Method of Descartes

When I was younger, among the branches of philosophy, I had studied a little logic and, among the subjects of mathematics, geometrical analysis and algebra, three arts or sciences which looked as if they ought to contribute something to my project. But in looking at them, I took care, because, so far as logic is concerned, its syllogisms and most of its other instructions serve to explain to others what one already knows or even, as in the art of Lully, to speak without judgment of things about which one is ignorant, rather than to learn what they are. Although philosophy does, in fact, contain many really true and excellent precepts, mixed in with them there are always so many injurious or superfluous ones that it is almost as difficult to separate them as to draw a Diana or a Minerva out of a block of marble which has not yet been carved. Then, so far as the analysis of the ancients and the algebra of the moderns are concerned, other than the fact that they deal only with really abstract matters, which have no apparent use, the former is always so concentrated on considering numbers that it cannot exercise the understanding without considerably tiring the imagination, and in the latter is so subject to certain rules and symbols that it has been turned into a confused and obscure art which clutters up the mind rather than a science which cultivates it. Those were the reasons why I thought I had to look for some other method which included the advantages of these three subjects but was free of their defects. And since a multitude of laws often provides excuses for vices, so that a state is much better ruled when it has only a very few laws which are very strictly observed, I thought that, instead of that large number of rules which make up logic, I would have enough with the four following rules, provided that I maintained a strong and constant resolution that I would never fail to observe them, not even once…. (he continues)

Rene Descartes, “Discourse on the Method”, part two, (Translated by Ian Johnston)

full text is here

He’s utilizing philoshophy to redefine a relationship between algebra, geometry and logic. I think he is actually talking about a revolution he’s about to start in geometry, as we see it today. The rest of the book was also interesting to know him, his personal path of life, sometimes a little Narcissist, sometimes sad.