In his fourth and very interesting book, on the fallacies of distance, magnitude, position, and figure, Aguilonius resumes the subject of the vision of solid bodies. He repeats the theorems of Euclid and Gassendi on the vision of the sphere, shewing how much of it is seen by each eye, and by both, whatever be the size of the sphere, and the distance of the observer. At the end of the theorems, in which he demonstrates that when the diameter of the sphere is equal to the distance between the eyes we see exactly a hemisphere, he gives the annexed drawing of the mode in which the sphere is seen by each eye, and by both. In this diagram E is the right eye and D the left, CHFI the section of that part of the sphere BC which is seen by the right eye E, BHGA the section of the part which is seen by the left eye D, and BLC the half of the great circle which is the section of the sphere as seen by both eyes.[10] These three pictures of the solids are all dissimilar. The right eye E does not see the part BLCIF of the sphere; the left eye does not see the part BLCGA, while the part seen with both eyes is the hemisphere BLCGF, the dissimilar segments BFG, CGF being united in its vision.[11] After demonstrating his theorems on the vision of spheres with one and both eyes,[12] Aguilonius informs us, before he proceeds to the vision of cylinders, that it is agreed upon that it is not merely true with the sphere, but also with the cylinder, the cone, and all bodies whatever, that the part which is seen is comprehended by tangent rays, such as EB, EC for the right eye, in Fig. 3. “For,” says he, “since these tangent lines are the outermost of all those which can be drawn to the proposed body from the same point, namely, that in which the eye is understood to be placed, it clearly follows that the part of the body which is seen must be contained by the rays touching it on all sides. For in this part no point can be found from which a right line cannot be drawn to the eye, by which the correct visible form is brought out.”[13] [10] It is obvious that a complete hemisphere is not seen with both eyes. [11] Aguilonius, _Opticorum_, lib. iv. pp. 306, 307. [12] In the last of these theorems Aguilonius describes and explains, we believe for the first time, the _conversion of relief_ in the vision of convex and concave surfaces. See Prop. xciv. p. 312. [13] Id., p. 313.