论文标题
第五个假设在欧几里得建立相似之处中的作用
The Role of the Fifth Postulate in the Euclidean Construction of Parallels
论文作者
论文摘要
我们归因于欧几里得的第五个假设是真正的建设性角色，这使得在平行结构中绝对必要。为此，我们提出了欧几里得建造几何特性的基础的一般原则的重建。结果，揭示了欧几里得建构的认识论作用。我们还研究了我们的解释对欧几里得和非欧国人几何形状之间的关系的一些首要含义。从欧几里得的角度讨论了限制相似之处的Bolyai结构，因为这里重建了这一点。
We ascribe to the Euclidean Fifth Postulate a genuine constructive role, which makes it absolutely necessary in the parallel construction. For that, we present a reconstruction of the general principles underlying the Euclidean construction of a geometric property. As a consequence, the epistemological role of Euclidean constructions is revealed. We also examine some first implications of our interpretation to the relation between Euclidean and non-Euclidean geometries. The Bolyai construction of limiting parallels is also discussed from the Euclidean point of view, as this is reconstructed here.
