Abstract: This chapter shows how, using basic beliefs, one can go on to make a geometrical discovery by visual means in a non-empirical manner. It focuses on a simple example in order to illustrate the general possibility of what Kant would call synthetic a priori judgements in geometry. It attempts to show how such a judgement can be knowledge. It is commonly asserted that diagrams have no non-redundant role in a proof, even in a geometric proof.

Keywords: geometrical knowledge, beliefs, a priori judgements, diagrams, discovery,