His reputation mainly rests on his Introduzione ad una teoria geometrica delle curve piane, which proclaims him as a follower of the Steinerian or synthetical school of geometricians.
In 1744 Alembert applied this principle to the theory of the equilibrium and the motion of fluids (Trcite de l'equilibre et du mouvement des fluides), and all the problems before solved by geometricians became in some measure its corollaries.
In 1747 he applied his new calculus to the problem of vibrating chords, the solution of which, as well as the theory of the oscillation of the air and the propagation of sound, had been given but incompletely by the geometricians who preceded him.
While eulogizing poverty and philosophy, he attacked the gods, musicians, geometricians, astrologers, and the wealthy, and denied the efficacy of prayer.
For this post he was especially fitted by his acquaintance with recent advances in science, and by his skill in a classical severity of demonstration, acquired by a thorough study of the works of the Greek geometricians.