After completing his mathematical and theological studies, he moved to Rome, where he assumed the position of professor at the Collegio Romano.
In 1651, Casati was sent on a mission to Stockholm in order to gauge the sincerity of Christina of Sweden's intention to become Catholic.
The astronomical work Terra machinis mota (1658) imagines a dialogue between Galileo, Paul Guldin, and Marin Mersenne on various intellectual problems of cosmology, geography, astronomy and geodesy.
For example, they discuss how to determine the Earth's dimensions, floating bodies, the phenomena of capillarity, and also describe the experiment on the vacuum made by Otto von Guericke in 1654.
Casati confuted the existence of both vacuum and atmospheric pressure, but he did not rely entirely on scientific observation, and refers to Catholic thought in order to back his claims.