Pyramids of Light and Shade; Why Distant Flames Look Round
Equal-angle pyramids carry equal light; an elongated flame or crescent looks round at a distance
Leonardo continues his optics of light and shadow, arguing that both luminous and shadowy rays are strongest at their points and that pyramids of light or shade reaching an equal thickness of angle carry equal illumination, however much their bases differ. A digression on the light of bodies observes that an elongated source, such as a candle flame, appears round at a great distance, which he extends to the stars: even were they horned like the crescent moon, distance would make them seem round. A final query asks why the derived shadow cast by an elongated light appears dark at its middle a b yet fades at its extremes c d. Diagrams of intersecting light-and-shadow pyramids and an annular shadow illustrate the page.
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Rays are strongest at their points
Both shadowy and luminous rays are of greater power and strength at their points than along their sides.
Pyramids of equal angle carry equal light (a b c, d e f)
Even though luminous pyramids spring from bases of different sizes and their points reach into shadowy places, if their various lengths bring them to an equal thickness of angle they carry equal light. The shadowy pyramids behave the same way, as the cut pyramids a b c and d e f show, alike in size and in light despite their unequal bases.
An elongated light looks round at a distance
The shape of a luminous body, though elongated, appears round at a great distance. A candle flame proves it, and the same would hold for the stars: even were they horned like the crescent moon, distance would make them appear round.
An annular shadow dark at its middle (a b, c d)
A question is posed about the derived shadow cast by an elongated light: why does it appear dark in the middle of its height, a b, while at its extremes c d it cannot be made out?