Advertisement

Newton and British Newtonians on the Foundations of the Calculus

  • Niccolò Guicciardini
Chapter
Part of the Archives Internationales D’Histoire Des Idées / International Archives of the History of Ideas book series (ARCH, volume 136)

Abstract

As is well known, Newton, working in perfect and splendid isolation while still a young scholar at Trinity, discovered the “new analysis” that is to say, he developed what we recognize today as the basic rules of the calculus. It is not my purpose here to trace the history of this discovery and of its developments in Newton’s published works and manuscripts. At the risk of oversimplifying the complexities of the vast amount of material presented in such an admirable manner by Whiteside in his eight volume edition of Newton’s mathematical papers, I shall outline what seem to me to have been the turning points in Newton’s research into the foundations of the calculus.

Keywords

Eighteenth Century Limit Procedure Ultimate Ratio Infinitesimal Interval Mathematical Quantity 
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.

Notes

  1. 1.
    MP I.392-448.Google Scholar
  2. 2.
    MP III.70-1.Google Scholar
  3. 3.
    Newton 1669.Google Scholar
  4. 4.
    Newton 1671, pp. 72-3.Google Scholar
  5. 5.
    MP III.80-1.Google Scholar
  6. 6.
    The Tractatus de quadratura curvarum,Newton 1704a, was published as an appendix to the first edition of Newton’s Opticks. A short version had already appeared in 1693 in the Latin edition of Wallis’s Algebra, Wallis, J. 1693-1699,2, pp. 390-396.Google Scholar
  7. 7.
    The “Addendum” to the De methodis is published in MP III.328-53. On the use of limit procedures in the De methodis see, for instance, MP III.283.Google Scholar
  8. 8.
    Newton Principles I.38.Google Scholar
  9. 9.
    Newton Principles I.29.Google Scholar
  10. 10.
    MP VIII. 126-9.Google Scholar
  11. 11.
    Newton Principles 1.38–39. On Newton’s mathematical style in the Principia see De Gand, F. 1986; Di Sieno, S. and M. Galuzzi 1987 and Kitcher, P. 1973.Google Scholar
  12. 12.
    On the concepts of infinity and continuity in ancient and medieval thought see, for instance, Kretzmann, N. 1982; Murdoch, J.E. 1982.Google Scholar
  13. 13.
    Newton Principles I.29–39.Google Scholar
  14. 14.
    MP VIII.597-599.Google Scholar
  15. 15.
    Quoted from the opening of Newton 1704 in MP VIII. 123.Google Scholar
  16. 16.
    L’Hospital, G.-F.-A. 1696.Google Scholar
  17. 17.
    Stone, E. 1730, p. xviii. On the history of the fluxional calculus see Cajori, F. 1919 and Guicciardini, N. 1989. Biobibliographical information on the history of British mathematics in the eighteenth century can be found in Taylor, E.G.R. 1966 and Wallis, P.J. and Wallis, R. 1986. Other works of interest are Schneider, I.1968 on Abraham De Moivre, Gowing, R. 1983 on Roger Cotes, Feigenbaum, L. 1985 on Brook Taylor, Tweedie, C. 1922 and Krieger, H. 1968 on James Stirling, Eagles, CM. 1977a and 1977b on David Gregory, Clarke, F.M. 1929 on Thomas Simpson, Tweedie, C. 1915, Turnbull, H.W. 1951, Scott, G.P. 1971 and Sageng, E. 1989 on Colin Maclaurin, Trail, W. 1812 on Robert Simson, Smith, G.C. 1980 on Thomas Bayes.Google Scholar
  18. 18.
    Newton, I. 1715. De Morgan, A. 1852; Newton, I. 1704a.Google Scholar
  19. 19.
    See the articles ‘Fluxions’ in Harris, J. 1704-1710.Google Scholar
  20. 20.
    Newton, I. 1711; Jones, W. 1706, p. 226; Anonymous 1713, pp. 121-2.Google Scholar
  21. 21.
    On Berkeley, G. 1734 see Cantor, G. 1984; Grattan-Guinness, I. 1969.Google Scholar
  22. 22.
    Newton, I. 1715, p. 179; Lai, T. 1975.Google Scholar
  23. 23.
    On Colin Maclaurin see Sageng, E. 1989.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Niccolò Guicciardini

There are no affiliations available

Personalised recommendations