Redefining Geometrical Exactness: Descartes' Transformation of the Early Modern Concept of Construction

In this detailed study, spanning essentially the period from the first printed edition of Pappus's Collection (1588, in Latin translation) a nd DescartesF death in 1650, Bos explores the current ideas about cons truction and geometrical exactness, noting that by the time Descartes entered the field the incursion of algebraic techniques, combined with an increasing uncertainty about the proper means of geometrical probl em solving, had produced a certain impasse. He then analyzes how Desca rtes transformed geometry by a redefinition of exactness and by a dema rcation of geometry's proper subject and procedures in such a way as t o incorporate the use of algebraic methods without destroying the true nature of geometry.