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

I.

On the manuscripts of the genuine Optics.

The manuscripts enumerated above are distinguished into two classes, V Vat.¹m and B Vat. v, of which the principal ones are V and B, and indeed so principal that the others are of no moment. For, in the first place, Vat. v not only never provides better readings than B, but even agrees with it in the most foolish errors, such as p. 14, 13 (οὐ arising from the compendium ☉^v); 16, 16; 52, 24. And those places where the compendia of manuscript B produced errors show that they derive their origin from B itself, such as p. 42, 13; 46, 25, 26 — for in B, -ϑ$^ω$ is often written for -ϑωσαν —; 54, 2; 56, 3; cf. furthermore regarding Vat. p. 32, 25; 34, 24; 50, 16; 52, 11, regarding v p. 30, 5; 32, 24; 46, 14 (βασης); 52, 10, 13; 56, 11, 13, 19*), and p. 20, 9, 10, 15; 22, 1; 38, 14, 19; 42, 3 etc., where in v one reads ν for γ, because in B these letters can scarcely be distinguished; also on p. 20, 16, οη is read for εη in v, because the letter ε is written more obscurely in B. At the passage which is p. 30, 17, we are compelled to posit a manuscript intermediate between B and Vat. v; for the words τῇ ὄψει ἡλίου are in B. To this class belongs A (see p. 80, 12, 16, 20; 82, 8, 12; 88, 5, 7, 11, 20; 90, 1, 2; 104, 17, 21, 23, 25; 106, 3, 4, 8; 108, 6; 114, 12; 116, 1). The Vatican manuscript was corrected by the second hand to the likeness of manuscript V (p. 22, 19; 26, 2; 28, 14; 74, 7; 88, 6 etc.), after it had been corrected by the second hand (p. 4, 27; 24, 4; 28, 7; 36, 25; 40, 9; 46, 14; 50, 7; 82, 26).

In the other class, it is apparent from their highest agreement in errors (p. 2, 7, 8; 8, 1; 24, 14; 34, 12; 36, 4, 10; 68, 13, 16; 76, 15; 78, 14, 16; 106, 2; 108, 15; 116, 18) that Vat.¹m are derived from the same archetype; for that Vat.¹ was not transcribed from m can be concluded from p. 68, 21 and p. 108, 11 (γενομένων). Nor is there any doubt that this archetype depends on V; for those things which m has better (p. 10, 10, 25; 102, 19; 104, 6 etc.) — I have noted nothing of this sort from Vat.¹ — are due to the scribe, who also amended other things at his own discretion, such as p. 24, 9; 68, 17, 20; 74, 4, 9, 10, 11; 80, 11; 82, 21, 22; 88, 7; 92, 9, at which places the agreement of the other class with V proves interpolation. And there is reason to believe that this archetype is common to the Laurentian codex XXVIII, 6 (f), which I demonstrated to be transcribed from V (see V, p. XXVI sq.); cf. p. 4, 8 παραφερομένων] V, εφερομένων f, περιφερομένων m; p. 10, 26 ΠΚ] V, πκ f, κ̅π̅ Vat.¹m; p. 12, 21 ΔΓΚ] in erasure V, βγκ fm; p. 50, 7 τῶν κώνων] V, τοῦ κυλίνδρου mg. m. 2; τῶν κώνων f, κυλίνδρων mg. m. 1; τῶν κώνων καὶ τῶν κυλίνδρων Vat.¹m; p. 68, 8 ΑΓΖ] corrected from A in V, αζ f, βεαζ Vat.¹, βαζ m; p. 82, 26 ΒΔΓ] βδεγ V (i.e. ΒΔΖΓ), βζδγ f Vat.¹m; p. 102, 17 τά] V, τὰ γάρ f, τὰ γάρ with γάρ deleted Vat.¹; p. 108, 5 ἐπὶ μιᾶς — 7 Γ, Ζ, Α] mg. m. 2 V, mg. m. 1 a little higher f, mg. m. 1 at p. 106, 26 Vat.¹, om. m; p. 108, 13 προηγεῖσθαι] V, προκεῖσθαι f Vat.¹m. *)

*) To this can also be referred p. 98, 3, where B undoubtedly had the same compendium which the Vatican had.