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Codex Arundel — f. 18r

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British Library, London — Arundel MS 263

Figura con lettere.

A lato della figura:

Il moto p s sarà fatto sanza potenzia del suo motore, perché li basta il moto naturale; e il moto a s sarà fatto tutto dalla potenzia del suo motore.

Infra i mobili d'equal figura e peso, che con equale impeto e distanzia percotano obbietti d'equale resistenzia, quel risalterà in più distante sito che da percussion di minor potenzia è causato. E così de converso risalterà in più propinquo loco, che si dividerà da percusione di magiore potenzia.

Se la magiore percussione genera minor balzo che la percussione minore, questo accade perché essendo l'inpito di magiore potenzia che la percussione, cioè in quanto al moto de' corpi gravi, egli è necessario che quanto il moto del mobile participa più della magior che de la minore potenzia, che 'l balzo ancora lui sia magiore o minore secondo le cause che lo conducano.

Il balzo che nella sopra scripta figura sarà di magior lunghezza e di minor alteza, fia quello del quale il mobile si partirà di b, e, percosso che sarà nell'obietto s, risalterà in d. Questo tal balzo nasce dalla potenzia dell'inpito e di quello participa di tanti gradi per quanti gradi b è remoto da a, e participa tanto de' gradi della percussione per quanti gradi b è remoto da p. Adunque direno che esso b è remoto da a per 1 grado, e da p è remoto per 13 gradi; così farà l'angolo oposito della risaltazione, il quale è d s c, che entra 13 volte nell'angolo p s c, sì come fece l'angolo a s b ch'entrò 13 volte nell'angolo b s p.

Figure with letters.

Beside the figure:

The motion p s will be made without power from its mover, because natural motion suffices for it; and the motion a s will be made entirely by the power of its mover.

Among moving bodies of equal shape and weight, which with equal impetus and distance strike objects of equal resistance, that one will rebound to a more distant place which is caused by a blow of lesser power. And conversely it will rebound to a nearer place, which is set off by a blow of greater power.

If the greater blow generates a smaller bounce than the smaller blow, this happens because, the impetus being of greater power than the blow, that is as regards the motion of heavy bodies, it is necessary that, as much as the motion of the moving body partakes more of the greater than of the lesser power, so the bounce too is greater or smaller according to the causes that produce it.

The bounce that in the above-written figure will be of greater length and of lesser height will be that from which the moving body departs from b, and, once it has struck the object s, will rebound to d. Such a bounce arises from the power of the impetus, and partakes of it by as many degrees as the degrees by which b is remote from a, and partakes of the degrees of the blow by as many degrees as b is remote from p. Therefore we shall say that b is remote from a by 1 degree, and from p is remote by 13 degrees; so will the opposite angle of the rebound do, which is d s c, that goes 13 times into the angle p s c, just as the angle a s b did, which went 13 times into the angle b s p.

The rebound of a struck body and the angle of its bounce

How the length and height of a rebound depend on impetus and the power of the blow

Physics & Mechanics

This leaf studies how a moving body rebounds after striking an object, distinguishing motion supplied by a mover from natural motion. Leonardo argues that among equal bodies striking equal targets a blow of lesser power sends the body rebounding farther, and works out that the rebound angle d s c goes into the angle p s c the same number of times (thirteen) that the incident angle a s b goes into b s p. A radial fan of trajectories drawn from the point of impact s illustrates the graded bounces.

On this page

Rebound distance and the power of the blow

Among moving bodies of equal shape and weight striking equal-resistance objects with equal impetus, the one struck by the lesser power rebounds farther, and the one struck by the greater power rebounds nearer. The bounce is greater or smaller according as the body's motion partakes more of the greater or the lesser power.

Measuring the rebound angle against the incident angle

The longest, lowest bounce is that of a body departing from b, which after striking the object s rebounds to d. Leonardo counts b remote from a by 1 degree and from p by 13 degrees, so the rebound angle d s c enters the angle p s c thirteen times, as the incident angle a s b enters b s p thirteen times.

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