When a surface is evenly lit: three geometric demonstrations
Curved and flat surfaces under a point light, with a note on derivative light
This page of Part Five carries three lettered diagrams demonstrating even illumination from a point light. Leonardo argues that a surface is equally lit in every part only when every part is equally distant from the light: on a curved surface b c d struck by light a this follows from the definition of the circle, while on a flat surface e f g h the middle lies nearest and is brightest, and on the slanted flat surface i k l m the lights are in the same proportion as the parts' distances from the light. A final rubric opens the topic of derivative light, defined as brightest where the whole luminous body is seen with half of its field.
On this page
A surface is evenly lit when every part is equally distant from its light
That surface will be equally illuminated which is equally remote from the body that lights it. If from the light a, lighting the surface b c d, lines equal to that surface are drawn, then by the definition of the circle the surface is equally lit in every part.
Flat surfaces e f g h and i k l m under the same light
If the surface is flat, as in the second demonstration e f g h, and its edges are equally distant from the drawn lines, the middle h is the part nearest the light and is the more illuminated the nearer it is to the light e. But if a flat surface i k l m has its edges at unequal distances from the light, then the nearest and the most remote parts have the same proportion in their lights as their distances have from the illuminating body.
The most excellent brightness of derivative light
The rubric opens a new topic: the most excellent brightness of derivative light. It is said to lie where the whole luminous body is seen together with half of its [field], the argument continuing on the following page.