Diagrams for Method 12 in the Archimedes Palimpsest

This paper discusses four diagrams in the Archimedes Palimpsest, a manuscript that provides among other texts the only extant witness to Archimedes’ Method. My study of the two diagrams for Method 12 aims to open up discussions about the following two questions. First, I want to question the assumed relationship between diagram and geometric configuration. Rather than a representation-represented relation, I argue that the two diagrams for Method 12 have a stronger independence from the geometric configuration they are related to. Their connection with the theorem rather lies in their role in shaping the way in which the proof is written. Secondly, I want to examine the connection between geometric intuition and figure. Geometric intuition is the recognition of certain properties or relations in a geometric configuration not through deduction and is held to be parallel to, if not dependent on, the empirical observation of a physical figure. Method 12 provides a curious case where an intuitive fact is not only unrepresented, but even hindered by the diagrams, and the proof assumes that the reader has come to realise that fact, which is most easily achieved when the diagrams are ignored.