中文摘要：

明安图是清代一位杰出的蒙古族数学家和天文学家，他去世后他的遗著《割圆密率捷法》，由他的学生在1774年完成，并且在1839年出版了这部著作．指出了明安图是世界上第一位卡塔兰数的发明人，他构建了一个几何模型，在这个几何模型中包含了用卡塔兰数作为系数的无穷级数．分析了明安图建立这些卡塔兰数所用的三个递推公式，其中的两个公式直到现在还没有被现代数学界认识．其独特的构造方法说明他具有卓越的数学才能．

英文摘要：

Ming Antu （16927 -17637） was an outstanding Mongolian mathematician and astronomer in the Qing Dynasty . His work Ge Yuan Mi Lu Jie Fa （Quick methods for trigonometry and for determining the precise ratio of the circle） was published in 1839, which was completed posthumously by his students in 1774. It is pointed out that Ming Antu was the first inventor of Catalan numbers in the world . He constructed one geometric model. in which some infinite series with Catalan numbers as coefficients were contained. An analysis on Ming Antu＇s three recurrence formulae of establishing these numbers is given, two of which have not been revealed to the modern maths field up till now. His methods are of structural characteristics and they demonstrate his great intelligence and superb techniques.