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Published online by Cambridge University Press: 24 April 2013
Six palimpsest folios – or, to be accurate, three bifolios – of the Verona manuscript, Biblioteca Capitolare XL (38), contain fragments of a Latin translation of Euclid's Elements: fols. 331v–r and 326v–r, 341r–v and 338r–v, 336r–v and 343r–v. The folios are dated to around a.d. 500, and the text is written in capital script in two columns. Unfortunately the folios have suffered severe damage from various chemical substances, which were used by nineteenth-century scholars in attempts to retrieve the underlying text. Nevertheless, an edition of the fragments finally appeared in 1964 by M. Geymonat.
I thank Prof. Michel Federspiel, Clermont-Ferrand, and Prof. Jean-Yves Guillaumin, Besançon, for their comments on an earlier draft of this paper. For more critical notes on this text, see E. Bohlin, ‘Some Notes on the Fragmentary Latin Translation of Euclid's Elements Preserved in the Codex Palimpsestus Veronensis Bibliothecae Capitularis XL (38)’, in F. Biville, M.-K. Lhommé, D. Vallat (eds.), Latin vulgaire – latin tardif IX. Actes du IXe colloque international sur le latin vulgaire et tardif, Lyon, 2–6 septembre 2009 (Lyon, 2012), 881–92.
1 Geymonat, M. (ed.), Euclidis latine facti fragmenta Veronensia (Milan, 1964)Google Scholar. For a more detailed description of the folios and previous research on them, see Geymonat pp. 5–9, 55–65. For an introductory survey of Euclid in the Middle Ages, see Folkerts, M., ‘Euclid in Medieval Europe’, in id., The Development of Mathematics in Medieval Europe. The Arabs, Euclid, Regiomontanus (Aldershot, 2006), 3.1–64Google Scholar.
2 Explanation of some of the critical symbols and conventions used in Geymonat's edition (for further details, see Geymonat [n. 1], 13): full stop (.) = illegible letter; dash (—) = two or more illegible letters; dash within square brackets ([—]) = illegible part of the text due to damaged parchment; full stop within square brackets ([.]) = illegible letter due to damaged parchment; letter(s) within round brackets = letter(s) illegible to Geymonat, but preserved in a transcript made by A. Mai in 1817 (see Geymonat [n. 1], 13 and 56–7; the transcript is found in Vat. lat. 9555, Bibl. Apost. Vat., fols. 96r–100v, 145r–v, 144r); letter(s) within angle brackets (< >) = letter(s) supplied by conjecture. In addition, small capitals are used in the edition for letters which are written in the palimpsest in smaller size than the regular script.
It should also be pointed out that the following two signs are used in the palimpsest as well as in the edition: interpunct (·) is used for separating pairs or groups of Greek letters; linea nasalis (ˉ) occurs at the end of a line and after the vowel to which it belongs.
3 Geymonat (n. 1), 38.
4 Geymonat (n. 1), 47.
5 Heiberg, J.L. (ed.), Euclidis Elementa. Edidit et latine interpretatus est I. L. Heiberg. Vol. IV. libros XI–XIII continens (Leipzig, 1885)Google Scholar.
6 Mai initially wrote religabunt in his transcript, but then corrected it to relicabunt; see Vat. lat. 9555 fol. 100r and Geymonat (n. 1), 44. Cf. n. 2 above.
7 The top line of fol. 341v col. 1 is illegible, but Geymonat, rightly as it seems, supplied GULAS SEDES and suggested that GULAS, together with AN at fol. 341r col. 2, line 23, was deleted by the corrector. In addition, at fol. 338r col. 2, line 11 only the correction conas, written above the line, can be read; Geymonat therefore suggested that triangulas originally was read in this line.
8 Geymonat (n. 1), 40.
9 Cf. Callebat, L. and Fleury, P. (edd.), Dictionnaire des termes techniques du De architectura de Vitruve (Hildesheim, Zurich and New York, 1995)Google Scholar, s.v. expedio (col. 108). (Note that not all attestations of the verb expedire in Vitruvius are recorded in the dictionary.)
10 On est with the infinitive = licet, oportet etc. with the infinitive, see Hofmann, J.B. and Szantyr, A., Lateinische Syntax und Stilistik (Munich, 1965), 349Google Scholar and e.g. Svennung, J., Orosiana. Syntaktische, semasiologische und kritische Studien zu Orosius (Uppsala, 1922), 78–81Google Scholar. The rationes may, in my view, be regarded as some type of inner object to expedire. As noted by E. Wistrand, moreover, there are in Vitruvius not a few occurrences of abstract nouns, e.g. ratio, carrying a very vague, or even redundant, force (see Wistrand, E., Vitruviusstudier [Gothenburg, 1933], 48–50Google Scholar); I suggest that this could be the case with our rationes too.
11 Euclid. elem. vers. M lines 332, 346, 356 (Folkerts, M. [ed.], ‘Boethius’ Geometrie II. Ein mathematisches Lehrbuch des Mittelalters [Wiesbaden, 1970], 215 and 217.Google Scholar) The reference is abbreviated according to the Thesaurus Linguae Latinae (TLL); see the Index to the TLL (Leipzig, 1990), 91.
12 If it is a misreading, it is to be put on Mai's account; cf. n. 2 above.
13 In his edition Geymonat did not point out that it was difficult to read; in fact, as Geymonat reports, Mai also read QUO IURE (see also Vat. lat. 9555 fol. 99v; cf. n. 2 above). Therefore, if Mai and Geymonat read correctly, it ought to be a corruption. On the other hand, since Mai's transcript was made in haste and not very diligently, it cannot be ruled out that Mai may have misread and Geymonat then was led into error by Mai (on the quality of Mai's transcript, see Geymonat [n. 1], 56–7).
14 Lowe, E.A., Codices Latini antiquiores. A Palaeographical Guide to Latin Manuscripts Prior to the Ninth Century. Part IV. Italy: Perugia–Verona (Oxford, 1947), 28Google Scholar.
15 Ippolito, A. (ed.), Marii Victorini Explanationes in Ciceronis rhetoricam (Corpus Christianorum. Series Latina: 132) (Turnhout, 2006)Google Scholar.
16 in duas aequales partes: Euclid. elem. vers. M lines 156 and 157 (Folkerts [n. 11], 193); in duas aequas partes: ibid. lines 262 and 263 (Folkerts [n. 11], 207).
17 per aequalia: Euclid. elem. vers. M line 240 (Folkerts [n. 11], 203).
18 Euclid. elem. vers. M line 271 (Folkerts [n. 11], 209). In line 197 (Folkerts [n. 11], 197), on the other hand, spatia should perhaps be implied thus: […] eaque [sc. spatia] diametrus in duo aequa [sc. spatia] partitur. If so, in duo aequa is not being used absolutely.
19 See Vat. lat. 9555 fol. 99v; cf. n. 2 above.
20 See Vat. lat. 9555 fol. 99v; cf. n. 2 above. See also Geymonat (n. 1), 24, line 6.
21 At fol. 331v col. 1, lines 7–9, <SOLI>DUM QUIPPE corresponds to στɛρɛὸν γάρ (Elements 11 Prop. 24 p. 70,18 Heiberg), at fol. 326v col. 2, lines 2–3, EICIATUR QUIPPE corresponds to ἐκβɛβλήσθω γάρ (Elements 11 Prop. 25 p. 74,11 Heiberg), and at fol. 338v col. 1, lines 1–2, CONPLEANTUR QUIPPE corresponds to συμπɛπληρώσθω γάρ (Elements 12 Prop. 8 p. 178,1 Heiberg).
