A Treatise on the Circle and the Sphere

It was written by Julian Coolidge, and published by the Clarendon Press in 1916.

[7] As is now standard in inversive geometry, the book extends the Euclidean plane to its one-point compactification, and considers Euclidean lines to be a degenerate case of circles, passing through the point at infinity.

Another key tool used by the book are the "tetracyclic coordinates" of a circle, quadruples of complex numbers

describing the circle in the complex plane as the solutions to the equation

[5] At the time of its 1971 reprint, it was still considered "one of the most complete publications on the circle and the sphere", and "an excellent reference".