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.
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Notes
MP I.392-448.
MP III.70-1.
Newton 1669.
Newton 1671, pp. 72-3.
MP III.80-1.
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.
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.
Newton Principles I.38.
Newton Principles I.29.
MP VIII. 126-9.
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.
On the concepts of infinity and continuity in ancient and medieval thought see, for instance, Kretzmann, N. 1982; Murdoch, J.E. 1982.
Newton Principles I.29–39.
MP VIII.597-599.
Quoted from the opening of Newton 1704 in MP VIII. 123.
L’Hospital, G.-F.-A. 1696.
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.
Newton, I. 1715. De Morgan, A. 1852; Newton, I. 1704a.
See the articles ‘Fluxions’ in Harris, J. 1704-1710.
Newton, I. 1711; Jones, W. 1706, p. 226; Anonymous 1713, pp. 121-2.
On Berkeley, G. 1734 see Cantor, G. 1984; Grattan-Guinness, I. 1969.
Newton, I. 1715, p. 179; Lai, T. 1975.
On Colin Maclaurin see Sageng, E. 1989.
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Guicciardini, N. (1993). Newton and British Newtonians on the Foundations of the Calculus. In: Petry, M.J. (eds) Hegel and Newtonianism. Archives Internationales D’Histoire Des Idées / International Archives of the History of Ideas, vol 136. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1662-6_14
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