Descartes was historically important not only as a mathematician but also as a philosopher who thought exceptionally highly of mathematics. What we have delineated in Part I is how he constructed his method of algebraic analysis as it appears in its fully developed form in the Géométrie of 1637. He considered this novel manner of analysis to occupy a central place in his universal method for discovering certain knowledge. This method played a crucial role in his philosophy and in his program for reforming the traditional sciences.