 EE', all others, if they are sufficiently produced both ways, must intersect the line BC. If !!(/>) < -JTT, then upon the other side of AD, making the same angle KAD = H(p), will lie also a line AK, parallel to the prolongation DB of the line DC, so that...  Geometrical Researches on the Theory of Parallels - Side 3av Nikolaĭ Ivanovich Lobachevskiĭ - 1891 - 50 siderUten tilgangsbegrensning - Om denne boken
 | Paul Carus - 1909 - 682 sider
...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... | |
 | Paul Carus - 1910 - 702 sider
...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... | |
 | Roberto Bonola - 1955 - 452 sider
...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... | |
 | Reinhard Laubenbacher, David Pengelley - 2000 - 292 sider
...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... | |
 | Lorenzo Magnani, N.J. Nersessian - 2002 - 432 sider
...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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