LAGRANGE, GIUSEPPE LUIGI. – Mathematician, born in Turin on 25 January 1736, died in Paris on 10 April 1813. His name was originally Lagrangia. A student at the Military School of Artillery in Turin, he was appointed a teacher there in 1755. From that time began his scholarly production and activity, which led him to found a private society among scholars devoted to science; this was later established as the Academy of Sciences and is still one of the foremost Italian academies.
In the proceedings of the Society he published important works that earned him the esteem and patronage of D'Alembert, through whom he shortly afterward obtained the directorship of the Academy of Berlin, where he remained for twenty years. In 1787 he moved to Paris.
He occupied himself with fundamental analytical questions concerning: the theory of functions; the simplification of infinitesimal calculus; the solution of numerical equations by separating the roots through the method of transforming the squares of the differences between the roots themselves; the calculation of functions by means of power series or polynomials, with a synthetic expression of the approximation (remainder); the integration of differential equations and the solution of finite-difference equations; and research into the periodic variations of the motion of the planets.
L. was therefore a great analyst, but also a great expositor. In addition to the Traité de la résolution des équations numériques, he wrote the celebrated Mécanique analytique (Paris 1787), a monumental work in which, on the basis of two principles—that of virtual work, due to Galilei, and that of lost forces, due to D'Alembert—he rigorously deduced all the equations of equilibrium and motion, also making use of the coordinates that took their name from him, through which the aforementioned equations assume a more concise form.