Thanks to Proclus' Commentary to Book I of Euclid's Elements, as well as the Summary of Eudemus, we can devise a relatively clear image of Greek mathematics during the 4th century B.C. Thus we know that the first writer who composed the elements of Geometry before Euclid, is Hippocrates of Chios. On the other hand in the Platonic Academy they employed the treatise of Theudios. Although we do not have any particular references it is most probable that they developped essays of geometric elements. Nonetheless in the Platonic Dialogues we notice an attempt to elucidate certain primary considerations from which follow all the remaing concepts. We do not know what Aristotle gained from the first and second generation of the Platonic Academy, the notion of "elements" are familiar to him. Although the organization regarding the "elements" does not constitue a particulat treatise of Aristotle, we can distinguish in numerous fragments, definitions and methods, which comprise a part of the Euclidean Elements. The Aristotelian Analytics includ an universal system of concepts from which dominates a theory of reasoning. Moreover beyond this solid foundation Aristotle absorbs the doctrines of Platonic knowledge. He adopted some of the doctrines and bestows his own definitions for basic geometric concepts. From these Euclid receives and includes them in his Elements. The Aristotelian definitions appeared in the eternal dialectical model of the centuries. In this essay the presence of Aristotelian and Euclidean definitions, proves that ancient Greek geometry was codified based on the model of Aristotelian Analytics.
Academy of Athens
