Gōugǔ yǐnméng 句股引蒙
Right-Triangle Beginner’s Introduction by 陳訏 (Chén Xū, 1650–1722, 清, zhuàn 撰), completed Kāngxī 61 (1722, rényín)
About the work
Chén Xū’s 5-juan introductory mathematical primer focused on right-triangle (gōugǔ) methods, completed in 1722. The work is structurally an introductory pedagogical compilation drawing eclectically on multiple established methodological traditions:
- Addition: Western pen-arithmetic position-fixing (left-to-right) per the KR3f0046 Tóngwén suànzhǐ
- Subtraction: Méi Wéndǐng’s pen-arithmetic position-fixing (top-to-bottom)
- Multiplication: Chéng Dàwèi’s 程大位 Suànfǎ tǒngzōng 算法統宗 pūdì jǐn (spread-the-ground brocade) method
- Division: Méi Wéndǐng’s chóusuàn 籌算 (counting-rod arithmetic) vertical-position notation
- Decimal-position notation: Western horizontal-decimal style
The right-triangle (gōugǔ) sections are the work’s principal technical content but suffer from several technical errors that the Sìkù 提要 carefully enumerates: misidentification of gōugǔ jiào (right-triangle difference) procedures; incorrect claims about right-triangle inscribed-circle properties; incorrect generalization that “the right-triangle’s hypotenuse-length is always twice the inscribed circle’s circumference”. These errors reflect Chén Xū’s status as a pedagogical compiler rather than an original mathematical contributor.
The work’s plane-trigonometry section is taken essentially verbatim from Méi Wéndǐng’s Píng sānjiǎo jǔyào 平三角舉要 (KR3f0026 portion) with brief explanatory comments. The 8-line trigonometric tables included use radius = 100,000 (the older Western convention from the Cèliàng quányì of the KR3f0013 Xīnfǎ suànshū) rather than the higher-precision Kāngxī tables — i.e., the work uses outdated tabular data.
The Sìkù 提要’s verdict balances criticism with appreciation of pedagogical merit: the work is a useful introductory primer despite its technical deficiencies. As the title Yǐnméng (Beginner’s Introduction) makes clear, the work’s purpose is propaedeutic — and for that purpose it succeeds.
For the principal Méi Wéndǐng works that Chén Xū draws on, see KR3f0026 Lìsuàn quánshū. For Chén Xū’s biography, see 陳訏.
Tiyao
[Full text in source file. Dated Qiánlóng 46 (1781), twelfth month.]
Translations and research
- Limited substantial secondary literature.
- 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.