Xiàhóu Yáng suànjīng 夏侯陽算經
Xià-hóu Yáng’s Mathematical Classic by 夏侯陽 (Xiàhóu Yáng, Sui period, zhuàn 撰); annotation traditionally attributed to 甄鸞 (Zhēn Luán, Northern Zhōu) in the Tang Yìwén zhì, but the Sìkù 提要 questions this attribution
About the work
A 3-juan practical-administrative mathematical handbook in 12 topical sections (shíèr mén 十二門), composed in the Sui period (c. 580–618). The work is one of the Suànjīng shíshū canonized under the Tang for the Suànxué guǎn curriculum. Distinguished within the Suànjīng shíshū corpus by its strong administrative-practical orientation: the topics covered are the mathematical-computational concerns that Tang government bureaus actually faced (taxation calculation in kèzū yōngdiào 課租庸調; grain-and-volume measurement; labor-service quotas in bùshù 步數; weights and measures (chènchǐdòushēnghé 稱尺斗升合) standardization). The work explicitly excludes the ancient nine-chapter material that “is not necessary for government-bureau and people’s affairs”, concentrating instead on the practical computational concerns of imperial administration.
The 提要 records the work’s complex transmission: the Sui Jīngjí zhì lists 2 juàn; the Tang Yìwén zhì lists 1 juàn annotated by Zhēn Luán plus another 1 juàn by Hán Yán; the Sòng Zhízhāi shūlù jiětí records the Yuánfēng (1078–1085) imperial-academy edition as 3 juàn without annotation. The Sìkù recension is recovered from the Yǒnglè dàdiǎn (where the work had been broken up and distributed under the various Jiǔzhāng topical headings) and reorganized into 3 juàn per the Yuánfēng arrangement and 12 mén per the original preface.
The 提要 doubts the Tang Yìwén zhì’s attribution of the annotation to Zhēn Luán, on the grounds that the work’s preface itself names Zhēn Luán as a predecessor whose annotations are already done — making it impossible for Zhēn Luán to also be the annotator. The most plausible reading: the Tang Yìwén zhì’s “Zhēn Luán annotation” notation is a copyist’s misattribution induced by the work’s own preface mentioning Zhēn Luán.
The work’s significance is principally institutional-administrative: as the Suànjīng shíshū member oriented to practical bureaucratic mathematics, it was an essential text for the Tang Imperial Academy mathematics curriculum and for any official aspiring to administrative office. The Sìkù editors specifically commend its value for “ancient-and-present institutional same-and-different” comparative research — i.e., for understanding the evolution of Chinese administrative practice across the dynasties. For the broader Suànjīng shíshū context, see KR3f0032, KR3f0033, KR3f0035, KR3f0036, KR3f0037, KR3f0039. For the principal author, see 夏侯陽.
Tiyao
[For full text see the source file. Key points: 提要 dated Qiánlóng 40 (1775), eleventh month — earlier than most other Suànjīng shíshū 提要 dates, suggesting the work was compiled and reviewed early in the Sìkù project. The 提要 cites internal-textual evidence (Sui-administrative terminology) for placing Xiàhóu Yáng in the Sui period; specifically notes the work’s institutional value for kǎojù (evidential research) on Tang-administrative history.]
Translations and research
- Limited substantial secondary literature. Treated briefly in:
- Martzloff, Jean-Claude. A History of Chinese Mathematics, Berlin: Springer, 1997.