Rújī yǐnméng 如積引蒙
An Elementary Introduction to the Rú-jī [Algebraic-Equation] Method by 汪曰楨 (撰)
About the work
汪曰楨 Wāng Yuēzhēn’s (1813–1881) introductory mathematical treatise in 12 juàn on the rújī 如積 method — the indigenous Chinese algebraic technique for setting up and solving polynomial equations representing geometrical-areal relations. The title’s yǐnméng 引蒙 (“introducing the ignorant,” i.e. an elementary primer) signals the work’s pedagogical orientation: it is a teaching text intended to make the indigenous Chinese algebraic tradition accessible to readers without prior algebraic training.
Abstract
The rújī method is the indigenous Chinese algebraic procedure for setting up polynomial equations to represent geometric configurations — specifically, configurations in which an unknown quantity (typically a length) appears in such a way that areas or volumes formed from it can be related to known quantities. The method is the geometric-algebraic foundation of the SòngYuán tiānyuán 天元 (“celestial element”) tradition, particularly as developed by 李冶 Lǐ Yě’s Cèyuán hǎijìng 測圓海鏡 (KR3fc015) and Yì gǔ yǎn duàn 益古演段 (KR3fc016).
汪曰楨 Wāng Yuēzhēn — better known as the leading Qīng-period chronologist (cf. his Lìdài chángshù jíyào 歷代長術輯要 KR3fb023) — was a polymath whose mathematical interests extended from chronology proper into algebraic and geometric mathematics. The Rújī yǐnméng is his introduction to the rújī tradition, presented in 12 juàn of graduated worked examples. The treatise builds systematically from the simplest area-and-square problems up to multi-variable systems requiring the elimination procedures developed by 朱世傑 Zhū Shìjié in the Sìyuán yùjiàn 四元玉鑑 (KR3fc017).
The pedagogical project reflects the mid-nineteenth-century interest in making the recovered SòngYuán algebraic tradition (the Cèyuán hǎijìng, the Yì gǔ yǎn duàn, the Sìyuán yùjiàn) genuinely usable for current mathematical work — a concern shared with 李善蘭 Lǐ Shànlán’s textbook-translation project of the same period (KR3fc078). Wāng Yuēzhēn approaches the problem from the indigenous side, distilling the procedural content of the SòngYuán classics into a teachable form, where Lǐ Shànlán approaches the same problem from the side of European symbolic algebra.
Dating: Wāng Yuēzhēn lived 1813–1881. The Rújī yǐnméng belongs to his mature mathematical work. notBefore 1830 (early productive period — say age 17, allowing for the formative work); notAfter 1881 (death year). The work is not precisely datable from internal evidence.
Translations and research
- 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. — Standard study of the late-Qīng mathematical reception.
- 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.
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 8.
Links
- SòngYuán rújī tradition: KR3fc015 Cèyuán hǎijìng, KR3fc016 Yì gǔ yǎn duàn, KR3fc017 Sìyuán yùjiàn
- Wāng Yuēzhēn’s chronological masterwork: KR3fb023 Lìdài chángshù jíyào
- CBDB (author): https://cbdb.fas.harvard.edu/cbdbapi/person.php?id=79282