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《九章算术》是中国古代的第一部数学专著。其中少广章所记载的开平方术和开立方术,奠定了中国古代方程理论的基础,同时在世界数学史上也占有重要的位置。英国和日本的一些学者认为,《九章算术》的开方术已经类似于欧洲十九世纪初期的方法了。国内以往对这一问题介绍较少。本文的目的在于,介绍开立方术的内容、原理并对它在数学史上的位置作一简单的评论。进一步的讨论已有另文介绍。开平方术与开立方术的原理相同,但前者更简单一些,故从略。一、《九章算术》开立方术的内容《九章算术》开立方术有明确的术文,本文以少广章第十九题为例,具体说明术文每句话的意义
The “Nine Chapters of Arithmetic” is the first monograph of mathematics in ancient China. The open square technique and Kaikai technique recorded by Shao Guangzhang laid the foundation for the ancient Chinese equation theory, and also occupied an important position in the history of mathematics in the world. Some scholars in the United Kingdom and Japan believe that the prescription of the “Chapter 9 Arithmetic” is similar to that of Europe in the early 19th century. There has been relatively little introduction of this issue in the past. The purpose of this paper is to introduce the content, principles, and make a brief comment on the position of Kaikai in the history of mathematics. Further discussion has already been introduced in another article. The principle of open square surgery is the same as open cubic surgery, but the former is simpler and therefore omitted. 1. The contents of the “Chapter 9 Arithmetic” open cube technique “Chapter 9 Arithmetic” has a definite technical text. This article takes the 19th title of Shao Guangzhang as an example to specify the meaning of each sentence in the text.