Philosophy 

'Nature is full of infinite causes which were never set forth in experience! 

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We have no lack of system or device to measure and to parcel out these poor days of ours; wherein it should be our pleasure that they be not squandered or suffered to pass away in vain, and without meed of honour, leaving no record of themselves in the minds of men; to the end that this our poor course may not be sped in vain. c.a. 12 v. a 

Our judgment does not reckon in their exact and proper order things which have come to pass at different periods of time; for many things which happened many years ago will seem nearly related to the present, and many things that are recent will seem ancient, extending back to the far-off period of our youth. And so it is with the eye, with regard to distant things, which when illumined by the sun seem near to the eye, while many things which are near seem far ofif. c.a. 29 v. a 

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Supreme happiness will be the greatest cause of misery, and the perfection of wisdom the occasion of folly. c.a. 39 v. c 

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Every part is disposed to unite with the whole, that it may thereby escape from its own incompleteness. 

The soul desires to dwell with the body because without the members of that body it can neither act nor feel. c.a. 59 r. b 

[Drawing: bird sitting in cage]  1 The sketch at the side of this sentence serves to recall the fact that as Vasari states Leonardo was in the habit of paying the price demanded by the owners of captive birds simply for the pleasure of setting them free. 

The thoughts turn towards hope.

1 c.a. 68 v. b 

O Time, thou that consumest all things! O envious age, thou destroyest all things and devourest all things with the hard teeth of the years, little by little, in slow death! Helen, when she looked in her mirror and saw the withered wrinkles which old age had made in her face, wept, and wondered to herself why ever she had twice been carried away. 

Time, thou that consumest all things! O envious age, whereby all things are consumed! 1 c.a. 71 r. a 

The age as it flies glides secretly and deceives one and another; nothing is more fleeting than the years, but he who sows virtue reaps 
honour. c.a. 71 v. a 

Wrongfully do men lament the flight of time, accusing it of being too swift, and not perceiving that its period is yet sufficient; but good memory wherewith Nature has endowed us causes everything long past to seem present. 

1 Gerolamo Calvi has shown in an article in the Archivio Storico Lombardo, Anno 
XLIX (191 6) Fasc. Ill that the source of this passage is to be found in Ovid's Meta- 
morphoses, Book XV, lines 232-6: 

Tlet quoque, ut in speculo rugas aspexit aniles 
Tyndaris, et secum, cur sit bis rapta, requirit. 
Tempus edax rerum, tuque, invidiosa vetustas, 
Omnia destruitis, vitiataque dentibus aevi 
Paulatim lenta consumitis omnia morte.' 

'Helen also weeps when she sees her aged wrinkles in the looking-glass, and tearfully asks herself why she should twice have been a lover's prey. O Time, thou great de- vourer, and thou, envious Age, together you destroy all things; and, slowly gnawing with your teeth, you finally consume all things in lingering death!' (Loeb.) 

The passage as it appears in the Codice Atlantico serves to show how Leonardo in borrowing enriched the Roman poet's thought with the melody of music by introducing the apostrophe to time and envious age as prelude as well as finale: 

'O tempo, consumatore delle cose, e o invidiosa antichita, tu distruggi tutte le cose e consumi tutte le cose da duri denti della vecchiezza a poco a poco con lenta morte! 

Elena quando si specchiava, vedendo le vizze grinze del suo viso, fatte per la vecchiezza, piagnie e pensa seco, perche fu rapita due volte. O tempo, consumatore delle cose, e o invidiosa antichita, per la quale tutte le cose sono consumate.' 

Immediately below this passage Leonardo wrote these words: 'this book belongs to Michele di Francesco Bernabini and his family'. It is a easonable inference that they refer to the copy of Ovid from which the lines were taken. Farther below in writing of the same time is a fragment: 'tell, tell me how things are passing yonder and whether Caterina wishes to make . . .' 

Caterina was the name of Leonardo's mother. He wrote the name when his thoughts had just been turning to the poet's description of the changes that time had made in Helen's beauty. From this has arisen the conjecture — it is nothing more! — that the sentence refers to her and that he was making some provision for her in her old age. 

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Whoever would see in what state the soul dwells within the body, let him mark how this body uses its daily habitation, for if this be con- 
fused and without order the body will be kept in disorder and confusion by the soul. c.a. 76 r. a 

O thou that sleepest, what is sleep? Sleep is an image of death. Oh, why not let your work be such that after death you become an image of immortality; as in life you become when sleeping like unto the hapless dead. 

Man and the animals are merely a passage and channel for food, a tomb for other animals, a haven for the dead, giving life by the death of others, a coffer full of corruption. c.a. 76 v. a 

Behold a thing which the more need there is of it is the more rejected: this is advice, listened to unwillingly by those who have most need of it, that is by the ignorant. Behold a thing which the more you have fear of it and the more you flee from it comes the nearer to you : this is misery, which the more you flee from it makes you the more wretched and without rest. c.a. 80 v. a 

Experience the interpreter between resourceful nature and the human species teaches that that which this nature works out among mortals constrained by necessity cannot operate in any other way than that in which reason which is its rudder teaches it to work. c.a. 86 r. a 

To the ambitious, whom neither the boon of life, nor the beauty of the world suffice to content, it comes as penance that life with them is 
squandered, and that they possess neither the benefits nor the beauty of the world. c.a. 91 v. a 

The air as soon as there is light is filled with innumerable images to which the eye serves as a magnet. c.a. 109 v. a 

In youth acquire that which may requite you for the deprivations of old age; and if you are mindful that old age has wisdom for its food, you will so exert yourself in youth, that your old age will not lack sustenance, c.a. 112 r. a 

There is no result in nature without a cause; understand the cause and you will have no need of the experiment. c.a. 147 v. a 

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Experience is never at fault; it is only your judgment that is in error in promising itself such results from experience as are not caused by our experiments. For having given a beginning, what follows from it must necessarily be a natural development of such a beginning, unless it has been subject to a contrary influence, while, if it is affected by any contrary influence, the result which ought to follow from the aforesaid beginning will be found to partake of this contrary influence in a greater or less degree in proportion as the said influence is more or less powerful than the aforesaid beginning. c.a. 154 r. h 

Experience is not at fault; it is only our judgment that is in error in promising itself from experience things which are not within her power. Wrongly do men cry out against experience and with bitter reproaches accuse her of deceitfulness. Let experience alone, and rather turn your complaints against your own ignorance, which causes you to be so carried away by your vain and insensate desires as to expect from experience things which are not within her power! 

Wrongly do men cry out against innocent experience, accusing her often of deceit and lying demonstrations! ca. 154 r. c 

O mathematicians, throw light on this error. 

The spirit has no voice, for where there is voice there is a body, and where there is a body there is occupation of space which prevents the 
eye from seeing things situated beyond this space; consequently this body of itself fills the whole surrounding air, that is by its images. c.a. 190 v.b 

The body of the earth is of the nature of a fish, a grampus or sperm whale, because it draws water as its breath instead of air. ca. 203 r. b 

How the movements of the eye of the ray of the sun and of the mind are the swiftest that can be: 

The sun so soon as ever it appears in the east instantly proceeds with its rays to the west; and these are made up of three incorporeal forces, namely radiance, heat, and the image of the shape which produces these. The eye so soon as ever it is opened beholds all the stars of our hemisphere. 

The mind passes in an instant from the east to the west; and all the great incorporeal things resemble these very closely in their speed. c.a. 204 v. a 

When you wish to produce a result by means of an instrument do not allow yourself to complicate it by introducing many subsidiary parts but follow the briefest way possible, and do not act as those do who when they do not know how to express a thing in its own proper vocabulary proceed by a method of circumlocution and with great prolixity and confusion. c.a. 206 v. a 

Two weaknesses leaning together create a strength. Therefore the half of the world leaning against the other half becomes firm. 

c.a. 244 v. a 

While I thought that I was learning how to live, I have been learning how to die.

c.a. 252 r. a

 Every part of an element separated from its mass desires to return to it by the shortest way. c.a. 273 r. b 

Nothingness has no centre, and its boundaries are nothingness. My opponent says that nothingness and a vacuum are one and the same thing, having indeed two separate names by which they are called, but not existing separately in nature. 

The reply is that whenever there exists a vacuum there will also be the space which surrounds it, but nothingness exists apart from occupation of space; it follows that nothingness and a vacuum are not the same, for the one is divisible to infinity, and nothingness cannot be divided because nothing can be less than it is; and if you were to take part from it this part would be equal to the whole, and the whole to the part. c.a. 289 v. b 

Aristotle in the Third [Book] of the Ethics: man is worthy of praise and blame solely in respect of such actions as it is within his power to do or to abstain from. c.a. 289 v. c 

He who expects from experience what she does not possess takes leave of reason. c.a. 299 r. b 

For what reason do such animals as sow their seed sow with pleasure and the one who awaits receives with pleasure and brings forth with pain? c.a. 320 v. b 

Intellectual passion drives out sensuality. c.a. 358 v. a 

The sexual drive to procreate is channeled into creativity. -D

The knowledge of past time and of the position of the earth is the adornment and the food of human minds. c.a. 373 v. a 

Among the great things which are found among us the existence of Nothing is the greatest. This dwells in time, and stretches its limbs into the past and the future, and with these takes to itself all works that are past and those that are to come, both of nature and of the animals, and possesses nothing of the indivisible present. It does not however extend to the essence of anything. c.a. 398 v. d 

CORNELIUS CELSUS 

The chief good is wisdom : the chief evil is the suffering of the body. Seeing therefore that we are made up of two things, namely of soul and body, of which the first is the better and the inferior is the body, wisdom belongs to the better part and the chief evil belongs to the worse part and is the worst. The best thing in the soul is wisdom, and even so the worst thing in the body is pain. As therefore the chief evil is bodily pain, so wisdom is the chief good of the soul, that is of the wise man, and nothing else can be compared to it. Tr. 3 a 

The lover is drawn by the thing loved, as the sense is by that which it perceives, and it unites with it, and they become one and the same thing. The work is the first thing born of the union; if the thing that is loved be base, the lover becomes base. When the thing taken into union is in harmony with that which receives it, there follow rejoicing and pleasure and satisfaction. When the lover is united to that which is loved it finds rest there; when the burden is laid down there it finds rest. The thing is known with our intellect. Tr. 9 a 

As a well-spent day brings happy sleep, so life well used brings happy death. Tr. 28 a 

Where there is most power of feeling, there of martyrs is the greatest martyr. Tr. 35 a 

What/ who you care about the most will incite the most feelings when they are lost. (Mother/ Jesus etc) -D

All our knowledge originates in our sensibilities. Tr. 41 a 

We obtain information from our senses - mainly vision. -D

Science, knowledge of the things that are possible present and past; prescience, knowledge of the things which may come to pass. Tr. 46 r. 

Futurology - the study of things which are going to be happening. Science fiction was a precursor and "prophets' and "prophecies" are similar. -D

Demetrius was wont to say that there was no difference between the words and speech of the unskilled and ignorant and the sounds and rumblings caused by the stomach being full of superfluous wind. This he said not without reason for as he held it did not in the least matter from what part of them the voice emanated, whether from the lower parts or the mouth, since the one and the other were of equal worth and importance. Tr. 52 a 

Nothing can be written as the result of new researches. Tr. 53 a 

To enjoy — to love a thing for its own sake and for no other reason. Tr. 59 a 

The senses are of the earth, the reason stands apart from them in contemplation. Tr. 60 a 

Life well spent is long. 

In rivers, the water that you touch is the last of what has passed and the first of that which comes : so with time present. Tr. 63 a 

Every action must necessarily find expression in movement. To know and to will are two operations of the human mind. To discern to judge to reflect are actions of the human mind. Our body is subject to heaven, and heaven is subject to the spirit. Tr. 65 a 

Many times one and the same thing is drawn by two violences, namely necessity and power. 

Water falls in rain; the earth absorbs it from necessity of moisture; and the sun raises it up not from necessity but by its power. Tr. 70 a 

The soul can never be infected by the corruption of the body, but acts in the body like the wind which causes the sound of the organ, wherein if one of the pipes becomes spoiled no good effect can be produced because of its emptiness. Tr. 71 a 

If you kept your body in accordance with virtue your desires would not be of this world. You grow in reputation like bread in the hands of children. b 3 v. 

There cannot be any sound where there is no movement or percussion of the air. There cannot be any percussion of the air where there is no instrument. There cannot be any instrument without a body. This being so a spirit cannot have either sound or form or force, and if it should assume a body it cannot penetrate or enter where the doors are shut. And if any should say that through air being collected together and compressed a spirit may assume bodies of various shapes,and by such instrument may speak and move with force, my reply to this would be that where there are neither nerves nor bones there cannot be any force exerted in any movement made by imaginary spirits. Shun the precepts of those speculators whose arguments are not confirmed by experience. b 4 v. 

OF WHAT FORCE IS 

Force I define as a spiritual power, incorporeal and invisible, which with brief life is produced in those bodies which as the result of accidental violence are brought out of their natural state and condition. I have said spiritual because in this force there is an active, incorporeal life; and I call it invisible because the body in which it is created does not increase either in weight or in size; and of brief duration because it desires perpetually to subdue its cause, and when this is subdued it kills itself. b 63 r. 

One ought not to desire the impossible. e 31 v. 

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 shapes which Plato attributed to them a vacuum would be occasioned between one and the other which is not true. I prove this here but first of all it is necessary to set forth certain conclusions. 

It is not necessary for any of the elements which invest one another to be of equal size in all its extent as between the part that invests and that which is invested. We see that the sphere of the water is manifestly of different degrees of thickness from its surface to its base, and that it would not only cover the earth if it had the shape of a cube that is of eight angles as Plato would have it, but it covers the earth having innumerable angles of rocks covered by the water and various protuberances and hollows without creating any vacuum between the water and the earth. Moreover as regards the air which clothes the sphere of the water together with the mountains and valleys which rise about this sphere there is not left any vacuum between the earth and the air. So that whoever has said that a vacuum is there produced has spoken foolishly. 

To Plato one would make answer that the surfaces of the figures that 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 but first must be set 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 this centre. Water does not move of itself unless it descends and in moving itself it descends. These four conceptions placed two by two serve me to prove that water that does not move of itself has its surface equidistant to the centre of the world, speaking not of drops or other small quantities that attract one another as the steel its filings, but of the great masses. f 27 r. 

Conception: Necessity wills that the corporeal agent be in contact with that which employs it. f 36 v. 

Observe the light and consider its beauty. Blink your eye and look at it. That which you see was not there at first, and that which was there is no more. 

Who is it who makes it anew if the maker dies continually ? 

f 49 v. 

The other proof that Plato gave to those of Delos is not geometrical, because it proceeds by instruments, the compass and the rule, and experience does not show it; but this is all mental and in consequence geometrical. f 59 r. 

Man has great power of speech, but the greater part thereof is empty and deceitful. The animals have little, but that little is useful and true; 1 and better is a small and certain thing than a great falsehood. f 96 v. 

You who speculate on the nature of things, I praise you not for knowing the processes which nature ordinarily effects of herself, but rejoice if so be that you know the issue of such things as your mind conceives. g 47 r. 

Words which fail to satisfy the ear of the listener always either fatigue or weary him; and you may often see a sign of this when such listeners are frequently yawning. Consequently when addressing men whose good opinion you desire, either cut short your speech when you see these evident signs of impatience, or else change the subject; for if you take any other course, then in place of the approbation you desire you will win dislike and ill-will. And if you would see in what a man takes pleasure without hearing him speak, talk to him and change the subject of your discourse several times, and when it comes about that you see him stand fixedly without either yawning or knitting his brows or making any other 
movement, then be sure that the subject of which you are speaking is the one in which he takes pleasure. g 49 r. 

Every evil leaves a sorrow in the memory except the supreme evil, death, and this destroys memory itself together with life. h 33 v. 

Nothing is so much to be feared as a bad reputation. This bad reputation is caused by vices. h 40 r. 

Though nature has given sensibility to pain to such living organisms as have the power of movement, — in order thereby to preserve the members which in this movement are liable to diminish and be destroyed, — the living organisms which have no power of movement do not have to encounter opposing objects, and plants consequently do not need to have a sensibility to pain, and so it comes about that if you break them they do not feel anguish in their members as do the animals. h 60 [12] r. 

OF THE SOUL 

Movement of earth against earth pressing down upon it causes a slight movement of the parts struck. 

Water struck by water creates circles at a great distance round the spot where it is struck; the voice in the air goes further, in fire further still; mind ranges over the universe but being finite it does not extend into infinity. h 67 [19] r. 

[Parallel of organism of nature and man] 

The water which rises in the mountains is the blood which keeps the mountain in life. If one of its veins be open either internally or at the side, nature, which assists its organisms, abounding in increased desire to overcome the scarcity of moisture thus poured out is prodigal there in diligent aid, as also happens with the place at which a man has received a blow. For one sees then how as help comes the blood increases under the skin in the form of a swelling in order to open the infected part. Similarly life being severed at the topmost extremity (of the mountain) nature sends her fluid from its lowest foundations up to the greatest height of the severed passage, and as this is poured out there it does not leave it bereft of vital fluid down to the end of its life. h 77 [29] r. 

Every wrong shall be set right. h 99 [44 v.] r. 

Movement is the cause of all life. h 141 [2 v.] r. 

He who does not value life does not deserve it. 1 15 r. 

Nature is full of infinite causes which were never set forth in experience. 1 18 r. 

What is it that is much desired by men, but which they know not while possessing? It is sleep. 1 56 [8] r. 

Wine is good, but water is preferable at table. 1 122 [74] v. 

Science is the captain, practice the soldiers. 1 130 [82] r. 

FLAX AND DEATH *

Flax is dedicated to death and human corruption: to death by the lakes with nets for birds beasts and fishes; to corruption by the linen cloths in which the dead are wrapped when they are buried, for in these cloths they sufifer corruption. 

And moreover this flax does not become separated from its stalks until it commences to soften and become corrupt; and it is this which one should use to make garlands and adornments for funeral processions, l 72 v. 

Truth alone was the daughter of time. m 58 v. 

Small rooms or dwellings set the mind in the right path, large ones cause it to go astray. ms. 2038 Bib. Nat. 16 r. 

Just as eating contrary to the inclination is injurious to the health, so study without desire spoils the memory, and it retains nothing that it takes in. ms. 2038 Bib. Nat. 34 r. 

Call not that riches which may be lost; virtue is our true wealth, and the true reward of its possessor. It cannot be lost; it will not abandon us unless life itself first leaves us. As for property and material wealth, these you should ever hold in fear; full often they leave their possessor in ignominy, mocked at for having lost possession of them. ms. 2038 Bib. Nat. 34 v. 

The earth is moved from its position by the weight of a tiny bird resting upon it. The surface of the sphere of the water is moved by a tiny drop of 
water falling upon it. b.m. 19 r. 

Every action done by nature is done in the shortest way. b.m. 85 v. 

Where the descent is easier there the ascent is more difficult. b.m. 120 r. 

That which is termed nothingness is found only in time and speech. In time it is found between the past and the future and retains nothing of the present; in speech likewise when the things spoken of do not exist or are impossible. In the presence of nature nothingness is not found: it has its associates among the things impossible whence for this reason it has no existence. 

In the presence of time nothingness dwells between the past and the future and possesses nothing of the present; and in the presence of nature it finds its associates among things impossible, whence for this reason it is said that it has no existence. For where nothingness existed there would be a vacuum. 

Amid the immensity of the things about us the existence of nothingness holds the first place, and its function extends over the things that have no existence, and its essence dwells in respect of time between past and future, and possesses nothing of the present. This nothingness has the part equal to the whole and the whole to the part, the divisible to the indivisible, and its power does not extend among the things of nature, for inasmuch as this abhors a vacuum this nothingness loses its essence because the end of one thing is the beginning of another. 

It is possible to conceive everything that has substance as divisible into an infinite number of parts. 

Amid the greatness of the things around us the existence of nothingness holds the first place, and its function extends among the things which have no existence, and its essence dwells as regards time between the past and the future, and possesses nothing of the present. This nothingness has the part equal to the whole and the whole to the part, the divisible to the indivisible, and it comes to the same amount whether we divide it or multiply it or add to it or substract from it, as is shown by the arithmeticians in their tenth sign which represents 
this nothingness. And its power does not extend among the things of nature. b.m. 131 r. 

Of the end of the world

The watery element remaining pent up within the raised banks of the rivers and the shores of the sea, it will come to pass with the upheaval of the earth that as the encircling air has to bind and circumscribe the complicated structure of the earth, its mass which was between the water and the fiery element will be left straitly compassed about and deprived of the necessary supply of water. 

The rivers will remain without their waters; the fertile earth will put forth no more her budding branches; the fields will be decked no more with waving corn. All the animals will perish, failing to find fresh grass for fodder; and the ravening lions and wolves and other beasts which live by prey will lack sustenance; and it will come about after many desperate shifts that men will be forced to adandon their life and the human race will cease to be. And in this way the fertile fruitful earth being deserted will be left arid and sterile, and through the pent up moisture of the water enclosed within its womb and by the activity of its nature it will follow in part its law of growth until having passed through the cold and rarefied air it will be forced to end its course in the element of fire. Then the surface of it will remain burnt to a cinder, and this will be the end of all terrestrial nature. b.m. 155 v. 

A disputation

Against. — Why nature did not ordain that one animal should not live by the death of another. 

For. — Nature being capricious and taking pleasure in creating and producing a continuous succession of lives and forms because she knows that they serve to increase her terrestrial substance, is more ready and swift in creating than time is in destroying, and therefore she has ordained that many animals shall serve as food one for the other; and as this does not satisfy her desire she sends forth frequently certain noisome and pestilential vapours and continual plagues upon the vast accumulations and herds of animals and especially upon human beings who increase very rapidly because other animals do not feed upon them; and if the causes are taken away the results will cease. 

Against. — Therefore this earth seeks to lose its life while desiring continual reproduction for the reason brought forth, and demonstrated to you. Effects often resemble their causes. The animals serve as a type of the life of the world. 

For. — Behold now the hope and desire of going back to one's own country or returning to primal chaos, like that of the moth to the light, of the man who with perpetual longing always looks forward with joy to each new spring and each new summer, and to the new months and the new years, deeming that the things he longs for are too slow in coming; and who does not perceive that he is longing for his own destruction. But this longing is in its quintessence the spirit of the elements, which finding itself imprisoned within the life of the human body desires continually to return to its source. 

And I would have you to know that this same longing is in its quintessence inherent in nature, and that man is a type of the world. b.m. 156 v. 

Therefore the end of nothingness and the beginning of the line are in contact jjne^vith another, but they are not joined together, and in such contact is the power* which divides the continuation of nothingness and the line. 

It follows that the point is less than nothing, and if all the parts of nothingness are equal to one we may the more conclude that all the points also are equal to one single point and one point is equal to all. 

And from this it follows that many points imagined in continuous contact do not constitute the line, and as a consequence many lines in continuous contact as regards their sides do not make a surface, nor do many surfaces in continuous contact make a body, because among us 
bodies are not formed of incorporeal things. 

The point is that which has no centre because it is all centre, and nothing can be less. 

The contact of the liquid with the solid is a surface common to the liquid and to the solid, and the lighter liquids with the heavier have the same. 

All the points are equal to one and one to all. 

Nothingness has a surface in common with a thing and the thing has a surface in common with nothingness, and the surface of a thing is not part of this thing. It follows that the surface of nothingness is not part of this nothingness; it must needs be therefore that a mere surface is the common boundary of two things that are in contact; thus the surface of water does not form part of the water nor consequently does it form part of the atmosphere, nor are any other bodies interposed between them. What is it therefore that divides the atmosphere from the water? It is necessary that there should be a common boundary which is neither air nor water but is without substance, because a body interposed between two bodies prevents their contact, and this does not happen in water with air because they are in contact without the interposition of any medium. 

Therefore they are joined together and you cannot raise up or move the air without the water, nor will you be able to raise up the flat thing from the other without drawing it back through the air. Therefore a surface is the common boundary of two bodies which are not continuous, and does not form part of either one or the other for if the surface formed part of it it would have divisible bulk, whereas however it is not divisible and nothingness divides these bodies the one from the other. b.m. 159 v. 

OF TIME AS A CONTINUOUS QUANTITY 

Although time is numbered among continuous quantities yet through its being invisible and without substance it does not altogether fall under the category of geometrical terms, which are divided in figures and bodies of infinite variety, as may constantly be seen to be the case with things visible and things of substance; but it harmonises 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 resembles 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 a certain given space of time. And if a line be divisible to infinity it is not impossible for a space of time to be so divided. And if the divided parts of a line may bear a certain proportion one Co another so also may the parts of time. b.m. 173 v. and 190 v. 

(liven the cause nature produces the effect in the briefest manner that it can employ. b.m. 174 v. 

Write of the nature of time as distinct from its geometry. b.m. 176 r. 

DISCOURSE 

Heat and cold proceed from the propinquity and remoteness of the sun. 

Heat and cold produce the movement of the elements. 

No element has of itself gravity or levity. 

Gravity and levity without increase arise from the movement of the element in itself in its rarefaction and condensation, as we see happen in the atmosphere in the creation of clouds by means of the moisture which is diffused through it. 

Gravity and levity when increased proceed along a perpendicular line from one element to another. And these unforseen events have as much more power as they have more of life, and as much more of life as they have more of movement. 

The movement originates in the fact that what is thinner can neither resist nor support above it what is more dense. 

Levity is born of gravity and gravity of levity; repaying in the same instant the boon of their creation they grow the more in power as they grow in life and have the more life in proportion as they have more movement; in the same instant also they destroy one another in the common vendetta of their death. 

For so it is proved: levity is not created unless it is in conjunction with gravity, nor is gravity produced unless it is continued in levity. But the levity has no existence unless it is underneath gravity, and gravity is as nothing unless it is above levity. And so it is with the elements. If for example a quantity of air lay beneath water then it follows that the water immediately acquires gravity; not that it is changed from its first condition but because it does not meet with the due amount of resistance; it therefore descends into the position occupied by the air which was beneath it and the air fills up the vacuum which the gravity so created has left in it. b.m. 204 r. 

Every continuous quantity is infinitely divisible; therefore the division of this quantity will never result in a point which is given as the extremity of a line. It follows that the breadth and depth of the natural line is divisible to infinity. 

It is asked whether all the infinites are equal or whether they are greater the one than the other. The answer is that every infinite is eternal and eternal things are of equal permanence but not of equal length of existence. For that which functioned first commenced to divide and has passed a longer existence, but the periods to come are equal. b.m. 204 v. 

No element has in itself gravity or levity unless it moves. The earth is in contact with the water and with the air and has of itself neither gravity nor levity. It has no consciousness of the water or air which surrounds it except by accident which arises from their movement. And this we learn from the leaves of plants which grow upon the earth when it is in contact with water or air, for they do not bend except by the movement of the air or water. 

From the foregoing we should say that gravity is an incident created by the movement of the lower elements in the higher. Levity is an incident created when the thinner element is drawn beneath the less thin which then moves being unable to resist and then acquires weight this being created so soon as the element lacks the power of resistance; which resistance being subdued by weight it does not change without change of substance; and in changing it acquires the name of levity. 

Levity is not produced except together with gravity, nor gravity without levity: this may be produced: for let air be suspended under water by blowing through a pipe, then this air will acquire levity from being beneath the water and the water will acquire gravity from having beneath it the air which is a body thinner and lighter than itself. 

Therefore levity is born of weight and weight of lightness, and they give birth one to another at the same time repaying the boon of their existence, and at the same instant they destroy one another as the avengers of their death. 

Levity and gravity are caused by immediate movement. 

Movement is created by heat and cold. 

Movement is an incident created by inequality of weight and force. 

The atmosphere has not of itself a natural position and always closes up over a body that is thicker than itself, never over the lighter when it is in contact with it except by violence. 

The movement of the elements arises from the sun. 

The heat of the universe is produced by the sun. 

The light and heat of the universe come from the sun and its cold and darkness from the withdrawal of the sun. 

Every movement of the elements arises from heat and cold. 

Gravity and levity are created in the elements. b.m. 205 r. 

The earth is in contact with the water and the air, and acquires as much weight from the water as from the air; and this is nothing unless they have movement. 

This we may learn from the leaves of plants born in the depths of the water which lies upon the meadows, and the leaves and branches of the trees, and similarly from the fact of plants born in the bed of the waters not bending down it is manifest that the air and the water do not give their weight to the earth. b.m. 266 v. 

EXAMPLE OF THE CENTRE OF THE WORLD 

Suppose the earth to be drawn to the position of the moon together with the water, and that the element of the air fills with itself the vacuum in the air which the earth in separating has left of itself, and that from the air there falls a vase full of air, it is certain that this vase after many wavering movements, that is falling and reflex, will come to a stop at about the centre of the elements. And the centre of the elements will remain in the air that is within the vase and it will not touch the vase. Or suppose the earth hollowed out like a ball full of wind, you will then be certain that this centre is not in the earth, but in the air clothed by the earth. bm. 267 r. 

Why does the eye see a thing more clearly in dreams than the imagination when awake? b.m. 278 v. 

Wisdom is the daughter of experience, which experience . . . Forster in. 14 r. 

And this man excels in folly in that he continually stints himself in order that he may not want, and his life slips away while he is still looking forward to enjoying the wealth which by extreme toil he has acquired. Forster in. 17 v. 

Here nature seems in many or for many animals to have been rather a cruel step-mother than a mother, and for some not a step-mother but 
a compassionate mother. Forster in. 20 v. 

I obey thee, O Lord, first because of the love which I ought reasonably to bear thee; secondly, because thou knowest how to shorten or 
prolong the lives of men. Forster in. 29 r. 

Shun those studies in which the work that results dies with the worker. Forster in. 55 r. 

Lo some who can call themselves nothing more than a passage for food, producers of dung, fillers up of privies, for of them nothing else appears in the world, nor is there any virtue in their work, for nothing of them remains but full privies. Forster in. 74 v.

 And thou, man, who by these my labours dost look upon the marvellous works of nature, if thou judgest it to be an atrocious act to destroy the same, reflect that it is an infinitely atrocious act to take away the life of man. For thou shouldst be mindful that though what is thus compounded seem to thee of marvellous subtlety, it is as nothing compared with the soul that dwells within this structure; and in truth, whatever this may be, it is a divine thing which suffers it thus to dwell within its handiwork at its good pleasure, and wills not that thy rage or malice should destroy such a life, since in truth he who values it not does not deserve it. 

For we part from the body with extreme reluctance, and I indeed believe that its grief and lamentation are not without cause. Fogli a. 2 r. 

The idea or the faculty of imagination is both rudder and bridle to the senses, inasmuch as the thing imagined moves the sense. 

Pre-imagining is the imagining of things that arc to be. Post-imagining is the imagining of things that are past. Fogli b. 2 v. 

Of neiv necessities

Neither promise yourself things nor do things if you see that when deprived of them they will cause you material suffering. Fogli b. 21 v. 

OF NECROMANCY 

But of all human discourses that must be considered as most foolish which affirms a belief in necromancy, which is the sister of alchemy, the producer of simple and natural things, but is so much the more worthy of blame than alchemy, because it never gives birth to anything whatever except to things like itself, that is to say lies; and this is not the case with alchemy, which works by the simple products of nature, but whose function cannot be exercised by nature herself, because there are in her no organic instruments with which she might be able to do the work which man performs with his hands, by the use of which he has made glass, etc. But this necromancy, an ensign or flying banner, blown by the wind, is the guide of the foolish multitude, which is a continual witness by its clamour to the limitless effects of such an art. And they have filled whole books in affirming that enchantments and spirits can work and speak without tongues, and can speak without any organic instrument, — without which speech is impossible, — and can carry the heaviest weights, and bring tempests and rain, and that men can be changed into cats and wolves and other beasts, although those first become beasts who affirm such things. 

And undoubtedly if this necromancy did exist, as is believed by shallow minds, there is nothing on earth that would have so much power either to harm or to benefit man; if it were true, that is, that by such an art one had the power to disturb the tranquil clearness of the air, and transform it into the hue of night, to create coruscations and tempests with dreadful thunder-claps and lightning-flashes rushing through the darkness, and with impetuous storms to overthrow high 1 The phrase is one used by Benjamin Jowett with regard to smoking. His advice was: 

'Do not set up for yourself any new necessities-' 

buildings and uproot forests, and with these to encounter armies and break and overthrow them, and — more important even than this — to make the devastating tempests, and thereby rob the husbandmen of the reward of their labours. For what method of warfare can there be which can inflict such damage upon the enemy as the exercise of the power to deprive him of his crops? What naval combat could there be which should compare with that which he would wage who has command of the winds and can create ruinous tempests that would submerge every fleet whatsoever ? In truth, whoever has control of such irresistible forces will be lord over all nations, and no human skill will be able to resist his destructive power. The buried treasures, the jewels that lie in the body of the earth will all become manifest to him; no lock, no fortress, however impregnable, will avail to save anyone against the will of such a necromancer. He will cause himself to be carried through the air from East to West, and through all the uttermost parts of the universe. But why do I thus go on adding instance to instance? What is there which could not be brought to pass by a mechanician such as this? Almost nothing, except the escaping from death. 

We have therefore ascertained 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 so much, not having regard to any deity, merely because there are an infinite number of persons who in order to gratify one of their appetites would destroy God and the whole universe? 

If then it has never remained among men, although so necessary to them, it never existed, and never can exist, as follows from the definition of a spirit, which is invisible and incorporeal, for within the elements there are no incorporeal things, because where there is not body there is a vacuum, and the vacuum does not exist within the elements, because it would be instantly filled up by the element. Fogli b. 31 v. 

Therefore O students study mathematics and do not build without foundations. Quaderni 1. 7 r. 

Mental things which have not passed through the understanding are vain and give birth to no truth other than what is harmful. And because such discourses spring from poverty of intellect those who make them are always poor, and if they have been born rich they shall die poor in their old age. For nature as it would seem takes vengeance on such as would work miracles and they come to have less than other men who are more quiet. And those who wish to grow rich in a day shall live a long time in great poverty, as happens and will to all eternity happen to the alchemists, the would-be creators of gold and silver, and to the engineers who think to make dead water stir itself into life with perpetual motion, and to those supreme fools, the necromancer and the enchanter. Quaderni 1 13 v. 

The certainty of mathematics

He who blames the supreme certainty of mathematics feeds on confusion, and will never impose silence upon the contradictions of the sophistical sciences, which occasion a perpetual clamour. 

The abbreviators of works do injury to knowledge and to love, for love of anything is the offspring of knowledge, love being more fervent in proportion as knowledge is more certain; and this certainty springs from a thorough knowledge of all those parts which united compose the whole of that thing which ought to be loved. 

Of what use, pray, is he who in order to abridge the part of the things of which he professes to give complete information leaves out the greater part of the matters of which the whole is composed? 

True it is that impatience the mother of folly is she who praises brevity; as though such folk had not a span of life that would suffice to acquire complete knowledge of one particular subject such as the human body. And then they think to comprehend the mind of God which embraces the whole universe, weighing and dissecting it as though they were making an anatomy. O human stupidity! Do you not perceive that you have spent your whole life with yourself and yet are not aware of that which you have most in evidence, and that is your own foolishness? And so with the crowd of sophists you think to deceive yourself and others, despising the mathematical sciences in which is contained true information about the subjects of which they treat! Or you would fain range among the miracles and give your views upon those subjects which the human mind is incapable of comprehending and which cannot be demonstrated by any natural instance. And it seems to you that you have performed miracles when you have spoiled the work of some ingenious mind, and you do not perceive that you are falling into the same error as does he who strips 
a tree of its adornment of branches laden with leaves intermingled with fragrant flowers or fruits, in order to demonstrate the suitability of the tree for making planks. Even as did Justinus, maker of an epitome of the histories of Trogus Pompeius, who had written an elaborate account of all the great deeds of his ancestors which lent themselves to picturesque description, for by so doing he composed a bald work fit only for such impatient minds as conceive themselves to be wasting time when they spend it usefully in study of the works of nature and of human things. 

Let such as these remain in the company of the beasts, and let their courtiers be dogs and other animals eager for prey and let them keep company with them; ever pursuing whatever takes flight from them they follow after the inoffensive animals who in the season of the snow drifts are impelled by hunger to approach your doors to beg alms from you as from a guardian. 

If you are as you have described yourself the king of the animals it would be better for you to call yourself king of the beasts since you are the greatest of them all! — why do you not help them so that they may presendy be able to give you their young in order to gratify your palate, for the sake of which you have tried to make yourself a tomb for all the animals? Even more I might say if to speak the entire truth were permitted me. 

But do not let us quit this subject without referring to one supreme form of wickedness which hardly exists among the animals, among whom are none that devour their own species except for lack of reason (for there are insane among them as among human beings though not in such great numbers). Nor does this happen except among the voracious animals as in the lion species and among leopards, panthers, lynxes, cats and creatures like these, which sometimes eat their young. But not only do you eat your children, but you eat father, mother, brothers and friends; and this even not sufficing you you make raids on foreign islands and capture men of other races and then after mutilating them in a shameful manner you fatten them up and cram them down your gullet. Say does not nature bring forth a sufficiency of simple things to produce satiety? Or if you cannot content yourself with simple things can you not by blending these together make an infinite number of compounds as did Platina and other authors who have written for epicures? 

And if any be found virtuous and good drive them not away from you but do them honour lest they flee from you and take refuge in hermitages and caves or other solitary places in order to escape from your deceits. If any such be found pay him reverence, for as these are as gods upon the earth they deserve statues, images and honours. But I would impress upon you that their images are not to be eaten by you, as happens in a certain district of India; for there, when in the judgment of the priests these images have worked some miracle, they cut them in pieces being of wood and distribute them to all the people of the locality — not without payment. 

And each of them then grates his portion very fine and spreads it over the first food he eats; and so they consider that symbolically by faith they have eaten their saint, and they believe that he will then guard them from all dangers. What think you Man! of your species? Are you as wise as you set yourself up to be? Are acts such as these things that men should do, Justinus? Quaderni 11 14 r. 

Let no one read me who is not a mathematician in my beginnings. Quaderni iv 14 v. 

Every action of nature is made along the shortest possible way. Quaderni iv 16 r. 

Thou, O God, dost sell unto us all good things at the price of labour. 1 Quaderni v 24 r. 

1 MS. 'Idio ci vende tutti li beni per prezzo di faticha.' Above it is the word 'oratio' and 'tu' to the right of it is perhaps connected by a stroke with idio'. 'Oratio' may either be interpreted as meaning 'a prayer' or it may be a reference to the poet Horace. The latter interpretation receives some support from the fact of the similarity of thought between the sentence which follows and a passage in the Satires of Horace, Bk. I, 9, 
58-9: 

'Nil sine magno 
Vita labore dedit mortalibus'. 

JOHANNES ANTONIUS DI JOHANNES AMBROSIUS DE BOLATE 

He who suffers time to slip away and does not grow in virtue the more one thinks about him the sadder one becomes. 

No man has a capacity for virtue who sacrifices honour for gain. Fortune is powerless to help one who does not exert himself. That man 
becomes happy who follows Christ. 

There is no perfect gift without great suffering. Our triumphs and our pomps pass away; gluttony and sloth and enervating luxury have banished every virtue from the world; so that as it were wandering from its course our nature is subdued by habit. Now and henceforth it is meet that you cure yourself of laziness. The Master has said that sitting on down or lying under the quilts will not bring thee to fame. 

He who without it has frittered life away leaves no more trace of himself upon the earth than smoke does in the air or the foam on the water. Windsor: Drawings 12349 v. 

Nothing grows in a spot where there is neither sentient, fibrous nor rational life. The feathers grow upon birds and change every year; hair grows upon animals and changes every year except a part such as the hair of the beard in lions and cats and creatures like these. The grass grows in the fields, the leaves upon the trees, and every year these are renewed in great part. So then we may say that the earth has a spirit of growth, and that its flesh is the soil; its bones are the successive strata of the rocks which form the mountains; its cartilage is the tufa stone; its blood the springs of its waters. The lake of blood that lies about the heart is the ocean. Its breathing is by the increase and decrease of the blood in its pulses, and even so in the earth is the ebb and flow of the sea. And the vital heat of the world is fire which is spread throughout the earth; and the dwelling place of its creative spirit is in the fires, which in divers parts of the earth are breathed out in baths and sulphur mines, and in volcanoes, such as Mount Etna in Sicily, and in many other places. Leic. 34 r. 

1 The sentence that commences 'The Master has said' seems to suggest that these are notes of Leonardo's precepts by a pupil, who apparently began by writing his own Falsehood is so utterly vile that though it should praise the great works of God it offends against His divinity. Truth is of such excellence that if it praise the meanest things they become ennobled. 

Without doubt truth stands to falsehood in the relation of light to darkness, and truth is in itself of such excellence that even when it treats of humble and lowly matters it yet immeasurably outweighs the sophistries and falsehoods which are spread out over great and high sounding discourses; for though we have set up falsehood as a fifth element in our mental state it yet remains that the truth of things is the chief food of all finer intellects — though not indeed of wandering wits. 

But you who live in dreams, the specious reasonings, the feints which palla players might use, if only they treat of things vast and uncertain, please you more than do the things which are sure and natural and of no such high pretension. Sul Volo 12 [n J r.