《缀术》中的“刍甍,方亭之问”初探

在分析《缉古算经》的写作目的及其具体内容的基础上，对《缀术》中的“刍甍，方亭之问”和“方邑进行之术”作了探讨，认为：前者是已知刍甍，方亭的体积及其边，高的差，求边和高的问题，因此《缀术》中有三次方程的内容，后者是解勾股形问题，类似于《缉古算经》最后６问，由此又对祖冲之的“开差幂”和“开差立”算法提出质疑，认为它们与“方邑进行之术”和“刍甍，方亭之问”无关。

REFLECTIONS ON "THE CHUMENG AND FANGTING PROBLEMS" IN ZHUI SHU

On analysing the object and contents of Ji Gu Suan Jing, this paper arrives at the following conclusions on Zhui Shu: first, the Chumeng or Fangting problem is, given the volume of a Chumeng or Fangting and the differences of its dimensions, to find the dimensions, hence Zhui Shu must have contained cubic equations ; Second, the Fang-Yi-Jin-Xing rules are those of right-angled triangles, similar to those contained in the last six problems of Ji Gu Suan Jing; third, Kai Cha Mi and Kai Cha Li, two rules given by Zu Chongzhi in his Zhui Shu, have no reference to the quadratic or cubic equations; fourth, Zhui Shu contains no quadratic or cubic equations of negative coefficients.