The Bird as a Mathematical Instrument
Air condensing beneath the wing, and a flying machine lacking only the bird's soul
Two paragraphs on the mechanics of bird flight. Leonardo reasons that a wing must beat faster than the pressed air can escape so that the air condenses beneath it and holds the bird aloft, and observes that air grows thicker near water and in the cold region but is purest in between. In the second passage, beside a small figure of a bird with open wings, he calls the bird 'an instrument operating by mathematical law' that man could build in all its motions—lacking only the bird's soul, which the flyer's own soul must supply. A worn right margin preserves illegible fragments of another page.
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The wing must outrun the escaping air
If the wing's motion is not swifter than the flight of the air it presses, the air will not condense beneath it and the bird will not stay aloft. The air nearest the wing takes up its motion and condenses most, while the air farther off stays still.
The varying thickness of air
Air has greater thickness where it is nearer to water and nearer to the cold region, and in the middle it is purer. The air of the cold region does not resist the motion of birds unless they gather much of it beneath themselves.
A flying machine lacking only the soul
Beside a bird with open wings, Leonardo declares the bird an instrument operating by mathematical law, one that man has the power to make with all its motions, wanting only the power of self-balancing. Such a man-made instrument would lack nothing but the soul of the bird, which the soul of man must counterfeit, and he judges that the more perceptible motions can be known and provided for.