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

XV PROLEGOMENA.

p. 22, 1, 15); cf. furthermore p. 6, 27; 30, 16; 40, 18. Similarly, where B is absent, Vat. v conspires with a poorly corrected V at p. 70, 4, and they 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. At p. 84, 18, I now doubt whether ὀρθήν should be omitted with V, although it stands 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 omitted); 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.*)

I have published the Latin translation from D alone, because I was able to collate only that one in its entirety; without doubt it can be amended from elsewhere. For the sake of a specimen, I will gather here what I have noted (besides the few things I gave in the apparatus) from ML and the Amplonian codex Q 387 (14th century, fol. 47^r — 52^r, at the end: explicit liber de uisibus). p. 3, 1 rectas ductas] eductas rectas Ampl.; ductas lineas] lineas eductas ML; 2 inmensarum] inmensurarum L in erasure; uisibus] uisibus quidem ML Ampl. (cf. p. 2, 3); 5 inciderit] incidunt L; 6 inciderit] incidunt L; 7 quidem] om. M; uero minori] minori uero ML; 11 quidem] om. M; 16 enim] quidem Ampl.; quidem] om. Ampl.; esto] om. M; 17 incidunt Ampl.; igitur] ergo Ampl.; p. 5, 1 uisus incidentes M; 2 fient] fieret L; et] puncta M in erasure; 3 non ergo uidebitur] mg. m. 1 Ampl.; simul uidebitur M; 4 ad totum M; simul] om. L; 8 quidem oculus L; 10 sit] om. L; 19 enim] om. L; autem] om. L; p. 7, 1 iam non L; 8 e] a Ampl.; minora] maiora Ampl.; p. 121, 8 epipedo Ampl.; 9 diametrorum] om. Ampl.; 11 nec] neque Ampl.; 12 demonstrabuntur Ampl. for p. 5, 12 trigoni — 16 uidentur and p. 7, 2 ad k — 4 uidebitur, L has entirely different things; and in general, even in other manuscripts, there exist other differences from the Greek words, of which there will be a place to speak in chapter III.

*) At p. 72, 7, the recension of Theon p. 208, 16 shows that with a corrected V and B, one should write οὖν instead of γάρ; at p. 68, 16, instead of ὥστε εἰσίν, one should supply καί εἰσίν with Theon p. 204, 25; thus the second class has preserved a trace of the truth. At p. 16, 27, καί should be deleted, because it is added only in the corrected V, which has no authority.