Demonstration in Chinese and Vietnamese mathematics 537
commentaries of Li Chunfeng on the Hai dao suan jing may have naturally
become paradigmatic texts imitated by the authors of examination essays
devoted to this particular text, and one can conjecture that the commentar-
ies of Liu Hui and Zhao Shuang, containing justifi cations of the algorithms,
in turn also may have been employed by the students and examinees as
models in their oral presentations and written examinations. Th e commen-
taries thus provided the standards of persuasiveness and consistency and
shaped the style and structure of the mathematical discourse in the branch
of the traditional Chinese mathematics perpetuated within the network of
offi cial educational institutions of the fi rst millennium ce.
Acknowledgements
I would like to express my gratitude to two anonymous referees for their
valuable suggestions, to Karine Chemla for her personal and professional
support throughout the preparation of the chapter, and to the Institute for
Advanced Study, Princeton where the fi rst draft of the paper was completed
in 2007. Th e fi nancial support for my work in France and Vietnam in
2006–7 was provided by the National Science Council, Taiwan (grant no.
95–2411-H-007–037), by the Leading Edge Research Foundation of the
National Tsing Hua University, Taiwan (grant no. 95N2521E21) and by the
Institut National de Recherche Pédagogique, France; I would like to express
my gratitude to all these institutions.
Appendix i
Th e fi rst part of the Appendix contains the original text of the ‘model
examination paper’ from the Chỉ minh lập thành toán pháp
(Guidance for understanding of the Ready-Made Computational Methods)
by Phan Huy Khuông’s ( CMLT 4: 30a–32b). When reproducing
the text, I preserved the original layout, that is, one line of the original
corresponds to one line of the transcription below. Th e original text does
not contain punctuation, and I introduce my own. Th e emendations of the
text are indicated with the brackets 〈〉 and : ‘〈A〉 B ’ means that the
sequence of characters A is suggested to be replaced by the sequence B