The principles of science in Aristotle and Euclid

Why did Greek science search for its own achievement in the axiomatic form? We try to answer this question by confronting Aristotelian epistemological program of axiomatisation of the sciences in the Posterior Analytics with its realisation in Euclid's Elements. It appears that the different Euclide an first principles fit quite exactly Aristotelian requirements. But the co nverse is not true. Moreover, it is not possible to draw a coherent concept of first principles from the text of the Posterior Analytics. We propound to resolve both types of difficulties by a single assumption. The historica l constitution of a deductive system stands from formalised procedures of t ransmission of knowledge in the discourse of an ideal teacher (who know eve rything) talking to an ideal pupil (who knows nothing). The system of first principles in the Posterior Analytics is thus unstable and intermediate be tween two coherent systems. The first one comprises terms to be understood (definitions), and propositions held to be true, either by necessity (axiom s) or contingently; these, in turn, can further be divided into hypotheses and postulates, depending on assent or dissent of the hearer. The second sy stem comprises axioms stating unprovable properties, definitions of terms a nd hypotheses of existence. Thus, the Posterior Analytics seek to reconcile the two Greek concepts of science. According to the first one, science is a system of interlocutive transmission; according to the later one, it is a system of objective knowledge. Euclid's Elements are at the end of this pr ehistorical development of ancient axiomatic.