BRIEF HISTORICAL NOTES ON THE THEORY OF CENTRES OF GRAVITY 

 RAFFAELE PISANO 

University of Rome “La Sapienza”, Italy

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Abstract

In recent works I have analyzed the historical development of the foundations of the theory of the centre of gravity during the Renaissance up until the appearance of Torricelli’s (1608-1647) mathematical problem in his Opera Geometrica (1644).

In recent works I have analyzed the historical development of the foundations of the theory of the centre of gravity during the Renaissance up until the appearance of Torricelli’s (1608-1647) mathematical problem in his Opera Geometrica (1644). Here, I shall briefly provide you with some notes from my own studies and works in progress. I am going to explore Torricelli’s organization of  his mechanical theory to see if it has a remote foundation in Archimedean thought, not only for the use of such techniques as the Reductio ad Absurdum as seen in Archimedes’ work (287-212 B.C.), but also for the logical foundations he shared with Bonaventura Cavalieri (1589-1647) seen in Torricelli’s emerging analysis. In particular, I have studied the Suppositio and Propositio, set up by Archimedes from a logical and historical point of view, as rational criteria for the determination of the centres of gravity. This kind of investigation has been developed through two categories of historical interpretation: the order of ideas as an element of understanding the evolution of scientific thought on one hand; and on the other, the use of logic as an element of scanning and control of the organization of the theory. This kind of examination of a theory through the use of categories is valid since the historical exploration of the foundations will not be analyzed using the traditional approach. Obviously, the content of this work could appear potentially factious, since it cannot be assumed to be the only possible perspective.  Key words:  Archimedes's rules, Ad Absurdum proof, Torricelli’s centre of gravity, Principle of virtual works.