After 2 month long search on the net, I was lucky enough to find a pdf on how Newton found the series for sine. It was a beautiful derivation mostly geometrical. But he used the Binomial Series.

Now what I look for is Newton's proof (sort of proof) of the Binomial Series . I have read that he interpolated areas under circles and hyperbolas but a succinct answer jumps in terms of what he actually did without is what I am looking for. I know he made tables then followed the pattern. But there must be a lot of geometrical work too which would have led him to this point. All sorts of interpolation.

That's what I want to understand. What did he actually do ? What was his geometrical work regarding it as well as what was his sort Interpolation of areas

  • $\begingroup$ Complete mathematical works of Newton are available on line. $\endgroup$ – Alexandre Eremenko Feb 12 '17 at 7:28
  • $\begingroup$ @AlexandreEremenko D.T Whiteside is not free. De Analysi ( series) is only in latin $\endgroup$ – Shashaank Feb 12 '17 at 7:30
  • $\begingroup$ Do you read Russian? Russian translation is free. $\endgroup$ – Alexandre Eremenko Feb 12 '17 at 7:31
  • $\begingroup$ @AlexandreEremenko No sorry . I don't know Russian. Only Hindi and English . I searched a lot but de Analysi is only in Latin and my ever answer is in de analysi ( I guess) $\endgroup$ – Shashaank Feb 12 '17 at 7:33
  • $\begingroup$ Why does the title mention Gregory, when the body doesn't at all? $\endgroup$ – Francois Ziegler Apr 1 '17 at 1:00

See : Derek T. Whiteside, Newton's Discovery of the General Binomial Theorem , Math. Gaz. 45 (Oct.1961).

For an English transaltion of De analysi per aequationes numero terminorum infinitas (1669) see :

  • $\begingroup$ Thanks a lot !! This was precisely what I was looking for . Huge thanks ! $\endgroup$ – Shashaank Feb 12 '17 at 10:34

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