PLAN OF THE CHAPTER

That diagrams play a crucial role in Greek mathematics is a fact often alluded to in the modern literature, but little discussed. The focus of the literature is on the verbal aspect of mathematics. What this has to do with the relative roles of the verbal and the visual in our culture, I do not claim to know. A description of the practices related to Greek mathematical diagrams is therefore called for. It will prove useful for our main task, the shaping of deduction.

The plan is: first, a brief discussion of the material implementation of diagrams, in section 1. Some practices will be described in section 2. My main claims will be that (a) the diagram is a necessary element in the reading of the text and (b) the diagram is the metonym of mathematics. I will conclude this section with a discussion of the semiotics of lettered diagrams. Section 3 will describe some of the historical contexts of the lettered diagram. Section 4 is a very brief summary.

This chapter performs a trick: I talk about a void, an absent object, for the diagrams of antiquity are not extant, and the medieval diagrams have never been studied as such. However, not all hope is lost. The texts – whose transmission is relatively well understood – refer to diagrams in various ways. On the basis of these references, observations concerning the practices of diagrams can be made.