Crossing lights on a sphere; when the eye can see no shadow
The dark pyramid f and the bright i g c, and proposition [734] on a light equal to or larger than the body
The text traces how the right light z passes the shadowy body on its left side at g toward p, and the left light k passes on its right side at i toward m, the two lines crossing at c to make a pyramid; the pyramid f i g formed by the window a b leaves f dark, which never sees the light, while i g c is always luminous. Proposition [734] then asks what light lets an eye placed behind it, even when farther from the sphere than the light is, never see any shadow: this holds when the luminous body is equal to or greater than the spherical shadowy body. Two small pen diagrams accompany the argument, an upper crossing-pyramid over a small sphere and a lower pairing of a sphere and a larger luminous body.
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Crossing lights make the dark pyramid f and the bright i g c
The right light z passes the shadowy body on its left side at g and goes to p; the left light k passes on the right side at i and goes to m, the two lines crossing at c to make a pyramid. Then a b touches the body at i g and forms the pyramid f i g: f is dark, never seeing the light a b, while i g c is always luminous because it sees the light.
A light equal to or larger than the sphere hides all shadow [734]
What light is it that, even when the eye stands farther from the spherical shadowy body than the light, lets the eye see no shadow while behind the light? When the luminous body is equal to or greater than the spherical shadowy body, the eye behind that light can never see any shadow on the body, because of the difference of the said light. Let c e d f be the spherical shadowy body, a b the light.