bubble - water. Why are the bubbles that water makes half-round, while those of air are perfectly round? Because the sides of the base of the half-round are spherical right angles, and the contact it has with the water gives no projection above itself which, by its weight, would have to bend and buckle.

a - b. Let it stand half under the water, and let the blades go underwater edge-on, and out of the water let them go face-on, and so the fall is gained.

1 r q p o n m K - 27 - d c b a v e - 20 - f - h g - t y x i S. If the line Kv is 27, the line vf is 20. Therefore we shall say: the water Kv, that is Ke, weighs 27 pounds and acts upon the blade e a with all its power; and the water Kf is 47 pounds and acts upon the blade f b with half its power, which is 23 and 1/2 pounds. Therefore the power of the water K e exceeds the power K f by half a pound of water.

Here is demonstrated the true powers of a quantity of water fallen upon the wheels of mills through various obliquities, from one and the same height to one and the same lowness, and with the same quality and quantity of wheels. Therefore we shall say that the aforesaid water departs from the height K e and descends onto the lowness S t, and its various obliquities are the lines K S, although I do not place this line among the oblique ones, because it falls perpendicular. The first oblique will be the line K i, the second is the line K x, the third is the line K y. Thus the water K S falls from the site K e and strikes the blade of the wheel e a at the middle of its descent and with a power of 4; and this water strikes that blade with all its weight, because it rests upon nothing. There follows the descent of the water K i, which strikes the blade f b at the point f. This water falls one and a half times the fall of K e, as the line m f shows, but it loses half its weight, as is shown in m o against K o. Now it is necessary to see and calculate the differences of the two aforesaid powers before we proceed further, and we shall say: if the power of 4 moves the blade e a and falls one braccio in height, with what power will the water move the blade f b, falling from a height of one braccio and a half with a power of 2? You will say thus: if the aforesaid power of [K i] were 4 as before, and falling one and a half times higher, it would be one and a half times more powerful than before, that is 6; but because the power is only 2, I must halve 6, and I will say that half of 6 [is] 3, whence we have lost one degree of power from the first wheel to the second.