中文摘要：

明末《崇祯历书》将西方三角学知识传入中国，但其偏重应用和计算而缺乏论证．清初中算家在接受、学习的同时，逐一补证了缺少证明的公式、定理，逐步精简公式的证明与应用，并努力用适合的方法重构西方三角学．通过对中算家会通三角学过程的考察，发现清初中算家以会通中西为目的，以探寻数学内在原理、融合中西数学为己任，彰显出求真务实的科学精神．

英文摘要：

In the late Ming Dynasty, the West trigonometry was brought into China through Chong Zhen Li Shu,but it was emphasized on the application and calculation with lack of proofs. In the early Qing Dynasty ,the Chinese mathematicians accepted and learned the West trigonometric knowledge, meanwhile, they complemented the trigonometric formulas and principles which were short of proofs one by one. They simplified the proofs and application of the trigonometric formulas step by step. Also,the Chinese mathematicians tried their best to use the proper methods for the reconstruction of the western trigonometry. Based on the study of communication process of the Chinese mathematicians on the trigonometry in the early Qing dynasty,it is found out that Chinese mathematicians was to have the communication between Chinese and western mathematics as their goal, to explore the inherent principles of mathematics and to combine Chinese with western mathematics as their responsibility. Their work has manifested realistic and pragmatic Spirits.