Meditations 1: Why does Descartes wants to do philosophy like a geometrician?

Descartes was what's called a rationalist philosopher. This means that he believed that reason could discover what is ultimately true. As with other rationalist philosophers, Descartes believed that mathematics was the most reliable kind of knowledge because it was based on the exercise of pure reason and offered certainty. Two plus two will always equal four, and we can be completely sure about this. We don't need to look around us for verification of this fact; we don't need to conduct any experiments. Once we understand the elements of a mathematical equation, we know for sure that their conclusions follow with absolute logical necessity.
As Descartes wanted to establish philosophical knowledge on foundations of absolute certainty, he thought that the geometrical method was the appropriate one to use. Geometry is not simply an abstract enterprise; it is also a practical discipline that could explain natural phenomena in the world around us. Philosophical arguments would then be presented as mathematical demonstrations—in axioms, postulates, and propositions. Descartes argued that doing so would allow us to gain indubitable knowledge, that is to say knowledge that would be impossible to doubt.