...rat Svo rvOttas cV avupov aiynriirrct)', itf> a /«'fj»; curif at rwv Suo op$u>v cAaaxrom. 7/fa/, »/"a straight line falling on two straight lines...on that side on which are the angles less than the ht'fl right angles. Although Aristotle gives a clear idea of what he understood by a postulate, he...

...by Euclid in his Postulate 5 as follows : " If a straight line falling on two straight lines makes the interior angles on the same side less than two...which are the angles less than the two right angles." This is a consequence of our assumption, for let the rays AC and BD be such that the sum of the ~k...

...by Euclid in his Postulate 5 as follows : " If a straight line falling on two straight lines makes the interior angles on the same side less than two...which are the angles less than the two right angles." This is a consequence of our assumption, for let the rays AC and BD be such that the sum of the angles...

...modern scholars. 5. That, if a straight line falling on two straight lines make the interior angle on the same side less than two right angles, the two...which are the angles less than the two right angles. This famous postulate, long since abandoned in teaching the beginner in geometry, is a remarkable evidence...

...straight line falling on two straight lines make the interior angle on the same side less than two rigfd angles, the two straight lines, if produced indefinitely,...which are the angles less than the two right angles. This famous postulate, long since abandoned in teaching the beginner in geometry, is a remarkable evidence...

...on two straight lines makes the interior angles on the same side less than two right angles, the two lines, if produced indefinitely, meet on that side on which are the angles less than two right angles." Under the term non-Euclidean geometry we shall understand a system of geometry which...

...fulling on two straight lines make the interior an; lie on the same side less than two right iinylefs, the two straight lines, if produced indefinitely, meet on that side on ivhich are the angles less than the two right angle s. This famous postulate, long since abandoned...

...hoheren Standpunkte aus (Leipzig, 1909), Bd. 2, p. 884. 2007. Euclid's Postulate 5 [The Parallel Axiom]. That, if a straight line falling on two straight lines...which are the angles less than the two right angles. — EUCLID. The Thirteen Books of Euclid's Elements [TL Heath] Vol. 1 (Cambridge, 1908), p. 202. 2008....

...fourth asserts the equality of all right angles, and the fifth is the famous ParallelPosfculate : " If a straight line falling on two straight lines make...meet on that side on which are the angles less than two right angles." 3. Attempts to prove the parallel-postulate. It seems impossible to suppose that...

...falling on two straight lines make the interior angles on the same side less than two right ingles, the two straight lines, if produced indefinitely,...meet on that side on which are the angles less than two right angles." 3, Attempts to prove the parallel-postulate. It seems impossible to suppose that...