Demonstration in Chinese and Vietnamese mathematics 521
( XTS 44: 1b–2a)
All [the candidates examined in] the Mathematical College 33 [have to] produce
records 34 of ‘general meaning’ for ten 35 tasks [represented with] mathematical
problems (lit. ‘problems and answers’). 36 [ Th ey have to] elucidate the numerical
values [of the problems], [and to] design [computational] procedures [that would
solve them]. [Th ey] elucidate in detail the internal structure of the [computational]
procedures [they designed]. 37 [If they do] so, then they pass. [When they are] tested
33 Des Rotours 1932 : 154 suggests ‘For mathematical studies.. .’ (‘Pour l’étude des
mathématiques.. .’); his suggestion shows that he may have been perplexed by the
heterogeneous headings of the paragraphs describing the examinations: in some cases the
beginning of the description mentions the degree, as in the case of the law examination for
the degrees jin shi and ming fa :... ‘All [the candidates for the degree] jin shi.. .’;
... ‘All [the candidates for the degree] ming fa.. .’ ( XTS 44: 2b, ll. 11–12), while in the
case of the examinations for the degrees ming zi and ming suan the names of the
corresponding schools, shu xue and suan xue were mentioned instead ( XTS 44: 2b, ll.
13–14). Th is specifi cation of the institution can mean that the candidates were examined in
the respective college and/or the only candidates admitted to the examination were those who
graduated from it.
35 Th is emendation of the original text containing the word ben (‘original’) is based on three
premises. Firstly, the descriptions of the other examinations in the Xin Tang shu containing
the clause ‘V X ’ with a verb V with the meaning ‘to examine’, ‘to ask’, etc., always have
a numeral in the position of X, e.g., (‘ask [to complete] ten tasks on general
meaning’), the examination for the degree ming jing ( XTS 44: 2b, ln.3);
(‘ask [to complete] 50 tasks on general meaning’), the examination on the degree ming jing ,
option ‘Th ree [Great] commentaries’ ( XTS 44: 2b, lns. 5–6); (‘ask [to
complete] 100 tasks on general meaning’), the examination on the degree ming jing , option
‘[Dynastic] Histories’ ( XTS 44: 2b, l. 8); (‘to pass [examination consisting
of ] 100 tasks on general meaning’), the examination on the Rites of the Kai-Yuan era
( XTS 44: 2b, l. 4), and (‘ask [to complete] one task on general meaning’)
in the description of the oral tests held every ten days in the Mathematical College ( XTS
44: 2a, l. 5). Secondly, ten is indeed the number of the tasks the candidates were supposed
to complete in this particular case. Th irdly, the word ben (as well as its modifi cation )
found in all the extant editions of the history is graphically relatively close to the word ‘ten’
, and the alteration of the text may have happened in an early edition and reproduced in
later editions.
34 Th e word used here, lu , does not appear in the description of other examinations; des
Rotours 1932 : 154, n. 3 writes ‘I am not certain of my translation, because I don’t understand
well the meaning of the word lu ’ (‘Je ne suis pas certain de ma traduction car je ne
comprends pas bien le sens du mot lu .’). Indeed, the term lu looks somewhat inappropriate
in the context of examination, since one of its principal meanings is ‘to copy, to record’. My
interpretation of this term as ‘writing a protocol [of computations]’ is discussed below.
36 Th e interpretation of the term wen da as ‘[mathematical] problem’ was argued for in Siu
and Volkov 1999.
37 A slightly diff erent translation of the two central excerpts of this paragraph was off ered in Siu
and Volkov 1999 : 92. See also des Rotours 1932 : 154–5.