Drawing on scholarship that traces the medieval appropriation of ancient methods of analysis and synthesis, I demonstrate that the intermingling of differing senses of analysis and synthesis, resolution, and composition predates the early moderns. Section 5.1 maps out five distinct ancient senses of resolution and composition and illustrates that several are conflated in the works of St. Thomas Aquinas, whose philosophy witnessed a resurgence with the rise of the Jesuit order in the sixteenth century. Section 5.2 examines how earlier methods of analysis and synthesis were taken up and developed by scholastic logicians influential in Descartes’ and Hobbes’ contexts. Sections 5.3 and 5.4 clarify Descartes’ and Hobbes’ claims about philosophical analysis and synthesis in light of this background. I demonstrate that the incoherencies generated by linking their philosophical methods solely to Zabarella’s regressus may be resolved by reinterpreting these claims in their wider context. The question as to whether/how their own and prior philosophical methods of analysis and synthesis shape the methodical procedures that Descartes and Hobbes employ to tackle scientific problems is shelved, but the philosophical texts examined indicate that they need not be directly connected.