Qiúbiǎo jiéshù 求表捷術
Rapid Methods for the Construction of Mathematical Tables by 戴煦 (撰)
About the work
戴煦 Dài Xù’s (1805–1860) principal mathematical treatise in 13 juàn on rapid procedures (jiéshù 捷術) for the construction of mathematical tables — primarily trigonometric tables (sin, cos, tan, cot, sec, csc) and logarithm tables, but extending to special-function tables required for astronomical and surveying work. The treatise is one of the most influential Chinese mathematical works of the mid-nineteenth century and a major document of the late-indigenous mathematical tradition immediately preceding the wholesale adoption of European mathematics under 李善蘭 Lǐ Shànlán’s translation programme.
Abstract
The construction of trigonometric and logarithmic tables to high precision (typically 7- or 10-decimal-digit precision, with entries every minute or every second of arc) was one of the principal computational projects of seventeenth-, eighteenth-, and nineteenth-century mathematics worldwide. In Europe, the principal tables in use were those of Briggs (logarithms), Pitiscus (trigonometric), and the later Vlacq, Vega, and Callet. In China, the principal tables were the Lǜlì yuānyuán 律曆淵源 imperial tables of 1722–1723 (which incorporated Briggs’s logarithms and Pitiscus’s trigonometry, recomputed under Méi Gǔchéng 梅穀成 and the Imperial Mathematics Bureau).
戴煦 Dài Xù’s Qiúbiǎo jiéshù presents a systematic theory of rapid table-construction. Where the European logarithm tables had been built by Briggs’s labour-intensive successive interpolation, and where the Chinese tables of 1722 had simply transliterated the European results, Dài Xù develops infinite-series methods — derived from the indigenous Míng Āntú / 項名達 Xiàng Míngdá cyclotomic-series tradition (cf. KR3fc069 Xiàngshù yīyuán, which Dài Xù had completed and edited) — for the direct computation of trigonometric and logarithmic values to arbitrary precision.
The 13-juàn organisation covers (in summary): (1) preliminaries on rational and irrational approximation; (2)–(4) trigonometric-function infinite series and their tabulation; (5)–(7) logarithm series and tables; (8)–(10) auxiliary functions and special-purpose tables; (11)–(13) astronomical applications. The work is unusual among indigenous Chinese mathematical works in its near-total focus on numerical-tabular methods rather than on procedural-algebraic problem-solving — the central computational concerns of mid-nineteenth-century European applied mathematics.
The Qiúbiǎo jiéshù was published in the 1850s — at exactly the moment that 李善蘭 Lǐ Shànlán was beginning his major translation project at the Lónghuá Mòhǎi Shūguǎn 龍華墨海書館 in Shànghǎi. The two streams (Dài Xù’s indigenous tabular methods and Lǐ Shànlán’s translated European symbolic algebra) represent the two roads available to mid-century Chinese mathematics. The Tàipíng war and Dài Xù’s death in 1860 cut short the indigenous-tabular stream; Lǐ Shànlán’s translation programme became the dominant tradition of late-Qīng Chinese mathematics.
Dating: composed during Dài Xù’s mature productive period in Hángzhōu. notBefore 1840 (mature work, age 35); notAfter 1860 (death year — Dài Xù reportedly committed suicide during the Tàipíng occupation of Hángzhōu).
Translations and research
- 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.
- Horng, Wann-Sheng [洪萬生]. 1991. “Li Shanlan, the Impact of Western Mathematics in China during the Late 19th Century.” Ph.D. diss., City University of New York. — Treats Dài Xù as part of the same generation.
- Wáng Pīng 王萍. 1972. Xī-fāng lì-suàn-xué zhī shū-rù 西方曆算學之輸入. Tái-běi: Zhōng-yāng yán-jiū-yuàn jìn-dài-shǐ yán-jiū-suǒ.
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 8.
Links
- Precursor cyclotomic-series tradition: KR3fc068 Gēyuán liánbǐlì shù tújiě; KR3fc069 Xiàngshù yīyuán
- Mid-century counterpart in European-mathematical translation: KR3fc078 Zégǔxī zhāi suànxué by 李善蘭
- CBDB (author): https://cbdb.fas.harvard.edu/cbdbapi/person.php?id=91692