Distant Motion Seems Triple-Slow; Mountain Summits Seen from Above
A triple-distance proof; why far summits darken toward the horizon
This page of Book Five, headed PARTE, carries two pen diagrams: a triangle lettered m, i, k, h with its apex at o and a graduated arc at right, and, lower down, a sketch of receding mountain ridges under rays from an eye. The text completes a proof that a motion l m at triple the distance from the eye o appears triple in velocity and length to a motion a to b made in the same time, since the space c d enters three times into the space a f. A new chapter, 'Of the summits of mountains seen from above downward,' then argues that summits seen one after another from high to low do not brighten in proportion to their distances but much less, since landscapes seen high to low toward the horizon grow darker.
On this page
Proof that triple distance makes motion appear triple-slow
Let l m be at triple the distance from the eye o compared with the distance a f. The motion l m appears triple in velocity and length to the motion a to b made in the same time, for while a moves to f, l m is shown to have moved only the space c d, which enters three times into the space a f.
Diagram of the perspective of motion
A triangle with its apex at o below and points m and i at the top, k and h across the middle, together with a graduated arc at the right, illustrates the triple-distance proof of apparent motion.
Mountain summits seen from above downward
The summits of mountains seen one after another from high to low do not brighten in the same proportion as the distances between those summits, but much less, since the distances of landscapes seen from high to low toward the horizon go darkening.
Sketch of receding mountain ridges
A pen sketch in the lower half of the page shows ridged mountain outlines under rays cast from an eye, illustrating summits seen from high to low toward the horizon.
Aerial darkening toward the horizon
Distances of landscapes seen from high to low up to the horizon go darkening, while those seen from low to high at the same distance as the first go always brightening. This governs how the summits are shaded relative to their bases.