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Codex Forster II — 081v

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© Victoria and Albert Museum, London

Asta sospesa, con:

1 2

La proporzione de' pesi attaccati a' bracci de la bilancia sempre si de' mi[s]chiare con quella del peso d'essi bracci.

S'e1 bracci della bilancia fieno ciascun per 2 libbre, e al mezzo dell'un fia attaccati 2 altre libbre, e allo stremo dell'opposito braccio sia attaccato una sola libbra, certo essi pesi staranno in equilibra, e giudicherai che 'l polo della bilancia sia dupla proporzione, cioè in mezzo a dupla proporzione, e fia in mezzo a sexquiterzia proporzione. E così t'inganneresti. Or volta carta e troverai la difinizione insieme colla figura; e così sempre variando i pesi de' bracci, si varia la proporzione del peso.

Suspended beam, with:

1 2

The proportion of the weights hung on the arms of the balance must always be combined with that of the weight of the arms themselves.

If the arms of the balance are each 2 pounds, and to the middle of one are hung 2 further pounds, and to the end of the opposite arm a single pound is hung, these weights will certainly stand in equilibrium, and you will judge the pole of the balance to be a double proportion, that is, at the middle of a double proportion, whereas it lies at the middle of a sesquitertian proportion. And thus you would deceive yourself. Now turn the page and you will find the definition together with the figure; and so, always varying the weights of the arms, the proportion of the weight varies.

The Weight of the Balance Arms Must Be Counted

A single beam with loads 1 and 2, warning against judging the pivot by hung weights alone

Physics & Mechanics Arithmetic & Proportion

A single horizontal beam diagram, marked with the loads 1 and 2, heads the leaf. Leonardo states the rule that the proportion of the weights hung on the arms must always be combined with the proportion of the weight of the arms themselves. With 2-pound arms, two pounds hung at the middle of one arm and a single pound at the end of the other stand in equilibrium, which tempts one to call the pole a double proportion when it is really sesquitertian. He directs the reader to turn the page for the definition and figure.

On this page

Mixing the hung load with the weight of the arms

If each arm weighs 2 pounds, two more pounds hung at the middle of one arm and a single pound at the end of the opposite arm will balance. One is tempted to read the fulcrum as a double proportion, but it actually falls at the middle of a sesquitertian proportion. Varying the weights of the arms continually varies the proportion of the load.

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