Write a report on Newtons discovery of the binomial series. Start by giving the statement of the binomial series in Newtons notation (see the epistola prior on page 285 of [4]
or page 402 of [2]). Explain why Newtons version in equivalent to Theorem 17 on page
807. Then read Newtons epistola posterior (page 287 in [4] or page 404 in [2]) and explain the patterns that Newton discovered in the areas under the curves y = (1×2) n/2
.
Show how he was able to guess the areas under the remaining curves and how he verified
his answers. Finally, explain how these discoveries led to the binomial series. The books
by Edwards [1] and Katz [3] contain commentaries on Newtons letters.
References:
1. C.H. Edwards, The Historical Development of the Calculus (New York: SpringerVerlag, 1979), pp. 178-187. e-book is available on the assignment material.
2. John Fauvel and Jeremy Gray, eds., The History of Mathematics: A reader (London:
MacMillan Press, 1987). e-book is available through UHWO library.
3. Viktor Katz, A History of Mathematics: An Introduction (New York: HarperCollins, 1993), pp.463-466.
4. D. J. Struik, ed., A Sourcebook in Mathematics, 1200-1800 (Princeton, NJ: Princeton University Press, 1969). e-book is available through UHWO library
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