 But geometric knowledge, which began close to visual thinking (Giaquinto 2007) and the practical manipulation of symbols, i.e., diagrams as concrete representations, gradually evolved to become a more abstract edifice. Already with Euclid, Archimedes and Apollonius there is an effort to give form to well-crafted concepts, which make precise, ideal, and general what was suggested by intuition; likewise, the way of handling diagrams is anything but naive (see e.g. prop. 10 in Book III, but also props. 7, 14 or 27 in Book I). And in due course, a critical stage was attained, when the assumptions of geometric knowledge were made explicit and subjected to scrutiny, looking for deeper foundations and for alternatives. At this stage, represented above all by the nineteenth century, the diagram had to be relegated in favor of more explicit, abstract, relational methods for the analysis of theoretical assumptions and developments.