The object of this paper was to ascertain, by a geometrical construction, the optical appearance presented by the binocular vision of a straight line and a circle, or of two straight lines. The problem discussed was, accordingly, the geometric one of the intersection of a cone with a plane, or of two cones with each other: and the conclusion arrived at was that the apparent image is always a conic section. The author took no account of the perspective of the presented combination of images, nor of the union or disunion of the extremities of the respective images when their lengths are different.