1·The phenomenal world, that is the world that we experience must, for example, satisfy the exhumes of Euclidean geometry.
现象世界，也就是我们所感知的世界，必须符合欧几里德几何学的发现。
2·Right triangles and Euclidean norms
直角三角形和欧几里德范数
3·Two-and three-dimensional Euclidean Spaces are metric Spaces as are inner product Spaces vector Spaces and certain topological Spaces.
二维和三维的欧几里德空间是度量空间。另外，内乘空间、向量空间以及某些拓扑空间等也都是度量空间。
4·Two-and threed imensional euclidean spaces are metric spaces as are inner product spaces vector spaces and certain topological spaces.
二维和三维的欧几里德空间是度量空间。另外，内乘空间、向量空间以及某些拓扑空间等也都是度量空间。
5·She would see the same number of rulers involved as did observer a, and so would likewise conclude that the ratio of circumference to radius did not conform with Euclidean geometry.
她将看到和观察者A一样数量的尺子。所以同样的，将可以做出这样的结论：圆周和半径的比率将和欧几里德几何不一致。