從出土文獻看秦漢計量單位石的變遷 (数学史の研究)

Abstract

Based on the unearthed documents, the paper will first focus on the characteristics of the often-used measurement unit shi 石 and its change during the period from Qin State of Warring States to Han dynasty, and will then study the related aspects of ancient mathematics and its relation to social background. The paper points out that though as a unit of weight, shi always kept the same standard, as a unit of capacity/volume, it was very complicated. In the affairs of storage department of government during the period from Qin State to Early Western Han Dynasty, a special system ofshi was used. We called it as a multi-valued system ofshi, in which the standard ofshi varied according to different kinds of foodstuffs but shared the same lower grade units dou 斗 and sheng 升: 1 shi=16displaystyle frac{2}{3} dou for grains of millet kind (su 粟, he 禾, zi 秶, shu 黍, ji 稷), 1 shi=20 dou for grains of paddy (dao 稻), 1 shi=10 dou for hulled grains of millet kind or paddy. 1 shi=15 dou for soybean (shu 菽), bean (da 荅), sesame seed (ma 麻) and wheat (mai 麥). The multi-valued system of shi made two most important kinds of foodstuff keep the same quantity measured in shi before and after being hulled. Because such a system was very easy to cause confusions, it was replaced by the system of big shi (da shi 大石) and small shi (xiao shi 小石) since the middle of Western Han Dynasty. The system of big shi and small shi are respectively based on the standard of millet and that of hulled grains in the multi-valued system of shi. But unlike the multi-valued system, big shi and small shi had different types of lower grade units dou and sheng, and in the same grade, the amount of 3 big units (shi/dou/sheng) always equal to that of 5 small units (shi/dou/sheng) The problems concerning foodstuffs in the Nine Chapters on Mathematics Procedures (Jiuzhang Suanshu 九章算術) shares the same rates of the list called "Rule for exchanges of foodstuffs and treated foodstuffs" (su mi zhi fa 粟米之法) at the beginning of chapter two. The list is quite identical to the values of the multi-valued system of shi and the laws of the earlier period, and there is no influence of the system of big shi and small shi to be found in the problems. In the Nine Chapters, hu 斛 is used as the unit of capacity/volume instead of shi and is 10 dou in mostly cases, but it has 3 values in 5 problems of Shanggong (商功) chapter, just as those of the multi-valued system of shi in the earlier period. It can be concluded that those problems were mainly handed down from the period before Early Western Han.