A formal system of the Gougu method 573
Gu Yingxiang ( 1553 ) Gougu Suanshu ( Mathematical Procedures
on Gougu) , 1553 edn.
Guo Shuchun ( 1985 ) ‘ Jiuzhang suanshu “Gougu” zhang de jiaokan he Liu
Hui gougu lilun xitong chutan
’ (Editorial research on the Gougu chapter in the Nine Chapters and
the system of Liu Hui’s gougu theory). Ziran kexue shi yanjiu 4 : 295 –304.
( 1987 ) ‘ Shilun Liu Hui de shuxue lilun tixi ’ (A
study on Liu Hui’s System of Mathematical Th eory). Ziran bianzheng fa
tongxu 9 : 42 –48.
( 1988 ) ‘ Jia Xian Huangdi Jiuzhang Suanjing Xicao chutan
’, Ziran kexue shi yanjiu 7 : 328 –334.
( 1992 ) Gudai shijie shuxue taidou Liu Hui (Liu Hui: A
Leading Figure of Ancient World Mathematics). Jinan.
Li Jimin ( 1993 ) ‘ “Shang Gao dingli” bianzheng “ ” ’ (Textual
research on “Shang Gao” theorem). Ziran kexueshi yanjiu 12 : 29 –41.
Li Rui ( 1806 ) Gougu Suanshu Xicao ( Detailed Outline of
Mathematical Procedures of Gougu ), in Li shi Yishu ( Posthumous
writings of Mr. Li ), ed. Ding Quzhong (1875).
Li Zhaohua ( 1993 ) ‘ Wang Lai Dijian Shuli Sanliang Suanjing Lüelun
’ (A short discussion on Wang Lai’s Dijian Shuli and
Sanliang Suanjing ) , in Tantian Sanyou , ed. Horng WannSheng.
Taibei : 227 –37.
Liu Dun ( 1993 ) ‘ Gougu suanshu xicao tiyao ’
(Introduction to the Detailed Outline of Mathematical Procedures for the
Right-Angled Triangle ) , in Zhongguo kexue jishu dianji tonghui, shuxue juan ,
ed. Guo Shuchun , vol. v. Zhengzhou : 67 –9.
Qian Baocong ( 1982 ) Zhongguo shuxue shi (History of
Mathematics in China). Beijing.
Tian Miao ( 1999 ) ‘ Jiegenfang , Tianyuan , and Daishu : algebra in Qing China ’,
Historia Scientiarum 9 (1): 101 –119.
( 2005 ) Z hongguo Shuxue de Xihua Licheng (Th e
Westernization of Mathematics in China). Jinan.
(forthcoming) ‘Rejection and adoption of Western mathematics: Chinese
mathematician’s study on the Gougu Procedure from the beginning of 17th to
the beginning of 18th century’.
Wang Lai ( 1799 ?) Dijian Shuli ( Th e Mathematical Th eory of
Dijian ), in Hengzhai Suanxue , book 4, Jiashu tang edn.
W u W e n j u n ( 1978 ) ‘ Churu xiangbu yuanli ’ ( Th e Out–in
Principle ), in Zhongguo gudai keji chengjiu (Scientifi c and
Technological Achievements in Ancient China). Beijing : 80 –100.
Xu Guangqi ( 1609 ) Gougu Yi ( Th e Principle of Gougu ), Tianxue
chuhan edn.
Yang Hui ( 1261 ) Xiangjie Jiuzhang Suanfa ( A Detailed
Explanation of the Nine Chapters of Mathematical Procedures ), Yijia tang edn.