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

This is known as Lobachevsky's Formula.

**References**

Manning, H. P. *Introductory Non-Euclidean Geometry.* New York: Dover, pp. 31-32 and 58, 1963.

© 1996-9

1999-05-25