2. TIME AND SPACE
Proportion in all things
Proportion is not only found in numbers and measurements but also in sounds, weights, times, spaces, and in whatsoever power there may be.206
Describe the nature of time as distinguished from the geometrical definitions. The point has no part; a line is the transit of a point; points are the boundaries of a line.
An instant has no time. Time is made by the movement of the instant, and instants are the boundaries of time.207
Although time is numbered among continuous quantities,* yet through its being invisible and without substance it does not altogether fall under the head of Geometry, which represents its divisions by means of figures and bodies of infinite variety, as may constantly be seen to be the case with things visible and things of substance; but it harmonizes with these only as regards its first principles, namely as to the point and the line. The point as viewed in terms of time is to be compared with the instant and the line may be likened to the length of a quantity of time. And just as points are the beginning and end of the said line so instants form the end and the beginning of any given space of time. And whereas a line is divisible to infinity, a space of time is not unlike such a division; and as the divisions of the line may bear a certain proportion to each other, so may the parts of time.208
3. SOUND AND SPACE
Just as a stone flung into the water becomes the centre and cause of many circles, and as sound diffuses itself in circles in the air; so any object, placed in the luminous atmosphere, diffuses itself in circles, and fills the surrounding air with infinite images of itself.209
I say that the sound of the echo is reflected to the ear after it has struck, just as the images of objects striking the mirrors are reflected into the eyes. And as the image falls from the object into the mirror and from the mirror to the eye at equal angles, so sound will also strike and rebound at equal angles as it passes from the first percussion in the hollow and travels out to meet the ear.210
Every impression continues for a time in the sensitive object that receives it, and that which was of greater power will continue in its receiver for a longer time, and the less powerful for a shorter time. . . .
The sensitive impression is that of a blow received on a resounding substance such as bells and like things, or like the note in the ear, which, indeed, unless it preserved the impression of the notes, could never derive pleasure from hearing a voice alone; for when it passes straight from the first to the fifth note the effect is as though one heard these two notes simultaneously, and thus one perceived the true harmony which the first makes with the fifth; for if the impression of the first note did not remain in the ear for some space of time the fifth which follows immediately after the first would seem alone; and a single note cannot create any harmony, and therefore any note sung alone would seem devoid of charm.
Likewise the radiance of the sun or other luminous body remains in the eye for some time after it has been seen, and the motion of a single firebrand whirled rapidly in a circle causes this circle to seem one continuous uniform flame.
The drops of rain seem continuous threads descending from the clouds; and herein one may see how the eye preserves the impressions of the moving things which it sees. . . .
The voice impresses itself through the air without displacement of air, and strikes upon objects and returns back to its source.211
The painter measures the distance of things as they recede from the eye by degrees just as the musician measures the intervals of the voices heard by the ear. Although the objects observed by the eye touch one another as they recede, I shall nevertheless found my rule on a series of intervals measuring 20 braccia each, just as the musician who, though his voices are united and strung together, has created intervals according to the distance from voice to voice calling them unison, second, third, fourth, and fifth and so on, until names have been given to the various degrees of pitch proper to the human voice.*212
4. PAINTING AND SCULPTURE
Comparison between Painting and Sculpture Painting requires more thought and skill and is a more marvellous art than sculpture, because the painter’s mind must of necessity enter into nature’s mind in order to act as an interpreter between nature and art; it must be able to expound the causes of the manifestations of her laws, and the way in which the likenesses of objects that surround the eye meet in the pupil of the eye transmitting the true images; it must distinguish among a number of objects of equal size, which will appear greater to the eye; among colours that are the same, which will appear darker and which lighter; among objects all placed at the same height, which will appear higher; among similar objects placed at various distances, why they appear less distinct than others.
The art of painting includes in its domain all visible things, and sculpture with its limitations does not, namely the colours of all things in their varying intensity and the transparency of objects. The sculptor simply shows you the shapes of natural objects without further artifice. The painter can suggest to you various distances by a change in colour produced, by the atmosphere intervening between the object and the eye. He can depict mists through which the shapes of things can only be discerned with difficulty; rain with cloud-capped mountains and valleys showing through; clouds of dust whirling about the combatants who raised them; streams of varying transparency, and fishes at play between the surface of the water and its bottom; and polished pebbles of many colours deposited on the clean sand of the river bed surrounded by green plants seen underneath the water’s surface. He will represent the stars at varying heights above us and innumerable other effects whereto sculpture cannot aspire.213
The sculptor cannot represent transparent or luminous substances.214
How the eye cannot discern the shapes of bodies within their boundaries were it not for shadows and lights; and there are many sciences which would not exist but for the science of shadows and lights—as painting, sculpture, astronomy, a great part of perspective and the like.
It may be shown that the sculptor does not work without the help of shadows and lights, since without these the material carved would remain all of one colour. . . . A level surface illumined by a steady light does not anywhere vary in the clearness and obscurity of its natural colour; and this sameness of the colour indicates the uniform smoothness of the surface. It would follow therefore that if the material carved were not clothed by shadows and lights, which are produced by the prominences of the muscles and the hollows interposed, the sculptor would not be able uninterrupted to watch the progress of his work, as he must do, else what he fashions during the day would look almost as though it had been made in the darkness of the night.
Of painting
Painting, however, by means of shadows and lights presents upon level surfaces, shapes with hollowed and raised portions in diverse aspects, separated from each other at various distances.215
The sculptor may claim that basso relievo is a kind of painting; this may be conceded as far as drawing is concerned because relief partakes of perspective. But as regards the shadows and lights it errs both as sculpture and as painting because the shadows of the basso relievo in the foreshortened parts, for instance, have not the depth of the corresponding shadows in painting or sculpture in the round. But this art is a mixture of painting and sculpture.216
That sculpture is less intellectual than painting
and lacks many of its inherent qualities
As I practise the art of sculpture as well as that of painting, and am doing both in the same degree, it seems to me that without being suspected of unfairness I may venture to give an opinion as to which of the two is of greater skill and of greater difficulty and perfection.
In the first place, a statue is dependent on certain lights, namely those from above, while a picture carries its own light and shade with it everywhere. Light and shade are essential to sculpture. In this respect, the sculptor is helped by the nature of the relief, which produces them of its own accor
d; while the painter has to create them by his art in places where nature would normally do so.
The sculptor cannot differentiate between the various natural colours of objects; the painter does not fail to do so in every particular. The lines of perspective of sculptors do not seem in any way true; those of painters may appear to extend a hundred miles beyond the work itself. The effects of aerial perspective are outside the scope of sculptors’ work; they can neither represent transparent bodies nor luminous bodies nor reflections, nor shining bodies such as mirrors and like things of glittering surface, nor mists, nor dull weather, nor an infinite number of things which I forbear to mention lest they be wearisome.
The one advantage which sculpture has is that of offering greater resistance to time. . . .
Painting is more beautiful, more imaginative and richer in resource, while sculpture is more enduring, but excels in nothing else.
Sculpture reveals what it is with little effort; painting seems a thing miraculous, making things intangible appear tangible, presenting in relief things which are flat, in distance things near at hand.
In fact, painting is adorned with infinite possibilities which sculpture cannot command.217
III. ARCHITECTURAL PLANNING
Leonardo’s manuscripts contain a number of architectural designs for domed cathedrals built on a central plan where structural problems are dealt with theoretically and from an artistic point of view. He also designed forts, villas, castles, pavilions, and stables for his patrons. His advice was sought regarding the completion of the cathedrals of Milan and Pavia.
He was interested in theoretical questions of practical importance —in problems such as what form of a church would best answer the requirements of acoustics. He wrote on arches and beams and the pressure which they sustain; on the origin and progress of cracks in walls and how to avoid them.
His ideas on town-planning and on arrangement of houses and gardens combine art with technical knowledge, and provide for plenty of light, air, and open space, noise-proof rooms, two-level highways, and issues of sanitation.
The diagrams reproduced from one of his notebooks indicate the rules as given by Vitruvius and by Leon Battista Alberti for the proportions of the Attic base of a column.
What is an arch?
An arch is nothing else than a strength caused by two weaknesses; for the arch in buildings is made up of two segments of a circle, and each of these segments being in itself very weak desires to fall, and as one withstands the downfall of the other the two weaknesses are converted into a single strength.
Of the nature of the weight in arches
When once the arch has been set up it remains in a state of equilibrium, for the one side pushes the other as much as the other pushes it; but if one of the segments of the circle weighs more than the other the stability is ended and destroyed, because the greater weight will subdue the less.218
Here it is shown how the arches made in the side of the octagon thrust the piers of the angles outwards as is shown by the lines hc and td which thrust out the pier m; that is they tend to force it away from the centre of such an octagon.219
An experiment to show that a weight placed on an arch does not discharge itself entirely on its columns; on the contrary the greater the weight placed on the arches, the less the arch transmits the weight to the columns. The experiment is the following: Let a man be placed on a steelyard in the middle of the shaft of a well, then let him spread out his hands and feet between the walls of the well, and you will see him weigh much less on the steelyard. Give him a weight on the shoulders, you will see by experiment that the greater the weight you give him the greater effort he will make in spreading his arms and legs and in pressing against the wall, and the less weight will be thrown on the steelyard.220
A new tower founded partly on old masonry.221
Water stairs
When the descent from the floodgates has been so hollowed out that at the end of its drop it is below the bed of the river, the waters which descend from them will never form a cavity at the foot of the bank, and will not carry away soil in their rebound, and so they will not proceed to form a fresh obstacle but will follow the transverse course along the length of the base of the floodgate from the under side. Moreover, if the lowest part of the bank which lies diagonally across the course of the waters be constructed in deep broad steps after the manner of a staircase, the waters which as they descend in their course are accustomed to fall perpendicularly from the beginning of this lowest stage, and dig out the foundations of the bank, will not be able any longer to descend with a blow of too great a force. And I give as an example of this the stair down which the water falls from the meadows of the Sforzesca at Vigevano, for the running water falls down it for a height of fifty braccia.222
The water should be allowed to fall from the whole circle ab.223
Town planning
Let the street be as wide as the universal height of the houses.224
[With plan of town showing high- and low-level roads.]
The high-level roads are six braccia higher than the low-level roads, and each road should be twenty braccia wide and have a fall of half a braccio from the edges to the centre. And in this centre at every braccio there should be an opening of the width of a finger one braccio long, through which rainwater may drain off into holes made on the lower-level roads. And on each side of this road there should be an arcade six braccia broad resting on columns.
And if anyone wishes to go through the whole place by the high-level roads he will be able to use them for this purpose, and so also if anyone wishes to go by the low-level roads. The high-level roads are not to be used by wagons or like vehicles but are solely for the convenience of the gentle-folk. All carts and loads for the service and convenience of the common people should be confined to the low-level roads. One house has to turn its back on another, leaving the low-level road between them. The doors serve for the bringing in of provisions such as wood and wine, &c. The privies, stables, and noisome places are emptied by underground passages situated at a distance of three hundred braccia from one arch to the rest, each passage receiving light through openings in the street above, and at every arch there should be a spiral staircase. . . . At the first turn there should be a door of entry into the privies, and this staircase should enable one to descend from the high-level to the low-level road.
The high-level roads begin outside the gates at the height of six braccia. The site should be chosen near to the sea, or some large river, in order that the impurities of the city may be carried far away by water.225
Plan of house
A building ought always to be detached all round in order that its true shape can be seen.226
[With architectural drawings.]
Large room for the master, room, kitchen, larder, guard-room, large room for the family, and hall.
The large room for the master and that for the family should have the kitchen between them, and in both the food may be served through wide and low windows or by tables that turn on swivels. The large room of the family is on the other side of the kitchen so that the master of the house may not hear the clatter.
The wife should have her own apartment and hall apart from that of the family, so that she may set her serving maids to eat at another table in the same hall. She should have two other apartments as well as her own, one for the serving maids, the other for the nurses, and ample space for their utensils. And the apartment will be in communication with the various conveniences; and the garden and stable in contact.
He who is stationed in the buttery ought to have behind him the entrance to the kitchen, in order to be able to do his work expeditiously; and the window of the kitchen should be facing the buttery so that he may extract the wood. And let the kitchen be convenient for cleaning pewter so that it may not be seen being carried through the house. I wish to have one door to close the whole house.227
A water mill
By means of a mill I shall be able at any tim
e to produce a current of air; in the summer I shall make the water spring up fresh and bubbling, and flow along in the space between the tables which will be arranged thus [drawing]. The channel may be half a braccio wide, and there should be vessels there with wines, always of the freshest. Other water should flow through the garden moistening the orange and citron trees according to their needs. These citron trees will be permanent, because their situation will be so arranged that they can easily be covered over and the continuous warmth which the winter season produces will be the means of preserving them far better than fire, for two reasons: one is that this warmth of the springs is natural and is the same as warms the roots of all the plants; the second is that fire gives warmth to these plants in accidental manner, because it is deprived of moisture and is neither uniform nor continuous, being warmer at the start than at the end and is very often overlooked through the carelessness of those in charge of it.
The herbage of the little brooks ought to be cut frequently so that the clearness of the water may be seen upon its shingly bed, and only those plants should be left which serve the fishes for food, such as watercress and like plants. The fish should be such as will not make water muddy, that is to say eels must not be put there nor tench, nor yet pike because they destroy the other fish.
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