综合几何 meaning in English

synthetic geometry

As we all known , with the founding of euclidean geometry in ancient greece , with the development of analytic geometry and other kinds of geometries , with f . kline " s erlanger program in 1872 and the new developments of geometry in 20th century such as topology and so on , man has developed their understand of geometry . on the other hand , euclid formed geometry as a deductive system by using axiomatic theory for the first time . the content and method of geometry have dramatically changed , but the geometry curriculum has not changed correspondingly until the first strike from kline and perry " s appealing
纵观几何学发展的历史，可以称得上波澜壮阔：一方面，从古希腊时代的欧氏综合几何，到近代解析几何等多种几何的发展，以及用变换的方法处理几何的埃尔朗根纲领，到20世纪拓扑学、高维空间理论等几何学的新发展，这一切都在不断丰富人们对几何学的认识；另一方面，从欧几里得第一次使用公理化方法把几何学组织成一个逻辑演绎体系，到罗巴切夫斯基非欧几何的发现，以及希尔伯特形式公理体系的建立，极大地发展了公理化思想方法，不管是几何学的内容还是方法都发生了质的飞跃。