does euclid's fifth postulate imply the existence of parallel lines
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In the fifth postulate its mentioned only for their intersecting and being farther
not for being parallel. ..
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yes it does
If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.
The fifth postulate refers to the diagram on the right. If the sum of two angles A and B formed by a line L and another two lines L1 and L2 sum up to less than two right angles then lines L1 and L2 meet on the side of angles A and B if continued indefinitely.
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