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Published online by Cambridge University Press: 05 January 2009
The reception of Euclid's Optica in the West has received scant attention, in contrast with the interest evoked by the Latin tradition of the Elements. A study of the extremely complex manuscript tradition of the Optica reveals that the translations of this work too were soon in the hands of many teachers, eager to learn what the great Geometer taught concerning vison and visual perspective. Three translations—two from the Arabic (Liber de radiis visualibus and Liber de aspectibus) and one from the Greek (Liber de visu)—were available to scholars before the close of the twelfth century. Furthermore, the Greco-Latin Liber de visu, by far the most widely known and carefully studied of the translations, appeared in at least three different versions before 1200. One of these versions is of particular interest as providing evidence of the diffusion of texts among the scholarly community in the latter part of the twelfth century. The version in question has survived in two manuscripts, Bodleian Library, Corpus Christi College 283, folios 163r–165v, and Seville, Bibl. Columbina 7.6.2, folios 43(44)v–54(55)r. Although the various translations and many other versions of Liber de visu are anonymous, the authors of this text are explicitly given in the colophon, which reads: Nota quod sexaginta et tria toreumata continentur in is to libra. Aimare, gralias age quia hoc opus sic glosulasti sub magistro Johanne de Beaumont. Explicit feliciter liber de visu. Whether Aimar was merely the scribe or perhaps the student of John of Beaumont, it is undoubtedly the latter that is to be primarily credited with the contents of the treatise. Unfortunately, neither The complete peerage nor the Dictionary of national biography list a John of Beaumont from the twelfth century, although the Beaumont family, with some reputation for learning, was prominent at that time in Normandy and England, particularly in the regions near Oxford. Whether John was a member of that illustrious line remains merely a matter for speculation. In any case, the treatise remains of interest to Euclidian scholars and historians of optics as a good witness to the twelfth century concern, not only with Euclid's visual theory, but particularly with his attempts to employ geometry in solving the problems of visual perspective.
1 For some discussion of these traditions see Haskins, Charles H., Studies in the history of mediaeval science, New York, 1924, chapters V, VI, IX.Google Scholar An indication of the complexity of the Latin tradition of the Elements is found in Clagett, Marshall, ‘The medieval Latin translations from the Arabic of the Elements of Euclid with special emphasis on the versions of Adelard of Bath’, Isis, 1953, 44, 131–54.CrossRefGoogle Scholar
2 See Lindberg, David C., A catalogue of medieval and Renaissance optical manuscripts (The Pontifical Institute of Mediaeval Studies: Subsidia mediaevalia, IV), Toronto, 1975, pp. 46–55Google Scholar, for a list of the Latin manuscripts containing the different translations and versions of the Optica. An edited Greek text of the Optica and an unedited Latin text of Liber de visu is included in the seventh volume of Heiberg, J. L. and Menge, H. (eds.), Euclidis opera omnia, Leipzig, 1895, pp. 3–121.Google Scholar An edited text of De visu, with an English translation and commentary, and the texts of the two Arabo-Latin translations are included in my ‘The mediaeval tradition of Euclid's Optics’, PhD dissertation, University of Wisconsin, 1972.
3 The Seville manuscript is at least in part a copy of Corpus Christi MS. 283 (hereafter C.C. 283), as is seen by the fact that the smeared area on Folio 165r of the latter manuscript appears as a blank space of exactly the same shape on Folio 52(53)r of the former. This part of C.C. 283 has been dated as late twelfth-early thirteenth century. See Lindberg, , op. cit. (2), p. 53.Google Scholar An early date is confirmed by the presence of only seven initial assumptions on folio 163r. All thirteenth-century texts of De visu have nine assumptions.
4 The colophon appears twice in C.C. 283, first in black ink and then in red, with slight differences. The black version has glossulati for glossulasti and benigniter for feliciter. The only other version of De visu which is not anonymous is found in MS. Vatican, Bibl. Apost., Vat. Lat. 3102, folios 37v–50r, which is ascribed to Witelo.
5 See The complete peerage (ed. by Doubleday, H. A. and de Walden, Lord Howard), 2nd edn., London, 1929, vii, 527–33, 737–42Google Scholar, for information on the Beaumont family in the twelfth century.
6 One of the Beaumont family, Hugh the Poor, is completely lost in obscurity after the middle of the twelfth century, as is pointed out by White, G. H. in ‘King Stephen's earldoms’, Transactions of the Royal Historical Society, 1930, 13, 79.CrossRefGoogle Scholar Could John have been a son of Hugh?
7 Arabic numerals are used throughout the text in the margins to mark the propositions; however, the digits are reversed, oriental fashion, for the last fifteen propositions. This numeration does not correspond to that found in Heiberg, as the Latin texts usually contained one, and sometimes two or three propositions not found in the Greek text.
8 The fifty-nine propositions of this text are not numbered. The frequent use, in the last twenty-eight propositions, of such expressions as ita habemus propositum, inde sic, intelligatur, item and vero, and their absence or extreme rarity in the first part indicate differences of authorship. Proposition 8 is given twice, one version from De visu, one from De radiis visualibus; propositions 24, 25, 31–33 and 60 of the edited text of De visu are not included in this manuscript.
9 I am here referring to proposition 40 as found in the edited text of my dissertation. Unless I am describing C.C. 283 or Milan T.91 I will use the numeration of that text.
10 Both manuscripts lack the penultimate propositions of Euclid's treatise; in the enunciation of proposition 48, fol. 164v, of C.C. 283 (proposition 49, folio 40r of Milan T.91) equales and inequales should be interchanged; in the enunciation of proposition 51, folio 165r, of C.C. 283 (proposition 52, folio 48r of Milan T.91) quinta should read quarto; in the enunciation of proposition 52, folio 165r, of C.C. 283 (proposition 53, fol. 48r of Milan T.91) nobis should be Omitted.
11 These folios, according to T. A. M. Bishop of the Faculty of History of Cambridge University, could date from the third quarter of the twelfth century.
12 See Curtze, Maximilian, ‘Über dem liber de similibus arcubus “des Ahmed ben Iusuf”’. Bibliotheca mathematica, 1889, 3, 15–16.Google Scholar
13 Milan T.91 has, on folio 48r: per secundam propositionem que talis est; but C.C 283 has, on folio 164r: per factam propositionem que talis est.
14 Cf. propositions 34 (folio 43v), 38 (folio 44v), 40 (folio 45r) in Milan T.91, where he stresses that the diagram is three-dimensional, i.e. made in aere.
15 Cf. proposition 37 (folio 44v) of Milan T.91, where the fact that the angle included in a semicircle is a right angle is given greater emphasis than in De visu.
16 Cf. propositions 45–50, folios 164v–165r of C.C. 283 (propositions 46–51, folios 47v–48r of Milan T.91).
17 For example in proposition 38, folio 44v, of Milan T.91, the very difficult lemma found in proposition 40 of De visu is ignored; in proposition 46, folio 164v, of C.C. 283 (proposition 47, folio 47v, of Milan T.91) the comments do not refer to the enunciation but are related to a simpler phenomenon treated as a special case in proposition 47 of De visu.
18 Cf. proposition 51, folio 165r, of C.C. 283 (proposition 52, folio 48r, of Milan T.91) and compare with De visu, proposition 52.
19 Cf. proposition 52, folio 165r, of C.C. 283, (proposition 53 folio 48v, of Milan T.91) and proposition 58, folio 165v, of C.C. 283 (proposition 59, folio 49r, of Milan T91).
20 Cf. propositions 13 and 15 folio 163v; propositions 32 and 33, folio 164r.
21 Cf. propositions 24–30, folio 164r. The conclusion of proposition 29, which states that the portion of a sphere seen by two eyes whose separation is less than the diameter of the sphere is the same as that seen by one eye further removed, is of some significance as it demonstrates an interest in the visual phenomenon itself, and not merely in the geometry. The text reads: Sic ergo sub duobus oculis F et G minus videtur, hoc est, sicut et ab uno, scilicet H.
22 Cf. Lindberg, , op. cit. (2), p. 46Google Scholar, for a list of manuscripts containing this translation of the Optica.
23 For proposition 4 see folio 60r of the British Museum text; for proposition 16, see folio 62v.