Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
권호 표지
DOI QR코드

DOI QR Code

One Quadratic Equation, Different Understandings: the 13th Century Interpretations by Li Ye and Later Commentaries in the 18th and 19th Centuries

  • Received : 2017.02.18
  • Accepted : 2017.06.07
  • Published : 2017.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

The Chinese algebraic method, the tian yuan shu, was developed during Song period (960-1279), of which Li Ye's works contain the earliest testimony. Two 18th century editors commentated on his works: the editor of the Siku quanshu and Li Rui, the latter responding to the former. Korean scholar Nam Byeong-gil added another response in 1855. Differences can be found in the way these commentators considered mathematical objects and procedures. The conflicting nature of these commentaries shows that the same object, the quadratic equation, can beget different interpretations, either a procedure or an assertion of equality. Textual elements in this paper help modern readers reconstruct different authors' understandings and reconsider the evolution of the definition of the object we now call 'equation'.

Keywords

References

  1. Li Ye, Ceyuan haijing (Sea Mirror of Circle Measurements), 1248. (李冶, <測圓海鏡>, 1248.)
  2. Li Ye. 益古演段 Yigu yanduan (The Development of Pieces of Areas according to the Collection Augmenting the Ancient Knowledge), 1259. (李冶, <益古演段>, 1259.)
  3. Edition of 1782, 文淵閣四庫全書 Wen yuan ge Siku quanshu (Complete library of the Four Treasuries, Wenyuan pavilion), original copy from National Palace Museum, Taiwan.
  4. Edition of 1789, 文津閣四庫全書 Wen jin ge Siku quanshu (Complete library of the Four Treasuries, Wenjin Pavilion), vol. 799. Facsimile. 2005.
  5. Edition of 1798, 知不足齋叢書 Zhibuzu zhai congshu (Collected works of the Private Library of Knowing Our Own Insufficiencies), reprint in Guo Shuchun (ed.), Zhongguo kexue jishu dianji tong hui: Shuxue pian, vol. 1, HeNanJiaoYuChuBanShe, 1993. (郭书春, <中國科學技術典籍通彙: 數學篇> 第一分冊, 河南教育出版社, 1993.)
  6. Nam Byeong-Gil, Mu-i hae (Solutions of No Difference), 1855. 南秉吉, <無異解>, 1855. In Kim, Yong-Un (ed.), Hanguk Gwahak Gisul Sa Jaryo Daekye: Suhak Pyeon, vol. 6, YeoGang Press, 1985. (金容雲, <韓國科學技術史資料大系: 數學篇> 第六卷, 驪江出版社, 1985.)
  7. P. Benoit, K. Chemla and J. Ritter, Histoire de fraction, fraction d'histoire, Birkhauser Verlag, 1992.
  8. K. Chemla, Etude du livre 'reflets des mesures du cercle sur la mer' de Li Ye. These de doctorat de l'universite Paris XIII, 1982.
  9. K. Chemla, Different concepts of equations in The Nine Chapters on Mathematical Procedures and in the Commentary on it by Liu Hui (3rd century), Historia Scientiarum 4(2) (1994), 113-137.
  10. K. Chemla, Positions et changements en mathematiques a partir des textes chinois des dynasties Han a Song-Yuan. Quelques remarques, Extreme-Orient, Extreme-Occident 18 (1996), 115-147. https://doi.org/10.3406/oroc.1996.1021
  11. K. Chemla, Artificial Language in the Mathematics of Ancient China, Journal of Indian Philosophy 34 (2006), 31-56. https://doi.org/10.1007/s10781-005-8168-5
  12. K. Chemla and Guo Shuchun, Les neuf chapitres. Le classique mathematique de la Chine ancienne et ses commentaires, Dunod, 2004.
  13. J. Dauben, Chinese Mathematics. I. V. Katz (ed.), The Mathematics of Egypt, Mesopotamia, China, India and Islam, A Source Book, Princeton University Press, 2007, 187-380.
  14. B. Elman, From philosophy to philology, Council on East Asian Studies, Harvard University, 1984.
  15. Guo Shuchun, Zhonguo gudai shuxue, ShanDongJiaoYuChuBanShe, 1991. (郭書春, <中國古代數學>, 山東教育出版社), 1991.
  16. Guo Shuchun, Zhongguo kexue jishu dianji tonghui: Shuxue pian, HeNanJiaoYuChuBanShe, 1993. (郭書春, <中國科學技術典籍通匯: 數學篇>, 河南教育出版社, 1993.)
  17. J. Hoe, The Jade Mirror of the Four Unknowns by Zhu Shijie. Mingming Bookroom, 2008.
  18. Hong Sung Sa, Hong Young Hee and Kim Young Wook, Hong JeongHa's Tianyuanshu and Zencheng Kaifangfa, Journal for History of Mathematics 27 (2014), 155-164. https://doi.org/10.14477/jhm.2014.27.3.155
  19. Horng Wann-Sheng, Chinese Mathematics at the Turn of the 19th Century: Jiao Xun, Wang Lai and Li Rui. In. Cheng-hung Lin and Daiwei Fu (eds.), Philosophy and Conceptual History of Science in Taiwan. Kluwer Academic Publishers, 1993, 167-208.
  20. Horng Wann-Sheng, Tan tian san you, MingWenShuJu, 1993b. (洪萬生, <談天三友>, 明文書局.)
  21. C. Jami, The Emperor's New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign (1662-1722), Oxford University Press, 2012.
  22. Lam Lay-Yong, A Critical Study of the Yang Hui Suan Fa. Singapore University Press, 1977.
  23. Lam Lay-Yong, Li Ye and his Yi Gu Yan Duan (old mathematics in Expanded Sections), Archive for History of Exact Sciences 29 (1984), 237-266. https://doi.org/10.1007/BF00348622
  24. Lam Lay-Yong and Ang Tian Se, Fleeting Footsteps, Tracing the Conception of Arithemtic and Algebra in Ancient China. World Scientific, 2004.
  25. Li Di, Tian yuan shu yu Li Ye, in Zhongguo shuxue tongshe. Song-Yuan juan, JiangSu-JiaoYuChuBanShe, 1997, 184-239. (李迪, 天元術與李冶, <中國數學通史. 宋元卷>, 江蘇教育出版社, 1997, 184-239.)
  26. Li Yan, Zhongsuan shi luncong, KeXueChuBanShe, 1955. (李儼, <中算史論叢>, 科學出版社, 1955.)
  27. Li Yan and Du Shiran, Chinese Mathematics, A Concise History, translated by J.N. Crossley, and W.C. Lun, 1987.
  28. Liu Dun and J. Dauben, The Qian-Jia School and its Successor in 19th Century Chinese Mathematics. In J.W. Dauben and C.J. Scriba (Eds.), Writing the History of Mathematics, Birkhauser, 1993, 300-306.
  29. U. Libbrecht, Chinese mathematics in the thirteen century. The Shu-shu chiu-chang of Ch'in Chiu-shao, The MIT Press, 1973.
  30. Jean-Claude Martzloff, Histoire des mathematiques chinoises. Masson, 1987.
  31. Mikami Yoshio, The Development of Mathematics in China and Japan. New York BG Teubner, 1931.
  32. J. Needham, Science and Civilisation in China, vol. III, Cambridge University Press, 1954.
  33. C. Pollet, Comparison of Algebraic Practices in Medieval China and India, PhD Thesis, National Taiwan Normal University/Universite Paris 7-Diderot, 2012.
  34. C. Pollet, The influence of Qing dynasty editorial work on the modern interpretation of mathematical sources: the case of Li Rui's edition of Li Ye's mathematical treatises, Science in Context 27(3) (2014), 385-422. https://doi.org/10.1017/S026988971400012X
  35. Qian Baocong, Suanjing shishu, ZhongHuaShuJu, 1963. (錢寶琮, <算經十書>, 中華書局, 1963.)
  36. Qian Bacong, Zhongguo shuxue shi, in Li Yan Qian Baocong Kexue Shi Chuanji, vol. 5, LiaoNingJiaoYuChuBanShe, 1964/1998. (錢寶琮, 中國數學史, <李儼錢寶琮科學史全集>, 第五冊, 遼寧教育出版社, 1964/1998.)
  37. I. Robinet, Wuji and Taiji 無極. 太極Ultimateless and Great Ultimate. In Fabrizio Pregadio(ed.), The Encyclopedia of Taoism, Routledge, 2008, 1057-9.
  38. Tian Miao, Jiegenfang, Tianyuan and Daishu: Algebra in Qing China, Historia Scientiarum, 9(1) (1999), 101-119.
  39. A. Volkov, Lam Lay-Yong, Ang Tian-Se. Fleeting Footsteps, Archives Internationales d'Histoire des Sciences, 46(136) (1996), 155-159.
  40. A. Volkov, Le Bacchette. In Chemla, Bray, Fu, Huang and Metaile (eds). La scienza in Cina, Storia della scienza, vol. 8, Enciclopedia Italiana, section I, vol. II., 2001.
  41. Wang Ling, The date of the Sun Tzu Suan Ching and the Chinese remainder problem, Actes du Xe Congres International d'histoire des Sciences, 1964, 489-492.
  42. Ying Jia-Ming, The Kujang sulhae: Nam Pyong-Gil's reinterpretation of the mathematical methods of the Jiuzhang suanshu, Historia Mathematica 38(1) (2011), 1-27. https://doi.org/10.1016/j.hm.2010.04.001
  43. Ying Jia-Ming, Mathematical Canons in Practice: The Case of a Nineteenth-Century Korean Scholar Nam Pyong-Gil and His Evaluation of Two Major Algebraic Methods Used in East Asia, East Asian Science, Technology and Society: An International Journal, 8(3) (2014), 347-362. https://doi.org/10.1215/18752160-2771829

Cited by

  1. 동양수학사에서의 조선수학의 역할과 의미 vol.31, pp.4, 2018, https://doi.org/10.14477/jhm.2018.31.4.169
  2. The procedure of the Section of Pieces of Areas in Li Ye and Yang Hui’s works: genealogy of diagrams and equations vol.33, pp.1, 2017, https://doi.org/10.1017/s0269889720000113