This paper presents a synthetic excursus across the centuries about the differential calculus. Archimedes represents the first sample of the building with his exhaustive method to which addictive and original contributions have been added by Leibniz and Newton giving bones to this new branch of mathematics. In fact by means of the discovery of the differentiation and of the integration the main line towards the infinitesimal calculus will be opened. Here it is possible to find out the pathos of the scientists as well as of the ones who have made them live.