Studies of the Balance: Weight, Friction, and Gravity

Two laws: resistance of the support and apparent weight

The upper-right corner states a 'second' law that the part of a support resists least which is farther from its point of fixture, and a 'first' law that a weight shows itself heavier when sustained by a weaker resistance. Together they frame how position and support strength govern felt weight.

Which weight makes the balance descend; friction at the pivot (a, d, n, c, b)

Beside a labeled balance Leonardo asks which of two weights causes its descent, answering that when the power of the excess that moves the balance equals the friction of the pole, the balance stays without motion. He adds that a weight moves more slowly as it gains lightness, and that gravity weighs along the line of its motion.

A descending weight accelerates, more in straight than curved motion

A marginal note by a balance diagram states that the more a weight descends the faster it becomes, but more in straight motion than in curved. It distinguishes the acceleration of free fall from that of a constrained, curving path.

Center of gravity of a suspended weight

Beside a weight hung from a cord Leonardo notes that the center of gravity of the suspended weight lies on the central line of that weight. The statement breaks off with 'If ...' before its qualification.

Higher and lower by the center of the world; the heavier part leads

A thing is called higher the more remote it is from the center of the world, and lower the nearer it comes to that center. Leonardo adds that the heavier part of bodies becomes the guide of their free motions.

Reckoning the excess against friction

Among the beam figures Leonardo works a small numeric reckoning: 2 of friction, 6 minus 2, leaving 4 as the excess. It ties the sequences of numbers ranged along the balance arms to the balance of moving force against friction.

Angolo superiore destro:

Due figure di bilancia, di cui una con:

A sinistra, schema di bilancia:

Figura di peso sospeso a corda:

A destra, figura di bilancia con:

Altro schema con:

A destra:

Schema di bilancia con:

Altro schema con:

Upper right corner:

Two figures of a balance, one of them with:

On the left, a diagram of a balance:

A figure of a weight suspended by a cord:

On the right, a figure of a balance with:

Another diagram with:

On the right:

A balance diagram with: