 such that a definite ratio between these lines obtains. In the case of locus problems involving more than six lines (in which three lines on one side of the equation must be shown to have a proportional relation to four lines on the other side), Pappus believed that the problem of dimensionality prohibited solutions to these problems, “since there is no figure of more than three dimensions”, so that “a figure contained by these lines is not understandable in any way” (ibid.). For Descartes, by contrast, geometrical sense can be made of the multiplication of any number of lines. Descartes provides a completely general solution to the Pappus problem: no matter how many lines, he demonstrates how it is possible to find an equation and produce a construction satisfying the required conditions (see Bos 2001: 313–334). More broadly, he provides a complete enumeration of the types of problem one encounters in geometry (defined by degree of complexity); enumerates the geometrical constructions required to solve problems in each class; and defines the class of geometrically acceptable constructions by whether or not they can be algebraically expressed.