...conflict with Proposition I of Lobatschewsky's Theory of Parallels. Says the Russian Pangeoraeter—"A straight line fits upon itself in all its positions....two points of the line, the line does not move)." These statements can not be made of any arc of any circle, and, hence, can not be made of Riemannian...

...and quite a number of the initial theorems. He defines the straight line in an original way saying: "A straight line fits upon itself in all its positions....two points of the line, the line does not move)." Now it is one thing to give us an idea of an object and quite another to so define it that its essential...

...multitode of those theorems whose proofs present no difficulties, 1 prefix here only those of which a knowledge is necessary for what follows. 1. A straight...through two unmoving points in the surface: (ie, if we torn the surface containing it ahout two points of the line, the line does not move.) 12 THEOEY OP...

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...conflict with Proposition I of Lobatschewsky's Theory of Parallels. Says the Russian Pangeometer — "A straight line fits upon itself in all its positions....two points of the line, the line does not move)." These statements can not be made of any arc of any circle, and, hence, can not be made of Riemannian...