How Primitive and Derivative Shadow Are Joined
A light-and-shadow diagram; the derivative shadow always rests on the primitive as its base
This page completes the geometric proof begun on the facing leaf, working through how points h, i and k see progressively less of the light a b until at k there is total privation of light and the simple derivative shadow begins. Chapter [562] argues that the derivative shadow is always joined to the primitive, differing only in that the primitive tinges the body it touches while the derivative pours through the air; a pen diagram lettered f, a, b, c, d demonstrates the point. Chapter [563] states that simple shadow always joins compound shadow, referring back to its second figure. Untranscribed marginal notes reading like corrections to the figure appear in the left margin.
On this page
Points h, i, k and the onset of shadow
At h the surface sees the half d b of the light a b and so has half the light of f; at i it sees only the quarter e b and is three quarters less luminous than f; at k it sees no part of the light, so there is privation of light and the beginning of the simple derivative shadow.
Primitive and derivative shadow are one continuous body
The derivative shadow is always joined to the primitive, which forms its base; they differ only in that the primitive tinges the body it touches while the derivative infuses all the air it penetrates. With f the luminous body and a o b c the shadowy body, the primitive shadow a b c and the derivative a b c d are born together as a simple shadow.
Untranscribed marginal corrections
The transcription does not include the handwritten annotations in the left margin, which appear to be notes flagging an error in the accompanying figure. They are recorded here only as visible marginalia, not read from the page.