---

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-Ma´anT, for their cooperation in providing photographs of the manuscript. Mr. GolchTn Ma´anT 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, Leid´en, 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.

---

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.- (i) Theory and terminology.- (ii) The focus of the parabola.- (iii) Construction of the parabola from focus and directrix.- 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.- (i) Corresponds to Props. 7 and 8.- (ii) Corresponds to Prop. 10.- (iii) Corresponds to Props. 11, 12 and 13.- Appendix B. Other ancient and medieval proofs of the focal property of the parabola.- (i) The Bobbio Mathematical Fragment.- (ii) Ibn al-Haytham.- 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.

---