It is a truism that philosophy and the sciences were closely linked in the age of Leibniz, Newton, and Kant; but a more precise determination of the structure and dynamics of this linkage is required. The subject matter of this volume is the interactions among the developments in philosophy and the transformations that the different branches of sciences, Baconian as well as classical, underwent during this period. Among the topics addressed are the transformations of metaphysics as a discipline, the emergence of analytical mechanics and its consequences for founding physics on metaphysics, the diverging avenues of 18th-century Newtonianism, the body-mind problem as dealt with by philosophers and physicians, and philosophical principles of classification in the life sciences. As an appendix, a critical edition and first translation into English of Newton's scholia from David Gregory's Estate on the Propositions IV through IX Book III of his Principia is added.