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On the Transmission of Mathematical Knowledge in Versified Form in China

  • Andrea Bréard
Chapter
Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 301)

Abstract

Versified mathematical algorithms and problems make their appearance in China around the end of the Song dynasty (eleventh century) and are widely spread among the sources of the Ming (1368–1644) and the Qing (1644–1911) dynasties.

Keywords

Mathematical Problem Mathematical Knowledge Root Extraction Educational Context Song Dynasty 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Brard, Andrea. 1999. Re-Kreation eines mathematischen Konzeptes im chinesischen Diskurs: Reihen vom 1. bis zum 19. Jahrhundert. Boethius, vol. 42. Stuttgart: Steiner Verlag.Google Scholar
  2. Brard, 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. Boston studies of philosophy of science, ed. Florence Bretelle-Establet et al. Dordrecht: Kluver.Google Scholar
  3. Chemla, Karine. 1994. Similarities between Chinese and Arabic mathematical documents (I): Root extraction. Arabic Sciences and Philosophy 4: 207266.Google Scholar
  4. Chemla, Karine, and Guo, Shuchun. 2004. Les Neuf Chapitres sur les procdures mathmatiques. Paris: Dunod.Google Scholar
  5. Cheng, Dawei Open image in new window (1533–1606). 1882. Zengbu Suanfa tongzong daquan Open image in new window  (Complemented collection of the Unified Lineage of Mathematical Methods). Open image in new window Taishantang edn.Google Scholar
  6. Cheng, Dawei Open image in new window (1533–1606). 1990. Suanfa tongzong jiaoshi Open image in new window  (Annoted edition of the Unified Lineage of Mathematical Methods). Hefei: Anhui jiaoyu chubanshe Open image in new window. Reprint of the 1716 edition.Google Scholar
  7. Elman, Benjamin A. 2001. A cultural history of civil examinations in late imperial China, Reprint edn. Taibei: SMC Publishing Co. Originally published Berkeley: University of California Press, 2000.Google Scholar
  8. Friedsam, Manfred. 2003. L’enseignement des mathmatiques sous les Song et Yuan. In Éducation et instruction en Chine, vol. II. Les formations spcialises, ed. C. Despeux, and C. Nguyen Tri, 49–68. Bibliothque de l’INALCO, vol. 5. Paris – Louvain: Editions Peeters.Google Scholar
  9. Giles, Herbert A. (trans.) 1900. Elementary Chinese. San Tzu Ching ( Open image in new window). Shanghai: Messrs. Kelly & Walsh. Reprinted in Peking, China 1940.Google Scholar
  10. Guo, Shuchun Open image in new window et al. (eds). 1993. Zhongguo kexue jishu dianji tonghui. Shuxue juan Open image in new window, 5 vols. Zhengzhou: Henan jiaoyu chubanshe Open image in new window.Google Scholar
  11. Honda, Seiichi Open image in new window. 1994. Open image in new window (“Children’s mathematical education during the Song, Yuan and Ming dynasties”). Kyūshū Daigaku Tōyōshi ronshū Open image in new window  (Oriental studies), 37–72.Google Scholar
  12. Lam, Lay Yong, and Tian Se Ang. 2004. Fleeting footsteps: Tracing the conception of arithmetic and algebra in ancient China, Revised edn. Singapore: World Scientific.Google Scholar
  13. Lee, H.C. Thomas. 2000. Education in traditional China. A history. Handbook of oriental studies, vol. 13. Leiden/Boston/Kln: Brill.Google Scholar
  14. Leung, Angela Ki Che. 2003. Medical instruction and popularization in ming-qing China. Late Imperial China 24(1): 130152.Google Scholar
  15. Li, Yan Open image in new window. 1954–1955. Mingdai de suanxue shuzhi Open image in new window (“Bibliography of mathematical works of the Ming Dynasty”). In Zhong suan shi luncong Open image in new window. (Collected essays on Chinese mathematics), vol. 2. 86–102. Beijing: Kexue chubanshe. Reprinted from Tushuguan xue jikan Open image in new window (Library science quarterly) 1.4 (1926), pp. 667–682.Google Scholar
  16. Libbrecht, Ulrich. 1973. Chinese mathematics in the thirteenth century. The Shu-shu chiu-chang of Ch’in Chiu-shao. Cambridge: MIT.Google Scholar
  17. Lowry, Kathryn A. 2005. The Tapestry of popular songs in sixteenth- and seventeenth-century China: Reading, imitation, and desire. Sinica Leidensia series, vol. 67. Leiden/New York: Brill.Google Scholar
  18. Martzloff, Jean-Claude. 1997. A history of Chinese mathematics. New York: Springer.CrossRefGoogle Scholar
  19. McLaren, Anne E. 2005. Constructing new reading publics. In Printing & book culture in late imperial China, ed. Cynthia J. Brokaw and Kai-Wing Chow, 152–183. Berkeley/Los Angeles: University of California Press.Google Scholar
  20. Qian, Baocong Open image in new window. 1963. Suanjing shi shu Open image in new window (Ten Books of Mathematical Classics). Beijing: Zhonghua shuju Open image in new window.Google Scholar
  21. Sakade, Yoshinobu Open image in new window Ogawa, Yōichi Open image in new window, and Sakai, Tadao Open image in new window (eds). 2000. Chūgoku nichiyō ruisho shūsei Open image in new window. Tokyo: Kyūko shoin Open image in new window.Google Scholar
  22. Siu, Man-Keung, and Alexei Volkov. 1999. Official curriculum in traditional Chinese mathematics: How did candidates pass the examinations? Historia Scientiarum 9(1): 87–99.Google Scholar
  23. Volkov, Alexei. 2002. On the origins of the Toan phap dai thanh (great compendium of mathematical methods). In From China to Paris: 2000 years transmission of mathematical ideas. Boethius, vol. 46, ed. Yvonne Dold-Samplonius, 369–410. Stuttgrat: Franz Steiner Verlag.Google Scholar
  24. Wang, Wensu Open image in new window. 1524. Xinji tongzheng gujin suanxue baojian Open image in new window (Mathematical mirror of old and new mathematical learning, newly collected and corrected). Manuscript copy of 41 juan from Beijing Library. Reprint in (Guo et al. 1993, vol. 2: 337–971).Google Scholar
  25. Wang, Ermin Open image in new window. 1994. Zhongguo chuantong jisong zhi xue yu shiyun koujue Open image in new window (“Chinese traditional recitation methods and arts of rhyming”). Zhongyang yanjiuyuan Jindai shi yanjiusuo jikan Open image in new window (Journal of the Institute of Modern Chinese History at the Academia Sinica), 23: 31–64.Google Scholar
  26. Wang, Wensu Open image in new window. 2008. Suanxue baojian jiaozhu Open image in new window (Critical edition of the Precious mirror of mathematical learning). Beijing: Kexue chubanshe Open image in new window.Google Scholar
  27. Wu, Jing Open image in new window. fl. 1450. Jiu zhang suanfa bilei daquan Open image in new window (Great compendium of analogical categories to the Nine Chapters of Mathematical Methods). Reprinted in (Guo et al. 1993, vol. 2: 1–333).Google Scholar
  28. Xu, Xinlu Open image in new window. 1573. Panzhu suanfa Open image in new window (Methods for Calculating on an Abacus). Xiong tainan Open image in new window edn. Complete title: Open image in new window (Newly engraved and corrected edition of the Method of Calculating on an Abacus , with verses for memorization transmitted secretly through family, for the use of scholars and commoners. Preserved in Japan, Naikau bunko, Open image in new window 56 Open image in new window 5 Open image in new window. Reprinted in (Guo et al. 1993, vol. 2: 1143–1164).Google Scholar
  29. Yang, Hui Open image in new window. 1275. Xugu zhaiqi suanfa Open image in new window (Selection of Strange Mathematical Methods in Continuation of Antiquity). Manuscript edn. Reprinted in (Guo et al. 1993, vol. 1: 1095–1117).Google Scholar
  30. Yang, Hui Open image in new window. 1842. Chengchu tongbian suanbao Open image in new window (“Mathematical treasure of variations on multiplication and division”). In Yang Hui suanfa Open image in new window, Open image in new window yijiatang congshu edn.Google Scholar
  31. Yu, Xiangdou Open image in new window (ed). 1599. Santai wanyong zhengzong Open image in new window (complete title: Santai’s orthodox instructions for myriad uses for the convenient perusal of all the people in the world, newly engraved Xinke tianxia simin bianlan Santai wanyong zhengzong Open image in new window ). Housed in Tōkyō Daigaku Tōyō Bunka Kenkyūjo Niida Bunko Open image in new window (Institute of Oriental Culture, University of Tokyo, Niida Collection). Reproduced in (Sakade et al. 2000, vols. 3–5).Google Scholar
  32. Zhang, Zhigong Open image in new window. 1962. Chuantong yuwen jiaoyu chutan Open image in new window (Preliminary inquiry into traditional language education). Shanghai: Shanghai jiaoyu chubanshe Open image in new window.Google Scholar
  33. Zhu, Shijie Open image in new window. 1839. Suanxue qimeng Open image in new window (Introduction to Mathematical Learning). Open image in new window Yangzhou edn. Reprinted in (Guo et al. 1993, vol. 1: 1123–1200).Google Scholar
  34. Zhou, Yongnian Open image in new window. 1895. Xianzheng dushu jue Open image in new window (Recipes of Effective Reading by Ancient Wisdom). Guiyang: Yan Xiu Open image in new window.Google Scholar
  35. Zhou, Mi Open image in new window. 1969. Zhiyatang zachao Open image in new window (Random Jottings from the Hall for Pursuit of Elegance). Biji xubian Open image in new window; 31. Taibei: Guangwen shuju Open image in new window.Google Scholar
  36. Zhu, Shijie Open image in new window and Guo, Shuchun Open image in new window (trans.) and Chen, Zaixin Open image in new window (Engl. trans.). 2006. Siyuan yujian Open image in new window (Jade Mirror of Four Unknowns). Shenyang: Liaoning jiaoyu chubanshe Open image in new window.Google Scholar
  37. Zhu, Shijie Open image in new window and Luo, Shilin Open image in new window (comm.). 1937. Siyuan yujian xicao Open image in new window (Detailed Explanations of the Jade Mirror of Four Unknowns). Wanyou wenku Open image in new window, vol. 2–700. Shanghai: Shangwu yinshuguan Open image in new window. Originally published 1836.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Laboratoire Paul PainlevéUniversité Lille IVilleneuve d’Ascq CedexFrance

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