From a first comparison between the works of Vincenzo Riccati and those of his father Jacopo, some differences between the scientific character of the two scholars clearly emerges: compare the versatile style, typically encyclopedic, of Jacopo, with Vincenzo's interests which appear to be concentrated on mathematical science and physics. Vincenzo's favorite field of research is analysis, in particular setting out the analytical treatment of mechanical problems, conducted by solving differential equations, properly constructed.

From a theoretical point of view, 'De usu motus tractorii' is the culmination of the old way of geometrically solving problems by the construction of curves. Vincenzo Riccati, somehow, put an end to this trend by showing that one could construct in a simple continuous way all transcendental curves from the differential equations that define them. From the practical point of view, the memoir of 1752 provides a very general theoretical model to explain, in a unified way, how a large number of traditional methods (those before 1750) worked and also future methods .... However, the work of Vincenzo Riccati did not bring him fame and has virtually been forgotten. It was clearly little read and little circulated. It probably came too late, at the end of the period of construction of the curves, when geometry has given way to algebra, and when series became the tool of choice to represent the solutions of differential equations. Although original and brilliant, it became immediately obsolete.

Riccati and Saladini also considered the principle of the substitution of infinitesimals in the 'Institutiones analyticae' Ⓣ, together with the application of the series of integral calculus and the rules of integration for certain classes of circular and hyperbolic functions. Their work may thus be considered to be the first extensive treatise on integral calculus .... Although both Newton and Leibniz had recognized that integration and derivation are inverse operations, they had defined the integral of a function as a second function from which the former function is derived; Riccati and Saladini, on the other hand, considered differentiation to be the division of a quantity into its elements and integration to be the addition of these elements and offered examples of direct integrations.

Given points A and B find the point C on a circular mirror so that a ray of light from A is reflected at C to B.

Riccati was also skilled in hydraulic engineering and, under government commissions, carried out flood control projects along the Reno, Po, Adige, and Brenta rivers. He was much honored for this work, which saved the Venetian and Bolognan regions from disastrous flooding, and was made one of the first members of the Società dei Quarante.