Descartes and the geometrization of thought: The methodological background of Descartes' géométrie

After the relationship between geometry and algebra exemplified in his distinction between geometrical and mechanical lines is examined, the basis for Descartes' limited approach to analytical geometry is discussed in connection with his reflections on method. It is argued that his epistemology, which required that conceptual thinking be accompanied by a construction supplied by the imagination, in conjunction with the significant role he attributed to mnemonic devices, helps to clarify the methodological background for Descartes' distinctive approach to geometry.