李淳风等人盖天说日高公式修正案研究

COMMENTARY ON THE REVISION MADE BY LI CHUNFENG AND HIS COLLEAGUES ABOUT THE FORMULA OF SOLAR ALTITUDE IN THE GAITIAN THEORY OF HEMISPHERICAL DOME

《周髀算经》中的日高公式是在平面大地的模型下建立起来的,李淳风等人在批评了这一公式与《周髀》盖天说不相符合的同时,重新依斜面大地的假设构造了三组公式,其中第一组公式成功地将不同高度上的重差测望问题转化为平面上一般的日高公式去处理,发展了刘徽的重差理论;第二组公式首次使中算典籍中出现了一般相似形问题;最后一组公式则提出了另一种测算太阳直径的方法。本文指出,由于李淳风等人对于"水平"概念的错误理解,使得盖天说的数学模型在当时的认识条件下接近"完善"。

The formula of solar altitude in Zhou Bi Suan Jing (The Arithmetical Classic of the Gnomon and the Circular Paths) was based on the model of a plane earth. Li Chunfeng and his colleagues pointed out that this formulas was inconsistent with its theory of hemispherical dome. Then they reconstructed 3 groups of formula which were based on the model of an earth inclining from north to south. The first group transformed the treatment of problems by a general formula of solar altitude, which developed Liu Hui's theory. It is interesting that they dealed with some general similar figures by the second group, which was the first time that such problems were discussed in ancient Chinese mathematical works. The last group gave a new method to measure the diameter of the sun, and this method was especially suitable for the moon and the stars. This paper shows that Li's revision made the mathematical model of hemispherical dome in Zhou Bi Suan Jing almost perfect.