Chasing Shadows: Mathematics, Astronomy, and the Early History of Eclipse Reckoning

Contents

Contents Preface xi CHAPTER ONE Heavenly Hide and Seek: An Introduction to Eclipse Reckoning in Early Times 1 1.1 Development and Cross-Cultural Transmission 5 1.2 Eclipses and Their Human Significance 13 1.3 Observation and Theory 14 1.4 Aims of This Study 20 CHAPTER TWO The Rudiments of Alignment: Basic Eclipse Theory 22 2.1 The Moon and the Sun 22 2.2 Eclipses 27 2.3 Prediction and Patterns of Eclipses 40 2.4 The Celestial Sphere 41 2.5 Mathematical Conventions 45 CHAPTER THREE An Accountancy of Appearances: Mesopotamian Eclipse Reckoning 48 3.1 Overview 48 3.2 The Earliest Accounting for Eclipses: Enūma Anu Enlil 54 3.3 Assyrian Eclipse Reckoning: The Letters and Reports 58 3.4 Babylonian Eclipse Reckoning 70 CONTENTS CHAPTER FOUR Beyond the Appearances: Greek Eclipse Reckoning 99 4.1 Overview 99 4.2 Early Greek Geometrical Celestial Conceptions 103 4.3 Sizes, Distances, and Measurement: Aristarchus and Archimedes 108 4.4 Early Greek Mathematical Astronomy 111 4.5 The Peak of Greek Mathematical Astronomy 121 4.6 Omens in Greek and Hellenistic Sources 147 CHAPTER FIVE Recipient and Remodeler: Indian Eclipse Reckoning 156 5.1 Overview 156 5.2 General Features of Eclipse Reckoning in India 170 5.3 Eclipses as Omens 178 5.4 Eclipse Observation Records in Inscriptions 181 5.5 Eclipse Reckoning in Indian Texts with Greco-Babylonian Influence: The Pañcasiddhāntikā of Varāhamihira 189 5.6 Eclipse Reckoning from the Fifth to the Tenth Century 205 5.7 Parameśvara and the Astronomical School in Kerala 259 CHAPTER SIX A Science of Configuration: Arabic Eclipse Reckoning 285 6.1 Overview 285 6.2 General Features of Eclipse Reckoning in the Islamic Near East 294 6.3 Major Contributions to Islamic Eclipse Reckoning 299 CHAPTER SEVEN Concluding Remarks 325 APPENDIXES A Abbreviations and Conventions 335 B A Comparison of NMAT and MAT Eclipse Predictions 336 C The Eclipse Tables in the Wajı̄z of al-Khāzinı̄ 342 viii CONTENTS Notes 353 Glossary 377 Bibliography 383 Index 393 ix This page intentionally left blank ...