Tychonic worries on Newton: comments from Book III of the 1822 Geneva Edition of Principia Mathematica

The third book of Isaac Newton's Principia Mathematica Philosophia Naturalis rigourously established the case for heliocentrism by integrating observations and Kepler's laws. It is structured around two main hypotheses: first, that the cosmos has a static centre located at the centre of planetary motion, and second, that if the Earth itself moved, this would concord with observational data. The first hypothesis directly mentions the possibility of having the Earth as a centre, even if all the propositions claim that the correct centre is the Sun. The Minim Friars Thomas Le Seur (1703-1770) and François Jacquier (1711-1788), along with their editor Jean-Louis Calandrini, chose to collaborate and publish their influential commentary in Geneve [Newton I. 1822 Philosophiae naturalis mathematica principia, auctore isaaco newtono, eq. aurato, perpetuis commentariis illustrata, communi studio pp. thomae le seur et francisci jacquier ex gallicana minimorum familia, matheseos professorum. vol. 4. Glasgow, Scotand: Duncan]-probably to avoid the Catholic prohibition on promoting heliocentrism. This article examines key contributions by these commentators, highlighting their strong scientific focus and commitment to strengthening heliocentric principles in astronomy. It also discusses the educational aim evident in many extensive notes, especially on propositions that stress the transition from geo-heliocentric to heliocentric perspectives (notably propositions 4, 13, 14 and 16).This article is part of the theme issue 'Newton, Principia, Newton Geneva Edition (17th-19th) and modern Newtonian mechanics: heritage, past & present'.