Conclusion to Part III

An investigation of the structure leads to a deeper understanding of the problems and procedures and to a different mathematical meaning, which remains to be unveiled. Chemla’s experience with the Nine Chapters led her to believe that that classic is also subject to the same phenomenon of reference between problems [Chemla (1997a)]. Some studies have already underlined the importance of analogical reasoning in China, such as [Volkov (1992)], which demonstrated its role in the commentary by Liu Hui to the Nine Chapters. Liu Hui prescribes ‘mending the void with the excess’ (yi ying bu xu 以盈補虛) as a procedure to solve problems in the first (Problems 25–26) of the Nine Chapters. This process is used for the computation of the area of an isosceles triangle, which is part of a figure called gui tian 圭田 . Half a triangle, ABC, is applied as a ‘missing’ part ADE to complete the rectangle ADEC…