 This example clearly illustrates how multiplication may be performed on lines, but its simplicity conceals a problem. Descartes’ predecessors regarded geometrical constructions of arithmetical operations in an extremely limited way: due to the fact that in geometry there are only three spatial dimensions, multiplication beyond the cube proved difficult. A number can be represented by a line, the square of a number by a surface (a square), and the cube of a number by a solid (a cube), but beyond the solid, there are no more dimensions in which to represent the multiplication of \(n &gt; 3\) lines (see Mancosu 2008: 112) (see  Fig. 7).  The “problem of dimensionality”, as it has since come to be known, constituted a serious obstacle to the use of algebra in geometry (ibid.). Suppose the problem is to raise a line to the fourth power \((x=a^4).\) For Descartes’ predecessors, this made absolutely no geometrical sense.