Angles of least light and the shadow directed to one point
Least-lit angles, the recomposed pyramid, and the bright surround of the derivative shadow
Continuing the window-and-sphere analysis of the facing page, the text grades the least-lit angles (e, k, f, o g) by how little of the horizon's light each sees, and shows how their lines recompose a pyramid like pyramid c that falls in the first degree of shadow. It explains that the luminous species multiplied at the window's edges a b make a brightness surrounding the derivative shadow, while the dark species end at points 7 and 8. Proposition [731] then states that every shadow directs its central line to a single point formed where the luminous lines intersect at the middle of the window's thickness. Faint diagram lines show through the paper from the neighbouring leaf.
On this page
Least-lit angles and the recomposed pyramid of shadow
The angle e sees no light; k sees only p t and f only t q, so both are of little light, and o g is the last degree, seeing no part of the horizon's light. These lines recompose a pyramid like pyramid c, which falls in the first degree of shadow because it too lies between equal angles, its axis passing through the center of the shadowy body to the middle of the light.
Bright surround and derivative shadow at the window's edges
The luminous species multiplied at the window's edges a b make a brightness that surrounds the derivative shadow cast by the shadowy body in the places 4 and 6, while the dark species multiply at o g and end in 7 and 8.
Every shadow directed to a single point at the window's middle [731]
Every shadow made by bodies directs itself, along its central line, to a single point made by the intersection of luminous lines in the middle of the space and thickness of the window. This appears by experiment: figure a room with a window to the north, s f, and observe the effect at the horizon.