Conclusion of Part II

Abstract

In the previous chapters I have followed the development of Descartes’ ideas about geometry from 1619 till 1637. That year saw the publication of the Geometry in which Descartes formulated his convictions about geometrical exactness, presented his canon for geometrical problem solving, and explained the techniques of algebraic analysis he had developed for translating problems into equations and for constructing the roots of these equations. After 1637 Descartes occasionally returned to geometrical matters but he did not essentially develop the results reached in the Geometry — it appears that he considered his project of geometrical investigation completed.¹ In the letter to Beeckman of 1619 he had written that he intended to achieve a “completely new science by which all questions in general may be solved”;² this goal he now had reached for geometry, the science which from the beginning inspired his vision of the scientific method.

Cf. e.g. Descartes to Plempius, 3-X-1637, [Descartes 1964–1974] pp. 409–412, i.p. p. 411: “Non ignoro Geometriam meam paucissimos lectores habituram; nam cùm ea scribere neglex-erim quae ab aliis sciri suspicabar, et paucissimis verbis multa (imò omnia quae unquam in illâ scientiâ poterunt inveniri) vel complecti vel saltem attingere sim conatus, lectores non modo peritos eorum omnia quae hactenus in Geometriâ et Algebrâ cognita mere, sed etiam valdè laboriosos, ingeniosos et attentos desiderat.”

Cf. Section 16.1, Note 6.