浑天说数理模型的构建尝试与失败——以祖暅《浑天论》为中心

Attempts and Failures to Construct a Mathematical model of the Theory of the Spherical Heavens:Centered on Zu Geng's Huntian Lun

文章重点考证了汉魏以来400年间浑天说数理模型的构建过程。张衡首先对浑天说进行数理描述,但是他的数据缺少测算依据。王蕃基于古代测算原理给出“天高数”和“周天里数”,不失为一次有效的数理探索。祖暅认同王蕃的两个数据和方法,同时补充了冬至、春秋分的相关数据及北极高数等。基于此,笔者尝试复原浑天说数理模型。文章讨论了祖暅应用他的浑天模型解释日月直径关系、四季寒暑成因、测地中之法等的原理,其中不乏个人创造和模型严谨化的趋势。祖暅及其先人的构建尝试与思想实践非常可贵,但是由于其依据“日影千里差一寸”旧制以及王蕃“天高数”遭到一行否定,浑天说数理模型的探索最终以失败而告终。

On the basis of historical materials,this paper focuses on the process of the development of the mathematical model of the theory of the Spherical Heavens in the 400 years following the Han Dynasty.Zhang Heng(张衡)was the first to describe the theory,but his data lacks the basis for calculation.That Wang Fan(王蕃)worked out the“height of heaven”and“perimeter of heaven”on the basis of the ancient theory of measurement was an effective exploration in mathematics.Zu Geng(祖暅)adopted Wang Fan's numerical values and methods and supplemented other related values of the winter solstice,spring and autumn equinox and altitude of the north celestial pole.This paper attempts to re-construct its mathematical model.Moreover,the paper discusses that using the mathematical model Zu Geng interpreted the diameter of the sun and moon,the causes of the four seasons,and a method of measuring the center of the earth.Zu Geng's method demonstrates his personal creativity and the precision of the model.The endeavors and thought process of Zu Geng and his predecessors are valuable.Due to the fact that the“one cun(寸)for a thousand li(里)”shadow principle and Wang Fan's“height of heaven”were rejected by Yixing(一行),the exploration of the mathematical model of the theory of spherical heavens ended in failure.