邹伯奇关于日影观测“椭圆影心非日心”的数学解读  

A Mathematical Interpretation of Zou Boqi's Assertion on Solar Shadow Measurement that“The Center of the Projection Ellipse is Not the Shadow of the Sun's Center”

作　　者：廖运章[1] 李杰民 LIAO Yunzhang;LI Jiemin(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China;School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang 524048,China)

机构地区：[1]广州大学数学与信息科学学院,广州510006 [2]岭南师范学院数学与统计学院,湛江524048

出　　处：《自然科学史研究》2023年第4期405-417,共13页Studies in The History of Natural Sciences

基　　金：2019年度《广州大典》与广州历史文化研究资金资助重点项目“晚清广州本土学者微积分著述的整理与研究”(项目编号:2019GZZ04)。

摘　　要：元代郭守敬用装有景符的四丈高表测量日影,改测表端投影为测横梁投影,将“仅如米许”的太阳像中心视为日面中心。《崇祯历书》认为太阳透过小孔斜射到密室地面的投影是椭圆,此后天文学家都认为椭圆光影之中心即太阳中心的投影。1844年前后,邹伯奇发现“椭圆影心非日心”,并从数学上予以解读,其说因未刊行而迄今少为人知。邹伯奇这一成果,是郭守敬圭表测影理论的完善,为日影测量之误差分析等提供了新判据,对圭表测影研究亦具有重要意义。During the Yuan dynasty,Guo Shoujing(郭守敬)greatly improved gnomon shadow measurement.One of the improvements he made was measuring the projection of the beam instead of the top of the gnomon.For a long time,people then mistakenly thought that the center of the projected ellipse was the shadow of the Sun's center.What is not previously known is that around 1844 Zou Boqi(邹伯奇)pointed out this mistake and the correct position of the shadow of the Sun's center.In this paper,through a study of the contents concerning“the center of the projected ellipse is not the shadow of the Sun's center”,Zou's research conclusion is refined as follows:the measuring location of the“old method”is on the left,and“Gou Shoujing's method”is on the right,“Zou Boqi's meth-od”pursues the real position;in addition,we have derived the mathematical formula of the length of the sundial shadow;and finally the application of Zou's research conclusion on the error analysis of solar shadow measurement is given.All in all,Zou's work is not only the theoretical perfection of Guo Shoujing's work on gnomon shadow measurement,but also provided a new important criterion for error analysis in the study of solar shadow measurement.His work is thus of great significance to the study of gnomon shadow measurement.

关 键 词：邹伯奇 日影测量 椭圆影心非日心 数学解读 

分 类 号：N092[自然科学总论—科学技术哲学]