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Geometrical Figures and Generality in Ancient China and Beyond: Liu Hui and Zhao Shuang, Plato and Thabit ibn Qurra – CORRIGENDUM

Published online by Cambridge University Press:  09 November 2009

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Type
Corrigendum
Information
Science in Context , Volume 22 , Issue 4 , December 2009 , pp. 647 - 650
Copyright
Copyright © Cambridge University Press 2009

In the article (Chemla 2005), I provided a critical edition and translation of two texts. One text was a passage from The Gnomon of the Zhou, a book dealing with mathematical astronomy and probably completed in the form in which we know it around the beginning of the Common Era (translation on pp. 127–135). The other text was a passage from The Nine Chapters on Mathematical Procedures, a book that in my view took its final form in the first century C.E. (translation on pp. 146–151). I edited and translated both texts along with the third-century commentaries with which they were handed down through written transmission. In Chinese sources of the past, the main text was distinguished from its commentaries by the size of the characters: main texts in larger characters, commentaries in smaller characters. I reproduced this contrast by using the same feature, using larger characters for the main text and smaller characters for the commentaries. Unfortunately, the contrast was modified in the printed version of the Chinese texts in Appendixes A and B (pp. 164–166) of my critical edition. I give the two texts again, together with the footnotes and the references, this time displaying the characters with adequate contrast.

NB: The sign “○” is used in Chinese transcriptions as the equivalent of a period, or full stop, in English; the inverted comma is used conventionally in Chinese transcriptions in connection with enumerations/lists.

Appendix B

Footnote 9

Footnotes

1 I skip here a section of the commentary that is not essential in the context of this corrigendum.

2 This is the text as given by the three ancient editions on the basis of which The Gnomon of the Zhou can be edited: the Southern Song edition, printed in 1213 by Bao Huanzhi ), the edition included in the Grand encyclopedia of the reign period Yongle (Li Jimin 1993a, 37, n. 1), and the edition printed by Hu Zhenheng in the Bice huihan collection in 1603 (Guo Shuchun and Liu Dun 2001, 68, n. 9, 10). The edition of the Collection Wuyingdian juzhen ban , edited by Dai Zhen on the basis of the Hu Zhenheng edition, which he modified with reference to the Yongle dadian (see the Tiyao added to the publication), gives the text as: ,, a suggestion adopted by Qian Baocong in his edition. Li Jimin 1993a, 37, n. 1, considers the former to conform to the original. Guo Shuchun and Liu Dun 2001, 68, n. 9, also holds this view. However, these publications are punctuated in different ways. I follow here Li Jimin. Guo Shuchun and Liu Dun 2001, 33, use the following punctuation: .

3 This is the text as given by the Southern Song edition, the edition printed by Hu Zhenheng, as well as the edition of the Collection Wuyingdian juzhen ban. Li Jimin (1993a, 37, n. 1) suggests that Dai Zhen modified the text of The Gnomon of the Zhou to make it conform to the quotation made by the commentator here. Li Jimin solves the problem of the divergence between the main text and that quoted by the commentator, by punctuating the commentary in a new way. I follow him on this point too. Guo Shuchun and Liu Dun (2001, 68, n. 11) mention the divergence but keep the text as it is found in all the ancient editions in both places and adopt here the following punctuation (Guo Shuchun and Liu Dun 2001, 33): .

4 This is the text as given by the Southern Song edition, the edition included in the Grand encyclopedia of the reign period Yongle (Li Jimin 1993a, 37, n. 3) and the edition printed by Hu Zhenheng (Guo Shuchun and Liu Dun 2001, 68, n. 12). The edition of the Collection Wuyingdian juzhen ban adds one character: . Qian Baocong (1963, 16, n. 2) adopts this suggestion. Li Jimin (1993a, 37, n. 3) considers that the ancient editions conform to the original text. Guo Shuchun and Liu Dun (2001, 68, n. 12) also hold this view. However, these publications are punctuated in different ways. I follow here Li Jimin. Guo Shuchun and Liu Dun (2001, 33) use the following punctuation: , .

5 This is the text as given by the Southern Song edition, the edition included in the Grand encyclopedia of the reign period Yongle and the edition printed by Hu Zhenheng (Guo Shuchun and Liu Dun 2001, 68, n. 10). The edition of the Collection Wuyingdian juzhen ban modifies it into: , a point of view adopted by Qian Baocong 1963, 16, n. 3. Li Jimin (1993a, 37, n. 4) considers that the ancient editions conform to the original text. Guo Shuchun and Liu Dun (2001, 68, n. 12) also hold this view.

6 This is the text as given by Dai Zhen's edition of the Collection Wuyingdian juzhen ban and adopted by Qian Baocong 1963, 16, n. 4. The Southern Song edition and the edition printed by Hu Zhenheng have for (Guo Shuchun and Liu Dun 2001, 68, n. 13). Li Jimin (1993a, 37, n. 5), Guo Shuchun and Liu Dun (2001, 34), and Ch'en Liang-ts'o (1993a, 7, n. 8) all adopt the latter in their editions. However, Guo Shuchun and Liu Dun 2001, 68, n. 12, give the former as a possible option. This is the option I consider best.

7 This is the text given by the Southern Song edition and the edition printed by Hu Zhenheng. The latter character wei is not found in Dai Zhen's edition of the Collection Wuyingdian juzhen ban. Qian Baocong (1963, 17, n. 5) adopts the latter text in his edition. Li Jimin (1993a, 38, n. 1) and Guo Shuchun and Liu Dun (2001, 34) both adopt the former option in their edition, even though they do not agree on punctuation. Here, I follow the punctuation of Guo Shuchun and Liu Dun. Note that Guo Shuchun and Liu Dun (2001, 68, n. 14) give the latter as a possible option.

8 This character is omitted in the Southern Song edition (Li Jimin 1993a 38, n. 2) and in the edition printed by Hu Zhenheng. Dai Zhen restores it in his edition for the Collection Wuyingdian juzhen ban. Qian Baocong (1963, 17, n. 6) adopts this emendation, an option also followed by Li Jimin 1993a, which I find preferable. Guo Shuchun and Liu Dun (2001, 69, n. 15) consider both options possible and follow the Southern Song edition (Guo Shuchun and Liu Dun 2001, 34).

9 Following an idea put forward by Li Jimin (1993b, 495–6) without however adopting his overall restoration of the sentence here, I suggest that the character contained in the ancient editions here has been wrongly copied in place of the similar character .

References

References

Chemla, K. and Shuchun, Guo. 2004. Les Neuf chapitres. Le Classique mathématique de la Chine ancienne et ses commentaires. Paris: Dunod.Google Scholar
Ch'en Liang-ts'so (Chen Liangzuo). 1993a. “Liu Hui gougu dingli shi tan (Tentative discussion on Liu Hui's proof of the theorem of base and height [Pythagorean theorem]).” Shuxueshi yanjiu wenji (Collected research papers on the history of mathematics): 1–7 (in Chinese).Google Scholar
Shuchun, Guo and Dun, Liu. 1998. Suanjing shishu (Ten canons of mathematics). Shenyang: Liaoning jiaoyu chubanshe, 2 volumes.Google Scholar
Shuchun, Guo and Dun, Liu. 2001. Dian jiao Suanjing shishu (Punctuated edition of the Ten canons of mathematics). Taipei: Jiuzhang chubanshe. Reedition of the former.Google Scholar
Jimin, Li. 1993a. “≪Shang Gao dingli≫ bianzheng.” Ziran Kexueshi Yanjiu (Research in the history of natural sciences) 12 (1):29–41 (in Chinese).Google Scholar
Jimin, Li 1993b. Jiuzhang suanshu jiaozheng (Critical edition of The Nine Chapters on Mathematical Procedures). 590 p. Xi'an: Shaanxi kexue jishu chubanshe (in Chinese).Google Scholar
Baocong, Qian. 1963. Suanjing shi shu (Ten classics of mathematics). Beijing: Zhonghua shuju, 2 volumes.Google Scholar

Reference

Chemla, Karine. (2005). Geometrical Figures and Generality in Ancient China and Beyond: Liu Hui and Zhao Shuang, Plato and Thabit ibn Qurra. Science in Context 18 (1), 123–166.CrossRefGoogle Scholar