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

14, 17, 23, 24).*) That PBv are related is shown by the common lacuna at p. 36, 11. Especially between PB there is such a close connection (see p. 2, 4; 8, 2, 21; 10, 1; 12, 11; 16, 5; 22, 3; 24, 8, 10; 26, 14; 32, 22; 34, 1, 4) that they must necessarily have been copied from the same antigraph; for that we should not think P was copied from B itself, there stand against it both the places where Pv agree (p. 2, 11; 12, 11; 26, 5; 32, 10) and p. 10, 20, where BVv have a common lacuna. Vv agree at p. 6, 9; 8, 24; 10, 1; 22, 3. The common errors of all codices are very rare and light (such as p. 10, 10; 20, 9; cf. p. 2, 4).

2. What is called the fifteenth book of the Elements [was] composed in the 6th century by a disciple of Isidorus of Miletus, the mechanician of Constantinople, from the master's schools (see p. 67 n.). Besides the codices PBVv, there has been added from p. 50, 17:

m — The Venetian codex of St. Mark 303, bombycine paper, 14th century, written in two columns. On fol. 1, where book XV begins on p. 50, 17 (ἐξηγήθη), there is the inscription "of Cardinal Bessarion of Tusculum." It contains, besides book XV, the ancient optics, catoptrics, Ptolemy's Almagest in an older hand with scholia, and other mathematical or astronomical writings. I collated it myself.

Also in this book, as is fitting, the relationship of the codices PBVv is the same. V is the best**), and to it is added m, where it exists (p. 50, 23; 52, 1; 54, 4, 15, 21; 56, 22; 58, 1, 11; 60, 1, 8; 62, 13; p. 62, 13, 20 V has been corrected to the likeness of codex m; cf. p. 58, 23. They also conspire in errors, such as p. 58, 4, 5, 14; 60, 4, 16, 24;

*) Cf. p. 2, 13; 12, 17, where V by correction has the reading of codex m.
**) See, e.g., p. 42, 1, 10; 46, 8; 48, 17.