1 In a folio of Codex Atlanticus, referring probably to some critics of his writings, Leonardo drew out the following sketch of a proem to prefix to some of the numerous treatises on various matters which he intended to write and never wrote.

“ Proem.

“ I know very well, that not being myself a literary man some presumptuous men think they may blame me alleging that I am a man without letters. Foolish people ! They do not know that I would be able to answer them, like as Marius to the Roman patricians, that I would be able to answer them, yes, telling them that they, while adorning themselves with the labours of others they do not want to allow me the merits of mine. They will say that as I know no letters, I am not able to say well that I wish to deal with. Now such people do not know that my things have to be drawn rather from experience than from the words of other people, which experience is master of those who wrote well, and this I take for my master and in all cases I will affirm it.”—(Codex Atlanticus, folio 119 verso a).

2 A similar collection to the present one on Aerodynamics I made of Leonardo's passages relating to Aerology in a paper presented to the Fifth Air Congress at the Hague (1-6 September, 1930), entitled “The Aerological Study of the Wind in Leonardo da Vinci.”

3 “ When the force generates more velocity than the escape of the resisting air, the same air is compressed in the same way as bed feathers when compressed and crushed by a sleeper. And that object by which air was compressed, meeting resistance on it, rebounds in the same way as a ball striking against a wall.“—(Codex Trivultianus, f. 6 v. 1487-90).

4 “ Air can be compressed and water not, and, when the movement by which it is compressed, is swifter than the escape of the same air that portion of air which is nearer to it becomes denser, therefore resists more, and when the motion made in it is swifter than the escape of the same air, its mover takes a contrary motion, as appears in birds, which not being able to send down the tips of their wings with that velocity with which they are moved by the force of their mover, it is necessary that the bird rises up to that extent for which the wing tips were not able to reach down; in the same way, a man who holds his breast near a wall and presses with his hands against this wall, if the wall does not give way, the man must come back.”—(Codex Trivultianus, f. 23 v. 1487-90).

5 “ Why birds keep up upon the air. Air which with great velocity is struck by a body compresses an amount of itself, in proportion with that velocity … and therefore the air being a body able to compress in itself when it is struck by a motion of greater velocity than is that of its escape, it compresses within itself and makes itself through other air like as the cloud, that is, of that density. But when the bird is in a wind, it can keep up upon it without beating its wings, because the pressure is made by air against wings, these being motionless.”—(Codex Atlanticus, f. 77 v.b. 1503).

6 “ If the motion of the wing which compressed the air is not greater than the escape of the compressed air, the latter will not compress below the wing, and therefore the bird will not keep up on the air. The air has the ability to compress and rarefy …”—(Codex Atlanticus, f. 161 r.a. 1505).

7 “ That part of air will have more similar motion to the motion of the wing by which it is compressed, which is nearer to that wing. And that will be more motionless which is more remote from that wing. That part of air will be more compressed which is nearer to the wing compressing it. The air of the cold regions will not resist the motions of a bird if it does not embrace a great extent of air below itself.”—(Codex Atlanticus, f. 161 r.a. 1505).

8 “ Air moves through air and moving compresses and its compression is in proportion to its velocity. And compressing it acquires heaviness and its stroke on its object is in proportion to its heaviness.

As it is to move the object against the motionless air so it is to move the air against the motionless object. Therefore the bird beating its heavy wings on the thin air causes it to compress and resist. And if air moves against motionless wings the same air supports the heaviness of the bird through air.

When the power of the motion of the air will be equal to the power of the descent of the bird, the same bird will keep up on the air motionless. And if the motion of the air will be more powerful, it will compress and will raise the bird up, and if the power, of the motion of the air will be less than the weight of the bird … [the note is here broken off]… . Air outside of its sphere has weight in itself. Air does not resist if it does not compress. Air does not compress if it is not moved. Air compresses when it moves within air by which it is stricken.”—(Codex Atlanticus, f. 180 r.a. 1505).

9 “ The same force as is made by the thing against air, is made by air against the thing. You see that the wings striking against the air cause the heavy eagle to keep up in the very high air, close to the sphere of the element of fire. [The ancients divided the world into four zones of decreasing density: earth, water, air, and fire].

Again you may see the moved air over the sea, which striking on the swelling sails, causes the loaded and heavy ship to go; therefore by these reasons, both demonstrated and quoted, you will know that the man with his connected and great wings, making force against the resistant air and conquering it, will succeed in subjugating it and rising above it.”(Codex Atlanticus, f. 381 v.a. 1486-90).

10 “ … it needs little force to sustain itself and to balance on its own wings and to direct them on the path of the winds and to govern its own course, and a little movement of the wings is sufficient, and a much more slow movement as the bird is larger.”—(Codex on the Flight of Birds, f. 17 (16) r. 1505).

11 “The bird [the artificial bird] is an instrument working according to mathematical law, an instrument which it is within the power of man to make with all its motions, though not with such a power [that of the natural bird]; but its power only extends to the faculty of balancing. We may therefore say that such an instrument compounded by man is lacking in nothing but the soul of the bird, and this soul must be replaced by the soul of the man.

The soul in the members of birds will without doubt better conform to their needs, than that of the man which is separated from them, and especially in the almost imperceptible motions of balance. But because we see that the bird provides for the more, perceptible varieties of motions, we are able through this experience to understand that the more perceptible ones could be known to the intelligence of the man, and that he will to a great extent be able to provide against the fall of that instrument of which the has made himself soul and guide.”—(Codex Atlanticus, f. 161 r.a. 1505).

12 “This is a collection without order drawn from several papers Which I have copied here, hoping to be able afterwards to put them in order to their own places, according to the matter with which they deal; and I think that before I have accomplished it I am to repeat the same thing many times. Therefore my reader do you not blame me as things are very many and memory cannot hold all, and say that it is not to be written as I wrote it before. And not to fall in this mistake it would be necessary, in each case that I have to copy something and not repeat it, that I would have to, read all the past, and specially as long intervals of time pass between writing from one time to another.”—-(Arundel Codex, Introduction, 1508).

13 “ Because as much it is to move the air against the bird in itself motionless, so much to move the bird against the air in repose. Therefore we will say on account of the first …”— (Arundel Codex, f. 163 v. 1508).

14 “ When wings are swifter to compress air, the air to escape from below wings, the air compresses and resists the motion of the wings; and the mover of the same wings [the bird] overcoming the resistance of air, arises in contrary motion to the motion of the wings.”—(Codex on the Flight of Birds, f. 11 (10) r. 1505).

15 “As it is to move the air against the motionless thing, so it is to move the thing against the motionless air.

When the bird moves with a slow descent and in a long path without beating of wings and that its declination leads it sooner towards the earth than is its intention, then it lowers the wings and moves them against the motionless air, and such a movement raises up the bird, not otherwise than if a wind wave strikes it below.”—(Codex E, f. 38 r. 1513-15).

16 “ Air in itself is compressible and rarefiable to infinity.”—(Idem, f. 47 v.).

17 “ The hand of the wing is that which causes the impetus, and then its elbow puts itself with the edge forward not to hinder the motion caused by the impetus, and when the same impetus is afterwards actually created, the elbow lowers and makes itself oblique, and oblique becomes the air, where the latter puts itself, as in form of a wedge, on which the wing raises itself up; and if the motion of the bird were not so performed during the time that the wing goes forward again, it would sink towards the end of the impetus; but it is not able to sink, because as much as the impetus lacks, so much the percussion of such an elbow resists this descent and raises the bird up.”—(Codex on the Flight of Birds, f. 15 (14) v. 1505).

“Always in raising the hand the elbow is lowered, and compresses the air and in the lowering of this hand the elbow is raised and remains edgewise, lest it hinder the motion through the air that strikes thereunder.

The lowering of the elbow at the time when the bird sends again the wings forwards edgewise a little on the wind, led by the impetus already acquired, causes the wind to strike under this elbow and form an edge on which the bird with the said impetus, without beating of its wings, mounts up; and if the bird is 3lbs., and the breast ⅓ the width of the wings, the wing will feel but ⅔ of the weight of such a bird.”—(Idem f. 18 (17) r.).

18 “ In beating the wings to keep up and to go forward: from the hand upwards causes to keep up, and the hand causes it to go forward.”—(Codex K, f. 9 r. 1505-09).

19 “ The straight course made by heavy bodies which with violent motion pass through air will be more powerful, and of a stronger percussion against impediments opposed to them, in its middle part than in any other of the same.

The reason of it is that when a heavy body starts from its strong mover, though this start is in the first degree of its power, nevertheless as it meets air without motion, it meets it in first degree of its resistance; and though the same air presents an amount of resistance greater than the power of the heavy body pushed against it, nevertheless as the body strikes a small part of air, the former remains victorious; therefore it drives it away from its space and in driving it away it diminishes a little its own tvelocity. Thus being this air pushed, it pushes and drives away other air and generates behind itself circular movements, of which the body moved in it is always the centre, like as the circles made in water which have their centre in the place stricken by the stone. And so each circle driving away the other which is before its mover, all is prepared along this line to movement, which so increases as the body pushing it approaches; therefore the same body, meeting less resistance of the air, increases its course with greater velocity, like as a boat pulled through the water, which in its first motion moves with difficulty, though its mover is at his greater strength, and when the same water with arched waves begins to assume motion, the boat following this motion meets little resistance, therefore it moves with more facility. Thus similarly the bullet (Fig. 1) meeting little resistance continues the motion started as long as it, something left of its original force, begins to weaken and to decline, therefore, changing its course it is no more assisted by the flight which has been prepared for it by the flying air; and in proportion as it declines it meets various resistances of air and it is slowing down, until it takes again its natural motion and it becomes again more velocious (also the boat by turning slows its motion).

Now I conclude, on account of the eighth proposition, that part of motion which is between the first resistance of the air and the beginning of its declination is more powerful and that is the middle of the course, which is made through air with straight, and direct line.”—(Codex A, f. 43 v. 1492).

20 “ The heavy body which descends through water always maintains the same speed (Fig. 2). This which has been stated occurs, as water does not open the way for the mobile as does air and cannot make undulating motion as air downwards. Therefore it is necessary for a mobile penetrating a medium of equal resistance that the motion of the mobile is of equal speed.”—(Arundel Codex, f. 10 v.).

21 “ If two equal bodies are situated one below the other perpendicularly, and at the same time left to fall, they in a long descent will consume their interval and will come to touch each other.

When the air is without fog or clouds you will find that in each degree of its height it acquires degrees of subtlety. And so conversely in each degree of lowness it acquires degrees of density, therefore if two equal bodies, situated one below the other for the space of a cubit, i.e., tied with a thread and left together to fall, they after a long motion will touch each other, because that below always is in thicker air than that above, and, besides this, the former has the labour of opening the air and of creating the undulatory motion of the air, which partially runs away above and jousts and strikes with eddying motions against the second body; while the other superior air runs in to fill the vacuum which remains behind such a body.”—(Codex M, f. 43. v. 1496-1500).

22 “ The wave of air which is generated by a body which moves through the same air will be much more velocious than the body by which it is driven.

What is above proposed occurs, because being the body of the air very quick and easy to the motion, when a body moves through it, the former comes to make the first wave on its first motion and at the same time that wave cannot be generated without causing another behind itself and that another. And so such a body moving through the air in each degree of time makes multiplications of waves below itself, which through their flight prepare their way of the motion for the movement of their mover. The wave of the air being successively created prepares the way of the motion for its mover.”—(Codex M, f. 45 v. 1496-1500).

23 “ The heavy body which free descends, in each degree of motion acquires a degree of weight. This takes rise from the 2nd of the first [allusion to a treatise on mechanics] which says: that body will be heavier which meets less resistance.

In this case of the free descent of heavy bodies one sees apparently, by means of the experience, already quoted, of the waves of the water, that the same wave is made by the air below the thing which descends, because it is pushed and from the opposite part pulled, that is that the air makes a whirling wave which assists in pushing downwards (Fig. 3). Now for such reasons the air which flies before the body which put it away, shows apparently that it does not resist the latter and consequently does not impede such a motion; thus in proportion as the wave descends, which moves quicker than the heavy body moving it, so the motion of the heavy body lasts, so the last wave moves itself more far from it and prepares an easier flight for the air which touches the heavy body.”—(Codex M, f. 46 r. 1496-1500).

24 “ The impetus at every degree of time acquires a degree of diminution and the prolongation of its essence issues from the air or the water, which shuts behind the mobile in filling the vacuum which has been left by the mobile which penetrates it; which air is more powerful to strike and to urge with its strokes behind the mobile than is the antecedent air to resist through compression the penetration of the mobile, and such a compression is it that diminishes the strength of the said mobile. …

… Water in itself is more dense than air and consequently heavier, therefore it makes itself more velocious to fill the vacuum which of itself is left by the fish in the place from which it swims away, and also the water which is stricken by it before itself, does not compress like as the air before the bird; on the contrary it makes an undulating motion which with its motion prepares and increases the motion of the fish; therefore it becomes more velocious than that of the bird, before which the air compresses itself.

The impetus is an impression transmuted by the mover into the mobile and maintained by the air or the water while moving to prevent the vacuum.

The impetus of the mobile through water is different from the impetus of the mobile through air, and such differences result from the varieties of the aforesaid liquid, as the air is compressible to infinity and water not.”—(Codex Atlanticus, f. 168 v.b. 1505-06).

25 “ The impetus is a virtue transmuted by the mover into the mobile and maintained by the wave which by such a mover is generated from the air through the air, and this issues from the vacuum which against the natural law would be generated if the subsequent [Leonardo in this passage wrote always precedent, obviously by mistake] air did not fill the vacuum empty of air, which was expelled from the space by the foresaid mover; and such a subsequent air would not leave [Leonardo wrote fill] its space from which it separated itself, if another quantity of air did not fill the space from which it separated itself; and so it is necessary that it successively continues; and in this way it would continue to infinity, if the air were not compressible to infinity.”—(Codex Atlanticus, f. 219 v.a. 1505-06).

26 “ It is to prove how the air does not push the mobile after that it has been separated from the power of its mover. … .”—(Leicester Codex, f. 29 v. about 1507).

27 “ If you wish to see what motion is made by air which is penetrated by a mobile, do you take the example from the water, i.e., under its surface, which is mixed with rare millet or other slight seed, which keeps up in each degree of height of water, and then do you drive inside it a mobile which keeps up in the water and you will see the revolutions of such water, which has to be in a square vase of glass in the form of a box.” (Fig 4).—(Leicester Codex, f. 29 v. about 1507).

28 “ Every natural act is made by the actual on the actuated in the shortest time possible; and the air stricken and condensed by a mobile, by which it is driven cannot be that air which fills the vacuum created by the mobile, which flies forwards; but this vacuum is filled by that air which is nearer to the mobile on its opposite part, i.e., the part whence it flies away, which air continually rarefies that compression and with this operation the said vacuum is filled (Fig. 5).

Never at the same time a greater power can be overcome by a less one; therefore the rapid motion of the rarefied air, to fill the vacuum left by the mobile, is more weaker than that of the air which compresses before the mobile; which compression of air cannot be caused by air more rarefied.

Therefore we have concluded that the mobile is not driven by the wave of air created by the impetus of the mover. And if you are wishing to say. that the undulatory motion which flies before the mobile, is that which prepares the motion for it, together with the air flying behind it to restore the normal rarefaction of air, to that it is to be answered that there such an air is undulated by the mobile and not by itself; and it is impossible that in the same time the mover drives its mobile and the mobile its mover; therefore you are wrong, because if the aforesaid undulatory motion is that which pulls behind itself the cause of its motion, it is impossible that one thing by itself alone could be cause of its creation: and those which are by themselves are eternal.”—(Leicester Codex, f. 29 v. about 1507).

28 “ The motion of the air has to be smaller before the mobile which penetrates it, than it is behind such a mobile.

The air which fills the vacuum left by the mobile which penetrates the same air, has in its entirety the same velocity as that of the mobile; but that part of the same air being revertive (i.e.), of whirling motion in form of eddies) is much more velocious than the motion of the aforesaid mobile.

Here it seems that as the mobile has less velocity of air behind than before it, that such air is the cause of the motion of this body; but that, on account of the seventh proposition, cannot be the case.

No one mobile will never be more velocious than the velocity of the power driving it. The wave created by the air before the mobile penetrating it scarcely passes the same mobile, as this would be against the seventh, here penultimate.

The air behind the mobile goes back in these parts in circulation which are contiguous to that air which flees behind the mobile (Fig. 6). That air which flees behind the mobile flying through it, is driven by the impetus given to it by such a mobile; which air with a greatly extended wave, striking against the other air, goes back and diminishing with great circulation in its extremities, at last stops and does not follow the mobile. ”—(Codex F, f. 74 r. 1508).

30 “ The air which first was behind the hole made by the mobile through the air a little accompanies the same mobile for the eighth.

8th—The air which successively surrounds the mobile which moves through it makes in itself various motions (Fig. 7). This is visible on the atoms which are in a sun beam when through a window it penetrates into a dark room; in which atoms if a stone is cast for the length of such a beam, one sees all the atoms whirling around the space which was filled by air along the way created in the same air by the mobile.

The air which moves to the filling of the vacuum created into it by the mobile has in itself various speeds and densities and motion.”—(Codex F, f. 74 v. 1508).,

31 “ The air below the mobile becomes dense and that above rare.

The weight descends through air and the same air moves in a contrary motion to fill continually the place left by the same weight and the motion of this air has to be curved, because arising in the shortest line it is prevented by the weight which descends, above it; therefore it is necessary that it curves and then goes back above the same weight to fill the vacuum left by it.

But, if so, the air would not compress under the velocity of the weight; being so, birds would not keep up on the air stricken by them; but here it is necessary to say that air has to compress under its striker and above has to rarefy, in order to fill the vacuum left by that striker.

And as to the air, as it has been proved in the seventh, there is no inconvenience to be compressed and rarefied almost instantaneously (which is not possible in water as long as it maintains its form) it is more easy to the air lateral and superior to the mobile, descending in it, to fill the vacuum left by the same mobile above itself, than to the air below to curve, and in a long and curved line move to the filling of such a vacuum, and also it is impossible, on account of the eighth, which proves that any impetus created in the air drives with itself the same air along that line in which this impetus has been created; like as the wind which as much as drives air so much its impetus moves, as can be seen in dust driven by such winds or in the atoms in the beam of the sun when one blows among them.

Therefore the air pushed by the impetus of the weight which descends through it flees along the line of the motion created by its mover, and the lateral air converts itself into lateral eddies and the superior one always descends above, always filling the vacuum left above itself by such a mobile in each degree of its movement.”—(Codex F, f. 87 r. and 87 v. 1508).

32 “The air which compresses below the mobile descending in an oblique situation through it, flies rather at the upper part of the mobile than at the lower part of it.

A continuous quantity of air in proportion as rarefies at one part it compresses in another. The less the rarefied air resists, the more the compressed air makes itself more resistant. Therefore the hindmost part of the mobile b will descend with greater impetus than its foremost part, and this is the cause that the front which first was low at the end of the refleoted motion rises up (Fig. 8).—(Codex G, f. 73 v. 1510-15).

On the things which descend through the air (Fig. 9). Air compresses before bodies which with velocity penetrate it, with a density which is more or less, according as the velocity is of more or less violence.

The board of a uniform width, length, depth and weight will not maintain at a great extent its oblique motion begun through air, which is penetrated by it, but it will turn back and then forwards, and thus with an undulating motion it will end its descent. And this happens as air alters its uniform natural density, because it compresses under the right angle of the front of the board, which front strikes and opens the air. But at the opposite extremity of the said board it [the air] does the contrary with its rarefaction, and because that rarefied air is less resistant, the back [Leonardo wrote front, evidently by mistake] of the board appears heavier.

The rarity acquired by the air behind the said board is more important than the density which is generated on the front of this board.

The explanation why air compresses is this: air compresses before bodies by which it is penetrated, because that which pushes a part of the air does not push all that is before it. And this is understood by the undulation which is generated before the bow of a ship.— (Codex E, f. 70 v. 1513-1515).

The air becomes rarer behind the motion of the mobile in proportion as it becomes denser before the same mobile.

The exactness of an oblique descent will not be continued by falling bodies of uniform greatness and weight in air of equal resistance. And this is caused by air compressed by the front of the body penetrating it, which by compressing resists and stops this front, therefore the opposite extremity of such a beam, as it is in rarefied air, immediately acquires heaviness and falls with more velocity than that which is delayed by the thickness of the air compressed by it.

And therefore the impetus made by the mobile towards the right angle turns to the left, maintaining this obliquity until other air compresses again. below it, which air again resists it and the oblique descent to the left again turns to the right, and then from right to left, and from left to right, until the motion is ended, etc.”—(Codex E, f. 73 r. 1513-1515).

33 And if it will be said by the adversary that the impetus driving the mobile is in that air which surrounds it from its middle backwards, this has to be denied, as the air which follows the mobile is pulled by it to fill the vacuum left by it; while that air which compresses before the mobile flees in an opposite course.

And if air goes back is apparent that it will strike against that which is pulled behind itself by the mobile, and when two things shock, rebounding motion of both arises, which are transmuted into whirling motions in opposition one another, which are conveyed by the air, filling the vacuum left by the mobile. And it is impossible that the motion of the mover could be increased at the same time by the motion of the mobile, as the motion of the mover is always more powerful than that, of the mobile.”—(Codex G. f. 85 v. 1510-1515).

34 “ As much air runs in behind the vacuum which is left by the bird perforator of the air, so much the bird flees away before the air, which continually is joined through contact with it. Therefore it is not the shutting of the air behind the bird which drives forwards the bird; but it is the impetus which, driving the bird forwards, opens and drives away the air by which it is sheathed, as well as draws to itself the air, etc.”—(Codex E, f. 53 r. 1513-1515).

35 The following note was written by Leonardo on September 25th, 1514, in the Bell Inn at Parma, as he himself indicates in this folio:—

“ If the air which envelopes the bodies moves together with such bodies.

The air which envelopes with herself the bodies will move together with them, and this will be shown by the observation of a horse when running in dusty roads.

If the motion of air is as velocious as is its mover.

Air will never be of equal velocity to that of its mover, and this will be shown by the motions of the aforesaid dust following the course of a horse, which in very little length of motion turns back with an eddying motion in which its impetus is consumed.”—(Codex E, f. 80 r. 1514).

36 “ On the resistance of air and balances. That body has less weight which more extends and that air more resists which in the same way more extends, i.e., that interposes between the weight and earth a greater amount of itself. But the proportion of weights is not according to the proportion of air, since if a spherical weight has a diameter of one foot and a similar weight has a diameter of 2 feet, in such a Case the air interposed between these weights and the earth will resist the weight of one foot in diameter for one degree and the weight of 2 feet in diameter for 4 degrees.

Therefore passing from one diameter to the other, it happens that the resistance of air is quadruple, while from one weight to the other the proportion is octuple, and therefore being quadruple the proportion of the two Resistance, i.e., as one to 4 and the proportion of the weight being ocuple, i.e., as one to 8, the resistance of 8 is twice the resistance of 4, and therefore the motion of the greater weight is of velocity double that of the motion of the less great, being air of the same resistance. But as air doubly compress against the mobile of double velocity the aforesaid motions will be of equal speed. But if motions are equal the air will not doubly compress but it will be equal.”— (The Arundel Codex, f. 96 v. 1508).

37 “ What difference is there between properties of water and of air?

Water in itself is neither condensable nor rarefiable, but is the same before the fish penetrating it, as it is behind this fish, and as much water as opens before its penetrator, so much it is which shuts behind such a penetrator.”—(Codex E, f. 71 v. 1513-1515).

38 “ Oh motion of ships (Fig. 10). These 3 ships of equal width, length and depth, if they are driven by equal powers will have motion of different velocity, because the ship which brings forward its wider part is more velocious and it is like to the shape of birds and gray mullet. And such ship opens sideways and before itself a great deal of water, which then with its revolutions presses the ship for two-thirds of its length backwards.

The contrary is done by the ship d c while the ship e f is the average between the aforesaid two.”—(Codex G, f. 50 v. 1510-1515).

39 “ What quality of air surrounds birds in flying. The air surrounding birds is above thinner than the usual thinness of the other air, as below it is thicker than the same, and it is thinner behind than above in proportionrto the velocity of the bird in its motion forwards, in comparison with the motion of its Wings towards the ground; and in the same way the thickness of the air is thicker in front of the bird than below, in proportion to the said thinness of the two said airs.”—(Codex E, f. 45 v. 1513-15).