張替 俊夫

九章算術』は『算数書』出土以前は数学書としては中国最古のものであった。我々は、我々の『算数書』研究を起点に、『九章算術』の劉徽注、李淳風注を含めた訳注を完成させることを目的としている。 本論文では、句股章の算題［一］～［八］に対する訳注を与える。

"The Nine Chapters on the Mathematical Art" was the oldest book of mathematics in China before the unearthing of "Suan-shu shu." The aim of our research is to provide a complete translation and annotation of it including annotations of Liu Hui(劉徽)and Li Chunfeng(李淳風)from the viewpoint of our previous work on "Suan-shu shu." This is the twenty-fourth article based on our research and results in which we studied the problems 16 to 20 of Chapter 7, Yingbuzu(盈不足)."The Nine Chapters on the Mathematical Art" was the oldest book of mathematics in China before the unearthing of "Suan-shu shu." The aim of our research is to provide a complete translation and annotation of it including annotations of Liu Hui(劉徽)and Li Chunfeng(李淳風)from the viewpoint of our previous work on "Suan-shu shu." This is the twenty-fourth article based on our research and results in which we studied the problems 16 to 20 of Chapter 7, Yingbuzu(盈不足).

In this paper, we discuss the triviality of bouquets by using the tangle description, and give a necessary and sufficient condition for a bouquet to be trivial. We also give a necessary and sufficient condition for a tunnel number one knot to be a 2-bridge knot and prove that if each component of a tunnel number one link is a trivial knot, then the link is 2-bridge.