Parallel Lines Never Intersect Quotes

[Euclid's] second postulate, for example, says that any line segment may be extended indefinitely. That is difficult for even the most querulous to argue with. The fifth, on the other hand, states that if two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side (labelled a and b in the diagram below) is less than two right angles (i.e. 180°), then the two lines inevitably must intersect each other on that side if extended far enough. If, on the other hand, a and b do add up to 180°, the two lines never meet so are said to be parallel. To mathematicians, that looks less like a postulate and more like a theorem in need of proving.