Casey’s Treatise on analytical geometry

John Casey’s Treatise on the analytical geometry of the point, line, circle and conic sections is a book from the end of the 19th century gathering a wide range of results and constructions in plane geometry known at those times. The Bibliothèque Nationale de France gives free access to a digitized version of the book (see there).

The book begins with the definitions of classical coordinate systems: cartesian coordinates, polar coordinates, projective homogeneous coordinates (which were then dubbed trilinear or barycentric). Casey has no taboo concerning points of the field of complex numbers: in particular, many statements make use of cyclic points or zero-radius circles. Much further into the book, the author introduces projections and perspectives, as well as quadratic cones, and harmonic divisions.