This, my third study on Greek mathematics, serves to complete a project. My first study, The Shaping of Deduction in Greek Mathematics (1999) analyzed Greek mathematical writing in its most general form, applicable from the fifth century bc down to the sixth century ad and, in truth, going beyond into Arabic and Latin mathematics, as far as the scientific revolution itself. This form – in a nutshell, the combination of the lettered diagram with a formulaic language – is the constant of Greek mathematics, especially (though not only) in geometry. Against this constant, the historical variations could then be played. The historical variety is formed primarily of the contrast of the Hellenistic period (when Greek mathematics reached its most remarkable achievements) and Late Antiquity (when Greek mathematics came to be re-shaped into the form in which it influenced all of later science). My second study, The Transformation of Mathematics in the Early Mediterranean (2004), was largely concerned with the nature of this re-shaping of Greek mathematics in Late Antiquity and the Middle Ages.

This study, finally, is concerned with the nature of Greek mathematics in the Hellenistic period itself. Throughout, my main concern is with the form of writing: taken in a more general, abstract sense, in the first study, and in a more culturally sensitive sense, in the following two.

The three studies were not planned together, but the differences between them have to do not so much with changed opinions as with changed subject matter.