  Another fundamental distinction Patrizi introduces is that between mathematical and physical space, a view which will have profound import for the main figures identified with early modern thought, such as Galileo, Kepler, Newton, Descartes and Leibniz. In Patrizi's system, mathematical space is a pure reality, ontologically prior to all bodies; its primary unit is the geometrical point. Physical space, on the other hand, contains bodies, which are not purely three-dimensional geometrical forms, but provide the additional factor of resistance, a view which can be seen as anticipating Leibniz's addition of the notion of force to Descartes' conception of bodies as geometrically definable (Kristeller 1964, 123). Thus Patrizi can be counted among the Renaissance thinkers such as Jacopo Mazzoni, Galileo's mentor at the University of Pisa, who posited mathematics as prior to physics and quite probably opened the doors to the mathematized physics which would come to dominate early modern science (Purnell 1972; Wallace 1998). Yet for Patrizi it is geometry which is the most valuable tool for the study of the physical world, not arithmetic. Perhaps oddly for someone with a background so deeply rooted in Platonism, Patrizi considered numbers to be merely products of thought, not constitutive or revelatory of the ultimate character of the natural world. Perhaps it would take the development of analytic geometry to alter such a view in due course. 