The History of Mathematical Proof in Ancient Traditions

Demonstration in Chinese and Vietnamese mathematics 517

Number

Treatises listed in

the Xin Tang shu

Identifi ed as the

following extant

t r e a t i s e s A u t h o r

D a t e o f

compilation

8 Wu jing suan

(Computations

in the fi ve

classical books)

Wu jing suan shu

(Computational

procedures [found]

in the fi ve classical

books)

Zhen Luan

( fl. c. 570 ce )

C. 570 ce

9 Zhui shu
(Mending
procedures)

Not extant Zu Chongzhi

(429–500) j^

Second half

of the fi ft h

century ce

1 0 Qi gu
(Continuation
[of the work]
of ancient
[authors])

Qi gu suan jing

(Computational

treatise on the

continuation

[traditions] of ancient

[mathematicians])

Wang Xiaotong

( b. ?– d. aft er

626 ce ) k^

C. 626 ce

1 1 Ji yi
(Records of
[things] left
behind for
posterity)

Shu shu ji yi

(Records of the

procedures of

numbering left

behind for

posterity)

Xu Yue

(b. before

185 – d. aft er

227)

C. 220 ce

1 2 San deng shu
(Numbers
of three ranks)

Not extant D o n g Q u a n

Prior to 570

ce

Notes:
a A book entitled Sun zi by one Sun Chao of the Jin dynasty (265–420) is
mentioned in the lists of proscribed books of the third through the tenth century, see
An and Zhang 1992 : 51; it is not impossible that this was the mathematical treatise
or its prototype and not the famous treatise Sun zi bing fa on the art of
war written in c. fi ft h century bce.
b Qian Baocong suggested that the treatise was compiled in c. 400 ce ; he also believed
that the extant version was altered during the Sui (581–618) and Tang (618–907)
dynasties, see SJSSa : 275; Guo 2001 : 14.
c In some sources the treatise credited to the authorship of Zhen Luan , fl. c. 570,
see SJSSa : 409.
d Th e date suggested by Qian Baocong; he also suggested that the extant version of
the text may have been modifi ed in the seventh century ce , see SJSSa : 409, Guo

Table 15.2 Continued