But no carefully devised calculus can take the place of insight, observation and experience.
The well-known Treatise on Differential Equations appeared in 1859, and was followed, the next year, by a Treatise on the Calculus of Finite Differences, designed to serve as a sequel to the former work.
Hence, early empiricism makes ethics simply a calculus of pleasures ("hedonism").
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.
It is not, however, necessary that the notation of the calculus should be employed throughout.