Authors: Leonardo da Vinci,Irma Anne Richter,Thereza Wells

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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 tranquil 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

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