...几何 ；“第五公设”；历程 ；启示 [gap=572]Key words: non-Euclidean geometry; Euclidean geometry; “The fifth postulate”; process; Inspiration.
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We introduce the Lobachevskian geometry and the Ricmanian geometry by proving the Euclidean of the fifth postulate.
通过对欧氏第五公设的试证，引入罗氏几何与黎氏几何。
Depending only on formal thinking, Euclid formed system through figure proof, firstly applied the fifth postulate in the 29th proposition.
欧几里德仅仅依靠形式思维，通过图形佐证形成体系，在第29个命题中首先运用第五公设。
By replacing the fifth postulate in the preceding paper with the condition of spherical symmetry of space we again obtain the Friedmann universe in relativistic cosmology.
将前文中第五个假定改为“空间具球面的对称性”后我们仍遵出费烈特猛宇宙。
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