DIOCLES On Burning Mirrors : The Arabic Translation of the Lost Greek Original 1. Life of Diodes 2. Diocles’ work: Title and Subject 3. The theory of conic sections up to the time of Diocles 4. Conics in On Burning Mirrors 5. Influence of On Burning Mirrors 6. Manuscripts and Text of On Burning Mirrors Editorial Procedures On Burning Mirrors Text and translation Photographs of Meshhed manuscript Commentary Appendix A. Text and translation of Eutocius’ excerpts from On Burning Mirrors Appendix B. Other ancient and medieval proofs of the focal property of the parabola Appendix C. Analysis of Archimedes’ problem and Diocles’ solution by O. Neugebauer Appendix D. Proof that rays reflected from the surface formed by the revolution of a parabola about a chord perpendicular to the axis do not all meet the circumference of a circle by O. Neugebauer Index of Technical Terms General Index. This publication would not have been what it is without the help of many institutions and people which I acknowledge most gratefully. I thank the Central Library and Documentation Center Iran and its director Mr. Iraji Afshar for permission to publish photo­ graphs of that part of ms. 392 of the Shrine Library Meshhed containing Diocles treatise. I also thank the authorities of the Shrine Library and especially Mr. Ahmad GolchTn MaanT for their cooperation in providing photographs of the manuscript. Mr. GolchTn­ MaanT also sent me most generously a copy of his catalogue of the astronomical and mathematical manuscripts of the Shrine Library. I am grateful to the Chester Beatty Library Dublin and the Universiteits Bibliotheek Leiden for providing me with microfilms of manuscripts I wished to consult and to the Biblioteca Ambrosiana Milan for granting me access to its manuscripts. The text pages in Arabic script and the Index of Technical Terms were set by a computer assisted phototypesetting system using computer programs developed at the University of Washington and a high speed image generation phototypesetting device. A continuous stream of text on punched cards was fed through the Katib formatting program which broke up the text into lines and pages and arranged the section numbers and apparatus on each page. Output from Katib was fed through the compositor program Hattat to create a magnetic tape for use on the VideoComp phototypesetter.