The first six propositions of Archimedes' 1.

Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes' Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg's modern edition (1881, 1913) to the first propositions in Eutocius' commentary on 1, J. L. Berggren ([1976]. 'Spurious Theorems in Archimedes' Equilibrium of Planes: Book I', 16.2 (1976), 87-103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1-5 to Props. 1-6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius' remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes' mechanics to the method of 1.