Hostname: page-component-89b8bd64d-r6c6k Total loading time: 0 Render date: 2026-05-13T02:48:11.510Z Has data issue: false hasContentIssue false
  • English
  • Français

The Influence of Qing Dynasty Editorial Work on the ModernInterpretation of Mathematical Sources: The Case of Li Rui's Editionof Li Ye's Mathematical Treatises

Published online by Cambridge University Press:  28 July 2014

Charlotte-V. Pollet
Charlotte-V. Pollet*
Affiliation:
National Chiao Tung University (Taiwan) E-mail: cpollet@nctu.edu.tw
Get access Rights & Permissions [Opens in a new window]

Argument

Recent studies in Sinology have shown that Qing dynasty editors acted asphilologists. This paper argues that the identification of their philologicalmethods and editorial choices suggests that their choices were not totallyneutral and may have significantly shaped the way modern historians interpretedspecific works edited by mathematicians of that dynasty. A case study of there-edition in 1798 of a Song dynasty treatise, the Yigu yanduan(1259), by a Qing dynasty mathematician will illustrate this point. At the endof the eighteenth century, Li Rui (1773–1817) was asked to prepare anedition of the mathematical works written by Li Ye (1192–1279) for aprivate collection. Li Rui was a talented mathematician, but he was also ameticulous editor and trained philologist. He adopted his editorial model fromthe preparation of the imperial encyclopaedia, the Sikuquanshu, but Li Rui also made some corrections to the text in an effortto restore an older version of Li Ye's treatises that had been lost.Convinced of the Chinese origin of algebra, Li Rui used philological techniquesto recover the lost materials and to restore the roots of “Chinesemathematics.” The Yigu yanduan contains twoalgebraic procedures to set up quadratic equations, one from the procedure ofCelestial Source (tian yuan shu) and theother from the Section of Pieces [of Areas] (tiaoduan). Curiously, the second procedure has not yet attracted theattention of scholars so far, although Li Rui's edition is the onetypically used by twentieth-century historians of mathematics. Today, theCelestial Source characterizes “Chinesealgebra.” However, the specific concerns of Li Rui about theprocedure of Celestial Source, combined with his editorialmethods, contributed to this perspective.

Information

Type
Research Article
Information
Science in Context , Volume 27 , Issue 3 , September 2014 , pp. 385 - 422
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

References

Ye, Li. 1248. 測圓海鏡 (Ceyuan haijing [Sea Mirror of Circle Measurements>]).

Ye, Li. 1259. 益古演段 (Yigu yanduan [The Development of Pieces of Areas according to the Collection Augmenting the Ancient Knowledge]).

Both edited in:

(1) Edition of 1789, 文淵閣四庫全書, (Wen yuan ge Siku quanshu [Complete Library of the Four Treasuries, Wenyuan pavilion]). Original edition, National Palace Museum, Taiwan.

(2) 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. Reprint. 2005.

(3) 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 中國科學技術典籍通彙: 數學篇 (Zhongguo kexue jishu dianji tong hui: Shuxue pian [Source Materials of Ancient Chinese Science and Technology: Mathematics Section>]). 郭书春, Guo Shuchun (ed). 河南教育出版社 (Henan jiaoyu chubanshe [Henan Education Press]), Vol 1. 1993.

Andrea, Bréard. 2012. “Divination with Hexagrams as Combinatorial Practice.” International Consortium for Research in the Humanities: Fate, Freedom and Prognostication. Jan. 29, 2013. University Erlangen-Nuremberg Reading session. Feb. 27. 2012. http://www.ikgf.uni-erlangen.de/content/articles/Andrea_Breard_-_Divination_with_Hexagrams.pdf (last accessed, March 2, 2014).Google Scholar
Chemla, Karine. 1982. “Etude du livre ‘Reflets des mesures du cercle sur la mer’ de Li Ye.” Ph.D. diss., University Paris XIII.Google Scholar
Chemla, Karine. 1993. “李冶, 測圓海鏡, 的結構及其對數學知識的表述” (Li ye, ceyuan haijing, de jiegou ji qi dui shuxue zhishi de biaoshu [The Structure and Representation of Mathematical Knowledge of Ceyuan haijing by Li Ye]), 數學史研究文集第五輯 (shuxue shi yanjiu wenji di wu ji [History of Mathematics Study Series, fifth volume]), 123–142.Google Scholar
Chemla, Karine. 1996. “Positions et changements en mathématiques à partir des textes chinois des dynasties Han à Song-Yuan. Quelques remarques.” Extrême-Orient, Extrême-Occident 18:115–147.Google Scholar
Chemla, Karine, and Shuchun, Guo. 2004. Les neuf chapitres. Le classique mathématique de la Chine ancienne et ses commentaires. Paris. Dunod.Google Scholar
Chemla, Karine. 2005. “What Is the Content of This Book? A Plea for Developing History of Science and History of Text Conjointly.” In History of Science, History of Text, edited by Karine Chemla, 201- 230. Dordrecht-Boston-London: Kluwer Academic Publishers.Google Scholar
Chia, Lucille. 2002. Printing for Profit: The Commercial Publishers of Jianyang, Fujian, 11th -17th Centuries. Cambridge: Harvard University Asia Center.Google Scholar
Dauben, Joseph. 2007. “Chinese Mathematics.” In The Mathematics of Egypt, Mesopotamia, China, India, and Islam, A Source Book, edited by Katz, Victor, 187–380. Princeton and Oxford: Princeton University Press.Google Scholar
Elman, Benjamin. 1984. From Philosophy to Philology: Social Aspects of Change in Late Imperial China. Cambridge: Harvard University Council on East Asian Studies.Google Scholar
Elman, Benjamin. 1990. Classicism, Politics, and Kinship. Berkeley: University of California Press.Google Scholar
Elman, Benjamin. 2005. On Their Own Terms: Science in China, 1550–1900. Cambridge MA: Harvard University Press.Google Scholar
Shuchun, Guo. 1993. 中國科學技術典籍通彙: 數學篇 (Zhongguo kexue jishu dianji tong hui: Shuxue pian [Source Materials of Ancient Chinese Science and Technology: Mathematics Section>]). 河南教育出版社 (Henan jiaoyu chubanshe [Henan Education Press]), Vol. 1–5.]).+河南教育出版社+(Henan+jiaoyu+chubanshe+[Henan+Education+Press]),+Vol.+1–5.>Google Scholar
Shuchun, Guo. 2010. 中國科學技術史. 數學卷. (Zhongguo kexue jishu shi: Shuxue juan [History of Chinese Science and Technology: Mathematics Volume>]). 科學出版社, 北京. (Kexue chubanshe [Beijing: Science Press>]).]).+科學出版社,+北京.+(Kexue+chubanshe+[Beijing:+Science+Press>]).>Google Scholar
Qi, Han. 1997. “Patronage scientifique et carrière politique: Li Guangdi entre Kangxi et Mei Wending.” Etudes chinoises 16 (2):7–37.Google Scholar
Qi, Han. 2001. “Astronomy, Chinese and Western: The Influence of Xu Guangqi's Views in the Early Mid-Qing.” In Statecraft and Intellectual Renewal in Late Ming China: The Cross Cultural Synthesis of Xu Guangqi, edited by Jami, Catherine, Engelfriet, Peter M., and Blue, Gregory, 360–379. Leiden: Brill.Google Scholar
Hashimoto, Keizo. 1988. Hsu Kuang-ch’I and Astronomical Reform: The Process of the Chinese Acceptance of Western Astronomy, 1629–1635. Osaka: Kansai University Press.Google Scholar
Hashimoto, Keizo. 2001. “From the Elements to Calendar Reform: Xu Guangqi's Shaping of Mathematics and Astronomy.” In Statecraft and Intellectual Renewal in Late Ming China: The Cross Cultural Synthesis of Xu Guangqi, edited by Jami, Catherine, Engelfriet, Peter M., and Blue, Gregory, 263–279. Leiden: Brill.Google Scholar
Yoke, Ho Peng. 1973. “Li Chih.” In Dictionary of Scientific Biography, edited by Gillispie, Charles, vol. 8, 313–320. New York: Charles Scribner's Sons.Google Scholar
Hoe, John. 2008. The Jade Mirror of the Four Unknowns by Zhu Shijie. Christchurch NEW ZEALAND: Mingming Bookroom.Google Scholar
Horiuchi, Annick. 2000. “La notion de yanduan: quelques réflexions sur les méthodes ‘algébriques’. de la résolution de problèmes en Chine aux X° et XI°.” Oriens-Occidens 3:235–258.Google Scholar
Wann-Sheng, Horng. 1993a. “Chinese Mathematics at the Turn of the 19th Century: Jiao Xun, Wang Lai and Li Rui.” In Philosophy and Conceptual History of Science in Taiwan, edited by Lin, Cheng-hung and Fu, Daiwei, 167–208. Dordrecht: Kluwer Academic Publishers.Google Scholar
Wann-Sheng, Horng. 1993b. 談天三友 (Tan tian san you [Three Friends Talking about the Heavens>]). 台北. 明文書局 (Taibei, ming wenshu ju [Taipei: Ming-Wen Bookstore>]).]).+台北.+明文書局+(Taibei,+ming+wenshu+ju+[Taipei:+Ming-Wen+Bookstore>]).>Google Scholar
Jami, Catherine. 1994. “Learning Mathematical Sciences during the Early and Mid-Ch’ing.” In Education and Society in Late Imperial China, 1600–1900, edited by Elman, Benjamin and Woodside, Alexander, 223–56. Berkeley: University of California Press.CrossRefGoogle Scholar
Jami, Catherine. 2012. The Emperor's New Mathematics: Western Learning and Imperial Authority During the Kangxi Reign, 1662–1722. Oxford: Oxford University Press.Google Scholar
Kent, Guy. 1987. The Emperor's Four Treasuries, Scholars and the State in the Late Ch’ien-lung Era. Cambridge: Council of East Asian Studies, Harvard University Press.Google Scholar
Guoping, Kong. 1988. 李冶传 (Li Ye zhuan [Biography of Li Ye>]). 石家庄: 河北教育出版社(Shijiazhuang: Hebei jiaoyu chubanshe [Shijiazhuang: Hebei Education Press>]).]).+石家庄:+河北教育出版社(Shijiazhuang:+Hebei+jiaoyu+chubanshe+[Shijiazhuang:+Hebei+Education+Press>]).>Google Scholar
Guoping, Kong. 1996. 測圓海鏡導讀 (Ceyuan haijing daodu [Review of Ceyuan Haijing]). In 中華傳統數學名著導讀叢書 (Zhonghua chuantong shuxue mingzhu daodu congshu [Reviews of Famous Traditional Chinese Mathematics Books]), 湖北教育出版社 (Hubei jiaoyu chubanshe [Hubei Education Press>]).]).>Google Scholar
Guoping, Kong. 1999. 李冶朱世杰與金元數學 (Li Ye Zhu Shijie yu jinyuan shuxue [Li Ye, Zhu Shijie and Jin-Yuan Mathematics]). In 中國數學史大系 (Zhongguo shuxueshi daxi [Collection of History of Chinese Mathematics>]). 河北科學技術出版社 (Hebei kexue jishu chubanshe [Hebei Science and Technology Press>]).]).+河北科學技術出版社+(Hebei+kexue+jishu+chubanshe+[Hebei+Science+and+Technology+Press>]).>Google Scholar
Lay-Yong, Lam. 1984. “Li Ye and his Yi Gu Yan Duan [Old Mathematics in Expanded Sections].” Archive for History of Exact Sciences 29:237–266Google Scholar
Lirong, Lan and Tianyang, Hong. 1985. 李冶和 “益古演段” (Li Ye he Yigu yanduan [Li Ye and the Development of Pieces of Areas according to the Collection Augmenting the Ancient Knowledge>]). 科學史譯叢 (Kexue shi yi cong [Collected Translations in History of Science]) 4:11–12.]).+科學史譯叢+(Kexue+shi+yi+cong+[Collected+Translations+in+History+of+Science])+4:11–12.>Google Scholar
Di, Li. 1999. 中國數學通史: 宋元卷 (Zhongguo shuxue tongzhi: Song Yuan juan [History of Chinese Mathematics: Song-Yuan Volume>]). 南京: 江蘇教育出版社 (Nanjing: Jiansu jiaoyu chubanshe [Nanjing: Jiangsu Education Press>]).]).+南京:+江蘇教育出版社+(Nanjing:+Jiansu+jiaoyu+chubanshe+[Nanjing:+Jiangsu+Education+Press>]).>Google Scholar
Yan, Li and Shiran, Du. 1987. Chinese Mathematics: A Concise History. Translated by Crossley, John N. and Lun, Anthony W. C.. Oxford: Clarendon Press.Google Scholar
Libbrecht, Ulrich. 1973. Chinese Mathematics in the Thirteenth Century: The Shu-shu chiu-chang of Ch’in Chiu-shao. Cambridge: MIT Press.Google Scholar
Liu, Dun, and Dauben, Joseph. 1993. “The Qian-Jia School and its Successor in 19th Century Chinese Mathematics.” In Writing the History of Mathematics, edited by Dauben, Joseph Warren and Scriba, Christoph J., 300–306. Basel: Birkhäuser.Google Scholar
Martzloff, Jean-Claude. 1988. Histoire des mathématiques chinoises. Paris: Masson.Google Scholar
Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. New York: Springer.Google Scholar
Rongzhao, Mei. 1966. 李冶及其數學著作 (Li ye ji qi shuxue zhuzuo [Li Ye and His Mathematical Works]). In 宋元術學史論文集 (Song Yuan shuxue shi lunwenji [Collection on Song-Yuan History of Mathematics]), edited by 錢寶琮, Qian Baocong, 104–148. 科學出版社 (Kexue chubanshe [Science Press>]).]).>Google Scholar
Mikami, Yoshio. 1913. The Development of Mathematics in China and Japan. Leibzig and New-York: BG Teubner.Google Scholar
Pollet, Charlotte. 2012. “Comparison of Algebraic Practices in Medieval China and India.” PhD diss., National Taiwan Normal University/Université Paris 7-Diderot.Google Scholar
Yuan, Ruan. 1799. 疇人傳 (Chou ren chuan [Biographies of Mathematicians]), vol. 82. 中華漢語工具書書庫 (Zhonghua hanyu gongju shu shuku [Collection of Chinese Reference Works>]). 安徽教育出版社 (Anhui jiaoyu chubanshe [Anhui Education Press>]).]).+安徽教育出版社+(Anhui+jiaoyu+chubanshe+[Anhui+Education+Press>]).>Google Scholar
Sarton, George. 1927. Introduction to the History of Science, vol. 2, part 2, 627–628.Google Scholar
Sivin, Nathan. 1973. “Copernicus in China.” In Colloquia Copernica II: Etudes sur l’audience de la théorie héliocentrique, 6:63–122. Warsaw: Union Internationale d’Histoire et Philosophie des Sciences.Google Scholar
Miao, Tian. 1999. “Jiegenfang, Tianyuan, and Daishu: Algebra in Qing China.” Historia Scientarum 9 (1):101–119.Google Scholar
Alexei, Volkov. 2006. “Le raisonnement par analogie dans les mathématiques chinoises du premier millénaire de notre ère.” In Durand-Richard M-J. L’analogie dans la démarche scientifique. L’Harmattan. Collection Histoire des Sciences.Google Scholar
Wei, Betty Peh-t’i. 2006. Ruan Yuan, 1764–1849: The Life and Work of a Major Scholar-Official in Nineteenth-Century China before the Opium War. Hong Kong: University Press.Google Scholar
Wenjun, Wu. 1985. 益古演段. 李冶的數學成就 (Yigu yanduan: Li Ye de shuxue chengjiu [Yigu yanduan: Li Ye's Achievement in Mathematics>]). 中國數學史大系 (Zhongguo shuxue shi daxi [Collection on History of Chinese Mathematics]) 2(3):104–130.]). 中國數學史大系 (Zhongguo shuxue shi daxi [Collection on History of Chinese Mathematics]) 2(3):104–130.' href=https://scholar.google.com/scholar?q=Wenjun,+Wu.+1985.+益古演段.+李冶的數學成就+(Yigu+yanduan:+Li+Ye+de+shuxue+chengjiu+[Yigu+yanduan:+Li+Ye's+Achievement+in+Mathematics>]).+中國數學史大系+(Zhongguo+shuxue+shi+daxi+[Collection+on+History+of+Chinese+Mathematics])+2(3):104–130.>Google Scholar
Yibao, Xu. 1990. 對 “益古集”的復原與研究 (Dui “yi gu ji” de fuyuan yu yanjiu [Restoration and Research on the Collection Augmenting the Ancient [Knowledge]]). In 數學史研究文集 (Shuxueshi yanjiu wenji [Research Anthology on History of Mathematics]), edited by Li Di, 1: 149–165. 九章出版社 (Jiu zhang chubanshe [Nine Chapters Press>]).]).>Google Scholar
Jia-Ming, Ying. 201 1. “The Kujang sulhae 九章術解: Nam Pyŏng-Gil's Reinterpretation of the Mathematical Methods of the Jiuzhang suanshu.” Historia Mathematica 38:1–27.Google Scholar
Andrea, Bréard. 2012. “Divination with Hexagrams as Combinatorial Practice.” International Consortium for Research in the Humanities: Fate, Freedom and Prognostication. Jan. 29, 2013. University Erlangen-Nuremberg Reading session. Feb. 27. 2012. http://www.ikgf.uni-erlangen.de/content/articles/Andrea_Breard_-_Divination_with_Hexagrams.pdf (last accessed, March 2, 2014).Google Scholar
Chemla, Karine. 1982. “Etude du livre ‘Reflets des mesures du cercle sur la mer’ de Li Ye.” Ph.D. diss., University Paris XIII.Google Scholar
Chemla, Karine. 1993. “李冶, 測圓海鏡, 的結構及其對數學知識的表述” (Li ye, ceyuan haijing, de jiegou ji qi dui shuxue zhishi de biaoshu [The Structure and Representation of Mathematical Knowledge of Ceyuan haijing by Li Ye]), 數學史研究文集第五輯 (shuxue shi yanjiu wenji di wu ji [History of Mathematics Study Series, fifth volume]), 123–142.Google Scholar
Chemla, Karine. 1996. “Positions et changements en mathématiques à partir des textes chinois des dynasties Han à Song-Yuan. Quelques remarques.” Extrême-Orient, Extrême-Occident 18:115–147.Google Scholar
Chemla, Karine, and Shuchun, Guo. 2004. Les neuf chapitres. Le classique mathématique de la Chine ancienne et ses commentaires. Paris. Dunod.Google Scholar
Chemla, Karine. 2005. “What Is the Content of This Book? A Plea for Developing History of Science and History of Text Conjointly.” In History of Science, History of Text, edited by Karine Chemla, 201- 230. Dordrecht-Boston-London: Kluwer Academic Publishers.Google Scholar
Chia, Lucille. 2002. Printing for Profit: The Commercial Publishers of Jianyang, Fujian, 11th -17th Centuries. Cambridge: Harvard University Asia Center.Google Scholar
Dauben, Joseph. 2007. “Chinese Mathematics.” In The Mathematics of Egypt, Mesopotamia, China, India, and Islam, A Source Book, edited by Katz, Victor, 187–380. Princeton and Oxford: Princeton University Press.Google Scholar
Elman, Benjamin. 1984. From Philosophy to Philology: Social Aspects of Change in Late Imperial China. Cambridge: Harvard University Council on East Asian Studies.Google Scholar
Elman, Benjamin. 1990. Classicism, Politics, and Kinship. Berkeley: University of California Press.Google Scholar
Elman, Benjamin. 2005. On Their Own Terms: Science in China, 1550–1900. Cambridge MA: Harvard University Press.Google Scholar
Shuchun, Guo. 1993. 中國科學技術典籍通彙: 數學篇 (Zhongguo kexue jishu dianji tong hui: Shuxue pian [Source Materials of Ancient Chinese Science and Technology: Mathematics Section>]). 河南教育出版社 (Henan jiaoyu chubanshe [Henan Education Press]), Vol. 1–5.]).+河南教育出版社+(Henan+jiaoyu+chubanshe+[Henan+Education+Press]),+Vol.+1–5.>Google Scholar
Shuchun, Guo. 2010. 中國科學技術史. 數學卷. (Zhongguo kexue jishu shi: Shuxue juan [History of Chinese Science and Technology: Mathematics Volume>]). 科學出版社, 北京. (Kexue chubanshe [Beijing: Science Press>]).]).+科學出版社,+北京.+(Kexue+chubanshe+[Beijing:+Science+Press>]).>Google Scholar
Qi, Han. 1997. “Patronage scientifique et carrière politique: Li Guangdi entre Kangxi et Mei Wending.” Etudes chinoises 16 (2):7–37.Google Scholar
Qi, Han. 2001. “Astronomy, Chinese and Western: The Influence of Xu Guangqi's Views in the Early Mid-Qing.” In Statecraft and Intellectual Renewal in Late Ming China: The Cross Cultural Synthesis of Xu Guangqi, edited by Jami, Catherine, Engelfriet, Peter M., and Blue, Gregory, 360–379. Leiden: Brill.Google Scholar
Hashimoto, Keizo. 1988. Hsu Kuang-ch’I and Astronomical Reform: The Process of the Chinese Acceptance of Western Astronomy, 1629–1635. Osaka: Kansai University Press.Google Scholar
Hashimoto, Keizo. 2001. “From the Elements to Calendar Reform: Xu Guangqi's Shaping of Mathematics and Astronomy.” In Statecraft and Intellectual Renewal in Late Ming China: The Cross Cultural Synthesis of Xu Guangqi, edited by Jami, Catherine, Engelfriet, Peter M., and Blue, Gregory, 263–279. Leiden: Brill.Google Scholar
Yoke, Ho Peng. 1973. “Li Chih.” In Dictionary of Scientific Biography, edited by Gillispie, Charles, vol. 8, 313–320. New York: Charles Scribner's Sons.Google Scholar
Hoe, John. 2008. The Jade Mirror of the Four Unknowns by Zhu Shijie. Christchurch NEW ZEALAND: Mingming Bookroom.Google Scholar
Horiuchi, Annick. 2000. “La notion de yanduan: quelques réflexions sur les méthodes ‘algébriques’. de la résolution de problèmes en Chine aux X° et XI°.” Oriens-Occidens 3:235–258.Google Scholar
Wann-Sheng, Horng. 1993a. “Chinese Mathematics at the Turn of the 19th Century: Jiao Xun, Wang Lai and Li Rui.” In Philosophy and Conceptual History of Science in Taiwan, edited by Lin, Cheng-hung and Fu, Daiwei, 167–208. Dordrecht: Kluwer Academic Publishers.Google Scholar
Wann-Sheng, Horng. 1993b. 談天三友 (Tan tian san you [Three Friends Talking about the Heavens>]). 台北. 明文書局 (Taibei, ming wenshu ju [Taipei: Ming-Wen Bookstore>]).]).+台北.+明文書局+(Taibei,+ming+wenshu+ju+[Taipei:+Ming-Wen+Bookstore>]).>Google Scholar
Jami, Catherine. 1994. “Learning Mathematical Sciences during the Early and Mid-Ch’ing.” In Education and Society in Late Imperial China, 1600–1900, edited by Elman, Benjamin and Woodside, Alexander, 223–56. Berkeley: University of California Press.CrossRefGoogle Scholar
Jami, Catherine. 2012. The Emperor's New Mathematics: Western Learning and Imperial Authority During the Kangxi Reign, 1662–1722. Oxford: Oxford University Press.Google Scholar
Kent, Guy. 1987. The Emperor's Four Treasuries, Scholars and the State in the Late Ch’ien-lung Era. Cambridge: Council of East Asian Studies, Harvard University Press.Google Scholar
Guoping, Kong. 1988. 李冶传 (Li Ye zhuan [Biography of Li Ye>]). 石家庄: 河北教育出版社(Shijiazhuang: Hebei jiaoyu chubanshe [Shijiazhuang: Hebei Education Press>]).]).+石家庄:+河北教育出版社(Shijiazhuang:+Hebei+jiaoyu+chubanshe+[Shijiazhuang:+Hebei+Education+Press>]).>Google Scholar
Guoping, Kong. 1996. 測圓海鏡導讀 (Ceyuan haijing daodu [Review of Ceyuan Haijing]). In 中華傳統數學名著導讀叢書 (Zhonghua chuantong shuxue mingzhu daodu congshu [Reviews of Famous Traditional Chinese Mathematics Books]), 湖北教育出版社 (Hubei jiaoyu chubanshe [Hubei Education Press>]).]).>Google Scholar
Guoping, Kong. 1999. 李冶朱世杰與金元數學 (Li Ye Zhu Shijie yu jinyuan shuxue [Li Ye, Zhu Shijie and Jin-Yuan Mathematics]). In 中國數學史大系 (Zhongguo shuxueshi daxi [Collection of History of Chinese Mathematics>]). 河北科學技術出版社 (Hebei kexue jishu chubanshe [Hebei Science and Technology Press>]).]).+河北科學技術出版社+(Hebei+kexue+jishu+chubanshe+[Hebei+Science+and+Technology+Press>]).>Google Scholar
Lay-Yong, Lam. 1984. “Li Ye and his Yi Gu Yan Duan [Old Mathematics in Expanded Sections].” Archive for History of Exact Sciences 29:237–266Google Scholar
Lirong, Lan and Tianyang, Hong. 1985. 李冶和 “益古演段” (Li Ye he Yigu yanduan [Li Ye and the Development of Pieces of Areas according to the Collection Augmenting the Ancient Knowledge>]). 科學史譯叢 (Kexue shi yi cong [Collected Translations in History of Science]) 4:11–12.]).+科學史譯叢+(Kexue+shi+yi+cong+[Collected+Translations+in+History+of+Science])+4:11–12.>Google Scholar
Di, Li. 1999. 中國數學通史: 宋元卷 (Zhongguo shuxue tongzhi: Song Yuan juan [History of Chinese Mathematics: Song-Yuan Volume>]). 南京: 江蘇教育出版社 (Nanjing: Jiansu jiaoyu chubanshe [Nanjing: Jiangsu Education Press>]).]).+南京:+江蘇教育出版社+(Nanjing:+Jiansu+jiaoyu+chubanshe+[Nanjing:+Jiangsu+Education+Press>]).>Google Scholar
Yan, Li and Shiran, Du. 1987. Chinese Mathematics: A Concise History. Translated by Crossley, John N. and Lun, Anthony W. C.. Oxford: Clarendon Press.Google Scholar
Libbrecht, Ulrich. 1973. Chinese Mathematics in the Thirteenth Century: The Shu-shu chiu-chang of Ch’in Chiu-shao. Cambridge: MIT Press.Google Scholar
Liu, Dun, and Dauben, Joseph. 1993. “The Qian-Jia School and its Successor in 19th Century Chinese Mathematics.” In Writing the History of Mathematics, edited by Dauben, Joseph Warren and Scriba, Christoph J., 300–306. Basel: Birkhäuser.Google Scholar
Martzloff, Jean-Claude. 1988. Histoire des mathématiques chinoises. Paris: Masson.Google Scholar
Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. New York: Springer.Google Scholar
Rongzhao, Mei. 1966. 李冶及其數學著作 (Li ye ji qi shuxue zhuzuo [Li Ye and His Mathematical Works]). In 宋元術學史論文集 (Song Yuan shuxue shi lunwenji [Collection on Song-Yuan History of Mathematics]), edited by 錢寶琮, Qian Baocong, 104–148. 科學出版社 (Kexue chubanshe [Science Press>]).]).>Google Scholar
Mikami, Yoshio. 1913. The Development of Mathematics in China and Japan. Leibzig and New-York: BG Teubner.Google Scholar
Pollet, Charlotte. 2012. “Comparison of Algebraic Practices in Medieval China and India.” PhD diss., National Taiwan Normal University/Université Paris 7-Diderot.Google Scholar
Yuan, Ruan. 1799. 疇人傳 (Chou ren chuan [Biographies of Mathematicians]), vol. 82. 中華漢語工具書書庫 (Zhonghua hanyu gongju shu shuku [Collection of Chinese Reference Works>]). 安徽教育出版社 (Anhui jiaoyu chubanshe [Anhui Education Press>]).]).+安徽教育出版社+(Anhui+jiaoyu+chubanshe+[Anhui+Education+Press>]).>Google Scholar
Sarton, George. 1927. Introduction to the History of Science, vol. 2, part 2, 627–628.Google Scholar
Sivin, Nathan. 1973. “Copernicus in China.” In Colloquia Copernica II: Etudes sur l’audience de la théorie héliocentrique, 6:63–122. Warsaw: Union Internationale d’Histoire et Philosophie des Sciences.Google Scholar
Miao, Tian. 1999. “Jiegenfang, Tianyuan, and Daishu: Algebra in Qing China.” Historia Scientarum 9 (1):101–119.Google Scholar
Alexei, Volkov. 2006. “Le raisonnement par analogie dans les mathématiques chinoises du premier millénaire de notre ère.” In Durand-Richard M-J. L’analogie dans la démarche scientifique. L’Harmattan. Collection Histoire des Sciences.Google Scholar
Wei, Betty Peh-t’i. 2006. Ruan Yuan, 1764–1849: The Life and Work of a Major Scholar-Official in Nineteenth-Century China before the Opium War. Hong Kong: University Press.Google Scholar
Wenjun, Wu. 1985. 益古演段. 李冶的數學成就 (Yigu yanduan: Li Ye de shuxue chengjiu [Yigu yanduan: Li Ye's Achievement in Mathematics>]). 中國數學史大系 (Zhongguo shuxue shi daxi [Collection on History of Chinese Mathematics]) 2(3):104–130.]). 中國數學史大系 (Zhongguo shuxue shi daxi [Collection on History of Chinese Mathematics]) 2(3):104–130.' href=https://scholar.google.com/scholar?q=Wenjun,+Wu.+1985.+益古演段.+李冶的數學成就+(Yigu+yanduan:+Li+Ye+de+shuxue+chengjiu+[Yigu+yanduan:+Li+Ye's+Achievement+in+Mathematics>]).+中國數學史大系+(Zhongguo+shuxue+shi+daxi+[Collection+on+History+of+Chinese+Mathematics])+2(3):104–130.>Google Scholar
Yibao, Xu. 1990. 對 “益古集”的復原與研究 (Dui “yi gu ji” de fuyuan yu yanjiu [Restoration and Research on the Collection Augmenting the Ancient [Knowledge]]). In 數學史研究文集 (Shuxueshi yanjiu wenji [Research Anthology on History of Mathematics]), edited by Li Di, 1: 149–165. 九章出版社 (Jiu zhang chubanshe [Nine Chapters Press>]).]).>Google Scholar
Jia-Ming, Ying. 201 1. “The Kujang sulhae 九章術解: Nam Pyŏng-Gil's Reinterpretation of the Mathematical Methods of the Jiuzhang suanshu.” Historia Mathematica 38:1–27.Google Scholar