# Spherical Geometry and Playfair's Axiom.

Recently I came across a variant of the Parallel Postulate known as Playfair's Axiom:

In Euclidean (planar) geometry there is at most one line that can be drawn parallel to another given one through an external point.

However, in the case of spherical geometry there exists no such line which can be drawn parallel.

I am having a doubt in this concept. Because if the surface is spherical in nature, then there always will be a point a diametrically opposite on the surface from where a parallel line can be drawn. So, why is it not taken into consideration or if it is then, am I missing an important concept?

• @durwasa.chakraborty I don't understand what you mean. What does it mean to be diametrically opposite to a line L? If you take a point $p$ and draw a great circle through it, the point diametrically opposite to $p$ is guaranteed to lie on it. – user7530 Jun 12 '15 at 15:21