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.  

the factors that the economies of the muslim empires prosper were:

1- land trade routes-located between three continents  

2- sea trade routes

trade contributed to the spread of muslim empires, and with that islamic culture led to a growing feeling of internationalism resulted in the transfer of technology, science, and other cultural forms.