Complete Works of Euclid, Vol. 8 (Phenomena and Musical Writings)

It has been said above in what respects the Vatican manuscript properly errs; I would add those things which it emphasizes at p. 10, 21; 42, 25. Furthermore, we detect phrasing in the Vatican manuscript different from V at p. 2, 12, 21—23, where it prefers φέρεσθαι κύκλον to the usual φέρ. ἐπὶ κύκλου (cf. p. 2, 18; 6, 3, 4 etc.); 6, 28. The Vatican is fuller at p. 4, 20, shorter at p. 6, 15; 16, 5—6; 18, 12—15; 27—p. 20, 1. V and the Vatican differ from each other in word order at p. 28, 5; 36, 4; 40, 8; 42, 3; 44, 1; 54, 6, 8. The difference also pertains to astronomical and mathematical vocabulary: the Vatican has ἡμισφαίριον for τμῆμα at p. 6, 17, σφαῖρα for κόσμος at 18, 11; σημεῖον for ἄστρον at 24, 7; it adds τροπικόν at p. 20, 2 and 34, 20, ὁρίζοντα at 20, 29, and omits κύκλος at p. 22, 18, 22; 24, 6; 40, 9, and περιφέρεια at 16, 7; 42, 24. A few times we have phrasing in the Vatican directed toward the same norm and rule. Since V writes ἐν ᾧ instead of ἐν ᾧ χρόνῳ, even though the noun does not immediately precede—for example, p. 60, 2, 4; 66, 9; 74, 1; 90, 11; 96, 4; 102, 6 (I should not have added χρόνῳ at p. 102, 6)—the Vatican does not omit χρόνῳ unless it can be easily supplied. At p. 30, 2 the Vatican adds μέρη; cf. p. 26, 26; 30, 15. V prefers ἐν ἴσῳ χρόνῳ in the plural number even in those places where the plural is read nearby (see p. 54, 11, 12; 62, 9; 64, 6; 86, 3), but the Vatican maintains agreement of numbers and writes ἐν ἴσοις χρ. in those places, though at p. 80, 10 it is little consistent, with ἐν ἴσῳ. Recension b at p. 62, 8 ἐλάσσοσι; 64, 3 ἐλαχίστοις refers to the same matter. V writes both ὑπὲρ γῆς and ὑπὲρ γῆν, the Vatican perpetually retains the genitive. To this also point the readings of the Vatican manuscript at p. 24, 12 καθ’ οὗ; (cf. p. 26, 9; 28, 22; 32, 6; 36, 8; 46, 20; 96, 1; 102, 2), p. 10, 19; 12, 3 τεθεωρήσθω (cf. p. 12, 1), p. 36, 7 ἀπειλήφθωσαν (cf. p. 46, 10; 48, 4 rec. b; 54, 15; 58, 7; 100, 8; 104, 8) and likewise p. 10, 15 μέν (cf. p. 26, 8; 28, 21; at p. 32, 1 it was inserted by a scribe’s error after τά). At p. 32, 5 it presents single letters for the two letters pertaining to the figure, cf. p. 26, 8; 28, 21; it retains two at p. 36, 1. I have now descended to trifles, to which it is pleasing to count these discrepancies of the Vatican codex: ἐστί added at p. 32, 9; 36, 12, omitted at 22, 18. ἄρα omitted in the apodosis at p. 18, 1; 32, 9; 42, 23; furthermore at p. 32, 2. γάρ omitted at p. 32, 7. μέν omitted at p. 14, 3; 30, 24. δέ added at the end of the exposition after λέγω at p. 36, 6, δή at 16, 1. After ὁμοίως (— δείξομεν) it has δή instead of δέ at p. 32, 21; 34, 6 (cf. p. 72, 18; 76, 24 and 102, 14); V and the Vatican agree at p. 42, 24 on δέ, which I should have accepted. The Vatican has δέ instead of μέν at p. 8, 16, and instead of καί at p. 58, 4. In the use of the particles τε-καί, V and the Vatican are accustomed to agree, but the Vatican adds τε at p. 24, 4; 34, 8, and omits it at 34, 24. The Vatican departs repeatedly from V in the omission of the article; see p. 6, 13; 10, 21; 22, 18; 24, 16; 34, 10, 23; 36, 2; it adds the article at p. 26, 17. Add the differing readings at p. 2, 24 ἅπαντα, p. 6, 12 ἔσται, p. 8, 6 διεξέρχεται, p. 24, 24 τέμνῃ, 25 ἐφάπτηται, p. 26, 3 μή.