Equal Shadows from Luminous Bodies of Different Sizes
Shadow cones f g o; when does a light see only half the shadowy sphere?
Leonardo notes that the brighter the lit background, the darker a shadowy body appears silhouetted against it, then opens a proposition on the equality of shadows cast by luminous bodies of different sizes at different distances. A pen diagram of circles and converging lines shows the shadowy body f o g r whose shadow f g o is generated equally by the near light d e and the remote light b c, because both are cut off from the shadowy body by the straight lines a b and r c. A second proposition begins: which luminous body will never see more than half of the shadowy sphere, proved when luminous and shadowy spheres are of equal size.
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A darker silhouette against a brighter light
The greater the light of the illuminated thing, the darker the shadowy body appears that stands out (is silhouetted) against it.
Equal shadow f g o from near light d e and remote light b c
The shadowy body f o g r casts the shadow f g o generated by the deprivation of the light d e at the near distance and of the light b c at the remote distance, both equally cut off from the shadowy body by the straight lines a b and r c. The same holds for a large light r s and a small light a c variously remote from the shadowy body n m o p.
When a light sees only half the shadowy sphere
Which luminous body will never see more than half the shadowy sphere: when the shadowy sphere is lit by a luminous sphere of equal size, its shadowed and lit parts are equal. Let a b c d be the shadowy sphere equal to the luminous sphere e f; the shadowed part a b c is then declared.