秦汉简牍算书“径田术”新探

A new interpretation of Jingtian shu(Method for measuring rectangular fields)in mathematical books on wooden and bamboo slips of the Qin and Han dynasties

“径田术”是秦汉简牍算书中的一种简便算法,用于计算广、纵均大于或者广、纵之一大于240步的矩形田面积.此术目前见于四种秦汉简牍算书文献,学界对“径田术”有过讨论,所得出的结论中有合理成分,但由于部分术文晦涩难懂等客观原因,这些结论还有可商榷之处.分析学界对“径田术”几种代表性观点,指出其中的合理成分和可商榷之处,在分析术文文意的基础上提出理解“径田术”的新思路.

The Jingtian shu(Method for measuring rectangular fields)is a convenient method found in wooden and bamboo mathematical books of Qin and Han dynasties for finding the area of a rectangular field when one or both of the width and the length are greater than 240 bu.This method is not found in traditional texts but in four excavated wooden and bamboo mathemat⁃ical books of the Qin and Han dynasties.Some scholars have talked about it,and the conclusions they made are reasonable to a certain extent.However,due to the obscurity of some languages in the method,these conclusions are still open to discussion.This paper analyzed several representative viewpoints of the academic circle,pointed out the elements that are reasonable and those that are still open to discussion in those points of view,and proposed a new way of interpreting this method based on the analysis of the textual meaning of the method.