Of flying things.

b a - d c

When the part of the wind a is moved to b, then c, a part of the same wind, will be moved to d, and the bird a will be at d, and it will have observed the nature of the wind that drives it, and the nature of its own obliquity and weight; and its motion will be proportioned to the motion of the wind in the same proportion that the side of the square has to the diagonal of that same square. And thus we have concluded that the proposition can be realized, namely that the bird, without beating its wings, can be made faster than the wind that drives it.

Of things that are moved by others with simple motion, the moving body is as fast as the speed of its mover. Therefore the bird, carried by the wind along the same straight line as that wind, will be of speed equal to that wind.

But if the things carried by the wind are more oblique toward the earth than the straight course of that wind, then the moving body will be faster than its mover. But if the obliquity of the things carried by the wind turns toward the sky, this is a manifest sign that the motion of the moving body is slower than the motion of the wind. And the reason is that obliquity turned toward the earth generates such motion by cause of its heaviness and not by favor of the wind; whereas the obliquity of the motion made by the moving body toward the sky is generated only by cause of the shape of the moving body, which shape is after the manner of a leaf. This, caught by the wind in its breadth, rises up high only by the favor of the wind, and it moves only as much as the wind moves, as will be shown in its place.

Of the cause of the circular motion of birds.

The circular motion of birds is generated by the unequal motion of their wings, which is caused by the percussion made in the air by one of the horns of the tail, which goes out above or below the path that the bird makes through the air it penetrates.