 To understand Descartes’ reasoning here, the parallel component determination AH must be regarded as simply continuing along its initial path because it does not come into contact with the surface of the sheet. To where must AH be extended? Since the ball has lost half of its initial speed and consequently will take twice as long to reach the circumference of the circle after impact, we double the length of AH by extending it to F. The ball must, therefore, land somewhere on the line dropped from F, but since it cannot land above the surface, it must land somewhere below CBE. It lands precisely where the line dropped from F intersects the circle at I (ibid.). Once we have I, we extend AB to I. Descartes observes that the degree of refraction “varies exactly in proportion to the varying degrees of penetrability of the respective bodies” (AT 7: 101, CSM 1: 161). He insists, however, that the quantities that should be compared to one another in this proportion are not the angles ABH and IBE themselves (the angles of incidence and refraction, respectively), “for the ratio or proportion between these angles varies with all the different inclinations of the rays” (ibid.). In other words, the angles of incidence and refraction do not vary according to any determinable proportion. Instead of comparing the angles to one another, Descartes compares the lines AH and HF (the sines of the angles of incidence and refraction, respectively), and sees that the proportion between these lines is that of 1/2, a ratio that all refractions between these two media, whatever the angles of incidence and refraction, must obey. Since the lines AH and HF are the sines of the angles, Descartes’ law of refraction is oftentimes referred to as the “sine law”.