Before formulating the laws of motion - Galileo distinguished between mathematical study and empirical Study. He - first - theoretically derived the relation between distance and time for uniformly accelerating motion by letting the ball 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 traveled equaled the square of the time on all occasion. Which one of the following characterizes Galileo's method?