Light and shadow: derivative shadows, the eye, and colour edges
Umbra and penumbra, the three kinds of shadow, and how a surface takes an object's colour
A dense study of light and shadow. Leonardo compares a window and its splayed edges to the species (images) that cross within the pupil of the eye, and argues at length about derivative shadows — why their border is darkest where it meets the lit field, and why the illuminated edge is in fact brighter there. He classifies shadow into three shapes (pyramidal, parallel, semi-pyramidal), explains how a light larger than its object yields two shadows separated by a doubly-lit triangle, and restates the painting principle that a surface partakes of the colour of the object facing it. A stray note asks whether a nail is driven better close to the hammer's mouth or apart from it.
On this page
The window's edges and species crossing in the pupil
The window behaves the same on every side where it borders the dark wall, above and below and left and right. The same happens to the species that enter the pupil and are thrown to right and left, crossing beyond the object placed before it.
Why a derivative shadow's edge is darkest at the light
Leonardo asks why the boundary of a derivative shadow stays intersected beyond the pyramid of maximum darkness, dark toward the shadowy pyramid's angle and light outside. His first answer: in n X, the further you move from X toward S the more light you find in a l, and the contrary in the opposite part, so the darkness a b grows toward o.
The three kinds of shadow
Behind an opaque body a light makes a pyramidal shadow, and shadows are of three shapes: the first pyramidal, the second parallel, the third semi-pyramidal. Two shadows arise from one light because the whole light g h sees the whole space a b c and also the space e d f.
A light larger than its object makes two shadows
When the light d e is larger than the object it illuminates the space d e r a, but the space c a b loses sight of the light as it nears the line c b, giving the second shadow p n o. The triangle S h b is seen by both halves of the light, and because two halves make one whole it is doubly lit and separates the two shadows.
A nail struck near the hammer's mouth
Inserted between two figures, a short question asks what drives the nail better — closer to the mouth of the hammer, or when it is separated from it. The note stands apart from the surrounding optics.
A surface takes the colour of its object
Citing 'the fourth of this', that the surface of every opaque body partakes of the colour of its object, Leonardo explains that species tinge the place where they cross and that unlike species mix their colours there. This is why black at the border of white shows no more black, colours being most intense at their edges.
