 The problem-solving techniques and mathematical results that Descartes presents in La Géométrie were both novel and incredibly influential on the practice of early modern mathematics. However, we can also locate in La Géométrie a philosophical significance: The blending of algebra and geometry and the peculiar approach to the “geometrical” status of curves which characterize Descartes’ mathematical program stand as notable contributions to the on-going philosophical debates that surrounded early modern mathematical practice. By drawing on the context in which Descartes’ mathematical researches took place, and examining the main questions and issues that shaped Descartes’ early mathematical researches, both the historical and philosophical significance of Books One and Two of La Géométrie will be highlighted in what  follows.[1]