The early modern tradition of geometrical problem solving; survey and examples

Abstract

In Section 1.5 I identified the early modern tradition of geometrical problem solving as the context of the debates on the interpretation of the exactness of construction during the period c. 1590 – c. 1650. The debates primarily concerned the solution of point construction problems, that is, problems that admitted one or a finite number of solutions only. Solving such problems was indeed seen as a major, if not the main, aim of geometry.¹

Thus in 1591 Viète’s formulated the objective of his analytical program as “to leave no problem unsolved” (cf. Note 6 of Chapter 6) and Descartes opened his Geometry of 1637 with the words“ All the problems of geometry...”(cf. [Descartes 1637] p.297). Knorr notes a similar preeminence of problems over theorems in classical Greek geometry, [Knorr 1986] p.300.