Abstract: In his commentary on the first book of Euclid’s Elements, Proclus says that “Euclid belonged to the persuasion of Plato and was at home in this philosophy; and this is why he thought the goal of the Elements as a whole to be the construction of the Platonic figures.” This is a remarkable statement and raises several questions. It is remarkable, for one, in the way it puts aside the immense wealth of other mathematical work in the Element. Proclus’ statement, however, is made as if it were perfectly clear, that is, as if there was nothing remarkable about it at all. We must, therefore, assume that Proclus’ readers would not have seen this as a controversial statement. What does this say about how they viewed the Elements? Part of the answer is surely the other remarkable aspect of Proclus’ statement, namely, his associating Euclid with Plato. Proclus was, of course, one of the last heads of the Platonic academy: his associating Euclid and Plato says, in effect, then, that Euclid’s Elements has a place among the studies of the academy, that it has educational value, or, to use the far more subtle Greek term, that it contributes to paideia.

In my talk, I shall discuss the structure and content of Book XIII with an eye to its possible contribution to paideia, though not neglecting its purely mathematical aspects. I shall try and make the case that, among other things, the educative value of Book XIII lies in its attention to wholeness, or rather in the way it turns readers’ own attention to wholeness and forces them to reflect on the whole of the Elements. This kind of educative value is peculiarly ancient; I hope that the talk will ultimately raise questions, however, as to our own goals in education and as to whether these ancient perspectives have anything to teach us moderns.