Foundations of Celestial Reckoning

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 曆, 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 consultedChapter 2. The Triple Concordance astronomical system: San tong li 三統曆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 practiceChapter 3. The Han Quarter Remainder system: Han si fen li 漢四分曆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. DiscussionChapter 4. The Uranic Manifestation astronomical system: Qian xiang li乾象曆I. IntroductionA. Liu Hong and his work

Christopher Cullen's expert translations and commentaries provide long-needed access to three foundational texts of Chinese astronomy, and an opening to a much wider understanding of an ancient scientific tradition comparable in richness and sophistication to that of the Mesopotamians and Greeks.- Alexander Jones, Institute for the Study of the Ancient World, New York University, USA"This book stands out as one of the notable landmarks in the progress of researching on Chinese systems. I highly recommend this important and well-written book for historians of science and all who are interested in Chinese mathematical astronomy."- Tang Quan, Xianyang Normal University, Journal for the History of Astronomy, August 2017"Cullen has provided another excellent contribution toward making Chinese astronomical texts available to a wider audience and giving the history of Chinese mathematical astronomy its well-deserved place within the general history of non-Western and premodern astronomy."- Benno van Dalen, Isis journal, March 2018"This volume will be a fundamental for the study of the history of ancient astronomy, not only Chinese, but also Arabic and, because of the transmission of Arabic astronomy to Byzantium in the late period Byzantine." - Touwaide, Byzantinische Zeitschrift issue 110 (= 2017/4).