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Newton’s Discovery of the General Binomial Theorem

Published online by Cambridge University Press:  03 November 2016

Extract

Newton was the greatest mathematician of the seventeenth century. Today, almost three centuries afterwards, we are just beginning to realize the full extent and variety of his achievement. Much of his mathematical work has never been published (though it ranges far through the fields of projective geometry and general point-correspondences to number theory and an exhaustive treatment of interpolation by finite differences) and is now, with few exceptions, to be found only in little known manuscripts in the Cambridge University Library. But Newton is remembered above all, and following his own wish, for his creation of the fluxional calculus and the theory of infinite series, two strands of mathematical technique which he bound inseparably together in his “analytick” method.

Type
Research Article
Copyright
Copyright © Mathematical Association 1961

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References

1. See my article’ ‘Henry Briggs: The Binomial Theorem anticipated”. Math. Gazette, Vol. XLV, pp. 912.Google Scholar
2. Compare (CUL. Add 3968.41:85) “In the beginning of the year 1665 I found the method of approximating series & the Rule for reducing any dignity of any Binomial into such a series. In those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more than at any time since.”Google Scholar
3.Especially by Child, J. M.: “Newton and the art of discovery,” in “Isaac Newton, (1642-1727).” London, 1927: 117129; and by Hofmann, Jos. E.: “Studien zur Vorgeschichte der Prior itatstreites zwischen Leibniz und Newton um die Entdeckung der hoheren Analysis. 1. Materialen zur ersten Schaffensperiode Newtons (1665-1675)” = Preuss, Abh. d.. Akad. d. Wiss. Math.-Naturw Kl. 2. Berlin, 1943.Google Scholar
4. Add 3968.41 76.Google Scholar
5. Compare Add 4000 14v: “(I) made these annotations out of Schooten & Wallis in winter between the years 1664 and 1665. At w ch time I found the method of Infinite series. And in summer 1665, being forced from Cambridge by the Plague, I computed ye area of ye Hyperbola at Boothby in Lincolnshire to two & fifty figures.” Such calculations, varying in length from 47D-57D, are to be found widely in Newton’s 1665 manuscripts.Google Scholar