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Codex Forster II — 098v

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© Victoria and Albert Museum, London

41

questo si conferma la proposta proposizione, cioè che se tu consideri bene nella bilancia di sopra, tu truovi b centro della bilancia a f, e ha il peso 4 sotto sé appiccato, che detto 4 distrebuisce di sé equalmente il suo peso alli 2 stremi delle corde che 'l [so]spendano. Ora per questa tal ragione f carica il suo braccio della bilancia con 2 libbre, e perché lo spazio c f entra 2 volte in a c essendo ancora 2 libbre in a, le 2 di f none stanno contra di quelle se non per una. E 'l 4 appiccato in d non resta ancora lui se non per uno, perché il suo spazio c d entra 4 volte in a c, che a questo modo trovi ragguagliato, che 4 e 2 di d f stanno pari con 2 di a.

La seconda figura di sotto, dando il 4 attaccato alle due corde equal peso di sé ai loro stremi, ciascuno è caricato di 2 libbre. Ma perché n o entra 2 volte in e n, bisogna aggiugnere al peso delle 2 libbre di o due altre libbre, e resterà pari in o 4 libbre contra le 2 di e.

41

this confirms the proposition set out, namely that if you consider well the balance above, you find b, the centre of the balance a f, and it has the weight 4 hung beneath it, which said 4 distributes its weight equally to the two extremes of the cords that suspend it. Now for this reason f loads its arm of the balance with 2 pounds; and because the space c f enters twice into a c, there being also 2 pounds at a, the 2 at f do not stand against them except by one. And the 4 hung at d likewise remains only as one, because its space c d enters four times into a c; so that in this way you find it reckoned even, that 4 and 2 of d f stand equal with 2 of a.

In the second figure below, the 4 attached to the two cords giving equal weight of itself to their ends, each is loaded with 2 pounds. But because n o enters twice into e n, one must add to the weight of the 2 pounds at o two further pounds, and there will remain even at o 4 pounds against the 2 of e.

Confirming the Balance Proof with Weights 4 and 2

Working the loads on the two balance figures of the facing page

Physics & Mechanics Arithmetic & Proportion

This page carries text only, continuing the demonstration whose figures are drawn on the facing sheet. Leonardo confirms the proposition by taking b as the centre of the balance a f, from which a weight of 4 hangs and shares itself equally between the two cord-ends; because the space c f enters twice into a c and c d four times, the loads reduce so that 4 and 2 at d f stand even against 2 at a. He then treats the second figure below, where the 4 on two cords loads each end with 2 pounds, but since n o enters twice into e n, two further pounds are added to give 4 at o against the 2 at e.

On this page

Equal sharing of a hung weight between cord-ends

The weight 4 hung at the centre b distributes equally to the two extremes of the cords that suspend it. Reduced by the lever spans, 4 and 2 at d and f come to stand even against 2 at a.

Spans c f, c d and n o counted into their arms

Because the space c f enters twice into a c and c d four times, the hung loads are scaled down accordingly. In the second figure, since n o enters twice into e n, two pounds are added to leave 4 at o against 2 at e.

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