a m, n r

Because of the 5 parts of the water of the cistern, 4 rest upon its bottom, and there they support and hold the fifth, the middle one, at n; and because the bottom, which opens into the pipe, is pierced, a counterweight must be supplied in the manner of a balance, similar to itself, which is given at m r.

h l s, b c

But if you were to say to me: 'here is a cistern which, through a small pipe, delivers its waters into another cistern like itself; how is it possible that the line h b can, through the pipe b c, push so much water up to l s?' To this I answer that when the line h b, not finding the foundation it sought to make its counterweight in the opposite cistern—and although that was much wider than the pipe—it pushed in so much water that within it a column of water equal to the weight h b could be found, and all the rest of the water of the 2 cisterns rested upon the bottoms, which were firm. [Editorial note: the manuscript has 'sopa' instead of 'sopra' (upon).]

Whoever should stop the bottom of a columnar vessel with its head and fill such a vessel with water … [the text breaks off]

n m f, 10

water is 100 pounds

I wish to see what force the water exerts more upon its bottom than upon its banks, and I shall do it in this way. I shall take a columnar vessel which has, in place of a bottom, a movable board, nailed with leather around the rims of the vessel's bottom, the leather keeping about 4 fingers of space away from the bottom, from the lower rims of that columnar vessel. And in the middle of that bottom let the cord of the balance be attached, and let the vessel be filled with water, which will rest upon that bottom. Now give as much weight to the opposite arm of the [continues at the right:]

balance, and as much weight as will stand against the water of the vessel, so much will the water weigh that rests upon that bottom. And all the rest of the weight of the water that does not press upon that bottom comes to discharge its weight upon the bank or sides of the vessel. But remember, before you weigh the water, to weigh the bottom first with the balance. Upon that balance you will put as much weight as the vessel's bottom weighs. And then add above as much weight as is the weight of the water that loads that bottom.