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中文摘要：
目的系统探讨和分析蒙日几何学派和高斯几何学派的微分几何思想。方法历史分析、比较研究和文献考证。结果曲面可以用立体的边界与孤立的二维薄膜两种方式验证。前者是制图工程师看待曲面的方式，属于蒙日几何学派的观点；后者是测地员考虑方式，属于高斯几何学派的观点。结论蒙日几何学派和高斯几何学派相辅相成，推动了微分几何的发展。
英文摘要：
Aim To systematically discuss and analyze Monge＇s and a Gauss＇s differential geometry thought. Methods Historic analysis and literature reviewed. Results Surface can be verified by means of boundary of solid and isolated two dimensional films. The former belongs to the view of Monge＇s differential geometry school and the latter is part of the view of Gauss＇s intrinsic geometry school. Conclusion The two schools supply each other and promote the development of differential geometry.
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