p

The centre of gravity of such a bird becomes the pole of its balance. When such a bird rises in circles on a single wind without beating its wings, it holds the impetus of the wind beneath its wings, which lifts it as though it were a wedge. When the wind strikes beneath its left wing, that wind then passes over the right wing, and this wind would overturn the bird were it not for the tail, which it at once twists so that the wind passes over it and forms a contrary wedge and beats within it and makes it turn. When it has turned so far that the wind strikes it on the beak, then the tail does not act except held straight; but it bends upward, so that the wind strikes it from above, and the breast is struck from below together with the wings from below; but because the left wing is struck more, since it holds it more bent, it is necessary that such a bird turn and swing its right wing against the coming of the wind.
When the tip of the right wing enters the line of the wind, then nothing is so apt or useful to make the wind strike between more equal angles as the bending of the head together with the neck against the coming of that wind. When the tail enters the line of the wind, then that tail is struck from below by the motion of the wind, and the head is struck from above, and each wing is struck from below. But the right wing, by its twisting, shows and yields itself to the wind's striking more than the left does, and therefore it travels more with the right than with the left, whence this motion comes to curve and always to rise, because it is thrust up from below by the wind.

Pushed downward.

Pushed evenly.

Pushed upward.

This one rises, because it has the wind beneath it.

This one does not rise, because it no longer has the wind beneath it.

This one descends, because it has the wind above it.
These three modes descend or rise with equal motion of the whole animal together with its extremities.

n - m

When the bird rises from below, the wind is greatly in its favour; and when it wishes to make use of it, from whatever quarter that wind comes, the bird sets itself obliquely above the coming of the wind, taking it beneath itself in the manner of a wedge, giving the start of its ascent with a slight leap. That start of the bird's ascent will be made with greater gain, which is increased by the impetus of the leap and by the wedge of the wind and by the sudden lowering of its wings.

You wished the utmost harm to Francesco and yet let him enjoy your property during his life. To me you wish the very worst, to ...
Whom did you love better, Francesco or me? This man wants it for you, and gives me mine only after my death, so that I cannot carry out my will, and he knows I cannot alienate my heir. Then he means to ask it of my heirs, and not as a brother but as a complete stranger; and I, as a complete stranger, will receive him and his. Have you given such monies to Lionardo? No. Then why should he be able to say that you drew him into this trap, whether feigned or real, if not to take from him his money too; or I will say nothing to him while he lives. So do you not wish to return the money lent on the Botro to his heirs; rather you wish him to pay the rents he has from that property.

Or did you not let him enjoy it during his life, provided that afterwards it returned to your sons? Now could he not still live many years? Yes? Now suppose that I am he. You wished me to be heir so that I could not, as heir, demand from you the monies I am to have from Francesco.

In what manner the bird goes against the wind.

The air, or the wind, comes from a to b, and the bird rises along the line q b, and then descends along the line c d, and then rises again by the same wind, and then descends again by the same rule. To move the wing against the air is as much as to move the air against the wing.

That wing which extends more strikes a greater quantity of air, and consequently descends less than the more gathered wing does. Whence the descent of such a bird is made along the line of that wing which gathers itself more.

The bird from a wishes to descend to b, and when it is at c, it turns its breast to the wind and beats its wings and leaps to d and then goes to f. The tail n m lies along the line of the motion the bird wishes to make in going to a, and it beats its wings along the line r S; but if that tail twisted along the line n o, then the same beating of wings would direct the bird to h, and if that tail bent to f, then the bird would bend, with the same flight, to g. That wing is retarded more which is struck by the air between more equal angles, or by a greater quantity of air.
Therefore, when the bird descends obliquely and feels itself sinking on the left wing, it will extend that wing more than the other, or twist it more into the face of the air where it strikes.

* Among things of equal size, that one will show itself most diminished ...
Among things of equal colour and size, that one will diminish most in its figure which is more remote from the eye that sees it.
All things of equal colour and magnitude will show themselves of equal size when they are equally remote from whoever sees them.
But if equal things have unequal distances included between the eye and them, that one will appear more diminished which is situated farther from the eye.
The excesses of diminution that equal things make at unequal distances will have among themselves the same proportions as the distances included between those things and the eye that sees them.

The differences that equal things make among themselves, being remote at various distances from the eye, have in themselves the same proportion as that of their various distances included between the eye and the things seen by it.

* Equal things, equally distant from the eye, will be judged of equal size by that eye.
* Equal things, remote at unequal distances from the eye, must appear of unequal size.
The angles of the pyramids by which things are seen ... Equal things will show themselves unequal when they are remote at various distances from the eye.

* Equal things, being remote at various distances from the eye, must appear of unequal size.