518 alexei volkov
below. Th e list could not be chronological either, given that according to
the conventional chronology the Zhou bi certainly was considered to ante-
date the treatise Hai dao and yet was listed aft er it. Th e only suggestion that
seems plausible is that the list followed the order in which the treatises were
actually studied. 25
According to the Tang liu dian (Six Codes of the Tang [Dynasty])
and to the Jiu Tang shu (Old History of the Tang [Dynasty]), the
students of the College were subdivided into two groups each comprising
fi ft een students. Th e fi rst group studied treatises [1–8], and the second
one treatises [9–10]. 26 In Table 15.1 and below I refer to the textbooks of
the groups [1–8] and [9–10] as constituting a ‘regular programme’ and
an ‘advanced programme’, respectively, given that the extant version of
the treatise [10] contains more diffi cult mathematical methods than those
found in [1–8] (in particular, solution of cubic equations), and that the
now lost treatise [9] was, according to Li Chunfeng, a diffi cult book (and,Notes: (continued)
2001 : 18. Compare with the date ‘fi ft h century? Very approximately’ suggested by
Martzloff 1997 : 124.
e Liu Hui in his ‘Preface’ of 263 ce suggested that the treatise was compiled on
the basis of an ancient prototype by Zhang Cang (?–152 bce ) and Geng
Shouchang ( fl. fi rst century bce ), see SJSSb : 83; for a discussion, see CG2004:- Th e opinion of Liu Hui is one of the numerous theories concerning the date of
compilation of the treatise; for an overview, see Li 1982. See also Cullen 1993a.
f Compare with the date ‘200 bce –300 ce ’ suggested by Martzloff 1997 : 124.
g Qian Baocong suggested that the treatise was completed between 466 and 485 ce
( SJSSa : 325), while Feng Lisheng argued for the interval 431–50 (Guo 2001 : 16).
h Guo 2001 : 25. Th e text of the original treatise written by Xiahou Yang most
probably in the fi rst half of the fi ft h century ce was lost by the eleventh century and
replaced by a compilation of Han Yan written in 763–79; see SJSSa : 551.
i Th e dates suggested for this treatise vary considerably; I adopt here the viewpoint of
Cullen 1993b and 1996 , being well aware of other opinions concerning the date of
compilation. Martzloff 1997 : 124 provides a hardly acceptable period of time: ‘100
bce (?) – 600 ce ’.
j Wang Xiaotong in his ‘Preface’ to the Qi gu suan jing mentions Zu
Gengzhi ( b. before c. 480 – d. aft er 525) and not his father Zu Chongzhi as
the author of the treatise ( SJSSb : 415).
k Martzloff 1997 : 125 suggests for Wang’s lifetime the dates ‘ c. 650–750’ which are
impossible given that his treatise was included in the collection of 656 ce.
25 An almost identical list can be found in the Jiu Tang shu (Old History of the Tang [dynasty])
( JTS 44: 17b), yet the order of the treatises in the ‘regular programme’ is diff erent: Jiu zhang ,
Hai dao , Sun zi , Wu cao , Zhang Qiujian , Xiahou Yang , and Zhou bi. Th e San deng shu is
mentioned as San deng.
26 TLD 21: 10b, JTS 44: 17b. Th e Xin Tang shu only mentions that the number of students
amounts to thirty, see XTS 44: 1b, des Rotours 1932 : 133.