522 alexei volkov
with three tasks on the Jiu zhang , and with one task on each [of the treatises] Hai
dao , Sun zi , Wu cao , Zhang Qiujian , Xiahou Yang , Zhou bi , Wu jing suan , [they]
pass [if out of ] ten [tasks they complete] six. [For the treatises] Ji yi and San deng
shu , [they do] ‘strip reading’, and for ten [excerpts they] succeed [if they complete]
nine. [When they are] tested with the Zhui shu and Qi gu , [they] produce records of
‘general meaning’ taking mathematical problems [as the examination tasks], [they
have to] elucidate the numerical values [of the problems], [and to] design [compu-
tational] procedures [that would solve them]. [Th ey] elucidate in detail the internal
structure of the [computational] procedures [they designed]. As for those [trea-
tises/examination papers] without commentaries, 38 [the candidates have to] make
the numerical data coherent, to design [computational] procedures and [should]
not make mistakes in the meaning and in the structure [of the procedures]. [If they
do] so, then they pass. For the Zhui shu [there are] seven tasks; for Qi gu [there are]
three tasks. [Th ey] pass [if out of ] ten [tasks they complete] six. [For the treatises]
Ji yi and San deng shu , [they do] ‘strip reading’, and for ten [excerpts they] succeed
[if they complete] nine. [Under the conditions listed above] they pass the degree
examination, [but if they drop] one treatise [of the two], even if [they] completed
six [tasks out of ten], [they] will not obtain the degree. 39Th is excerpt leaves several questions unanswered. In particular, it remains
unclear whether the examination works of the candidates were written in
the same format as tasks on other subjects, 40 or whether they had some
specifi c format relevant to the mathematical contents of the treatises. In
Siu and Volkov ( 1999 ) the authors suggested the following hypothesis: the
candidates were given mathematical problems similar (but not identical) to
those contained in the treatises of the chosen ‘programme’, that is, problems
belonging to the categories for which the candidates knew the solutions yet
with modifi ed numerical parameters. Th e change of parameters may have
implied a modifi cation, sometimes considerable, of the known algorithms38 Th e meaning of this phrase remains unclear; see a discussion of it in the concluding section of
the present article.
39 Th e last remark apparently could refer to the case when the candidate failed all the tasks related
to the Qi gu.
40 A discussion of the expression ‘general meaning’ is necessary here. Th is term occurs only in
the descriptions of the examinations on the degrees ming jing (in the general description
and in the description of two options; see above), ming suan , examination on the Rites of
the Kai-Yuan era , as well as the description of the instruction in the Mathematical
College (see above). One can suggest that the term ‘questions on meaning’ refers to a kind of
task focusing on the capacity of the examinee to provide a plausible interpretation of a given
text or texts. Lee off ers two examples of questions and answers on ‘general meaning’, da yi
(interestingly, he renders this very term as ‘written elucidation’) in the context of examination
on Confucian classics; he suggests that this kind of questions ‘tested mainly familiarity, that is,
memory, of the classics’ (Lee 2000 : 142).