Galileo's quanti: understanding infinitesimal magnitudes
The author discusses Galilei's solution to Aristotle's wheel paradox. Galilei introduced two kinds of infinitesimals: infinitesimal quanti, an infinite number of which produces an infinite sum, and infinitesimal non-quanti or indivisibles, an infinite number of which produces a finite sum. Moreover, an infinitesimal can be either filled or void. Aristotle (or his pupil) wrote about two rotating concentric circles of which the biggest one rolls on a straight line: ``How it is that a greater circle when it revolves traces out a path of the same length as a smaller circle, if the two are concentric?'' Yet, ``when they are revolved separately, then the paths along which they travel are in the same ratio as their respective sizes.'' Galilei views circles as polygons with an infinite number of infinitesimal sides. These sides are non-quanti. Galilei explains the paradox by arguing that the line traced out by the smaller circle is just as long as the line traced out by the bigger circle because during the rotation infinitely many void non-quanti are added. The author argues that Galilei's views on infinitesimals influenced his pupil Torricelli.
scientific article; zbMATH DE number 6305093
scientific article