The symbol π in modern mathematics corresponds to the numerical relation between the circumference of a circle to its diameter in ancient Chinese texts. A pair of numbers representing this numerical relation is referred to by the term lü, which is a concept that lies as the basis of mathematical knowledge and proofs in ancient texts written in Chinese. A pursuit for a more precise lü has been one of the works of generations of practitioners of mathematics. This not only can be observed in the mathematical Canon and its different layers of commentaries, in which the numerical relation has been much more accurately acquired before the end of the sixth century in terms of our modern knowledge of π, but also existed in musical temperament texts produced by ancient scholars who are usually excluded from the modern general historical account of mathematics. These musical temperament texts attest to a scientific culture that is different from that of mathematical practice on which modern historians of mathematics usually focus. This report will take an example around the end of the 16th century, Zhu Zaiyu (1536–1611), to show that the question of π has been discussed in ways that are different from those in former mathematical works. This report sheds light on the differences between the practices of dealing with lü of a circle and of proving the correctness in the two different scientific cultures.

Scholars believe that the early print edition of the Archimedean corpus used by Galileo, Fermat, Descartes, Newton, and other proficient mathematicians was David de Flurance Rivault’s ‘Archimedis opera quae extant novis demonstrationibus commentariisque illustrata’ (1615), a conclusion further supported by marginalia and archival evidence. Rivault, however, did not write for an audience already trained in the mathematical sciences. Instead, his edition targeted the noblesse d’épée—members of the French nobility who, in his experience as a soldier and tutor for Louis XIII, often undervalued the utility of mathematics. To address their needs and interests, Rivault significantly adapted the geometry in Archimedes’ works and repeatedly emphasized the practical applications of mathematics, particularly in reasoning and warfare.

This presentation examines Rivault’s pedagogical strategies in his treatment of ‘Sphere and Cylinder’ and their broader implications for the reception of Archimedes. It explores how Rivault framed Archimedes as a figure of nobility and military heroism in the supplementary material alongside substantial modifications to the mathematical content. These modifications included revised definitions, the addition of propositions, and a complete reworking of demonstrations into a clear Proclean schema. Although Rivault sought to popularize and contextualize ancient mathematics within the socio-political realities of seventeenth-century France, his heavily mediated edition ultimately found an audience with readers who arguably did not require such an extensive adaptation. The presentation concludes by exploring the reasons for the popularity of Rivault’s reworked Archimedes and what this reveals about the dynamics of the reception of ancient Greek mathematics in early modern Europe.