Raffaele Pisano (Lille): “Analysing Mathematical Methodology in Newton’s Principia Geneva Edition ([1739–1742] 1822): The Relationship Physics–Mathematics”

Abstract: The third edition of Newton’s (1642–1727) Principia Mathematica Philosophiae Naturalis (1726) adds some new important results to the two previous ones (1687, 1713). Between 1739–1742 a new deeply commented edition was published in Geneva (1822). The editors were the mathematicians: Thomas Le Seur (1703–1770) and François Jacquier (1711–1788), belonging to the minim friars. The Swiss scientist Jean–Louis Calandrini (1703–1758) gave a fundamental support to the edition with his physical notes on mechanics and mathematical describing. The comments (footnotes) are more extensive than the Newtonian text. This edition is composed by 3 vols., (the third one by 2 tomes). Newton’s propositions are detailed annotated and commented: mathematical and physical aspects, geometrical proofs, methodology, discoveries and advancements after Newton’s works are cleverly reported. Based on ours previous works – and a current project (Oxford University Press, 5 vols. expected 2020) – we mainly aim to understand and explain: 1) the genesis of the edition, how did the editors grasp and expound Newton’s methods? 2) the development of mathematical physics in the fertile period 1725–1740, 3) a comparison between the approach to mathematical physics of that epoch and Newton’s original one, 4) the role of the Geneva Edition, why the necessity to publish a commented edition was felt?  In our talk, we present Newton’s Geneva edition and selected case studies on the relationship between physics and mathematics read by means of history and historical epistemology of science.