Reduction of Absurdity: Notes on the Editorial Transformations of Greek Diagrams

This chapter studies a subsection of Greek mathematical diagrams: the diagrams used for proofs by contradiction. In some of those proofs, the configuration required for the assumption of the proof is visually impossible. It is shown that manuscript diagrams tend to emphasize the impossibility of such configurations. This is different from many modern editions, where the diagram tries to represent the case as close to plausibility as is possible. In general, it is noted that such diagram traditions tend to be stable, in both manuscript and print transmissions. The major rupture in the tradition occurred during the Renaissance, in both print and manuscript, and seems to represent a specifically Renaissance attitude of disdain towards the medieval transmission.