In his Geometria del Compasso (Pavia, 1797), he proved that any geometrical construction which can be done with compass and straightedge, can also be done with compasses alone. However, the priority for this result (now known as the Mohr–Mascheroni theorem) belongs to the Dane Georg Mohr, who had previously published a proof in 1672 in an obscure book, Euclides Danicus. This problem was the source of a musical composition called "Mascheroni Circles", performed by David Stutz on the album Iolet.
In his Adnotationes ad calculum integrale Euleri (1790) he published a calculation of what is now known as the Euler–Mascheroni constant, usually denoted as (gamma).
He died in Paris.