Demonstration in Chinese and Vietnamese mathematics 519
as becomes clear from an inspection of the number of years allotted to the
study of the treatises, the most diffi cult book in either programme).^27 Th e
study in each programme required seven years. Books [11–12] were studied
simultaneously with the other treatises in both programmes; the time nec-
essary for their study was not specifi ed. 28
Th e conventional identifi cation of the twelve treatises constituting the
curriculum is found in a number of modern works and is summarized in
Table 15.2.
Th e conventional identifi cation of the Tang dynasty textbooks with the
extant treatises contains a number of points that have never been suffi ciently
clarifi ed. For instance, there are three treatises listed in the bibliographical
section of the dynastic history Xin Tang shu which, hypothetically, might be
identifi ed as the textbook Jiu zhang listed in Table 15.1 and mentioned in
the chapter on state examination of the same history: they are the Jiu zhang
suan shu compiled by Xu Yue, the Jiu zhang suan jing compiled by Zhen
Luan ( XTS 59: 13a), and the Jiu zhang suan shu commented on ( zhu ) by Li
Chunfeng ( XTS 59: 13b), all three treatises in nine chapters ( juan ). If the
latter treatise is assumed to be the textbook used for instruction, it remains
unclear whether it was identical with the only extant Song dynasty edition
of the treatise commented ( zhu ) by Liu Hui and accompanied with the
explanations of the commentaries ( zhu shi ) by Li Chunfeng (see below).
Th e Zhang Qiujian from the curriculum could be either the Zhang Qiujian
suan jing in one juan commented on by Zhen Luan ( XTS 59:
13a), or a three- juan edition of the treatise commented on by Li Chunfeng
( XTS 59: 13b); however, the earliest (and only extant) Song dynasty edition
in three juan mentions Zhen Luan as the commentator while containing
only commentaries signed by Li Chunfeng ( SJSSb : 343). As for the treatise
listed in the curriculum as Xiahou Yang , the bibliographical chapter of the
Xin Tang shu mentions two books the titles of which bear reference to this
name: one is the Xiahou Yang suan jing commented on by Zhen Luan, and
27 Li Chunfeng wrote about Zu Chongzhi and his book as follows: ‘
[He] was the best of mathematicians. Th e
title of the book [he] compiled is Mending procedures. No one of the faculty [lit. ‘functionaries’]
of the [Mathematical?] College was able to comprehend thoroughly the profound [ideas it
contained]. Th is is why [they] abandoned [the book] without [even trying] to understand [it].’
( SS 16: 4a). Martzloff ’s translation of the last part of this quotation reads ‘He [Zu Chongzhi
- A.V.] was excluded (from the textbooks used for teaching) because none of the students of
the Imperial College could understand him’ (Martzloff 1997 : 45, n. 22 ), and it is somewhat
misleading, since Li Chunfeng’s statement was clearly pointed against the personnel of the
College (and not against its students), while the high esteem he expressed for the book of Zu
Chongzhi was apparently related to his decision to introduce the Zhui shu into the curriculum
as the cornerstone of the advanced programme.
28 Siu and Volkov 1999.