He transmitted Lagrange's ideas to his pupils, including Ottaviano Fabrizio Mossotti, Antonio Bordoni and Gabrio Piola.

Brunacci believed that Lagrange's approach, developed in the "Théorie des fonctions analytiques", was the correct one and that the infinitesimal concept was to be banned from analysis and mechanics.

Brunacci passed his idea of analysis on to his students, among which Fabrizio Ottaviano Mossotti, Gabrio Piola and Antonio Bordoni.

He cooperated with the public administration, in 1805 he was in the Committee for the Naviglio Pavese (Pavia Canal) project and the following year as inspector of Waters and Roads.

In 1809 he joined the Committee for the new measurements and weights system and from 1811 he was inspector general of Public Education for the entire Italian Kingdom.