A Forgotten Differential Equation Studied by Jacopo Riccati Revisited in Terms of Lie Symmetries

In this paper we present a two parameter family of differential equations treated by Jacopo Riccati, which does not appear in any modern repertoires and extend the original solution method to four equations, translating Riccati approach terms Lie symmetries. To get complete solution, hypergeometric functions come into play, which, course, were unknown Riccati’s time. Re-discovering introduced called himself dimidiata separazione (splitted separation), arrive at closed form integration equation, more general one contribution, also known repertoires.