Un teorema di Newton
V.I. Arnol'd, "Kepler's Second Law and the Topology of Abelian Integrals (According to Newton)", Kvant Selecta.
"Kvant (Russian: Квант for "quantum") is a popular science magazine in physics and mathematics for school students and teachers, issued since 1970 in Soviet Union and continued in Russia. The idea of the magazine was introduced by Pyotr Kapitsa. Its first chief editors were physicist Isaak Kikoin and mathematician Andrei Kolmogorov.
In 1999, American Mathematical Society published translation of selected articles from Kvant on algebra and mathematical analysis as two volumes in the Mathematical World series. Yet another volume, published in 2002, included translation of selected articles on combinatorics."
"In modern notation, Kepler's equation can be written as x-esinx = t. This equation has played an important role in the history of mathematics. Since the time of Newton, mathematicians have looked for a solution that expresses x as a series expansion in powers of the eccentricity e. The corresponding series converges for |e| \le 0.6627434... In attempting to explain the origin of this constant, Augustin Cauchy created complex analysis*. Numerous fundamental mathematical notions and results, such as Bessel functions, Fourier series, the topological index of vector fields, and the argument principle in the theory of complex functions, also made their first appearance in investigations connected with Kepler's equation."
* cfr. A. Wintner, "The Analytical Foundations of Celestial Mechanics", p. 217, footnote....Continua