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