Balances, cord bends, and pulleys multiplying weight
Two verso sheets on a four-weight balance, doubling of load at a cord's bend, and 'spiritual' lines of force
Two verso half-sheets (274a and 274b) continue the study of weights, cords, and levers. One long passage sets out a procedure for balancing four weights on a 'quadrangular' balance, subtracting numbers and doubling counterweights according to the spacings from the fulcrum. Other notes show that a weight doubles at the bend of a cord and there breaks, that a cord run over five pulleys multiplies the hung weight by the number of its lines, and that 'spiritual' (immaterial) lines of force are equal in strength to corporeal ones. Small figures carry further numeric labels beyond those transcribed.
On this page
A weight doubles at the bend of a cord
Every weight hung on a straight cord acts along the whole cord and at the start of its straightness. But if the cord bends and changes its line, the weight doubles at the middle of that bend ('kneeling'), and there, from excess load, the cord breaks.
A cord over five pulleys multiplies the weight
Besides the first straight line of the cord that supports the hung weight, for as many lines as the cord makes beyond the first through its many bends over the pulleys, that many times is the weight on the first line multiplied. Leonardo notes this should be recorded in the treatises on cords.
Spiritual (force) lines and lever action
Spiritual (immaterial) lines and corporeal ones are of equal strength; an is a spiritual line. On the lever a b pulled at n, the force acts along the spiritual line c b as if pulling along a c; and because a c goes 4 times into a b, the weight b must go 4 times into n.
Balancing four weights on a quadrangular balance
Subtract the smaller number from the larger and use the remainder to lay out the arm and spacings; double the counterweight's proportion for each spacing between the fulcrum and the larger weight. Of the four weights, the largest and smallest are set opposite the two middle ones, the smaller middle weight standing nearer the fulcrum.