DAMIANUS OF LARISSA

(fl. probably fifth to sixth centuries CE), optics.

Damianus is the name of the author of a short monograph in optics, the Optical Hypotheses. Nothing is known of the author, and the work is never mentioned in the ancient technical corpus. The latest cited authority is Ptolemy. The text is therefore later than the second century CE, but several features of the exposition suggest that Damianus was affiliated with some Neoplatonic school of late antiquity, most likely the one that flourished at Alexandria in the fifth and sixth centuries CE with Ammonius and his pupils.

Contents of the Treatise . The Optical Hypotheses were very likely aimed at providing a concise introduction to some basic notions in optics. It may be that they are a redaction of an introductory lecture to some major technical work. In fact, the manuscript tradition assigns them a role among the prefatory material to the Euclidean Optics. A historically sound assessment of the value of Damianus’s text must take such a crucial feature into account. The treatise is divided into fourteen parts of variable length. The contents of each part are summarized at the very beginning in a list of one-sentence chapters. The most complete title found in the manuscripts is in fact Chapters of the Optical Hypotheses of Damianus of Heliodorus of Larissa. A tentative identification of this Heliodorus with Ammonius’s brother must remain a conjecture unless new evidence is found.

The main thesis of the treatise is the identity of sight and solar light. Chapter 13 is devoted to an extensive treatment of this topic with numerous examples. In this way, a common set of assumptions provides foundations both to optics and to an investigation of the properties of solar rays. The contents of the treatise can be summarized as follows. Sight is something emitted from the eye (chapter 1), and what is emitted is in fact light (2). Sight moves in a straight line (3), and the visual rays comprise a right-angled cone (4–5). The cone is made of a discrete set of rays (6) and anything seen is viewed under an acute or right angle (7); what is seen from a larger angle seems larger (8). We see primarily by means of the light along the axis of the cone, because of the forward character of the visual power (10). The vertex of the visual cone is inside the pupil (11). We see either directly or by broken rays, the latter either reflected or deflected (that is, refracted) (12). Visual and solar rays behave identically and propagate instantaneously (13). Reflections and deflections of both visual and solar rays occur at equal angles (14). Such statements are proved either inductively through a number of examples or by providing theoretical, and mainly teleological, explanations. The latter ascribe some kind of necessity to phenomena that had been since long established by means of technical devices or experiments. This happens, for instance, in chapter 3. In it, a teleological argument (whose source is very likely Hero) grounded on the principle of economy corroborates Ptolemy’s experimental proof that sight moves in a straight line.

Geometrical explanations, when present in the Optical Hypotheses, are particularly simple and not supported by any mathematical proofs. A case in point is the reason why the cone of vision is right-angled. This is because Nature prefers a well-defined form, namely the right angle, to an indeterminate one, as any acute or obtuse angle is (the source is Proclus). Statements employing a refined technical lexicon are present, but they might well have served to give the Optical Hypotheses an aura of exactness: the assertion that reflection at equal angles occurs with respect to any homeomeric line, or the quotation of Archimedes’ definition of straight line serve as examples. A remarkable “mistake” is Damianus’s claim that deflection also occurs at equal angles. The claim is argued on the sole basis of an asserted similarity between reflection and deflection. To save Damianus from such a seemingly obvious blunder, it has been proposed that the equal angles were the ones that the refracted ray forms with the normal to the surface and the incident ray when produced. Another explanation could be that A” double refraction may produce in suitable conditions equality of angles of incidence and refraction. Of some interest is the term diaklasis (deflection) employed by Damianus. The same word is typical of the very late commentator Olympiodorus, a pupil of Ammonius.

Damianus’s Sources . The Optical Hypotheses offer some interesting pieces of documentary information. Damianus ascribed (chapter 14) to Hero a proof of the equal-angle rule for reflection. The proof is identical with the one attested in the treatise that has come down to us, in Latin translation only and attributed to Ptolemy, under the title De speculis. Damianus asserted (chapter 3) that Ptolemy showed by some device that sight moves in a straight line and forms a right-angled cone (possibly a misconception for right cone). Most likely, this happened in the first book of Ptolemy’s Optics, which is now lost. Plenty of examples in the Optical Hypotheses already, in fact, appear in what remains of Ptolemy’s treatise. Damianus also quoted (chapters 5, 8, and 12 respectively) almost exactly proposition 1 and definition 4 of the Euclidean Optics, and definition 6 of the Catoptrics. Two examples in the Optical Hypotheses coincide with examples in the introduction preceding one redaction of Euclid’s Optics. Finally, a reference, in the context of a citation of the isoperimetric theorem, to the circle as “the most spacious” plane figure tallies with terminology typical of Neopla-tonic commentators. The identity of the basic assumptions in optics and in a theory of the propagation of solar rays is already in Geminus. Other, similar examples can be adduced: Damianus’s text is just a bit more than a patchwork of quotations from standard works. However, it need not follow that the author directly drew from all the sources here mentioned. Most of the examples were commonplace in the optical literature, and it is likely he worked on epitomes and compilations.

BIBLIOGRAPHY

WORK BY DAMIANUS

Damianos Schrift über Optik, mit Auszügen aus Geminos, griechisch und deutsch herausgegeben von Richard Schöne. Berlin: Reichsdruckerei, 1897. The critical edition of Damianus’s text. The editor wrongly relied on manuscripts carrying a Byzantine recension and neglected what very likely will turn out to be the best manuscript. A new edition is much needed.

OTHER SOURCES

Eastwood, Bruce S. “Metaphysical Derivations of a Law of Refraction: Damianos and Grosseteste.” Archive for History of Exact Sciences 6 (1969/1970): 224–236, in particular 225–232. A full discussion of the bewildering rule of equal angles in refraction is here offered, and the first proposal expounded in the text above is made.

Hultsch, Friedrich. Berliner philologische Wochenschrift 46 (12 November 1898): 1413–1417. This review of Richard Schöne’s editions includes several corrections. It supplements Schöne’s prolegomena on important points and contains the interpretation of Damianus’s equal-angle rule as a double refraction. Hultsch wrote also the notice in Pauly-Wissowa, G., et al., eds., Paulys Real-Encyclopädie der Classischen Altertumswissenschaft. 2nd ed., 1st Series. 24 vols. in 43 tomes. Stuttgart, Germany: J.B. Metzler, 1894–1963, Vol. IV, Tome 2: 2054–2055, where he proposed that Damianus was Heliodorus’s son and pupil and that the former abridged a work of the latter. Hultsch’s view that Heliodorus’s work was in thirteen chapters relies on a wrong assessment of the contents of some manuscripts.

Knorr, Wilbur R. “Archimedes and the Pseudo-Euclidean Catoptrics: Early Stages in the Ancient Geometric Theory of Mirrors.” Archives Internationales d’Histoire des Sciences 35 (1985): 28–105, in particular 89–96. A general assessment of Damianus’s treatise, with particular emphasis on its dating, may be found in this text. Knorr proposes the identification of Heliodorus with Ammonius’s brother, and refutes with a detailed discussion Heiberg’s contention that the author of the introduction to a redaction of the Euclidean Optics, usually but on no grounds believed to be Theon, had drawn from Damianus’s work.

Tannery, Paul. “Rapport sur une mission en Italie.” Archives des missions scientifiques et littéraires, 3^e série, 13 (1888): 405–455. Reprinted in Id., Mémoires Scientifiques, tome II (1912), n. 44: 269–331. Detailed information on those of the manuscripts that were copied by the famous calligrapher Angelus Vergecius may be found in this work.

Todd, Robert B. “Damianus.” In Dictionnaire des Philosophes Antiques, edited by Richard Goulet. Paris: CNRS Editions, 1994.

———. “Héliodore De Larissa.” In Dictionnaire des Philosophes Antiques, edited by Richard Goulet. Paris: CNRS Editions, 2000. An account of Damianus’s work and a discussion of its connection with late Platonism in this text.

———. “Damianus (Heliodorus Larissaeus).” In Catalogus Translationum et Commentariorum: Mediaeval and Renaissance Latin Translations and Commentaries 8, edited by Virginia Brown. Washington, DC: Catholic University of America Press, 2003. This is a valuable exposition of the Fortleben of Damianus’s work, with an overview of the manuscript tradition.

Fabio Acerbi