Книга: Problem of Apollonius: Euclidean Geometry, Circle, Tangent, Apollonius of Perga, Pappus of Alexandria, Adriaan van Roomen, Hyperbola, Compass and Straightedge Constructions, Franciscus Vieta

High Quality Content by WIKIPEDIA articles! n Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga (ca. 262 BC ? ca. 190 BC) posed and solved this famous problem in his work ?????? (Epaphai, 'Tangencies') this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them (Figure 2) and each solution circle encloses or excludes the three given circles in a different way.