Aristotelian philosophy is generally regarded as incompatible with the mathematical methods and principles that form the basis of modern science. This book offers an entirely new perspective on this presumed incompatibility. It surveys the tradition of the Oxford Calculators from its beginnings in the fourteenth century until Leibniz and the philosophy of the seventeenth century and explores how the Calculators' techniques of quantification expanded the conceptual and methodological limits of Aristotelianism. In the process, it examines a large number of authors, some of them never studied in this context. Exploring the relationship between various late medieval disciplines, the book sheds new light on the problem of continuity vs. discontinuity between scholasticism and modern science. Beyond its historiographical purpose, this book also hopes to be a source of inspiration for present-day philosophers of science.