The discussion centers on the historical methods of differentiation developed by Newton and Leibniz, specifically focusing on their algorithms and processes for calculating derivatives. Participants express interest in exploring the historical context and examples of these techniques.
Participants generally agree on the historical significance of Newton and Leibniz's contributions to differentiation, but there is no consensus on the specific algorithms or processes they used, as some participants are still seeking concrete examples.
The discussion highlights a lack of specific examples of the historical algorithms, indicating a dependence on the provided references for further exploration. There are also unresolved aspects regarding the interpretation and application of infinitesimals in their methods.
Here is the infinitesimal definition of the derivative that Leibniz (and Newton implicitly) used: df = f(x+dx) - f(x), and df/dx = (f(x+dx) - f(x))/dx. For instance, if f(x) = x^2, then df = (x+dx)^2 - x^2 = 2xdx + dx^2, and then you get rid of dx^2 because it's the square of an infinitesimal, so it's infinitely smaller than 2xdx. Thus we have df = 2xdx, so df/dx = 2x.DeeAytch said:Thank you for responding.
I am looking specifically for examples of the algorithms as they were employed historically. If nobody can provide that, then I suppose I'll dig through the sources you listed.