边冈“相减相乘”法源于一行说

On Bian Gang's Method of "Subtract Before Multiply" Being Derive from Yi Xing

晚唐边冈总结的"相减相乘"法,是中国古代历法计算中的重要方法,以往人们不清楚它的来源,实际上它由僧一行《大衍历》中的黄赤道差计算公式推广而来,源自中国传统算法。它对历法中极值问题的计算,类似于"等周问题"中的简单命题"等周长矩形的面积以正方形最大"。

The method of ＂subtract before multiply＂ summarized by Bian Gang of late Tang dynasty is an important one about ancient Chinese calendric calculation. Previously, nobody knew where it derived from. In fact, it was spread from the calculating formula for the difference of ecliptic longitude and right ascension in monk Yi Xing＇s Dayan Calendar. Being derived from traditional Chinese algorithm, it was similar to the simple proposition of isoperimetric problem that of all isoperimetric rectangles only the area of a square was maximum.