Where the Cord Attaches Does Not Change the Lever
Three balances with pulleys: the counterlever is fixed by the perpendicular fm from the pivot to the cord
Three balance studies explore how a load carried by a cord over a pulley acts on a pivoted staff, each with a semicircle marking the counterlever radius. In the middle figure the cord na leads down over pulley n to a weight, weight e hangs from the opposite end, and an analytical line extended above pivot m through points b, f and c shows the hypothetical arms over which the cord might lead; the note argues that the point of attachment along ac is indifferent because the effect always depends on the perpendicular fm dropped from the balance's centre to the cord. The lower pair repeats the idea with an arm counterbalanced by a rectangular weight and a cord led over a pulley from point n. Leonardo concludes that n is worth as much as a in terms of lever.
On this page
Balance with a third weight hung on the cord
A balance staff on a central pivot carries a weight on a cord at one end, while from the other end a cord led over a pulley at roughly staff height carries a second weight, with a third weight suspended from the cord between pulley and staff. A semicircle about the pivot marks the counterlever radius.
The attachment point along ac is indifferent (line fm)
The cord na leads down over pulley n to weight n, and weight e hangs from the opposite end; an analytical line above pivot m marks points b, f and c as possible upward extensions of the balance, with fm drawn perpendicular. At whatever point cord nc is attached along the length ac it makes no difference, because the effect always uses the perpendicular fm from the centre of the balance to the line of the cord.
n counts as much as a for the lever
In the right-hand of the lower pair, an arm counterbalanced by a rectangular weight pivots at m; its end rises perpendicularly to n, from which a cord leads diagonally beyond the pivot and over a pulley to a suspended weight, matched by a like weight hung under n. A pen-stroke from pivot m to point a marks the counterlever: n is as much as a in terms of lever.