An Opaque Surface Between a Black and a White Object
Why the surface reads black, white or a mixed tone, and is darkest nearest the black body
Continuing the proof of the previous chapter, this folio sets a white opaque surface a b c between a black object r s and a white object n m, invoking the rule that every body fills the surrounding air with the species of its colour. The black object darkens the region a g, the white object whitens b c, and the overlap zone a b takes a colour composed of white and black. Leonardo then argues the surface is darkest at a because a lies nearer the black body, appealing to the definition of the circle and to the geometric 'angle of contingency', which lets point b see only the extremity r of the black body while also receiving light from the white object n m. A small circle-and-rectangle diagram lettered m, n, r, s sits in the text column.
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A surface coloured by a black and a white object at once
By the cited proposition every body fills the surrounding air with the species of its colour, so the black object r s darkens the region a g of the opaque body while the white object n m whitens the region b c. Where both are seen, at a b, the surface takes a colour composed of white and black, that is, a mixed tone.
Darkest nearest the black body
The surface is much darker at a than at b because a lies nearer the black body r s. This graded darkening of a single surface, set between a dark and a light object, is offered to the painter as the mechanism behind the tone of a shadowed plane.
The angle of contingency limits what point b receives
Leonardo grounds the gradation in the definition of the circle and in the geometric angle of contingency, the smallest angle there is. Because of it, point b can see nothing of the black body except its extremity at the point r, while additionally receiving the brightness of the white object n m.
Diagram of the two objects and the opaque surface
A small pen diagram inset in the column shows a circle with a rectangular figure and the letters m, n, r, s, laying out the black and white objects and the opaque surface between them. It is drawn, not transcribed, and keys the lettered points a, b, c, g, r, s used in the proof.