The Book on the Art of Computation Excavated from the Han Dynasty Tomb 1 at Shuanggudui: A Transcription with Annotation and Discussion of Related Issues

Among the batch of slips excavated from the Han dynasty tomb 1 at Shuanggudui (双古堆), Anhui Province, China, were some mathematical texts. They are in bad shape, and slightly more than 30 fragmentary slips were assembled together and given the title the Book on the Art of Computation (算术书 Suanshu shu). So far only 4 slips of the Book on the Art of Computation have been transcribed. This work, based on all previous efforts by other related researchers, transcribes all the published slips for the first time, and groups together those slips that are supposed to deal with the same problem. The results indicate that only slips 3, 28+27+21+20+5, and 24+25 are comparatively complete and clear in meaning. Compared with the related problems of the Nine Chapters on the Art of Computation (九章算术 Jiuzhang suanshu), it can be confirmed that the data on the above mentioned slips correspond well with Problems 25 and 1 of Chapter 6 Junshu (均输, Equitable Distribution), and Problem 8 of Chapter 4 Shaoguang (少广, Slightly Increasing the Width), respectively. Considering the background of Zhang Cang (张苍), a presumed compiler of the Nine Chapters, and the owner of the Book on the Art of Computation, that is, the occupant of the Han dynasty tomb 1 at Shuanggudui, it is believed that these two figures had the opportunity and high probability of having associated with each other with regard to mathematics. Our conclusion is that the Book on the Art of Computation excavated at Shuanggudui is a mathematical work that possibly took as one of its key sources a given version of the Nine Chapters collated by Zhang Cang.