The brightest point on a screen: shadow and light pyramids
Proving where a lit body and its dark field cast the most excellent brightness on a wall
A closely reasoned geometric demonstration from Part Five, illustrated by a large diagram of a luminous body, a small shadow-caster, and a receiving wall. Leonardo takes the luminous body b c between the dark fields d c and a b, the small shadowy body n m, and the wall p s on which the shadowy and luminous images fall. He proves that point r on the wall receives the most excellent brightness, since there the whole luminous body is seen with only half the dark field, whereas point s sees two dark spaces worth double the light, and the pavement brightens from s to r and darkens again from r to o.
On this page
Point r receives the most excellent brightness on the wall
Let the luminous body be b c, its right and left dark fields d c and a b, the small shadowy body n m, and the wall p s where the shadowy and luminous images imprint. Upon this wall, the point r has the most excellent brightness of any part of the pavement, because at r the whole luminous body b c is seen with only half the dark field, that is c d.
The shadow pyramid c d r against the luminous pyramid b c r
The rectilinear concurrences of the shadowy pyramid c d r and the luminous pyramid b c r show that at r as much dark field c d is seen as there is luminous body b c. At point s both a b and c d are seen in shadow, two dark spaces worth double the light b c; moving from s toward r loses the darkness a b and brightens the pavement, while moving from r to o sees less of the light and darkens again toward o.