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Paris Manuscript G — 172

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Bibliothèque de l'Institut de France, Paris

De moto e del mobile.

Qual removerà da sé più un medesimo mobile, o una gran potenzia con piccolo moto o una minore potenzia con maggior moto?

Quel moto dirivativo fatto da un medesimo mobile sarà di maggiore lunghezza, il quale arà maggiore moto primitivo da un medesimo motore.

Pruovasi perché la sperienzia ci mostra che sempre una medesima potenzia ha tal proporzione col suo moto primitivo, col moto dirivativo del suo mobile che...1

Pruovasi per la quinta di questo che dice: «In fra le varie lunghezze del moto primitivo si ritroverrà le lunghezze varie del moto dirivativo d'un medesimo mobile essere nelle medesime proporzioni alli lor moti primitivi», perché se la potenzia d'un medesimo motore move da sé il mobile lo spazio d'un dito 'n un tempo armonico, la medesima potenzia removerà da sé il medesimo mobile in 2 tempi armonici due delle medesime dita. E questo nasce perché «sempre il moto dirivativo ha una medesima proporzione col moto primitivo».

Non sempre si genera l'impeto nel mobile, perché il motore ancor lui non ha sempre moto impetuoso.

Come ci mostra il lieve carro tirato dalli buoi in loco piano, che immediate che essi boi terminano il moto, egli è terminato il moto d'esso carro.

On motion and the moving body. Which will drive one and the same moving body further from itself: a great power with little motion, or a lesser power with greater motion? That derivative motion made by one and the same moving body will be of greater length which has the greater primitive motion from one and the same mover. It is proved because experience shows us that one and the same power always has such a proportion with its primitive motion, and with the derivative motion of its moving body, that... It is proved by the fifth [proposition] of this [book], which says: 'Among the various lengths of primitive motion, the various lengths of the derivative motion of one and the same moving body will be found to be in the same proportions as their primitive motions,' because if the power of one and the same mover moves the moving body from itself the space of a finger in one harmonic time, the same power will drive the same moving body from itself, in two harmonic times, two of the same fingers. And this arises because 'the derivative motion always has one and the same proportion with the primitive motion.' Impetus is not always generated in the moving body, because the mover itself does not always have impetuous motion. As the light cart drawn by oxen on level ground shows us: that as soon as the oxen end their motion, the motion of that cart is ended.

On Motion and the Moving Body: Power Versus Motion

Derivative motion proportional to primitive; the oxen-drawn cart as proof of dependence

Physics & Mechanics

This text page poses the question of which drives a moving body further: a great power with little motion, or a lesser power with greater motion. Leonardo answers that the derivative motion is longest where the primitive motion given by the same mover is greatest, citing a proposition that the lengths of derivative motion stay in the same proportions as their primitive motions, so that a power moving a body one finger in one 'harmonic time' will move it two fingers in two such times. He adds that impetus is not always generated in the moving body, because the mover itself does not always move impetuously. The point is illustrated by a light cart drawn by oxen on level ground, which stops the instant the oxen stop.

On this page

Great power with little motion versus lesser power with more

The derivative motion of a given body is longest when its primitive motion from the same mover is greatest. Experience shows a single power keeps a fixed proportion between its primitive motion and the derivative motion of its body, so the lengths of derivative motion follow the same proportions as the primitive motions that cause them.

The oxen-drawn cart: motion ceasing with its mover

Impetus is not always generated in a moving body, because the mover itself does not always move impetuously. The light cart drawn by oxen on level ground shows this: the moment the oxen end their motion, the cart's motion is ended too.

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