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

which is called Lobachevsky's formula.

**References**

Manning, H. P. *Introductory Non-Euclidean Geometry.* New York: Dover, p. 58, 1963.

© 1996-9

1999-05-25