The ordinary operations of algebra suffice to resolve problems in the theory of curves.
Not everyone found Lagrange's approach to the calculus the best however, for example de Prony wrote in 1835:-
Lagrange's foundations of the calculus is assuredly a very interesting part of what one might call purely philosophical study: but when it is a case of making transcendental analysis an instrument of exploration for questions presented by astronomy, marine, geodesy, and the different branches of science of the engineer, the consideration of the infinitely small leads to the aim in a manner which is more felicitous, more prompt, and more immediately adapted to the nature of the questions, and that is why the Leibnizian method has, in general, prevailed in French schools.
The second work of Lagrange on this topic Leçons sur le calcul des fonctions appeared in 1800.
Napoleon named Lagrange to the Legion of Honour and Count of the Empire in 1808. On 3 April 1813 he was named grand croix of the Ordre Impérial de la Réunion. He died a week later.
J J O'Connor and E F Robertson