A Balance with One Arm Inclined Downward
How much must the straight arm weigh, and how much thicker, to balance a four-ounce inclined arm?
A column of fourteen small equally spaced circles marks the degrees of descent, the first two labelled a and b and the last two c and d. Beside it a balance is drawn with the arm ab horizontal and bc inclining diagonally downward, its ends a and c and pivot b picked out, with dotted analytical lines dropping from the ends, the pivot and the midpoint of the inclined arm. Leonardo sets himself the problem of a balance whose arms are of equal length, one of them inclined and weighing four ounces, and asks how much the straight arm ought to weigh and how much thicker one arm must be than the other for the two to resist each other at the position of equality.
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Column of degrees of descent (a, b … c, d)
A vertical column of fourteen small, equally spaced circles represents the degrees of descent. The first two circles are labelled a and b and the last two c and d.
Balance with one level arm and one inclined arm (a, b, c)
The balance has the arm from a to the pivot b horizontal, while the arm bc inclines diagonally downward. Dotted analytical lines descend from the two ends, from the pivot and from the midpoint of the inclining arm, setting up the geometry of the counterweight problem.
The weight-and-thickness problem posed
Leonardo wants a balance of arms of equal length, one inclining downward (bc) and weighing four ounces. He then asks how much the arm that stands straight ought to weigh, and how much thicker one arm ought to be than the other, so that each resists the other at the position of equality.