The Foundations of Celestial Reckoning

The Foundations of Celestial Reckoning gives the reader direct access to the foundational documents of the tradition of calculation created by astronomers of the early Chinese empire between the late second century BCE and the third century CE. The paradigm they established was to shape East Asian thought and practice in the field of mathematical astronomy for centuries to come. It was in many ways radically different from better known traditions of astronomy in other parts of the ancient world. This book includes full English translations of the first three systems of mathematical astronomy adopted for use by imperial astronomical officials, together with introductory material explaining the origin and nature of each system, and a general introduction to the work as a whole. The translations, which are accompanied by the original Chinese text, give a consistent rendering of all technical terms, and include detailed explanatory notes. The text in which the second of the three systems is found also includes a unique collection of documents compiled around 178 CE by two experts in the field, one of whom was the author of the third system translated in this book. Using material transcribed from government archives of the two preceding centuries, these scholars carefully document and review controversies and large-scale official debates on astronomical matters up to their own time. Nothing equivalent in detail and clarity has survived from any other ancient culture. The availability of the totality of this material in English opens new perspectives to all historians of pre-modern astronomy.

Christopher Cullen is Emeritus Director of the Needham Research Institute, Emeritus Fellow of Darwin College, and Emeritus Honorary Professor of the University of Cambridge. He is editor of the Needham Research Institute Series (Routledge).

Chapter 1. General IntroductionA. The world of early imperial ChinaB. What was a li ?, and what did it do?C. How did a li work?D. DatesE. How was a li calculated?F. How were the data of a li determined?G. A note on translating computational proceduresH. Arrangement of the textI. Works consulted?Chapter 2. The Triple Concordance astronomical system: San tong li ???I. IntroductionA. An astronomical system and its creatorB. Structure of the systemC. Organisation of the textD. Text usedII. Text, translation and commentsA. Concordance constantsB. Sequence ConstantsC. The Five PacersD. Concordance WorkingsE. Sequence WorkingsF. Year WorkingsG. [The Twelve Stations]H. The 28 LodgesI. [The Nine Roads]J. [Concordances and Rule Heads]K. APPENDIX 1: Intercalations in theory and practice?Chapter 3. The Han Quarter Remainder system: Han si fen li ????I. IntroductionA. The system and its backgroundB. Authorship of the textC. Structure of the systemD. Organisation of the textE. Methods of calculationF. Text usedII. Text, translation and commentsA. Methods for [astronomical] systemsB. Basic solar and lunar constantsC. [Lunar eclipse constants]D. Procedures for sun and moonE. Planetary constantsF. Planetary ProceduresG. Planetary MotionsH. [Months, qi and lodges]I. [The solar table]J. The system originK. Discussion?Chapter 4. The Uranic Manifestation astronomical system: Qian xiang li???I. IntroductionA. Liu Hong and his work