Mechanics in the Querelle des Anciens et des Modernes.

The debate about the superiority of ancient versus modern culture, known as the Querelle des anciens et des modernes, also found expression in conflicting positions about the developing mathematical methods of natural philosophy. Isaac Newton explicitly referred to the authority of Euclidean geometry as a justification for the conservative form of the proofs in his Principia Mathematica, where he avoided the use of analytic geometry and infinitesimal calculus, the central innovations of seventeenth-century mathematics, as much as possible. Rather, he modeled his proofs, just like the overall structure of the treatise, as closely as possible on Euclid’s geometry. A century later, however, Joseph-Louis Lagrange announced in the introduction to his Mechanique Analytique that no geometrical diagrams would be found there and that Newtonian mechanics was presented exclusively in the form of analytic equations. This essay analyzes the relationship of this radical change in the theoretical methodology of mechanics to the actors’ ideas about ancient science and its authority. It also discusses the consequent development of a conception of ancient science as distinct from modern science and the relation of this conception to a history of science in our contemporary sense.