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中文摘要：
中国古代天文学家设计的食分算法与食限的大小及定义方式密切相关，而后者又受到月亮视差的影响，因此，传统历法中日食食分的计算是一个比较复杂的问题。中国古代天文学家将日食食限定义为日食视食甚时刻视月亮到视黄白交点的距离，使得他们所设计的日食食分算法具有明晰的天文意义。在论述中国历法家对日食食限的定义方法以及基于这种定义而给出的简明的日食食分算法的基础上，将中国古代日食食限与食分算法的历史沿革划分为三大阶段。
英文摘要：
The magnitude of solar eclipse is an important item in mathematical astronomy in ancient China. The algorithm of solar-eclipse-magnitude designed by Chinese astronomers is not only related to the limit of solar eclipse but also to the lunar astronomers. According to Chinese astronomers after the 8th century, the solar eclipse limit had been taken as the distance between the apparent moon and the apparent node of solar and lunar orbit at the moment of the middle eclipse. Based on this definition, a beautiful model of the algorithm of solar-eclipse-magnitude was designed by Chinese calendar-makers. This paper shows that the astronomical meaning of the said model is clear and correct.
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