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Practices of reasoning: persuasion and refutation in a seventeenth-century Chinese mathematical treatise of “linear algebra”
Published online by Cambridge University Press: 02 October 2020
Argument
This article documents the reasoning in a mathematical work by Mei Wending, one of the most prolific mathematicians in seventeenth-century China. Based on an analysis of the mathematical content, we present Mei’s systematic treatment of this particular genre of problems, fangcheng, and his efforts to refute the traditional practices in works that appeared earlier. His arguments were supported by the epistemological values he utilized to establish his system and refute the flaws in the traditional approaches. Moreover, in the context of the competition between the Chinese and Western approaches to mathematics, Mei was motivated to demonstrate that the genre of fangcheng problems was purely a “Chinese” achievement, not discussed by the Jesuits. Mei’s motivations were mostly expressed primarily in the prefaces to his works, in his correspondence with other scholars, in synopses of his poems, and in biographical records of some of his contemporaries.
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References
Bréard, Andrea. 2010. “Knowledge and Practice of Mathematics in Late Ming Daily life Encyclopedias.” In Looking at It from Asia: The Processes that Shaped the Sources of History of Science, edited by Bretelle-Establet, Florence, 3057–329. Dordrecht, Heidelberg: Springer.Google Scholar
Chemla, Karine. 2000. “Les problèmes comme champ d’interprétation des algorithmes dans les Neuf chapitres sur les procédures mathématiques et leurs commentaires. De la résolution des systèmes d’équation linéaires.” Orient-Occident 3:189–234.Google Scholar
Chemla, Karine, and Guo, Shuchun. 2004. Les Neuf Chapitres: Le Classique mathématique de la Chine ancienne et ses commentaires. Paris: Dunod.Google Scholar
Chen, Jiang-Ping Jeff. 2010. “The Evolution of Transformation Media in Spherical Trigonometry in 17th- and 18th-century China, and its Relation to ‘Western Learning.’” Historia Mathematica 37:62-109.Google Scholar
Chen, Jiang-Ping Jeff. 2015. “Trigonometric Tables and the Explicating of their Construction Principles in China.” Archive for History of Exact Sciences 69
(5):491–536.CrossRefGoogle Scholar
Chen, Jiang-Ping Jeff. 2018. “A Systematic Treatment of Linear Algebra in 17th-century China.” In The College Mathematics Journal 49
(3):169-179, DOI: 10.1080/07468342.2018.1448670.CrossRefGoogle Scholar
Cheng, Dawei 程大位. [1592] 1993. Suanfa tongzong 算法統宗 (Unified Lineage of Mathematical Methods). Reprint in Guo et al. 1993(2):1217–1421.Google Scholar
Chu, Ping-yi, 1997. “Scientific Dispute in the Imperial Court: The 1664 Calendar Case.” Chinese Science 14:7–34.Google Scholar
Dauben, Joseph, and Xu, Yibao. 2013. Nine Chapters on the Art of Mathematics. Shengyang: Liaoning Education Press.Google ScholarPubMed
Engelfriet, Peter. 1998. Euclid in China: The Genesis of the First Translation of Euclid’s Elements in1607 and Its Reception up to 1723. Leiden: Brill.Google Scholar
Guo, Shuchunet al (ed.). 1993. Zhongguo kexue jishu dianji tonghui shuxue juan 中國科學技術典籍通匯數學卷 (Comprehensive Collection of Treatises in Chinese Sciences and Technology, Mathematics). Zhengzhou: Henan Education Press.Google Scholar
Han, Qi. 2015. “Chinese Literati’s Attitudes toward Western Science.” Historia Scientiarum 24
(2):76–87.Google Scholar
Hart, Roger. 2011. The Chinese Roots of Linear Algebra. Baltimore: The Johns Hopkins University Press.Google Scholar
Hart, Roger. 2013. Imagined Civilizations China, the West, and Their First Encounter. Baltimore: The Johns Hopkins University Press.Google Scholar
Hu, Minghui. 2015. China’s Transition to Modernity, the New Classical Vision of Dai Zhen. Seattle and London: University of Washington Press.Google Scholar
Jami, Catherine. 2012. The Emperor’s New Mathematics: Western Learning and Imperial Authority in China during the Kangxi reign (1662–1722). Oxford: Oxford University Press.Google Scholar
Lam, Lay-Yong, and Shen, Kangshen. 1989. “Methods of Solving Linear Equations in Traditional China.” Historia mathematica 16:107–122.Google Scholar
Li, Changmao 李長茂. [1661] 2002. Suanhai shuoxiang 算海說詳 (Explicating the details in the Sea of Mathematics). Reprint in XXSKQS 1044:557–720.Google Scholar
Li, Yan, [1957] 1998. “Shisan, shisi shiji Zhongguo minjian shuxue 十三十四世紀中國民間數學 (China’s Folklore mathematics during the 13th and 14th centuries).” Reprinted in Li and Qian 1998, 2:403–490.Google Scholar
Li, Yan and Du, Shiran. 1987. Chinese Mathematics, a Concise History. Translated by Crossley, John and Anthony, W.-C. Lun.Oxford: Clarendon Press.Google Scholar
Li, Yan and Baocong, Qian, 1998. Li Yan and Qian Baocong kexueshi quanji 李俨钱宝琮科学史全集 (The Complete Collection of Works in History of Sciences by Li Yan and by Qian Baocong). Liaoning: Liaoning chubanshe.Google Scholar
Li, Zhizao. [1613] 1993. Tongwen suanzhi 同文算指 (Instructions for Calculation in Common Script). Reprint in Guo et al. 1993, 4:77–278.Google Scholar
Liu, Dun. 1986. “Qinchu lisuan dashi Mei Wending 清初历算大师梅文鼎 (Mei Wending: the Master of Both Calendar-calculating and Mathematics in the Early Qing Dynasty).” Ziran bianzhengfa tongxun自然辩证法通讯, Journal of Dialectics of Nature 1:52–64.Google Scholar
Liu, Dun. 1993. “Fangcheng lun tiyao 《方程論》提要 (A synopsis to Fangcheng lun).” In Guo et al. 4:317–321.Google Scholar
Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics (translated by Stephen Wilson). Berlin: Springer-Verlag.CrossRefGoogle Scholar
Martzloff, Jean-Claude. 1981. Recherches sur l’Œuvre Mathématique de Mei Wending (1633-1721). Paris: Collège de France and Institut des Hautes Etudes Chinoises.Google Scholar
Mei, Wending 梅文鼎. 1680. Zhongxi suanxue tong chuji 中西算學通初集 (the Initial Collection of Integration of Chinese and Western mathematics). This only rare copy was mistakenly included in the Selected Essentials of Mei Family’s Collection in Tsinghua University, Beijing. Catalogue No: 丙 108/7376.01, CAL 312005000853.Google Scholar
Mei, Wending. [1693] 1970–1972a. Bisuan 筆算 (Brush Calculation). Reprint in Congshu Jinghua 叢書菁華 (Series Essence), edited by Yiping Yan. Taiepei: Yiwen yinshuguan.Google Scholar
Wending, Mei. [1701] 1970–1972b. Qiandu celiang 塹堵測量 (Measured with Prisms). Reprint Congshu Jinghua, edited by Yiping Yan. Taiepei: Yiwen yinshuguan.Google Scholar
Wending, Mei. [1723] 1970–1972c. Lixue yiwen bu 歷學疑問補 (the Supplement to [Answers to] the Doubts Concerning the Study of Astronomy). Reprint in Congshu Jinghua, edited by Yiping Yan. Taiepei: Yiwen yinshuguan.Google Scholar
Mei, Wending. 1707–08. Wuan lisuan shumu 勿庵曆算書目 (The List and Notes of Works in Mathematics and Astronomy by [Mei] Wuan). I consulted the copy at Fusinian Library at Academia Sinica, Taiwan. Catalogue No: 082 823.1, v. 149.Google Scholar
Mei, Wending. [1674] 1993. Fangcheng lun 方程論 (Discussions on Juxtaposition and Calculation). Reprint in Guo et al. 4:323-408.Google Scholar
Mei, Wending. [1763] 2002a. Jixuetang wenchao 績學堂文鈔 (Hand-copied Records of Compositions at Jixue Hall). Reprint in XXSKQS 1413:325–445.Google Scholar
Mei, Wending. [1763] 2002b. Jixuetang Shichao 積學堂詩鈔 (Hand-copied Records of Poems at Jixue Hall). Reprint in XXSKQS 1413:446–514.Google Scholar
Peterson, Willard. 1986. “Calendar Reform Prior to the Arrival of Missionaries at the Ming Court.” Ming Studies 1, 45–61. Doi: 10.1179/014703786788764194.CrossRefGoogle Scholar
Ruan, Yuan 阮元. [1799] 2002. Chouren zhuan 疇人傳 (Biographies of Mathematicians and Astronomers). Reprint included in XXSKQS 516:53–526.Google Scholar
Schreck, Johann. [1631] 2009. Dace 大測 (Grand Measure). In Chongzhen Lishu 崇禎曆書 (Astronomical Compendium of the Chongzhen Reign), compiled and translated by Adam Schall von Bell et al. I use the edition collated by Pan Nai. Shanghai: Shanghai Guji Chubanshe.Google Scholar
Shen, Kangshen, Crossley, John, and Lun, Anthony W.-C.. 1999. The Nine Chapters on the Mathematical Art. Oxford: Oxford University Press.Google Scholar
Siku quanshu 四庫全書 (The Complete Texts of the Four Repositories). Reprint. Taipei: Taiwan Shangwu yingshuguan. 1983.Google Scholar
Tong, Qingjun, and Feng, Lisheng. 2007. “Mei Wending Zhongxi Suanxue Tong Tanyuan 梅文鼎《中西算学通》探源 (Discussion on Mei Wending’s Zhong Xi Suan Xue Tong).” Journal of Inner Mongolia Normal University (Natural Science Edition) 36
(6):716-7127.Google Scholar
Wang, Wensu 王文素. [1524] 1993. Suanxue Baojian 算學寶鑑 (The Precious Mirror of Mathematics). Reprinted in Guo et al. 2:337–971.Google Scholar
Wang, Yangzong. 1995. “Kangxi, Mei Wending, and ‘Xixue Zhongyuan Shuo’ 康熙, 梅文鼎, 与‘西学中源’说 (Kangxi [Emperor], Mei Wending, and the Doctrine of Western Learning [Being of] Chinese Origin).” Chinese Culture: Tradition & Modernization 3:77–84.Google Scholar
Wu, Jing 吳敬. [1450] 1993. Jiuzhang suanfa bilei daquan 九章算法比類大全 (the Comprehensive Collection of Computational Methods in Nine Chapters with Analogous [Problems and Rules]). Reprinted in Guo et al. 2:5-333.Google Scholar
Xuxiu siku quanshu 續修四庫全書 (The Sequel of the Complete Texts of the Four Repositories). Reprint. Shanghai: Guji Chubanshe, 2002. Abbreviated as XXSKQS.Google Scholar
Yüzhi shuli jingyun 御製數理精蘊 (The Essence of Numbers and Their Principles Imperially Composed). Reprinted in Guo et al. 1993, vol. 3.Google Scholar
Zhou, Xiaohan. 2018. “Elements of Continuity between Mathematical Writings from the Song-Yuan (13th – 14th Century) Dynasties and the Ming Dynasty (15th Century): Comparing Yang Hui’s Mathematical Methods (1261 C.E.) and Wu Jing’s Great Compendium (1450 C.E.).” Ph.D. diss., Université Paris Diderot.Google Scholar
Zhu, Yiwen, 2010. “Shu: suan yu shu–yi jiushu zhi fangcheng wei li 數: 筭與術–以九數之方程為例 (Chinese Mathematics: Counting Sticks and Techniques—Using Fangcheng as an Example).” Hanxue yanjiu 漢學研究 (Chinese Studies) 28
(4): 73–105.Google Scholar
Zhu, Yiwen, 2018. “How Were Western Written Calculations Introduced into China?—An Analysis of Tongwen Suanzhi (Arithmetic Guidance in the Common Language, 1613). Centaurus, DOI: 10.1111/1600-0498.12169. Published online.Google Scholar