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Paris Manuscript F — 162

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Bibliothèque de l'Institut de France, Paris

Due figure di oggetti trascinati dall'acqua:

La cosa lata1 portata dalla corrente del fiume in fra la superfizie e 'l fondo dell'acqua, s'ella si scontra in acqua più tarda che l'acqua che la porta, s'ella si troverà in quel tempo obbliqua in verso l'avvenimento del fiume, immediate salterà dal fondo alla superfizie dell'acqua. E se tale obbliquità guarderà dirieto alla fuga dell'acqua, nello scontrarsi nella corrente pigra, subito si gitterà in verso el fondo. E se tale obbliquità guarderà a destra o sinist[r]a [della] larghezza del fiume, essa si gitterà a essa destra o sinistra d'essi lati del fiume, e così seguirà per qualunche aspetto2.

Acqua contro un ostacolo, con:

n a b c

Qua[l] parte della grossezza dell'acqua ritarderà3 il suo corso per tanta grossezza, quant'è quella del suo impedimento, e non si tarderà al contatto d'esso impedimento, ma tanto discosto a quello, quanto darà la regola del quinto? Come: sia lo impedimento superfiziale grosso un dito. L'acqua a b si fermerà, ovver tornerà 'n dirieto, essendo il moto tardo tutto lo spazio a b, e nel termine si [s]conterrà4 nella corrente, e andrà sotto. Trova5 la regola come debbe essere lungo a b.

Two figures of objects dragged by the water:

The broad thing carried by the current of the river between the surface and the bottom of the water, if it meets water slower than the water that carries it, and if it is at that time oblique toward the oncoming of the river, will immediately leap from the bottom to the surface of the water. And if such obliquity faces back toward the flight of the water, on meeting the sluggish current it will at once cast itself toward the bottom. And if such obliquity faces to the right or left of the width of the river, it will cast itself to that right or left of those sides of the river, and so it will follow for whatever aspect.

Water against an obstacle, with:

n a b c

Which part of the thickness of the water will retard its course by as much thickness as that of its impediment, and will be retarded not at the contact of that impediment, but as far away from it as the rule of the fifth will give? As: let the surface impediment be one finger thick. The water a b will stop, or turn back, the motion being slow throughout all the space a b, and at the end it will meet again with the current and go beneath. Find the rule for how long a b ought to be.

Objects Dragged by a Current; Water Checked by an Obstacle

How an object's obliquity steers it, and the rule of the fifth at a barrier

Hydraulics Physics & Mechanics

Two river-mechanics notes with three marginal sketches of objects and an obstacle in a current. Leonardo describes how a broad object drifting between the surface and the bed rises, sinks, or veers according to how its oblique face meets slower water. He then asks how far upstream of an obstacle the flow is checked, invoking a 'rule of the fifth' and lettering the retarded stretch n a b c, and sets himself the task of finding the rule for its length.

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A broad object's obliquity decides whether it rises, sinks or veers

A broad object carried by the current between surface and bed, on meeting slower water, leaps to the surface if it is oblique toward the oncoming river, but plunges to the bottom if its obliquity faces back down the flow. If the oblique face turns to the right or left of the river's width, the object casts itself to that side, and so it behaves for whatever aspect it presents.

How far upstream an obstacle checks the flow: the rule of the fifth

Leonardo asks over what length the water's course is retarded by an obstacle, noting that the check begins not at contact with the impediment but at a distance set by 'the rule of the fifth', with the barrier a finger thick. The water a b stops or turns back over that slow stretch n a b c, then rejoins the current and passes beneath; he resolves to find the rule for how long a b should be.

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