Answer
In Euclidean geometry, the geometry is on the plane while in elliptic geometry, the geometry is on a sphere. In Euclidean geometry, a basic assumption states that if there is a given line and a point is taken which is not on that given line, only one line can be drawn parallel to the given line.
Passing through that particular point while in hyperbolic geometry, it is assumed that given a point not on a line, there is an infinite number of lines through the point that does not intersect the given line.
