Statics of the balance: weight, equilibrium and oblique descent
Propositions on why heavy bodies fall and when balance arms weigh equal
This densely written sheet sets out a chain of propositions on the statics of weights and the balance. Leonardo argues that every heavy body tends toward the center, that the heavier body descends faster and along the straighter path, and that a body is 'heavier according to its position' when its descent is less oblique. Further propositions treat the equilibrium of a balance whose arms are equal, the effects of unequal arms and of weights hung in proportion to arm length, and the relation between the velocity of descent and the weight. A column of small balance-beam and triangle diagrams runs down the right margin to illustrate the text.
On this page
Heavy bodies fall toward the center; the heavier descends faster
Leonardo states that the motion of every heavy body tends toward the center, and that the heavier a body is the more swiftly it descends. A body is heavier in descending when its motion runs straighter to the center, and heavier 'according to its position' when in the same place its descent is less oblique. A more oblique descent, over the same distance, covers less than a direct one.
Velocity of descent proportional to weight
Among all heavy bodies the velocity of descent and the weight are taken in the same order and proportion. If a weight of 2 falls in one unit of time, a weight of 1 will fall the same distance in 2 units of time; Leonardo calls this proportion 'untransposed.'
Equilibrium when the balance arms are equal
A balance is in equilibrium when the arms measured from the center of revolution are equal: with equal weights hung it will not depart from equality, and if displaced from the level it returns to the site of equality. Leonardo begins to set the center at a.
Unequal arms and proportional weights
If the balance arms are unequal but the weights equal, it tips toward the longer arm. If instead the arms are proportional to the weights hung on them, so that the greater weight is on the shorter arm, the two will be equally heavy according to position.
Balance-beam and triangle sketches in the margin
The right-hand margin carries a column of small pen sketches of balances and triangular supports, each keyed to one of the statical propositions written in the body of the page.