| Abstract: | One of the many commentators of the Chiu chang suan shu (Nine Chapters on the Mathematical Art), written approximately in the first century, is Yang Hui, who wrote Hsiang chieh chiu chang suan fa (A Detailed Analysis of the Mathematical Methods in the “Nine Chapters”) and the Chiu chang suan fa tsuan lei (Reclassification of the Mathematical Methods in the “Nine Chapters”) in 1261.The seventh chapter of the Chiu chang suan shu is called ying nu or ying pu tsu meaning “too much and not enough” or “surplus and deficiency.” It has been pointed out by historians of mathematics that the method known in Europe as the Rule of False Position is the same as the Chinese ying pu tsu method used in this chapter. Yang has made a detailed and thorough study of the twenty problems in this chapter. He has not only explained and expanded the method of ying pu tsu, but he has also suggested alternative and simpler solutions for some of the problems.This paper endeavours to translate the twenty problems, to analyse the ying pu tsu method, and above all to present a critical study of Yang's alternative methods. |
