Published online by Cambridge University Press: 03 November 2016
It is well known that a curve has only one equation in Cartesian co-ordinates When referred to a given pair of lines as axes, but it does not appear to be so well known that a curve can have many equations in polar co-ordinates, all referred to the same pole and initial line. This fact, although of considerable importance in the study of curves by means of their polar equations, appears to be consistently ignored by most text-books.