Browse > Article
http://dx.doi.org/10.14477/jhm.2016.29.6.325

Jin-Yuan Mathematics and Quanzhen Taoism  

Guo, Shuchun (Institute for the History of Natural Sciences, Chinese Academy of Sciences)
Publication Information
Journal for History of Mathematics / v.29, no.6, 2016 , pp. 325-333 More about this Journal
Abstract
Chinese Mathematics during the period of Jin (1115-1234) and Yuan (1271-1368) is an integral part of the high achievements of traditional mathematics during the Song (962-1279) and Yuan dynasties, which is another peak in the history of Chinese mathematics, following the footsteps of the high accomplishments during the Warring States period (475-221 BCE), the Western Han (206 BCE-24 ADE), Three Kingdoms (220-280 AD), Jin dynasty (265-420 AD), and Southern and Northern Dynasties (420-589 AD). During the Jin-Yuan period, Quanzhen Taoism was a dominating branch in Taoism. It offered certain political protection and religious comforts to many during troubled times; it also provided a relatively stable environment for intellectual development. Li Ye (1192-1279), Zhu Shijie (fl. late 13th C to early 14th C) and Zhao Youqin (fl. late 13th C to early 14th C), the major actors and contributors to the Jin-Yuan Mathematics achievements, were either heavily influenced by the philosophy of Quanzhen Taoism, or being its followers. In certain Taoist Classics, Li Ye read the records of the relations of a circle and nine right triangles which has been known as Dongyuan jiurong 洞渊九容 of Quanzhen Taoism. These relations made significant contributions in the study of the circles inscribed in a right triangle, the reasoning of which directly led to the birth of the Method of Celestial Elements (Tianyuan shu 天元术), which further developed into the Method of Two Elements (Eryuan shu ⼆元术), the Method of Three Elements (Sanyuan shu 三元术) and the Method of Four Elements (Siyuan shu 四元术).
Keywords
Jin-Yuan Mathematics; Quanzhendao; Li Ye; Zhu Shijie; Zhao Youqin; Dongyuanjiurong; theory of inscribed circles of right triangles; tianyuanshu; eryuanshu; sanyuanshu; siyuanshu;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Guo Shuchun, Jiuzhang Suanshu Huijiao (A critical edition of the Jiuzhang Suanshu), Shenyang: Liaoning jiaoyu chubanshe, 1990. Revised, 2004. Also printed in Taipei by Jiuzhang chubanshe. 九章算术. 郭书春汇校. 沈阳: 辽宁教育出版社.1990. 汇校 <九章筭术> 增补版. 沈阳: 辽宁教育出版社、台北: 九章出版社.2004.
2 Li Ye, Ceyuan Haijing, Vol. 4, Guo Shuchun (Ed.), Zhongguo kexue jishu dianji tong hui, Shuxue juan, Book 1. Zhengzhou: Zhengzhou Henan jiaoyu chubanshe. 1993. [元] 李冶. 测圆海镜, 第4 卷. 郭书春主编. 中国科学技术典籍通汇.数学卷, 第1 册. 郑州: 郑州河南教育出版社.1993.
3 Li Shanlan, Jiurong Tubiao, Gujin Suanxue Congshu, Book 48, 1898. [清] 李善兰. 九容图表. 古今算学丛书, 第48 册.1898.
4 Qian Baocong, About problems of Ceyuan Haijing, Song yuan shuxueshi lunwenji, Beijing, Kesue chubanshe, 1965. In Li Yan, Qian Baocong Kexueshi Quanji, vol. 9, edited by Guo Shuchun, Liu Dun. Shenyang: Liaoning jiaoyu chubanshe, 1998, 703-706 钱宝琮. 有关 <测圆海镜> 的几个问题. 钱宝琮等. 宋元数学史论文集. 北京: 科学出版社.1965: 271-274. 郭书春、刘钝等主编. 李俨钱宝琮科学史全集, 第9 卷. 沈阳: 辽宁教育出版社.1998: 703-706.
5 Yang Hui, Xiangjie Jiuzhang Suanfa, Yijiatang Congshu Ben. Guo Shuchun (ed.) Zhongguo Kexue Jishushi Shuxue Juan, Book 1. Zhengzhou: Henan jiaoyu chubanshe, 1993, p. 974. [南宋] 杨辉. 详解九章算法. 宜稼堂丛书本. 郭书春主编. 中国科学技术史.数学卷, 第一册. 郑州: 河南教育出版社.1993: 974.
6 Li Ye, Jingzhai Gujin Tou, Beijing, Zhonghua shuju, 1995, p. 186-187. 李冶. 敬斋古今黈. 北京: 中华书局.1995:186-187.
7 Guo Shuchun, Li Ye, Zhongguo kexue jishushi.Renwu juan, Beijing, Kesue chubanshe, 1998. 郭书春. 李冶. 中国科学技术史.人物卷. 北京: 科学出版社.1998.
8 Horng Wansheng, Quanzhenjiao and jin yuan mathematics-Li Ye as an example. Ed. Wang Qiugui, Proceedings of International Symposium on Jin Yong's Novels, Taipei, Yuan liú chuban shiye gufen youxian gongsi, 1999, 67-83. 洪万生. 全真教与金元数学-以李冶 (1192-1279) 为例. 王秋桂主编. 金庸小说国际学术研讨会论文集. 台北: 远流出版事业股份有限公司.1999: 67-83.
9 Guo Shuchun, Li Ye's Achievement in Mathematics and Taoism. 郭书春. 李冶的数学造诣与道家思想.
10 Su Tianjue, Guochao mingchen shilue. [元] 苏天爵. 国朝名臣事略.
11 Tao Hongjing, Zhengao, Vol. 18, Daozang, Ming Wanli Edition, Photocopy of Shanghai Hanfenlou, 1923-1926. [晋] 陶弘景. 真诰, 卷十八.道藏.明万历刊本.上海函芬楼影印.1923-1926.
12 Guoqingfan, ZhuangziJishi, Book 4, Zhonghua Shuju, 1961, 771-772. 郭庆藩. 庄子集释, 第4 册. 北京: 中华书局.1961:771-772.
13 Panshanqiyun Wang Zhenren Yulu, Daozang, Ming Wanli Edition, Photocopy of Shanghai Hanfenlou, 1923-1926. 盘山栖云王真人语录, 道藏. 明万历刊本. 上海函芬楼影印.1923-1926.
14 Gai Jianmin, Daojiao Kexue Sixiang Fafan, Beijing, Shehui Kexue Wenxian Chubanshe, 2005. 盖建民. 道教科学思想发凡. 北京: 社会科学文献出版社.2005.
15 Qian Baocong, Zhongguo Shuxueshi(History of mathematics in China), Beijing, Kexue Chubanshe, 1964, p. 175. Also Guo Shuchun, Liu Dun (Eds.) Li Yan, Qian Baocong Kexueshi Quanji, Book 5, Shenyang: Liaoning jiaoyu chubanshe, 1998, p. 194. 钱宝琮主编. 中 国数学史. 北京: 科学出版社.1964:175. 又: 郭书春, 刘钝主编 : <李俨钱宝琮科学史全集, 第5 册. 沈阳: 辽宁教育出版社.1998:194.
16 Yi Ye, Fanshuo, Quoted from [6]. [元] 李冶. 泛说. 转引自[6].
17 Yi Ye, Yigu Yanduan, Ed. by Guo Shuchun, Zhongguo Kexue Jishu Shi(History of Science and Technology in China), Mathematics, Book 1, Zhengzhou: Henan jiaoyu chubanshe, 1993, 873-941. [元] 李冶. 益古演段. 郭书春主编. 中国科学技术史.数学卷, 第1 册. 郑州: 河南教育出版社.1993: 873-941.
18 Zhu Shijie, Suanxue Qimeng, Ed. by Guo Shuchun, Zhongguo Kexue Jishu Shi(History of Science and Technology in China), Mathematics, Book 1, Zhengzhou: Henan jiaoyu chubanshe, 1993, 1123-1200. [元] 朱世杰. 算学启蒙. 郭书春主编. 中国科学技术史.数学卷, 第1 册. 郑州: 河南教育出版社.1993:1123-1200.
19 Zhu Shijie, Siyuan Yujian, Ed. by Guo Shuchun, Zhongguo Kexue Jishu Shi(History of Science and Technology in China), Mathematics, Book 1, Zhengzhou: Henan jiaoyu chubanshe, 1993, 1205-1280. Also, Siyuan Yujian in Chinese and English, Modern translation by Guo Shuchun, Shenyang: Liaoning jiaoyu chubanshe, 2005. [元] 朱世杰 : 四元玉鉴. 郭书春主编. 中国科学技术史.数学卷, 第1 册. 郑州: 河南教育出版社.1993:1205-1280. 又, 中英文对照本 <四元玉鉴>. 郭书春今译, 陈在新英译. 沈阳: 辽宁教育出版社.2005.
20 Zu Yi, Postface of Siyuan Yujian, See [18] 祖颐. <四元玉鉴> 后序. 见[18].
21 Quoted from [14]. 转引自[14].
22 Li Sicong, Dong Yuanji, Daozang, Ming Wanli Edition, Photocopy of Shanghai Hanfenlou, 1923-1926. [北宋] 李思聪. 洞渊集. 道藏. 明万历刊本. 上海函芬楼影印.1923-1926.
23 Li Di, Li Ye, A Mathematician of China in 13th century, Shuxue Tongbao, 1979, 3. 李迪. 十三世纪我国数学家李冶. 数学通报.1979, 3.
24 Guo Shuchun, Liu Hui, the Master of Mathematics in Ancient Times, Jinan: Shandong Kexue Jishu Chubanshe, 1992, 222-226. Revised and printed in traditional chinese, Taipei, Mingwen Shuju, 1995, 222-226. 郭书春. 古代世界数学泰斗刘徽. 济南: 山东科学技术出版社.1992:222-226. 繁体字修订本. 台北: 明文书局.1995:222-226.
25 Li Pengfei, Sanyuan Yanshòu Canzan Shu, 1291, Daozang, Ming Wanli Edition, Photocopy of Shanghai Hanfenlou, 1923-1926. 李鹏飞. 三元延寿参赞书自序.1291. 道藏. 明万历刊本. 上海函芬楼影印.1923-1926.
26 Huangdi Yinfujing, Daozang, Ming Wanli Edition, Photocopy of Shanghai Hanfenlou, 1923-1926. 黄帝阴符经, 道藏. 明万历刊本. 上海函芬楼影印.1923-1926.
27 Zhao Youqin, Gexiang Xinshu, Siku Quanshu Wenyuange Printing, Taipei, Photocopy of Shangwuyinshuguan, 1986. [元] 赵友钦. 革象新书. 四库全书文渊阁本. 台北: 商务印书馆影印.1986.