 A similar approach is taken by Descartes when he treats the problem of constructing mean proportionals, where in this case, he appeals to his famous mesolabe compass, an instrument that is used in Book Three of the La Géométrie to solve the same problem. As in 1637, this compass is used to construct curves (the dotted lines in  figure 3)  that allow us to identify the mean proportionals between any number of given line segments. And as Viète before him, in the Private Reflections Descartes uses this construction of mean proportionals to identify the roots of standard-form cubic equations (see Bos 2001, 240–45).