...as for example, "We must allow two parallels, one on the one and one on the other side" (page 292). "Under this assumption we must also make a distinction of sides in parallelism" (page 292). "The farther parallel lines are prolonged on the side of their parallelism, the more they...

...other side of the perpendicular from A will lie also a line AM, parallel to the prolongation DC' of DC, so that under this assumption we must also make a distinction of sides in parallelism." This sensed relation then is Lobatchevsky's parallelism, and that it is a sensed relation, a one-sided...

...intersect the line BC. If fl (p) < £ -, then upon the other side of AD, making the same angle DAK = fl (p) will lie also a line AK, parallel to the prolongation...assumption we must also make a distinction of sides in parnllelism. 14 THEOEY OF PAEALLELS. All remaining lines or their prolongations within the two right...

...intersect the line BC. K' If n(p) < jjr,5 then upon the other side of AD, making the same angle DAK = H(p) will lie also a line AK, parallel to the prolongation...those that intersect, if they lie within the angle HAK = 2U(p) between the parallels; they pertain on the other hand to the non-intersecting AG, if they lie...

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...H(p) for AD = p. If n(p) is <!/27t, then upon the other side of AD, making the same angle DAK = Yl(p) will lie also a line AK, parallel to the prolongation...must also make a distinction of sides in parallelism. Because of the fact that the diagrams can contemplate only finite parts of straight lines it is easy...

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