returning to turin in early 1765, lagrange entered, later that year, for the académie des sciences prize of 1766 on the orbits of the moons of jupiter. d'alembert , who had visited the berlin academy and was friendly with frederick ii of prussia, arranged for lagrange to be offered a position in the berlin academy .

This is all lower case. Can you fix that?
Returning to Turin in early 1765, Lagrange entered, later that year, for the Académie des Sciences prize of 1766 on the orbits of the moons of Jupiter. D'Alembert , who had visited the Berlin Academy and was friendly with Frederick II of Prussia, arranged for Lagrange to be offered a position in the Berlin Academy .