Reckoning air-thickness before distance for colour
Chapter 198 continued: calculate the degrees of thickness first, then distance, so colours keep their beauty
A text page of the Treatise on Painting continuing the proof of chapter 198 that a colour need not change over varying air. Leonardo instructs the reader to reckon first the thicknesses of the air and then the distances, so that colours shifted in position keep their beauty. He assigns colour h to air of 4 degrees of thickness, g to 2 degrees, and e to the first degree, then checks the converse distances (e at 2 and a half degrees, g at 2, a h at one) against a third calculation using the half-degree c d, which is worth a whole degree of the thinner air above. The whole page is dense running prose without a diagram.
On this page
Reckon thicknesses first, then distances
Half a degree of distance in the double-thickness air below occupies as much colour as a whole degree of the thinner air above. Calculating first the air-thicknesses and then the distances, colours varied in position will not have changed in beauty: colour h in air of 4 degrees, g in 2 degrees, e in the first degree.
Converse distances checked by a third calculation
In equal but converse proportion, colour e stands 2 and a half degrees from the eye, g at 2, a h at one. Since this does not meet the thickness-proportion, a third reckoning uses the half-degree c d, alike but not equal to a b, which is worth a whole degree of the air above and so restores the count to 4.
Air of double thickness halves the colour's reach
The air below is of double thickness to the air above, which is twice as thin as the air bordering it below. This is why colours placed in the thicker, lower air are occupied more strongly and must be moved further off to keep an equal appearance.