The science of weights: gravity, levity and the spheric body
Definitions of the central line, the mathematical and natural planes, the three centers of a body, with balances in air and water
A theoretical page of Leonardo's science of weights, drafted and redrafted as numbered definitions and propositions. He states that no part of an element has gravity or levity within its own element, defines the central line running to the center of the world, contrasts the mathematical plane (touching a straight line along its whole length) with the natural plane (touching at a point), and reasons about where a spheric body comes to rest. He distinguishes the three centers of an irregular body (natural gravity, accidental gravity, magnitude), and in the margin notes that water weighs in air while air is light under water. Small balances shown in air and in water carry the numbers 21-21 and 12-12.
On this page
Gravity and levity as two equal, contrary actions
Leonardo holds that no part of an element has gravity or levity within its own element. Gravity and levity are two actions equal in power and contrary in their motions, caused by one element being drawn or pushed into another.
The mathematical plane, the natural plane, and the spheric body
The mathematical plane is touched along its whole length by a straight line laid on it, while the natural plane, every part of equal height, meets that line only at a point. A spheric body rests only at the middle of the mathematical plane, but at any point of the natural plane, since it there stays equally distant from the center of the world.
The three centers of an irregular body
Every body of irregular figure has three centers: one of natural gravity, one of accidental gravity, and one of magnitude. In a uniform body these three coincide in one same point, and the central line extends from a suspended body's center to the center of the world.
Water weighs in air, air is light under water
In the right margin Leonardo notes that a vessel of water drawn through the air has all its water weighing in the air, yet no part of that water has gravity within its whole. Conversely, air drawn beneath the water is wholly light, though in itself no part has levity or heaviness.
Balances of greater against lesser levity
Two small figures show a balance in air and in water, marked 21-21 and 12-12. The second is captioned as the power of greater levity against lesser levity.
