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Suan Shu Shu Bamboo Texts to the Nine Chapters on the Art of Mathematics

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Fairbank Center for Chinese Studies Harvard University The Evolution of Mathematics in Ancient China. From the newly discovered 數Shu and 算數書 Suan shu shu Bamboo Texts to the Nine Chapters on the Art of Mathematics Joseph W. Dauben Department of History Herbert H. Lehman College and Ph.D. Program in History The Graduate Center City University of New York Fairbank Center for Chinese Studies Harvard University The Evolution of Mathematics in Ancient China. From the newly discovered 數Shu and 算數書 Suan shu shu Bamboo Texts to the Nine Chapters on the Art of Mathematics 1934: 楚帛書 Chu boshu The Chu Silk Manuscript State of Chu, Warring States period Excavated: 1934/1942 Zidanku, Changsha radiocarbon date: 305±30 BCE Purchased: 1965 Arthur M. Sackler 數術 “Numerals and Arts/Skills” If […] and the length of the lunar months becomes too long or too short, then they will not fit the proper degree and spring, summer, autumn, and winter will [not] be […] regular; the sun, moon, and planets will erratically overstep their paths. When (the months) are too long, too short, contrary, or chaotic, (the growth of) the grasses and trees have no regularity. This is [called] yao, “demonic” (influences or omens). When heaven and earth create calamities, the Heaven’s Cudgel (Tianpou) star creates (sweeping) destruction, sending (the destruction) down through all four regions (of the earth). Mountains collapse, springs gush forth geysers. This is called “contravention.” If you contravene the years (and) the months, then upon entering the seventh or eighth day of the month there will be fog, frost, and clouds of dust, and you will not be able to function according (to heaven’s plan) [Li and Cook 1999: 174] 1972–1974: 馬王堆 Mawangdui , Changsha, Hunan (186-168 BCE) Excavated: 1972 to 1974 Three Western Han dynasty tombs: Li Cang, chancellor to the prince of Changsha State and the Marquis of Dai; Li Cang’ wife, the Marquise of Dai; and their son. Tomb No. 1 Tomb No. 2 Tomb No.3 Wooden Tablet with Burial Date Length 30cm Unearthed from Tomb No.3 “On the first Wuchen day of Yisi, the second month of the twelfth year, the chamberlain in charge of funeral services, holding a memorial with funeral articles, presents a list of the delivery for inspection.” i.e. the twelfth year in the reign of Emperor Wendi of Han (168 BCE) Wooden Outer Coffin from Tomb No.1 Length: 672cm Width: 488cm Height: 280cm Coffin with Painted Design on Black Lacquer Coating Length 256cm width 118cm height 114cm Unearthed from Tomb No.1 Second Inner Coffin with Painted Design on Vermilion Lacquer Coating Length 230cm width 92cm height 89cm Innermost Coffin Decorated with Brocade Length:202cm Width:69cm Height:63cm Xin Zhui Marquise of Dai Scene of Banquet on the T-shaped Paintings on Silk Book of Changes (Zhou Yi ) Length 30cm width 21.5cm Unearthed from Tomb No.3 “Harmony of Yin and Yang” (He Yin Yang) Drawing of Daoyin, a Physical Exercise Chart Length 100cm width 50cm (Tomb No. 3) 44 Daoyin positions are illustrated, such as breathing exercises, limb stretching and gymnastics, and each position is labeled with its particular term and function. The exercise of Five Fowls was created by Hua Tuo, a famous doctor in the Eastern Han Dynasty and was based on Dao-yin. “Ten Questions” (十問 Shi Wen) Tomb No.3 Prescriptions for 52 Diseases (Wu Shi Er Bing Fang) Guard of Honor Length 219cm width 99cm Unearthed from Tomb No.3 A painting on silk was found on the western wall of the coffin chamber. At the top left: the tomb owner Divination by Five Stars (Wu Xing Zhan) 天文氣象雜占 Divination by Astrological and Meteorological Phenomena Excavated: 1973 Mawangdui Western Han (202 BCE – 9 CE) 29 comets (彗星 hui xing) recorded over a period of about 300 years. ca. 223 BCE 1975: 睡虎地秦 简 Shuihudi Qin jian Qin Bamboo Slips from Shuihudi Excavated: 1975 Tomb #11 at 城關睡虎地 Shuihudi, Yunmeng County, Hubei Province The tomb belonged to a Qin administrator. From Shuihudi: Bamboo strips written with documents of law; Painted lacquer spoon with wooden body in the shape of phoenix; kitchen utensil (bottom, height 13.3 cm); Flattened lacquer pot with colored painting of ox and horses: wine vessel or water vessel (in background), height 22.8 cm. 1983: 張家山漢簡 Zhangjiashan Han jian (Han Bamboo Slips from Zhangjiashan) 202–186 BCE Excavated: 1983 Tomb No. 247, Zhangjiashan Jiangling County, Hubei Province 算數書 Suan Shu Shu Wen Wu (2000) 算數書 Suan Shu Shu (A Book on Numbers and Computations) Peng Hao, ed. Beijing: Science Press, 2001. The first of the bamboo slips shown here on the right, with the title of the book clearly shown in the uppermost part of the right most slip: Suan Shu Shu. Suan Shu Shu, Peng Hao, ed. Beijing: Science Press, 2001. Title of the book: 算數書 Suan Shu Shu (A Book on Numbers and Computations) 筭 suan Suan Shu Shu, Peng Hao, ed. Beijing: Science Press, 2001. 1993: 郭店楚簡 Guodian chujian Guodian Chu Bambo Slips Excavated: 1993 Guodian, Jingmen, Hubei Warring States period (mid-4th –early 3rd-century BCE). Tu Weiming, Yenching Institute, Harvard University Guo Yi discussing the Tao Te Ching (1993) 1996: 走馬樓簡牘 Zoumalou jiandu Zoumalou Bamboo Documents Census count Wooden tablets unearthed from Ancient Well No. J22 Zoumalou, Changhsha, Hunan Wu Kingdom (222-280) of the Three Kingdoms (220-280) Excavated: 1996 2002: 里耶古城秦代 简牍 Liye gucheng Qindai jiandu Liye Ancient City Qin Dynasty Bamboo Documents Multiplication table Liye, Longshan County, Hunan “Four times eight is thirty-two; five times eight is forty…” Excavated: April, 2002 Qin Dynasty (221 BCE-206 BCE) Length 22cm width 4.5cm Unearthed at Liye city site, Longshan in 2002 2007: 嶽麓書院藏秦簡 Yuelu shuyuan cang qinjian Qin Slips Collected by the Yuelu Academy 嶽麓書院 Founded in 976 in the 9th year of the Song Dynasty during the reign of Emperor 開寶 Kaibao . Zhu Xi and . Zhang Shi . Emperor Song Taizu 宋太祖 Figure 1, p. 77 Figure 2, p. 78 Figure 3, p. 79 Figures 11 and 12, p. 83 Figure 13, p. 83 2008: 清华简 Qinghua jian Tsing-Hua Bamboo Slips Booking a Place in History: Rare ancient Chinese bamboo books dating back more than 2,000 years come home By ZAN JIFANG NO.48 NOV.27, 2008 Tsinghua Warring States Bamboo Strips Professor 李学勤 Li Xueqin 战国竹简重回故土 发布时间： 2008-10-30 13:21 来源：文摘报 近日，清华大学宣布，2100枚战国时期的竹简入藏清华，它 是由校友赵伟国从境外拍卖会买到后捐赠给清华的。 经过专家组鉴定，这批“清华简”属于战国中晚期，距 今大约2300~2400年左右，出土于古代的楚国境内。 “清华简”最长的有46厘米，最短的不到10厘米。“10 厘米就相当于我们现在的‘口袋书’了，这在 以前从未发现 过。” 战国竹简重回故土 发布时间： 2008-10-30 13:21 来源：文摘报 近日，清华大学宣布，2100枚战国时期的竹简入藏清华，它 是由校友赵伟国从境外拍卖会买到后捐赠给清华的。 经过专家组鉴定，这批“清华简”属于战国中晚期，距 今大约2300~2400年左右，出土于古代的楚国境内。 “清华简”最长的有46厘米，最短的不到10厘米。“10 厘米就相当于我们现在的‘口袋书’了，这在 以前从未发现 过。” Conservation of the 2388 Warring States Bamboo Strips from Chu at the Tsinghua University Center for Unearthed Documents Research and Protection The strips include invaluable texts such as “Bao Xun”-- the last words of King Wen of the Zhou Dynasty to his son, and some other important contents, including a multiplication table. Tsinghua University Center for Unearthed Documents Research and Protection Peking University Qin Bamboo Slips June 14, 2012 Sackler Museum of Art and Archaeology, Peking University Guo Han Feng Shuchun Wei Lisheng 北大秦简中的数学文献 韩巍（北京大学中国古代史研究中心） 北大秦简中的数学文献 Mathematical Documents among the Qin Bamboo Strips at Peking University 韩巍（北京大学中国古代史研究中心） Han Wei (Peking University Research Center for Ancient Chinese History) 日書 Ri shu Comparable illustration in black ink only found in the “Day Book” from Shuihudi tomb 11. slips 150r1-154r1 [KALINOWSKI 2008] 湖南大學 嶽麓書院 嶽麓書院藏秦簡《數》書釋文·簡注 計算田地產量或租稅的算題 嶽麓書院藏秦簡整理小组（执筆：肖 燦 ） 1. 說 明 2. 计算土地面积的算題 《数》书經整理得到： 一，有編號的簡共二百三十余枚。 谷物换算 殘片二十余片，無編號。 3. 二，有完整算题75例。（现存题设条件和问题或答案能依据简 文列出算法式的算题就视为完整算题）。 衰分算題 又有单独成題的“术”17例。 4. 又有记录有谷物体积重量比率、兑换比率的簡32枚， 未計入算題數目。 贏不足算題 湖南大學 又有記錄量制的簡3枚，未計入算題數目。 嶽麓書院 5. 凡 例 6. 少廣算题 一 釋文中異體字、假借字一般隨文注出，外加（ ）號。 二 簡文原有錯字，一般在釋文中隨注正字，外加 計算體積的算題 〈 〉號。原有脫字或衍文，釋文不加更動， 7. 竹簡殘斷，不能復原。 在注釋中說明。 三 簡文原有殘缺字，可據殘筆或文例補足的， 8. 勾股算题 外加〔〕 號。不能辨識的殘缺字，用 □ 表示， 每字一格。其他符號： 營軍之術（此算題暫時未歸類） ……字跡模糊，字數不能確定。 9. 10. 量制 湖南大學 嶽麓書院 嶽麓書院藏秦簡《數》書釋文·簡注 計算田地產量或租稅的算題 嶽麓書院藏秦簡整理小组（执筆：肖 燦 ） 1. 說 明 2. 计算土地面积的算題 《数》书經整理得到： 一，有編號的簡共二百三十余枚。 谷物换算 殘片二十余片，無編號。 3. 二，有完整算题75例。（现存题设条件和问题或答案能依据简 文列出算法式的算题就视为完整算题）。 衰分算題 又有单独成題的“术”17例。 4. 又有记录有谷物体积重量比率、兑换比率的簡32枚， 未計入算題數目。 贏不足算題 湖南大學 又有記錄量制的簡3枚，未計入算題數目。 嶽麓書院 5. 凡 例 6. 少廣算题 一 釋文中異體字、假借字一般隨文注出，外加（ ）號。 二 簡文原有錯字，一般在釋文中隨注正字，外加 計算體積的算題 〈 〉號。原有脫字或衍文，釋文不加更動， 7. 竹簡殘斷，不能復原。 在注釋中說明。 三 簡文原有殘缺字，可據殘筆或文例補足的， 8. 勾股算题 外加〔〕 號。不能辨識的殘缺字，用 □ 表示， 每字一格。其他符號： 營軍之術（此算題暫時未歸類） ……字跡模糊，字數不能確定。 9. 10. 量制 湖南大學 嶽麓書院 嶽麓書院藏秦簡《數》書釋文·簡注 計算田地產量或租稅的算題 嶽麓書院藏秦簡整理小组（执筆：肖 燦 ） 1. 說 明 2. 计算土地面积的算題 《数》书經整理得到： 一，有編號的簡共二百三十余枚。 谷物换算 殘片二十余片，無編號。 3. 二，有完整算题75例。（现存题设条件和问题或答案能依据简 文列出算法式的算题就视为完整算题）。 衰分算題 又有单独成題的“术”17例。 4. 又有记录有谷物体积重量比率、兑换比率的簡32枚， 未計入算題數目。 贏不足算題 湖南大學 又有記錄量制的簡3枚，未計入算題數目。 嶽麓書院 5. 凡 例 6. 少廣算题 一 釋文中異體字、假借字一般隨文注出，外加（ ）號。 二 簡文原有錯字，一般在釋文中隨注正字，外加 計算體積的算題 〈 〉號。原有脫字或衍文，釋文不加更動， 7. 竹簡殘斷，不能復原。 在注釋中說明。 三 簡文原有殘缺字，可據殘筆或文例補足的， 8. Gou-Gu Problems 外加〔〕 號。不能辨識的殘缺字，用 □ 表示， 每字一格。其他符號： 營軍之術（此算題暫時未歸類） ……字跡模糊，字數不能確定。 9. 10. 量制 □有圓材薶（埋）地，不智（知）小大，斲之，入材一寸而 得平一尺，問材周大幾可（何）。即曰，半平得五寸，令相 乘也，以深 [0304] 一寸为法，如法得一寸，有（又）以深益之，即材徑也。 [0457] □有圓材薶（埋）地，不智（知）小大，斲之，入材一寸而 得平一尺，問材周大幾可（何）。即曰，半平得五寸，令相 乘也，以深 [0304] 一寸为法，如法得一寸，有（又）以深益之，即材徑也。 [0457] Suppose there is a circular [piece of] wood buried in the ground, whose size is unknown, but cutting to a depth of 1 cun gives a chord of 1 chi, it is asked how great is the circumference of the [circular piece of] wood? [The method] says: half the chord is 5 cun, multiply it by itself and using the depth of 1 cun as the divisor, dividing gives the result in cun, again adding the depth [of the cut] gives the diameter of the wood.
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    MONUMENTA SERICA Journal of Oriental Studies Vol. LVI, 2008 Editor-in-Chief: ROMAN MALEK, S.V.D. Members of the Monumenta Serica Institute (all S.V.D.): JACQUES KUEPERS – LEO LEEB – ROMAN MALEK – WILHELM K. MÜLLER – ARNOLD SPRENGER – ZBIGNIEW WESOŁOWSKI Advisors: NOEL BARNARD (Canberra) – J. CHIAO WEI (Trier) – HERBERT FRANKE (München) – VINCENT GOOSSAERT (Paris) – NICOLAS KOSS, O.S.B. (Taibei) – SUSAN NAQUIN (Princeton) – REN DAYUAN (Beijing) – HELWIG SCHMIDT-GLINTZER (Wolfenbüttel) – NICOLAS STANDAERT, S.J. (Leuven) Monumenta Serica Institute – Sankt Augustin 2008 Editorial Office Monumenta Serica Institute, Arnold-Janssen-Str. 20 53757 Sankt Augustin, Germany Tel.: (+49) (0) 2241 237 431 • Fax: (+49) (0) 2241 237 486 E-mail: [email protected] • http://www.monumenta-serica.de Redactors: BARBARA HOSTER, DIRK KUHLMANN, ROMAN MALEK Manuscripts of articles, reviews (typewritten and on floppy-disks, see Information for Authors), exchange copies, and subscription orders should be sent to the Editorial Office __________ Taipei Office Monumenta Serica Sinological Research Center 天主教輔仁大學學術研究院 華裔學志漢學研究中心 Fu Jen Catholic University, Hsinchuang 24205, Taipei Hsien E-mail: [email protected] • http://www.mssrc.fju.edu.tw Director: ZBIGNIEW WESOŁOWSKI, S.V.D. ISSN 0254-9948 Monumenta Serica: Journal of Oriental Studies © 2008. All rights reserved by Monumenta Serica Institute, Arnold-Janssen-Str. 20, 53757 Sankt Augustin, Germany Set by the Authors and the Editorial Office, Monumenta Serica Institute. Technical assistance: JOZEF BIŠTUŤ, S.V.D. Printed by DRUCKEREI FRANZ SCHMITT, Siegburg Distribution – Orders – Subscriptions: STEYLER VERLAG, P.O. Box 2460, 41311 Nettetal, Germany Fax: (+49) (0) 2157 120 222; E-mail: [email protected] www.monumenta-serica.de EBSCO Subscription Services, Standing Order Department P.O.
  • Divination and Autonomy:New Perspectives From

    Divination and Autonomy:New Perspectives From

    jocp_1623 124..141 lisa raphals DIVINATION AND AUTONOMY: NEW PERSPECTIVES FROM EXCAVATED TEXTS History is written by the victors. Much of the philosophical discussion of excavated texts has centered on the Guodian and Shanghai Museum texts, which augment or comment on the texts of the received tradition. This perspective omits the counterparts and com- petitors of the Warring States philosophers: the technical experts. The technical expertise traditions (medicine, the mantic arts, and astrocalendrics) were the counterparts and competitors of the phi- losophers, and far outnumber them in the perhaps narrow context of tomb texts. Both the received tradition and excavated texts attest to contact and competition between mantic experts and the “schoolmen” asso- ciated with Masters texts. Both livelihoods relied on literacy and specialist expertise. Both claimed access to divine knowledge and authority. Their competition thus involved career choice, patronage, students, and the status of modes of knowledge. In addition, it is now widely agreed that the bases of cosmological speculation first appeared in the ideas and methods of Warring States technical specialists, whose terms and techniques were later incorpo- rated into the yin-yang and Five-phase theories of Han cosmol- ogy. This view was first argued by Angus Graham some twenty years ago, and third-century excavated texts on these technical arts have reinforced it by supplementing the sparser record in the received tradition.1 In particular, technical experts were responsible for several developments that contributed to systematic thought and cosmology. These include (i) interest in symmetry, already visible in the oracle bone inscriptions; (ii) the articulation of a yin-yang polarity, abstracted as patterns of change, represented by numbers.
  • February-March 2021

    February-March 2021

    February-March 2021 February-March Vol. 872 Revival of Traditional Opera in the New Era 10 国内零售价： 元 USA $5.10 UK ₤3.20 Australia $9.10 Europe €5.20 Canada $7.80 Turkey TL.10.00 2-903 CN11-1429/Z 邮发代号 Express February-March 2O21 An Odyssey between Past and Present The Observation of Chinese Calligraphy and Sculpture in Real Life /10 Administrative Agency: 主管：中国外文出版发行事业局 China International Publishing Group （中国国际出版集团） Publisher: China Pictorial Publications 主办: 社 Address: 社址: 33 Chegongzhuang Xilu 北京市海淀区车公庄西路33号 Haidian, Beijing 100048 邮编: 100048 Email: [email protected] : [email protected] 邮箱 Editorial Board: 编委会: Li Xia, He Peng 李 霞、贺 鹏 Bao Linfu, Yu Jia 鲍林富、于 佳 Editor-in-Chief: Li Xia 总编辑: 李 霞 Editorial Directors: Qiao Zhenqi, Yin Xing 编辑部主任: 乔振祺、殷 星 English Editor: Liu Haile 英文定稿: 刘海乐 Editorial Consultants: 语言顾问: Scott Huntsman, Nathan Bennett 苏 格、白浩天 Operations Supervisor: Xu Shuyuan 业务主管：许舒园 Editors and Translators: 编辑、翻译: Bian Xiuhong, Gong Haiying 卞秀红、龚海莹 Hu Zhoumeng, Li Yiqi 胡周萌、李艺琦 Li Zhuoxi, Wang Shuya 李卓希、王舒雅 Zhao Yue, Zhou Xin 赵 月、周 昕 Social Media Operation Specialist: 海外社交媒体运营专责: 22 Cecile Zehnacker 塞西尔·泽纳凯 Graphic Designer: Stanisa Vebe Shineta 图表设计: 林美珠 Operation: Zhang Yingjie 编务: 张英杰 Design: Alinea Productions 设计: 利雅法盛 Features Director of Brand Center: Wang Shuo 品牌中心执行主任: 王烁 Chinese Opera: Revival of Traditional Telephone: 86-10-68717725 电话: +86-10-68717725 Art in the New Era /14 Remittance to: 邮购收款人： Publishing and Distribution Department, Mao Weitao: Artistic Bravery /20 人民画报社出版 China Pictorial 发行部 Zhang Huoding: Chasing Legal Adviser: Yue Cheng 法律顾问: 岳 成 the Dream of Peking Opera /26 Printing: Toppan Leefung Changcheng 印刷:北京利丰雅高长城 Printing (Beijing) Co., Ltd.
  • The Syntax of Chinese

    The Syntax of Chinese

    This page intentionally left blank The Syntax of Chinese The past quarter of a century has seen a surge in Chinese syntactic research that has produced a sizeable literature on the analysis of almost every construction in Mandarin Chinese. This guide to Chinese syntax analyzes the majority of constructions in Chinese that have featured in theoretical linguistics in the past twenty-five years, using the authors’ own analyses as well as existing or potential alternative treatments. A broad variety of topics are covered, including categories, argument structure, passives, and anaphora. The discussion of each topic sums up the key research results and provides new points of departure for further research. This book will be invaluable both to students wanting to know more about the grammar of Chinese, and to graduate students and theoretical linguists interested in the universal principles that underlie human languages. james huang is a Professor in the Department of Linguistics at Harvard University. audrey li is a Professor in the Department of Linguistics and Department of East Asian Languages and Cultures at the University of Southern California. yafei li is a Professor in the Department of Linguistics at the University of Wisconsin–Madison. cambridge syntax guides General editors: P. Austin, B. Comrie, J. Bresnan, D. Lightfoot, I. Roberts, N. V. Smith Responding to the increasing interest in comparative syntax, the goal of the Cambridge Syntax Guides is to make available to all linguists major findings, both descriptive and theoretical, which have emerged from the study of particular languages. The series is not committed to working in any particular framework, but rather seeks to make language-specific research available to theoreticians and practitioners of all persuasions.
  • A Study of the Warring States Graphs: Structural Discrepancies Between the Chu Area and Qin State

    A Study of the Warring States Graphs: Structural Discrepancies Between the Chu Area and Qin State

    A STUDY OF THE WARRING STATES GRAPHS: STRUCTURAL DISCREPANCIES BETWEEN THE CHU AREA AND QIN STATE by YUKIKO NAGAKURA B.A., University of Alberta, 1995 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (Department of Asian Studies) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 2000 © Yukiko Nagakura, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver, Canada Date /OsJ. J.0 ^OnS) DE-6 (2/88) Abstract Chinese graphical forms of the Warring States period have traditionally been characterized as varying by region. This thesis investigates discrepancies observable in the scripts of the Warring States Chu and Qin regions, as extant in inscriptions and epigraphy on a variety of media. With the postulate that the Warring States graphical forms were part of a continuous evolution of guwen from the Shang period to the Script Reform that followed the Qin Unification, these discrepancies are treated as the accumulations of a common diachronic process. To define this process, the two-step formation of semanto-phonetic graphs is adopted as jiajie augmented with semantic determiners, and evolutionary modifications tending to induce graphical divergence are classified for simple and multi-element graphs, based on the work of Boodberg, Boltz, Chen, Qiu, He, Gao and others.