Which parts of a sphere are most and least illuminated
Reflected rays on a mountain, and how a shadowed body is lit by arcs of the luminous hemisphere
A leaf of the Treatise on Painting on the physics of light and shade. A short opening argument shows that a mountain lit from the point a receives no direct light along certain faces (from b to d and from c to f), only reflected rays, because light travels in straight lines. Two lettered propositions then determine which part of a shadowed sphere set within a luminous hemisphere is least and most illuminated, according to how large an arc of the light each point can see. Two ink diagrams accompany the argument, and the sheet also carries the running head, a marginal section number, and a catchword that are not part of the transcription.
On this page
A mountain lit from point a receives only reflected light on its shaded faces
If the object is this figured mountain and the light is the point a, then from b to d and likewise from c to f there is no light except by reflected rays. This follows because luminous rays act only along a straight line, and the secondary, reflected rays do the same.
Which part of the sphere is least illuminated
The part of the shadowed body seen by the smaller part of the luminous body is least illuminated. With the shadowed body a s q r lit by its hemisphere n c e f, the points a and o are seen by equal arcs and so are equally lit, while r sees only the smaller arc o d f, p sees only d f, and q sees only the far edge f, so each in turn is darker.
Which part of the sphere is most illuminated
That part of a sphere is of most intense brightness which is accompanied by the smallest sum of shadowed images. The demonstration takes f n o as the shadowed spherical body and a b c as the luminous hemisphere, and breaks off as the proof of the illuminated point begins.
Diagram of a shadowed sphere within a luminous hemisphere
A semicircular hemisphere of light is drawn with an inscribed circle (the shadowed sphere) and radiating construction lines carrying the letter labels used in the two propositions. The figure lets each point on the sphere be paired with the arc of light it can see.
Small diagram of a mountain lit by a point source
At the top of the page a small mountain profile is drawn with a straight ray reaching it from a point at the right, illustrating the claim that only faces struck along a straight line are directly lit while the rest depend on reflected light.