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Paris Manuscript I — 130

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Bibliothèque de l'Institut de France, Paris

I2 11 v.

De proporzione di moti o potenzie o resistenzie.

Se sopra un corpo tenero o liquido sara[n] posati o gittati 2 mobili di doppio peso e d'equale figura, domando: quale si caccerà più in dentro, o 'l maggiore o 'l minore?

Non anderà più l'un che l'altro, perché ogni potenzia trova resistenzia equale a sé di contatto.

Due cubi:

Vero è ch'io mi potrei forse ridire, imperò che i cubi1 di ottupla figura e peso l'uno all'altro, il maggiore ha di basa 4 tanti più che 'l minore, onde togliendo la quarta parte della basa del maggiore, essa è equale alla basa del minore, ma essa quantità ch'è sopra la basa del maggiore, è 2 tanti alta più che 'l minore cubo e 2 tanti si ficcherà. Adunque tutto il cubo maggiore che 'l minore ch'è di subduplo diamitro al maggiore ovver lati ...2.

Of the proportion of motions, powers or resistances.

If upon a soft or liquid body two moving bodies of double weight and of equal shape are laid or thrown, I ask: which will drive itself further in, the larger or the smaller? Neither will go further than the other, because every power finds a resistance equal to itself at the point of contact.

Two cubes:

It is true that I might perhaps take this back, for of cubes that stand as 8 to 1 in figure and weight, the larger has a base 4 times greater than the smaller; so, taking away the fourth part of the larger's base, it equals the base of the smaller. But that quantity which stands above the base of the larger is twice as high as the smaller cube, and will sink twice as far. Therefore the whole larger cube [drives in more] than the smaller, which is of half the diameter, or side, of the larger ...

On the proportion of motions, powers and resistances

Do two equal shapes of double weight sink equally into a soft body? A two-cube argument

Physics & Mechanics Geometry Arithmetic & Proportion

A full page of text with a small sketch of two cubes at the right margin. Leonardo poses a problem on the proportion of motions, powers and resistances: if two bodies of equal shape but one twice the weight of the other are laid or thrown onto a soft or liquid surface, which drives in deeper? He answers that neither penetrates more, because every power meets a resistance equal to itself at the point of contact. He then reconsiders with two cubes standing as 8 to 1 in figure and weight, reasoning about their bases and heights and how far each would sink.

On this page

Which weight drives deeper into a soft body?

If two bodies of equal shape, one of double the weight, are laid or thrown onto a soft or liquid body, which sinks in further, the larger or the smaller? Leonardo answers that neither goes further than the other, because every power finds a resistance equal to itself at the contact.

The two-cube argument

Reconsidering with two cubes whose figure and weight stand as 8 to 1, Leonardo notes the larger's base is 4 times the smaller's, so a quarter of the larger base equals the smaller base; but the quantity above that base is twice as high, and so sinks twice as far. The smaller cube is of half the diameter, or side, of the larger.

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