Notes on mechanics and mathematics in Torricelli as physics-mathematics relationship in the history of science

In ancient Greece, the term “mechanics” was used when referring to machines and devices in general and intended to mean the study of simple machines (winch, lever, pulley, wedge, screw and inclined plane) with reference to motive powers and displacements of bodies. Historically, works considering these arguments were referred to as Mechanics (from Aristotle, Heron, Pappus to Galileo). None of the treatises entitled Mechanics avoided theoretical considerations on its object, particularly on the lever law. Moreover, there were treatises which exhausted their role in proving this law; important among them are the book on the balance by Euclid and On the Equilibrium of Planes by Archimedes. The Greek conception of mechanics is revived in the Renaissance, with a synthesis of Archimedean and Aristotelian routes. This is best represented by Mechanicorum liber by Guidobaldo dal Monte who reconsiders Mechanics by Pappus Alexandrinus, maintaining that the original purpose was to reduce simple machines to the lever. During the Renaissance, mechanics was a theoretical science and it was mathematical, although its object had a physical nature and had social utility. Texts in the Latin and Arabic Middle Ages diverted from the Greek and Renaissance texts mainly because they divide mechanics into two parts. In particular, al-Farabi (ca. 870-950) differentiates between mechanics in the science of weights and that in the science of devices. The science of weights refers to the movement and equilibrium of weights suspended from a balance and aims to formulate principles. The science of devices refers to applications of mathematics to practical use and to machine construction. In the Latin world, a process similar to that registered in the Arabic world occurred. Even here a science of movement of weights was constituted, namely Scientia de ponderibus. Besides this there was a branch of learning called mechanics, sometimes considered an activity of craftsmen, other times of engineers (Scientia de ingeniis). In the Latin Middle Ages various treatises on the Scientia de ponderibus circulated. Some were Latin translations from Greek or Arabic, a few were written directly in Latin. Among them, the most important are the treatises attributed to Jordanus De Nemore, Elementa Jordani super demonstratione ponderum (version E), Liber Jordani de ponderibus (cum commento) (version P), Liber Jordani de Nemore de ratione ponderis (version R). They were the object of comments up to the 16th century. The distribution of the original manuscript is not well known; what is certain is that Liber Jordani de Nemore de ratione ponderis (version R), finished in Tartaglia’s (1499-1557) hands, was published posthumously in 1565 by Curtio Troiano as Iordani Opvsculum de Ponderositate. In order to show a mechanical tradition dating back to Archimedes’ science, at least till the 40s of the 17th century, we present Archimede’s influence on Torricelli’s mechanics upon the centre of gravity (Opera geometrica).