The Anonymous Tract On Isoperimetric Figures

The Introduction to the Syntaxis, transmitted as an anonymous compilation of edited extracts from commentaries on Ptolemy’s Book I, has drawn our attention already at three points. In dealing with its section on compound ratio, we have contested Mogenet’s thesis that the Introduction was composed by Eutocius, and have argued that it be assigned instead to a commentator named Arcadius, active in the mid-5th century (see Part I, chap. 7). The Introduction’s chapter on isoperimetric figures preserves certain testimonia on Archimedes’ treatment of the circle, which, when coordinated with the witness of Pappus and Theon, contribute to the argument for the reconstruction of DC*, the lost prototype of the extant ancient and medieval texts of the Dimension of the Circle (chaps. 1 and 3). Moreover, the same chapter on isoperimetrics betrays interesting parallels with the medieval Latin De curvis superficiebus, and so supports the case for the lost prototype CS* (chap. 8). Another section of the Introduction, its account of long division, will concern us in the next chapter. We turn now to a more systematic examination of its account of isoperimetric figures.