Infinitesimal Methods in the Works of Thabit ibn Qurra and L, Euler in Spherical Trigonometry

作     者：Golikova N.G. Al-Dabbagh J.J. 

作者机构：Department of Higher Mathematics Moscow A cadamy of city Economy and Building Lyusinovskaya 43 app. 116 Moscow 115093 Russia 

出 版 物：《Journal of Mathematics and System Science》 (数学和系统科学（英文版）)

年 卷 期：2013年第3卷第8期

页      面：381-384页

学科分类：07[理学] 08[工学] 080203[工学-机械设计及理论] 0802[工学-机械工程] 0712[理学-科学技术史(分学科，可授理学、工学、农学、医学学位)] 

主　　题：L.Euler lbn Qurra spherical trigonometry infinitesimals 

摘      要：In one of his astronomical works the prominent arabic medieval scientists Thabit ibn Qurra （836-901） studied the visible motion of the Sun and found the points, where its velocity is maximum or minimum. He also lbund the points on the ecliptic, where this velocity is equal to the average velocity of the Sun over all the ecliptic. For this purpose he used the idea of infinitely small arcs and their ratios in different points of the circle. The great scientist Leonard Euler （1707-1783） introduced in his works on spherical trigonometry the line-element ds of the surface of the sphere, i.e. the differential of the arc length. He constructed the spherical trigonometry as an inner geometry on the surface of the sphere. He replaced the trigonometry lines, which were in use befbre him, by trigonometric functions.