徐有壬优化八线互求的方法研究

Research on Xu Youren's Methods for Mutual-deduction of Series with Trigonometrical Functions

徐有壬的八线互求方法是清代数学的重要内容之一.详细阐述了徐有壬正弦求正矢级数的推导方法及其比例商除法、还原术和借径术,探讨了其八线互求方法的特点.

Xu Youren＇s method for mutual-deduction of series with trigonometrical functions is one of the important contents of Chinese mathematics in the 19th century.This paper elucidates his methods for expanding one trigonometrical function into a series of the other one,including his method such as geometrical deduction,proportional division,inversive method and substitution method,probes into the characteristics of his method of mutual-deduction of series with triangle functions.