Liùjiǔ xuān suànshū 六九軒筭書
The Liù-jiǔ xuān Mathematical Book by 劉衡 (撰)
About the work
劉衡 Liú Héng’s (1776–1841) general collection of mathematical investigations in 3 juàn, gathered under the studio name Liùjiǔ xuān 六九軒 (“Six-nine Studio”). The collection is the most general-purpose of Liú Héng’s mathematical works, presenting investigations across multiple branches of the mid-Qīng mathematical syllabus.
Abstract
The Liùjiǔ xuān suànshū is the general-collection counterpart of Liú Héng’s more specialised treatises (KR3fc063 on sundials, KR3fc064 on surveying with the right-triangle sighting-rod, KR3fc065 on tabular root-extraction, KR3fc066 on the jiègēnfāng algebraic equation, KR3fc067 on the four-term proportion). Where those works treat single problem-types in depth, the Liùjiǔ xuān presents shorter investigations across multiple topics — typically problems that interested Liú Héng but did not merit a self-contained treatise.
The 3-juàn organisation broadly follows the standard mid-Qīng mathematical syllabus: arithmetic-and-algebraic procedures in juàn 1, geometric-and-surveying procedures in juàn 2, and miscellaneous problems including computational shortcuts in juàn 3. The work as a whole shows Liú Héng’s working method: a procedural mathematician whose interest is in efficient computation rather than theoretical reformulation, in the lineage of 楊輝 Yáng Huī’s practical-arithmetic tradition.
Liú Héng is associated with the mid-Jiā-qìng to Dàoguāng generation working largely outside the metropolitan Yángzhōu / Sūzhōu circles centred on 阮元 Ruǎn Yuán. His mathematical output is unusually voluminous for a provincial scholar; the Liùjiǔ xuān suànshū preserves the mid-Qīng practical-arithmetic tradition that is otherwise underrepresented in the surviving Qīng mathematical literature.
Dating: Liú Héng lived 1776–1841. notBefore 1800 (early mature work, age 24); notAfter 1841 (death year). The collection-format implies extended composition rather than a single dated compilation.
Translations and research
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 7–8.
- Tián Miǎo 田淼. 2003. Zhōng-guó shù-xué de xī-huà lì-chéng 中國數學的西化歷程. Jǐ-nán: Shān-dōng jiāo-yù chū-bǎn-shè.