 A look at some of the problems and proposals found in these mathematical works will help situate Descartes in his early modern mathematical context and will also help to highlight the results from this period that have an important connection to what is found in the opening books of the 1637 La Géométrie. To make these connections clear, the brief narrative below emphasizes the proposals Descartes made during the 1618–1629 period concerning (1) the criteria for geometrical curves and legitimately geometrical constructions, and (2) the relationship between algebra and geometry.