We extend the proposal that the rows of the magic square can be regarded as a series. We show that the first and fourth rows lie in a projective plane and that the formulae for the quadratic Casimir and the dimension formulae extend to this plane. A new result is that this plane contains two lines whose points correspond to six symmetric pairs. There are also two degenerate lines. We give universal formulae for the values of the quadratic Casimir and for the dimensions. The dimension formulae are obtained in [13].