Billy taught mathematics and theology at Jesuit colleges all his life, in particular those colleges which were in the administrative region of Champagne, a region which covered the present-day northeastern French districts of Marne and parts of Ardennes, Meuse, Haute-Marne, Aube, Yonne, Seine-et-Marne, and Aisne. From 1629 to 1630 he taught mathematics at the Jesuit College at Pont à Mousson, during this time he was still studying theology.
From 1631 to 1633 Billy taught mathematics at the Jesuit college at Rheims. He became a close friend of Bachet, who was one of his pupils at Rheims. After this Billy taught in Grenoble and then was rector of a number of Jesuit Colleges in Chalons, Langres and in Sens. From 1665 to 1668 he was professor of mathematics at the College of Dijon. One of his pupils in Dijon was Ozanam but this was before he was appointed to the chair of mathematics so, since there were no formal mathematics classes at the College, he taught Ozanam privately.
Billy corresponded with Fermat and produced a number of results in number theory which have been named after him. Billy had collected many problems from Fermat's letters and, after the death of his father, Fermat's son appended de Billy's collection under the title Doctrinae analyticae inventum novum as an annex to his edition of the Arithmetica of Diophantus (1670). Itard writes in :-
It is an elaborate study of the techniques of indeterminate analysis used by Fermat and, on the whole, it explains them correctly. From it one can guess at Fermat's general line of activity in a field in which there are few pertinent documents.He also published astronomical tables such as Tabulae Lodoicaeae seu universa eclipseon doctrina tabulis, praeceptis ac demonstrationibus explicata. Adiectus est calculus, aliquot eclipseon solis & lunae, quae proxime per totam Europam videbuntur . This was a table of eclipses for the years 1656 to 1693 and included solar and lunar tables. Billy is also important in being one of the first to reject the role of astrology in science, along with superstitious notions about the malevolent influence of comets.
Among Billy's most important works are: Abrégé des préceptes d'algèbre (1637); Nova geometricae clavis algebra (1643); Tractatus de proportione harmonicae (1658); and Diophantus geometria sive opus contextum ex arithmetica et geometria simul (1660).
Article by: J J O'Connor and E F Robertson