That action is best which procures the greatest happiness for the greatest numbers.Hutcheson: Inquiry concerning Moral Good and Evil, sect. 3. (1720.)
Priestley was the first (unless it was Beccaria) who taught my lips to pronounce this sacred truth,that the greatest happiness of the greatest number is the foundation of morals and legislation Bentham: Works, vol. x. p. 142.
The expression is used by Beccaria in the introduction to his Essay on Crimes and Punishments. (1764).