In Sardinia, to the Antenora.

a - b

Here the two currents of the waters meet together in the line a b, and in such collision they go whirling wholly among themselves, because from the surface to the bottom they strike one another. And once such a revolution is created, it is driven out of the place where it was created by the impetus of the waters coming from above; and in such transposition this revolution has acquired two motions, that is, its natural one about its own centre, and the second is that which it gains from place to place. Therefore this will be a straight revolving motion, which, when it occurs in water or in air, removes the ground with great hollowings and scourings.
When the currents of the waters are not equal, the revolutions are made by the encounters of these waters along a straight line. But if such water-currents are not equal, these collisions will carry the whirlings of such water toward the bank of the water of lesser power, and boring under it with their doubled motions, that is straight and revolving, they go hollowing out the banks below, where the upper parts, sustained by these, undermining upon their failed foundations, are again consumed by that whirlpool.
When the waters are unequal, their encounters go whirling and the less powerful water enters with the branches of the lower eddies beneath the branches of the higher eddies, that is, those born of the more powerful waters. When the water of greater power strikes the water of lesser power, then the line of the eddies curves, entering with its convex side into the body of the water of lesser power. When the curvature of the line of the eddies enters with its convexity among the water of lesser power, then that lesser water stays in that boundary without motion, whence it dams up and rises and gains heaviness; whence by the acquired weight it multiplies in power and makes impetus against the water that before overcame it, so that the line of the eddies bends into the contrary position, and where before it was convex it becomes concave. And so the lesser water is often driven by the greater, and the greater is driven by the lesser, but the lesser is driven the more, the more it is of lesser power.

f - g - r - t - n a b m.

When the water n climbs over the hill a b, that water divides over that hill and runs half on this side and half on that; whence that crest stays sharp and forms the promontories t r on this side and not on that, because on that side the waves come into a and spoil those that had been begun. And in b it does not happen so, because the water that comes into its pool m escapes by g f.

The gonfalonier should cancel the book and the notary make me a writ of the moneys received, and then I will build freely. Saturday, the 5th day of March, I had from Santa Maria Nuova 50 gold ducats; there remain to me 450, of which I gave 5 the same day to Salai, who had lent them to me.

The simple power of a man will never move the wing of the raven with that speed with which the raven moved it, when it was attached to the bird. And the experiment will be manifest in their noise, because that of the man will never make so much noise as it made when it was attached to the bird.

The heavy body, placed in the position of equality, does not move of itself. That flowing heavy body will move of itself the faster, which will pass through a less oblique position.

n - d - m b - Sa
The bird n d m climbs on high with a revolving motion by means of the aid of the wind, which one may say ascends screw-wise. And such motion is made by falling along two lines, of which one is toward the centre of its revolving path along the line d b, the other is made along the line of its circle along which such bird moves, that is, along d a. Therefore it will not fall wholly along the line d b, nor along the line d a, but along the middle line d S, which partakes of the two extremes, and is moreover the nearer to a than to b in proportion as the motion d a is faster than the motion a b.

Here half of the circle is made with the favour of the wind that makes itself a wedge to it, and the other half with the favour of the impetus born of its descent.

The bird climbs screw-wise through the air, always descending, in the likeness of water carried on high by the hollow screw, which always descends while ascending. As much does it act to move the flowing heavy body upon a dense oblique surface, as the dense heavy body upon a yielding site.

Why the bird sustains itself upon the air.
The air that is struck by a moving body of greater velocity condenses with a greater sum of itself.
This is proved because the less dense fluid body will never sustain upon itself the more dense, as by experience one sees the anvil float upon molten bronze, and gold and liquefied silver stay beneath the fusion of lead. And for this reason, the air being a body apt to condense within itself, when it is struck by a motion of greater velocity than that of its flight, it presses within itself and makes itself, among the other air, in the likeness of a cloud, that is of that density. But when the bird finds itself amid the wind, it can sustain itself upon it without beating its wings, because that office which the wing performs against the air, the air being without motion, the same does the moved air against the wings, they being without motion.