Jiǔzhāng lùyào 九章錄要
Selected Essentials of the Nine Chapters by 屠文漪 (Tú Wényī, fl. 1680–1720, 清, zhuàn 撰)
About the work
Tú Wényī’s 12-juan re-organization of the Jiǔzhāng tradition combined with imported Western methods. Structurally parallel to 杜知耕 Dù Zhīgēng’s KR3f0050 Shùxué yào but with different emphasis and scope:
- Where Dù Zhīgēng (杜知耕) is detailed: Tú Wényī (屠文漪) is brief, and vice versa
- Dù: Fāngtián thorough, Tú: Gōugǔ thorough
- Dù: Shǎoguǎng treats solids fully; Tú: Shǎoguǎng treats edge-and-corner-distinctions
- Dù: incorporates Western methods at problem-by-problem level by appending principle-explanations under questions; Tú: incorporates Méi Wéndǐng’s analyses by gathering-and-collecting them at the section-level
Both works draw eclectically on present-and-ancient methodology and sometimes overlap, sometimes diverge. The 提要’s judgment: “viewing them combined, [the two works] also can mutually-illuminate each other”.
Tú Wényī’s distinctive contribution is the jièzhēng 借徵 (borrowing-evidence) entry — equivalent to the jiècuī diéjiè 借衰叠借 (borrowing-decreasing iterated-borrowing) method that handles certain classes of indeterminate-and-proportional problems by setting up an auxiliary “false” answer, computing what would follow from it, and then adjusting to the true answer. Dù Zhīgēng’s parallel work does not address this method, so Tú Wényī’s treatment supplements Dù’s coverage. The 提要 acknowledges that Tú Wényī’s exposition is “not extremely refined-and-dense” but “on the cleverness of borrowing-numbers [he] has fundamentally obtained the great essentials”.
For the parallel work, see KR3f0050 Shùxué yào by Dù Zhīgēng. For Tú Wényī’s biography, see 屠文漪.
Tiyao
[Full text in source file. Dated Qiánlóng 46 (1781), fifth month.]
Translations and research
- Limited substantial secondary literature.
- Han Qi 韓琦, Tōng-tiān zhī xué 通天之學, Beijing: Sānlián, 2018.