The larger the bird, the more disproportionate its wings are with respect to smaller birds.

The circular ring that receives, in contact with its sides, the sides of a square, is composed of two circles each double the other. Similar portions have among themselves the same proportions as those of their wholes. Therefore two portions taken from two quarters of two circles double one another will themselves also be double one another. Which is the portion that is sought? The half-portion that is sought, equal to the given half-portion (in quantity but varying in figure), is drawn from the greatest half-portion.

d-e-a-c-n-f. That surface remakes its first quantity, to which are restored the quantities removed. Therefore, if from the curvilinear ring d e a c f n the half-portion d a c is taken away and there is given back to it as much value with the portion e c n, the aforesaid surface reacquires its first value. Therefore such a ring has varied its figure and not its quantity. The circle that is in contact with the 4 sides of a square is the half of that circle which touches the 4 corners of the same square. Of the 2 circles double one another, the half of the one is worth the whole of the other. It follows that if 2 circles are, one 30 times greater than the other, the thirtieth part of the one is worth the whole of the other. That proportion which the wholes of similar figures have among themselves, the same their similar parts have.

e-c-4-6o-a-5 3 d b. The triangle a b c of curvilinear base is worth the triangle a b d of curvilinear base. It is proved by one of Euclid's, where it says: all triangles made on equal bases between parallel lines are equal among themselves. Take away therefore the straightness of the rectilinear base a b ... Since then the pyramid a b 5 is worth the sector 3 4 5, and the part of this pyramid a b d is worth the half-portion o, remove 8 of these pyramids a b 5 and you have the whole minor circle entire together with the circular ring. Then ...

If the sector 3 4 5 enters 32 times into the greatest sector, the whole minor circle will enter 32 times into the whole greatest circle. a b 5 is the thirty-second part of the greatest sector and is worth the whole sector 3 4 5, and this thirty-second part is divided into two unequal parts, namely a b d of curved base and a d 5 a rectilinear triangle. Now if such triangle a b 5 is worth the triangle 3 4 5, and this triangle 3 4 5 is 1/8 of the whole circle, multiply again by 8 the triangle a b 5 and you will have made a triangle equal to the whole minor circle. Take away the half and you will have made the ring of the minor circle, that is, the circular ring. Then take a b d from the whole sum of the 4 portions, and there will remain to you the 4 portions less the triangle a b d, equal to the ring less its half-portion o.