A Historical Look at Analytic Geometry

[DeeAytch]

Hello,

Analytic geometry has provided us with such profound tools for thinking that it is hard to imagine what thinking must have been like before we had such tools. Two particular developers of these tools are Pierre de Fermat and Renee Descartes in 17th century France.

I would like to compare the analytic geometry of these two mathematicians. Particularly, how Fermat's Method of Adequality relates to the work of Descartes. Also, how, if at all, they influenced each other.

Thoughts?

Thanks,
DeeAytch.

 

[Tobias Funke]

I don't feel comfortable giving you a detailed answer (the most I "know" is that I've heard that Fermat's thinking was more like the modern approach than Descartes'), but you may want to check out Morris Kline's Mathematical Thought from Ancient to Modern Times, Vol. 1. I think Carl Boyer's A History of Mathematics is also good. Wikipedia itself may or may not be of much help, but the sources at the bottom are usually quite good.

Of course, the best way is to read Fermat and Descartes. I'd link you, but if it's not one of the first results of a google search, I don't know an easy way to read them. Maybe somebody more knowledgeable than I can help, but those are a start.