The History of Mathematical Proof in Ancient Traditions

Demonstration in Chinese and Vietnamese mathematics 533

bibliographical chapters of dynastic histories, as Table 15.3 shows), whose
lifetime presumably was not too distant from that of Liu Hui, off er a slightly
narrower range of styles. Th e best-known contribution of Zhao is his jus-
tifi cation of a series of quadratic identities with the help of geometrical
diagrams, to a certain extent similar to those used by Liu Hui in his com-
mentaries on the ninth chapter of the Jiu zhang suan shu. 59
Th e actual intentions that Liu Hui and Zhao Shuang had when writing
their commentaries on the Jiu zhang suan shu and Zhou bi suan jing , respec-
tively, do not seem related to any kind of educational activity. However,

59 Gillon 1977 ; Cullen 1996 : 206–17; CG2004: 695–701.

Number

Th e extant treatises

used in the

Mathematical College

Commentators as

specifi ed in offi cial

histories

Commentator(s) of

the extant treatises

9 Qi gu suan jing

(Computational

treatise on the

continuation of

[traditions] of ancient

[mathematicians])

Li Chunfeng (?)

( Jiu Tang shu ); i^ L i

Chunfeng ( Xin Tang

shu )

Th e author (Wang

Xiaotong )

1 0 Shu shu ji yi
(Records of the
procedures of
numbering left behind
for posterity)

Zhen Luan ( Jiu Tang

shu and Xin Tang shu )

Zhen Luan

a^ Li 1977 : 269–271 quotes these and other sources mentioning the names of
commentators.
b^ Zhen Luan is mentioned as the commentator and the author ( JTS 47: 6b).
c^ Th e title is mentioned as Jiu zhang suan jing ( SS 207: 3b).
d^ Liu Xiaosun of the Sui dynasty (581–618) authored the ‘computations’, cao.
e^ Conventionally identifi ed as Zhao Junqing also known as Zhao Shuang
, the author of the commentary found in the extant edition of the treatise.
f^ Th e Jiu Tang shu mentions three diff erent editions of the treatise, two commented
upon by Zhao Ying and Zhen Luan, and one compiled by Li Chunfeng ( JTS 47: 5b).
g^ Th e Xin Tang shu mentions four diff erent editions commented upon by the three
commentators separately (Li Chunfeng is credited with the authorship of two
commentaries) ( XTS 59: 12b, 13b).
h^ In the Song shi the treatise is mentioned as authored by Wang Xiaotong ( SS 207: 3a).
i^ In the Jiu Tang shu both Wang Xiaotong and Li Chunfeng are mentioned as the
authors ( JTS 47: 6b); probably, the text of the history is corrupted and Li Chunfeng
was originally mentioned as a commentator.

Table 15.3 Continued