Three views on epistemological status of geometry

The subject of this paper is the epistemological status of geometry. This problem appeared in the beginning of XIX century, after the birth of non-euclidean geometries. This scientific discovery had a big influence on philosophy of science. We will deal with different systems of geometry, interpreted by means of physics. We will discuss several positions regarding their epistemological status. The key question is about the nature of geometry as a science- is there one real geometry of our world and which one? Both euclidean and non-euclidean geometries can be seen as to be in accordance with our experience by introduction of a different lows of physics but the question is if the couple P + G (physics + geometry) can be empirically tested. We will expose three different positions about these problems : Kant's apriorism, empiricism and conventionalism.