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The Astronomical Interpretation of Catoptrica

Published online by Cambridge University Press:  19 October 2012

Bernardo Machado Mota
Bernardo Machado Mota*
Affiliation:
University of Lisbon, Portugal E-mail: bernardomota@campus.ul.pt
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Argument

A Catoptrica attributed to Euclid appears in manuscripts amongst treatises dealing with elementary astronomy. Despite this textual background, the treatise has always been read literally as a theory of mirrors, and its astronomical significance has gone unnoticed. However, optics, catoptrics, and astronomy appear strongly intermingled in sources such as, amongst others, Geminus, Theon of Smyrna, Plutarch and Cleomedes. If one compares the optical reasoning put forward in these sources to account for the formation of moonlight with arguments of Catoptrica, one is able to shed new light on several principles and propositions of Catoptrica, some of which had been deemed corrupt, meaningless, and obscure. Moreover, the present analysis offers a glimpse at the context of a specific stage in the evolution of ancient catoptrics: Whether literally or by analogy, several of its results appear to have been set against a wider astronomical background, which explains the inclusion of Catoptrica in the group of texts loosely defined as “little astronomy.”

Type
Research Article
Information
Science in Context , Volume 25 , Issue 4 , December 2012 , pp. 469 - 502
Copyright
Copyright © Cambridge University Press 2012

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References

Abbreviation: KGW = Kepler: Gesammelte Werke. München: C. H. Beck (1937-).Google Scholar
Ariew, Roger. 1984. “Galileo's Lunar Observations in the Context of Medieval Lunar Theory.” Studies in History and Philosophy of Science 15 (3):213–226.CrossRefGoogle Scholar
Aujac, Germaine. 2002. Geminos. Introduction aux phénomènes. Paris: Les Belles Lettres.Google Scholar
Björnbo, Axel Anthon, and Vogel, Sebastian. 1912. Alkindi, Tideus und Pseudo-Euklid. Drei optische Werke. Leipzig: Teubner.Google Scholar
Burke, Robert Belle. 1928. The Opus Majus of Roger Bacon. Vol. 1. Philadelphia: University of Pennsylvannia Press.Google Scholar
Burnyeat, M. F. 2005. “Archytas and Optics.” Science in Context 18 (1):35–53.CrossRefGoogle Scholar
Burton, Harry E. 1945. “The Optics of Euclid.” Journal of the Optical Society of America 35 (5):357–372.CrossRefGoogle Scholar
Cherniss, Harold. 1951. “Notes on Plutarch's De Facie in Orbe Lunae.” Classical Philology 46:137–158.CrossRefGoogle Scholar
Cherniss, Harold F. 1957. “Concerning the Face which Appears in the Orb of the Moon.” In Plutarch. Moralia, vol. 12, edited by Henderson, Jeffrey, 1–223. Cambridge MA: Harvard University Press.Google Scholar
Delatte, Armand. 1939. Anecdota Atheniensia et ali. Tome II: Textes relatifs à l'histoire des sciences. Paris: Librairie E. Droz.Google Scholar
Diels, Hermann. [1879] 1965. Doxographi Graeci. Berlin: Walter de Gruyter.Google Scholar
Donahue, William H. 2000. Johannes Kepler. Optics. Paralipomena to Witelo & Optical Part of Astronomy. Sante Fe NM: Green Lion Press.Google Scholar
Duhem, Pierre. [1908] 1994. Sozein ta phainomena – Essai sur la notion de théorie physique de Platon à Galilée. Paris: Librairie philosophique J. Vrin.Google Scholar
Evans, James, and Berggren, J. Lennart. 2006. Geminos's Introduction to the Phenomena. A Translation and Study of a Hellenistic Survey of Astronomy. Princeton and Oxford: Princeton University Press.Google Scholar
Friedlein, Gottfried. [1873] 1967. Procli Diadochi In Primum Euclidis Elementorum Librum Commentarii. Hildesheim: Georg Olms.Google Scholar
Görgemanns, Herwig. 1970. Untersuchungen zu Plutarchs Dialog De Facie in orbe lunae. Heidelberg: Carl Winter Universitätsverlag.Google Scholar
Heath, Thomas L. 1913. Aristarchus of Samos the Ancient Copernicus. Oxford: Clarendon Press.Google Scholar
Heath, Thomas L. 1949. Mathematics in Aristotle. Oxford: Oxford University Press.Google Scholar
Heath, Thomas L. [1925] 1956. The Thirteen Books of Euclid's Elements. Vol. 1. New York: Dover.Google Scholar
Heath, Thomas L. [1932] 1991. Greek Astronomy. New York: Dover.Google Scholar
Heiberg, Johan Ludvig, and Menge, Heinrich. 1895. Euclidis Opera Omnia. Vol. 7. Optica, Opticorum Recensio Theonis, Catoptrica cum scholiis antiquis. Leipzig: Teubner.Google Scholar
Hicks, Robert Drew. 1979. Diogenes Laertius. Lives of Eminent Philosophers, vol. 2. Cambridge: Harvard University Press.Google Scholar
Hiller, Eduardus. 1878. Theonis Smyrnaei Philosophi Platonici Expositio Rerum Mathematicarum ad Legendum Platonem Utilium. Leipzig: Teubner.Google Scholar
Hogendijk, Jan P. 1985. “Diocles and the geometry of curved surfaces.” Centaurus 28:169–184.CrossRefGoogle Scholar
Jones, Alexander. 1987. “On Some Borrowed and Misunderstood Problems in Greek Catoptrics.” Centaurus 30:1–17.CrossRefGoogle Scholar
Kohl, Karl. 1924–1925. “Über das Licht des Mondes, eine Untersuchung von Ibn al-Haitham.” Sitzungsberichte der Physikalisch-medizinischen Sozietät in Erlangen 56–57:305–398.Google Scholar
Knorr, Wilbur R. 1983. “The geometry of burning-mirrors in antiquity.” Isis 74:53–73.CrossRefGoogle Scholar
Knorr, Wilbur R. 1985. “Archimedes and the Pseudo-Euclidean Catoptrics: early stages in the ancient theory of mirrors.” Archives internationales d'histoire des sciences 35/114–115:28–105.Google Scholar
Knorr, Wilbur R. 1994. “Pseudo-Euclidean Reflections in Ancient Optics.” Physis 31:1–45.Google Scholar
Lejeune, Albert. 1947. “Archimède et la loi de la réflexion.” Isis 38:51–53.CrossRefGoogle Scholar
Lejeune, Albert. 1949. “Les Postulats de la Catoptrique dite d'Euclide.” Archives internationales d'histoire des sciences 2: 598–613.Google Scholar
Lejeune, Albert, 1957. Recherches sur la catoptrique grecque. Brussels: Académie royale de Belgique.Google Scholar
Lehn, Waldemar H., and Werf, Siebren van der. 2005. “Atmospheric refraction: a history.” Applied Optics 44:5624–5636.CrossRefGoogle ScholarPubMed
Mckirahan, Richard. 2008. Philoponus. On Aristotle Posterior Analytics 1.1–8. London: Duckworth.Google Scholar
Morgan, Morris Hicky. 1914. Vitruvius. The Ten Books On Architecture. Cambridge MA: Harvard University Press.Google Scholar
Morrow, Glenn. [1970] 1992. Proclus. A Commentary on the First Book of Euclid's Elements. With a new foreword by Ian Mueller. Princeton: Princeton University Press.Google Scholar
Mugler, Charles, 1964. Dictionnaire historique de la terminologie optique des Grecs. Paris: Klincksieck.Google Scholar
Nix, Ludwig, and Schmidt, Wilhelm. 1976. Heronis Alexandrini opera quae supersunt omnia, vol. 2: Mechanica et Catoptrica. Leipzig: Teubner.Google Scholar
O'Brien, Dominic. 1968. “Derived Light and Eclipses in the Fifth Century,” Journal of Hellenic Studies 88:114–127.CrossRefGoogle Scholar
Ovio, Giuseppe. 1918. L'Ottica di Euclide. Milan: Hoepli.Google Scholar
Prickard, Arthur Octavius. 1911. Plutarch on the Face which appears on the Orb of the Moon. Winchester and London: Warren and Son and Simpkin Language.Google Scholar
Rashed, Roshdi. 2002. Les catoptriciens grecs. Vol I: Les miroirs ardents. Paris: Les Belles Lettres.Google Scholar
Rose, Valentin, and Müller-Strübing, Hermann. 1867. Vitruvii De Architectura libri decem. Leipzig: Teubner.Google Scholar
Sabra, Abdelhamed I. 1989. The Optics of Ibn al-Haytham. Books I-III On Direct Vision. Vol II: Introduction, Commentary, Glossaries, Concordance, Indices. London: Warburg Institute.Google Scholar
Sesiano, Jacques. 1988. “Les miroirs ardents de Dioclès.” Museum Helveticum 45:193–202.Google Scholar
Simon, Gérard. 1994. “Aux origines de la théorie des miroirs: sur l'authenticité de la Catoptrique d'Euclide.” Revue d'histoire des sciences 47 (2):259–272.CrossRefGoogle Scholar
Smith, A. Mark. 1996. Ptolemy's Theory of Visual Perception. Philadelphia: American Philosophical Society.Google Scholar
Szabó, Arpad. 1978. The Beginnings of Greek Mathematics. Translated by A. M. Ungar from the German original of 1969. Dordrecht: Reidel.CrossRefGoogle Scholar
Takahashi, Ken'ichi. 1992. The Medieval Latin Traditions of Euclid's Catoptrica. Kyushu University Press.Google Scholar
Todd, Robert. 1990. Cleomedis Caelestia. Leipzig: Teubner.Google Scholar
Todd, Robert B. and Bowen, Alan C.. 2004. Cleomedes’ Lectures on Astronomy. A Translation of the Heavens with an Introduction and Commentary. Berkeley: University of California Press.Google Scholar
Toomer, Gerald. 1976. Diocles on Burning Mirrors. Berlin: Springer Verlag.CrossRefGoogle Scholar
Toulmin, Stephen. 1967. “The Astrophysics of Berossos the Chaldean.” Isis 63:65–76.Google Scholar
Tredennick, Hugh. 1976. Aristotle. Posterior Analytics. Cambridge: Harvard University Press.Google Scholar
Ver Eecke, Paul. 1938. Euclide, l'Optique et la Catoptrique. Paris: Bruges.Google Scholar
Wallies, Max. 1909. Ioannis Philoponi in Aristotelis Analytica Posteriora Commentaria cum Anonymo in librum II (= Commentaria in Aristotelem Graeca 13.3). Berlin: Georg Reimer.Google Scholar