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Paris Manuscript I — 216

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Bibliothèque de l'Institut de France, Paris

I2 54 v.

de'1 moti qual fu quello della velocità.

E se questi che hanno detto che quanto più si diminuisce il mobile, che il suo motore lo caccia più velocemente, proporzionevolmente secondo la sua diminuizione in infinito, sempre acquistando velocità di moto, e' seguiterebbe che un attimo2 sarebbe quasi veloce come la immaginazione o l'occhio, che subito discorre alla altezza delle stelle, e per conseguente il suo viaggio sarebbe infinito, perch'ogni3 quantità continua è divisibile in infinito, perché la cosa che infinitamente si po diminuire, infinitamente si farebbe veloce e [in] infinito cammino si moverebbe, la qual opennione è dannata dalla ragione e per consequente dalla sperienzia.

E ancora seguiterebbe che se la4 bombarda caccia da sé la sua ballotta 3 miglia in 20 tempi musicali o armonici5 con 100 libbre di polvere e mille di ballotta, che a torre una libbra di ballotta [che] farebbe con detta polvere appresa6 nel medesimo tempo? Adopera7 per la regola del8

Against infinite speed; the bombard reprised

... of the motions, which was that of speed. And if those who have said that the more the moving body is diminished, the more its mover drives it swiftly — proportionally, according to its diminution, to infinity, always gaining speed of motion — it would follow that an instant would be almost as fast as the imagination or the eye, which at once runs to the height of the stars; and consequently its journey would be infinite, because every continuous quantity is divisible to infinity, for the thing that can be infinitely diminished would become infinitely fast and would move over an infinite path — which opinion is condemned by reason and, consequently, by experience.

And it would still follow that, if the bombard drives its ball 3 miles in 20 musical or harmonic time-units with 100 pounds of powder and a thousand of ball, what would it do with one pound of ball, with the said powder ignited, in the same time? Apply, by the rule of the [three] ...

Against Infinite Speed from an Ever-Smaller Ball

Why endless diminution cannot mean endless velocity, with the bombard as proof

Physics & Mechanics Weapons & Fortification Arithmetic & Proportion

Leonardo refutes those who claim that the smaller the moving body, the faster its mover drives it, in proportion and without limit. Since continuous quantity is divisible to infinity, that rule would make an ever-diminished body infinitely fast, an instant nearly as quick as the eye reaching the stars, and its path infinite, an opinion he says is condemned by reason and by experience. He then reprises the bombard case: it drives its ball 3 miles in 20 musical or harmonic time-units with 100 pounds of powder and a thousand of ball, and he asks what one pound of ball would do with the same powder in the same time, applying the rule of three.

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Infinite diminution would give infinite speed, an absurdity

If a mover drove a body ever faster as the body is diminished, in proportion and to infinity, then since every continuous quantity is divisible to infinity, an infinitely diminished body would become infinitely fast, an instant nearly as swift as the eye reaching the stars, its journey infinite. Leonardo condemns this opinion by reason and by experience.

The bombard test: 3 miles in 20 harmonic time-units

The bombard drives its ball 3 miles in 20 musical or harmonic time-units with 100 pounds of powder and a thousand of ball. Leonardo asks what one pound of ball would do with the same ignited powder in the same time, and begins to apply the rule of three.

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