秦汉量制与《九章算术》成书年代新探——基于文物考古材料的研究

A New Investigation on the Measurement System of Capacity and the Time When the Nine Chapters on Mathematical Procedures Was Compiled:Research Based on Cultural Relics and Archaeological Materials

论文考察了前人关于量制单位斛的使用不早于新莽的证据和论证,指出其中存在的问题,从出土文献和传世文献两个方面证明新莽以前就有斛的使用,同时也证明了一些被认为是新莽时代特有的数字表示法是早已有之的。论文还分析新莽容积(体积)计量系统的继承与变化;证明《九章算术》反映了时代更早的容积(体积)系统的特征,它很可能是斛取代石的过程中之重要一环,而新莽铜嘉量的颁行则是这一过程中的里程碑,但并非终曲。论文证明《九章算术》中石和斛分工、分别表示重量和体积(容积)很可能是耿寿昌所为,这为刘徽关于《九章算术》最后成书于耿寿昌的记载提供了新的证据。

This paper examines and points out problems in the evidence and arguments used by scholars to demonstrate that the usage of the measurement unit hu 斛 for capacity was no earlier than the Wang Mang Xin dynasty（9-23 AD）.Based on evidence from both unearthed documents and received literature,it proves that the usage of hu appeared earlier than the Xin dynasty.It also demonstrates that some special expressions of numbers that were formerly considered unique to the Xin dynasty had actually existed much earlier.This paper analyzes what the Xin＇s measurement system of capacity or volume inherited from the previous system,and what were the changes in the new system.It proves that the Nine Chapters on Mathematical Procedures shows the features of the system of capacity earlier than the Xin,and that the Nine Chapters was likely an important step in the process that led to the unit hu 斛 being substituted for the unit shi 石 for capacity（or volume）,while the issue of national copper vessels for standard units of capacity was a milestone,not the end of the process.The paper proves that it was most likely Geng Shouchang who expressed weight and capacity（or volume） distinctly with shi and hu respectively,without confusing them,offering new evidence to support Liu Hui＇s record that Geng finalized the compilation of the Nine Chapters.