LA LEGGE GRAVITAZIONALE DELL’INVERSO DEL QUADRATO NEI PRINCIPIA DI NEWTON

Abstract

We revisit the question concerning the accuracy of the inverse-square gravitational  law, as raised in section IX, book I of Newton’s Principia, and in some sections of book III. We argue that the problem has been thoroughly discussed and basically solved  by Newton himself. We point out in particular the relations with the well-known Bertrand’s theorem. Bertrand approached the same problem in more abstract terms. We remark, however, that much of Bertrand’s proof is essentially contained in Principia.