On the Horizon: the Nile's white distance and the perspective pyramid
Aerial diminution over the plains of Egypt, and a diagram proving the visual pyramid embraces infinite space.
The chapter on the horizon continues with three lettered notes. Leonardo describes how, looking up the Nile toward Ethiopia across three thousand miles of rising plain, the intervening thickness of air turns everything white so that the horizon is lost from view, an effect he says makes a fine subject in painting, to be rendered with flanking mountains in diminished colours. A small diagram, with the eye at a b, the receding degrees d n m o p, and the plane c d, demonstrates that the pyramid of the perspectivists embraces infinite space, its visual lines gaining height at every degree yet never filling the plane nor reaching the height of the eye. A final note observes that figures which diminish little are little distant from the eye, so the natural horizon meets the eye of the figure portrayed.
On this page
The white, lost horizon up the Nile toward Ethiopia (label c)
Looking along the Nile's course toward Ethiopia across three thousand miles of plain that rises with the river, so great a thickness of air interposes between the eye and the Ethiopian horizon that everything turns white. Thus that horizon is confused, indeed unknown, and lost from our knowledge.
Rendering distant horizons with diminished colours
Such horizons make a very fine sight in painting. One must render the flanking mountains with degrees of diminished colours, as the order of the diminution of colours over long distances requires.
The perspective pyramid embraces infinite space (label d)
With the eye at a b cutting the degrees of an infinite distance d n m o p, the visual lines strike the plane c d, gaining height at every degree yet never reaching the eye's height. Being a continuous quantity, the plane c d is divisible to infinity and can never be filled by the visual lines, even were the space b s infinite.
Figures that diminish little are near the eye (label e)
Figures that diminish little are little remote from the eye. Whence of necessity the boundary of the natural horizon always meets the eye of the figure portrayed.