  In this paper, we give a geometrization and a generalization of a lemma of
differential Galois theory. This geometrization, in addition of giving a nice
insight on this result, offers us the occasion to investigate several points of
differential algebra and differential algebraic geometry. We study the class of
simple \D-schemes and prove that they all have a coarse space of leaves.
Furthermore, instead of considering schemes endowed with one vector field, we
consider the case of arbitrarilly large families of vector fields. This leads
us to some developments in differential algebra, in particular to prove the
existence of the trajectory in this setting but also to study simple \D-rings.
