The figures of derivative shadow and its swift motion
Three shapes of cast shadow, and how a shadow can outrun the body that casts it
A page of the Treatise on Painting on the derivative (cast) shadow. Leonardo distinguishes two sorts of derivative shadow and its three figures — pyramidal (from a shadowing body smaller than the light), parallel (from one equal to it), and a columnar or pyramidal form disgregable to infinity — illustrated by three small cone-and-column diagrams. He then argues, with a lettered figure (a, b, c, d, e), that a cast shadow can move many thousands of times faster than the body casting it. Small pen diagrams sit between the columns of text.
On this page
The two sorts of derivative shadow
Leonardo divides the varieties of derivative shadow into two kinds: one mixed with the air lying opposite the primitive shadow, the other the shadow that strikes upon the object which cuts the derivative shadow. This opens the treatise's systematic anatomy of cast shadow.
Three figures: pyramidal, parallel, and columnar
The derivative shadow has three figures: pyramidal, born from a shadowing body smaller than the luminous; parallel, born from one equal to the luminous; and a form disgregable to infinity that is columnar and pyramidal, since after the first pyramid it makes an intersection and generates an infinite pyramid, finding infinite space.
A shadow swifter than its body (a, b, c, d, e)
Leonardo argues a cast shadow can move many times faster than its casting body. With a the luminous and b the shadowing body moving from b to c along line b d, in the same time the derivative shadow of b sweeps the whole space b e, which can contain thousands of times the space b c.
Diagrams of the three shadow figures
Three small pen figures are set between the columns of text: a narrowing cone, a straight column, and a widening cone, illustrating the pyramidal, parallel and columnar derivative shadows described in the text.