 Though there is some dispute among commentators about Descartes’ level of expertise in algebra during this early 1619–1623 period (compare Bos 2001, 245 with Sasaki 2003, 126), texts from 1628–1629 show Descartes making great advances in algebra in a relatively small amount of time. Two textual sources are of particular interest: (1) The specimen of algebra given to and transcribed by Beeckman in 1628 upon Descartes’ return to Holland, and (2) a text on the construction of roots for cubic and quartic equations given to Beeckman in early  1629.[4]  In the Specimen, Descartes presents a rather basic problem-solving program (or schematism) for algebra that relies on two-dimensional figures (lines and surfaces). The texts given to Beeckman several months later, which Descartes composed while in Holland, show a great advance over what’s found in the Specimen, since in these texts he appeals to conic sections (or solids) in his problem-solving regime. For instance, Descartes constructs two mean proportionals by the intersection of circle and parabola (a method he had discovered around 1625 according to Bos 2001, 255). More impressively, in a different text from this same period, Descartes offers a method for constructing all solid problems, i.e., for solving all third- and fourth-degree equations.