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Library/Codex Madrid I/f 52v-f 53r

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Codex Madrid I — f 52v-f 53r

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Biblioteca Nacional de España, Madrid

(Dall'alto al basso:)

La forza, el peso, la percussione, el moto materiale, sono equalmente causa e gieneratori l'uno dell'altro, e ciascun nascie per violentia.

Forza e pesso sono i' molti casi tanto simili, che quasi pare essere una medesima cosa, e i' molti altre operationi tanto disforme e varie, che per 2 nomi si conciede essere nominate. E dove esse si trovano essere simili, è quando tu voi307 spingiere o ttirare, che tanto fa la forza quanto il peso. E dove si diformano è che lla forza per sé si consuma, come si vede ne' balestri che stano lungo tenpo308 dalla forza piegati. El peso nell'aria senpre è equale. La gravità ha a peso. La forza è spirituale, perché tanto pesa un balestro quando è in sua forza, come quando è discarico. I' desiderio del peso è verso il cientro, e lla forza è di tornare per la linia dond'è creata.

Se lla forza e 'l peso saranno d'equal moto, e che lla forza sia causa del peso, cierto la potentia d'esso peso non potrà mai superare quella della forza, ma sarà minore o equale. Se309 sarà minore, questo acaderà quando tu piegassi un albero, e che ttu li attacassi un picol peso, che nel dirizarsi tirerebe tal peso con seco. E ttal sarebbe il moto fatto dal peso, quale quello dell'albero che llo tira con seco nel suo dirizarsi. Se tal forza sarà equale al peso, questo acaderebbe quando tale albero310, dopo alquanto moto fatto nel suo dirizarsi, resstasi piegato, e che 'l peso che llo tiene rimanesi sospeso nell'aria. Cierto alora queste 2 potentie serebon equali, perché il peso non pò tornare in baso e ll'albero non si pò dirizare. Sse311 il peso fia causa della forza312, essendo l'uno d'equale moto all'altro, ancor la forza non potrà mai superare tal peso, anzi fia minore overamente equale. Se sarà minore, questo acaderà quando un gran peso sarà attacato a un sottile vinculo o vergiella, la quale non potendo a ttanta potenta resistere, con equal moto a cquel del peso a lei atacato, si piega e aconpagnia tal peso, insino che si posa in tera. Qui resta il peso tanto più legieri che prima, quant'è il peso che cont[r]asta colla forza del vincol piegato. Onde disfaren la sententia detta di sopra, e direno meglio: Se lla forza e 'l peso saranno d'equal moto, esse saran313 senpre d'equal potentia314, ancora che scanbievolmente esse sieno causa l'una dell'altra.

(From top to bottom:)

Force, weight, percussion and material motion are equally the cause and the generators of one another, and each is born by violence.

Force and weight are in many cases so alike that they almost seem to be one and the same thing, and in many other operations so unlike and various that they are allowed to be named by 2 names. And where they are found to be alike is when you wish to push or to pull, for force does as much as weight. And where they differ is that force consumes itself of itself, as is seen in crossbows that stand long bent by force; the weight in the air is always equal. Gravity has weight. Force is spiritual, because a crossbow weighs as much when it is in its force as when it is discharged. The desire of the weight is toward the centre, and force's is to return along the line whence it was created.

If force and weight are of equal motion, and force is the cause of the weight, certainly the power of that weight can never surpass that of the force, but will be less or equal. If it be less, this will happen when you bend a tree and attach to it a small weight, which, in straightening itself, would draw that weight with it; and such would be the motion made by the weight as that of the tree that draws it with itself in its straightening. If such force be equal to the weight, this would happen when such a tree, after some motion made in straightening itself, remains bent, and the weight that holds it remains suspended in the air. Certainly then these 2 powers would be equal, because the weight cannot return downward and the tree cannot straighten itself. If the weight be the cause of the force, the one being of equal motion to the other, again the force can never surpass that weight, but rather will be less or else equal. If it be less, this will happen when a great weight is attached to a slender bond or little rod which, being unable to resist so great a power, bends with motion equal to that of the weight attached to it and accompanies that weight until it comes to rest on the ground. Here the weight remains so much the lighter than before as is the weight that contends with the force of the bent bond. Whence we shall undo the statement made above, and shall say better: if force and weight are of equal motion, they will always be of equal power, even though they are reciprocally the cause of one another.

Force, Weight, Percussion and Motion: the Four Powers

Force is spiritual and consumes itself; weight desires the centre of the earth

Physics & Mechanics

This text-only verso sets out Leonardo's definition of the four powers of nature — force, weight, percussion and material motion — which he says are equally the cause and generators of one another, each born through violence. He contrasts force and weight: alike when pushing or pulling, but different in that force consumes itself over time (as in a long-bent crossbow) while weight in air is always constant, the weight's desire being toward the centre of the earth and force's being to return along the line by which it was created. He then reasons that when force and weight move together with equal motion they must be of equal power, illustrating with a bent tree lifting a small suspended weight and a slender rod bending under a great load.

On this page

The four powers generate one another by violence

Force, weight, percussion and material motion are equally the cause and the generators of one another, and each is born by violence. Force and weight are so alike when pushing or pulling that they seem one thing, yet are named separately where they differ.

Force is spiritual and self-consuming; weight is constant

Force consumes itself of itself, as in crossbows kept long bent, while weight in air is always equal; a crossbow weighs the same whether spanned or discharged, so force is 'spiritual.' The weight's desire is toward the centre, force's is to return along the line whence it was created; with equal motion the two powers prove always equal.

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