The science of light and shadow: primitive and derivative
Definitions of rays and percussion, and how lit and shaded surfaces reveal a body
This densely written sheet sets out the theoretical foundations of Leonardo's science of light and shadow. In parallel columns he defines light as the dispeller of darkness and shadow as its privation, distinguishes primitive from derivative light and shadow, and explains the 'concourse' and 'percussion' of rays that every body sheds into the surrounding air. He insists that the forms of dense, opaque bodies can only be known when clothed in lit and shadowed surfaces, and lists a program of studies (several lights on one body, one light on many, and so on). Interspersed are a right triangle measured 6-8-10 with its squared numbers, a semicircle-and-triangle figure, and an upside-down note on why a marksman misses a fish seen in water.
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Definitions: primitive and derivative light and shadow
Light is the dispeller of darkness and shadow the privation of light. Primitive light is the cause of illuminating shadowed bodies; derivative lights are the parts of bodies lit by that first light. Primitive shadow is the part of a body the light cannot see, while derivative shadow is merely the striking of shadowy rays.
Labelled diagram a b c d
A small diagram is keyed d c b a, with a = primitive light, b = derivative light, c = primitive shadow, and d = derivative shadow, illustrating the four terms defined in the columns of text.
Concourse and percussion of rays
Every body makes a concourse of rays, filling the surrounding air with infinite likenesses of itself. The 'shadowy and luminous concourse' is the sum of rays leaving a body and running through the air without striking; the 'percussion' is the place that stops and cuts that concourse upon itself.
A body's form is known only through its lit and shaded surfaces
Leonardo argues that the figures of dense, opaque bodies can never be known by mortal eyes unless clothed in shadowed and luminous surfaces, and that the eye set opposite the division of light from shade best perceives a body's quality. He adds a 'proof of the cat seeing by night', holding this to be the office of smell and hearing, not of the eye.
Why the marksman misses the fish in water
An inverted note in the first column observes that whoever shoots best with crossbow or harquebus will least strike a fish in the water, because the fish is not where it appears — an early statement of refraction displacing the apparent position of a submerged object.
Right triangle 6-8-10 and its squares
A right triangle is measured 6-8-10, with neighbouring figures 36, 64 and 100 confirming that the squares on the two legs sum to the square on the hypotenuse. A further triangle stands on the diameter of a semicircle, labelled o c b with the number 94.