Complete Works of Euclid, Vol. 7 (Optics and Catoptrics)

XIV PROLEGOMENA.

Besides the manuscripts already mentioned, the Laurentian codex XXVIII, 3 also contains our Optics, but in this part (φ) it is transcribed from f, as I demonstrated in V, p. XXVI. In the Vatican Greek codex 246 (paper, 15th century), among other things on fol. 17^r, the definitions are read with these varying readings: p. 2, 1 Euclidis optici termini, 8 ἄν om., προσ- written above, 11 δέ] δ', ἐλάσσονος ἐλάσσονα, 16 μὲν ὑπό] ἐπί. I have not found other manuscripts.

There remain, therefore, only V and B; of which V seems to be preferable, not only because it is older, but also because B, although it often has a better reading (p. 12, 24 — 25; 16, 17; 20, 1; 22, 19; 24, 9; 34, 23; 36, 14; 52, 2; 54, 13; 56, 20; likewise Vat. v, where B is lacking, p. 60, 18; 68, 2; 74, 7; 82, 5; 88, 6; 100, 24; 114, 15 — the readings p. 16, 17; 36, 14; 74, 7 are confirmed by Theon’s recension p. 166, 14; 180, 9; 210, 12 —; perhaps also p. 8, 12; 26, 20; 34, 21; 38, 1; 42, 16 and p. 40, 9; 66, 22 ἔτι δέ, which are confirmed by Theon’s reading p. 184, 4; 204, 14), is not free from the suspicion of interpolation. For instance, at p. 6, 26, the origin of the error is understood from the reading of manuscript V, while it is not understood from the reading of manuscript B; p. 18, 10; 36, 16, the error is not correctly amended; p. 26, 11 it conspires with V m. 2 in a superfluous conjecture, likewise p. 20, 28 (for cf. p. 22, 1, 15); cf. furthermore p. 6, 27; 30, 16; 40, 18. Similarly, where B is missing, Vat. v conspire with a poorly corrected V at p. 70, 4, and have a false conjecture at p. 80, 12; cf. p. 64, 11. Furthermore, the error at p. 118, 21 in the Vatican arose from that compendium which V preserved. As for p. 84, 18, I now doubt whether ὀρθήν should be omitted along with V, although it exists in Theon at p. 216, 12, but before γωνίαν; for at p. 36, 18; 38, 23, B was later corrected to the likeness of Theon’s recension p. 180, 16; 182, 17, and at p. 54, 4 it conspires with it at p. 192, 19 in a less refined reading against V. Theon’s recension also argues for the interpolations of manuscript B at p. 162, 3 (= p. 10, 19); 170, 2 (= 20, 4); 180, 14 (= 36, 16); 188, 18 (= 46, 13); 196, 22 (= 58, 15); 202, 6 sq. (= 64, 11); 204, 14 (= 66, 22 εὐθεῖα om.); 244, 3 (= 118, 4). Therefore, in accepting the readings of the second class, even if they are good in themselves, one must act cautiously, and one should not depart from V without a certain cause.*)

*) P. 120, 6, this is the reading of manuscript f: note that it ought to be written thus: "but if the diameter at the junction..." (rest follows as in V, which can be restored from here; cf. m).