I will discuss how the so-called "Jesuit edition" (1739-42) of the Principia attributed to Thomas Le Seur and François Jacquier was actually organized and financed by Jean-Louis Calandrini and the printer Barrillot of Genève. How could a representative of a staunch Calvinist family, prominent in Genève, cooperate with two minim Catholic friars based in Rome? Which roles Calandrini on the Swiss side, and Le Seur and Jacquier on the Roman side played? It will be shown that, contrary to what is generally believed, Calandrini wrote most of the annotations, especially those related to book 3. I will claim that the subdivision of labour between the Swiss and the minim friars reveals that they acted under different local pressures. In Switzerland the Principia had been attacked by prominent members of the Bernoulli family (most notably, Johann and his nephew Nicolaus). Annotating the propositions that had been criticized by the Bernoullis might have been somewhat embarrassing for Calandrini. On the other hand, one of the main objectives of book 3 of the Principia was to show the truth of the Copernican hypothesis, a feature that could not be ignored in Rome, not even during the enlightened papacy of pope Lambertini (1740-1758). Annotating book 3 could not be easily done without revealing an approval for Newton's achievement in the cosmological debate between heliocentrism and geocentrism. It seems likely that Calandrini and the minims subdivided their labour in function of exigencies determined by their association to different social contexts.