Notebooks

by Leonardo da Vinci

The weight which descends freely acquires a degree of movement with every degree of time, and with every degree of movement it acquires a degree of velocity.

Every weight desires to descend to the centre by the shortest way; and where there is greater weight there is greater desire, and that thing which weighs the most if left free falls most rapidly. The less the slant of the opposing substance the greater its resistance. The weight passes by nature into whatever supports it and thus penetrating from support to support it grows heavier as it passes from body to body until it realizes its desire….

If weight desires stability, force always desires flight; weight of itself is without fatigue, while force is never exempt from it. The more weight falls the more it increases and the more force falls the more it diminishes.

Weight is natural and force is accidental. Weight desires stability and permanence, and force is desirous of flight and death. Weight, force, and a blow resemble each other as regards pressure.

Nothing that can be moved is more powerful in its simple movement than its mover.111 Of the mover or the movable thing The power of the mover is always greater than the resistance of the thing moved.112

A man who wants to make a bow carry a very long way must be standing entirely on one foot and raising the other so far from the foot he stands on as to afford the requisite counterpoise to his body which is thrown forward on the first foot. And he must not hold his arm fully extended, and in order that he may be more able to bear the strain he must hold a piece of wood which as used in crossbows extends from the hand to the breast, and when he wishes to shoot he should suddenly leap forward and at the same instant extend his arm with the bow and release the cord.

Primary movement is that which is made by the movable thing during the time when it is joined to its mover.

Derived movement is that which the movable thing makes through the air after it is separated from its mover. Derived movement has its origin in primary movement and it never has swiftness or power equal to the swiftness or power of this primary movement. The course of this movable thing will conform to the direction of the mover’s course when all the parts of this movable thing have movement equal to the primary movement of their mover.

Impetus is a power impressed by the mover on the movable thing. Every impression tends to permanence or desires permanence. This is shown in the impression made by the sun in the eye of the spectator and in the impression of the sound made by the clapper as it strikes the bell.

Impetus under another name is called derived movement, which arises out of primary movement, that is to say when the movable thing is joined to its mover.

There are two different kinds of percussion, simple and complex. The simple is made by the movable thing in its falling movement upon its object. Complex is the name given when this first percussion passes beyond the resistance of the object which it strikes first, as in the blow given to the sculptor’s chisel which is afterwards transferred to the marble that he is carving.

Every spherical body of thick and resisting surface when moved by an equal force will make as much movement in the rebounds caused by its impact upon a concrete ground as if it were thrown freely through the air.

How admirable Thy justice, O Thou First Mover! Thou hast not willed that any power should be deprived of the processes or qualities necessary for its results; for, if a force have the capacity of driving an object conquered by it, a hundred braccia, and this object while obeying it meets with some obstacle, Thou hast ordained that the force of the impact will cause a new movement, which by diverse rebounds will recover the entire amount of the distance it should have traversed.

Speak first of motion then of weight as produced by motion, then of the force that proceeds from weight and motion, then of the percussion that springs from weight, motion and often from force.

Simple friction is that made by the thing moved on the place where it is dragged. Compound friction is that which the thing moved makes between two immovable things. Irregular friction is that made by the wedge of different sides.

The movement of friction is divided into parts of which one is simple and all the others are compound. Simple, when the object is dragged along a plane smooth surface without any intervention. This is the only friction that creates fire when it is powerful—that is to say it generates fire—as can be seen at waterwheels when the water is removed between the whetted iron and the wheel.

A thing which is consumed entirely by friction in its long movement will be consumed in part at the start of this movement.

I have found that the ancients were in error in their reckoning of weights, and that this error has arisen because in a considerable part of their science they have made use of poles which had substance and in a considerable part of mathematical poles, such as exist in the mind and are without substance; which errors I set down here below.

The helms formed on the shoulders of the wings of birds are provided by resourceful nature as a convenient means of deflecting the direct impetus, which often takes place during their headlong flight. For a bird finds it much more convenient to bend by direct force one of the smallest parts of the wings than the whole of them; and the reason why their feathers are made very small and very strong is that they may serve as cover for one another and in doing so arm and fortify each other with marvellous power.

Inasmuch as all beginnings of things are often the cause of great results, so we may see a small almost imperceptible movement of the rudder to have power to turn a ship of marvellous size and loaded with a very heavy cargo, and that, too, amid such a weight of water as presses on its every beam, and in the teeth of the impetuous winds which are enveloping its mighty sails. Therefore we may be certain in the case of those birds which can support themselves above the course of the winds without beating their wings, that a slight movement of wing or tail which will serve them to enter either below or above the wind, will suffice to prevent the fall of the said birds.

There are some birds which are in the habit of moving their wings more swiftly when they lower them than when they raise them, and this is seen to be the case with doves and such birds. There are others which lower their wings more slowly than they raise them, and this is seen with crows and similar birds.

The bird spreads out the feathers of its wings more and more as its flight becomes slower and this is according to the law—which says: That body will become lighter which acquired greater breadth.

When the bird desires to rise by beating its wings it raises its shoulders and beats the tips of the wings towards itself, and comes to condense the air which is interposed between the points of the wings and the breast of the bird, and the pressure from this air raises the bird.

The genius of man may make various inventions, encompassing with various instruments one and the same end; but it will never discover a more beautiful, a more economical, or a more direct one than nature’s, since in her inventions nothing is wanting and nothing is superfluous.

A bird is an instrument working according to mathematical law, which instrument it is in the capacity of man to reproduce with all its movements but not with as much strength, though it is deficient only in power of maintaining equilibrium.

A substance offers as much resistance to the air as the air to the substance. See how the beating of its wings against the air supports a heavy eagle in the highly rarefied air close to the sphere of elemental fire. Observe also how the air in motion over the sea fills the swelling sails and drives heavily laden ships.

Nature is perceived through the senses, mainly through the sense of sight. The art of painting is embedded in the process of seeing. Fields of views are conveyed through visual rays into the eye. The painter must analyse this experience in order to reproduce the visual image appearing in the eye on his picture plane. His painting should give the impression of a window through which we look out into a section of the visible world.

Experience tells us that the eye takes cognizance of ten different qualities of objects;* namely: light and darkness—the first serves to reveal the other nine—the other serves to conceal them—colour and substance, form and position, distance and nearness, movement and rest.

The touch passes through the perforated tendons and is transmitted to this same place; these tendons spread out with infinite ramifications into the skin … and carry impulse and sensation to the limbs; and passing between muscles and sinews dictate their movement to them; and they obey and in the act of obeying they contract because the swelling of the muscles reduces their length drawing the nerves with it. These nerves are interwoven amid the limbs and spread out to the extremities of the fingers transmitting to the ‘sensus communis’ the impression of what they touch.

The nerves with their muscles serve the tendons even as soldiers serve their leaders; and the tendons serve the ‘sensus communis’ as the leaders their captain, and this ‘sensus communis’ serves the soul as the captain serves his lord.

So, therefore, the articulation of the bones obeys the nerve, and the nerve the muscle, and the muscle the tendon and the tendon the ‘sensus communis’ and the ‘sensus communis’ is the seat of the soul, and the memory is its monitor, and its faculty of receiving impressions serves as its standard of reference. How the sense waits on the soul, and not the soul on the sense, and how, where the sense that should minister to the soul is lacking, the so...

The eye which is the window of the soul is the chief organ whereby the understanding can have the most complete and magnificent view of the infinite works of nature.

Now do you not see that the eye embraces the beauty of the whole world? … It counsels and corrects all the arts of mankind … it is the prince of mathematics, and the sciences founded on it are absolutely certain. It has measured the distances and sizes of the stars; it has discovered the elements and their location … it has given birth to architecture and to perspective and to the divine art of painting.

O excellent thing, superior to all others created by God! What praises can do justice to your nobility? What peoples, what tongues will fully describe your function? The eye is the window of the human body through which it feels its way and enjoys the beauty of the world. Owing to the eye the soul is con...

So I hold that the invisible powers of imagery in the eyes may project themselves to the object as do the images of the object to the eyes. An instance of how the images of all things are spread through the air may be seen if a number of mirrors be placed in a circle, and so that they reflect each other for an infinite number of times. For as the image of one reaches another it rebounds back to its source, and then becoming smaller rebounds again to the object and then returns, and so continues for an infinite number of times.

The circle of light which is in the centre of the white of the eye is by nature adapted to apprehend objects. This same circle contains a point which seems black. This is a nerve bored through, which penetrates to the seat of the powers within where impressions are received and judgement formed by the ‘sensus communis’.

Necessity has provided that all the images of objects in front of the eye shall intersect in two planes. One of these intersections is in the pupil, the other in the crystalline lens; and if this were not the case the eye could not see so great a number of objects as it does. … No image, even of the smaller object, enters the eye without being turned upside down; but as it penetrates into the crystalline lens it is once more reversed and thus the image is restored to the same position within the eye as that of the object outside the eye.*

I say that the power of vision extends through the visual rays to the surface of non-transparent bodies, while the power possessed by these bodies extends to the power of vision. Likewise each body pervades the surrounding air with its image; each separately and all together do the same; and not only do they pervade it with the semblance of the shape, but also with that of their power.

You will see when the sun is over the centre of our hemisphere that wherever it reveals itself there are semblances of form; and you will also perceive the reflections of its radiance as well as the glow of its heat; and all these powers proceed from the same source by means of radiant lines that issue from its body and they end in the opaque objects without entailing any diminution at the source.

Is not that snake called lamia seen daily by the rustics attracting to itself with fixed gaze as the magnet attracts iron, the nightingale which hastens to her death with mournful song? … Maidens are said to have power in their eyes to attract to themselves the love of men….

Perspective is the bridle and rudder of painting.

Painting is based upon perspective which is nothing else than a thorough knowledge of the function of the eye. And this function simply consists in receiving in a pyramid the forms and colours of all objects placed before it. I say in a pyramid, because there is no object so small that it will not be larger than the spot where these pyramids are received into the eye. Therefore if you extend the lines from the edges of each body as they converge you will bring them to a single point, and necessarily the said lines must form a pyramid.

Perspective is divided into three parts, of which the first deals only with the line-drawing of bodies; the second with the toning down of colours as they recede into the distance; the third with the loss of distinctness of bodies at various distances. Now the first part which deals only with lines and boundaries of bodies is called drawing, that is to say the figuration of any body. From it springs another science that deals with shade and light, also called chiaroscuro which requires much explanation.

Perspective is nothing else than the seeing a place behind a sheet of glass, smooth and quite transparent, on the surface of which all the things may be marked that are behind this glass.

Of several bodies, all equally large and equally distant, that which is most brightly illuminated will appear to the eye nearest and largest.

The air is full of infinite straight and radiating lines intersected and interwoven with one another, without one occupying the place of another. They represent to whatever object the true form of their cause.

If the eye be in the middle of a course with two horses running to their goal along parallel tracks, it will seem to it as if they were running to meet one another. This, as has been stated, occurs because the images of the horses which impress themselves upon the eye are moving towards the centre of the surface of the pupil of the eye.

Now imagine two lines starting from your ears and going to the ears of that image which you see of yourself in the eye of the other person. You will clearly recognize that these lines converge in such a way that they would meet in a point a little way beyond your own image mirrored in the eye.

Leonardo excelled in modelling by gradations of light and dark, and was a developer of chiaroscuro (the modelling of forms from white to black) and sfumato (the ‘smoked’ effect of blurring edges).

The four simple colours, red, blue, green, and yellow were related to the four elements, fire, air, water, and earth, the way in which objects were enveloped in space was similar to the way in which the elements came in contact with one another.