On the tip of the wings that rise. The tips of the wings, when they rise to the utmost height, are farther apart from one another than when they lower to the lowest depth. And when such wings rise again on high, their outermost parts follow the descent already begun, until they straighten the curvature they had formed. Then they bend into the contrary curvature, which they carry near to their utmost elevation; and even though such a wing returns downward, its tip continues the elevation already begun until, the first curvature destroyed, it has generated another, turned in the contrary aspect.

a b c d; b - n d - a m e - c

By what is said above, the tips of the wings make a greater motion than their length requires, since they are not flexible. It is proved thus: let the motion of the tips of the flexible wings be a c, and of the non-flexible ones b d. The motion a b of the tips of the flexible wings exceeds the motion b d of the non-flexible wings, and these two lines of such motions are shown, the one to be smaller than the other, because one is part of the other.

But because the wing-tips in rising and lowering make a smaller motion than the parts of the feathers joined to them, and before such tips begin to extend those joined feather-parts return in the contrary motion, it is necessary that one part of the tip of these feathers turn backward with the remainder of the feather while the tip goes forward, like the finger that rises as much as its hand descends; which finger will be said to be immobile because it does not change place, and for this reason we shall say that the tip of the flexible wing has a motion like that of the non-flexible wings.

In the impetus made through the air by birds, it is better and easier to bend the part than their whole. The part of the bird that bends within the air will make its whole bend, as is seen with the bending of the rudder in its ship.