e f d c a b

The sudden changes of the wings and tail of birds produce sudden changes of line in their motions. Suppose a bird moves toward the east and suddenly turns toward the west. This sudden turn is made by spreading the wing on the side toward which it wishes to turn, setting it against the buffeting of the air along the line by which it was moving, while drawing the opposite wing toward itself and bending the tail so that that wing is spread. As if to say: the bird a d f was flying toward you and wishes at once to turn back on its right side d f; then it will spread that wing d f more than usual and present it more fully to the wind, and the opposite wing a c it will fold into c b, and the tail c d it will turn into e d. Then the fury of the impetus, struck by the air, acts more on the part of the bird that is farther from the centre of its gravity, and on the nearer part it acts less.

When the bird rises in a circle without beating its wings, it keeps the centre of its gravity much lower than the tips of the wings, and receives the wind, from whatever side it comes, wedge-fashion beneath itself — that is, under the tail, or under the breast, or under either wing.

Impetus once begun circular can of itself continue circular about a pole, like the motion of millstones or grinding wheels; and it can continue circular and straight, like the wheel of a cart rolled straight outside its pole, or like reflected motion made along an oblique line by spherical bodies. Likewise the flight of birds: 'although the beginning of the birds' impetus were caused by straight motion, it can continue in circular motion for as long as that impetus lasts.'

The motion of equality made by the flight of birds can suddenly be transmuted into oblique or into straight, toward the sky or toward the earth. Toward the sky it will be done when the elbows of the wings are turned, together with the tail, toward the ground.

c b a

If the water a b strikes the tail of the fish, which stands as on a pole above the centre of its accidental gravity, without doubt that fish will bend about that centre of its; but the tail will bend more with the current of the water than the body, which, being harder, resists more in the contrary motion.

b d c a n

Here the water stands still and the fish a b strikes the water with its tail a toward c. Then the fish turns, in contrary motion, that part which is in front of the centre of its gravity, and moves it from b to d, almost as if the fish stood still and the water moved against its tail along the line n a.

Test with a pair of oars, or of boards made oar-fashion, short, as though hollowed, of the kind from skiffs.

c b a

The right wing b c has to resist one-fifth more than the left wing, being one-fifth longer than that opposite wing. For this reason it is clearly shown that, striking a fifth more air than its opposite does, its motion is thereby retarded, the other goes forward, and it curves the straight motion around the more extended wing.

m

The descending bird keeps itself straighter and safer from overturning with its wings hollowed beneath than with its wings flat.
The lower the bird's gravity is below the wings, the safer the bird is from turning upside down, as is seen above at m.

Make a small one on the water and test it with the wind in shallow water, over some part of the Arno with the natural wind and then as you please, and twist the sail and the rudder.
Tomorrow look at all these cases and copy them, then cancel the originals and leave them in Florence, so that if those you carry with you should be lost, the invention may not be lost.

Write of swimming under water and you will have the flying of the bird through the air. It is good there at the outfall the mills make into the Arno by the sluice of the Ponte Rubaconte.
In two different ways the bird can turn in any direction while always beating its wings: the first is if, in equal time, it moves one wing downward faster, with an equal quantity of motion, than the other, sharing the motion toward the tail; the second is if, in equal time, the motion of one wing is longer than the motion of the other.
Again, in beating the wings downward obliquely, if they are bent or moved, one lower and the other farther back, the part that drives the wing lower will, by the first, rise higher, and the opposite part of the wings, of longer backward motion, will go farther forward, again by that first. Hence for this cause the motion of such a bird will be curved about the part of the bird that lies higher.
There are all these motions made by the bird without beating its wings, which are subject to one single rule alone; and these motions rise above the wind, showing themselves obliquely to it, and receive it under the wings wedge-fashion.

First. — To move the water or the air against the object is as much as to move that object against the air or the water.
Second. — The centre of gravity of the fish lying level in the water, or of the bird lying level in the air, is placed midway between extremes that resist equally.

A vessel.
Wood.
Wine.
Colours.
Oil and soap.
Bed.
Vineyard.
Arrigo.
Guglielmo.
Chest.
Carry the drawing.
Cat.
Lead.
Money.
Tails of vair (squirrel fur).
Bones of lanterns for colouring.

And a little walnut oil.
White mistletoe (birdlime).
Turpentine.
Honey.
Serapino (sagapenum gum).
White soap.
The largest quantity is the birdlime, and the turpentine and honey shall be equal.
The serapino is ground with vinegar.
See the true measure of the pole.

The festival hall must have its serving arranged so that the food passes first before the lord and then before the guests; and let the passage be such that it can come into the hall without passing before the crowd more than one wishes; and let the entrance of the hall be placed on the opposite side, facing the lord. And let the stairs be convenient and so wide that the people going by them do not, jostling the masqueraders, spoil their costumes when the throng of men issues forth ... with such masqueraders ... Such a hall should have two rooms at each end ... and its double privies ... and besides this, one door for the serving and one for the masqueraders.