How the Eye's Position Changes the Light and Shade Seen
The reflected pyramid of light and the viewpoint from which no shadow shows
Continuing the theme, this page of Book Five proves that the proportions of lit and shadowed parts a body presents vary as widely as the positions of the eye that views it: from eye q the lit part d m appears much smaller than the shadowed part n o, demonstrated by the pyramid d q o cut at k h parallel to its base at point i. A new chapter asks from what position shadow is never seen on shadowed spheres, and answers that an eye set inside the 'reflected pyramid' of a body's illuminated images sees no shadow at all. The reflected pyramid is labeled a b c and the lit part b c d, with the eye at e. A diagram of a lit sphere with crossing sight-lines accompanies the argument, and the page bears a running head and folio number.
On this page
Light and shade vary with the eye's position
Let a n o be the shadowed body and p the light embracing it, which lights the part m d n while n o m stays dark. The eye q sees all of d m o, in which the lit part d m is much smaller than the shadowed part n o, as proven by the pyramid d q o cut at k h parallel to its base and divided at point i.
The viewpoint from which a sphere shows no shadow
An eye situated within the reflected pyramid of a body's illuminated images will never see any shadowed part of that body. The reflected pyramid is a b c and the lit part b c d; the eye e within it cannot gather all the illuminated images b c d unless it stands at the luminous point a, from which no shadow is ever seen.