In his founding treatise, the Dialogues Concerning Two New Sciences, Galileo boasted that he was setting forth "a very new science dealing with a very ancient subject." ...No one before him, he declared, had discovered that "the distance traversed, during [successive] equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity."...Galileo's rule can be expressed differently, that the total distance fallen is proportional to the square of the total elapsed time....he devised an experiment in which he "diluted" gravity, slowing down the motion of falling. For this purpose he used an inclined plane... He allowed a small metal ball to roll down the board at different inclinations, and recorded the distances and times....Galileo presented the numerical values that he found in his experiments as proof... Thus he could proudly boast of an agreement to within "one-tenth of a pulse beat."