In 1620, he went to Dole, also part of the Spanish Empire, to teach mathematics and learn theology in view of being ordained to the priesthood.
He there advised Philip IV, king of Spain, on military questions, specially fortifications, and taught mathematics as well.
His most famous book is Theoremata de centro gravitatis partium circuli et ellipsis (1632) in which he determined the centre of gravity of the sector of a circle, for the first time.
At the request of della Faille's family, the Flemish painter Anthony van Dyck painted a portrait of the mathematician in 1629.
The portrait shows the mathematician in his Jesuit outfit with a set of tools (including a compass,[2] a t-square and a globe).