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总览 评价 董杰 ， 郭世荣 * （ 内蒙古师范大学科学技术史研究院，呼和浩特 010022； ） 摘要： 在文献梳理的基础上，认为《大测》《测量全义》分别将欧洲玉山若干、芬克的正切定理介绍到中国。采用纵贯比较的研究方法，对清初正切定理的表达方式与几何证明
董杰， 郭世荣*
（
内蒙古师范大学科学技术史研究院，呼和浩特 010022； ）
摘要：
在文献梳理的基础上，认为《大测》《测量全义》分别将欧洲玉山若干、芬克的正切定理介绍到中国。采用纵贯比较的研究方法，对清初正切定理的表达方式与几何证明方法进行考察。结果认为，清初中算家对正切定理的研究各不相同，但遵循着证明更为简洁、计算更加方便的演变历程。对原理与便捷的追求是促使清初正切定理研究演变的内在动因，而将西方三角学化为中国传统勾股的范围中，则是这一演变重要的外在因素。
关键词：
正切定理；演变；动因；清初
DONG Jie1,， GUO Shirong2,*
（
1、Institute for the History of Science and Technology, Inner Mongolia Normal University, Huhhot 010022； 2、Institute for the History of Science and Technology of Inner Mongolia Normal University, Hohhot,010022； ）
Abstract：
The late of Ming Dynasty, chongzhenlishu (The Chong zhen Reign Treatise on Astronomy and Calendrical Science) brought the West trigonometry into China. On the basis of literature searching, we think that the Dace (Great Measurement) and Celiang Quanyi（The Complete Theory of Surveying）respectively introduced the geometric proof of the law of tangents of Regiomontanus and Thomas Fincke into China. Using longitudinal comparative research methods, we inspected the expression of the tangent and geometry theorem proving method during early Qing Dynasty. We get the results that the Chinese mathematicians' study on the theorem of tangent was different, but they followed the evolution process of more simple proof and more convenient calculation. The pursuit of principle and convenience was intrinsic motivation that urged the evolution of the study of the tangent theorem. On the other hand, the fusion of western trigonometry into Chinese traditional Pythagorean was important external factors of the evolution.
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