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Witelo's Recension of Euclid's ‘De visu’
Published online by Cambridge University Press: 29 July 2016
Extract
Witelo, the thirteenth-century author of an extensive treatise on optics entitled Perspectiva, was thoroughly acquainted with most of the optical works available in the Latin West at that time. Among the works he studied was Euclid's Optica (in a Latin translation under the title De visu). It is the purpose of this paper to demonstrate that in fact Witelo had produced an earlier recension of Euclid's treatise, a work not generally attributed to him. Although this earlier investigation into optics is also entitled Perspectiva, to avoid confusion it will be referred to here as the Recension. This Recension is found in the following manuscripts:
Florence, Bibl. Riccardiana, MS 885 (s. xiv) fols. 132r–143v (Props. 1–15, 18, 17–23, 26–28, 16).
Milan, Bibl. Ambrosiana, MS R. 47 sup. (s. xiii) fols. 133r–148r (Props. 1–23, 26–61).
Paris, Bibl. Nat., MS lat. 7366 (s. xiv) fols. 90v–97v (Props. 1–23, 26–34).
Paris, Bibl. Nat., MS lat. 10252 (a.d. 1476) fols. 159 (154)v–172 (167)r (Props. 1–23, 26–30).
Toruń, Ksiąžnica, Miejska im. Kopernika, MS Gymnasialbibl. R.4°.2 (s. xiv) pp. 3–30 (Props. 1–23, 26–61).
Vatican, Bibl. Apost. Vaticana, MS Vat. lat. 3102 (s. xiv) fols. 37v–50r (Props. 1–23, 26–61).
Vienna, Österr. Nat. Bibl. MS 5303 (s. xv–xvi) fols. 32r–41v (Props. 1–23, 26–30).
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References
1 For Witelo's Perspectiva see Opticae thesaurus (with Alhazen's De aspectibus <e>ed. Friedrich Risner [Basel 1572; reprint edition New York 1972]) 1–474. See Lindberg's, David introduction to this reprint for a biographical summary of Witelo's life and bibliographical material on his work. All references to passages of the Perspectiva here refer to the pages of this reprint.ed. Friedrich Risner [Basel 1572; reprint edition New York 1972]) 1–474. See Lindberg's, David introduction to this reprint for a biographical summary of Witelo's life and bibliographical material on his work. All references to passages of the Perspectiva here refer to the pages of this reprint.' href=https://scholar.google.com/scholar?q=For+Witelo's+Perspectiva+see+Opticae+thesaurus+(with+Alhazen's+De+aspectibus+ed.+Friedrich+Risner+[Basel+1572;+reprint+edition+New+York+1972])+1–474.+See+Lindberg's,+David+introduction+to+this+reprint+for+a+biographical+summary+of+Witelo's+life+and+bibliographical+material+on+his+work.+All+references+to+passages+of+the+Perspectiva+here+refer+to+the+pages+of+this+reprint.>Google Scholar
2 Euclid's Optica appeared in at least three twelfth-century Latin translations: the Graeco-Latin (usually entitled Liber de visu) and two Arabo-Latin translations, Liber de radiis visualibus and Liber de aspectibus. Liber de visu is found in seven different versions. For a list and discussion of these versions see Lindberg, D. C., A Catalogue of Medieval and Renaissance Optical Manuscripts (Subsidia Mediaevalia 4; Toronto 1975) 46, 47, 50–54. A text of De visu is found in Heiberg, J. L. and Menge, H., Euclidis opera omnia VII (Leipzig 1883–1916) 3–121. An edition of the Latin text of De visu is included in my doctoral dissertation, ‘The Mediaeval Tradition of Euclid's Optics’ (Wisconsin 1972) 66–109. For an English translation of the Optica see Burton, H., ‘The Optics of Euclid,’ Journal of the Optical Society of America 35 (1964) 357–72.Google Scholar
3 Thorndike, L. and Kibre, P., A Catalogue of Incipits of Mediaeval Scientific Writings in Latin 2 (Cambridge, Mass. 1963) 1547, attribute this recension (as found in MSS Vat. Lat. 3102 and Riccardiana 885) to Witelo. However, they also attribute the same treatise, as found in MS Torun R. 4°, to Euclid (ibid. 1547).Google Scholar
4 This list is taken from Lindberg's Catalogue 54. The numbers of the propositions given correspond to the numeration of the propositions of De visu as found in my dissertation. Note that in all of the manuscripts propositions 24 and 25 of De visu are lacking. Of the various manuscripts of De visu and its versions only two, MSS Glasgow, Univ. Libr., Gen. 1115 (BE. 8.y.18) fols. 177v–188r and Milan, Bibl. Ambrosiana, T. 91 sup. fols. 39r–49r, are without these two propositions, which are additions to the Greek text of the Optica. The first proposition of the Recension appears as a gloss to the text of De visu in MS Dresden, Sächsische Landesbibl., Db 86 fol. 111r.Google Scholar
5 The propositions of De visu that do not appear in the Perspectiva are props. 19–23.Google Scholar
6 Repr. ed 134–5. Note that there is a discrepancy between the text and the diagram as found in the reprint edition of the Perspectiva. The simplest way to remove this inconsistency is to reverse the diagram and let the first dexteriore in the text read sinisteriore and the first sinisteriore read dexteriore. I have given the text as in the printed edition, but have relettered the diagram.Google Scholar
7 MS Paris Lat. 10252 ff. 165v–166r. The numbers of the propositions from the Recension here and in the following examples are the numbers of the Recension, not of De visu. Google Scholar
8 Theisen, diss. 73.Google Scholar
9 Repr. ed. 148.Google Scholar
10 Vat. Lat. 3102 f. 44r.Google Scholar
11 Theisen, diss. 81–82.Google Scholar
12 Repr. ed. 136.Google Scholar
13 MS Paris Lat. 10252 f. 166v.Google Scholar
14 Repr. ed. 136.Google Scholar
15 MS Paris Lat. 10252 f. 166v.Google Scholar
16 Repr. ed. 129.Google Scholar
17 MS Paris Lat. 10252 f. 162r.Google Scholar
18 Theisen, diss. 70.Google Scholar
19 Repr. ed. 122–123.Google Scholar
20 MS Paris Lat. 10252 f. 163r–163v.Google Scholar
21 Theisen, diss. 70–71.Google Scholar
22 Repr. ed. 148.Google Scholar
23 MS Paris Lat. 10252 f. 169v–170r.Google Scholar
24 Theisen, diss. 80–81.Google Scholar
25 See MS Vat. Lat. 3102 f. 45v. The author comments: ‘Credo contentum esse corrigendum vel eo quod hic apparet deficere vel eo quod deductio non apparet maturata.’Google Scholar
26 The first proposition states: ‘Nullum visorum simul videtur totum.’ In De visu Euclid argues that this is true because the visual rays take time to scan the object seen. The author of the Recension argues that the enunciation is true because a ray normal to the object seen is shorter than all the other rays and consequently arrives in the least time.Google Scholar
27 See Lindberg's, introduction to the repr. ed., p. ix.Google Scholar