Studies of shadow, light-angles, and the cutting of a saw
Brightness and shadow length of equal bodies, the angle-proportion of light, and why one saw cuts more
This crowded page mixes two lines of inquiry. Under the heading 'Of shadow', Leonardo argues that the illuminated parts of equal bodies are brightest where their derivative shadow is shortest, their brightnesses standing in proportion to the lengths of the shadow-pyramids, so that body f, lit by half as much sky, is half as bright as e (c d e a b). Alongside, a pair of saw figures raises a mechanics problem: why, with equal contact, force, time, motion and weight, one saw cuts more than another; and a further note reasons that a saw sinking one braccio per hour with one braccio of contact needs its weight doubled when the contact is doubled to keep the same rate.
On this page
Of shadow: brightness and the length of the shadow-pyramid
The illuminated parts of equal bodies are the brighter where the derivative shadow is the shorter, their brightnesses in the same proportion as the lengths of the shadow-pyramids. Body f is half less illuminated than e because the portion of sky that lights it is half as large, as shown in c d e a b.
Quality of light from the angle of the illuminating ray
The quality of the lights follows the proportion of the angle enclosed between the illuminated body and the axis of the illuminating ray. If the acute angle r c d enters 4 times into the angle c m n, then c r is 4 times less luminous than c n; and the obtuse angles a r d and m n o extend the proportion.
Why one saw cuts more; contact, weight and rate
With equal contact, force, time, motion and weight, Leonardo asks why one saw cuts more than another. In a paired note a saw that sinks one braccio per hour through one braccio of contact, weighing 10 pounds, needs its weight doubled when the contact is doubled to 2 braccia to keep the same rate.