1) the parallel axiom (Euclid)
欧氏平行公理
1.
The article proves sine rule and that vertical line of a line crosses its slant lines are both equivalent for the parallel axiom (Euclid) on the combined axiom; the sequence axiom; the repeatability axiom; the continuity axiom (the axiom system of Hilbert), so they are equivalent for each other .
在结合公理Ι1-8,顺序公理Ⅱ1-4,合同公理Ⅲ1-5和连续公理Ⅴ1-2(这里采用希尔伯特的公理体系)的基础上证明了正弦定理、一条定直线的垂线和斜线一定相交与欧氏平行公理是等价的,进一步证明论题。
2) axiomatic approach in mathematics
欧氏公理化方法
3) parallel axiom
平行公理
1.
The paper introduces the "parallel "relation in the geometry defined by the axiom system of projective geometry,then changes accidence axiom I8 for "parallel axiom",and obtains a new geometry-affine geometry.
在公理化方法定义的几何中引进“平行”关系,然后把结合公理I_8改成“平行公理”,我们就得到一种新的几何——仿射几何。
4) Euclidean plane
欧氏平面
1.
According to the character of the optimal tour of Euclidean plane TSP problem, the sub-path and related notions are presented.
根据欧氏平面TSP最优环路的性质提出了子路径及相关的概念,利用点集凸壳设计了环路构造算法,并以点集Delaunay三角剖分图为启发信息设计了改进的遗传算法,通过中国144城市TSP等验证了算法的有效性。
5) Euclidean geometry without continuity
无连续公理欧氏几何
6) euclid parallel postulate
欧几里得平行公设
补充资料：平行公理
hilbert的《几何基础》的五组公理之一：
平行公理
v 通过直缐外一点至多可引一直缐平行於该直缐。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条