The Tower's Colour Proved by Proportion; Sunbeams in Clouds
Line-lengths measure how air tints a tower, and rays break through the gaps between clouds.
Completing the tower demonstration, Leonardo argues from the eye n, to which the images of the five parts of the tower a e (a, b, c, d, e) converge. If the air were of uniform thickness, the colour taken on by the tower's foot e and by part b would be in the same proportion as the line lengths e m and b s; but since air is thicker the lower it lies, the colour proportion must be greater still, for line m e is both longer and passes through non-uniform air. An upper marginal diagram sets out this geometry. A new chapter then treats solar rays that penetrate the openings between clouds, illuminating everything they cross and tinging the dark places behind them, with a lower diagram of rays radiating from a cloud.
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The air's tint on a tower expressed as a ratio of line-lengths
For the tower a e seen from eye n, if the air were uniform the colour taken on by the foot e and by part b would be as the lengths of lines e m and b s. Because the air is thicker the lower it lies, the colour ratio is greater than that, since line m e is longer and crosses air of uniformly non-uniform thickness.
Solar rays through the openings of the clouds
Rays that pass through the gaps between the various densities and rounded masses of the clouds light up every place where they cross and illuminate even the shadows. They tinge with their own light all the dark places behind them, which darknesses appear in the intervals between the rays.