8 - The Euclidean Sectio Canonis

Summary

The little treatise called the Sectio Canonis consists of a short introduction and twenty propositions presented and argued in the manner of theorems. It is attributed to Euclid in the manuscripts, and by Porphyry, who quotes it at length (Comm. 98.14–103.25 has the first sixteen propositions, and there are brief extracts elsewhere). The text Porphyry used was not quite identical with ours, and includes – probably wrongly – one proposition that our MSS lack (see n. 19 below). Parts of the treatise are also quoted by Boethius, again not quite in the form that our MSS transmit. If Euclid is indeed the author, the work will have been written around 300 b.c., but the attribution has been debated. Some scholars have doubted that it is all the work of a single writer, or even of a single period, speculations encouraged by the possibility that Porphyry and Boethius did not know the Sectio as a whole, in the form in which it has reached us (see especially Barbera 1984b). There are no good reasons, however, for denying Euclid's authorship of the main part of the treatise, at least as much as Porphyry quotes. Grounds have been suggested for thinking that either propositions 17–18 or propositions 19–20 come from a different pen, but they are not strong (see n. 57 below). The introduction is perhaps more questionable.