The parallel postulate in Euclidean geometry is equivalent to the statement that , in two-dimensional space , for any given line R and point P not on R , there is exactly one line through P that does not intersect R ; i.e. , that is parallel to R . In hyperbolic geometry there are at least two distinct lines through P which do not intersect R , so the parallel postulate is false .
The parallel postulate in Euclidean geometry says that in two dimensional space , for any given line l and point P not on l , there is exactly one line through P that does not intersect l . This line is called parallel to l . In hyperbolic geometry there are at least two such lines through P . As they do not intersect l , the parallel postulate is false .