principia for the Common Reader. Oxford: Clarendon Press, 1995.Google Scholar
  11. [Chang 2008] Chang, Hasok, “The Historian of Science: Painter, Guide, or Connoisseur”. Centaurus 50 (2008): 37–42.Google Scholar
  12. [Collini 2000] Collini, Stefan, “General Introduction”. In Economy, Polity, and Society: British Intellectual History 1750–1950. Edited by Stefan Collini, Richard Whatmore, and Brian Young. Cambridge: Cambridge University Press, 2000.Google Scholar
  13. [Costabel 1989] Costabel, Pierre, “Courbure et Dynamique: Jean I Bernoulli Correcteur de Huygens et de Newton”. Symposium Leibniz et Bernoulli (Basel, June 15-17, 1987). Studia Leibnitiana Sonderheft 17 (1989): 12–24.Google Scholar
  14. [De Gandt 1995] De Gandt, François, Force and Geometry in Newton’s Principia. Princeton: Princeton University Press, 1995.Google Scholar
  15. [Dauben 1992a] Dauben, Joseph, “Are There Revolutions in Mathematics?” In Echeverria, J., Ibarra, A., and Mormann, T., editors. The Space of Mathematics, Philosophical, Epistemological, and Historical Explorations, pp. 205–229. Berlin: Walter de Gruyter, 1992a.Google Scholar
  16. [Dauben 1992b] Dauben, Joseph, “Conceptual Revolutions and the History of Mathematics: Two Studies in the Growth of Knowledge”. In Gillies, D., editor. Revolutions in Mathematics, pp. 49–71. Oxford: Clarendon Press 1992b.Google Scholar
  17. [Erlichson 1990] Erlichson, Herman, “Comment on ‘Long-buried Dismantling of a Centuries-old myth: Newton’s Principia and Inverse-square Orbits’ by Robert Weinstock”. American Journal of Physics 58 (1990), 882–4.Google Scholar
  18. [Erlichson 1994] Erlichson, Herman, “The Visualization of Quadratures in the Mystery of Corollary 3 to Proposition 41 of Newton’s Principia”. Historia Mathematica 21 (1994): 148–61.Google Scholar
  19. [Guicciardini 1995] Guicciardini, Niccolò, “Johann Bernoulli, John Keill and the Inverse Problem of Central Forces”. Annals of Science, 52 (1995): 537–575.Google Scholar
  20. [Guicciardini 19999] Guicciardini, Niccolò, Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736. Cambridge: Cambridge University Press, 1999.Google Scholar
  21. [Guicciardini 2009] Guicciardini, Niccolò, Isaac Newton on Mathematical Certainty and Method. Cambridge, Mass.: MIT Press, 2009.Google Scholar
  22. [Goldstein 2001] Goldstein, Herbert, Classical Mechanics, 3d edition. Addison Wesley, 2001.Google Scholar
  23. [Hall 1980] Hall, Alfred R, Philosophers at War: The Quarrel between Newton and Leibniz. Cambridge: Cambridge University Press, 1980.Google Scholar
  24. [Hermann 1710] Hermann, Jacob, “Extrait d’une Lettre de M. Herman à M. Bernoulli, datée de Padoüe le 12. Juillet 1710”. Mémoires de l’Académie des Sciences (1710): 519–521.Google Scholar
  25. [Hiscock 1937] Hiscock, Walter George, David Gregory, Isaac Newton and Their Circle: Extracts from David Gregory’s Memoranda 1677–1708. Oxford: for the Editor, 1937.Google Scholar
  26. [Jardine 2000] Jardine, Nicholas, “Uses and Abuses of Anachronism in the History of the Sciences”. History of Science 38 (2000): 251–270.Google Scholar
  27. [Keill 1708] Keill, John, “Epistola ad Clarissimum Virum Edmundum Halleium Geometriae Professorem Savilianum, de Legibus Virium Centripetarum”. Philosophical Transactions 26 (1708): 174–8.Google Scholar
  28. [Keill 1714] Keill, John, “Observationes de Inverso Problemate Virium Centripetarum”. Philosophical Transactions 29 (1714): 91–111.Google Scholar
  29. [Keill 1716] Keill, John, “Défense du Chevalier Newton”. Journal Litéraire 8 (1716): 418–33.Google Scholar
  30. [LaCapra 1983] LaCapra, Dominick, Rethinking Intellectual History: Texts, Contexts, Language. Ithaca, NY: Cornell University Press, 1983.Google Scholar
  31. [Levi 1974] Levi, Albert W., Philosophy as Social Expression. Chicago: The University of Chicago Press, 1974.Google Scholar
  32. [Mahoney 1973] Mahoney, Michael S., The Mathematical Career of Pierre de Fermat (1601–1665). Princeton: Princeton University Press, 1973. (2d rev. ed., 1994)Google Scholar
  33. [Nauenberg 1994] Nauenberg, Michael, “Newton’s Principia and Inverse Square Orbits”. The College Mathematics Journal 25 (1994): 211–222.Google Scholar
  34. [Nauenberg 2010] Nauenberg, Michael, “The Early Application of the Calculus to the Inverse Square Force Problem”. Archive for History of Exact Sciences 64 (2010): 269–300.Google Scholar
  35. [Newton 1715] Newton, Isaac, “An Account of the Book Entituled Commercium Epistolicum”. Philosophical Transactions 29 (1715): 173–224. [Facsimile in Hall, Philosophers at War (1980), pp. 263–314].Google Scholar
  36. [Newton 1959-1977] Newton, Isaac, The Correspondence of Isaac Newton. Edited by Herbert W. Turnbull, John F. Scott, A. Rupert Hall, and Laura Tilling. 7 vols. Cambridge: Cambridge University Press, 1959–1977. (cited as Correspondence)Google Scholar
  37. [Newton 1967-1981] Newton, Isaac, The Mathematical Papers of Isaac Newton. Edited by Derek T. Whiteside. 8 vols. Cambridge: Cambridge University Press, 1967–81. (cited as Mathematical Papers)Google Scholar
  38. [Newton 1972] Newton, Isaac, Philosophiae Naturalis Principia Mathematica, The Third Edition (1726) With Variant Readings. Edited by Alexandre Koyré and I. Bernard Cohen, assisted by Anne Whitman. Cambridge: Cambridge University Press, 1972.Google Scholar
  39. [Newton 1984] Newton, Isaac, The Optical Papers of Isaac Newton. Vol.1. The Optical Lectures 1670–1672. Edited by Alan E. Shapiro. Cambridge: Cambridge University Press, 1984.Google Scholar
  40. [Newton 1999] Newton, Isaac, The Principia: Mathematical Principles of Natural Philosophy … Preceded by a Guide to Newton’s Principia by I. Bernard Cohen. Translated by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz. Berkeley: University of California Press, 1999.Google Scholar
  41. [Popkin 2003] Popkin, Richard H., The History of Scepticism: From Savonarola to Bayle. Oxford: Oxford University Press, 2003.Google Scholar
  42. [Pourciau 1991] Pourciau, Bruce, “On Newton’s Proof that Inverse-Square Orbits Must Be Conics”. Annals of Science 48 (1991): 159–72.Google Scholar
  43. [Pourciau 1992] Pourciau, Bruce, “Newton’s Solution of the One-Body Problem”. Archive for History of Exact Sciences 44 (1992): 125–46.Google Scholar
  44. [Pourciau 2009] Pourciau, Bruce, “Proposition II (Book I) of Newton’s Principia”. Archive for History of Exact Sciences 63 (2009): 129–167.Google Scholar
  45. [Shapin 1981] Shapin, Steven, “Of Gods and Kings: Natural Philosophy and Politics in the Leibniz- Clarke Disputes”. Isis 72 (1981): 187–215.Google Scholar
  46. [Shapiro A 1993] Shapiro, Alan, Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton’s Theories of Colored Bodies and Fits of Easy Reflection. Cambridge: Cambridge University Press, 1993.Google Scholar
  47. [Shapiro A 2004] Shapiro, Alan, “Newton’s ’Experimental Philosophy”’. Early Science and Medicine 9 (2004): 185–217.Google Scholar
  48. [Shapiro B 1983] Shapiro, Barbara J., Probability and Certainty in Seventeenth-Century England: A Study of the Relationships Between Natural Science, Religion, History, Law and Literature. Princeton: Princeton University Press, 1983.Google Scholar
  49. [Speiser 1996] Speiser, David, “The Kepler Problem from Newton to Bernoulli”. Archive for History of Exact Sciences 50 (1996): 103–116.Google Scholar
  50. [Terrall 1999] Terrall, Mary, “Metaphysics, Mathematics, and the Gendering of Science in Eighteenth-Century France”. In The Sciences in Enlightened Europe. Edited by William Clark, Jan Golinski and Simon Schaffer. Chicago: University of Chicago Press, 1999.Google Scholar
  51. [Truesdell 1960] Truesdell, Clifford, “A Program toward Rediscovering the Rational Mechanics of the Age of Reason”. Archive for History of Exact Sciences 1 (1960): 3–36.Google Scholar
  52. [Truesdell 1973] Truesdell, Clifford, “The Scholar’s Workshop and Tools”. Centaurus 17 (1973), 1–10.Google Scholar
  53. [Weinstock 1982] Weinstock, Robert, “Dismantling a Centuries-Old Myth: Newton’s Principia and Inverse-Square Orbits”. American Journal of Physics 50(7) (1982): 610–617.Google Scholar
  54. [Weinstock 1989] Weinstock, Robert, “Long-Buried Dismantling of a Centuries-Old Myth: Newton’s Principia and Inverse-Square Orbits”. American Journal of Physics 57(9) (1989): 846–849.Google Scholar
  55. [Weinstock 2000] Weinstock, Robert, “Inverse-Square Orbits in Newton’s Principia and Twentieth-Century Commentary Thereon”. Archive for History of Exact Sciences 55(2) (2000): 137–162.Google Scholar
  56. [Whiteside 1970] Whiteside, Derek T., “The Mathematical Principles Underlying Newton’s Principia Mathematica”. Journal for the History of Astronomy 1 (1970): 116–38.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Università degli Studi di BergamoBergamoItaly

Personalised recommendations