I am sorry not to have known the mathematician who first made use of this method because I would have cited him. Regarding the researches of d'Alembert and Euler could one not add that if they knew this expansion they made but a very imperfect use of it. They were both persuaded that an arbitrary and discontinuous function could never be resolved in series of this kind, and it does not seem that anyone had developed a constant in cosines of multiple arcs, the first problem which I had to solve in the theory of heat.