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Codex Forster II — 123v

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© Victoria and Albert Museum, London

Sei esempi di pesi sospesi a corde con o senza carrucole, con:

a - 100 - 100; d - 200 - 100 - 100; b - 200 - 100 100; c - 200 - 100 m; 100 - 50 50 - 100; (d) - 2001 - 100

Fra le figure.

Le corde sentano 100 libbre di là dal polo e 100 di qua, onde il mezzo della corda sopra la carrucola sente 200 libbre, sì che in tal loco si romperà.

La corda inginocchiata2 a qualunche carrucola che coll'uno stremo al peso e coll'altro al suo motore si congiugne, sentirà più che 'l doppio fatica che non fa quella che s'astende in fra 'l peso e 'l superiore motore che tal peso leva, ancora che i pesi della corda inginocchiata e 'l peso della diritta sieno equali. Verbi grazia, sia la corda inginocchiata c, e sia la corda diritta d, e ciascuna abbia appiccato 100 libbre. Dico che le 100 libbre di c ne spiccano altre 100 di m, onde la sua corda patisce 200 e d ne sente sol 100

Six examples of weights suspended by cords with or without pulleys, with:

a - 100 - 100; d - 200 - 100 - 100; b - 200 - 100 100; c - 200 - 100 m; 100 - 50 50 - 100; (d) - 2001 - 100

Among the figures.

The cords bear 100 pounds on the far side of the pole and 100 on the near side, so that the middle of the cord over the pulley bears 200 pounds, and therefore it will break in that place.

A cord bent [knee-shaped] over any pulley, joined by one end to the load and by the other to its mover, will feel more than double the effort of one that stretches between the load and the upper mover which lifts that load, even though the weights on the bent cord and on the straight one are equal. For example, let the bent cord be c and the straight cord be d, and let each have 100 pounds hung on it. I say that the 100 pounds of c draw off another 100 at m, so that its cord suffers 200, while d feels only 100.

Loads on cords bent over pulleys

Why the tension doubles where a cord passes over a pulley

Physics & Mechanics Machines & Devices

Six examples across the top of the sheet show weights of 100 and 200 pounds suspended from cords, some running over pulleys, labelled a, b, c, d and m. Leonardo argues that a cord carrying 100 pounds on each side of a pulley bears 200 at its middle over the pulley, and so will break there. He then contrasts a cord bent (knee-shaped) around a pulley, which suffers more than double the effort, with a straight cord carrying the same load.

On this page

Tension is doubled at the pulley

A cord bearing 100 pounds on the far side of the pole and 100 on the near side has 200 pounds at its middle, where it passes over the pulley, and it is there that it will break.

Bent cord c versus straight cord d

The cord bent around a pulley, joined at one end to the load and at the other to its mover, feels more than double the effort of a straight cord carrying the same weight. With bent cord c and straight cord d each loaded with 100 pounds, the 100 of c draw off another 100 at m, so c suffers 200 while d feels only 100.

Reader's Edition — described with AI from the e-Leo transcription.