刘徽与王莽铜斛

LIU HUI AND THE BRONZE STANDARD MEASURE OF WANG MANG

王莽铜斛是新莽时期刘歆(?—23年)制造的标准量器,原器现存台湾省,其形制与《汉书·律历志》所记相同(图1),即: "其法用铜,方尺而圜其外,旁有庣焉。其上为斛,其下为斗。左耳为升,右耳为合、龠。

The three paragraphs about the bronze standard measure of Wang Mang in Liu Hui's Annotations to Nine Chapters on the Mathemancal Art have been evoking much controversy among historians of mathematics. The author of the article reanalyses the paragraphs with reference to the inscriptions on the bronze standard measure of Wang Mang and the Lu Li Zhi (Chapter on Calendar and Temperament) in Han Shu (History of the Han Dynasty) and Sui Shu (History of the Sui Dynasty), and comes to the conclusion that the first and second para graphs were written by Liu Hui, who had investigated the bronze standard measure of Wang Mang by means of π=157/50 and π=3927/1250 respectively, while the third was written by Li Chunfeng with some material of Liu Hui and has nothing to do with Zu Chongzhi.