The Notes to the Axioms or Laws of Motion in the Geneva Edition of Newton’s Principia.

The decomposition of forces, the movement of the gravity centre of a body or of a system of bodies, the impact and its rules are among the numerous crucial contributions given by Newton in his Principia. In the section Axiomata sive leges motus of his masterpiece Newton gave the fundamentals of these three topics. He was very clear, but he did not offer many examples and applications of his concepts. In contrast to this approach, the editors of the Geneva Edition supply a long series of examples and explanations in the notes (s) 24–105 of the first Book. Such notes are particularly significant for the history of mathematics and physics because they allow us to understand what the problems related to the theory of collisions, the construction of machines, the movement of the gravity centre of system of bodies or of a rigid body were. Therefore, the exposition of the main content of these notes will allow the reader to grasp how Newton’s approach was developed and used in the 30 s of the eighteenth century in order to solve a series of both practical and theoretical problems, but it also will permit us to understand the interrelation between Newtonian and non-Newtonian concepts within physics.