The structure of Descartes's \textit{Géométrie} (Q2714845)

The author discusses Descartes ''La géometrie'' of 1637 as a treatise which was to provide geometrical problem solving as it was practiced at that time. In order to explain that practice, Bos discusses in particular a problem by Christopher Clavius (dividing a triangle in two equal parts by drawing a line from a point outside the triangle). Geometrical problem solving required a twofold method. On the technical level an analytical procedure was needed which would lead the geometer to the solution of a problem. On the methodological side an answer was required to the question which constructions were acceptable in geometry. The author has meanwhile published a comprehensive book on all related questions: Redefining geometrical exactness. Descartes' transformation of the early modern concept of construction. New York: Springer (2001; Zbl 0972.01020).