I consulted chiefly the illustrations in Felix Plater's De Corporis humani structura et usu, published in 1583 and reprinted this year, 1603. With these I compared the Anatomia Pragensis of my friend Johannes Jessenius of Jessen, not so much because he was able above all to profit by following Aquapendente, but because the fortune of war gave him considerable anatomical experience himself. If, mathematician as I am, I have passed over anyone of greater worth in this discipline, I hope they will treat me with indulgence[...]

I say vision occurs when the image (idolum) of the whole hemisphere of the world which is in front of the eye, and a little more, is formed on the reddish white concave surface of the retina (retina). I leave it to natural philosophers to discuss the way in which this image or Picture (picture) is put together by the spiritual Principles of vision residing in the retina and in the nerves, and whether it is A made to appear before the soul or tribunal of the faculty of vision by a spirit within the cerebral cavities, or the faculty of vision, like a magistrate sent by the soul, goes out from the council chamber of the brain to meet this image in the optic nerves and retina, as it were descending to a lower court. For the equipment of opticians does not take them beyond this opaque surface which first presents itself in the eye. I do not think that we should listen to Witello (Bk 3, Proposition 20), who thinks that these images of light (idola lucis) go out further through the nerve, they meet at the junction halfway along each optic nerve and then separate again one going to each cerebral cavity. For, by the laws of optics (leges optices), what can be said about this hidden motion, which, since it takes place through opaque and hence dark parts and is brought about by spirits which differ in every respect from the humors of the eye and other transparent things, immediately puts itself outside the field of optical laws? So, whereas Witello argues thus in Book 3, Proposition 20: the images (species) must be united, therefore (Proposition 21) refraction must take place at the back of the vitreous humor, and (Proposition 22) the spirits must be pellucid, I reverse this argument: spirits are not an optical body, and their thin hollow nerve is not optically in a direct line. Even if it were, it would immediately become bent by the movements of the eye and the opaque parts of the nerve would become opposed to the light entering the tiny opening or door of the passage. Hence light neither passes through the posterior surface of the vitreous humor nor is refracted there, but falls upon it. And indeed how could images (species) entering perpendicularly be refracted ? It is strange that this did not occur to Witello when he was writing Book 3, Proposition 31. Hence in 3, Proposition 33 he was put into by no means minor difficulties over this joining of images (species) at the junction of the nerves. For if this union in the mid-path of the nerves is to be asserted, it must be done in terms of natural philosophy. For it is undeniably certain that no optical image could penetrate to this point. It seems then clear that, if any nerve went to its seat in the brain freely in a straight line, with two eyes we would think we saw two things instead of one. Either this junction takes place so that when one eye is closed this hidden seat in the brain should not cease from its function of judging. Or perhaps the actual doubling of the seats is not only on account of the eyes, but is for the purpose of correct judgement of distances, as with the pair of eyes. Therefore, in order that visible things may be judged correctly and a distinction made between what is seen with one and with two eyes, this junction of the passages must take place. Here this one optical conclusion from the first chapter can be stated: the spirits are affected by the qualities of color and light, and this affection (passio) is, so to speak, a coloring and a lighting. For in vision images (species) of strong colors remain behind after looking, and these are united with colors printed by a fresh look, and a mixture of both colors is made. This image (species) existing separately from the presentation of the thing seen is not present in the humors or coats of the eye, as shown above; hence vision takes place in the spirits and through the impression (impressio) of these images (species) on the spirit. But really this impression does not belong to optics but to natural philosophy and the study of the wonderful. But this by the way. I will return to the explanation of how vision takes place.

Thus vision is brought about by a picture [pictura] of the thing seen being formed on the concave surface of the retina. That which is to the right outside is depicted on the left on the retina, that to the left on the right, that above below, and that below above. Green is depicted green, and in general things are depicted by whatever colors they have. Thus, if it were possible for this picture on the retina to persist if taken out into the light by removing the anterior parts of the eye which form it, and if it were possible to find someone with sufficiently sharp sight, he would recognize the exact shape of the hemisphere compressed into the confined space of the retina. For a Proportion is kept, so that if straight lines are drawn from separate points on the thing seen to some determined point within the eye, the separate parts are depicted in the eye at almost the same angle as that at which these lines meet. Thus, not neglecting the smallest points, the greater the acuity of vision a given person, the finer will be the picture formed in his eye.

In order that I may proceed to treat this process of depiction and prepare for a demonstration of it, I say that this picture consists of as many cones of equal size as there are points in the thing seen, in pairs always with the same base, namely the width of the lens (crystallinus) or part of it. Thus while one cone of each pair has its vertex at the point seen and its base on the lens (nothing is altered by refraction through the cornea), the other has the same base on the lens as the first one and the vertex at a point in the picture depicted on the retina; this cone undergoes refraction in passing from the lens. All the outer cones meet in the pupil, so that they intersect in that space, and [there] right becomes left.

In order that this argument can be better grasped, I will repeat it in detail. Take any visible point directly opposite the eye such that a line through the opening of the nerve and the center of the pupil falls on this visible point. Now, when any point emits light into the world, it sends rays in all directions and thus into the whole of the small aperture of the cornea, and illuminates the iris and its dark center or pupil (foramen uveae). Since the iris is opaque and black, it deflects and stops the rays falling round its sides and admits rays only through its center, to the extent allowed by the pupil. But since the cornea and, behind it, the aqueous humor (both of which I take as the same medium so far as density is concerned) constitute a denser medium than air, rays emitted from a point inclined to the cornea are refracted towards the perpendicular. Thus rays which at first diverged in the air, converge on entering the cornea such that although the full extent of the circle described on the cornea by those incident rays which reach the Perimeter of its opening is wider than the circle of the pupil, the rays falling outside the pupil are cut off, while those entering it are made to converge, even in the small depth of the aqueous humor, and go on to illuminate a part of the surface of the lens smaller than the pupil. All the rays entering the anterior surface of the lens which come from a point at a determined, proportionate distance (which is specific to each eye and not the same in each) fall on it almost perpendicularly due to the similar convexity of the cornea and lens. Thus rays from a point seen directly opposite and at an appropriate distance almost never undergo further refraction at the anterior surface of the lens, even though the lens is a denser medium than the aqueous humor. Here again regarding refraction I ascribe the same density to the lens and its capsule (aranea), just as below to the vitreous humor and the hyaline coat (tunica hyaltrea). Thus as many of these rays emitted by a single point as are admitted through the pupil descend through the entire depth of the lens, converging increasingly as they go, until they reach its hyperbolic posterior surface. Thus if it were possible to represent a series of these rays in a section through the eye, that going from the top of the cornea to the bottom of the lens would make one and the same conical surface, of which the width is determined by the position of the pupil, and the vertex reaches to a point somewhere behind the eye. These rays having then proceeded in a cone through the posterior surface of the lens into the vitreous humor, a medium more rare than the lens, are refracted away from the perpendiculars drawn to the surface at the point of refraction, such that the refracted rays run together towards the axis. Thus they terminate in a shorter and blunter cone than that by which they came. Hence, all these rays coming from one visible point finally join in another point, the very center and extremity of the optic nerve, where this is joined to the retina. For nature has measured the depth of the vitreous humor between the lens and the retina according to this density of the lens and the magnitude of these refractions.

The most distinct vision occurs only when all the light from the same point, however much dispersed by the width of the cone admitted through the pupil, is brought by two refractions, one in the cornea and the other at the posterior surface of the lens, to a bright focus at one point on the retina, the very opening of the nerve carrying the visual faculty or spirit. To this point no other rays from any other luminous point can come, because of the blackness and opacity of the choroid (uvea), the narrowness of the pupil, the ciliary processes, and other considerations mentioned above. Thus far we have spoken of the visible as a point, not a body, so that it has no parts, and no distinction of right from left, above from below. But this is not actually what is visible, but rather an element or rather limit of the thing seen. Hence vision of a point as just explained is not to be taken as the completion of vision but as one element in it. For as in the thing seen there are many points, so there are many as it were elements in the vision of that thing. Witello 3, 19, remains nevertheless true: nothing is seen unless with some magnitude proportionable to it. Thus let there be some point near the first one, side by side with it, and to the right of it. This point also sends light to the cornea and the underlying iris, and it looks towards the pupil obliquely. Thus rays entering the circle of the pupil form a kind of scalene cone which at the pupil intersects the upright cone from the first point, and after intersection goes to the left within the choroid, falling on part of the surface of the lens illuminated by the first point and on a part not illuminated by it, but more to the left. In fact more or less the same thing happens as we showed in Chapter 2 in a closed chamber. The pupil (papilla) corresponds to the window and the lens to the screen opposite it, provided that the pupil and lens are not so near that intersection is incomplete and everything is confused. Thus at the anterior surface of the lens the cone going to the left is refracted towards the upright cone, and, although still passing through the lens obliquely, falls so much the more upright on the hyperbolic [posterior] surface of the lens. There again, though not enough, it is refracted towards the direct first cone, such that it is separated from the cone less in the vitreous humor than in the lens, yet still remains separated, and so goes to the left side of the retina. But Nature has found an admirable way of preventing the disturbance of the proportions of the visible hemisphere which would occur if points outside in the air, mutually opposite to those on the retina on a line through the center of the eye, were deflected from an opposite position through the threefold refraction of the ray, at the cornea and at the surfaces of the lens, and passed down at an angle into the depths of the eye and so were focussed on to a portion of the retina smaller than a hemisphere. For Nature has placed the center of the retina, not at the junction of the axes of the cones penetrating the vitreous humor but a long distance inside, and she extended the edge of the retina at both sides, such that the longer cones, which are more widely separated, intercept perpendicularly placed and therefore narrow sections of the retina, while the shorter ones, which are less widely separated at the sides of the retina, mark off at an acute angle, broad sections of the retina obliquely set towards them. Thus the rays coming from opposite points, though after refraction no longer opposite, nevertheless fall on corresponding opposite points of the retina (retiformis), and hence there is compensation. And so if, finally, straight lines are drawn from points on the visible hemisphere through the center of the eye and the vitreous humor, these will impress points forming a picture of the radiating points on the retina opposite. If this did not occur, the size of things seen indistinctly to the side would keep changing as when the eyes were turned, as happens when spectacles are worn. For these, although fixed immovably in relation to the eye, if they are moved round with it, represent things at rest as having some motion due to the varying amount of the hemisphere appearing at the sides.

Now we must proceed further into the difference between direct and lateral vision. First, the cone of direct vision is bounded simply by the choroid, such that it falls entirely on the cornea, whereas some of the oblique cones are displaced to the side of the cornea itself. They may be too wide for the choroid, so that light is poorly measured out to the retina. The direct cone is circular or upright, the oblique ones compressed or scalene. The axis of the direct cone is not refracted at the cornea, whereas the axes of the oblique ones are refracted there. All the lines of the direct cone are almost perpendicular in the lens, but none of the oblique ones. The direct cone is cut equally by the anterior surface of the lens; the oblique ones are cut unequally, since the anterior surface of the lens slopes more, and thus cuts an oblique cone lower down. The direct cone cuts the hyperbolic surface or convex bulge of the lens circularly and equally; the indirect ones cut it unequally. All the rays of the direct cones are focussed at one point on the retina, which is essential in this matter; the lines of the indirect ones cannot all be focussed at a single point, for the causes already given, and so they form a less distinct picture. The direct cone comes to a point at the center in the middle of the retina, the oblique ones to the sides. The direct cone falls upright on the retina; the lateral ones fall obliquely because, as already described, the center of the retina is below the intersection of the axes of the cones in the vitreous humor. Finally, the sensory power or spirit diffused through the nerve is more concentrated and stronger where the retina meets direct cones due to its source and where it has to go: from that point it is diffused over the sphere of the retina, gets further from the source, and thus grows weaker. But as with a funnel and in a fishing net with a sack which were likened above to the retina, the sides all send the liquid or the fishes into the canal or sack; thus the sides of the retina do not usurp for themselves its sensory capacity, but whatever they can, they bring into the perfection of direct vision.  Thus, when we see a thing perfectly, we see it within the entire surrounding area of the visible hemisphere. For this reason oblique vision satisfies the soul least and only invites the turning of the eyes in that direction in order that they see directly. This is how Witello 3, 17, should be interpreted. For by the perpendicular alone nothing is seen distinctly. But direct and properly distributed, or distinct, vision is brought about by all the rays from the same point (from which a perpendicular can be drawn through the center of the pupil and of the humors) being collected at the very center of the opening of the nerve (as in Witello, 3, 29).

The color of the retina is neither dark nor black, in case it should tint the colors of things, nor dazzling white, in case too much brightness should pour into the vitreous humor and the things appearing white and bright above this should be made to seem too colored. See the corollary to Chapter I, Proposition 30 and 31. The shape the retina is larger than a hemisphere. It must in the first place be a hemisphere, thus proportionate to the picture received of things, as already said. Moreover, the border extends as far as the ciliary processes so that when eyeball is filled with the vitreous humor the retina is kept stretched with the collar narrower than the belly. It cannot be tied on due to the softness and subtlety of the visual spirit, for which indeed there are canals through the nerve, contrary to the nature of the rest of the nerves, such that the substance of the nerve does not impede it. Now if the retina did not occupy more than a hemisphere, it could easily become wrinkled and slip back on to the junction of the nerve. In any case, the gap between the hemisphere and the ciliary processes had to be filled, for otherwise this would have to be achieved by the choroid or by the vitreous humor. How much better that it should be done with the retina! This extends the visual function into the border. Although none of the cones formed by the lens reach this border, nevertheless slits appear formed by the ciliary processes, such that some light can enter from the sides through the ciliary processes and be received by the ample border of the retina. For a line drawn from the extreme edge of the cornea through the adjacent edge of the pupil almost falls on to the junction of the lens with the ciliary processes; one drawn through the opposite edge of the pupil almost touches the origin of the ciliary processes from the choroid. By this means Nature has brought it about that we see more than a hemisphere with the eyes fixed, or in any case as much as is admitted through the corner of the eye, with a minimum of movement. Indeed with slightly wider vision you would be able to see your ears, especially if they were large, with the eyes on the same side. I have often been surprised at seeing the sun and my shadow both appearing as if in front, rather than being opposite each other. It seems to be Nature's precaution to protect the eyes that, when they are not actually turned away, things approaching come immediately into view wherever the eyes are looking. And this preserves the whole living thing, for certainly it takes care to preserve itself and this adaptation helps it to look after its body.

The vitreous humor has a skin, so that it is not weakened end made flaccid by the moisture of the nerves or the retina, and so that it does not run into the aqueous humor at the front through fissures in the ciliary processes. It must differ in density from the lens and from the aqueous humor because of refraction. For unless it was rarer than the lens, the rays would not be bent away from the perpendicular and brought together to the axis of each cone. Since the vitreous is denser than the aqueous humor, the rays entering through the ciliary slits can fall more deeply through it and draw near the outermost cones formed through the lens.

The lens also has a coating such that, soft as it is, it does not run into the aqueous humor. But the lens does not reach as far as the sides of the retina, so that in this space the rays of the cones may be focussed to a point. Thus, to be nourished and connected with the supply of nutriment, it has to be attached by the ciliary processes to the choroid (choroidea). These are entirely black, in order not to admit light; and dense, such that the lower chamber of the vitreous humor may, as it should, be dark, and such that an illuminated vitreous humor should not dilute the images (species); which will doubtless come about by their becoming inflated and swelling up in bright light and shrinking when light is reduced, like the choroid (uvea). The posterior surface of the lens is of hyperbolic or similar shape, such that the rays passing down through the hyperbola and converging in the same upright cone may be focussed at a nearer point on the same axis. That this is not possible with any other shape is demonstrated below. The anterior surface of the lens bulges such that when a radiant point shines obliquely on to the pupil, this surface is cut more at a slant by the scalene cone, and so the amount intercepted by the cone is kept the same so far as possible. And in order that it may meet perpendicularly all the rays (arriving from the same given point) which are refracted by the cornea, and are brought together towards a single point after refraction, I assume this anterior surface of the lens to be simply circular or spherical.

The entire choroid with the ciliary processes is present to produce sufficient darkness, in case too much light should be harmful. It does nothing towards the formation of the image (species) or picture, nor if it did would it ever complete or perfect it, given that the pupil is too wide for the size of the eye. Indeed in darkness it dilates to three times its width in sunlight, so that in darkness most of the surface of the lens is uncovered in order to allow more of the weak light focus to a point through the lens (focussing itself not being affected by the pupil) stimulate the sense so much the more clearly. The more light there is, on the contrary, the narrower the pupil, in order to exclude more light in case too strong a light should injure the sense. Thus the position of this pupil is where the rays intersect, and it exists for the sake of the lens itself. Yet this intersection does not take place in a point, but is spread out over a long cone due to the circular surface of the lens. Thus the position of the pupil forms the base of this cone of intersections. For between the pupil and the lens there is no intersection, and if anything were exposed to vision there it would be seen inverted and indistinct. The inner side of the choroid is rough, for if it were smooth it would reflect the rays reflected to it from the surface of the lens. In fact, it surrounds the retina with a totally black coating of similar substance. For the retina gets its nourishment through the choroid to which it owes the blackness of its anterior parts. Supposing the retina itself were transparent, the black cancels this.

The aqueous humor is necessary to fill the chamber and to provide a single continuous medium as far as the lens for transmitting rays refracted at the cornea. The cornea itself is seen to be a small part of a spheroid, such that rays falling perpendicularly on the anterior surface of the lens can be focussed to a single point. Nothing prevents the roundness of the cornea from being perfect, as explained below.

To assist the reader who does not have anatomical illustrations at hand, I here include a copy of Felix Plater's Table 49. I wish I had placed this selection at the beginning of this work, for then I could have adapted the text to it. There was no need to add explanation of letters and signs beyond that of Plater himself. I have added only the references to my text.

There are 19 figures, for the engraver added the last two (of the organs of hearing) without my instruction.

I. A line drawing showing a projection of the membranes and fluids (humores) as found in the actual eye. Where: A, lens; B, vitreous humor; C, aqueous humor; D, related coat; E, opaque part the sclerotic (crassa tunica); F, choroid (uvea); G, retina (retiformis); H, hyaloid (hyaloides); I, lens capsule; K, ciliary processes of the choroid coat; L, boundary of the choroid on the sclerotic; M, cornea part of the sclerotic, of which the convex bulge noticed by others is indicated by a dotted line; N, N, eye muscles; O, optic nerve; P, thin membrane of the nerve; Q, thick membrane [sclerotic] of the nerve.

II. The eye intact with the muscles, taken out of the skull and with the eyelids removed.

III. The eye-ball viewed from the front.

IV. The sclerotic with part of the optic nerve.

V. The sclerotic, cut transversely.

VI. The choroid with part of the optic nerve.

VII. The inverted interior surface of the same.

VIII.The retina with the substance of the optic nerve.

IX. The hyaloid coat.

X. The ciliary processes, radiating from the front of the hyaloid coat.

XI. The lens capsule.

XII. The lens in its capsule.

XIII. The naked lens, viewed from the side.

XIV. The lens viewed from the front.

XV. The three humors together, aqueous, vitreous lens, partly shaded.

XVI. The vitreous humor with the lens.

XVII. The vitreous humor alone seen from the front.

XVIII. The aqueous humor shown in position over the lens.

XIX. The aqueous humor above viewed from the front.

A, in II, IV, VI, VIII. Visual or optic nerve.

B, in II, IV, VI. Thin coat covering the nerve.

C, in II, IV, V. Sclerotic surrounding the nerve.

DDD, II. The eye muscles on one side.

EE, II, III. Part of the related coat extending under the eyelid.

*, II, III. Expanded part of the same, intact.

F,. II, III, IV, V. Dark part of iris of the eye, which the white surrounds.

G. II, III, IV, V. Black pupil or center of eye, in middle of the iris.

Note in II, IV, V at G the arc, indicated by a dotted line, rising from the sides of the iris and forming part of a smaller circle than the globe of the eye. This was added by me from the observations of others. Note also the bulge of the cornea rising from the white.

H, II, III. Small segment of flesh at corner of the eye.

I, II, III. Tear ducts.

K, IV, V. Vessels dispersed over the sclerotic.

LL, V, VI. Fibres by which the choroid is attached to the sclerotic.

MM, VI. Boundary of the choroid, where it stops at the cornea.

N. VI, VII. Opening in the choroid, or pupil.

OO, VII. Beginning of the ciliary processes.

P, VII. Beginning of the choroid, extending from the thin coat.

Q, VIII. Dimensions of the retina extending above the middle of the eye.

R, IX. Pocket of the hyaloid coat holding the lens.

S, XI, XII. Width of the lens capsule.

T, in XII, XIII, XVIII. Spherical posterior part of thin lens (according to others Protruding in a cone; according to me hyperbolic).in XIV, XVI. Flattened anterior part of same.

V, XV, XVI. Dimensions of the vitreous humor.

X, XV, XVIII, XIX. Dimensions of the aqueous humor. Y, XV. Region at which the vitreous humor is separated from aqueous by the hyaloid coat.

Z, XV, XVIII. Region in which the choroid is bathed by the aqueous humor.

&, XVII. Cavity remaining in the vitreous humor after the lens has been removed.

§, XIX. Corresponding cavity in the aqueous humor.

3. Demonstration of the conclusions stated conceit how vision takes place through the lens 

What happens using the eye with an aqueous sphere been described. I shall now show how the exact opposite happens with a piece of paper. First, the following can be deduced directly from what has been said: namely, the reason why, if the paper almost touches the globe, the shape of the globe (if it is a urinary flask, with a long collar is depicted on the paper, by sunlight radiating into the sphere with a bright border. For whatever rays enter the globe do not yet in that position intersect with the axis. Since the paper touches the globe, all the rays that could pass through the globe are here. Then the border is brightest given that the most concentrated rays intersect with each other in a circle (but not yet in the axis), as is seen in , , , , in the figure [fig. 4] and as agrees with previous demonstrations. When the paper is moved away a twentieth of the diameter of the globe from the glass (although the illumination comes from far off) some rays in the middle of the figure now begin to intersect with the axis, here at , and the middle of the figure becomes brighter. The figure becomes smaller as the paper is moved farther away, but the cone formed by these lines does not alter in section in a swiftly changing succession of circles, for it does not decrease proportionately, but quickly at first and then slowly. The genuine cause of this is the succession of rays. For, of the rays that intersect in the axis and then separate, the outer ones first form the boundary at , , , ; these are succeeded by the inner ones forming the boundary at , , , . If this cone formed by refracted and intersecting rays were to appear intact in the air, it would be seen as a figure generated by an arc with one end rotated in a circle, the other remaining aloft, and the arc curving inwards; for the cone is slender in the middle and very sharp-pointed. Where the paper meets the point of the cone, at , the illumination is strongest, so that with a hot son it can burn a fire dust (pelvis pyrius) in cold water. For, by Proposition 15, indeed not all but nevertheless most of the rays intersect there in a single central point. The remaining rays , which have already intersected, are dispersed round this point, and form a set of rays going towards a single center. When the paper is moved beyond the last point , the inside of the figure disappears with the intersection of all the rays. We can thereby understand how great the burning powers would be if all the rays that can pass through the globe came together.

Through a globe of denser medium than the surroundings, any point beyond the intersections of the parallels depicts itself strongly on a piece of paper placed at the last point of intersection of the rays, but not in front of or behind this point, and the picture made up of all the points appears inverted.

The cause of its depicting itself strongly is that the globe brings together to a single point a large number of rays goings out from a given point which are near the perpendicular, as demonstrated above. This does not happen with the rays intersecting more rapidly at , because the more rapid intersection at o is effected by the rays , , sent in more weakly from the sides being more refracted. Indeed the place of intersection on the paper is occupied by other rays (passing through the globe from the same luminous point) which have not yet intersected, but which have been focussed and are bright and thus obliterate the rays intersecting at . Again, cones coming from other points of the luminous thing are still too widely separated, as here , and produce confusion by partly overlapping.

By contrast, at the final intersection , a large number of rays coming from the same luminous point and lying near the ultra-powerful perpendicular , run together at a single point, as shown in Proposition 15, and because cones converge to a sharp point they occupy no other region. Thus single points are depicted separately and distinctly. Only a few rays from other points on the visible thing arrive, but by now intersected and weaker, as would happen if one of the cones terminated in ; then the vertex of the new cone would fall on the intersection with the old one, which is how whatever confusion there is in this picture is brought about. For the image is inverted, not because of the intersections already described of the rays in front of the glass, but because every point of the thing seen, radiating perpendicularly into a sphere, depicts itself in a very strong cone behind the glass. Thus the axes of the cones intersect in the center of the sphere, these having undergone no refraction. This is the genuine cause of the inversion of the picture brought about by a sphere denser than the surroundings, when it is not covered up by anything solid but an opening is left [...]

When a screen with a small window is placed in front of the globe within the limit of the sections of the parallels, and the window is smaller then the globe, a picture of the visible hemisphere is projected on to the paper, formed by most of the rays brought together behind the globe at the limit of the last intersection of the rays from a luminous point. The picture is inverted, but purest arid most distinct in the middle.

So great is the uncertainty in this matter and indeed such its novelty that unless we take the greatest care, it may easily become confused. Indeed I was held up myself for a long time, until I convinced myself that all the different effects had the same explanation. Let a be the center of a globe of water bc, in front of which is placed an opaque screen dg with a small window ef smaller than the globe [fig. 5]. Let the visible thing be hi. The paper is at k, where the final intersection of the radiation from h takes place. If the screen were absent, by Proposition 20, I would depict itself at the final intersection of its rays at l, and the point h at the point k. But they would project the lateral rays of the cones so that they intersect each other and overlap. But with the screen in position, no more of the rays for h can enter the sphere than can pass through ef and then nearly all meet at k, and this cone is reduced as if by pruning, so that no rays can be projected so as to intersect at l and cause confusion there. Again, the brightest part of the radiation going in the cone il, namely the radiation through the center a, is clearly cut off by the screen de, and the very bright tapering apex l, which could produce confusion at k, is absent. In fact no more of the radiation from I is left than can go through ef. This consists of the rays that successively intersect in the width mn, by Proposition 19, and after intersection cut al and fall on the paper placed at k; they fall on the near side of l, and not at a point but spread out because they have already intersected at m. Thus, the picture is dark and indistinct at the sides. Hence, if you move the sides of the paper nearer they are better depicted but not yet accurately, for the intersections are spread out not only in depth at mn (which would not matter greatly) but also laterally.

Because the intersection takes place through ef, after ie and if have been cut by hk, the rays pass through mn before meeting al, by Proposition 19. Hence, the rays leaving I on the right leave mn on the left, nor can there be another intersection by which they could return to be right.

The small window ef must be narrow, for if it were wider it would not perform its functions. And it must be near the globe, for if it were too far distant the rays entering from the visual hemisphere would be too few and more confused.