Saturday, May 03, 2008

Large number of small changes

The methods that Newton uses to prove 1/r2 are highly geometrical; .......At first sight, too, this geometry looks classical,......Yet, on closer inspection, we see that it is slightly different; Newton is doing new things with it that had not been done before. For time and again, Newton, approaches a deep and difficult dynamical problem by imagining the whole motion as split up into a very large number of very small changes.

And this deceptively simple idea is the basis for one of the greatest advances in the whole of mathmatics...

Acheson D., 1089 and all that, OUP