 In addition, we find in Descartes’ early work an interest in the relationship between algebra and geometry that will be crucial to the program of geometrical analysis presented in Book One of La Géométrie, where at this early stage of his research, Descartes, like his contemporaries, is exploring the application of geometry to algebraic problems. For instance, as pointed out above, Descartes uses the construction of mean proportionals to solve algebraic equations in the Private Reflections, and in the same text he also shows an interest in the geometrical representation of numbers and of arithmetical operations. The same interest appears again in the later Progymnasmata de solidorum elementis excerpta ex manuscripto Cartesii (Preliminary exercises on the elements of solids extracted from a manuscript of Descartes, ca. 1623), a text in which Descartes offers a geometrical representation of numbers and of four of the five basic arithmetical operations (the four operations he treats are addition, subtraction, multiplication, and division).