Descartes: A Biography

c CUNYB/Clarke     December, :

 Descartes: A Biography

had already concluded his training as a Calvinist preacher, had graduated

from Leiden University, and had received a doctorate in medicine from

the University of Caen in Normandy. Beeckman had known Willebrord

Snellius (–)–after whom the law of optical refraction is named –

and had done some experiments with him. He was thus a most appropriate

contact for someone like Descartes who was anxious to acquire as much

scientific knowledge as possible during this somewhat unstructured period

in his life. Beeckman was in Breda to visit with his girlfriend, Cateline de

Cerf, while Descartes was officially enlisted in the army of Prince Maurits

of Nassau.Beeckman recorded in his journal that he met Descartes on

November, and that the Frenchman from Poitou discussed a mathe-

matical 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.

Despite such an inauspicious introduction, the two men struck up a friend-

ship and began to exchange questions about mathematical problems and

their solutions. Beeckman was the senior scholar, not only in age but in

the extent to which he had thought about applying mathematics to the

solution of physical problems. In the first months of their acquaintance,

between Novemberand April,Beeckman shared a number of

problems with Descartes and asked for his help with the mathematics