The motion of a shadow is faster than the body that casts it
Quality of shadows, the velocity of the shadow relative to the opaque body, and the pyramidal shadow
Three chapters open here. Chapter 592 (Quality of shadows) states that, under equal reductions of light, the proportion of darkness between two cast shadows equals the proportion of darkness of the colours where those shadows meet. Chapter 593 (Of the motion of the shadow) argues that, with the light source fixed, a shadow always moves faster than the opaque body casting it, proving the case with a diagram of a luminous point a, an opaque body b moving to c, and a shadow d moving to e. A second labelled sketch stacks luminoso, ombroso and ombra; chapter 594 (Of the pyramidal shadow) is announced at the foot of the page.
On this page
The shadow moves faster than the opaque body (593)
With the luminous source immobile, the motion of the shadow is always faster than that of the body generating it. In equal time the opaque body b moves to c while the shadow d moves to e, and the velocities stand to one another as the lengths of their motions. If the light itself moves at the body's speed the two match; if the light is faster the shadow lags; if the light is slower the shadow outruns the body.
Quality of shadows (592)
Among equal reductions of light, the proportion of darkness to darkness of the shadows produced equals the proportion of darkness to darkness of the colours where those shadows are joined.
Diagram of luminous body, opaque body and shadow
A small stacked diagram labels three horizontal bands as luminoso (the light), ombroso (the opaque body) and ombra (the shadow), illustrating the ranked comparison of their motions discussed in the text.