524 alexei volkov
1777.^45 Th e mentions are very short and do not provide any information
concerning the contents and the procedure of the examinations. Since the
state mathematics examinations were abolished in China by the end of the
Song dynasty (960–1279), one can only guess what may have been the pro-
cedure and the contents of the Vietnamese state mathematics examinations
and their relationship with the Chinese examinations of the Tang and Song
dynasties. To my knowledge, no original Vietnamese mathematics exami-
nation papers have been found so far. Fortunately, there exists a ‘model’
mathematics examination paper published in 1820 by Phan Huy Khuông
, apparently in order to provide the students with an idea of the best
way to answer an examination question. Phan placed the mock examina-
tion essay that occupied almost six pages in the last, fourth chapter of his
treatise entitled Chỉ minh lập thành toán pháp (Guidance
for understanding the Ready-made Computational Methods ) ( CMLT 4:
30a–32b). Th is text sheds light on the examination procedure in Vietnam;
moreover, it indirectly corroborates the hypothesis concerning the Chinese
examination procedure mentioned in the section above.
Th e original manuscript is preserved in the library of the Institute for
Han-Nom Studies (Hanoi). 46 In my work I used a microfi lm copy of the
manuscript preserved in the library of the Ecole française d’Extrême Orient
(Paris). Th e catalogue Tran and Gros (1993) provides only very sparse
information about the author and the contents of the book. Th e treatise
opens with a picture of an abacus (p. 3a) which is an exact reproduction
of the picture found in the Chinese mathematical treatise Suan fa tong
zong (Summarized fundamentals of computational methods)
by Cheng Dawei compiled in 1592 ( SFTZ : 113). Th e picture is
followed by a table of correspondences between powers of 10, monetary
units, units of length, weight, and volume (p. 3b). Two following pages
present thirty-two diagrams of various plane fi gures (referred to as ‘shapes
of fi elds’, Chin. tian shi ) (pp. 4a–b) of which the areas are calculated in
Chapter 2 of the treatise.
Th e model examination essay consists of a solution of a mathematical
problem written by an imaginary examinee; for the full translation of the
examination paper see Appendix i. Th e problem reads as follows: three
categories of offi cials, A, B and C, are to be remunerated with 1000 cân
of silver, yet out of this amount only the sum S = 5292 lượng was
supposed to be distributed among the functionaries. 47 It is claimed in the
45 Volkov 2002.
46 It is listed under number 433 in Tran and Gros 1993: i 258.
47 Cân and lượng , technically, are measures of weight (1 cân = 16 lượng ), but were also used
as monetary units in China and Vietnam, being applied to silver.