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Paris Manuscript I — 213

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Bibliothèque de l'Institut de France, Paris

I2 53 r.

precipitare

De moto.

Domando, se 2 mobili d'equal figura e peso e materia saran di dupla velocità, s'elle faranno doppio viaggio l'una all'altra o no.

Perché si vede li archi, ovver balestri, di gran braccia fare grande e tarda portata, e si vede balestri di corte braccia e grosse fare veloce e corte portate, e le percussioni del corto fanno nel terzo del lor moto gran passata e le lunghe fanno poca. In questa descrizione bisogna dimostrare tutte le forze matematiche, con ciò sia che in questi balestri accade diverse cause che fanno molti vari effetti, con ciò sia che in fra loro si trova chi ha gran montata, chi l'ha corta, chi è lungo e sottile, chi è grosso e corto, chi è largo, chi è stretto. Così si vanno variando con figure e con effetti in molti modi.

** Onde direno che quanto più un medesimo motore accompagna più la cosa mobile, più la remove da sé1.

On motion: the carry of bows and crossbows

To precipitate (fall).

On motion. I ask, if two moving bodies of equal figure, weight and material be of double velocity, whether they will make double the journey, one compared to the other, or not.

For one sees that bows, or crossbows, with long arms make a great and slow carry, while crossbows of short and thick arms make a fast and short carry; and the percussions of the short one make, in the third of their motion, a great passage, while the long ones make little. In this description one must demonstrate all the mathematical forces, since in these crossbows various causes occur that produce many varied effects: for among them one finds one with a great draw, one with a short draw, one long and slender, one thick and short, one broad, one narrow. Thus they go on varying, in figure and in effect, in many ways.

Hence we shall say that the more one and the same mover accompanies the moving body, the more it removes it from itself.

On Motion: Bows and Crossbows as a Test of Force

Do two bodies at double the speed travel double the distance? The varied carry of long and short bows

Physics & Mechanics Weapons & Fortification

Under the heading 'De moto' Leonardo asks whether two bodies of equal shape, weight and material, one at double the other's speed, will cover double the distance. He answers empirically from archery: bows or crossbows with long arms give a great but slow carry, while short thick arms give a fast, short one, the short bow driving hardest in the middle third of its stroke. He calls for all the mathematical forces to be demonstrated, since crossbows vary endlessly in draw, length, thickness and breadth, and concludes that the more a single mover accompanies a body, the farther it drives it.

On this page

Does double speed mean double distance?

Leonardo asks whether two moving bodies of equal figure, weight and material, one of double velocity, will make double the journey of the other or not. The whole page tests this proportional question against the observed behaviour of shooting weapons.

Long slow carry versus short fast carry

Bows and crossbows with long arms make a great but slow carry, while those with short, thick arms make a fast, short one; the short bow's percussion drives farthest in the third of its motion. Because these weapons vary in draw, length, slenderness, thickness and breadth, all the mathematical forces must be demonstrated to explain their many varied effects.

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