Descartes:00025

Beeckman recorded in his journal that he met Descartes on 10 November, and that the Frenchman from Poitou discussed a mathematical problem with him. The terms in which Descartes expressed the problem suggest that he was still held captive by the language and style of argument of his scholastic training, and by the definitions of Euclid. He tried to prove that there is no such thing as an angle between two intersecting lines. He argued as follows. An angle is where two lines, AB and CB, meet at a point. However, if one were to divide further the angle ABC by the line DE, the point of intersection would also be subdivided into two parts. That is impossible, since, by definition, a point has no size and cannot be divided. Therefore, there is no point at which the original two lines intersect, and hence there is no genuine angle at their intersection.