When it is said that Descartes was the inventor of analytical geometry, the impression is often given that by Cartesian Geometry is simply meant a system in which the position of a point is determined by means of its coordinates referred to two fixed straight lines, either at right angles or oblique. A little consideration shows us that it is not correct to say that this system was invented by Descartes, as we find that Apollonius, Bk. V, Prop. 52, gives the values of the coordinates of the centre of curvature of a point on a conic referred to two rectangular axes. It will no doubt interest the readers of the Mathematical Gazette to know what is was that Descartes invented, and what led him to it.