Water forced upward by the power of counterweights will rise more readily through pipes than through the open air, because the pipes keep it united; whereas water that has no guidance of a pipe scatters violently and divides into minute particles, almost like mist, if it is driven by excessive power. Water that rises upward acquires, at every degree of motion, degrees of thickness and of slowness. The counterweights that, pressing upon the reservoirs of water, force such water upward are of three natures, namely: either of a nature heavier than water, or lighter, or equal. They are also of three forms; namely: either wider than the width of the reservoir, or narrower, or equal. The regular natures of counterweights that press the reservoirs are nine; namely: wider than the reservoir and heavier than the quality of the water; wider and lighter; wider and equal; narrower and heavier; narrower and lighter; narrower and equal; equal and heavier; equal and lighter; equal and equal. And it is possible — even though the material of the counterweight were lighter than water — to make the counterweight so tall that it would perform the office of a material heavier than water. As if to say: wood is lighter than water; nonetheless, if one were to take a beam and set it upright, it would perform the office of a counterweight of lead. In short, to show you that it is impossible that any movement of water from low to high can be created by any instrument made by man, by whose descent one might raise other water from the end of that descent, of like weight and height to that which descended.

I conclude that where water descends little, it shows itself of pyramidal form; and although the more it thins the less it weighs, yet that weight which strikes is much heavier than if it had come down to the place of percussion in that thin figure. On motion. Gravity that descends freely acquires, at every degree of motion, degrees of velocity and of weight. a) All things that push one another will be, among themselves, of equal motion and touching, or continuous. No effect in nature is without a reason. Understand the reason and you need no experiment. Along the right margin, a figure of two vessels from whose bottom falls a vein of 'pyramided' water, or a series of 13 little balls: I let water fall from a vessel, from a height of 50 braccia, so that the thread of descending water is 50 braccia long. I ask which braccio will hold in itself the greater weight of water, the first or the last. Again: I let fall, from a height of 50 braccia, 50 little balls at equal division of time; that is, from releasing the first and then the second there will be an interval of musical time. And so it will be done from the second to the third, and it will continue likewise to the last, so that before the last descends, the first will be together with the others in the air. I ask, of the intervals of these balls, which is greater, the first or the last. The air scatters it and makes it slow: therefore the percussion is everywhere alike. I say that, although water in a greater descent gives a greater percussion only because it is of greater weight all together in the air, and only rests below, and above is not attached but rather is pushed …

To define the descent, or rather the quality of the intervals of the balls, I say first, by the ninth of this, that the descent of each ball, dividing it into equal degrees by height, in each degree of that motion the ball acquires one degree of velocity. Hence this proportion of degrees of velocity is a continuous arithmetic proportion, because the excesses, or differences, of the velocities are proportional among themselves. Hence I conclude that these spaces were equal, because they always exceed, or surpass, one another by equal increment; and for this reason the water that pours from a like height likewise does the same, acquiring at every degree of motion one degree of velocity; whence by arithmetic proportion it goes on exceeding degree by degree of its descent, and for this it is necessary that the water, where it moves more, thins more. But then there arises another doubt, since if that water thins more, it weighs less, and by the second of the first of this, which says that the thing that weighs less is less swift in its descent — therefore such water does not thin, for if it thinned it would be of slower motion, let us say in that part of its descent by half of its beginning. And besides this, if it did not become twice as fast, it would follow that in twice the time a vessel would be filled at that thinning that it would not at its beginning; and this would be impossible, because the water that above poured in one hour would not arrive at the place where it thins by half in the space of two hours; whence it would be necessary that such water went off in smoke, or indeed multiplied continually into various twists, and this is not seen in experience. And if you would say that it was of uniform thickness, to this one would answer by the second of the first said above, that being faster at the end than at the beginning — let us say double — twice as much water would arrive at the end of the descent as that which pours above, which cannot stand in nature. And if you would say that it was of uniform thickness and equal velocity, you would deny the second conclusion of the first, which you accepted as true. Now by the last conclusion made concerning the descent of the discrete quantity of the balls with continuous arithmetic proportion, one concludes the descent of the continuous quantity of the water. If the water thinned, in the long run its pyramid would terminate in a point.

And if indeed we would say that the water, in its perpendicular descent in a continuous straight line, becomes thinner and faster, and that becoming thinner it is lighter and cannot — by the fifth — be faster, I will say that the water which rests upon it from above is that which pushes it; and you will tell me that, being slower, it cannot push it.

It is impossible that water which moves any instrument can ever … Water that descends will never raise from the place where it settles water to the height whence it departed, of a weight like its own. I conclude that in a certain part of the descent that water thins and becomes fast, in such a way that the air divides it and makes it, from continuous quantity, discrete; but the eye cannot discern it. And so then the descent is discrete.