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中文摘要：
目的系统分析和探讨非欧几何诞生的两种思想。方法运用文献考证和历史分析的方法对非欧几何诞生的两种思想进行研究。结果非欧几何诞生的两种重要思想分别是欧氏第五公设研究和运用微分几何研究；前者利用无模型观点直观揭示了非欧实质，后者以模型为依据不但利于人们理解和接受，而且产生了更一般的非欧几何。结论两种思想研究的结合，使非欧几何真正诞生和快速发展，实现了非欧几何与欧氏几何的统一，为空间概念的扩展创造了必要条件。
英文摘要：
Aim To analyze and discuss systematically two thoughts causing the birth of Non-Euclidean geometry. Methods Literature reviewed and historic analysis. Results The two important thoughts causing the birth of Non- Euclidean geometry were the fifth axiom research of Euclidean and the application of Differential geometry research ; the former, from free-model point of view reveals the essence of Non-Euclidean geometry, the latter, based on models, not only promotes people to understand and accept it but also generates a more general Non-Euclidean geometry. Conclusion The combination of two thoughts makes the Non-Euclidean geometry emerge and develop rapidly, achieves the unity of Non-Euclidean geometry and Euclidean geometry and creates necessary conditions for the extension of space concept.
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