'A bird,' he says in his Treatise, 'is an instrument working according to mathematical law, which instrument it is within the capacity of man to reproduce with all its movements, but not with a corresponding degree of strength, though it is deficient only in power of maintaining equilibrium. We may say, therefore, that such an instrument constructed by man is lacking in nothing except the life of the bird, and this life must needs be supplied from that of man. The life which resides in the bird's members will, without doubt, better conform to their needs than will that of a man which is separated from them, and especially in the almost imperceptible movements which produce equilibrium. But since we see that the bird is equipped for many apparent varieties of movement, we are able from this experience to deduce that the most rudimentary of these movements will be capable of being comprehended by man's understanding, and that he will to a great extent be able to provide against the destruction of that instrument of which he himself has become the living principle and the propeller.' In this is the definite belief of da Vinci that man is capable of flight, together with a far more definite statement of the principles by which flight is to be achieved than any which had preceded it--and for that matter, than many that have succeeded it. Two further extracts from his work will show the exactness of his observations:-- 'When a bird which is in equilibrium throws the centre of resistance of the wings behind the centre of gravity, then such a bird will descend with its head downward. This bird which finds itself in equilibrium shall have the centre of resistance of the wings more forward than the bird's centre of gravity; then such a bird will fall with its tail turned toward the earth.' And again: 'A man, when flying, shall be free from the waist up, that he may be able to keep himself in equilibrium as he does in a boat, so that the centre of his gravity and of the instrument may set itself in equilibrium and change when necessity requires it to the changing of the centre of its resistance.'