This article maps out the lexical landscape of precision from the late seventeenth to the early eighteenth century and investigate the various meanings of precision, both as a word and a concept, within the Paris Observatory and beyond. It argues that precision was first an attribute of instruments supposed to produce numerical measurements, like clocks and divided circles or sectors attached to optical devices. Less often, precision was applied to observers, the handling of instruments, and observational methods, including mathematical corrections applied to raw data. When all these aspects were combined the numerical result finally was also deemed to be precise. Moving to the debate about the shape of the Earth that shook the Academy of Sciences in the 1730s, it follows the way in which wider audiences were conveyed the various meanings of precision. Between the Cartesian resistance to the emergence of a professional science of precision and the pedagogical approach followed by the Newtonians such as Maupertuis, it argues that Cassini III embraced the professionalism of modern science, but did not feel that methodological precision was out of the reach of an educated public. While Maupertuis has seemed content with a discussion focusing on the precision of instruments and results, Cassini III set himself the hefty task of producing an accessible account of precision as a method of inquiry.