Notebook on Mechanics and Natural Philosophy

If a weight is suspended from the pivot original: "polo"; here referring to the fulcrum or central point of rotation of the balance, such weight will not be felt by the balance, unless that weight is greater than the weight of the balance itself.

A horizontal line representing a balance beam with vertical lines at each end and marks along its length.

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A balance beam divided into segments with labels 'a', 'b', 'c', 'd' and lines indicating weights or positions.

If the arms of an equal balance are divided into several equal parts, and equal weights are placed at their ends, and the weight is equal to the balance, I say that such weight will not be felt by the balance. Leonardo is describing a state of perfect equilibrium where the weights neutralize each other's effect on the beam's tilt.

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A simple horizontal line with two vertical uprights.

If at the end original: "capo" of a balance with two equal arms there is placed a weight of 2 pounds, and at the pivot original: "polo" there is placed a weight of 4 pounds, I say that such a balance will be at the limit of its equality meaning it remains perfectly level, and the addition of the weight placed at the pivot will not be felt by the balance.

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A complex geometric diagram showing a weight suspended from a system of lines forming a triangle and rectangle. Points are labeled with letters 's', 'o', 'a', 'b', 'c'. A weight hangs from point 'o' via a cord.

If there is a balance with equal arms and a weight is suspended from any part of its length, its weight will always maintain the same gravity effective weight or pressure. Because of this, if weight m is suspended from the pivot a in the middle of the balance n m, and the weight is as much as the balance, I say that such weight will not be felt by the pivot of said balance n m, unless the balance itself already had weight. And if in the balance a b, the weight p is suspended from arm a c, and the weight p is suspended from arm c b, I say that the weight of the balance will not be increased by weight m, since that weight m is suspended from the center of gravity of said balance, which is the pivot c.

And if weight m weighed 2 pounds and the balance weighed just as much, the pivot c would support 4 pounds. But if you were to weigh the balance a b with another balance above it, r s, you would not find that such weight varied by the movement of weight m from the pivot c toward one or the other end of that balance. This is proven by the sixth proposition of the present work, which says: the weight that hangs from the pivot of the balance does not weigh down original: "aggrava"; meaning to disturb the equilibrium or add "effective" weight to one side that balance. And here weight m, by the cords m o, hangs from the pivot c of the balance a b; therefore, such weight m does not weigh down the balance a b, but indeed hangs from the pivot c.

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If the balance a b with equal arms is loaded with equal weights, and at its ends a b there are two pulleys original: "pulee o carrucole", and over those passes a rope in the middle of which hangs a weight of equal gravity to the weights of that balance.

A balance beam labeled 'm' and 'n' with a weight hanging from a cord exactly in the center.

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If from the balance of equal arms m n a weight is suspended from any part of said balance, being of equal weight to the balance itself, such weight will never be felt by that balance, but certainly by its pivot. This appears here below, where the balance m n, suspended from its pivot o, has the weight p suspended from its middle, and then at the pivot m, moving toward n.

A balance beam labeled 'm' and 'n' with a weight hanging from a cord toward the right side of the beam.

A red library stamp consisting of a royal crown over the initials "B.M." (British Museum).

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