P is the point on the line A B such that (P A)^_/(P B)^_ = 1. It can also be thought of as the point of intersection of two parallel lines. In 1639, Desargues became the first to consider the point at infinity (Cremona 1960, p. ix), although Poncelet was the first to systematically employ the point at infinity. A point lying on the line at infinity is a point at infinity. In particular, a point with trilinear coordinates α:β:γ is a point at infinity if it satisfies a α + b β + c γ = 0. Points at infinity therefore do not have exact trilinear coordinates.

circular point at infinity | complex infinity | line at infinity