Newton's early computational method for dynamics (Q1316105)

On the margin of a letter to Hooke of December 13, 1679, Newton drew a diagram for the orbit of a body in a constant central field. Since the first publication of this letter in 1929, several Newton scholars have pointed out that the diagram contains a considerable error, which has long been attributed to some failure in Newton's method of computation. In this paper, it is demonstrated with an iterative method based on Newton's mathematical development of the concept of curvature, that Newton's computation of the orbit was correct: he made an error while drawing the figure representing the orbit, but not in calculating it.