《算数书》"少广""大广"二问的释读与校勘

对<算数书>"少广"术文进行释读与算法分析,同时与<九章算术>"少广"术进行对比,认为<算数书>的"少广"术正确地选用了"最小公倍数"进行分数通分.这一算法是在对"最小公倍数"的正确认识指导下完成的,表明在<算数书>的时代,中国古代数学的"最小公倍数算法"已经十分纯熟.<算数书>"大广"问中缺失的数字,一直为研究者所关注.在假定残文数字和文字无误的前提下,借助计算机的帮助,可以获得11种成立的可能;通过对<算数书>用语习惯和算法合理性的分析,确定其中2种是最可能的结果,从而为解决<算数书>"大广"问的校勘困难提出一种新的思路.

Annotations and Collations on Problems "Shaoguang" and "Daguang" of Suanshushu

Through critical reading and following the collation principles on ancient mathematics text,this paper gives some new collations to Suanshushu(Writings on Reckoning:a book of arithmetic written on bamboo strips in about 186 BC).Based on those collations,the paper gives some deep explanations to the Shaoguang problem of Suanshushu.Especially it points out that the Shaoguang algorithm was based on the method of the lowest common multiple(LCM).And the most important result in this paper is that the restoration to the problem Daguag Method(The General Rule for Rectangular Fields) in Suanshushu.Taking the fact for this problem that the remaining words and figures were "correct",and then with the help of computer,the paper gets about 11 possible answers.Further considering the character gaps and expressing style,it points out that only 2 possible answers among them might be the plausible restorations.