第五公设的证明带给我们的启迪

Inspirations drawn from the proof of the Fifth Postulate

在证明第五公设的过程中,直接证法提出了等价命题;萨开里开辟了一条通向非欧几何的途径——反证法;高斯是预见非欧几何的第一人;罗巴切夫斯基大胆地提出了反问题并敢于批判权威,标志非欧几何的诞生.可见,思维方式的转变可以打破惯性思维的束缚,开拓新天地.

In the process of proving the Fifth Postulate, people utilized the method of direct proof to present equivalent proposition. However, Sakali created an approach leading to non Euclidean geometry, namely, proof by contradiction. Gauss is the first person that foresaw non Euclidean geometry. Lobachevsky not only proposed inverse problem but was brave to question authority, which marked the formation of non Euclidean geometry. Therefore, the transformation of thinking mode can break the shackles of the inertia thinking so as to broaden new horizons.