Research on the Thinking of Logarithm and Binomial Express and Euler's Numbers in the Late Qing Dynasty

Dai Xu, who spent all his life on the academic research of mathematics and worked with pioneering spirits and unremitting assiduity, made contributions to the study of logarithm and Euler's numbers, especially to the study of the expansion equation of logarithmic trigonometric function which was ¿without parallel¿ in his times and has been ever esteemed advanced and representative in the Chinese history of mathematics. His book A Quick Method of Making Mathematical Tables was translated into English by J. Edkins (1825 -1905) in 1854 and officially published in London. Because of the repercussions it had in the world, Dai Xu ranked high among the mathematicians of various countries the world over. This paper lays stress on the expatriation on the expansion equation of logarithmic trigonometric function that Dai Xu proposed in his study of logarithm and Euler's numbers and on the impact, significance and contributions that Dai Xu Number once made. As a well-known Chinese mathematician who brought forth new ideas in the mathematical field in the late Qing Dynasty.