Mar 6, 2025 © Ulrich Theobald
Celiang fayi 測量法義 "Principles of measurement and surveying" is a text on astronomy written during the late Ming period 明 (1368-1644) by Xu Guangqi 徐光啟 (1562-1633), who also compiled the Xinfa suanshu 新法算書.
It consists of three volumes, each with a length of 1 juan and focusing on the application of Western geometric principles introduced by Matteo Ricci (1552-1610; Ch. Li Madou 利瑪竇), particularly in surveying and measurement. The first part, the Celiang fayi proper, explains the fundamental principles of right-angle trigonometry using Western geometric knowledge. It employs a question-and-answer format to teach land surveying techniques, including methods for measuring height and distance.
The second part, Celiang yitong 測量異同 "Comparison of surveying methods", compares traditional Chinese surveying techniques, particularly the trigonometrical gougu 勾股 methods from the Jiuzhang suanshu 九章算術 with the new methods introduced by Ricci. By highlighting their differences, Xu aimed to promote and integrate Western mathematical approaches into Chinese practices.
The last part, Gougu yi 勾股義 "Principles of right-angle trigonometry", extends the discussion of right-angle triangle principles to astronomical measurement, demonstrating how these concepts can be applied to celestial observations. The purpose of these three texts was to introduce the correct application of the "Elements" (Chinese translation Jige yuanben 幾何原本) by the ancient Greek mathematician Euclid (fl. 300 CE), ensuring a proper understanding of Western geometry and its practical applications in China.
The text is part of the series Tianxue chuhan 天學初函, Zhihai 指海, Haishanxianguan congshu 海山仙館叢書, Siku quanshu 四庫全書 and Zhong-Xi suanxue congshu 中西算學叢書.
Sources:
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Fung, Kam-wing. 2019. "From Matteo Ricci, Hsu Kuang-Chʻi, and Chʻen Chin-Mo to Emperor Kʻang-Hsi: The Spread of Western Surveying in China." Transactions of the International Conference of Orientalists in Japan 64: 24–54.
Han, Qi; translated by Andrea Eberhard-Bréard, and Charles Burnett. 1972. "Astronomy, Chinese and Western: The Influence of Xu Guangqi’s Views in the Early and Mid-Qing." In Statecraft and Intellectual Renewal in Late Ming China, edited by Catherine Jami, Peter Engelfriet, and Gregory Blue, 360–79. Leiden. Brill.
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Jami, Catherine, and Keizo Hashimoto. 1972. "From the Elements to Calendar Reform: Xu Guangqi's Shaping of Mathematics and Astronomy." In Statecraft and Intellectual Renewal in Late Ming China, edited by Catherine Jami, Peter Engelfriet, and Gregory Blue, 263–278. Leiden: Brill.
Kim, Yung-sik. 2019. "Accommodating Westerners’ Knowledge in the Chinese Calendar: Confucian Scholars on Xu Guangqi’s Slogan." Han’guk Kwahaksa Hakhoeji = Korean Journal for the History of Science 41 (2): 151–67.
Li Xueqin 李學勤, and Lü Wenyu 呂文郁, eds. 1996. Siku da cidian 四庫大辭典, vol. 2, 1736. Changchun: Jilin daxue chubanshe.
Siu, Man-Keung, and Peter Engelfriet. 1972. "Xu Guangqi’s Attempt to Integrate Western and Chinese Mathematics." In Statecraft and Intellectual Renewal in Late Ming China, edited by Catherine Jami, Peter Engelfriet, and Gregory Blue, 279–310. Leiden: Brill.
Yao Miaofeng 姚妙峰, and Ji Zhigang 紀志剛. 2017. "Celiang fayi zai Zhongguo: Fanyi, chuanbo yu fazhan 《測量法義》在中國——翻譯、傳播與發展." Xianyang Shifan Xueyuan xuebao 咸陽示範學院學報 32 (02): 13-23.
