Only after their deaths would it have gone to the Society, save an annual allowance of 40 onze for himself, which he posthumously donated to establish a chair of experimental physics at a Jesuit college.

[3] In the spring of 1755, he presented a brief memorandum to Emmanuel de Nay, count of Richecourt (1697–1768), the prime minister of the Grand Duchy of Tuscany, concerning an ambitious project: measuring the variation in the obliquity of the ecliptic with the great gnomon in Santa Maria del Fiore.

The document, preserved in the archives of the Opera del Duomo, bears in the margin the order to start work on the project immediately.

That same year, on July 18, Ximenes sent the Grand Duke of Tuscany a memorandum asking to be appointed professor of Geography at the Florentine "studio", or university, and the administration was so efficient that, exactly three months after the request, he was appointed Reader in Geography to His Imperial Majesty with a salary of 700 lire (equivalent to that of a workman) and a grant of 9,000 lire to buy the instruments necessary for practicing his profession.

In Ximenes' day, one of the astronomical problems debated in scientific circles was how to measure the secular variation in the obliquity of the ecliptic.

Its solution was thought to be a kind of benchmark for the new theory of gravity, since it could be calculated by taking into account the gravitational perturbation of Venus and the other planets.

Relations between the two got gradually worse especially after the case about the water of Lake Bientina which, at the end of the 1750s, led the two Jesuits to oppose each other in front of the Emperor in Vienna.