Lavori virtuali e principio conservativo nel Mechanicorum Liber di Guidobaldo del Monte

From a historical point of view, the principle of virtual work and the so-called “principle of conservation” follow different paths. Some authors identified a first statement of the principle of virtual works in pseudo-Aristotle’s Mechanical Problems. The principle of virtual work was defined by Bernoulli in this way: “for a system of forces that maintains a point, a surface, on a body in equilibrium, the sum of positive energies equals that of negative energies, considered with their absolute value”. According to some authors, we can find signs of the “principle of conservation” in Galileo Galilei’s Mechanics: “that whatever is gained in force by their means is lost in time and in speed”. In Guidobaldo del Monte’s Mechanicorum Liber the concept of virtual work and the relation of compensation of force, time, weight and space seem to be connected. In this essay, I will investigate this connection. Firstly, I present the well-known statements about the roots of the principle of virtual works and the “principle of conservation”. Secondly, I will examine the procedures used by Guidobaldo to study the behaviour of simple machines in equilibrium. Finally, I will analyse the relation between the equilibrium conditions of systems subjected to constraint reactions and the compensation process that allows the increase of force in the simple machines.