First I shall test by experiment before I proceed further, because my intention is to consult experience first and then with reasoning show why such experience is bound to operate in such a way. And this is the true rule by which those who analyse the effects of nature must proceed: and although nature begins with the cause and ends with the experience, we must follow the opposite course, namely, begin with the experience, and by means of it investigate the cause.12
O marvellous necessity, thou with supreme reason constrainest 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.13
Nature does not break her law; nature is constrained by the logical necessity of her law which is inherent in her.14
Necessity is the mistress and guide of nature.
Necessity is the theme and inventor of nature, its eternal curb and law.15
Nature is full of infinite causes that have never occurred in experience.16
In nature there is no effect without cause; understand the cause and you will have no need of the experiment.17
III. MATHEMATICAL DEMONSTRATION
The method recommended by Leonardo for submitting the results of his investigations corresponds to Euclidean geometry.
The presentation must be made in logical sequence. First came the statement of the theorem, the ‘proposition’; then came ‘concessions’ or ‘petitions’, i.e. axioms which neither require nor are capable of proof and must be taken for granted; whereupon followed the examination of the subjects under consideration.
Let no man who is not a mathematician read the elements of my work.18
There is no certainty where one can neither apply any of the mathematical sciences nor any of those which are connected with the mathematical sciences.19
Whoever condemns the supreme certainty of mathematics feeds on confusion, and can never silence the contradictions of the sophistical sciences, which lead to an eternal quackery.20
Science is an investigation by the mind which begins with the ultimate origin of a subject beyond which nothing in nature can be found to form part of the subject. Take, for example, the continuous quantity in the science of geometry: if we begin with the surface of a body we find that it is derived from lines, the boundaries of the surface. But we do not let the matter rest there, for we know that the line in its turn is terminated by points, and that the point is that ultimate unit than which there is nothing smaller. Therefore the point is the first beginning of geometry, and neither in nature nor in the human mind can there be anything which can originate the point. . . . No human investigation can be called true science without passing through mathematical tests; and if you say that the sciences which begin and end in the mind contain truth, this cannot be conceded and must be denied for many reasons. First and foremost because in such mental discourses experience does not come in, without which nothing reveals itself with certainty.21
Specification of what I ask should be taken for granted in my proofs with perspective. I ask, let it be granted that all rays passing through the air be of the same kind and travel in straight lines from their source to the objects that they strike.22
Here you must proceed methodically; that is, you must distinguish between the various parts of the proposition so that there may be no confusion and you may be well understood. 23
See to it that the examples and proofs that are given in this work are defined before you cite them.24
IV. EXPERIMENT
But before you base a law on this case test it two or three times and see whether the tests produce the same effects.25
This experiment should be made many times so that no accident may occur to hinder or falsify this proof, for the experiment may be false whether it deceived the investigator or no.26
When you put together the science of the motion of water, remember to include in each proposition its application and use, in order that these sciences may not be useless.27
Science is the captain and practice the soldiers.28
O speculator on things, boast not of knowing the things that nature ordinarily brings about; but rejoice if you know the end of those things which you yourself devise.29
Those who fall in love with practice without science are like a sailor who enters a ship without helm or compass, and who never can be certain whither he is going.30
Mechanics is the paradise of mathematical science, because by means of it one comes to the fruits of mathematics.31
V. SEARCH FOR TRUE KNOWLEDGE
ALCHEMY
Leonardo admonishes alchemists to observe the processes of nature rather than search for gold. These early chemists whose operations extended through the Middle Ages left behind an extensive literature. Until men like Leonardo began to observe Nature for the sake of learning her ways, no real progress was made. In the following quotation modern scientific views are intermingled with medieval poetical fancies—gold is called an emblem of the sun, natural organisms are called ‘elements’.
Nature is concerned with the production of elementary things. But man from these elementary things produces an infinite number of compounds; although he is unable to create any element except another life like himself—that is, in his children.
Old alchemists will be my witnesses, who have never either by chance or by experiment succeeded in creating the smallest element which can be created by nature; however, the creators of compounds deserve unmeasured praise for the usefulness of the things invented for the use of men, and would deserve it even more if they had not been the inventors of noxious things like poisons and other similar things which destroy life or mind; for which they are not exempt from blame. Moreover, by much study and experiment they are seeking to create not the meanest of Nature’s products, but the most excellent, namely gold, true son of the sun, inasmuch as of all created things it has most resemblance to the sun. No created thing is more enduring than this gold. It is immune from destruction by fire, which has power over all other created things, reducing them to ashes, glass, or smoke. And if gross avarice must drive you into such error, why do you not go to the mines where Nature produces such gold, and there become her disciple? She will in faith cure you of your folly, showing you that nothing which you use in your furnace will be among any of the things which she uses in order to produce this gold. Here there is no quicksilver, no sulphur of any kind, no fire nor other heat than that of Nature giving life to our world; and she will show you the veins of the gold spreading through the blue lapis lazuli, whose colour is unaffected by the power of the fire.
And examine well this ramification of the gold and you will see that the extremities are continuously expanding in slow movement, transmuting into gold whatever they touch; and note that therein is a living organism which it is not in your power to produce.32
Of all human opinions that is the most foolish which believes in necromancy, the sister of alchemy. But it is more open to reprehension than alchemy because it never gives birth to anything except things like itself, that is to say, lies; this does not happen in alchemy, whose function cannot be exercised by nature herself, because there are in her no organic instruments wherewith she might do the work that man performs with his hands, by the use of which he has made glass, &c. But this necromancy, the flag and flying banner blown by the wind, the guide of the stupid multitude, which is constantly witness to the limitless effects of this art; and they have filled books, declaring that enchantments and spirits can work and speak without tongues, and can speak without organic instruments—without which speech is impossible—and can carry the heaviest weights and bring tempest and rain; and that men can be turned into cats and wolves and other beasts, although indeed it is those who affirm such things who first become beasts. And surely if this necromancy did exist, as is believed by shallow wits, there is nothing on earth that would have so much importance alike for the harm and the service of man; if it were true that there were in such an art a power to disturb the tranqu
il serenity of the air, and convert it into darkness, to create coruscations and winds with dreadful thunder and lightning flashing through the darkness, and with impetuous storms to overthrow high buildings and to uproot forests; and with these to shake armies and break and overthrow them, and—more important than this—to create the devastating tempests and thereby deprive the peasants of the reward of their labours. For what method of warfare can there be which can inflict such damage upon the enemy as the power to deprive him of his harvests? What naval battle could be compared with that which he could wage who has command of the winds and can make ruinous gales that would submerge any fleet whatsoever? Surely whoever commands such violent forces will be lord of the nations, and no human ingenuity will be able to resist his destructive forces. The buried treasures, the jewels that lie in the body of the earth, will all be made manifest to him. No lock or fortress, however impregnable, will avail to save anyone against the will of such a necromancer. He will have himself carried through the air from East to West, and through all the opposite parts of the universe. But why should I enlarge further on this? What is there which could not be done by a craftsman such as this? Almost nothing, except the escape from death.
We have, therefore, explained in part the mischief and the usefulness that belong to such an art if it is real. And if it is real, why has it not remained among men who desire it so much, not having regard to any deity? For I know that there are numberless people who, in order to gratify one of their appetites, would destroy God and the whole of the universe. If this art has never remained among men, although so necessary to them, it never existed, and never will exist.33
It is impossible that anything of itself alone can be the cause of its creation; and those things which are of themselves are eternal.34
II
THE UNIVERSE
In Leonardo’s time the universe was conceived as the work of an omnipotent and purposeful creator. Inside an all-inclusive sphere four elements had concentric regions assigned to them. Earth occupied the centre. Surrounding it was water; then came a layer of air; and then, enveloping the whole, fire. These four elements did not remain at rest in their own realms, but were constantly shaken and thrown into neighbouring fields; and it was their nature to drift back to where they belonged—their law of gravitation, so to speak. Leonardo had grown up with this conception based on ancient traditions and accepted it on the whole; and as he was self-educated it is at times difficult to discern whether certain of his notes expressed original ideas or were transcriptions from books procured during his self-education.
In explaining phenomena, however, he did not refer to hypothetical unknown agencies but to the activities of nature. While agreeing with some established theories he rejected others by his strictly empirical and experimental method.
He set out to examine the interactions of four natural powers: namely, weight and force, movement and percussion. These he observed at work within the four elements, in the heat of the sun and in the flame, in the wind, in the wave and the stream, in the formation of the earth’s crust, in the growth of plants, in the muscular energy of men and animals.
He proceeded to establish laws governing the release of power and its transmission. Why not control this power and make it available for mechanical work?
He experimented with leverage, haulage, propulsion, collision. Various inventions resulted from his studies. Yet it occurred to him that man might abuse his privilege in order to cause destruction. Furthermore, might not Nature rise in revolt and provoke a cataclysm? The first part of the present chapter contains a description of the physical world as Leonardo envisaged it. In the second part some of his notes on power and on theoretical mechanics have been co-ordinated. The third part gives a few of his numerous notes on applied mechanics: on friction, on weighing instruments, tackles, wheels, screws, etc. His efforts to construct a flying machine are described in Chapter III.
I. THE FOUR ELEMENTS
Anaxagoras *
Everything comes from everything, and everything is made from everything, and everything can be turned into everything else; because that which exists in the elements is composed of those elements.1
The configuration of the elements
Of the configuration of the elements; and first against those who deny the opinion of Plato, saying that if these elements invest one another in the forms which Plato* attributed to them a vacuum would be caused between one and the other. I say this is not true, and I here prove it, but first I desire to propound some conclusions. It is not necessary that the elements which invest one another be of corresponding size in all the parts that invest and are invested. We see that the sphere of the water is manifestly of varying depth from its surface to its bottom; and that it not only would invest the earth when that was in the form of a cube, that is, of eight angles, as Plato will have it; but that it invests the earth which has innumerable angles of rocks and various prominencies and concavities, and yet no vacuum is generated between the earth and the water; again, the air invests the sphere of water together with the mountains and valleys which rise above that sphere, and no vacuum remains between the earth and the air, so that anyone who says that a vacuum is there generated speaks foolishly.
To Plato I would reply that the surfaces of the figures which the elements would have according to him could not exist. Every flexible and liquid element has of necessity its spherical surface. This is proved with the sphere of water. Let me begin by setting forth certain conceptions and conclusions. That thing is higher which is more remote from the centre of the world, and that is lower which is nearer to the centre. Water does not move of itself unless it descends and in moving it descends. These four conceptions, linked two by two, serve to prove that water that does not move of itself has its surface equidistant to the centre of the world, speaking of the great masses and not of drops or other small quantities that attract one another as the steel its filings.2
The bodies of the elements are united and in them there is neither gravity nor lightness. Gravity and lightness are produced in the mixture of the elements.3
[With a drawing of four concentric circles enclosing the four elements and a weight placed on top.]
Why does not the weight remain in its place?
It does not remain because it has no support.
Where will it move to? It will move towards the centre. And why by no other lines? Because a weight which has no support falls by the shortest road to the lowest point, which is the centre of the world. And why does the weight know how to find it by so short a line? Because it does not go like a senseless thing and does not move about in various directions.4
The watery element will be pent up within the raised banks of the rivers and the shores of the sea. Hence the encircling air will have to envelop and circumscribe an increased and more complicated structure of earth; and this great mass of earth suspended between the element of water and fire will be hampered and deprived of the necessary supply of moisture. Hence the rivers will remain without their waters; the fertile earth will put forth no more garlands of leaves; the fields will no more be decked with waving corn; all the animals, finding no fresh grass for pasture, will perish; food will be lacking to the ravening lions and wolves and other beasts of prey; and men after many desperate shifts will be forced to abandon their life, and the human race will cease to be. In this way the fertile and fruitful earth being deserted will be left arid and sterile; but owing to the water being confined in its womb, and owing to the activity of nature, it will continue for a little while in its law of growth, until the cold and rarefied air has disappeared. Then the earth will be forced to close with the element of fire and its surface will be burnt to cinders, and this will be the end of all terrestrial nature.5
1. WATER
Water held a great fascination for Leonardo. He looked upon it as the driving force of the universe and thought that he might solve the mysteries of creation by studying the laws of its movement through earth and air.
Drawings and memoranda scattered over manuscripts of different dates show that the subject absorbed his attention more or less continuously. We can see him walking, notebook in hand, along the seashore contemplating the ebb and flow of the tides, the winds as they trouble the surface of the water, the surge of the waves, the drift of the sands; or he might be standing by the riverside watching the currents and eddies and inspecting the deposits on the banks; or lingering by a stagnant pond looking at the reflections, the lustre on plants, and the play of the fish beneath. He would throw a stone into the still water and compare the ever-widening circles on the surface with waves of sound ringing through the air. Another time he may be walking up a mountain valley in order to trace a brook to its source while observing the waterfalls and the ceaseless grinding of rocks and pebbles.
The existence of marine shells and fossils inland and at high altitudes and the varying strata of soil or rock led him to conceive of streams as chief agents in the formation of the earth’s surface, and he foreshadowed the conception of gradual evolution. As an engineer he embarked on schemes of canalization, irrigation, and drainage and the utilization of water-power for pumping, sawing, and grinding. As an architect he designed fountains and landscape gardens. As an artist he loved to introduce streams winding through rock formations into his backgrounds, for he claimed that the painter can represent both the human figure and inanimate nature, that man must be visualized as forming part of creation. His imaginative description of the Deluge (see pp. 178- 84) draws a picture of the destructive power of this element. He also wrote a book on The Nature of Water, which lay in his room when the Cardinal of Aragon paid him a visit at Amboise in 1517 (see p. 356). A manuscript entitled ‘On the Nature, Weight and Movement of Waters’ is now known as the Leicester Codex (Bill and Melinda Gates Collection).
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