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Studies in the History of Natural Sciences  2021, Vol. 40 Issue (2): 194-217    DOI:
ARTICLES     
Preliminary Research on Zhou Shuxue's Knowledge of Cewang
QU Zhaohua
Institute for the History of Natural Sciences, CAS, Beijing 100190, China;
University of Chinese Academy of Sciences, Beijing 100049, China
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Abstract  Lizong suanhui (历宗算会, Assembly of Mathematical Methods Connected with the Calendar) is a traditional Chinese mathematical work compiled by Zhou Shuxue (周述学), a famous scholar of the Ming Dynasty. The features of the interpretation and organization of cewang (测望,method of surveying distant bodies) problems in this book deserves our attention. However, these features have rarely attracted the specific attention of prior researchers. This paper conducts a relatively detailed analysis on this, pointing out that Zhou Shuxue used the principle of rongheng rongzhi (容横容直, inscribed horizontal and vertical rectangles) based on the principle of churu xiangbu (出入相补, out-in complementary) contained in related proofs and figures in Yang Hui's (杨辉) mathematical book as the basis of his understanding of a series of methods of cewang. He reclassified the corresponding problems into several grand classifications of danbiao cewang (单表测望, measuring with single rod), chongbiao zaiwang (重表再望, measuring with two equal rods), chongju ceshen (重矩测深, measuring the depth of something with two trisquares), sanwang (三望, measuring three times) and siwang (四望, measuring four times) etc., uniformly naming these classifications with measuring tools plus the conditions of the solving methods. He also reorganized each type of problem above into smaller classifications: whether or not the height of the surveyor's eye is 0, zheng ceguang (正测广, surveying the width in vertical direction) and xie ceguang (斜测广, surveying the width in oblique direction), and surveying one point and two points, etc.. Compared to those of Gu Yingxiang (顾应祥), Zhou's classifications of these problems were more rational, and the names of these classifications given by him were more unified, which indicated his deeper understanding of the problems and methods of cewang.

Key words： cewang (测望,method of surveying distant bodies)      Lizong suanhui (历宗算会, Assembly of Mathematical Methods Connected with the Calendar)      Zhou Shuxue (周述学)      the middle and late Ming Dynasty      Gu Yingxiang (顾应祥)      Yang Hui (杨辉)     
Received: 31 December 2020      Published: 27 January 2022
ZTFLH:  N092  
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QU Zhaohua. Preliminary Research on Zhou Shuxue's Knowledge of Cewang. Studies in the History of Natural Sciences, 2021, 40(2): 194-217.

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http://www.shns.ac.cn/     OR     http://www.shns.ac.cn/Y2021/V40/I2/194

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