We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, (...) for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline. (shrink)

RésuméDe l'delimination des causes finales par la mathématisation de la physique à l'hypothèse de Kant‐Laplace sur la formation du système solaire, puis au développement des sciences de la vie qui déterminent un nouveau champ de rationalité, le théme de la création au 18ème siècle est parti‐culièrement apte a manifester l'évolution des rapports entre sciences, philosophie et métaphysique, jusqu'à son progressif effacement dans des philosophies aussi differentes que celles de Diderot, Hume et Kant.