The Geometry, introduction and survey

Abstract

The documents from c. 1619 discussed in Chapter 16 make clear that from early on Descartes viewed the scientific enterprise with a strong programmatic interest. His program encompassed the whole of science, which he saw primarily as a problem solving endeavor, with arithmetical and geometrical problems as paradigms. Thus he formulated his programmatic ideas (in the letter to Beeck-man) by giving a classification of problems concerning continuous and discrete quantity and by defining the nature of the solutions to be achieved in each class. We may consider the program as Descartes’ earliest interpretation of what it meant to solve scientific problems exactly. The starting point of his interpretation of exactness was classical Greek geometry; geometrical problem solving meant construction by the intersection of curves and his classification of problems can be seen as a modification of Pappus’. He singled out the manner of tracing by motion as the primary criterion for the acceptability of curves; regular motions such as those provided by the “new compasses” (cf. Section 16.4) were acceptable; other motions, such as the ones generating the quadratrix or the linea proportionum, were, if not rejectable, at least of lower status.