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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, Descartes'' theorem, named after René Descartes, establishes a relationship between four kissing, or mutually tangent, circles. The theorem can be used to construct a fourth circle tangent to three given, mutually tangent circles. Geometrical problems involving tangent circles have been pondered for millennia. In ancient Greece of the third century BC, Apollonius of Perga devoted an entire book to the topic. Unfortunately the book, which was called On Tangencies, is not among his surviving works.