公式还是立成表:中国古代历法家的数学思维方式

Formula or Li Cheng Biao:the Mathematical Thinking Mode of the Ancient Chinese Calendar Makers

唐代以后历法制定呈现公式化趋势,但在实际天文计算中并未直接使用公式,而是有意识地构造并使用了各类立成表。文章以宋《观天历》中任意时刻太阳改正项算法为例,说明中国古代历法家构造公式用以阐理,同时编排立成表用于实际计算。研究表明,历法家一方面重视公式构造理论上的推陈革新,另一方面对复杂算法公式的实践性与可操作性也有明确的应对策略,坚持公式化与公式算表化并重。

Since the Tang Dynasty,the Calendar showed a formalized trend while the algorithm formulae were not used directly in the actual astronomical calculation,but they have consciously constructed and used various of Li Cheng Biao.Taking the algorithm of solar equation of center in Guantian Li in the Song dynasty as an example,the paper illustrated the historical fact that the formula is used to explain the Aufbau Principle and Li Cheng Biao for actual calculation simultaneously.The research showed that the ancient Chinese calendar makers attached equal importance to the formulation and tabulation of formula.On the one hand,they emphasized on formulaic algorithm,and on the other hand,they constructed Li Cheng Biao to deal with the practicality and operability of complex algorithm formulas.