CHAPTER SEVEN

THEON(?)'S PREFACE TO EUCLID'S OPTICA

As we have seen above Theon of Alexandria published a revised version of Euclid's Elements. We also have a revised version of the OpticaiBB which has been traced to Theon, though unlike the edition of the Elements it is not designated in this way in the mss. This revision is prefaced by an introductory essay, 144.1-55.2 Heiberg. 189 Heiberg argued that this is the authorized report by a pupil of his teacher's introduction to his exposition ("Lehrvortrag") of the work. 19° This piece is interesting in various ways. The first of these is that isagogical questions are not at all at issue explicitly, though we may infer that the authenticity of the bnypacpft was regarded as unproblematic. Moreover the report may well be incomplete, the pupil (or a later scriba) preserving only what he believed to be really interesting. The second point of interest is that the lecturer very firmly places Euclid's treatise in the context of physics and sense­ perception.191 The original version of Euclid's Optica is the most

188 Both versions ed. Heiberg (1895). Heiberg (1882) 139 bases the ascrip­ tion to Theon on a scholion in Paris. gr. 2468: 'to 1tpooiJ.LtoV be tij~ tou 8erov6~ ecrnv E~T]yrlCJEro~. Because this ms. was written in 1565, the ascription has little or no authority; we may observe that the scholion is not (!) found in Heiberg's edition of the scholia to the later version at Heiberg (1895) 251 ff. Even so, Heiberg's view was accepted by authorities such as Heath (1921) 1.441, Ziegler (1934) 2079, Neugebauer (1975) 2.893, and Knorr (1989) 452 n. 17; also by Fraser (1972) 1.389. Toomer (1976b) 322 writes that "there is no direct evidence [my italics] ... that Theon was responsible for this version, though he remains the most likely candidate". 189 Preliminary ed. with facing German transl. Heiberg (1882) 138-45. 190 Heiberg ( 1882) 138-9, 145-6: the words aJtoowcvu~. h:oJ.LtSE ( 144.1), ecpucrKEV (144.9) do not apply to Euclid but to the lecturer: an example of what came to be called alto cprovij~. for which practice see Richard ( 1950). For earlier evidence concerning the noting down of a master's lectures see Sedley (1989) 103-4, and Dorandi (1997b) 46, 48, who argues that certain works by Philodemus are alto cprovij~ [scil., of Zeno of Sidon]; for similar evidence concerning the Sceptical Academy see Mansfeld (1994) 193. For Marinus see below, Ch. VIII. 191 For the physicalist aspects of the introduction to Heron(?)'s Catoptrica see above, Ch. Vl 5. Even purely geometric optics fails to avoid physics THEON(?)'s PREFACE TO THE OPTICA 59 purely mathematical of all extant ancient treatises on, or accounts of, optics and vision, though his visual rays are real physical entities. Greek optics and theories of vision are in several ways defective; naturally, light is not given the predominant role it plays since the discoveries of ibn al-Haytham/ Alhazen, Kepler, and Descartes, but as a rule is only a necessary partner of the (e.g., fiery, or pneumatic) rectilinear visual rays, or of the visual cone which, depending on the particular theory at issue, may be formed by the rays themselves or by the medium that is influ­ enced by the agent of seeing. These rays or this cone, issuing from their base in or upon the eye, are so to speak a kind of fingers, or sticks, which touch the objects that are seen and then report back. 192 In conformity with the mainstream tradition of ancient geometrical optics Theon(?) too posits that the eye sends out a cone of straight visual rays. 193 In this context, however, it is important to note that the great Ptolemy in his Optica-only books 11-V are extant in a medieval Latin translation from the Arabic, while the end of book V is lost too-refined this traditional geometric optics even further, but also revised it and far more straightworfardly placed it in a physical setting. On the one hand he argued that the rays in the cone form a continuum, and so turned them into mere abstrac­ tions. On the other he payed proper attention to the indispensable role played by the illumination of the sensible object and the qualities such an object must have in order to reflect illumination, to the perception of the proper object of vision, colour, and via colour to the apperception of other qualities of the object. And he performed experiments to underpin his theoretical views. 194 Several arguments in support of Euclid's doctrine of visual perception are offered by Theon(?) in the course of his exposition, e.g. that the eye is globular, not hollow like the ears, nostrils, and mouth, as it would be had it been a purely receptive organ. We altogether, see Lindberg (1976) 11-7 on the mathematicians, and on Greek optics in general the impressive overview of Crombie (1994) 1.155-76, who demonstrates that the theories gradually came to include more and more physics and physiology. 192 See below, pp. 127-8, complementary note 192. 193 As is postulated in the first definition of Euclid's Optica in both recensions. Also other matters explained in Theon(?)'s introduction pertain to the definitions. 194 Ed.: Lejeune (1956) 11; see further Lejeune (1947), Lejeune (1948) 38-41, 65-6, on the lost book I of the treatise, Neugebauer (1975) 2.894-6, Simon (1988) 83-91, and esp. Smith (1988), Crombie (1994) 1.162-70.