Hegel and Newtonianism pp 167-177 | Cite as

# Newton and British Newtonians on the Foundations of the Calculus

## 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## Preview

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## Notes

- 1.MP I.392-448.Google Scholar
- 2.MP III.70-1.Google Scholar
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- 4.Newton 1671, pp. 72-3.Google Scholar
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- 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.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.Newton
*Principles*I.38.Google Scholar - 9.Newton
*Principles*I.29.Google Scholar - 10.MP VIII. 126-9.Google Scholar
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*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.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.Newton
*Principles*I.29–39.Google Scholar - 14.MP VIII.597-599.Google Scholar
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