Perspective: apparent size and distance from the eye
Why two equal bodies differ more in apparent size the nearer they lie to the observer
A note on linear perspective arguing that of two equal bodies set one behind the other, the difference in their apparent sizes grows the closer they are to the eye and shrinks the farther away they are. The rule is grounded in proportion: at 1 and 2 braccia the near body looks twice the far one (double proportion), while at 100 and 101 braccia the difference is slight (inverse proportion), so that apparent size stands to apparent size as distance to distance. A diagram of two equal spheres on a groundline, with sightlines converging to the eye at the right, illustrates the argument.
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Equal bodies differ more in size the nearer they are to the eye
Between two similar and equal objects placed one behind the other at a fixed distance, the difference in their apparent sizes is greatest when they lie close to the eye. The more remote they become, the less their sizes seem to vary. This is the basic law relating apparent magnitude to distance from the observer.
Double and inverse proportion of size to distance
The rule is proved through the proportions of the distances: a body at 1 braccio and another at 2 braccia stand in double proportion, so the near one appears twice the far one. At 100 and 101 braccia the near body exceeds the far only as 100 falls short of 101, an inverse proportion. Apparent size is to apparent size as distance is to distance from the eye.
Diagram of two equal spheres sighted to the eye
A horizontal groundline carries two equal spheres at the left, with straight sightlines running from them to a point at the right that stands for the eye. The converging lines show geometrically how two equal bodies subtend different angles according to their distance.