The Chinese Roots of Linear Algebra

Appendix B: Chinese Mathematical Treatises

Appendix B Chinese Mathematical Treatises Bibliographies of Chinese Mathematical Treatises This appendix represents a preliminary attempt to assemble a comprehensive bibliography of all of the Chinese mathematical treatises that have been recorded in Chinese bibliographies throughout history. At present, there are no comprehensive bibliographies of Chinese mathematical treatises. In fact, the standard bibliography for Chinese mathematical treatises , Complete Record of the Four Treasuries, Mathematics Volume (Sibu zong lu suanfa bian  ), edited by Ding Fubao  and Zhou Yunqing  (Shanghai: Shang wu yin shu guan  , 1957), is very incomplete and out of date, listing only a fraction of the mathematical treatises that are recorded in Chinese bibliographies. Similarly, none of the recent Western historical studies of Chinese mathematics provide an adequate bibliography of Chinese mathematical treatises; in fact, bibliographies are often limited to several of the more important texts. This appendix is divided into the following sections: 1. The first presents a comprehensive list of Chinese bibliographies that record titles of Chinese mathematical treatises. These bibliographies are ordered by the dynasty of the treatises recorded, earliest first. 2. The second section, given in the form of a table, presents a comprehensive list of all titles of Chinese mathematical treatises recorded in all available Chinese bibliographic treatises. Most of these treatises are no longer extant. In some cases, different treatises may have the same title; similarly, one treatise may be given different titles. In addition, the titles of Chinese treatises often included the number of chapters (juan). Differences in the recorded numbers of chapters for a title may indicate that portions of the text were lost, or that various titles were incorporated as one title. Therefore, each different title, as well as each variation in the number of chapters, is listed in this table as a separate entry. In order that information on titles can be compared, the table is arranged in columns, each column representing one of the most 213 214 B Chinese Mathematical Treatises important bibliographies for Chinese mathematical treatises of the late imperial period. From this table, then, it can easily be seen whether a title is listed in several bibliographies. 3. The final section, “Notes,” then records each listing exactly as found in each bibliography, numbered as a reference to the table. This allows me to record any further information found in the bibliography, for example whether a treatise is listed with other treatises, whether an author or date is provided, or whether a notation states that the treatise is corrupt or incomplete. In cases where a treatise is known to be extant, I have included that fact in these notes. Collections and Abbreviations BJTCS Baojing tang congshu . BSJJZ Ba shi jingji zhi / . CSJCCB Congshu jicheng chubian  . ESWSBB Ershi wu shi bu bian &+/ . GGTSKS Guangu tang suo kan shu . GGTSMCK Guangu tang shumu congkan . GXJBCS Guoxue jiben congshu  . HSYWZ Han shu yiwen zhi, she bu    . JDJL Jing dian ji lin . JSGJBS Jishan guan ji bu shu  . KGSSSFCS Kuai ge shi shi shan fang cong shu   . LJYYWZ Liao Jin Yuan yiwen zhi   . MDSMTBCK Ming dai shumu ti ba congkan 0 . MSYWZ Ming shi yiwen zhi, bubian, fubian /   . PXLCS Puxue lu congshu (. QMACS Qianmo an congshu qi juan  . SBBY Sibu bei yao  . SBCK Sibu cong kan  . SKQS Wenyuan ge Siku quanshu   . SLCSJB Song lin congshu jia bian . SSJJZ Sui shu jingji zhi, bu . SSYWZ Song shi yiwen zhi, bu fu bian / . SXCS Shi xue cong shu /. TSJJYWHZ Tang shu jingji yi wen he zhi, bu lu  . WJTCS Wenjing tang congshu  . WJTSSMCK Wujin Tao shi shumu congkan . XYXSQS Xi yuan xiansheng quan shu  . YHSFJYS Yuhanshan fang ji yi shu, shi bian mulu lei  / . YHSFJYSXB Yuhanshan fang ji yi shu xu bian, shi bian mulu lei   / . Bibliographies of Chinese Mathematical Treatises 215 YJZCSEJ Yujian zhai congshu er ji &. YYTCS Yueya tang congshu . ZBZZCS Zhibuzu zhai congshu  . ZGLDSMCK Zhongguo lidai shumu congkan  0 . ZGLDYWZ Zhongguo lidai yiwen zhi  0 . ZXCZZ Zhou xu chi za zhu . Bibliographies of the Earlier Han (206 B.C.E.–9 C.E.) Ban Gu  and Yan Shigu . Qian Han shu yiwen zhi, yi juan  . In BSJJZ, CSJCCB. Liu Guangfen . Qian Han shu yiwen zhi zhu, yi juan   . In ESWSBB. Liu Xiang and Hong Yixuan . Bie lu yi juan  . In WJTCS, JDJL. . Qi lue yi juan  . In WJTCS, JDJL. Liu Xiang and Ma Guohan . Qi lue bie lu yi juan  . In YHSFJYS . Liu Xiang and Tao Junxuan . Bie lu yi juan  . In JSGJBS. . Qi lue bie lu er...