The middles of the shadows.

a, r t f, o n m / The middle of the length of each derivative shadow lies straight to the middle of the primary shadow and of the derivative light, and to the center of the shadowing body and of the luminous body. / This happens of necessity, for the luminous lines being straight, those that pass from the extremes of the shadowy bodies enclose within their convergence all that air which, through the opposition of that shadowy body, cannot see the luminous body, and therefore becomes dark. / The body being equally embraced by light, the parts of the shadow will be equal in themselves relative to its middle, because the general parts of the shadowy body are likewise equidistant from its middle, and so every body has a middle in itself. / The aforesaid luminous lines touching each extreme of whatever thing is enclosed within them, they are equally distant from the middles of the length of whatever thing they enclose. / Let R t and o n be the shadowy bodies; r t f and likewise o m n be the shadows of those bodies; f a, m a be the central lines of each shadow, light, and body. / The outermost sides of the shadows.

a S, m o n, b e, c f, d g, h i r t K / The triangle b h i is seen by the light m o, and likewise by the light a m. / That part of the primary and derivative shadow will be less dark the farther it is from its middle. / This happens because the more the shadow departs from its middle, the more it is seen by a greater quantity of luminous rays; and everyone knows that where there is more light, there is less shadow. / The triangle d g r sees nothing of the light a S, and so too the part of the shadowy body enclosed within that triangle. The triangle f t K and likewise c r i are seen by the light a m, n S, and will be brighter shadows, like the part of the ball enclosed within their angles. And the triangles b h i and likewise e t K are brighter still, and their outer boundaries are the edge of the shadow — as is the part of the ball enclosed at the points of the angles, because each is seen by half the light, o a and S a.