Though competent, Cavalleri is little remembered. He was perhaps doubly unfortunate; firstly, in an age that produced figures such as the
Bernoulli family, Euler,
Lacaille,
D'Alembert,
Reaumur, and
Lagrange, even a prominent professor of mathematics is easy to overlook. Secondly, Cavalleri's essay on tides, though penetrating in that he recognised debatable points in both Cartesian and Newtonian theory, amounted to the last substantial support for the Cartesian theory of vortices; in effect a futile rearguard action. It is true that Fontenelle has been referred to as the last defender of the vortices, but unlike Cavalleri he wrote as an interpreter and populariser, rather than as an analyst or formulator of material theory. On the one hand Cavalleri's objection to Descartes' theory was mainly that it effectively dismissed the obvious tidal influence of the sun. On the other he rejected Newton's theory of remote gravitational attraction. The latter idea might seem naive, but even in 21st century
theoretical physics there are echoes of dissatisfaction with the concept of
action at a distance. He tried to construct a theoretical basis for an inverse square law of gravitational attraction arising from Cartesian vortices. Newton however, had already raised theoretical objections to Descartes' vortex theory, and Cavalleri not only failed to refute the objections, but misinterpreted a modified vortex theory by
Philippe Villemot which attempted to reconcile vortices with Newtonian attraction. Cavalleri's essay, although having received the prize from the Académie, more or less lapsed into obscurity thereafter. Possibly this was because of its being biased towards Cartesian rather than Newtonian gravitational theory;
Pope Benedict XIV had ordered two priests to produce a new, annotated edition of
Newton's Principia. In the commentary the other three winning essays were included, but Cavalleri's was omitted. ==Works==