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Paris Manuscript F — 157

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Bibliothèque de l'Institut de France, Paris

L'onda circulare nata nella superfizie dell'acq[ua] inclusa nel vaso percosso, finisce per quella linia che là fu creata dal moto del suo motore.

O[g]ni mobile che genera refressione, termina il suo corso per la linia della incidenzia1.

Questo accade per essere il moto incidente di maggiore potenzia che 'l moto refresso, e quel ch'è più potente, ha più durabilità che 'l men potente.

Sarà più potente il moto del mobile incidente che 'l suo moto refresso, perché la percussione della incidenzia fatta nell'obietto denso diminuisce parte dell'impeto congiunto a esso mobile. La qual diminuizione non lascia potente tal moto refresso, come era detto incidente; benché in ogni grado di moto l'impeto del mobile si diminuisca per sé sanza percussion di denso, e non resta che tal percussione nol diminuisca assai più, imperò che se tu misuri il moto che tal mobile arebbe fatto sanza incidenzia, e misuri li moti nati da molti balzi tra su e giù, e' sarà più lungo il moto continuato a un medesimo loco, che quel che tante volte da le incidenzie è interrotto, ancora che 'l principio dell'impeto in ciascun di loro fussino2 di potenzia equale in fra loro.

The circular wave that arises on the surface of the water enclosed in a struck vessel ends along that line which was there created by the motion of its mover.

Every moving body that generates a reflection ends its course along the line of incidence.

This happens because the incident motion is of greater power than the reflected motion, and that which is more powerful has more durability than the less powerful.

The motion of the incident body will be more powerful than its reflected motion, because the percussion of the incidence made upon the dense object diminishes part of the impetus joined to that body. This diminution does not leave the reflected motion as powerful as the incident one was said to be; although at every degree of motion the impetus of the body diminishes of itself even without percussion against something dense, and it remains true that such percussion diminishes it far more. For if you measure the motion that such a body would have made without incidence, and measure the motions born of many bounces up and down, the motion continued along one same course will be longer than that which is so many times interrupted by the incidences, even though the beginning of the impetus in each of them were of power equal among themselves.

Reflection of a Moving Body and the Circular Wave in Water

Why incident motion outlasts its rebound, and how percussion strips away impetus

Physics & Mechanics Hydraulics

A continuous, diagram-free physics discourse on how a moving body loses power when it rebounds. Leonardo opens with the circular wave raised on the surface of water enclosed in a struck vessel, then generalises that any moving body which reflects ends its course along the line of incidence, the incident motion always being more powerful than the reflected one. He argues that percussion against a dense object strips away part of the impetus, so a motion continued along one path travels farther than the same impetus broken by many bounces up and down.

On this page

Incident motion outlasts its reflection because percussion consumes impetus

Every moving body that generates a reflection ends its course along the line of incidence, and the incident motion is more powerful and more durable than the reflected one. Percussion against a dense object diminishes part of the impetus joined to the body, so the rebound is left weaker than the incidence was. Measuring a motion continued in one course against one broken by many bounces up and down, the continuous one runs longer even when each began with equal impetus.

The circular wave raised in a struck vessel of water

The circular wave that arises on the surface of water enclosed in a struck vessel ends along the line that was there created by the motion of its mover. Leonardo uses this ripple as the opening instance of his general law that reflected motion terminates along the line of incidence.

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