Given a point and a Line , draw the Perpendicular through and call it . Let
be any other line from which meets in . In a Hyperbolic Geometry, as moves off to infinity
along , then the line approaches the limiting line , which is said to be parallel to at .
The angle which makes with is then called the angle of parallelism for perpendicular
distance , and is given by
See also Hyperbolic Geometry, Lobachevsky's Formula
References
Manning, H. P. Introductory Non-Euclidean Geometry. New York: Dover, pp. 31-32 and 58, 1963.