The balance and centres of gravity
Continuous vs discontinuous weight; when a balance stays level or turns oblique
A dense text page, written with the sheet turned upside down, on the statics of the balance. Leonardo argues that the centre of a suspended weight always lies below the centre of its support, distinguishes continuous from discontinuous gravity, and works through when a beam rests level and when it settles oblique. Small lettered diagrams of balances and hanging rods, with weights such as 4 and 2, accompany each case, and a closing note stages an adversary's objection.
On this page
The centre of a suspended weight lies below its support
Leonardo states that the centre of every suspended heavy body lies beneath the centre of its support, and promises a proof. The heading treats the position of a continuous weight hung in the arms of a balance. It opens his study of equilibrium.
Continuous versus discontinuous gravity
A balance is drawn with the weights 4 and 2. Leonardo distinguishes two kinds of gravity: continuous, when the body is of a single piece, and discontinuous, when it is divided into two or more pieces. The distinction organises the cases that follow.
When the balance keeps the position of equality
For a rod a b hung anywhere along its length, within the span of the balance, the beam always rests level. Leonardo insists this can only happen when the centre of the suspended weight lies below the centre of the balance. Labels n, d, c, b, 4, a key the diagram.
Suspenders proportioned to the weights they bear
For a parallel weight hung at any obliquity, the little suspending cords rest on arms proportioned to the loads they carry. The diagram is lettered d, c, b, a, e, q, r, S. The rule links arm length to weight.
When the beam remains oblique
If the ends of the balance do not stand by a perpendicular line above the ends of the parallel weight, the beam settles obliquely. Leonardo asks after the quality of that obliquity, to be found when the central line a b is set straight. The case is drawn in the central column.
The heavier part goes to the lower side
In the left column Leonardo notes that if a is the mover of the weight n b p q, that weight will turn with its heavier part to the lower side. A small diagram lettered b, n, a, q, p accompanies the rule. It states plainly how an unbalanced load settles.