Shùxué yào 數學鑰
Key to Mathematics by 杜知耕 (Dù Zhīgēng, fl. 1680s-1700s, 清, zhuàn 撰)
About the work
Dù Zhīgēng’s 6-juan re-presentation of the classical Jiǔzhāng mathematical tradition, with imported European xiàn / miàn / tǐ (line / surface / solid) categorical apparatus and detailed diagrammatic annotation. The work follows the standard Jiǔzhāng nine-chapter sequence (Fāngtián, Sùbù, Cuīfēn, Shǎoguǎng, Shānggōng, Jūnshū, Yíngnü, Fāngchéng, Gōugǔ) but classifies each problem under the European-derived xiànmiàntǐ (line-surface-solid) three-fold scheme, providing both diagrammatic exposition and concise textual annotation.
The work is structurally parallel to 方中通 Fāng Zhōngtōng’s KR3f0051 Shùdù yǎn but differs in emphasis: Fāng Zhōngtōng’s work is more comprehensive in scope but loosely organized; Dù Zhīgēng’s Shùxué yào is more rigorously pedagogical with consistent example-format (“for each chapter setting examples must mark its general-pattern at the chapter-head; for each question-and-answer where there is some side-applicability must append its procedure under the entry; the cited evidentiary text must indicate its source — gathering-and-collecting especially detailed”). The Sìkù 提要 commends the work’s rigor: each problem displays its classical antecedents, its derivative applications, and its source-citations.
The 提要 quotes Méi Wéndǐng’s Wù’ān lìsuàn shūjì (KR3f0028) characterization: “[among] recent compositions, like Lǐ Chángmào’s Suànhǎi xiángshuō also has discoveries but cannot fully cover the Nine Chapters*; only Fāng Wèibó’s [Fāng Zhōngtōng’s]* Shùdù yǎn outside the Nine Chapters has very rich gathering-and-collecting; Dù Duānbó’s [Dù Zhīgēng’s] Shùxué yào*, diagrammatically-annotating the* Nine Chapters*, quite hits the essential vital-points — can serve as a model for the calculation school. His statement is indeed not slanderous*“. Through Méi Wéndǐng’s commendation the work entered the early-Qīng mathematical pedagogical canon.
The work survives in two recensions; one was tampered with by an unknown editor “who much disordered the [original]” — the Sìkù-recension is the original first-printing.
For Dù Zhīgēng’s biography, see 杜知耕. For the parallel work, see KR3f0051 Shùdù yǎn (currently lacking source files in the Kanripo recension). For Méi Wéndǐng’s commendation, see KR3f0028 Wù’ān lìsuàn shūjì.
Tiyao
[Full text in source file. Dated Qiánlóng 46 (1781), fourth month.]
Translations and research
- Limited substantial secondary literature. Briefly treated in:
- Han Qi 韓琦, Tōng-tiān zhī xué 通天之學, Beijing: Sānlián, 2018.
- Mei Rongzhao 梅榮照, Míng-Qīng shù-xué-shǐ lùn-wén jí 明清數學史論文集, Nánjīng: Jiāngsū Jiào-yù Chūbǎnshè, 1990.