When circles don't look like circles: An optical theorem in Euclid and Pappus

Archive for History of Exact Sciences - Tập 44 - Trang 287-329 - 1992
Wilbur R. Knorr1
1Stanford University

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Andersen, K. 1987. “Ancient Roots of Linear Perspective,” in From Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe, ed. J. L. Berggren and B. R. Goldstein, Copenhagen: University Library Andronicos, M. 1984. Vergina: The Royal Tombs, Athens: Ekdotike Athenon S.A., 1984 Brownson, C. D. 1981. “Euclid's Optics and its Compatibility with Linear Perspective,” Archive for History of Exact Sciences, 24: 165–194 Edgerton, S. Y. Jr. 1975. The Renaissance Rediscovery of Linear Perspective, New York: Basic Books Euclid, Optics: see Heiberg 1895 ; Ver Eecke 1959 Euclid, Phaenomena: see Menge 1916 Friedlein, G. (ed.). 1873. Procli Diadochi In Primum Euclidis Elementorum Librum Commentarii, Leipzig: Teubner (repr. Hildesheim: Olms, 1967) Gericke, H. 1984. Mathematik in Antike und Orient, Berlin: Springer Heath, T. L. 1921. A History of Greek Mathematics, Oxford: Clarendon Press, 2 vols. Heiberg, J. L. 1882. Literargeschichtliche Studien über Euklid, Leipzig: Teubner Heiberg, J. L. (ed.). 1895. Euclidis Opera Omnia, vol. VII (Euclidis Optica, Opticorum recensio Theonis, Catoptrica, cum scholiis antiquis), Leipzig: Teubner Hultsch, F. (ed.). 1876–78. Pappi Collections Quae Supersunt, 3 vols., Berlin: Weidmann (repr. Amsterdam: Hakkert, 1965) Jones, A. 1989. “Pappus' Notes to Euclid's Optics,” paper read at the meeting of the Canadian Society for History and Philosophy of Mathematics, Universite Laval Kemp, M. 1990. The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat, New Haven: Yale University Press Knorr, W. R. 1982. “Observations on the Early History of the Conics,” Centaurus, 26: 1–24 Knorr, W. R. 1985a. “Ancient Versions of Two Trigonometric Lemmas,” Classical Quarterly, 35: 362–391 Knorr, W. R. 1985b. “Archimedes and the pseudo-Euclidean Catoptrics: Early Stages in the Ancient Geometric Theory of Mirrors,” Archives internationales d'histoire des sciences, 35: 28–105 Knorr, W. R. 1986. Ancient Tradition of Geometric Problems, Boston: Birkhäuser Knorr, W. R. 1990. “Pseudo-Euclidean Reflections in Ancient Optics,” paper presented at a conference on history of optics, organized by A. I. Sabra, for the Dibner Institute, May 30–June 2, 1990 Knorr, W. R. 1992. “Geometric Optics in the Hellenistic Period and Later Antiquity (3rd century B.C. to 6th century A.D.)” in Aufstieg und Niedergang der römischen Welt, ed. W. Haase, ser. II, vol. 37, pt. 4/5 Knorr, W. R. “On the Principle of Linear Perspective in Euclid's Optics” (to appear in Centaurus) Lejeune, A. 1948. Euclide et Ptolemee: Deux stades de l'optique geometrique grecque, Louvain: Bibliothèque de l'Université Menge, H. (ed.). 1916. Euclidis Opera, vol. VIII (Phaenomena et scripta musica), Leipzig: Teubner Morrow, G. 1970. Proclus: A Commentary on the First Book of Euclid's Elements, Princeton: Princeton University Press Pappus, Collection: see Hultsch 1876–78; Ver Eecke 1933 Pedersen, O. 1974. A Survey of the Almagest, Odense: Odense University Press Proclus, In Euclidem: see Friedlein 1873; Morrow 1970 Richter, G. M. A. (n.d.; ca. 1970). Perspective in Greek and Roman Art, London and New York: Phaidon Simon, G. 1988. Le regard, l'être et l'apparence dans l'optique de l'antiquité, Paris: Éditions du Seuil Theon of Alexandria, Recensio Opticorum: see Heiberg 1895; Ver Eecke 1959 Ver Eecke, P. 1933. Pappus d'Alexandrie: La Collection mathématique, 2 vols., Paris and Bruges: Desclee de Brouwer Ver Eecke, P. 1959. Euclide: L'Optique et la Catoptrique, Paris: Blanchard (repr. of the edition of 1938) White, J. 1967. The Birth and Rebirth of Pictorial Space, 2nd ed., Boston: Boston Book and Art Shop