Chinese Mathematics in the Thirteenth Century: The Shu-shu by Ulrich Libbrecht

By Ulrich Libbrecht

One reviews chinese language arithmetic essentially as one of many methods of apprehending the entire brain of a civilization that used to be completely interconnected inside of itself, by way of highbrow strategies, social association, and aesthetic expression. the level to which thirteenth-century chinese language arithmetic expected glossy or Western effects isn't of actual relevance. As Nathan Sivin states in his Foreword, "Ideas which...were perceived basically because the superseded and erroneous backdrop of 'modern' anticipations needs to now be evaluated as heavily because the latter, for they performed no less significant a job in defining the traditional scientist's perception of the normal world—and hence the path and magnificence of his investigations."

That stated, a latest Westerner can hardly ever suppress declaring the 2 most crucial ways that Ch'in Chiu-shao complex the math of his time and position: he acknowledged the "Chinese the rest theorem" for indeterminate equations of the 1st measure, that's extra basic than Gauss's rule of 1801; and his set of rules for fixing equations of upper measure (including the 10th measure) is similar with Horner's (1819). those effects additionally entailed methodological advances: Ch'in's account of his approach for fixing indeterminate difficulties is the 1st as a rule acknowledged mathematical formula within the chinese language literature; and his paintings on equations of upper measure was once totally speculative, or experimental, going way past the normal bounds of chinese language mathematics—the resolution of only functional problems.

One additional comparative ancient be aware is probably not out of order. Libbrecht writes, "Chinese arithmetic types a part of medieval arithmetic, of the algorithmic part we discover in all civilized international locations at the moment. In interpreting Ch'in's textual content, i attempted to put it inside this algorithmic mathematical belief, which used to be the preamble to trendy algebraic logistic." enforcing this technique, the writer compares the therapy of indeterminate equations in this interval in India, Islam, and Europe and reveals that Ch'in's suggestions have been remarkable. This on my own should still reveal the significance of this examine to common mathematical history.

The essence of the booklet continues to be its perception into chinese language proposal and existence, as published via the overall ideas that emerge and interrelate and through the sensible mathematical difficulties posed via Ch'in that tie into the standard realities of his time. it truly is specifically this final element that makes the ebook valuable to China students generally.

this is often the 1st quantity within the MIT East Asian technological know-how sequence, of which Nathan Sivin is common editor.

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42 There were only seven copies of this encyclopedia; some of them still exist in Chinese libraries (see Hummel (1), pp. 121 f), but only a small part of the material they contain has been published. As we know from the 仿6-/:, 《cA, 扫 幻 打 -jAw/jun《-饥《 that critical not;es were added, we are in want of a valuable source of information. For general information on the mathematical works in the Ssu-k^u ch^uan-shu, see Li Yen (8^), pp. 4 6 4 ff. ng, p. 10, and Kuo Pai-kung (1'), p. 61. ,, Some of the textual emendations are quot;ed in Sung Ching-ch’ang’s commeiUary, discussed lat;er in this chapter.

133 C h. 9, p. 2a. T his is a note o 打 Sim 呂C hi 打g-ch,a 打g. 964 (second edition: T a ip e h ,I % 7). I 打con­ nection w ith C h ,in C hiu-shao there are no1:es by C h ,ien T a-h sin ,L u H sinyuan a n d K u K uang-ch^i. See pp. 208 f (in the 1964 edition, p p. 830-834). 135 A ppe 打dix, p. 3a. 136 In 化e "w eekly likiraiy sup p lem en t,, o f 化e / •vAzTi />。 0 天津益 惟報,no. 79. I have 打o t seen this ai'ticle. 5 General Structure of the Shu-shu chiu-chang The modern edition of the 斯 M-血 cA/WA口灼《 con化ins the fo^ lowing parts: A.

4 8 . This title is of course a mistake. See Li Yen (8^), p. 478. 68 Ch. 69, p. 25a. 69 Ch,ien Pao-tsung (8') ,p. 291. 70 See p. 49. 71 (2') ,P. 65. ti-c/wng e打cyclopedia. ^ 打o mention is made of this fact. The text says: ‘‘Mr. Mao also took along that which the first-degree graduatie Li [Li Jui] of Yuan-ho had colla化d, from the latter’s private Ubrary. As for the Ssu-k^u kuan-pen, I also rely on the comparative study made by Mr. ’’ In this edition there is a blank space between these sentiences; we find the same in Ch’ien T , ai-chi’s 錢泰吉 沁z-旅 ( 1838),73 where Sung Ching-ch’ang is quoted, showing clearly that Li Jui is not connect;ed with the 斯 collection.

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