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Planetary Hypotheses with Introduction and Commentary Ptolemy’s Planetary Theory: An English Translation of Book One, Part A of the Planetary Hypotheses with Introduction and Commentary by Elizabeth Anne Hamm A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto © Copyright by Elizabeth Anne Hamm, 2011 Abstract Ptolemy’s Planetary Theory: An English Translation of Book One, Part A of the Planetary Hypotheses with Introduction and Commentary Elizabeth A. Hamm Institute for the History and Philosophy of Science and Technology University of Toronto 2011 This study comprises a translation and commentary of Book I of the Planetary Hypotheses by the second century A.D. Greco-Roman astronomer, Claudius Ptolemy. It closely examines the Planetary Hypotheses on its own and in relation to Ptolemy’s other writings. Where necessary I rely on astronomical, philosophical, and technological works by other writers in order to better situate Ptolemy’s ideas into the context of Greco- Roman science. The dissertation is organized into three sections. Section I consists of an extended introduction to the Planetary Hypotheses. I offer a synopsis of the Planetary Hypotheses and a history of the text in Sections I.1 and I.2. Section I.3 consists of a brief introduction to notation and sexagesimal numbers while Section I.4 analyzes the aim and function of Ptolemy’s planetary models. Section II is a translation of the existing Greek text of the Planetary Hypotheses, namely Book I Part A, and a précis of Book I, Part B. The translation is made from J.L. Heiberg’s edited Greek text and the précis relies on the English translation by Bernard Goldstein, the French translation by Regis Morelon, and the Arabic Manuscripts found in the British Library (Arabic-A) and the Library at the University of Leiden (Arabic-B). ii The footnotes include variant readings from the different Greek and Arabic Manuscripts. A list of all existing manuscripts of the Planetary Hypotheses can be found in Section I.2 Section III is a commentary of the entirety of Book I (Parts A and B). This section is arranged so that it loosely follows the order of topics found in the Planetary Hypotheses. Section III.1 examines the Planetary Hypotheses in terms of instrument- making. Section III.2 discusses the geometric models that Ptolemy presents along with a discussion of the changes that he makes. I give an overview of the period relations and mean motions presented in the Planetary Hypotheses in Section III.3 and III.4 and the new frame of reference in Section III.5. Section III.6 briefly examines Book II of the Planetary Hypotheses and Section III.7 addresses the relationship of Book I and Book II and contextualizes this work in the history of Greco-Roman science. Finally, Section III.8 examines the role the Planetary Hypotheses played in developments within Medieval Islamic astronomy. While I focus on the changes that Ptolemy made to the models in the Planetary Hypotheses from his theories in the Canobic Inscription, Handy Tables, and the Almagest, this work aims to explore the motivations behind these changes. Additionally, I contextualize the Planetary Hypotheses within Greco-Roman and Islamic astronomy and technology. What emerges from this dissertation is a consideration of Ptolemy’s ideas about the practice of science and an analysis of how he modeled astronomical observations. iii Acknowledgements I could not have completed this dissertation without the support of many advisors, colleagues, friends, and family. First and foremost I would like to thank my supervisor, Professor Alexander Jones, for his expert guidance, his attention to detail, and for rigorously pushing me beyond the limits of what I thought I was capable. He has patiently taught me to be an historian and for this I am eternally grateful. I would like to thank my two dissertation committee members: Professor Craig Fraser has provided constructive criticism at the many stages of this project and years of guidance and support; and Professor Ingrid Hehmeyer has offered me valuable advice, mentorship, and many interesting discussions on Arabic science that were beneficial for the later sections of my work. I would like to acknowledge, with thanks, my external reader, Professor James Evans, whose meticulous examination saved me from making several mistakes and who provided me with a number of insightful comments. I am grateful to the faculty and to the staff at the Institute for the History and Philosophy of Science and Technology, and in particular to Denise Horsely and Muna Salloum for their administrative support and their kindness. Additionally, I would like to thank Brother Raphael Patton at Saint Mary’s College of California for first introducing me to Ptolemy’s Almagest and for encouraging me to pursue my interests in the history of astronomy. I am indebted to my many wonderful friends for their good humor, kindness, and encouragement over the years. In particular, I would like to thank those whose support and counsel has been essential to the completion of this dissertation: Sarah Amato, iv Erin Ellerbeck, Erin Hochman, Michelle Hoffman, Siamak Khajehpour, Brent Knowles, Jessica Lee, Yue Liu, Steve Maddox, Rene Mader, Kate McLean, Joseph Rochon, Monica Schut, Nathan Sidoli, Chris Studholme, Yen Tran, Emma Wensing, and Brian Wilson. I would especially like to thank Jacqueline Feke, in whom I found a fellow lover of the history of ancient science and a dear friend. With heartfelt appreciation I thank those closest to me. My parents, Scott and Consuelo Burns, offered unconditional love and support; this endeavor would not have been possible without their kindheartedness and encouragement. My beloved sister, Heather Burns, has been a source of much needed perspective, an untiring supporter, and a most treasured friend. Finally, my husband, Geoff Hamm, has provided unwavering encouragement, strength, and understanding. He has supported me in more ways than I can count and with much love and gratitude I dedicate this dissertation to him. v Table of Contents Section I: Introduction ........................................................................................................ 1 I.1 Description of the Planetary Hypotheses .................................................................. 5 I.2 History of the Text..................................................................................................... 8 I.3 Notations and Sexagesimals ................................................................................... 15 I.4 The Aim and Function of Ptolemy’s Models ......................................................... 19 Section II: Translation....................................................................................................... 44 II.1 Translation of Book I, Part A................................................................................. 44 II.2 Précis of Book I, Part B.......................................................................................... 65 Section III: Commentary................................................................................................... 72 III.1 Sphairopoiia.......................................................................................................... 72 III.2 Geometric Models................................................................................................. 97 III.3 Mean Motion: Simple Periods ............................................................................ 140 III.4 Mean Motion: Complex Periods......................................................................... 168 III.5 Frame of Reference............................................................................................. 181 III.6 Book I Part B ...................................................................................................... 185 III.7 The Planetary Hypotheses as a whole ................................................................ 214 III.8 The Planetary Hypotheses in Islamic Astronomy .............................................. 224 Bibliography ................................................................................................................... 229 vi List of Figures Figure 1 Epicycle Model................................................................................................... 33 Figure 2 Eccentric Model.................................................................................................. 34 Figure 3 Solid Sphere Planetary Model............................................................................ 36 Figure 4 Sawn-off Sphere Planetary Model...................................................................... 37 Figure 5 Eccentric Model................................................................................................ 102 Figure 6 Epicyclic Model................................................................................................ 103 Figure 7 Solar Model ...................................................................................................... 109 Figure 8 First Lunar Model............................................................................................. 113 Figure 9 Second Lunar Model ........................................................................................ 115 Figure 10 Planetary Model.............................................................................................. 119 Figure 11 Mercury Model..............................................................................................
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