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Paris Manuscript G — 171

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Bibliothèque de l'Institut de France, Paris

Che cosa è impeto.

Impeto è quel che per altro nome è detto moto derivativo, il quale nasce dal moto primitivo, cioè quando esso mobile era congiunto col suo motore.

Mai in nessuna parte del moto dirivativo si troverrà alcuna velocità equale a quella del moto primitivo. Pruovasi perché «in1 ogni grado del moto che ha la corda dell'arco, si perde dell'acquistata potenzia congiuntali dal suo motore». E perché ogni effetto participa della sua causa, il moto dirivativo della saetta va diminuendo a gradi la sua potenzia, e così participa della potenzia dell'arco, la qual sì com'ella fu generata a gradi, così a gradi si destrugge, ecc.

L'impeto impresso dal motore nel mobile è infuso in tutte le parte unite d'esso mobile; e questo si manifesta, perché ogni parte d'esso mobile, così intrinsica come superfiziale, son d'equal moto, eccetto nel moto circunvolubile, perché in quello sempre la parte più impetuosa si raggira intorno alla meno impetuosa, cioè quelle che son più vicine al centro del mobile. E quella pa[r]te che prima si mosse, resta sempre più distante dal principio del suo moto, s'ella non [è] impedita; e questo succede, perché ella è più potente in essa circunvolubilità.

E se per lo avversario si dicessi: l'impeto che move il mobile, è nell'aria che lo circunda dal mezzo in dirieto, questo si niega, perché l'aria che seguita il mobile, è tirata da esso mobile per riempiere il vac[u]o da lui lasciato. E ancora l'aria che si condensa dinanzi al mobile, si fugge in dirieto in contrario corso.

Lungo il margine destro.

Seguita quel che manca di sotto.

E se l'aria ritorna in dirieto, elli è manifesto segno ch'ella si percote in quella che 'l mobile si tira dirieto, e quando due cose si percotano, e' nasce il moto refresso di ciascuna. Li quali si convertano in oppositi moti revertiginosi, li quali son portati dall'aria riempitrice del vacuo, che di sé lascia il mobile. «È2 impossibile che 'l moto del motore sia aumentato dal moto del mobile 'n un medesimo tempo», perché sempre è più potente il motore che 'l mobile, ecc.

What impetus is. Impetus is that which by another name is called derivative motion, which is born from primitive motion, that is, when the moving body was joined with its mover. Never in any part of derivative motion will any velocity be found equal to that of primitive motion. It is proved because 'in every degree of the motion that the bowstring has, some of the power imparted to it by its mover is lost.' And because every effect partakes of its cause, the derivative motion of the arrow goes diminishing its power by degrees, and so partakes of the power of the bow, which, just as it was generated by degrees, so by degrees is destroyed, etc. The impetus impressed by the mover in the moving body is infused into all its united parts; and this is shown because every part of that moving body, both internal and superficial, is of equal motion, except in rotational motion, because in that the more impetuous part always turns around the less impetuous, that is, those nearer to the centre of the moving body. And that part which first moved remains always more distant from the beginning of its motion, if it be not impeded; and this happens because it is more powerful in that rotation. And if by the adversary it were said: the impetus that moves the moving body is in the air that surrounds it from the middle backward, this is denied, because the air that follows the moving body is drawn by that moving body to fill the void it leaves behind. And still the air that condenses in front of the moving body flees backward in a contrary course.

Along the right margin.

Continue what is missing below. And if the air returns backward, it is a manifest sign that it strikes against that which the moving body draws behind it; and when two things strike one another, the reflex motion of each is born. These are converted into opposite whirling motions, which are carried by the air that fills the void the moving body leaves of itself. 'It is impossible that the motion of the mover be increased by the motion of the moving body in one and the same time,' because the mover is always more powerful than the moving body, etc.

What Impetus Is: Derivative Motion and the Moving Body

Impetus born of the mover, its decay by degrees, rotation, and the role of surrounding air

Physics & Mechanics

This closely written text page defines impetus as 'derivative motion', born from the primitive motion a body has while joined to its mover, and argues that no part of derivative motion ever equals the velocity of primitive motion. Using the bowstring and arrow as example, Leonardo says power is lost by degrees just as it was gained by degrees, and that the impetus impressed by the mover is infused equally into every part of the moving body, except in rotational motion where the outer, swifter parts turn about the slower ones near the centre. He then refutes the objection that the surrounding air drives the body forward: the air behind is merely drawn in to fill the void the body leaves, while the air compressed in front flees backward. A margin note continues the argument, adding that two colliding airs produce reflex whirling motions and that a mover's motion can never be increased by the moving body's motion.

On this page

Impetus as derivative motion born of the mover

Impetus is derivative motion, arising from the primitive motion a body has while joined to its mover; no part of it ever equals the primitive velocity. Like the arrow leaving the bowstring, its power is destroyed by degrees just as it was generated by degrees, and the impetus is infused equally into every part of the body.

Denying that surrounding air propels the body

Against the claim that the air behind pushes the mobile forward, Leonardo answers that the following air is only drawn in to fill the void the body leaves, while the air compressed ahead flees backward. Where the two airs collide, reflex whirling motions are born, and the mover always stays more powerful than the moved.

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