 Whether Descartes had the hidden agenda that Mancosu suggests, the explicit claims used to define the program of problem-solving presented in La Géométrie point to the limitations of Descartes’ mathematics. As we have seen above, Descartes’ primary focus is on a standard for geometry’s “exactness of reasoning” that is bound to clear and distinct motions for construction and to the finite equations to represent curves so constructed. Consequently, there is no room in the program of La Géométrie to use infinitesimal in the construction of curves or to treat curves represented by infinite equations. As such, Descartes eliminated from his geometrical program the very elements of mathematical and geometrical reasoning that made it possible for Newton and Leibniz to develop the calculus come the late seventeenth century. Nonetheless, given how quickly Descartes honed his mathematical skills and how quickly he developed his innovative program for geometry, it would not be too risky to accept Descartes’ self-assessment and maintain some confidence that the calculus would have been in his reach had he considered the infinitesimal and the infinite: