Complete Works of Euclid, Vol. 6 (Optics, Catoptrics, etc.)

Since the books XIV—XV, which are attributed [to Euclid], were not in the edition of Theon (for book XV is two centuries later than that, and in many Theonine codices neither this one nor that one is read), it is to be expected that a different relationship exists between P and the Theonine [codices] in these books; and this expectation does not deceive us. For in these books, P is so far from offering a more complete and better reading than the others that it should rather be numbered among the inferior ones. Thus, in this part, it was copied from a different antigraph, which is confirmed also by the fact that the Data are interposed between books XIII and XIV. Therefore, that archetype which offered the ancient recension, from which books I—XIII were taken, contained only these [books]. As for the Data, the judgment should rest with my colleague.

The best of these codices is M, which differs from the rest not only in that it contains the fourteenth book alone without the fifteenth, but it offers an entirely different recension of Hypsicles' words, which the others show to be better, for instance in places such as p. 2, 13, 15 sq.; 4, 1 (κρίνοντι — κρινοῦντι); 6, 22 (’Αριστεροῦ — ’Αρισταίου); 6, 23 (συγκρίσει instead of σύγκρισις, a reading which it is nearly incredible that Friedlein expressly condemned); cf. furthermore p. 2, 4, 16; 6, 7; it lacks the interpolations of the others [at] p. 10, 9; 16, 9; 18, 13. Therefore I have preferred the reading of codex M wherever it could be done without damage; although it too has quite a few errors, mostly in omitting (it is apparent from p. 6, 16; 8, 3; 24, 16 that it derives from an archetype written with abbreviations). Among the rest, the first place is owed to codex V, which often agrees alone with M (as for example p. 2, 12; 4, 3; 6, 2, 4, 9; 8, 17, 18, 24; 10, 2; 12, 3, 7; 22, 19; 26, 19; 32,