All insects of this clan have power to rise with straight movement, for as they raise themselves these wings remain perforated with the front wings much higher than those behind. And this continues as long as the impulse which urges them upwards; and then as they lower their wings the larger become joined to the smaller, and so as they descend they again acquire fresh impulse.46
[With drawing of a dragonfly.]
The pannicola flies with four wings, and when those in front are raised those behind are lowered.
But it is necessary for each pair to be sufficient of itself to sustain the whole weight.
When one pair is raised the other is lowered.
In order to see the flying with four wings go into the moats and you will see the black ‘pannicole’.47
Animal as it plunges from one Element into another.48
This note accompanies a drawing of a flying gurnard with its tail turned, its wings outspread on the point of launching from water into air. On the same sheet are drawings of a butterfly, an ant-lion, and a bat, all with outspread wings.
IV. FLYING MACHINE
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.49
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. We may therefore say that such an instrument constructed by man is lacking in nothing except the life of the bird, and this life must needs be imitated by the life of man. The life which resides in the bird’s members will without doubt better obey their needs than will that of man which is separated from them and especially in the almost imperceptible movements which preserve equilibrium. But since we see that the bird is equipped for many sensitive varieties of movement, we are able from this experience to deduce that the most obvious 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 has made himself life and guide.50
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.
From these instances, and the reasons given, a man with wings large enough and duly attached might learn to overcome the resistance of the air, and conquering it succeed in subjugating it and raise himself upon it.
If a man has a tent 12 braccia wide and 12 high covered with cloth* he can throw himself down from any great height without hurting himself.51
The man in flying machines must be free from the waist upwards in order to be able to balance himself as he does in a boat, so that his centre of gravity and that of his machine may counterbalance each other and shift where necessity demands through a change in the centre of its resistance.52
Remember that your bird must imitate no other than the bat, because its membranes serve as framework or rather as a means of connecting the framework, that is the frame of the wings.
If you imitate the wings of feathered birds these are more powerful in structure because they are penetrable, that is their feathers are separate and the air passes through them. But the bat is aided by its membrane which binds the whole and is not penetrated by the air.53
Dissect the bat, and concentrate on this, and on this model arrange the machine.54
Suppose that there is a body suspended, which resembles that of a bird, and that its tail is twisted to an angle of different degrees; you will be able by means of this to deduce a general rule as to the various twists and turns in the movements of birds occasioned by the bending of their tails. In all the various movements the heaviest part of the body which moves becomes the guide of the movement.55
When the mover of a body has power divisible in four through its four chief ministering members, it will be able to employ them equally and unequally, and also all equally and all unequally, according to the dictates of the various movements of the flying body.
If they are all moved equally the flying body will be in regular movement.
If they are used unequally in continuous proportion, the flying body will be in circling movement.56
The bird I have described ought by the help of the wind to rise to a great height and this will be its safety; since even if all the above-mentioned revolutions were to befall it it would still have time to regain a position of equilibrium provided that its parts have a great resistance; so that they can safely withstand the fury and impetus of the descent by aid of the defences which I have mentioned, and of its joints made of strong tanned leather and its rigging made of cords of very strong raw silk; and let no one encumber himself with iron bands for these are very soon broken at the joints and they become worn out; and for this reason it is well not to encumber oneself with them.57
IV
THE ARTS
I. THE ARTIST’S COURSE OF STUDY
Leonardo’s notes for a treatise on painting may be arranged under the following headings: A student must learn how the eye functions; how the shapes, sizes, and recessions of objects that are put in its way can be co-ordinated; and how they are revealed by the play of light on their surfaces; he must also study their structure and life. He must understand these fundamentals in order to create in a conforming manner and spirit.
1. THE EYE AND THE APPEARANCE OF THINGS
How do we observe nature, and what is the proper analysis of our observation? These are initial questions for both painters and scientists.
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.
He was able to achieve this by the science of perspective, which provided a mathematical method of constructing a three-dimensional space which included any number of individual objects, on to a two-dimensional surface, a method which met not only the requirements of verisimilitude but also those of unification and harmony (compare p. 183).
(a) The Five Senses
The ancient speculators have concluded that the faculty of judgement which is given to man is quickened by an instrument with which the five senses are connected by means of the organ of perception (imprensiva); and to this instrument they have given the name of ‘sensus communis’. And this name is used simply because it is the common judge of the other five senses, namely seeing, hearing, touch, taste, and smell. The ‘sensus communis’ is activated by the organ of perception (imprensiva) which is situated midway between it and the senses. The organ of perception works by means of the images of the things transmitted to it by the five senses, which are placed on the surface midway between the external things and the organ of perception. . . .
The images of the surrounding things are transmitted to the senses, and the senses transmit them to the organ of perception, and the organ of perception transmits them to the ‘sensus communis’, and by it they are imprinted on the memory, and are retained there more or less distinctly according to the importance or power of the thing given. The sense which is nearest to the organ of perception functions most quickly; and this is the eye, the chief and leader of all others; of this only will we treat and leave the others in order not to be too long.
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.1
How the five senses are the ministers of the soul
The soul apparently resides in the seat of judgement, and judgement apparently resides in the place called ‘sensus communis’ where all the senses meet; and it is in this place and not throughout the body as many have believed; for if that were so it would not have been necessary for the instruments of the senses to meet in one particular spot; it would have sufficed for the eye to register its perception on its surface instead of transmitting the images of the things seen to the ‘sensus communis’ by way of the optic nerves; for the soul would have comprehended them upon the surface of the eye.
Similarly with the sense of hearing, it would suffice merely for the voice to resound in the arched recesses of the rocklike bone which is within the ear, without there having to be another passage from this bone to the ‘sensus communis’, whereby the voice must address the common judgement.
The sense of smell is also forced of necessity to have recourse to this same judgement.
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 soul in such a life lacks conception of the function of this sense, as is seen in the case of a mute or one born blind.2
Of the ten functions of the eye which all concern the painter
Painting extends over all the ten functions of the eye; that is, darkness, light, body, colour, shape, location, remoteness, nearness, motion, and rest. My little work will be woven together of these functions, reminding the painter according to what rules and in what fashion he should imitate with his art all these things, the work of nature and ornament of the world.3
(b) The Eye
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.4
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 content to stay in its bodily prison, for without it such bodily prison is torture.5
O marvellous, O stupendous necessity, thou with supreme reason compellest all effects to be the direct result of their causes; and by a supreme and irrevocable law every natural action obeys thee by the shortest possible process. Who would believe that so small a space could contain the images of all the universe? O mighty process! What talent can avail to penetrate a nature such as these? What tongue will it be that can unfold so great a wonder? Verily none! This it is that guides the human discourse to the considering of divine things. Here the forms, here the colours, here all the images of every part of the universe are contracted to a point. What point is so marvellous? O wonderful, O stupendous necessity—by thy law thou constrainest every effect to be the direct result of its cause by the shortest path. These are miracles . . . forms already lost, mingled together in so small a space it can recreate and recompose by expansion. Describe in thy anatomy what proportion there is between the diameters of all the lenses (spetie) in the eye and the distance from these to the crystalline lens.6
The eye whereby the beauty of the world is reflected is of such excellence that whoso consents to its loss deprives himself of the representation of all the works of nature. The soul is content to stay imprisoned in the human body because thanks to our eyes we can see these things; for through the eyes all the various things of nature are represented to the soul. Whoso loses his eyes leaves his soul in a dark prison without hope of ever again seeing the sun, light of all the world; How many there are to whom the darkness of night is hateful though it is of but short duration; what would they do if such darkness were to be their companion for life?7
The air is full of an infinite number of images of the things which are distributed through it, and all of these are represented in all, all in one, and all in each. Accordingly if two mirrors be placed so as to exactly face each other, the first will be reflected in the second and the second in the first. Now the first being reflected in the second carries to it its own image together with all the images reflected in it, among these being the image of the second mirror; and so it continues from image to image on to infinity, in such a way that each mirror has an infinite number of mirrors within it, each smaller than the last, and one inside another. By this example it is clearly proved that each thing transmits its image to all places where it is visible, and conversely this thing is able to receive into itself all the images of the things which are facing it.
Consequently the eye transmits its own image through the air to all the objects which face it, and also receives them on its own surface, whence the ‘sensus communis’ takes them and considers them, and commits to the memory those that are pleasing.
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.
If at night you place a light between two flat mirrors which are a cubit’s space apart, you will see in each of these mirrors an infinite number of lights, one smaller than another in succession.
If at night you place a light between walls of a room every part of them will become tinged by the images of this light, and all those parts which are directly exposed will be lit by it. . . . This example is even more apparent in the transmission of solar rays, which pass through all objects and into the minutest part of each object, and each ray conveys to its object the image of its source.
That each body alone of itself fills all the surrounding air with its images, and that this same air at the same time is able to receive into itself the images of the countless other bodies which are within it, is proved by these instances; and each body is seen in its entirety throughout the whole of this atmosphere, and each in each minutest part of it, and all throughout the whole and all in each minutest part; each in all, and all in every part.8
If the object in front of the eye sends its image to it, the e
ye also sends its image to the object; so of the object no portion whatever is lost in the images proceeding from it for any reason either in the eye or the object. Therefore we may rather believe that it is the nature and power of this luminous atmosphere that attracts and takes the images of the objects that are within it, than that it is the nature of the objects which send their images through the air. If the object opposite the eye were to send its image to it, the eye would have to do the same to the object; whence it would appear that these images were incorporeal powers. If it were thus it would be necessary that each object should rapidly become smaller; because each object appears by its image in the atmosphere in front of it; that is the whole object in the whole atmosphere and all in the part; speaking of that atmosphere which is capable of receiving in itself the straight and radiating lines of the images transmitted by the objects. For this reason then it must be admitted that it is the nature of this atmosphere which finds itself among the objects to draw to itself like a magnet the images of the objects among which it is situated.
Prove how all objects, placed in one position, are all everywhere and all in each part.
I say that if the front of a building or some piazza or field which is illuminated by the sun has a dwelling opposite to it, and if in the front which does not face the sun you make a small round hole all the illuminated objects will transmit their images through this hole and will be visible inside the dwelling on the opposite wall which should be made white, and they will be there exactly, but upside down; and if in several places on the same wall you make similar holes you will have the same result from each.
Notebooks Page 14