Why do you think that descartes wants to do philosophy like a geometrician?

I believe Descartes' was hoping to reconstruct the foundation of knowledge, and he in this manner required something unquestionable - math.  

René Descartes was a French mathematician, philosopher and researcher. Named the father of current western rationality, a lot of ensuing Western logic is a reaction to his works. The main thing that he trusted he could be sure of was that he was questioning, prompting his acclaimed expression phrase "Cogito ergo sum," meaning I think, therefore I am. 

Yes it was hope that works