[1] Manfredi was one of a group of young men at the University who became interested in the techniques of Cartesian geometry and differential calculus, and who engaged in experiments and astronomical observation.

[2] Eustachio Manfredi became more interested in astronomy, but Gabriele persisted with mathematics, studying the works of Leibniz and of Johann and Jacob Bernoulli on infinitesimal calculus.

[1] After graduating, Gabriele went to Rome at the end of 1702, where he became librarian to Cardinal Pietro Ottoboni, a historian, antiquarian and astronomer.

[1] In 1708 Manfredi began working for the Chancellery of the Senate of Bologna, where he rose to the rank of first chancellor and remained until he retired in 1752.

[3] In his work De constructionae aequationum differentialium primi gradu (1707) Manfredi set forth the results he had obtained so far in solving problems related to differential equations and the foundations of calculus.