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Paris Manuscript I — 246

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Bibliothèque de l'Institut de France, Paris

I2 69 v.

Della sommità dell'onde.

La somma altezza dell'onde non consumerà sotto di sé il suo fondo, imperò che poco lo tocca per la quinta del sesto, che dice1 che ogni cosa pesa per la linia del suo moto. Onde diremo tale onda moversi verso l'aria, la qual si fugge dalla sua percussione e in verso l'aria pesa; e se vi fia pure alquanto di confregazione, ella fia di poco vigore e poco consuma tale fondo.

Della infima bassezza dell'onda.

Quella cosa che fia più causa di rompere la rettitudine del cominciato corso dell'acqua, fia più da essa acq[ua] consumato e remosso.

Adunque noi direno che se l'aria fussi causa di rompere la rettitudine della elevazione dell'onda, che essa sarebbe consumata da tale percussione d'acqua. Ma tale aria non è causa di rompere tal corso, anzi sol n'è causa il peso che acquista l'acqua per uscire del suo elemento; e si tarderebbe in tal sito, s'ella fussi quantità discreta, ma per essere di quantità continua, egli è necessario che l'un'acqua spinga e l'altra tiri per l'essere congiunte.

On the summit of the waves. The highest crest of the waves will not consume the bed beneath it, because it touches it little—by the fifth [proposition] of the sixth [book], which says that everything weighs along the line of its motion. Hence we shall say that such a wave moves toward the air, which flees from its impact, and toward the air it weighs; and if there be even a little friction, it will be of little force and will consume that bed but little.

On the lowest trough of the wave. That thing which is more the cause of breaking the straightness of the water's begun course will be more consumed and removed by that water. We shall therefore say that if the air were the cause of breaking the straightness of the wave's rise, it would be consumed by such impact of water. But that air is not the cause of breaking such a course; rather, the sole cause is the weight the water gains in leaving its element. And it would linger in that place if it were a discrete quantity; but, being of continuous quantity, it is necessary that one water push and the other pull, because they are joined.

On the Crest and the Trough of a Wave

The crest barely wears the bed; the trough suffers the water's weight, not the air

Hydraulics Physics & Mechanics

Two paragraphs on where a wave does and does not consume the riverbed. At the summit of the wave the bottom is scarcely worn, since—by the principle that everything weighs along the line of its motion—the crest moves upward toward the air and presses on the air, not the bed, so any friction is slight. At the trough, whatever most breaks the straight course of the water is most worn away; Leonardo argues that the air does not break the wave's rise, but rather the weight the water gains in trying to leave its element. Because water is a continuous and not a discrete quantity, one part must push while the joined part pulls. The page is text only.

On this page

The crest scarcely consumes the bed

The highest crest of the waves barely wears the bottom beneath it, because everything weighs along the line of its motion, and the crest is moving upward toward the air. It therefore presses on the air, which flees its impact, so that any friction against the bed is of little force.

The water's weight, not the air, breaks the wave

Whatever most breaks the straight course of the water is most consumed by it. The air is not the cause of breaking the wave's rise; the sole cause is the weight the water gains in leaving its element. Being a continuous and not a discrete quantity, one joined part must push while the other pulls.

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