In this paper I consider the ancient problem of the dependence of synthetic geometry of the diagrams and the demand of necessity and universality for its results. I defend that the source of this necessity is a priori, a special kind of intuition that, in analogy to ordinary empirical intuition, restricted to the apprehension of the particular features of the objects, pass trough those to the apprehension of the shared properties of a class of objects. I will try to suggest that the postulation of that kind of intuition is not a mere philosophical device, but that it find evidence in the geometrical practice, especially in the development this discipline suffered in the nineteenth century, in hands of Poncelet and Klein, between others.
Synthetic geometry; Construction; Schemata; Invariances; A priori
