同文馆毕业生杨兆鋆及其数学工作

【作者】 王全来；

【导师】 李兆华；

【作者基本信息】 天津师范大学 ， 科学技术史， 2001， 硕士

【摘要】 杨兆(均金)，字诚之，号须圃，浙江乌程人。咸丰四年(公元1854年)生，卒年界 于民国五年(公元1916年)到民国二十年(公元1931年)间。同治六年(公元1868 年)入上海广方言馆学习，同治十年(公元1871年)由两江总督曾国藩第二次咨 送到京师同文馆英文馆学习。光绪五年(公元1879年)，杨兆(均金)毕业后升迁出馆， 任苏松太道公署翻译。光绪十年(公元1884年)，随许景澄公使出洋。归国后，被 以道员身分发江苏补用。 光绪十九年(公元1893年)，杨兆(均金)任金陵同文馆教习，兼授算学。光绪二十 三年(公元1897年)，任江南储材学堂督办。光绪二十八年(公元1902年)，以“江 苏候补道赏四品卿衔差”任出使比利时钦差大臣。光绪三十一年(公元1905年) 被召回国。 杨兆望于光绪二十四年(公元1898年)自撰《须曼精庐算学》二十四卷，除此 之外，据《清艺文志补编》所载，杨氏还撰有《杨须圃出使奏议》。 从《须曼精庐算学》二十四卷的内容来看，除卷一“椭曲同诠”和卷二“抛摆 致用”外，其余各卷的类型问题均可在《同文馆算学课艺》中找到源头。在学习算 学的过程中，杨氏还对一些内容进行过认真思考，颇有心得，尽管其思考所得之结 果远不能与清末从事数学研究、翻译的数学家相比。在《须曼精庐算学》中，杨氏 最具代表性的工作为 1.关于测量方法的研究。杨氏不拘泥于“勾股测量”和“三角测量”法，巧妙 地把四面体理论应用于测量之中，提出了所谓的“四面体测量”法。 2.关于圆锥三曲线问题的研究。杨氏虽没有提出新的命题，但其综合应用《圆 锥曲线说》中的知识，对《圆锥曲线说》中的部分命题给出了自己的证明方法。杨 兆(均金)继李善兰求椭圆焦点的作图问题之后，独立提出和研究了求双曲线焦点的作图 问题。 3.关于平圆容切问题的研究。杨氏虽未正确解诀阿波罗尼圆和“弧矢形上求相 切二圆心”的作图问题，但是其提出并解决了其它关于圆与圆之间的作图问题。“平 圆容切”是中算史上第一部专论圆与圆之间相容的作图问题的著作。 4.关于“垂线诸求”及“勾股容方”问题的研究。杨氏在《同文馆算学课艺》 的基础上，完善了由勾股十三事、中垂线，求勾、股、弦问题。他在“勾股容方” 中探讨了三种特殊的勾股形内容长方问题的作图，并对勾股形内容长方四事求解问 题进行了研究。 杨兆(均金)的数学工作也深受李善兰的影响，最具典型的代表是“勾股容三事” “测圆海镜”和“椭圆作图”及“抛摆致用”中求射程、射角问题。 杨兆(均金)是洋务教育中所培养的众多人才之中的杰出代表，他不仅精通外交，而 且对算学亦有一定的研究。通过对杨兆望数学工作的介绍，我们可以看出，杨氏所 撰《须曼精庐算学》这部富有心得的数学著作对了解清末数学的发展具有重要意义， 对客观评价京师同文馆的数学教育亦有一定的价值。更多还原

【Abstract】 Yang Thaojun was born in Wucheng County (now Huzhou City), Zhejiang Province in the fourth year of the reign of Emperor Xianfeng (i.e. 1854 A.D.). He styled himself Chengzhi. His alternative name was Xupu.He died during the period from the fifth year (i.e.1916 A.D.) to the twentieth year of Mingguo.He went to school at Shang Hal Guang Fang Yan Kuan in the sixth year of the reign of Emperor Tongzhi (i.e.1868 A.D.). He was sent for English Kuan in Jing shi Tong Wen kuan to learn by Zeng Guofan who acted as a president in the region, including Jiangxi, Jiangsu and Anhui in the tenth year of the reign of Emperor Tongzhi (i.e.1871 A.D). He became a translator of Su Song Dai Dao department after graduating in the fifth year of the reign of Emperor Guangxu (i.e.1879 A.D.). He followed Xu Jingcheng (1845 A.D.? 900 A.D.) to go to overseas as a retinue in the tenth year of the reign of Emperor Guangxu (i.e.1884 A.D.). After many years, he came back and was a candidate bestowed Dao Yuan in Jiangsu Province. Yang Zhaojun was a mathematic teacher at Jin Ling Tong Wen Kuan in the nineteenth year of the reign of Emperor Guangxu.He turned surveillance at Jiang Nan Chu Cal Xue Tang in the twenty-third year of the reign of Emperor Guangxu (i.e.1897 A.D.). After five years, he was an ambassador of Chinese embassy in Beljium. He was asked to come back in the thirty-first year of the reign of Emperor (1uangxu (i.e. 1905 A.D.). His work on mathematics was Xu Man Jing Lu Suan Xue (24 volumes total) written in the twenty-fourth year of the reign of Emperor Guangxu (i.e.l898 A.D.). In addition, he still wrote Yang Xu Pu Chu Shi Zou Yi according to Qing Yi Wen Zhi Bu Bian. The typical problems of other volumes derived from Tong Wen kuan Mathematical Exercises except the first volume "Tuo Qu Tong Quan"and the second volume" Pao Bai zhi Yong" During his learning mathematics, Yang Zhaojun meditated some mathematic problems and got a few new results. These results were not important in view of mathematicians who engaged in studying and translating mathematics. The paper analyzes and studies four aspects of Yang’s mathematical work. These are 2 The paper analyzes and studies four aspects of Yang抯 mathematical work. These are as follows. 1. The research on the measurement methods. Yang put forward?tetrahedron measurement?method by himself after he studied the two methods, which included 搑ight triangle measurement?and 搃nclined triangle measurement? He felicitously applied some tetrahedron theories to the measurement. 2. The research on ellipse, hyperbola and parabola. Yang attested some propositions in Conics by his own proof methods although he advanced few new propositions. Li Shanlan who was a lead teacher at Jing Shi Tong Wen kuan solved many construction problems of elliptical focal points. After that time ,Yang zhaojun studied and propounded a few construction problems of hyperbolic foci. 3. The research on the geometric construction problems of contact of circles. Yang couldn抰 correctly resolve Apollon抯 circles and 揻inding a center of one circle which circumscribed the other. They both contacted a determined chord of circular segment and their centers were in this circular arc? However, he studied and resolved, other construction problems of contact of circles. Yang抯 Ping Yuan Rong Qie was the first treatise on this in the history of traditional Chine更多还原