In these days of examinations and syllabuses it is perhaps not superfluous to remind teachers of the maxim that they ought to teach more than their pupils need to learn. To be an expert on circles it is necessary to study other conics, and to appreciate homographies it is as well to know something about other correspondences.

The ideas of correspondence and characteristics of systems of conics are due to the French mathematician Chasles (c. 1850) and a large collection of illustrations of these subjects may be found in T. Lemoyne's Les Lieux Géométriques (Vuibert, 1923). These illustrations include, though in a summary form, the subject of the present article. Reference may also be made to the last example in C. Taylor's Ancient und Modern Geometry of Conics, and to a note in Salmon's Conic Sections.