Early traces of the principle of virtual work in Hellenistic texts: Exegesis of problems 1, 2 and 3 in pseudo-Aristotle’s Mechanica Problemata

Abstract

Our aim is to try to trace, in the history of mechanics, the first formulation of the principle of virtual work (PVW). This important question is, of course, connected with the origin of the concept of kinematics and its relation with the concept of dynamics. Now it is widely accepted that the Principle of Virtual Velocities (later called Virtual Work) was known in a geometrical form by the author of the Greek text Mechanica Problemata (The Mechanical Problems). Indeed, this text does not appear to be a theoretical treatise but rather a collection of solved exercises, mainly concerning statics, the functioning of machines and some dynamics. In this paper we present our exegesis of the first three problems of the Mechanica Problemata, because we believe that deeply understanding its content may allow us to clarify the Greek origin of the Principle of Virtual Work, to locate in space and time the birth of mathematized mechanics and to prove that Renaissance mechanics derives from Greek sources.