Before formulating the laws of motion, Galileo distinguished between mathematical study and empirical study. He, first, theoretically derived the relation between distances and times for uniformly accelerating motion by letting the bail roll a quarter, then half, then two-thirds and so on of the length of the groove and then measured the times on each occasion, which he repeated hundred times. He calculated, based on this study, that the distance travelled equalled the square of the time on all occasions.
Which one of the following characterizes Galileo's method?