Today if I want to calculate an elliptical orbit of some object due to the gravity of another, I use Runge-Kutta integration, and I can see the individual steps I use shown in that article.
Back "in the day..." Kepler, Newton, and others might have used what we now call Kepler's Equation: $M=E-e \sin(E)$ where given M one had to solve for E.
I would like to see how Kepler, Newton, and similar contemporaries actually performed the calculation of the position in the orbit for a specified time. Are there reproductions, or images of their notes, showing the actual steps each of them used to solve this equation?
Did Newton or Leibniz also use some form of integration as an independent method to obtain the motion of an elliptical orbit as well? Are there images or reproductions of those calculations available anywhere?