In the Age of Enlightenment, we can say that the mechanics inherited from Newton and Leibniz will undergo a series of improvements, mainly that implemented by Lagrange with Analytical Mechanics (1788). In the 100 years that elapsed from 1687 (publication of Principia) to Lagrangian Mechanics, the most notable fact is the transition from Newton's geometric mechanics to its formalization in an algebra, promoted by Lagrange, but passing through the differential formulation proposed by Euler around 1750. In the text we highlight the role played by d'Alembert, giving a more analytical character to the mechanical problems encountered and rehearsing a reform of Newton's laws when he proposes a principle that bears his name.