The Historical Development of the Calculus pp 189-230 | Cite as

# The Calculus According to Newton

Chapter

## Abstract

When we say that the calculus was discovered by Newton and Leibniz in the late seventeenth century, we do *not* mean simply that effective methods were then discovered for the solution of problems involving tangents and quadratures. For, as we have seen in preceding chapters, such problems had been studied with some success since antiquity, and with conspicuous success during the half century preceding the time of Newton and Leibniz.

## Keywords

Fundamental Theorem Infinite Series Binomial Expansion Affected Equation Cosine Series
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.

## References

## Primary References

- [NP]D. T. Whiteside (ed),
*The Mathematical Papers of Isaac Newton*. Cambridge University Press, 1967–81, 8 volumes.MATHGoogle Scholar - [NW]D. T. Whiteside (ed),
*The Mathematical Works of Isaac Newton*. New York: Johnson Reprint, 1964. 2 volumes.MATHGoogle Scholar - [NC]H. W. Turnbull et al. (eds),
*The Correspondence of Isaac Newton*. Cambridge University Press, 1959–78. 7 volumes.MATHGoogle Scholar - [PM]F. Cajori (ed),
*Newton’s Mathematical Principles of Natural Philosophy*, A. Motte’s Translation Revised. University of California Press, 1934.MATHGoogle Scholar

## Secondary References

- [1]C. B. Boyer,
*The History of the Calculus and its Conceptual Development*. New York: Dover (reprint), Chapter V, 1959.MATHGoogle Scholar - [2]J. Hadamard, Newton and the Infinitesimal Calculus, in
*Newton Tercentennary Celebrations*. Cambridge: The Royal Society, 1947.Google Scholar - [3]P. Kitcher, Fluxions, limits, and infinite littleness—A study of Newton’s presentation of the calculus.
*Isis***64**, 33–49, 1973.MathSciNetMATHCrossRefGoogle Scholar - [4]L. T. More,
*Isaac Newton, a Biography*. New York: Dover (reprint), 1962.Google Scholar - [5]C. J. Scriba, The inverse method of tangents: A dialogue between Leibniz and Newton.
*Arch Hist Exact Sci***2**, 113–137, 1962.MathSciNetCrossRefGoogle Scholar - [6]D. T. Whiteside, Sources and strengths of Newton’s early mathematical thought, in R. Palter, (ed),
*The Annus Mirabilis of Sir Isaac Newton 1666–1966*. M.I.T. Press, 1970.Google Scholar - [7]D. T. Whiteside, The mathematical principles underlying Newton’s
*Principia Mathematica. J Hist Astron***1**, 116–138, 1970.MathSciNetGoogle Scholar

## Copyright information

© Springer-Verlag New York, Inc. 1979