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 .

How would the previous sentence be correctly capitalized?
Answer: 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 .
large terrace on the front with a lot of sun.

How would the previous sentence be correctly capitalized?
Answer: Large terrace on the front with a lot of sun.
the greatest interest among the games are ball games. strange as it is football, basketball, and volleyball at the most popular games.

How would the previous sentence be correctly capitalized?
Answer: The greatest interest among the games are ball games. Strange as it is football, basketball, and volleyball at the most popular games.
these laws specify factors which the council must take into consideration when you develop guidelines.

How would the previous sentence be correctly capitalized?
Answer: These laws specify factors which the Council must take into consideration when you develop guidelines.