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Paris Manuscript I — 167

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Bibliothèque de l'Institut de France, Paris

I2 30 v.

somma d'acqua,1 perché s'un'acqua fussi bene di minore grossezza che l'altra, non fa caso. Diciamo che un'acqua sia di subdupla grossezza a un'altra, e ch'essa sia poi di doppia velocità, perché esse acque scontrandosi insieme sono d'equal grandezza nel contatto; come provai nella terza del quinto: essendo la maggiore un braccio quadro e la minore un mezzo, la minore non percote la maggiore se non nella sua metà, e così la maggiore percote la minore colla sua metà, onde i contatti fatti dalle percussioni sono equali in quantità e disequali per dupla potenzia, per lo doppio veloce che ha l'una all'altra.

E così la cosa notante sarà sospinta della retta linia del suo corso con proporzionevole torcimento.

De ritrosi.

I retrosi so' alcuna volta molti che mettano in mezzo un gran corso d'acqua, e quanto più s'appressano al fine del corso, più son grandi, e si2 creano in superfizie per l'acque che to[r]nano indirieto dopo3

Collision of waters of unequal size and speed; of eddies

...quantity of water; for if one water were indeed of smaller thickness than the other, it makes no matter. Let us say that one water is of sub-double thickness to another, and that it is then of double velocity; for these waters, meeting together, are of equal size at the contact — as I proved in the third [proposition] of the fifth: the greater being one square braccio and the smaller a half, the smaller strikes the greater only in its half, and likewise the greater strikes the smaller with its half, so that the contacts made by the percussions are equal in quantity and unequal by double power, on account of the double swiftness that the one has to the other. And thus the floating thing will be thrust from the straight line of its course with a proportional twisting. Of the eddies. The eddies are sometimes many, which place a great course of water in their midst, and the nearer they approach the end of the course, the larger they are, and they are created at the surface by the waters that turn back after...

Collision of Currents of Unequal Size and Speed

Equal contact, unequal force; and how eddies grow toward the course's end

Hydraulics Physics & Mechanics

Leonardo analyses two waters that meet head-on when one is half the thickness but double the velocity of the other. Citing his own earlier proposition, he argues that at the contact the two are of equal size (the smaller strikes only the greater's half and vice versa), so the contacts are equal in quantity yet unequal by double power because of the doubled speed. A floating body is therefore thrust from its straight path with a proportional twist. A closing note headed 'Of the eddies' observes that eddies are often numerous, enclosing a great current, and grow larger nearer the end of the course.

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Equal contact but double power when currents collide

When one water is of half the thickness but double the velocity of another, the two are of equal size at the contact: the smaller strikes the greater only in its half, and the greater the smaller with its half. The contacts are thus equal in quantity yet unequal by double power, on account of the doubled swiftness.

A floating body twisted from its course; eddies at the course's end

The floating thing is thrust from the straight line of its course with a proportional twisting. Under the heading 'Of the eddies,' Leonardo notes that eddies are sometimes many, enclosing a great current in their midst, and grow larger the nearer they approach the end of the course, created at the surface by waters that turn back.

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