The pre-Galilean geometricization of motion: Giovanni da Casale's Quaestio de velocitate and the Italian Reception of the Treatise De latitudinibus formarum

• Applicant: Dr. Daniel Antonio Di Liscia
• Subject Area: History of Philosophy ; History of Science
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 547575878

The research project investigates the problem of the geometrisation of motion within the late medieval tradition of the calculators. It is closely related to two previous projects by the same applicant on natural philosophy, logic and mathematics of the late Middle Ages. This project focuses mainly on three documents that prove that a mathematical treatment of motion was already present within the framework of Aristotelian natural philosophy before Galileo. An examination of this problem will shed new light on the question of continuity/discontinuity between late medieval natural philosophy and modern physics. The project also aims to open up new perspectives in the field of contemporary philosophy of science. In this context, the mathematical treatment of the infinite and the various medieval theories on the composition of the continuum will also be considered. The above-mentioned documents will be critically edited and interpreted: 1) The long and complex question on motion according to the category of quality by Giovanni da Casale (c. 1350), the three questions by Biagio Pelacani da Parma (c. 1350-1416) on the treatise De latitudinibus formarum, which is usually attributed to Jacobus de Sancto Martino in the current scholarship, and an anonymous question closely related to Biagio's questions. Casale's question is conveyed (very inadequately) in an old printed edition from 1505, as well as in at least thirteen other manuscripts (some of which were identified by the applicant for the first time for this project). Pelacani's three questions are conveyed in at least two old printed editions and seven manuscripts, while the first question most likely survived in two different versions. The anonymous question Utrum omnis forma habeat latitudinem nobis presentabilem per figuras geometricas is known only in the Venice manuscript, Biblioteca Nazionale Marciana VI, 62, ff. 63ra-68ra and has survived only in fragments. For the interpretation of the texts, above all six areas of discussion will be considered, which are typical of the calculator’s approach: 1) The twofold point of view in the analysis of movement; 2) The application of the "analytical languages" (herein: a. De maximo et minimo, b. De primo et ultimo instanti or de incipit and desinit, c. De actione et reactione, d. De proportionibus motuum, e. De intensione et remissione formarum); 3) The technical terminology: perfectio, latitudo, mensura; 4) The geometrical system of representation; 5) The epistemological context; 6) The ontological background. Within the project, two international workshops will be organized: one on "Logic, Mathematics, and Motion Analysis in Italy" and another on "Formulations, Proofs, and Interpretations of the Mean Value Theorem".

• DFG Programme: Research Grants