Where the First Light and First Shadow Fall on a Sphere
A sphere lit by the sky-hemisphere: point c has double the light of b, three-quarters more than a
Continuing the proof begun on the facing page, Leonardo shows that light diminishes in proportion as the illuminating angle narrows, so under the eaves of a house point a receives far less light than point d. He then applies the rule to any body lit by the sky-hemisphere, mapping on a spherical object where the first light and first shadow fall. A second proposition, illustrated by a lower diagram of a sphere beneath a luminous hemisphere, argues that the point seeing the greatest span of sky is brightest: point c has double the light of b and three-quarters more than a.
On this page
Light beneath the eaves falls off with the base of the angle
The lights follow the proportion of the bases n c and e c of their angles. Beneath the eaves of the roof, point a has as much less light than d as the base b c of angle b a c is smaller than the base e c, and so on always in proportion, the light being of one quality.
First light and first shadow on a body lit by the sky
On a spherical object beneath the hemisphere k and f, point b is lit by the whole span a e c, part d by the hemisphere e f, o by g f, n by m f, and h by s f — so one learns where the first light and first shadow lie on any body.
Brightest where most sky is seen: c, b, a compared
The part of a shadowy body lit by the greatest sum of light is brightest. Taking body a b c against the illuminated hemisphere i d f n, point c has double the light of b and three-quarters more than a, because c is lit by the sky d g f e, b only by d f, and a only by the quarter g d.