ALHAZEN

...[perpendi]cular; after the section Refraction was often called "sectioning" the line of travel., the form is on a line even further from the perpendicular than the line it was on before. And the form that was on a line closer to the perpendicular also extends, after the section, onto a line closer to the perpendicular, but with a greater proximity than the line it was on. The same is true for all forms extending from a single point. When this is tested with subtle experimentation, it will be found exactly as we have said. We shall demonstrate the method by which this can be tested through true experimentation in our discourse on refraction original: "sermonē de refractione"; then all things depending on refraction will be uncovered. We shall not use those things there in the demonstration which we have used in this treatise.

Therefore, if two points deviate to one side of the visible object—when their forms extend to a single point on the surface of sight—they will cross each other along two lines. Their position relative to the eye, in respect to the visible object, will be the opposite of the position of the two primary lines along which the two forms were extending to the surface of sight. Thus, the position of the two points on the crystalline surface superficiei glacialis|the "icy" or crystalline lens, once thought to be the seat of vision where the two forms arrive will be opposite to the position of the two points from which the forms originate.

All forms, therefore, that are refracted from one point on the surface of sight, reach the crystalline surface in reverse. Moreover, the form of any point opposite the eye reaches the entire surface of sight; therefore, it will be refracted from the entire surface of sight. And a form refracted from the entire surface of sight is refracted toward some area of the crystalline surface, not to a single point. For if refracted forms were to converge at a single point after refraction, they would have to cross the perpendiculars at whose ends they were refracted, or pass through them, or the form would have to leave the surface in which it was being refracted. But no refracted form meets the perpendicular at whose endpoint it was refracted after the refraction, nor does it pass through it, nor does it leave the surface in which it was refracted. All of this is made manifest through experimentation.

Thus, the form of a single point of the visible object that reaches the crystalline surface after refraction will not be at a single point, but in some area of the crystalline surface. The arrangement of the forms of different objects or different points on the surface of the visible object reaching the crystalline surface through refraction will not be the same relative to each other as their arrangement on the surfaces of the visible objects themselves, but rather the opposite. Therefore, none of the refracted forms of visible objects reaching the crystalline surface exist as they do on the surfaces of the visible objects. And it has already been shown [in section 18] that forms arriving along perpendiculars are ordered on the crystalline surface according to their true existence, because they extend straight from the surfaces of the visible objects to the crystalline surface. Thus, none of the forms of visible objects reaching the crystalline surface are ordered on that surface according to their actual arrangement on the surfaces of the visible objects, except for forms extended only along the lines of direction verticationes|the specific paths or orientations along which light travels of the perpendiculars.

If, therefore, the sense of sight of visible objects comes from forms reaching it from the surfaces of the visible objects, the eye will perceive nothing from the forms of visible objects reaching it except from those lines of direction whose ends converge at the center of sight alone; for sight perceives nothing from the forms of visible objects unless they are ordered according to their existence on the surfaces of the visible objects.

Again, if the center of sight is not the center of the crystalline surface: the straight lines that exit from the center of the surface of sight, and extend through the opening of the uvea The "uvea" here refers to the pupil or the opening of the iris., and reach the visible objects, would not be perpendicular to the crystalline surface, but rather would strike it at an angle. Nor would their arrangement on the crystalline surface be uniform, except for one line only—namely, the one passing through both centers.

Thus, the crystalline lens cannot perceive the forms coming from the surfaces of visible objects to its own surface except along the lines of direction of these lines—namely, those that are perpendicular to the surface of sight (which is the surface of the cornea); for the forms on these perpendiculars alone are ordered on the crystalline surface according to their arrangement on the surfaces of the visible objects. If the crystalline lens perceives visible objects from the forms coming to it, and it only perceives a form from the lines of direction of these lines, and these lines are not perpendicular to its surface, it would then perceive forms from lines of direction whose positions relative to its surface are varied and slanted. It would perceive forms from lines of direction of various slanting positions, and it would perceive all the refracted forms from lines of direction of various positions at its surface.

And if it were to perceive all refracted forms from lines of direction of various positions, nothing would be distinguishable to it from the visible things, because of what was demonstrated above. And since it is not possible for it to perceive refracted forms from lines of direction of various positions, it is not possible for it to perceive the forms of visible objects from the lines of direction of the lines that are perpendicular to the surface of sight, unless those lines were also perpendicular to its own surface, and their positions on the surface were uniform. And these lines will not be perpendicular to its surface unless the center of its surface and the center of the surface of sight were the same point.

Therefore, if the sense of sight of visible objects comes from the forms reaching it from the colors and lights of those objects—and does so distinctly—it is necessary that the center of the surface of sight and the center of the crystalline surface be one common point, and that sight perceives nothing from the forms of visible objects except along the lines of direction of straight lines whose ends converge at one and the same point only. And it is not impossible for the two centers to be the same, since it has been shown [in sections 6 and 8] that the two centers are within the posterior center of the uvea, and on a single straight line passing through all the centers. And since it is not impossible for the two centers to be the same, and for the straight lines exiting from the centers to be perpendicular to both surfaces—namely, the crystalline surface and the surface of sight—it is also not impossible for the visual perception of visible objects to occur from the forms of light and color reaching it from the surface of visible objects, provided that the perception of these forms occurs only along the lines of direction of the perpendiculars. And this is so that the nature of sight may receive those things which come to it from the forms of visible objects; and also that the nature of sight be further specialized so that it does not receive those things which come to it from the forms except along its own lines of direction, not from all lines of dir—