 This example illustrates the procedures involved in Descartes’ method. Intuition and deduction can only performed after enumeration2 has reduced the problem to an ordered series of simpler problems. The simplest problem is solved first by means of intuition, and the more complex problems are solved by means of deduction. The order of the deduction is read directly off the enumeration by inversion. Note that identifying some of the problems in the series (specifically Problems 3–4 in the second series in  Table 1)  require experiment. One must observe how light actually passes through different types of transparent media in order to determine how these media affect the angles of incidence and refraction. 