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从唐代司马贞起直至今日,不同时期的学者对《史记.律书》中一组十二律寸分之数的性质认定及数据校勘方面各有解释。而本文发现,北宋沈括早已以定性为管积的“实积之数”说,给这一组律数究竟应该阐释为何数的问题,基本画上了句号。沈括之后的历代探索,大多追寻小司马“九分之寸法”说的思路,将其视作本质为数字律数的管长分数以十约成的管长寸分之数,即间接的管长之数,然其说明显不如沈括之说更符合数理;有的则提出了先秦“管长之数”说,将这组律数视作经过管口校正的、真正的管长之数。但本文在《史记.律书》这一“案发现场”发现的种种线索与证据表明,其说与司马迁所说没有联系,它只是一个具有打开思路作用的“大胆假设”。
From the time of Sima Zhen in the Tang Dynasty up to today, scholars of different periods have each explained the nature of a group of twelve laws in the Records of the Historian and the data collation. However, this paper finds that Shen Kuo in the Northern Song Dynasty has long characterized the number of products as the number of products in the Northern Song Dynasty. The exploration of the past after Shen Kuo, most of them pursuing the idea of a small Sima “nine-tenths of a inch,” considers it as the number of tube-length fractions whose tenor is the essence of the number-law, that is, the indirect tube However, the explanation is obviously not as good as that of Shen Kuo-tzu, which is even more in line with mathematical theory; while others put forward the theory that “the number of managers” number. However, the various clues and evidences found in the “court of record” in the book of “Historical Records” show that it has no connection with what Sima Qian said, and it is only a “bold assumption” that opens the way of thinking.