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Library/Paris Manuscript M/130

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Paris Manuscript M — 130

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Bibliothèque de l'Institut de France, Paris

The lines of the text are grouped by a curved stroke of the pen. The lines of the text are grouped by a curved stroke of the pen.

On motion.

Among weights that are the same,1 that one will be propelled2 the farthest from a given power, which has the smallest size.

The converse.

Among weights that are the same3 that are propelled by a given power, the one that has the greatest size will have the smallest motion.

Aristotle says that if a power moves a body a given distance in a given amount of time, the same power will move half of that body twice the distance in the same amount of time.

Therefore, the millionth part of that weight will be propelled by the same power one million4 times that distance in the same amount of time. Or if that weight were one ounce and it had gone one mile in a certain amount of time, then the millionth part would go one million miles…5

The lines of the text are grouped by a curved stroke of the pen.

On motion. Among weights that are the same, the one that will be propelled farthest from a given power is the one that has the smallest size. The converse. Among weights that are the same and are propelled by a given power, the one that has the greatest size will have the smallest motion. Aristotle says that if a power moves a body a given distance in a given amount of time, the same power will move half of that body twice the distance in the same amount of time. Therefore, the millionth part of that weight will be propelled by the same power one million times that distance in the same amount of time. Or, if that weight were one ounce and it had gone one mile in a certain amount of time, then the millionth part would go one million miles...

On motion: smaller weights are thrown farther

Aristotle's rule of power, weight and distance extended to the millionth part

Physics & Mechanics Arithmetic & Proportion

This 'On motion' note states a rule and its converse: among equal weights driven by a given power, the smallest is thrown farthest, while the largest moves least. Leonardo cites Aristotle's principle that a power moving a body a certain distance in a certain time will move half that body twice as far in the same time. He pushes the idea to an extreme, concluding that the millionth part of a weight would be carried a million times as far — an ounce that went one mile becoming a million miles.

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Rule and converse: size of weight versus distance propelled

Among weights that are the same, the one propelled farthest from a given power is the one of smallest size. Conversely, among equal weights driven by a given power, the one of greatest size will have the smallest motion.

Aristotle's rule extended to the millionth part of the weight

Aristotle says that a power moving a body a given distance in a given time will move half that body twice the distance in the same time. Leonardo concludes that the millionth part of the weight would be propelled a million times that distance — an ounce that went one mile becoming a million miles.

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