Xiángjiě jiǔzhāng suànfǎ zhájì 詳解九章算法札記
Critical Notebook on the Detailed Exposition of the Nine Chapters Mathematical Methods by 宋景昌 (撰)
About the work
宋景昌 Sòng Jǐngchāng’s textual-critical notebook accompanying his 1842 editing of 楊輝 Yáng Huī’s KR3fc011 Xiángjiě jiǔzhāng suànfǎ for the Yíjiātáng 宜稼堂 cóngshū. Produced in the closing months of the 1842 cóngshū editorial work — notBefore conservatively set at 1840 to allow for the work’s preparation across the cóngshū’s preparation period, notAfter at the 1842 publication date.
Abstract
The work belongs to the zhájì 札記 genre — a running scholarly notebook of textual emendations, procedural verifications, and editorial decisions made during the preparation of a critical edition. Sòng Jǐngchāng’s specific task was the collation of the recovered Korean Chosŏn recension of Yáng Huī’s Xiángjiě against the Sòng-fragment survivals in the Yǒnglè dàdiǎn and against the citations of Yáng Huī’s work in subsequent YuánMíng mathematical literature.
The zhájì records, in entry-by-entry form, the textual problems encountered and their resolution: where the Korean and Yǒnglè lines agree, the reading is straightforward; where they disagree, Sòng Jǐngchāng supplies a procedural cǎo (computation) to verify which reading produces the correct mathematical result, and emends the text accordingly. The methodology is sophisticated: where surface philological reasoning would be inadequate to choose between variant readings, Sòng Jǐngchāng’s mathematical competence allows him to use the mathematical correctness of each reading as the decisive criterion.
The work is essential reading alongside the Yíjiātáng Xiángjiě, providing the running justification for the published critical text. Together with the parallel apparatus produced by 沈欽裴 Shěn Qīnpéi and 羅士琳 Luó Shìlín for the KR3fc017 Sìyuán yùjiàn recovery (their xìcǎo and bǔshì), the Zhájì establishes the Yíjiātáng cóngshū as the first methodologically-rigorous edition of the four great SòngYuán mathematical works.
Translations and research
- Lam Lay-Yong. 1969. “On the Existing Fragments of Yang Hui’s Hsiang Chieh Suan Fa.” Archive for History of Exact Sciences 6: 82–88. — Uses Sòng Jǐngchāng’s apparatus throughout in reconstructing the Xiáng-jiě’s textual history.
- Lam Lay-Yong. 1977. A Critical Study of the Yang Hui Suan Fa: A Thirteenth-Century Chinese Mathematical Treatise. Singapore: Singapore University Press. — Discusses the 1842 Yí-jiā-táng recovery and Sòng Jǐngchāng’s role.
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 5. Beijing: Běi-jīng shī-fàn dà-xué chū-bǎn-shè.