It has been acknowledged that, while Descartes’s usage of the term “a priori” is at odds with the now-current Kantian meaning, it also fails to correspond to the standard Aristotelian notion. However, there is, as yet, little agreement as to the exact positive meaning Descartes associates with the term. As such, this book offers a clear and historically adequate account of this disputed issue. Descartes’s concept of apriority is interpreted as resulting from an interplay of two trends: development of a universal method of discovery based upon Descartes’s ground-breaking reinterpretation of heuristic procedures in mathematics, and a substantial transformation of the Renaissance-Aristotelian conception of scientific reasoning. This interpretation stems from a fresh and innovative account of some central and controversial topics of Descartes scholarship and from a historically-informed outline of the situation in mathematics and in philosophy of science in Descartes’s times. The book will thus contribute to a better understanding of several fundamental issues in the philosopher’s thought. It will also help to shed light upon the challenging and strangely neglected question of why Kant decided to employ the term “a priori” in a way which differs so dramatically from the once well-established Aristotelian usage.