404 others for everyone to see. In order that I may achieve my purpose, I ask you to grant me the following: namely, that if there are two mobiles, one of which is moved more swiftly than the other, these mobiles joined together will be moved on the one hand more swiftly than the one which alone was moved more slowly, but more slowly than the one which was moved more swiftly. As if, for example, mobile a is moved faster than b, I say that the mobile composed of both a and b will go down more slowly than a alone, but more swiftly than b alone. {1}This is clearer than daylight: for who doubts that the slowness of b will retard the swiftness of a, and, on the contrary, that the swiftness of a will intensify the motion of b, and that in this way a motion intermediate between the swiftness of this a and the slowness of b will take place?
DO. I shall never dare deny this.
AL. This having been presupposed, if for my adversaries such a thing can be done, let a great amount of something be moved more swiftly than a small amount (let them be of the same matter); and let a on the one hand be the great amount and b the small amount. If therefore b is moved more slowly than a, therefore, from these things that have been assumed above, the mobile composed of both a, b will be moved more slowly than a alone: and a, b are of the same matter: therefore the larger amount of the same matter will be moved more slowly than the smaller amount of the same matter; which is surely diametrically opposed to their view, and is contrary to what has been presupposed.It is therefore not true, that a great amount is moved more swiftly than a lesser, if they are of the same matter; although Aristotle, against the Ancients, has presupposed this as something known, throughout Book IV of the <i>De Caelo</i>.Consider, thus, how firm the foundations are on which rests his refutation of the opinion of those who did not assume (as indeed should not be assumed) the purely and simply heavy and the purely and simply light, but only the comparatively lighter and heavier: and, consequently, you can see the strength of the reasons by which he tried to attribute to earth and to fire absolute heaviness and absolute lightness, and even to water and to air heaviness in their proper region.But, having put these things aside, returning to our subject I say that the same reasoning must also be made in the case of the void; namely, mobiles which are of the same matter, though unequal in size, are carried with the same swiftness: which will be demonstrated exactly the same way as in the case of a plenum.
DO. You can return to the solution of the remaining problems {1}, which I await with eager ears.
AL. Receive now my solution to one problem, which can be known solely on the basis of the things assumed above: namely, the problem in which