... and of the primitive and derivative pyramid. A point in itself is an indivisible part, being separate yet alike to all and capable of all, and all the indivisibles are alike to the one and able to contain all within it. As experience shows in the points of the angles of the apertures, in which — the solar rays having passed through them — those angles form the boundary and apex of the primitive and derivative pyramid. This derivative one, though of lesser efficacy, is nonetheless able, in the long run, to widen and dilate with the concourse of its rays much more than the primitive. And this same experiment you will see in concave mirrors, which, having taken the solar rays according to their capacity, lead them pyramidally to the indivisible part of the point; which, although it be the smallest part of the sun, or of the solar rays that illuminate and heat the whole surface of the mirror, nonetheless in that point is gathered the whole sum and power both of heat and of splendour, of which the whole surface of the mirror is made capable. The derivative pyramid, at parity of quantity, is alike in all its powers to the primitive, and, once past that parity, becomes as much weaker as in size it exceeds the quantity of the primitive.

f — d a – c – e – g b. Let a b be the mirror that reflects the rays struck back on it by the sun; let a b c be the primitive pyramid; let a b be its base and c the apex, an indivisible part, which — as much as it is smaller than its base — becomes proportionally the more luminous and hot. c is the common boundary to the 2 pyramids; c d e is called the derivative pyramid, and because in size it is like the first, it will still be alike in all its parts to the parts of the first, both for heat and for brightness. In the concourse made by the rays continued from d to f and from e to g, the part of the pyramid at f g is as much less hot and luminous than at d e as, by quantity, e d enters into f g.

S – c a – n – d f m – o – e b - h. The points of the pyramids caused by the solar rays from the concave and dense surfaces of the mirrors are of as much less power, one than another, as the mirrors are smaller from one point than from the other. As much as by quantity the mirror c d and the mirror d e, each by itself, enter into the mirror a b, so much are the pyramid or point o e n of less power than the point m. The point f will be twice as hot as S h, because there the 2 bases of the derivative pyramids intersect.

n m - o

n - u t - S r. Of the eye. When the 2 eyes lead the visual pyramid onto the object, that object will be seen by the eyes and well comprehended. The pyramid that is led to the object is r S n, the object is n, and the place that does not break it is the aperture t u.

o c r m a – f q u g t p h – e S. Of the eye. It is possible that, having a thing before the eyes and directing themselves to it with all their power, that thing be not seen by the eyes. Although it be distinguished from the ground by colour and be an evident body, the road being free and open, it will seem closed, and the closed part will seem open. Let S e be the eyes, r the thing set before the eyes, t u the road or aperture whence the eye wishes to know r. I say that the right side of the aperture p t will be carried, or will seem to be, in the left part at r c, and the left u q will be transported to the right side at m r, and all the part m c will seem to be of the colour of the wall where e is; and although it be far from that wall, nonetheless it will seem continued at the same distance. The aperture will appear in 2 places of the object: t g goes from right to left, and it seems that the aperture c o is judged by the eye e m q f; and thus by the eye S it seems that the wall is broken at h p and that from there the object a m is seen.

n m; p t - a c

h g m f e - d c - b a. Every ... The impact of the derivative shadow, born in a pyramidal opaque body, will be of varied darkness. The impact of shadows departing from a pyramidal body will not be of a figure similar to its origin. The light that is greater than the apex and smaller than the base of the pyramidal opaque body set opposite it will cause the shadowed concourse to produce, in its impact, a shadow of forked figure and of varied quality of darkness. If the luminous body, greater than the opaque, makes ... If the opaque body smaller than the luminous makes two shadows, and the opaque body alike; the one greater than the luminous makes one; the pyramidal body that has part of itself greater and part smaller than the luminous will make a forked shadow.