『九章算術』に関する研究IV : 少廣章を中心として

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  • キュウショウ サンジュツ ニ カンスル ケンキュウ 4 ショウコウショウ オ チュウシン ト シテ
  • A Study on Nine Chapters on the Mathematical Art Focusing on the Chapter IV

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This paper is a research on Chapter 4 of Nine Chapters on the Mathematical Art. The contents of Chapter 4 are 24 problems and five methods for solving the problems. The one method is called Shaoguangshu and another methods are called Kaifangshu, Kaiyuanshu, Kailifangshu, and Kailiyuanshu. We have obtained the following three findings through this research. First, we have reproduced and interpreted the five methods faithfully by Suanchou (Divining Blocks) and clarified that the five methods are very effective and important for solving problems in Nine Chapters on the Mathematical Art. Second, we clarified that division of fractional numbers will be operated by multiplication of whole numbers not by its inverse, multiplication of fractional numbers in Shaoguangshu, and this is same to Chapter 1, because the tool is Suanchou. And finally, we clarified that some previous views of Chapter 4 might be wrong, and we submitted interpretations concerning a lot of items that are used in Nine Chapters on the Mathematical Art, especially in Chapter 4, and reproduced the process of solving some problems.

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