424 karine chemla
the correctness of the algorithms provided. 3 However, soon aft er its com-
pletion, the book became a ‘Classic’ ( jing ) and retained this status in the
subsequent centuries, which accounts for the specifi c fate it had not only in
China, but also in Korea and Japan. On the one hand, as is clear from the
references made to it, the book remained a key reference work for practi-
tioners of mathematics in China until at least the fourteenth century, and
this fact most probably explains why it is the earliest extant text to have
been handed down through the written tradition. On the other hand, com-
mentaries on it were regularly composed, two of which were perceived as
so essential to the reading of the text that they were handed down with the
Classic itself. In fact, no ancient edition of Th e Nine Chapters has survived
that does not contain the commentary completed by Liu Hui in 263 and the
explanations added to it by a group of scholars under the supervision of Li
Chunfeng. 4 Th is detail of textual preservation indicates how closely linked
to each other these texts became, to the extent that, at some point in history,
they constituted, for Chinese readers, an integrated set of texts that were no
longer dissociated. As a consequence, if we, as contemporary exegetes, are
to understand how Th e Nine Chapters was approached in ancient China,
it is important that we, like Chinese readers, read the text of the Classic in
relation to that of its commentaries.
Th is relationship proves important in several respects. On the one hand,
through the commentaries, one can establish that even though the prob-
lems contained in Th e Nine Chapters all appear to be particular statements,
they were read by the earliest readers whom we can observe as general
statements. Th e commentators exhibit the expectation that the algorithm
linked to a problem should solve not simply this problem, but the category
of problems for which the problem, taken as paradigm, stood. 5 On the other
hand, the commentators make explicit some theoretical dimensions that3 In Chemla 1991 and 1997/8, I have given several hints indicating that the situation is not
so simple. However, since the focus of this chapter lies elsewhere, I shall not dwell on this
question. Th e reason why this issue is crucial for us here will become clear in Part ii of this
chapter. Let us stress that the title of Th e Nine Chapters contains the character shu ‘procedure’
which introduces the statement of the algorithms contained in both books.
4 Below, for the sake of simplicity, we refer to this layer of the text by the expression of ‘Li
Chunfeng’s commentary’. In fact, the situation is less simple than is presented here. Th ere are
problems in distinguishing between the two layers of commentaries (I have summarized the
state of our present knowledge on the topic in CG2004: 472–3). In the present chapter, I have
attempted to deal with my topic in a way that is not jeopardized by this diffi culty.
5 In fact, this presentation of Th e Nine Chapters is simplifi ed. An algorithm can be given aft er
a set of problems. Moreover, there are cases when an algorithm is given outside the context
of any problem, or constitutes an instantiation of such an algorithm. However, this does not
invalidate the main thesis.