A sphere equal to the pupil is always seen as half
At any distance such a sphere shows exactly half; a smaller pupil sees less than half
Leonardo argues that a spherical body equal in size to the pupil viewing it is always seen as exactly half, at any distance, because its diameter terminates within equal angles formed by parallel visual lines. If instead the pupil is smaller than the sphere, the sphere can never be seen as half: less is seen the nearer it lies, and more the farther away. Diagrams of the eye and spheres with visual lines illustrate the two cases, and a third analogous figure is noted.
On this page
A sphere equal to the pupil is seen as half
If a spherical body equals the pupil that sees it, then at every distance—supposing the eye could discern them—it is seen as neither more nor less than half. Its apparent portion does not change with distance in this special case.
Diameter ending within equal angles of parallel lines
The cause is geometric: the sphere's diameter, with its extremities, always terminates within equal angles between the visual lines, which are parallel. This equality of angle keeps the seen portion fixed at one half.
A pupil smaller than the sphere never sees half
If the pupil is smaller than the sphere before it, it can never see the sphere as half, at any distance. It sees so much less the nearer the sphere is, and so much more the more remote it is.
