| The project of constructing a complete system of knowledge---a system capable of integrating all that is and could possibly be known---was common to many early-modern philosophers and was championed with particular alacrity by Rene Descartes. The inspiration for this project often came from mathematics in general and from geometry in particular: Just as propositions were ordered in a geometrical demonstration, the argument went, so should propositions be ordered in an overall system of knowledge. Science, it was thought, had to proceed more geometrico.;I offer a new interpretation of 'science more geometrico ' based on an analysis of the explanatory forms used in certain branches of geometry. These branches were optics, astronomy, and mechanics; the so-called subalternate, subordinate, or mixed-mathematical sciences. In Part I, I investigate the nature of the mixed-mathematical sciences according to Aristotle and some 'liberal Jesuit' scholastic-Aristotelians. In Part II, I analyze the metaphysics and physics of Descartes' Principles of Philosophy (1644, 1647) in light of the findings of Part I and an example from Galileo. I conclude by arguing that we must broaden our understanding of the early-modern conception of 'science more geometrico' to include concepts taken from the mixed-mathematical sciences. These render the geometrical manner more flexible than previously thought. |
