The principles of Galilei-Newton's theories consist of two laws: the law of inertia, formulated already by Galilei, and the law of gravity, added later by Newton. And even though we must give up any attempt of explanation of these two basic principles, we must so much more strongly insist on having at least a clear statement of their content; and even on this point we shall encounter several difficulties. These difficulties will force us to divide these laws in a greater number of simple basic ideas, in a greater number of fundamental principles.