A historical outline of the theorem of implicit functions

In this article a historical outline of the implicit functions theory is presented starting from the wiewpoint of Descartes algebraic geometry (1637) and Leibniz (1676 or 1677), Johann Bernoulli (1695) and Euler (1748) infinitesimal calculus. The critical contribution is highlighted due to the Italian mathematician Ulisse Dini who settled the matter in modern form inside the real functions theory. The paper supplies the documented proof of Dini's priority in the so called implicit functions theorem. In the meanwhile the historical lack in attributing the theorem to Dini can be ascribed to the fact that he published his proof only in his Lezioni [3], written for supporting his teaching.