Geometry in Descartes’ system

Resumen

What struck the young student of mathematics at the college of La Fleche was the absolute certainty of their demonstrations. More specifically, he was impressed by the contrast between these proofs and the literary tradition, for “/ had compared the moral writings of the ancients pagans to the most proud and magnificent palaces built on nothing but sand and mud”. Still, while he grants the are unquestionable, Descartes discovered both in geometry and arithmetic, an essential useleness and futility, an appreciation he will maintain all throughout his life. These first impressions might account for two emotions “joy and unease” frequently to be found at once in Descartes’ mathematical works. In his work we find a combination of joy of discovery, clear ideas and of mastership over methods, and uneasiness caused by the puerile, futile character of the very mathematical object itself. This ambivalence is present clearly and explicitly throughout Geometry.