Jean De Groot

This paper examines geometrical arguments from Galileo's Mechanics and Two New Sciences to discern the influence of the Aristotelian Mechanical Problems on Galileo's dynamics. A common scientific procedure is found in the Aristotelian author's treatment of the balance and lever and in Galileo's rules concerning motion along inclined planes. This scientific procedure is understood as a development of Eudoxan proportional reasoning, as it was used in Eudoxan astronomy rather than simply as it appears in Euclid's Elements. Topics treated include the significance of the circle in Galileo's demonstrations, the substitution of rectilinear elements for heterogeneous factors like weight and curvilinear distance, and the way in which elements of a motion are used to measure other elements of the same motion. The indirectness of Galileo's proofs, his conception of speed as relative and comparative, and the meaning of his concept of moment all come into clearer focus. Conclusions are drawn about Galilean idealization, and also about the contrast of literal versus figural modes of explanation in Galileo's science

It is shown that Aristotle’s references to automata in his biological treatises are meant to invoke the principle behind the ancient conception of the lever, i.e. that points on the rotating radius of a circle all move at different speeds proportional to their distances from the center. This principle is mathematical and explains a phenomenon taken as whole. Automata do not signify for him primarily a succession of material movers in contact, the modern model for mechanism. For animal locomotion and embryological development, Aristotle models his dunamis concept on the idea of mechanical potential that the lever principle displays.

In _Aristotle’s Empiricism_, Jean De Groot argues that an important part of Aristotle’s natural philosophy has remained largely unexplored and shows that much of Aristotle’s analysis of natural movement is influenced by the logic and concepts of mathematical mechanics that emerged from late Pythagorean thought. De Groot draws upon the pseudo-Aristotelian_ Physical Problems_ XVI to reconstruct the context of mechanics in Aristotle’s time and to trace the development of kinematic thinking from Archytas to the Aristotelian _Mechanics_. She shows the influence of kinematic thinking on Aristotle’s concept of power or potentiality, which she sees as having a physicalistic meaning originating in the problem of movement. De Groot identifies the source of early mechanical knowledge in kinesthetic awareness of mechanical advantage, showing the relation of Aristotle’s empiricism to more ancient experience. The book sheds light on the classical Greek understanding of imitation and device, as it questions both the claim that Aristotle’s natural philosophy codifies opinions held by convention and the view that the cogency of his scientific ideas depends on metaphysics