Transformation of Euclid’s Optics in Late Antiquity

in Nuncius
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The tradition of Euclid’s Optics includes a number of versions and translations, whether in Greek, Arabic or Latin. They differ from each other to various extents with respect to their form, structure and content. Textual divergence concerns the very core of geometric optics, i.e. the opening definitions and first propositions. In these parts the variance of the different versions is most striking. Thus the tradition of the Euclidean text involved a transformation of the visual model that cannot be explained merely philologically or by incidental elements in the process of transmission. This paper aims to explain these textual transformations as an intentional process of updating and adapting geometric optics to the best of its understanding at a given time. For this purpose, the different versions of Euclid’s Optics are placed in the context of and compared with late antique and early medieval sources. From Ptolemy through al-Haytham, experience had been used as an argument either to refute or to defend the geometric model of vision. Indeed, the visual ray hypothesis turns out to be more or less or not at all compatible with experience in the various versions of Euclid’s Optics. Their divergence thus provides evidence of a lively tradition of Euclidean Optics whose core has been transformed by discussing and testing the visual model on empirical grounds.

Transformation of Euclid’s Optics in Late Antiquity

in Nuncius




M.F. Burnyeat“Archytas and Optics,” Science in Context2005 18:35–53.


Arthur E. Haas“Antike Lichttheorien,” Archiv für Geschichte der Philosophie1907 20:345–386; David C. Lindberg Theories of vision from al-Kindi to Kepler (Chicago: University of Chicago 1976) pp. 1–17.


Johan L. HeibergLitterargeschichtliche Studien über Euklid (Leipzig: Teubner1882) pp. 90 130 148.


Harry Edwin Burton“The Optics of Euclid,” Journal of the Optical Society of America1945 35:357–372.


W. Knorr“Pseudo-Euclidean reflections” (cit. note 9), pp. 294–234, 42–43; Alexander Jones, “Peripatetic and Euclidean theories of the visual ray,” Physis1994 31: 47–76 here pp. 51–56.


Euclid“The Book of Euclid on the Difference of Aspects/ Kitāb Uqlīdis fī Ikhtilāf al-manāẓir” in The Arabic version of Euclid’s Optics2 vols. edited by Elaheh Kheirandish (New York Springer 1999) vol. 1 pp. 1–229.


Text edited by Wilfred R. TheisenThe Mediaeval Tradition of Euclid’s ‘Optics’ (PhD dissertation: The University of Wisconsin1971) pp. 336–384.


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    Figure 1

    The oldest manuscript of the so-called Heiberg A version of Euclid’s Optics (OGA) – Vienna, Österreichische Nationalbibliothek, Vindob. Cod. Phil. gr. 31, ff. 254v–271v (12th century), here f. 254v: Title, Definitions, and propositions 1, 2, and the beginning of 3.

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    Figure 2

    The oldest manuscript of the so-called Heiberg B version of Euclid’s Optics (OGB) – Vatican Library, Vat. gr. 204, ff. 42v–58r (10th c.), here f. 47r: propositions 8 (end), 9, 10, and the beginning of 11.

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    Figure 3

    Ps-Euclid, De speculis – detail of manuscript (13th century) Oxford, Bodleian Library, Digby 40, f. 13v; prop. 4. and diagram:129 The continuous visual cone: The pupil of the eye is at d; the ray emitted from d is db falling on eg. The farther the ray (radius) db reaches out the broader becomes its base eg.


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