Lionardo da Vinci

Optics

Optics 

'These are the miracles — forms already lost mingled together in so short a space, it can recreate and reconstitute by its dilation. Why nature did not make a uniform power in the visual faculty. 

Nature has not made a uniform power in the visual faculty but has given this faculty greater power in proportion as it is nearer to its centre, and this it has done in order not to break the law given to all other powers which have more potency in proportion as they approach nearer to this centre. 

And this is seen in the act of the percussion of any body, and in the supports of the arms of the balance where the gravity of the weight is lessened as it draws nearer; it is seen in the case of columns walls and pillars; it is seen with heat and in all the other natural powers. Why nature made the pupil convex, that is raised up like part of a ball: 

Nature has made the surface of the pupil situated in the eye convex in form so that the surrounding objects may imprint their images at greater angles than could happen if the eye were flat. d i r. 

 

OF THE EYE 

Why the rays of luminous bodies become larger in proportion as they are farther removed from their source: 

The rays of luminous bodies increase the more as they proceed farther from their beginnings. This is proved thus: let a be the luminous body of which the image is impressed in the pupil of the eye of the beholder and let us say that c is the pupil upon which the impression is made, and the same image is impressed also upon the thick part of the upper lid b and on the lower lid o, and from the upper and lower lids the second images are reflected in the pupil of the eye c. But as regards the pupil that receives the three said images which are divided by the images of the lids of the eyes (in this instance almost closed), it seems that the images of the luminous bodies impressed on the thick parts of the lids of the eyes are as though actually subdivided and that these divisions are pyramidal because the intervals between the lids are also pyramidal. And since to the pupil which receives these three images it seems that the two images which rebound upon it from the lids are joined together above and below to the image of the centre which represents the luminous body, it seems to this pupil that the image b is in a n, and the image o appears to be in a m, and that the two images are divided by the image of the luminous body a. 

 

And since in closing together the rims of the eyelids it is necessary that the watery substance continually keeps the lids moistened as they rub upon the eye, so this moisture fills up the angle that is produced by the contact made by the lids with the pupil of the eye, and the surface of this watery substance is concave, as is proved in the fourth of the eighth of water where it states that 'the contact which water makes with its moist bank will always have its surface concave', and that 'if this bank is dry the surface of the water that borders upon it will be convex'. 

This angle therefore finding itself created by the contact between the lid of the eye and its pupil will have the surface of the aqueous humour filling up this angle of the concave figure. And since every concave mirror shows within the pyramidal concourse of its rays the image of its object upside down, it follows therefore that the weights or lids of the eyes mirrored within this hollow together with the image of the light will show these lids inverted; and this is the reason why when the pupil is within the concourse of the pyramidal rays of the concave mirror the pupil sees the pyramids formed by the rays of the spaces between the lids upside down. 

And this is the true reason of the rays of luminous bodies which the more they extend seem to approach nearer to the eye. Such a demonstration however ought to be divided into its parts in order to render it more intelligible, setting out first its conceptions and other propositions necessary for such proof. d i v. 

 

Whether the Images of objects are taken by the visual faculty to the surface of the eye or whether they pass within it: 

The glasses of spectacles show us how the images of objects pause at the surface of these glasses and then by bending themselves penetrate from this surface to the surface of the eye, from which surface it is possible for the eye to see the shapes of the aforesaid objects. 

This is proved to be possible because this surface is the common boundary between the air and the eye, in that it separates the vitreous humour from the air and separates the air from this vitreous humour. And if we wish to affirm that the images of the objects stop on the surfaces of the spectacles one might say that in the spectacles of old men the object would seem much larger than the reality, and but for the interposition of this glass between the eye and the object this object would show itself of its natural size; therefore [this not being so] is a clear proof that the convergence of the images of any object which is cut by the interposition of transparent bodies will impress itself on the surface of these bodies and will there create a new convergence which will lead the images of these objects to the eye. d 2 r. 

How the images of any object whatsoever which pass to the eye through some aperture imprint themselves on its pupil upside down and the understanding sees them upright: 

The pupil of the eye which receives through a very small round hole the images of bodies situated beyond this hole always receives them upside down and the visual faculty always sees them upright as they are. And this proceeds from the fact that the said images pass through the centre of the crystalline sphere situated in the middle of the eye; and in this centre they unite in a point and then spread themselves out upon the opposite surface of this sphere without deviating from their course; and the images direct themselves upon this surface according to the object that has caused them, and from thence they are taken by the impression and transmitted to the common sense where they are judged. This may be proved thus: — let a n be the pupil of the eye \ h, and let p be a small round hole made in the paper with the fine point of a style, and let m b be the object placed beyond this opening. I maintain that the upper part of this object cannot come to the upper part of the pupil of the eye through the straight line m a because at v its passage is impeded by the interposition of the paper. But this upper extremity m passes in a straight course through the hole to n the lower part of the pupil, or you would say of the crystalline sphere, and from there it directs its course to the centre of this sphere, then rises to the upper part of the opposite side and from there as has been said it runs to the common sense. d 2 v. 

Why the mirror in its images of objects changes the right side to the left and the left to the right: 

The image of every object is changed in the mirror so that its right side is opposite to the left of the object reflected and similarly the left to the right. This is of necessity the case because every natural action is performed by nature in the shortest manner and the briefest time possible. Let a b be a face which sends its image to the mirror c d, this face will have another face in this mirror turned towards it, so that it will have the left eye c opposite to the right a and similarly the right eye d will be opposite to the left eye b. 

And if it should be urged by the opponent that the right eye of the image was opposite to the right of the object we might project the lines from the right eye of the image to the right eye of the object and similarly from the left to the left, these lines being a d and b c which are seen to intersect; and it is proved that in all cases of lines intersecting the right extremity of the one is always opposite to the left extremity of the other, and this result is not produced by the shortest line because the diagonal of a square is always longer than its side, and here a d is the diagonal of the square a b c d of which a c is one of its sides; and thus is concluded what was necessary in order to prove such a result. 

And this effect in the mirror would be as though someone who was looking at you, someone that is who has the left eye opposite to your right, were as by a miracle transposing left and right as is the case with letters used in stamping and wax which takes the impress of the cornelian, d 4 r. 

OF THE HUMAN EYE 

The pupil of the eye changes to as many different sizes as there are differences in the degrees of brightness and obscurity of the objects which present themselves before it: 

 

In this case nature has provided for the visual faculty when it has been irritated by excessive light by contracting the pupil of the eye, and by enlarging this pupil after the manner of the mouth of a purse when it has had to endure varying degrees of darkness. And here nature works as one who having too much light in his habitation blocks up the window half-way or more or less according to the necessity, and who when the night comes throws open the whole of this window in order to see better within this habitation. Nature is here establishing a continual equilibrium, perpetually adjusting and equalising by making the pupil dilate or contract in proportion to the aforesaid obscurity or brightness which continually presents itself before it. You will see the process in the case of the nocturnal animals such as cats, screech-owls, long-eared owls and suchlike which have the pupil small at midday and very large at night. And it is the same with all land animals and those of the air and of the water but more, beyond all comparison, with the nocturnal animals. 

And if you wish to make the experiment with a man look intently at the pupil of his eye while you hold a lighted candle at a little distance away and make him look at this light as you bring it nearer to him little by little, and you will then see that the nearer the light approaches to it the more the pupil will contract. 

Whether the eye sees bright and dark things at the same time: The crystalline humour which dwells within the pupil is condensed on meeting with shining things and becomes rarefied on meeting with dark things; and the truth of this is shown in closing the eye, for then the images retained which were of bright things seem dark and those of dark things seem bright; and this happens more with weak eyes than with those that are strong, and of this I will speak more fully in its place. 

There follows the discourse concerning the eye of the nocturnal animals which see better by night than by day. And this comes about because the size of the eyes is greater than the whole of the brain, especially in the case of the long-eared and short-eared owls, the white owls, the little owls and horned owls and suchlike creatures, but it does not occur with man who has a greater brain in proportion to the size of his eyes than any other animal that lives on land, and can see but little light after day-time. d 5 v. 

There follows concerning the eye of the nocturnal animals which see more by night than by day, and this arises in great part from the fact that as was said before there is a much greater difference between the size of the pupil when dilated and contracted than there is in the case of the animals which are active by day, for if the pupil of the man doubles its diameter at night, that is to say it is increased to four times what it is by day, the diameter of the pupil of the horned owl or the long-eared owl is increased to ten times what it is by day which amounts to saying that the pupil is a hundred times as large as it is by day. 

Furthermore the ventricle situated in the brain of man called the imprensiva is more than ten times the whole of the eye of man, and of this the pupil in which the sight has its origin is less than a thousandth part; and in the case of the long-eared owl the pupil at night is considerably larger than the ventricle of the imprensiva situated in its brain. From this it follows that the imprensiva in man is greater in proportion to the pupil, it being in fact ten thousand times as great whereas in the case of the horned owl they are almost equal. 

And this imprensiva of man in comparison with that of the long eared owl is like a great room which receives the light through a small hole as compared with a small room which is entirely open. For within the great room there will be night at midday and in the small one which is open there will be day at midnight when the weather is not overcast. And herewith may be shown the workings of the most powerful causes by means of the anatomy of the eyes and the imprensiva of these two animals, namely of man and of the horned [long-eared?] owl. 

That object will seem of greater radiance and size which is seen by a larger pupil. One may make an experiment of this with our eyes by making as small a hole as possible in a sheet of paper and then bringing it as near as possible to the eye, and if then you look at a star through this hole you are only making use of a small part of the pupil, which sees this star with a wide space of sky round it and sees it so small that hardly anything can be less. And if you make the hole near to the edge of the said paper you will be able to see the same star with the other eye at the same time and it will appear to you to be large, and thus in the said time you will see the one star twice with your two eyes and once it will be small and the other time large. Further you will be able to see the whole body of the sun and with only a moderate amount of radiance, for the more its size is diminished so in proportion is its radiance as was set forth above. And from this it arises that the large pupils (luce?) see but little of the daylight because the excess of radiance impedes their vision. d 5 r. 

The image of the sun is unique in all the watery sphere which sees and is seen by this sun, but it seems divided into as many parts as are the eyes of the animals which from different positions behold the surface of the water. 

This that is set forth is proved because however far the eyes of the navigators carried by ships may move through the universe they behold at the same time the image of the sun through all the waters of their hemisphere in all the movements made in all the aspects. 

If the eye was as large as the sphere of the water it would see the image of the sun covering a great part of the ocean. 

This is shown because if you were to move yourself upon a bridge from which you can see the image of the sun in the waters of its river, and you move yourself about twenty-five braccia, you will see the image of the sun move just as far in the surface of the said water. And so if one were to put together all the images that are seen during this movement you would have a single image which would be of the shape of a fiery beam. Now imagine yourself to make a circle of which this beam is the diameter, and that the whole of this circle is full of these images, without doubt you would see one image the diameter of which would be twenty-five braccia; now you must understand that if a pupil were to have its diameter the same twenty-five braccia it would without moving itself see in the same water an image of the sun which would revolve in seventy-eight braccia and four sevenths. 

If through the long distance at which the eye was from the watery sphere the watery sphere should become diminished to the size of an ordinary image of the sun, as is shown in perspective, you would see the sphere of this water which is seen by the sun was a single image of this sun. 

This is proved in perspective how things remote from the eye even when they are exceedingly large seem very small in bulk, and this may be seen without any elaborate demonstration if you raise your eyes to the sky when it is bedecked with stars, for you will see there many stars which are many times larger than the earth and yet appear very small on account of their great distance, and the light which you perceive in them is not their own but is merely an image of the sun reflected in them. For of themselves these stars have no light, but they have a surface like the watery sphere suitable for receiving and giving back the light of the sun which is reflected in them. d 6 r. 

 

OF THE HUMAN EYE 

The pupil of the eye has a power of vision all in the whole and all in each of its parts; and an object placed in front of the eye which is less than its pupil does not occupy the place in the eye of any other distant object, and although it is compact it serves the function of a transparent object. 

Here the adversary says that the power of vision is reduced to a point and that it follows from this that every object placed in front of the pupil which is greater than this point will occupy the attention [of the eye], I say in reply to him that if it were true that the power of vision was reduced to a point, the convexity of the eye which with its parts is turned towards a great part of the universe which is opposite to it would not be able to have such a curve unless it were equidistant from this point and its surface were cut at an equal distance from this point, so that each of them with the same actual proportions correspond in the points of the angles to the proportions of the images of the bodies that meet at this point. 

To such a one it is necessary to appeal to experience and then to show this experience to be conclusive; and first as regards experience if you place in front of the pupil the thick end of a sewing needle of medium width as near as possible you will see that the perception of any object placed behind this needle at however great a distance will not be interfered with. 

What I say is entirely borne out by experience and necessity confirms it; for if this visual faculty be reducible to a point every object however small placed in front of it would occupy the attention of a great part of the heaven, for if a great part of the heaven transmits the images oi its stars to the pupil an object placed near to it and equal to the half of its diameter would cover almost the half of the sky. This is why nature in order that nothing may be lacking for the eyes of the animals has caused this pupil to have the smallest number of obstructions and less than may seem possible, among which the faculty of vision would be the greatest because as has been said every object how- ever small set over against it would take up a great amount of space. 


Moreover, experiment proves that sheets of canvas made out of thick horse-hair and placed in front of the eyes do not cover anything behind them and conceal it the less in proportion as they are nearer to the eye, whereas if the faculty of vision were focused in a point the nearer to it were the horse-hairs, the larger would be the space that they would occupy. As therefore experience demonstrates the contrary it is true that the visual faculty is infused through the whole pupil and makes use of every part of it and looks beyond this horsehair encompassing it and penetrating through the thickest part of it, and of necessity forming pyramids near the aforesaid horse-hairs. d 6 v. 

Every concave place will appear darker if seen from the outside than from within. 

And this comes about because the eye that is outside in the air has the pupil much diminished, and that which is situated in a dark place has the pupil enlarged and with the lesser eyeball the power is diminished, and in like manner this power increases in proportion to the increase of its pupil, and when the pupil is of feeble power every small obscurity will appear dark, and as it grows in power every great obscurity will appear lit up. 

Excess of light injures the eye and in order to protect it from being injured in this way the visual faculty takes the help which any one gets who shuts part of a window in order to lessen the excessive brightness which the sun produces in his dwelling. d 7 r. 

Why the right object does not seem the left to the eye: 

The images of the objects in the eye when making their entry into the eye deflect their rays in a way that is proved in perspective when these images pass from the density of the water to the thinness of the air. But to come back to the proposition that the right object does not appear the left in the eye, we see clearly by experiment that the images which penetrate into the vitreous humour by the pupil of the eye meet together in the sphere of the crystalline humour, as to which two considerations present themselves, namely whether the visual faculty resides in it or at the extremity of the optic nerve, which extremity catches these images and transmits them to the common sense as do the nerves of the sense of smell. And if this faculty resides in the centre of the crystalline humour it catches the images with its surface, and they are referred there from the surface of the pupil, where the objects are mirrored or reflected there from the surface of the uvea which bounds and clothes the vitreous humour which has darkness behind its transparency, just as behind the transparency of the glass we find the darkness of the lead in order that objects may be the better mirrored
in the surface of this glass. But if the visual faculty is in the centre of the crystalline sphere all the objects which are given it from the surface of the pupil of the eye will appear in the true position in which they are, and will not change from the right to the left and will seem larger, as is shown in perspective. And if this crystalline sphere takes these images reflected from the concavity of the uvea it will take them upright although the uvea is a concave mirror, and it will take them upright because the centre of the crystalline sphere is concentric with the centre of the sphere of the uvea. 

It is true that the images which pass to this uvea as they are outside the eye pass to it through the centre of the crystalline sphere, and having arrived at the uvea they become inverted as also are those which pass to the uvea without passing through this humour. We may surmise therefore, admitting this visual faculty to reside at the extremity of the optic nerve, that from here it may be seen in the crystalline sphere that all the objects caught by it are upright, for it takes those that were inverted in the uvea and inverts them once again, and consequently this crystalline sphere presents the images upright which were given to it inverted. To such master in optics one would perhaps say that the spherical surface of the crystalline sphere united to the sphere of the vitreous humour does not change its nature, and it is as though the whole was vitreous, and that for this reason the vitreous sphere does not fulfil the same function as it would if it were surrounded by the air. The reply to this however is that this result cannot occur because a ball of crystal placed in water fulfils the same function as it does in air. d 7 v. 

The images of the objects placed before the eye pass to the vitreoussphere by the gate of the pupil, and they intersect within this pupil insuch a way that the vitreous sphere is struck on its left side by the right ray of the right sphere, and it does the same on the opposite side; afterwards it penetrates this vitreous sphere, and the rays contract and find themselves much closer together when they are on the opposite side of this sphere than when they strike it in the beginning. 

And this process of contraction proceeds from the fact that the rays of the images approach the perpendicular when they pass from the thin to the dense, and that the albugineous humour is here much thinner and more subtle than the space enclosed by the surface of the vitreous sphere. Afterwards (the image) ought to enlarge as it returns into this albugineous humour, but it does not follow this rule because it is constrained to obey the nature of the vitreous sphere from whence it proceeds rather than that of the albugineous humour through which it passes. 

And this is why it makes a pyramid as it issues forth from the vitreous sphere and passes through the albugineous humour, and intersects its sides at the point /; and passes to the visual faculty g at the
extremity of the optic nerve g s. 

Of the intersection of the images of the objects received by the eye within the albugineous humour: 

Experience which shows that the objects transmit their images or likenesses intersected within the eye in the albugineous humour shows [what happens] when the images of the illuminated objects penetrate through some small round hole into a very dark habitation. You will then receive these images on a sheet of white paper placed inside this habitation somewhat near to this small hole, and you will see all the aforesaid objects on this paper with their true shapes and colours, but they will be less, and they will be upside down because of the said intersection. 

These images if they proceed from a place that is lit by the sun will actually seem painted upon this paper, which should be very thin and seen in reverse; and the said hole should be made in a very thin sheet of iron. Let a b c d e be the said objects lit by the sun, o x be the facade of the dark habitation in which is the said hole at n tn, s t the said paper where the rays of the images of these objects inverted are cut, for as their rays are straight a which is right becomes left at \ and e which is left becomes right at /, and so it is within the pupil. d 8 r. 

Why the point of the style when placed across the pupil of the eye throws a great shadow upon the object: 

When the point of the style is placed crosswise before the pupil of the eye, the diameter of its thickness being considerably less than the diameter of this pupil, it will occupy more or less space against other objects in proportion as it is nearer or more remote from the eye; and this occupation of space will obscure but will not prevent the passage
of the images of the aforesaid objects. d 9 r. 

Why the rays of the luminous bodies increase in proportion to the space that is interposed between them and the eye: 

The lengths of the rays created by the luminous bodies increase with the increase of the space that is interposed between these bodies and the eye. It is necessary here first to define what are the rays of the luminous bodies, and whether they have their origin in the eye which looks at these bodies or in fact proceed from these luminous bodies, and if we should conclude that they proceed from the eye it is necessary to define why and in what manner. 

Why the luminous bodies show their contours full of straight luminous rays: 

The rays which reveal the contours of luminous bodies do not derive their origin from these bodies but from their images which imprint themselves upon the thickness of the lids of the eyes that look upon these bodies. This we learn in the first place by the inductive method which teaches us that the eye when wide open does not show us such rays round luminous bodies, and that if the image of a star or other light should pass to the eye through the smallest perforation made in the paper placed before the eye, such luminous [images] will always be without rays. But the real proof is shown by the ninth of Perspective where it is stated: — the angle of the incidence is always equal to the angle of the reflection, — therefore, the rays, which seem as though they extend from the luminous body to make contact with the eye that beholds it, start when the eye, being almost closed up, looks through the narrow crack that intervenes between the eyelids, at that luminous body of which the image is reflected in the thick parts of the lids which end these coverings, and after making this impress is reflected on the pupil of the eye; which pupil receives three images from the same luminous body, namely two in the thick parts of the lids of the coverings of the eye and one in the pupil, and through these three images being very near one to another, they seem to the eye to be continuous and joined to the image of the pupil. 

And the proof that experience offers us to confirm this proposition is shown when you raise or lower the face while keeping the eye firmly fixed upon the luminous body; for as the face is raised the eye will
lose all the lower rays of this luminous body. This comes about because the image of this luminous body does not proceed to imprint itself in the thic\ part of the lower lid of this eye 1 ; where the luminous body does not see it, it cannot there imprint its image, and where the falling ray does not strike it does not produce the reflex ray, and for this reason the pupil does not take it. And so it will happen when the face is lowered, for then the thick part of the upper covering of the eye neither sees nor is seen by that luminous body, for which cause the image as has been said cannot imprint itself there, and in consequence the eye can not there discern what is not there; but it sees this image in the lower covering, and this lid sees and is seen by the luminous body, and thus we have proved our intent. 

The adversary says that the ray bends because it goes to the sense from the thin to the dense. d 9 v. 

The images of the objects infused in the opposite air are all in all this air and all in every part of it. This is proved: — 

Conception of the objects. All that air sees the object opposite to itself which is seen by the same object. 

This is proved by the third of this which says that all the visions made in the same quality of air are rectilinear. 

Therefore since it is possible to draw a straight line from the eye to

(1 The words in italics are crossed out in the manuscript. )

each part of the air seen by this eye this vision is rectilinear. And this is also proved by what Aristotle says: — 'every natural action is made in the briefest way possible'. The vision therefore will be made by the shortest line, that is by a straight line. 

 

OF THE IMAGES OF THE OBJECTS INFUSED THROUGHOUT 

THE AIR 

The objects have their images infused in all the air that is seen by these objects: which images are all in all the above-mentioned air and are all in every part of it. 

How the eye does not know the boundary of any body: 
The eye will never be capable of [perceiving] the true boundary of the figures of any body when they show up against the far distance. This may be proved: let a b be the pupil of the eye and c p the body
placed opposite to the eye of which we have noted that c is the upper extremity, and let n m be the background against which this extremity ought to be perceived by the eye. I maintain that it is not possible to ascertain in what part of this background the extremity of this body terminates, and this is proved by the help of the third [section] of this [treatise] in which it is stated that the faculty of vision is not in a point as the painters who have treated of perspective would have us to suppose, but is all in the whole of the pupil into which the images of the objects penetrate, and within the eye in a larger space than that occupied by this pupil. But these images are the more clearly to be perceived in proportion as they are nearer to the centre of this faculty [of vision] located in the said space and the less clearly in proportion as they are farther removed from this centre. 

If therefore the visual faculty a b takes in the extremity of the object c the centre line of the visual faculty r sees c in the part of the background /, and the upper extremity of this visual faculty that is s sees c in the background h and the lower part of the visual faculty sees c in the background d\ and thus it goes spreading itself through the whole background d h; and through this such extremity is not known to the eye because the sense of the visual faculty is spread through all this faculty which offers to the judgment a vague perception of this extrcmitv c, and so much more or less as it is nearer or more remote from this centre line of the visual faculty, and so much more or less as it is more remote or nearer to the eye. d 10 v. 

A stone thrown through the air leaves in the eye which sees it the impression of its movement, and drops of water do the same as they descend from the clouds when it rains. c.a. 79 r. c 

 

OF THE NATURE OF SIGHT 

I say that sight is exercised by all animals through the medium of light; and if against this any one should instance the sight of nocturnal animals, I would say that these in exactly the same way are subject to
the same law of nature. For, as one may readily understand, the senses,  when they receive the images of things, do not send forth from themselves any actual power; but on the contrary the air which is between the object and its sense, serving as a medium, incorporates within itself the images of things, and by its own contact with the sense presents them to it, if the objects either by sound or smell project themselves to the eye or the nose by virtue of their incorporeal powers. Here the light is not necessary, nor is it made use of. 

The forms of objects do not enter into the air as images unless they are luminous; this being so, the eye cannot receive the same from that air which does not contain them, but only touches their surface. 

If you wish to speak of the many animals which hunt their prey by night, I answer that when that small amount of light sufficient for them to see their way fails them, they avail themselves of their powers of hearing and smell, which are not impeded by the darkness, and in which they are far in advance of man. If you watch a cat in the daytime leaping among a lot of pieces of crockery you will see that these will remain whole; but if it does the same by night it will break a considerable number. Night birds do not fly unless the moon is shining either full or in part, but their time of feeding is between the hour of sunset and the total darkness of the night. 

No substance can be comprehended without light and shade; light and shade are caused by light. c.a. 90 r. b 

 

 

OF THE EYE 

Since the eye is the window of the soul, the latter is always in fear of being deprived of it, to such an extent that when anything moves in front of it which causes a man sudden fear, he does not use his hands to protect his heart, which supplies life to the head where dwells the lord of the senses, nor his hearing, nor sense of smell or taste; but the affrighted sense immediately not contented with shutting the eyes and pressing their lids together with the utmost force, causes him to turn suddenly in the opposite direction; and not as yet feeling secure he covers them with the one hand and stretches out the other to form a screen against the object of his fear. 

Preamble to perspective — concerning the functions of the eye: 
Consider now, O Reader, what trust can we place in the ancients who have set out to define the nature of the soul and of life, — things incapable of proof, — whilst those things which by experience may always be clearly known and proved have for so many centuries either remained unknown or have been wrongly interpreted. 

The eye which thus clearly offers proof of its functions has even down to our own times been defined by countless writers in one way, but I find by experience that it acts in another. c.a. 119 v. a 

All the images of the things set over against the eye converge in shining lines on the surface of the eye; and these intersect on the surface of the eye at equal angles. 

The atmosphere is all in all and all in every part of it filled with the images of the bodies which are enclosed within it. c.a. 120 r. d 

I find by experience that the black or almost black fringe of colour (colore crispo ovver rasposo) which appears round the pupil serves for no other purpose except to increase or diminish the size of this pupil; to increase it when the eye is looking towards a dark place; to diminish it when it is looking at the light or at a luminous thing. 

And you should make the experiment of holding a light near to the eye, and make it when you are looking into the darkness and then turn the eye to this light, and you will be convinced by this experiment. c.a. 125 r. a 

If the object in front of the eye sends its image to it the eye also Knds its image to the object, so of the object and of the image proceeding from it no portion is lost for any reason either in the eye or the object. Therefore we can sooner believe that it is the nature and power of this luminous atmosphere that attracts and takes into itself the images of the objects that are within it than that it is the nature of the objects which transmits their images through the atmosphere. 

If the object in front of the eye were to send its image to it the eye would have to do the same to the object, whence it would appear that these images were incorporeal powers. If it were thus it would be
necessary that each object should rapidly become less; because each body appears as an image in the atmosphere in front of it, that is the whole body in the whole atmosphere and the whole in the part, and all the bodies in the whole atmosphere and all in the part, referring to that portion of it which is capable of receiving into itself the direct and radiating lines of the images transmitted by the objects. For this reason then it must be admitted that it is the nature of this atmosphere which finds itself among the objects to draw to itself like a magnet the images of the objects among which it is situated. 

A proof how all the objects placed in one position are all in the whole of it and all in each part: 

I maintain that if the front of a building or some piazza or field which is illuminated by the sun has a dwelling over against it, and in that part of the front which does not face the sun you make a small
round hole, all the objects which are lit by the sun will transmit their images through this hole, and will be visible inside the dwelling on the opposite wall which should be made white. And they will be there
exactly, but inverted; and if in different parts of the same wall you make similar holes you will produce the same effect in each. 

Therefore the images of the illuminated objects are all everywhere on this wall and all in each of its smallest parts. The reason is this: we know clearly that this hole ought to give some light to this dwelling
and the light which passes through it is caused by one or by many luminous bodies : if these bodies are of different colours and shapes the rays which make their images will be of different colours and shapes
and so also will be the representations on the wall. c.a. 135 v. b 

 

The flea and the man can approach the eye and enter into it at equal angles. For this reason does not the judgment deceive itself in that the man does not seem larger than this flea? Enquire as to the
cause. c.a. 190 v. b 

The greater the spherical body the less is the proportion of itself that it shows to the eye when the eye does not change its position. c.a. 216 r. a 

A proof of the manner in which glasses aid the sight: 
Let a b be the glasses and c d the eyes, and suppose these to have grown old. Whereas they used to see an object at e with great ease by turning their position very considerably from the line of the optic
nerves, but now by reason of age the power of bending has become weakened, and consequently it cannot be twisted without causing great pain to the eyes, so that they are constrained of necessity to place the object farther away, that is from e to /, and so see it better but not in detail. But through the interposition of the spectacles the object is clearly discerned at the distance that it was when they were young, that is at e, and this comes about because the object e passes to the eye through various mediums, namely thin and thick, the thin being the air that is between the spectacles and the object, and the thick being the thickness of the glass of the spectacles, the line of direction consequently bends in the thickness of the glass, and the line is twisted, so that seeing the object at e it sees it as though it was at /, with the advantage that the position of the eye with regard to its optic nerves is not strained and it sees it near at hand and discerns it better at e than at / and especially the minute portions. c.a. 244 r. a 

In just such proportion as the eye when it functions is nearer than the ear it will the more preserve the images of the objects imprinted upon it. c.a. 250 r. a 

Among the solar images preserved within the eye that which the eye has retained for a less time will appear more luminous, c.a. 262 r. b 

I say that the power of vision extends by means of the visual rays as far as the surface of bodies which are not transparent, and that the power possessed by these bodies extends up to the power of vision, andthat every similar body fills all the surrounding air with its image. Each body separately and all together do the same, and not only do they fill it with the likeness of their shape, but also with that of their 

You see with the sun when it is at the centre of our hemisphere, how there are images of its form in all the parts where it reveals itself, and you see how in all these same places there are also the images of its
radiance, and to these must also be added the image of the power of its heat; and all these powers proceed from the same source by means of radiant lines which issue from its body and end in the opaque objects without it thereby undergoing any diminution. 

The north star remains continually with the images of its power spread out, becoming incorporated not only in thin but in thick bodies, in those transparent and those opaque, but it does not on this account
suffer any loss of its shape. 

Confutation 

Those mathematicians, then, who say that the eye has no spiritual power which extends to a distance from itself, since, if it were so, it could not be without great diminution in the use of the power of
vision, and that though the eye were as great as the body of the earth it would of necessity be consumed in beholding the stars : for this reason they maintain that the eye takes in but does not send forth anything from itself. 

Example 

What will these say of the musk which always keeps a great quantity of the atmosphere charged with its odour, and which, if it be carried a thousand miles, will permeate a thousand miles with that thickness of atmosphere without any diminution of itself? 

Or will they say that the sound which the bell makes on its contact with the clapper, which daily of itself fills the whole countryside with its sound, must of necessity consume this bell? 

Certainly, it seems to me, there are such men as these — and that is all that need be said of them. 

Is not that snake called lamia seen daily by the rustics attracting to itself with fixed gaze, as the magnet attracts iron, the nightingale, which with mournful song hastens to her death? 

It is said also that the wolf has power by its look to cause men to have hoarse voices. 

The basilisk is said to have the power by its glance to deprive of life every living thing. 

The ostrich and the spider are said to hatch their eggs by looking at them. 

Maidens are said to have power in their eyes to attract to themselves the love of men. 

The fish called linno, which some name after St. Elmo, which is found of? the coasts of Sardinia, is it not seen at night by the fishermen, shedding light with its eyes over a great quantity of water, as though they were two candles ? And all those fishes which come within the compass of this radiance, immediately come up to the surface of the water and turn over, dead. c.a. 270 v. c 

If you take a light and place it in a lantern tinted green or other transparent colours you will see by experiment that all the objectswhich are illuminated by this light seem to take their colour from the
lantern. 

You may have also seen in churches how the light which comes through stained-glass windows assumes the colour of the glass of these windows. If this does not convince you, watch the sun at its setting when it shows itself red through the vapour, how it dyes red all the clouds which take their light from the sun. 

 

Opinions 

All these instances are given in order to prove how all things or certainly many things transmit the appearance of their powers together with the image of their form without any injury to themselves; and this also may happen with the power of the eye. 

 

Contrary opinion 

Furthermore if anyone wished to say that the eye was not adapted to receive like the ear the images of objects without transmitting some potency in exchange for these, this may be proved by the instance of
the small hole made in a window which gives back all the images of the bodies which are opposite to it; therefore one may say that the eye does the same. 

Refutation 

If the small hole cited as an example without sending forth anything except its form without incorporeal power gives back to the house the images of objects in their colour and form and there inverts them, the eye would have to do the same so that everything seen would appear there inverted. 

Proof to the contrary 

The circle of the light which is in the middle of the white of the eye is by nature suitable to apprehend objects. This same circle has in it a point which seems black and this is a nerve bored through it which
goes within to the seat of the powers charged with the power of receiving impressions and forming judgment, and this penetrates to the common sense. Now the objects which are over against the eyes act with the rays of their images after the manner of many archers who wish to shoot through the bore of a carbine, for the one among them who finds himself in a straight line with the direction of the bore of the carbine will be most likely to touch the bottom of this bore with his arrow; so the objects opposite to the eye will be more transferred to the sense when they are more in the line of the transfixing nerve. 

That water which is in the light that surrounds the black centre of the eye serves the same purpose as the hounds in the chase, for these are used to start the quarry and then the hunters capture it. So also
with this, because it is a humour that derives from the power of the imprensiva and sees many things without seizing hold of them, but suddenly turns thither the central beam which proceeds along the line
to the sense, and this seizes on the images and confines such as please it within the prison of the memory. c.a. 270 r. b 

 

Why objects as they come upon the small surface of the eye appeal large arises from the fact that the pupil is a concave mirror; and one sees for example with a glass ball filled with water that anything
placed at the side either inside or outside appears larger. c.a. 309 r. b 

Nothing can be seen that does not transmit its image through the air. 

Therefore nothing that is spiritual or transparent can see anything set over against it, for this requires that it have within itself a thick opaque instrument and being thus it is not termed a spirit. 

Prove how nothing can be seen except through a small fissure through which the atmosphere passes filled with the images of objects that intersect within the thick and opaque sides of the above-mentionec fissures. And for this reason nothing which has not substance can discern either the shape or colour of any object, seeing that it is necessary that there should be a thick opaque instrument in order that through the fissure in it the images of the objects may assume their colours and shapes. c.a. 345 r.

 

Seeing that the images of the objects are all spread throughout all the air which surrounds them, and are all in every point of the same it must be that the images of our hemisphere enter and pass together
with those of all the heavenly bodies through the natural point I which they merge and become united, by mutually penetrating and intersecting each other, whereby the image of the moon in the east and
the image of the sun in the west at this natural point become united and blended together with our hemisphere. 

O marvellous Necessity, thou with supreme reason constrainest effects to be the direct result of their causes, and by a supreme and irrevocable law every natural action obeys thee by the shortest possible
process! 

Who would believe that so small a space could contain the images of all the universe? O mighty process! What talent can avail to penetrate a nature such as these ? What tongue will it be that can unfold so great a wonder? Verily, none! This it is that guides the human discourse in the considering of divine things. 

Here the figures, here the colours, here all the images of every part of the universe are contracted to a point. Oh what point is so marvellous! 

O wonderful, O stupendous Necessity thou by thy law constrainest all effects to issue from their causes in the briefest possible way! 

These are the miracles, . . . forms already lost, mingled together in so small a space, it can recreate and reconstitute by its dilation. 

How it may be that from indistinct causes there may issue effects manifest and immediate, as are the images which have passed through the aforesaid natural point. 

Write in thy Anatomy what proportion there is between the diameters of all the lenses of the eye, and the distance from these to the crystalline lens. c.a. 345 v. b 

 

The point is in itself an indivisible part, separated from and similar to all, and possessing the capacity of all, and all the indivisible parts are similar to the one and are such as may all be contained in that one, as
is shown by experience in the points of the angles of the air-holes, for when the solar rays have passed through these the angles become the termination and point of the primitive and derived pyramid. 

This derived pyramid although of less force is none the less capable of going a long way enlarging and expanding itself with the concourse of its rays much more than the primitive. 

And this same phenomenon may be seen in concave mirrors, for these after taking the solar rays according to their capacity lead them in pyramid fashion to the divisible part of the point, and although it is the least part of the sun or rather of the solar rays which illumine and warm all the surface of the mirror, this point nevertheless contains within itself the whole sum and power whether of heat or radiance of which all the surface of the mirror is capable. The derived pyramid when equal in bulk is similar in all its powers to the primitive, and when this equality is exceeded it becomes so much weaker in proportion as its size surpasses the bulk of the primitive. c.a. 347 r. a 

EYE 

The thing seen through an aperture that is less than the base of the visual pyramid will be seen along a line that goes crosswise, and the thing on the right hand will go to the left eye, and will not be able
to be seen by two eyes at one and the same time and if it is seen it will be imperfectly discerned. c.a. 347 v. a 

OF THE EYE AND LIGHT 

If you look at a luminous body in the far distance through a small hole it will seem to grow less, and if you look at it near at hand it will not undergo any change. That is that if you look at this light at a
distance of one or two braccia from the aforesaid hole it will not undergo any change whether you are looking at it through this hole or outside of it. c.a. 351 v. b 

How and why many things seen in a mirror come to the eye upside down. 

Why anything seen in a mirror appears greater than it is. 

Why anything looking at itself in a mirror appears less. 

What sort of mirror it is which shows the things exactly. 

What sort of mirror shows them outside itself. 

How the mirror is the master of painters. 

Why the eye goes varying hour by hour, enlarging and lessening. 

Why the pupil in proportion as it has a greater light in front of it becomes less, and why on the other hand it increases in the dark. 

Why the things seen by the eye when continuing are small within the eye and appear large. 

Why a thing seen through a chink with both the eyes becomes double and is transposed; that is to say the thing seen on the right hand goes to the left eye, and similarly that on the left hand goes to the right. 

Why a building among clouds appears greater. 

Why the eye cannot see perfectly except in a straight line. 

Why pyramidal lines which start from the eyes come to a point in the thing seen. 

Why when the said pyramid proceeds from the eyes and comes to a point in an object that is in water the lines bend as they reach the water and do not keep their straightness. 

How the things seen form a pyramid only in the eye. 

How the two eyes form a pyramid in the thing seen. c.a. 360 r. c 

 

That eye will preserve within itself more images of the sun which is looked upon a greater number of times by this sun. c.a. 369 r. c 

A dark place will seem sown with spots of light and a shining place with dark round spots, when seen by the eye which has recently gazed many times and rapidly at the body of the sun. c.a. 369 v. d 

Method of seeing the sun in an eclipse without causing suffering of the eye: 

Take a sheet of paper and make holes in it with a knitting-needle and look at the sun through these holes. Tr. 10 a 

The eye which finds itself in the centre between the shadows and the lights that surround the shaded bodies, will see in these bodies the greater shadows that are in them meeting themselves within equal
angles that is of the visual incidence. Tr. 16 a 

Every man always finds himself in the centre of the earth's circumference and below the centre of its hemisphere and above the centre of this earth. Tr. 24 a 

The movement of an object near to a stationary object often causes this stationary object to seem to transform itself to the movement of the moving object and the moving object to seem stationary and fixed. 

PAINTING 

Things in relief seen close at hand with one eye will seem like a perfect picture. 
[Diagram ] 

If with the eyes a b you observe the point c, this point c will appear ndf. 

But if you look at it with one eye only it will seem to you h in m o, and painting will never of itself have these two varieties. Tr. 69 a 

The medium that is between the eye and the object seen transforms this object to its own colour. So the blueness of the atmosphere causes the distant mountains to seem blue; red glass causes anything that the eye sees through it to seem red. The light created by the stars round about them is obscured by the darkness of the night that lies between the eye and the radiance of the star. Tr. 70 a 

 

PERSPECTIVE AND MOVEMENT 

Every body that moves rapidly seems to colour its path with the impression of its hue. The truth of this proposition is seen from experience; thus when the lightning moves among dark clouds the speed of its sinuous flight makes its whole course resemble a luminous snake.  So in like manner if you wave a lighted brand its whole course will seem a ring of flame. This is because the organ of perception acts more rapidly than the judgment. a 26 v. 

Why the movement of water although slower than that of man always seems swifter: 

The reason of this is that if you look at the movement of the water your eye will not be able to fix on anything, but its action is as that of things seen in your shadow when you are walking; for if the eye attempt to distinguish the nature of the shadow, the wisps of straw or other things contained in it appear of rapid movement and it seems that these are much more swift to flee from the said shadow than the shadow is to proceed. a 58 v. 

If the eye looks at the light of a candle at a distance of four hundred braccia, this light will appear to this eye which looks at it increased a hundred times its true quantity; but if you place a stick in front of it somewhat larger than this light, this stick which would appear two braccia wide will hide it. This error therefore comes from the eye which takes the luminous images not only with the point of its light but also with the whole of this light, and of this I will define the reason in another place. c 6 r. 

The eye will retain and preserve better within itself the images of luminous things than of shaded things. 

The reason is that the eye in itself is completely dark, and since like amid like cannot be distinguished, the night or other dark things can [not] be retained or recognised by the eye. The light is entirely contrary, and the more it is divided the more it tends to destroy and change the customary darkness of the eye and so leaves its image imprinted. c 7 v - 

A rod or cord in rapid oscillation appears to be double. 

This occurs when a knife is fastened, and the top of it is forcibly pulled to one side and released, so that it quivers many times. The same thing happens with the cord of a lute when one tests it to see if it is a good one. The double movement takes place because when the movement extends to the extremity of the thing moved it is much swifter at this extremity. But this extremity stops and turns back when its desire has been fulfilled, and as the pause is made first at one and then at the other extremity of the movement, the eye must necessarily take the impression of two images of the same thing moved. But tell me why a false cord of a lute makes, as it quivers, two or three images and sometimes four? c 15 r. 

[The effect on the eye of sudden light] 

The eye which is used to the darkness is hurt on suddenly beholding the light and therefore closes quickly being unable to endure the light.  This is due to the fact that the pupil in order to recognise any object in the darkness to which it has grown accustomed, increases in size, employing all its force to transmit to the receptive part the image of things in shadow. And the light, suddenly penetrating, causes too large a part of the pupil which was in darkness to be hurt by the radiance which bursts in upon it, this being the exact opposite of the darkness to which the eye has already grown accustomed and habituated, and which seeks to maintain itself there, and will not quit its hold without inflicting injury upon the eye. 

One might also say that the pain caused to the eye when in shadow by the sudden light arises from the sudden contraction of the pupil,  which does not occur except as the result of the sudden contact and
friction of the sensitive parts of the eye. If you would see an instance of this, observe and note carefully the size of the pupil when any one is looking at a dark place, and then cause a candle to be brought be- 
fore it, and make it rapidly approach the eye, and you will see an instantaneous contraction of the pupil. c 16 r. 

PAINTING 

First — The pupil of the eye contracts as the light reflected in it increases. 

Second — The pupil of the eye expands as the brightness of day or of any other light reflected in it grows less. 

Third — The eye sees and knows objects of vision with greater intensity when the pupil is more dilated; and this is proved in the case of the nocturnal animals such as cats and others, and birds such as the owl and suchlike in which the pupil undergoes a great variation from large to small in the dark and in the light. 

Fourth — The eye when placed in an illuminated atmosphere can discern the darkness within the windows of habitations which are themselves in light. 

Fifth — All colours when placed in shadow seem to be equally dark. 

Sixth — But all colours placed in light keep their essence unchanged. 

e 17 v. 

If the object interposed between the background and the eye is less than the pupil of the eye no part of the background will be covered by this object. f 28 v. 

The rays of luminous bodies that are remote from the eye will seem of great length, because no object which sends an image is in closer proximity to the pupil of the eye than the object imprinted on the rim
of the eye which touches the pupil and from there sends the image to the eye. 

The rays of luminous objects will seem shorter when these objects are near to the eye than when they are far away, because, if the lids of the eyes are half closed as is done by those who wish to see rays round the light, and these lids occupy little space below and above this light,  and the rays therefore are not able to open more than whatever may be this space seen by the eye, it is necessary that in this short space one sees short rays, and in a long space long rays as is shown above [diagram], f 29 r. 

How the rays that are seen around a luminous body in contracting the eyelids are produced in the eyes and not elsewhere: 

 

 


OPTICS 245 

Convex mirrors will reflect the rays that they receive from the luminous body in all the parts that see the mirror where the luminous body sees it. 

The luminous body sends three images of itself to the eye, of which one goes straight to the pupil; the other two strike upon the convexity of the eyelids and from there leap back in opposite movements to the opposite edges of the eyes, and from the edges they leap back into the eyeball ('luce'), and join themselves below and above to the first image, with the brilliance which has been imprinted on the eyelids in the form of rays; and the luminous body does this when the eye is drawn together as when one takes aim at a target. 

This is proved: — let the eye be inclined as has been said and you will see two groups of rays around the luminous separated body, of which one part goes upwards and the other downwards; and if you hold your finger up against the light, putting it crosswise a little below the luminous body, and raise it towards the light with a slow movement until you reach the origin of the light from below, and then observe how instantly this luminous body will lose all its rays above; and if you make a contrary movement crosswise with your finger, commencing above the light, and with slow movement lower your finger until it meets the summit of the light, you will then see that all the rays below are lacking; and this proves our proposition, for if a be the luminous body, then a o the first ray from its centre goes straight to the pupil of the eye, that below, a m, strikes upon the convexity of the eyelids below the eyelashes, and makes several images, and these, as soon as they are formed, are reflected upon the lid n, which forms the thick part of the covering of the eye; and from there it leaps back into the eyeball ('luce'), together with all the images formed in the hairs of the eyelids, and these are somewhat long and are separated and proceed with points raised spreading themselves out towards the extremities as do the real eyelashes. 

Now to bring our purpose to a conclusion, I call t s the part between the commencement of the light and your eye; you will cut the ray a m,  consequently, because of this the ray will not make its impression on
the convexities or curves of the eyelids below, and therefore the ray above will cease at n and consequently in the eyeball ('luce'), for if the cause of the images m be lacking the effects of the rays m n will be lacking. Here then is the explanation of why when the ray is covering the light below, the ray above is lost altogether. 

The adversary here says that it seems to him that this image proceeds from the luminous body and passes between the eyelids and imprints itself on the thick part of the edges of the eyelids, and that from there they leap to the pupil, and that this image emits rays because it is divided by the hairs through which it passes. 

To this the reply is that in this event whatever might fill the image below the rays above would not fail. f 30 r. and 29 v. 

There is the same proportion one with another between the spaces that there are between the images of the stars upon the surface of the eye and that of the spaces interposed between the stars of the heaven. 

Although the images of the stars may be all in all the surface of the eye and all in each of its parts, and each image may be superimposed upon each of the other images as it appears to another eye which regards it after the manner of the surface of a mirror, it remains none the less the fact that from the inner side of the pupil which covers for it the arrival from without of an image of the star, this image will not turn to imprint itself in another part of the eye but will remain without impression in the eye, because the spot to which it directed itself is impeded by the aforesaid interposition. f 31 v. 

The images of opaque bodies do not superimpose themselves one upon another when the eye that scrutinises them is without movement. 

In the same mirror or pupil is the image of all the objects placed before it, and each of these objects is all in the whole surface of the mirror and all in each of its smallest parts. 

There is an example of this in the movement of the eye; if it sees the moon with all the stars in this mirror, and marks them on its surface, and then the eye moves a little, it will be able to distinguish them so many times upon this mirror, clearly marked one above the other, and this it will be able to do an infinite number of times. f 32 r. 

The whole pupil of the eye which with each of these circles from the greater to the less goes diminishing an infinite number of times can see the whole body of the star; but it will see it as much smaller as it
sees it with a less expansion. 

Why in Looking at the heaven one sees many stars of great radiance, and in looking at them through a very minute hole made in a sheet of paper placed in contact with the eye you see again the same number ot stars but they will be much diminished. f 32 v. 

OF THE FACULTY OF SIGHT 

If all the images which come to the eye met in an angle, by the definition of the angle they meet in a mathematical point which is proved to be indivisible; then all things seen in the universe would seem one and that would be indivisible, and there would be no more space from one star to another which would be reckoned in such an angle. 

And if experience shows us all things separated with spaces proportioned and definite, this power which imprints the images of objects is also itself divisible into as many larger and smaller parts as there are
images of the things seen. We conclude therefore that the sense takes the images which are reflected on the surface of the eye, and then judges them within, and therefore they do not meet in a point nor as
a consequence in an angle. 

Every surface of a transparent body both within and without is formed fitted to receive the images of its objects. 

In no part of transparent bodies enclosed by their surfaces is there lacking the power to receive or create some image, but each is well fitted to afford a passage to the images of the surface. f 34 r. 

That luminous body will show itself of less size at the same distance which loses more of its radiance. 

This is shown by an iron rod heated through part of its length when in a dark place; although it is of uniform thickness, it appears to be considerably bigger in the heated part, and the more so as it is more
heated. The reason for this follows: — 

Every luminous body makes visible rays in the image which it transmits to the eye; and the rays are so much longer as it is of greater brilliance; and so conversely. f 37 r. 

 

248 OPTICS 

Many are the times that the images of one and the same luminous body will be two or three times at the same time in the same eye. 

They will be twice there when the eye closes somewhat as it does when it looks at light which is too strong and when the head is somewhat bending as in the figure a, in this case it makes two rays; one
strikes against the humid circumference of the lower eyelid and then leaps back to the pupil, and the other ray goes straight to this pupil; it will recur three times as in the figure b, one on the eyelid above, one on that below and one in the centre of the pupil. And the aforesaid two or three images of the light arriving at the same sense appear one single image, but greater than corresponds to the image of the same body which transmits to the two eyes two images, and the sense takes them for one single image. f 36 v. and 37 r. 

As regards the pupil of the eyes of all animals both those of the land and those of the water, nature has so ordained that when they are affected by greater or less brightness the pupil that is the black portion
of the eye contracts or expands. This happens because as the excess of brightness causes a change in the eye the eye or pupil closes up after the manner of a purse, consequently the great brightness becomes small in size and in splendour in proportion to its contraction or diminution. 
When these pupils are in darkness they become large and the brightness is diminished; in this way it comes about that they increase according to the increase of this brightness, and so the quantity of the
objects seen by such a pupil is increased. 

And this supplies a reason why when the light of a candle is removed farther away from the eye, this light having thereby its brightness diminished the pupil increases and it causes the figure of the light to
increase. f 39 v. 

The image of the sun imprinted on the surface of the water creates rays which shine over a great distance both within and outside the water as though it was a real light. 

Why when the image of the light of the candle diminishes upon the eyeball when this candle is removed to a great distance from this eye it does not diminish in the judgment of the spectators except in degree
of radiance. f 40 r. 

The eye contracts and diminishes the pupil to such an extent in looking at luminous things that when afterwards looking at things of less radiance they appear shaded. 

It the eye which has been in a shaded place should then see objects of only a moderate degree of brightness they will appear extremely bright. 

And the reason of this is that the pupil increases so much while in the dark places that it afterwards sees objects of a moderate degree of brightness incorrectly. f 50 r. 

In every spot in which the sun sees the water the water also sees the sun, and in each of its parts it can present the sun's image to the eye. f 61 v. 

If you bring your eye as near as you can to the surface of the sea you will see the image of the sun in a wave of the water, and you will be able to measure it and you will find that it is very small. 

If you bring your eye near the surface of the water of the sea or of a pool which is between your eye and the sun you will find that the image of the sun on this surface shows itself very small. But if you
retire a distance of several miles from this sea you will perceive a proportionate increase in the image of the sun; and if the first image preserves the true shape and radiance of the sun as do mirrors, the second does not keep either the shape or the radiance of the sun but is a figure with broken contour lines and a lesser degree of radiance. 

The figure of the image with contour lines broken and confused is formed by the blending of many images of the sun reflected to your eye by many waves of the sea, and the lesser degree of radiance springs from the fact that the shadowed and luminous images of the waves come to the eye all mingled together and consequently their light is affected by their shadows. 

This however cannot happen with the surface of a single wave when you have approached very near to it with your eye. f 63 v. 

The image of the sun in the convex mirror increases as it recedes from this mirror and the solar body disappears as it recedes, f 76 r. 

Show first how every light remote from the eye makes rays which appear to increase the figure of this luminous body; and from this it follows that . . . 

The eye does not diminish its light at any distance, because the image of the light which imprints itself on the surface of the eye illuminates within as do the windows of paper, which diffuse the light taken by them through those places which see this paper, and which at first could not see the cause of the illumination of this paper when the paper was not there. The sun also on being reflected in the mirrors
causes the image without passing within to be reflected outwardly as though it were a real light; and if the lead were not behind this glass of the mirror, the image of the sun which imprints itself on the surface of the glass would pass within and cast its light within or behind this mirror. And thus does the eye which receives within the light of this image and spreads it considerably in the visual faculty. f 94 v. 

[Distant lights and reflection] 

Why as the image of the light of the candle diminishes when it is removed to a great distance from the eye the size of this light does not diminish but it lacks only the power and brightness of its radiance. 

A light that is less in quantity is less also in illuminating power, but in that it does not change its position it does not lose its first quantity of radiance in all the places where it formerly shone. This is proved: 
the light of the sun given to the surface of the water is reflected back and emits rays as though it were a material light both within and without, and actually illuminates the objects set over against it and
also those within. f 95 r. 

[Presbyopia] 

Why when men are somewhat advanced in years they see better at a distance. 

Sight is better at a distance than near at hand with men who are somewhat advanced in years because the same thing transmits a smaller impression of itself to the eye when it is remote than when it is near. 

g 90 r 

Things near to the eye will seem of greater bulk than those remote. Things seen with both eyes will seem rounder than those seen with one eye. 

 

OPTICS 251 

Things seen between light and shadow >vill appear to have the highest relief. h 49 I 1 J r - 

Man and owl] 

All things seen will appear larger at midnight than at midday and larger in the morning than at midday. 

This takes place because the pupil of the eye is considerably smaller at midday than at any other time. 

To just such extent as the eye or pupil of the owl is greater in proportion to the creature than is that of man it sees more light at night than man does; as a consequence at midday it sees nothing unless its
pupil grows smaller and in the same way at night it sees things larger than by day. h 86 [38] r. 

The larger the pupil the larger will be the appearance of the objects it sees. 

This is evident when we look at luminous and especially at heavenly bodies. When the eye emerges from the darkness and suddenly looks at these bodies they will appear larger at first and will then diminish. And if you look at these bodies through a small hole you will see them smaller because a smaller part of the pupil is functioning in this act. h 88 [40] r. 

When the eye emerging from darkness suddenly sees a luminous body it will appear much larger at the first glance than as it goes on looking at it. 

A luminous body will seem larger and more luminous when seen with both eyes than when seen with one. 

This luminous body will appear of less size when it is seen by the eye through a smaller hole. 

The luminous body of elongated shape will show itself rounder in form when it is situated at a greater distance from the eye. 

H 9 I [43] V. 

When at night the eye finds itself between the light and the eye of a cat it will see this eye looking like fire. h 109 [34 v.] r. 

Objects seen by the same eye will sometimes appear large and sometimes small. h 133 [10 r.] v. 

 

 


252 OPTICS 

Example of the enlargement and contraction of the pupil through the movement of the sun or other luminous body: 

The darker the sky the greater the stars will seem, and if you light up the atmosphere these stars will show themselves less. And this change proceeds only from the pupil which expands and contracts according to the clearness of the atmosphere which finds itself between the eye and the luminous body. Let the experiment be made with a candle placed above the head while you are looking at this star; afterwards proceed to lower this candle, little by little, until it is near the ray that comes from the star to the eye, and you will then see the star diminish so much that you will almost lose sight of it. 119 v. 

The pupil of the eye in the open air varies its size with every degree of the sun's movement. And as it varies its size the same object when seen by it will appear of different sizes, although it often happens that the comparison with surrounding things does not allow this change to be discerned when you look at a particular object. 1 20 r. 

No opaque body of spherical shape seen by two eyes will ever show itself of perfect roundness. 
[Diagram ] 

a is the position of your right eye; b is the position of the left. If you close the right eye you will see your spherical body around the centre b, and if you close the left eye, then the said body will surround the centre a} 1 43 r. 

The more nearly an object approaches to the eye the more it shows itself at a greater angle; and the image of this thing does the opposite, seeing that in proportion as it is found by measurement to be nearer to the eye it shows itself less in shape. 1 49 [1] v. 

[Eyeball of glass] 

In order to see what function the eyeball ('luce') 2 serves in the pupil cause a thing resembling the eyeball to be made out of glass. 

k 118 [38] v. 

1 MS. has b. 

2 A note in M. Ravaisson-Mollien's edition of the Paris Manuscripts is as follows: 
'Le mot "luce" est sou vent pris pour prunelle, mais signifie proprement (voir la page suivante) (118 [38] r.) toute la partie de l'ceil qui luit, la prunelle avec 1'iris.' 

 

OPTICS 253 

[The structure and anatomy of the eye] 

The pupil of the eye is situated in the centre in the eyeball ('luce')  which is of the shape of part of a sphere which takes the pupil at the centre of its base. This 'luce' forming part of a sphere takes all the
images of the objects and transmits them by the pupil within to the place where the vision is formed. 

In the anatomy of the eye, in order to be able to see the inside well without spilling its watery humour, you should place the complete eye in white of egg and make it boil and become solid, cutting the egg and the eye transversely so that no part of the middle portion may be poured out. k 119 [39] r. 

[Optical illusions. A brand of fire] 

There is as much to move the eye when the luminous object remains fixed as there is to move this object when the eye remains fixed. 

What is said in the first part is proved by the past, and I will prove the second part by the help of this same past. 

For if when the eye is fixed you draw a brand of fire in a circle or from below the eye upward this brand will seem to be a line of fire which rises upwards from below, and yet this brand cannot actually be
in more than one part of this line at one time. 

And in the same way if this brand remain fixed and the eye move downward from above it will appear to this eye that the brand is rising up from below in a continuous line. k 119 [39] v. 

[Optical illusions. Brands of fire. Stars] 

If the eye that looks at the star turns swiftly in an opposite direction, it will appear to it that this star forms itself into a curving line of fire. 
[Diagram ] 

Let a b c be the eyeball ('luce') of the eye which looks at the star d; I maintain that if the eyeball moves the part a rapidly to c then b in coming to the place a will take the appearance of a continuous line of
the colour of the star. And this occurs because the eye preserves for a certain space of time the image of the thing that shines, and because this impression of the radiance of the star is more enduring in the
pupil than was the time of its movement, this impression continues together with the movement in all the positions which pass opposite to the star. k 120 [40] r. 

 

254 OPTICS 

When the eye changes its position which has been fixed in relation to a near object it will seem to it that distant objects are very rapid and that the first is without movement and that the star moves by the line
of the eye. 
[Diagram] 

Let us say that the eye a has fixed its range of vision upon the object c and that while having its vision fixed upon c it itself moves actually from a to b\ the star d when seen by the lines of the eye other than the central ones will appear to it very swift, and in the time during which the eye goes from a to b, the star will appear to it to have moved the whole part of the sky d e. k 122 [42] v. 

But if the eye which changes its position keeps its vision fixed upon the star it will seem to it that all the objects seen on the lines that are not central are fleeting and vanish away in movement contrary to that
of the eye. 
[Diagram] 

Let us say that the eye b having its vision fixed upon the star d e itself moves actually from £ to a; it will then appear to the eye that as its lines which are not central have exchanged so many times the images of the object c it will be moved in a direction contrary to that of the eye from n to c. k 122 [42] r. 

In proportion as a thing that descends shall descend from a higher position it will appear at the beginning of its movement to be obliged to descend nearer to the eye that sees it than does a thing that descends from a low position. 
[Diagram] 

This which has been said springs from the background of the movable thing, which is the sky where this movable thing shows up prominently, and the lower the movable thing upon this background the more does the eye see it on a more distant background; as if the eye p sees the movable thing at e and sees it occupy the part of the sky d which seems almost above it; and if it sees the movable thing below at /; this eye sees it occupy the part of the sky a, and in proportion as the distance is from a to d so to the eye p it seems that it has it more at the zenith when at e than at /z, that is that when falling from d it seems to it that it ought to fall nearer than when falling from a.  k 123 [43] r. and 122 [42] v. 

 

OPTICS 255 

Ii the proportion of the movement of two movable things is the same as that of their distance from the eye in the same direction the movements of these movable things will always appear equal although they may be of almost infinite diversity. 

If half the diameter of the base of a pyramid measures three-quarters of its hypotenuse nothing can remain stable upon the said hypotenuse; but if this should be longer it will support anything, k. 123 [43] v. 

Among the things of equal movement that will appear swifter which is nearer, and the thing will seem slower which is more remote. 
[Diagram] 

Because everything that moves is seen on the field where it ends, and the distant thing in like movement to that of the near thing will occupy less of the field than this near thing in the same time, for which cause occupying a greater space of field it appears so much swifter as the field that it has covered is greater. k 124 [44] r. 

\ Spherical bodies] 

If the spherical body is equal to the pupil that sees it even though it may be at infinite varieties of distances, provided that it can be defined and that the eye is able to discern it it will never be seen as more or less than half. And this happens because its diameter with its extremities always terminates within equal angles between parallel visual lines. 

But if the pupil be less than the spherical body situated in front of it it will never at any variety of distance be able to see the half; and it will see as much less in proportion as it is nearer to it, and as much more as it is more remote. k 124 [44] v. 

An object less than the pupil placed before the eye will not cover up any distant object for this pupil. 

No spherical body less than the pupil will ever be seen by a single pupil without it seeing more than half of it although it be at whatever distance it may wish. And it will see so much more of it as the medium
is nearer and so much less as it is more remote from the eye that sees it. k 125 [45] r. 

[Movements] 

In the cases of the movement of the thing between the eye and the perforation of the paper you have to make the perforations with very small holes and to pull the thing which moves as thin as a wisp of
straw, and in the movement to touch yourself with it on the eyelashes,  the paper in front to be a quarter of a braccio distant from the eye and the air to be visible through the openings. Furthermore if you approach nearer to the paper so that the eyelashes almost touch, and move the face at d to right and left, with a short movement, you will see that the hairs appear to be moving beyond this hole in a contrary direction to the movement made by your eye. But if the movement of the object is beyond the perforated paper the eye will then see the true movement of the object. k 125 [45] v. and 126 [46] r. 

[Contrary movements seen at the same time] 

Again it is possible for the same pupil to see the same object at the same time make two opposite movements without the pupil changing. 
[Diagram ] 

That which is set forth above is seen by the pupil when it sees through a small hole made in the paper by the point of a needle, and keeping the eye close to it and interposing between the eye and the hole a very fine straw, which as you move it from right to left your eye will see in its true movement between the hole and it, in the true position in which this straw actually finds itself moving; and beyond this hole it will see it moving in the opposite direction to its true movement; so that at one and the same time it sees the true and the false movements separately the one from the other. k 127 [47] r. 

[Visual faculty] 

And the reason of this is that as every vision transmits itself by a straight line if the medium be uniform, the part a of the pupil sees beyond the hole at s, and it would be impossible to see it through this hole at q through a b q, that is by a line that is not straight. Suppose now that o is lowered to n; p will see o at r, and if o is lowered as far as m then o will appear to the lower part of the eye c to be raised to the extremity q. 

The pupil which sees beyond the hole something smaller than itself and near to it, will see with the right part of the pupil the left part of the object, and with the left part it will see the right part of this object; and with the centre of the pupil it will see the centre of the surface of the object, given that it is visible and that the centre of the pupil has in itself visual faculty. k 126 [46] v. 

PUPIL SEEING AN OBJECT TWICE 

It is possible for the same pupil to see the same object twice, in two places at the same time. 
[Diagram] 

The lower part b of the pupil a b sees the object c cover d, and the upper part a of the same pupil sees the same object c cover the wall g /, beyond the hole e, in the position g. 

Therefore the object c is seen at the same time at d and g, and it is this that I wished to demonstrate. k 127 [47] v. 

As the light diminishes so the pupil of the eye that beholds this light expands. Therefore the. eye which looks through a pea-shooter has a larger pupil than the other, and sees the object larger and clearer than the other eye does. You may make a proof of this if you look with both eyes at a white line against a black background, one looking at it through a pea-shooter and the other through the luminous air. 

l 13 v. and 14 r. 

When the eye in the luminous air is looking at a place that is in shadow this space will seem of much greater darkness than it is. 

This happens simply because the eye which is in the air diminishes its pupil the more as the air which reflects it is more luminous; and as the pupil becomes more contracted so the thing seen by it shows itself less luminous. 

But when the eye enters into any shaded spot immediately the obscurity of this shaded spot will appear to diminish. 

This takes place because in proportion as the pupil enters into the more shaded air so its outline increases and this increase causes the great darkness to seem to diminish. l 41 v. 

Of concave mirrors of equal diameter, that which is of less concavity will unite a greater sum of rays in the percussion of the concourse of these rays, and as a consequence it will kindle a fire with greater rapidity and force- b.m. 86 v. 

 

258 OPTICS 

It is impossible for the reflection of anything upon the water to be similar in shape to the object which is reflected, in view of the fact that the centre of the eye is above the surface of the water. b.m. 93 v. 

If the seat of judgment of the eye lies within it the direct lines of the images are broken at its surface because they pass from the thin to the dense. 

If you stand under water and look at something within the air you will see this thing out of its position, and it will be the same with a thing within the water seen from the air. b.m. 220 r. 

The concourse of the lines created by the images of the objects placed before the eye does not meet in the point within this eye by straight lines. b.m. 221 v. 

Here let us treat of actual movements because as regards spiritual movements there has been some treatment by others. 

Actual movement made with swift impetus will never conceal from the eye the object which is behind the body that is moving, if only it be near to the eye and not too much greater than this eye. As would
be the movement of certain instruments worked by women, made for convenience of gathering their threads together, which are called 'winders' ('arcolai') among the Florentines and by the Lombards
'turrets' ('bicocche'). For these in their revolving movement are so swift that through being perforated they do not obstruct to the eye anything behind them. Forster 11 101 r. 

[Central line and other lines of eye] 

The eye has one central line and all the things that come to the eye along this line are seen distinctly. 

Round about this line are an infinite number of other lines that adhere to this centre line and these have so much less strength in proportion as they are more remote from the central line. Quaderni iv 12 r. 

[Phenomenon of sun shining on rain-drops] 

And the drop that falls in rain as seen by the eye seems illuminated by the sun, and in its course it seems continuous over so great a space as it shows all the colours of the rainbow, and this it makes greater or
less according to the distance.  

\BranJ moved in circle seems an unbroken circle] 

The firebrand whirled in a eircle passes through an infinite number of adjacent lines and therefore this circle appears united in the air.  Quaderni iv 12 v. 

 

Necessity has provided that all the images of bodies set over against the eye intersect in two places, of which the one intersection is formed within in the pupil the other within in the crystalline sphere; and if
this were not the case the eye would not be able to see so great a number of things as it does. This is proved because all the lines that intersect form this intersection at a point, since of bodies nothing is visible except their surfaces, the edges of which are lines by the converse of the definition of the surface, and every smallest part of the line is equal to a point, because smallest is said of that thing than which nothing else can be smaller, and this definition is like that of the point. It is possible therefore for the whole circumference of a circle to transmit its image to its intersection as is shown in the fourth [section] of this [treatise]  which says : — all the smallest parts of the images penetrate one another
without occupation one of another. These demonstrations are as an example of the eye : — no image of however small a body enters within the eye without being turned upside down, and as it penetrates the crystalline sphere it is turned again upside down, and so the image within the eye becomes upright as was the object outside the eye. Windsor: Drawings 19150 v. 

How every great mass sends forth its images which have the capacity of diminishing to infinity: 

The images of every great mass which is divisible to infinity may be diminished to infinity. Windsor: Drawings 191 51 r. 

OF THE CENTRAL LINE OF THE EYE 

There is only one line of the images that penetrate to the visual*  faculty that has no intersection, and this has no sensible dimensions because it is a mathematical line and has its origin in a mathematical
point which has no dimensions. 

Necessity requires according to my opponent that the central line of all the images which enter through the fine and narrow openings into a dark place shall be turned upside down together with all the images
of the bodies that surround it. 

 

OF THE INTERSECTION OF THE IMAGES IN THE PUPIL 

OF THE EYE 

The intersections of the images at the entrance of the pupil do not mingle one in another in that space where this intersection unites them; and this is evident because if the rays of the sun pass through
two panes of glass in contact one with another, the one of these being blue and the other yellow, the ray that penetrates them does not assume the hue of blue or yellow but of a most beautiful green. And the same process would occur with the eye if the images yellow and green in colour should come to mingle one with the other at the intersection which they make within themselves at the entrance of the pupil, but as this does not happen such a mingling does not exist. 

OF THE NATURE OF THE RAYS FORMED BY THE IMAGES
OF BODIES AND THEIR INTERSECTION 

The straight line of the rays which transmit through the air the form and colour of the bodies whence they proceed does not itself tinge the air nor can they tinge one another at the contact of their intersection, but they only colour the place where they lose their existence, because this place sees and is seen by the original source of these rays, and no other object that surrounds this original source can be seen from the place where this ray is cut off and destroyed, leaving there the spoil it has carried off. This is proved by the fourth, on the colour of bodies, which says the surface of every opaque body shares in the colour of surrounding objects; so we conclude that the place which by means of the ray that carries the image sees and is seen by the source of this 'image is tinged by the colour of this object. 

How innumerable rays from innumerable images can converge in a point: 

As in a point all lines pass without occupation the one of the other through their being without body, so may pass all the images of the surfaces, and as each given point faces every object opposite to it and every object faces the opposite natural point, also through this point may pass the converging rays of these images which after passing it will reform and increase again to the size of these images. But their impressions will appear reversed as is shown in the first above, where it is said that every image intersects at the entrance of the narrow openings made in an extremely thin substance. 

In proportion as the opening is smaller than the shaded body by so much the less will the images transmitted through this opening penetrate one into another. The images which pass through the openings in a dark place intersect at a point so much nearer the opening as this opening is of less width. . . . 

It is impossible that the images of bodies should be seen between the bodies and the openings through which the images of these bodies penetrate; and this is evident because where the atmosphere is illuminated these images do not become visible. 

When images are duplicated by mutually penetrating one another they always have double depth of tone. Windsor: Drawings 19152 r. and v. 

Describe how no object is itself defined in the mirror but is defined by the eye which sees it within the mirror, for if you look at your face in the mirror the part resembles the whole, seeing that the part is all in the whole of the mirror and it is all in every part of the same mirror, and the same happens with the whole image of every object placed opposite to this mirror. Windsor mss. r 209