Dīng Jù suànfǎ 丁巨算法
Dīng Jù’s Mathematical Methods by 丁巨 (撰)
About the work
A brief late-Yuán practical-arithmetic primer in 1 juàn by Dīng Jù 丁巨, dated Zhìzhèng 15 (1355) by its preface. Survives only as a partial reconstruction; the catalog records 1 juàn though the original juàn-count is unclear in the bibliographic sources. The work is one of the principal documentary survivals of late-Yuán mid-popular mathematical pedagogy, sitting between the high algebraic tradition of 朱世傑 Zhū Shìjié’s Sìyuán yùjiàn (KR3fc017, 1303) and the early-Míng practical-mathematical compilations of 吳敬 Wú Jìng (KR3fc023, 1450).
Abstract
The Dīng Jù suànfǎ is preserved in incomplete form. The most complete witness is a fragment of about 10 problems-and-solutions transmitted through the early-Míng Yǒnglè dàdiǎn 永樂大典 and recovered in the late Qīng by the Yíjiātáng circle; subsequent citations in Míng mathematical works (notably 吳敬 Wú Jìng’s KR3fc023 Jiǔzhāng xiángzhù bǐlèi suànfǎ dàquán of 1450 and 程大位 Chéng Dàwèi’s KR3fc027 Suànfǎ tǒngzōng of 1592) preserve additional problem-and-solution material attributed to Dīng Jù.
The work’s mathematical content is elementary by SòngYuán standards: it covers the basic arithmetic operations on integers and fractions, the standard proportional-exchange procedures, and a small number of right-triangle and area problems. What is distinctive is its presentational style: Dīng Jù gives the procedural recipes in a notational shorthand suited to computation on the abacus (suànpán 算盤) rather than on the counting-rod board. The transitional moment matters historically — Dīng Jù’s primer is one of the earliest works in which the abacus-based pedagogical orientation of late-imperial Chinese arithmetic is clearly visible, anticipating the full systematization in 程大位 Chéng Dàwèi’s 1592 Suànfǎ tǒngzōng.
Dīng Jù’s biographical information is extremely thin. The preface signs him simply by name, with no native-place or office indication; the surrounding documentary record is silent. Conventionally he is placed in the lower-Yangzi region on the basis of the work’s circulation pattern and its presentational style, but this is inference rather than evidence. NotBefore and notAfter are both fixed at the 1355 preface date.
Translations and research
- Lam Lay-Yong. 1986. “Linkages: Exploring the Similarities between the Chinese Rod Numeral System and Our Numeral System.” Archive for History of Exact Sciences 37: 365–392. — Discusses the transition from counting-rod to abacus pedagogy that the Dīng Jù suàn-fǎ embodies.
- 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. — Standard Chinese reference.
- Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer.