Notebook on Mechanics and Natural Philosophy

If a lever is equal and on one side supports a quantity of weight which is suspended from a single thread attached to the lever at one point, and from another point of the same lever multiple threads depart which support the same weight as the single one was meant to do, I ask if the force of the same lever is changed by hanging the weight from multiple threads or from only one, or not. And if it is changed, I say that it changes greatly, because the weight hanging from multiple threads is equal to the sum of multiple weights, each of which is attached to its own thread at that same point and at the points of the lever where said threads are fixed; from which it follows that if the attachment points of the threads are near or far from the center original: "centro", referring to the fulcrum or pivot point of the lever, the force original: "forza", here meaning the mechanical advantage or effective weight of the lever will be changed.

Four diagrams of horizontal levers. The top-left shows a lever with a single vertical line supporting a weight. The top-right shows a lever where multiple lines originate from different points along the bar and converge to support a single weight. The middle-left shows a similar configuration with a wide spread of supporting lines. The middle-right shows a weight hanging from a single point on a tilted lever.

If that which was spread across multiple points of the lever is gathered into a single point of the same, the force of the lever will be changed in proportion ...?

Two diagrams of balances. The left one shows a beam with a central fulcrum and weights hanging from the ends, with a vertical support. The right one shows a similar balance but with a different suspension mechanism above the fulcrum, labeled with points and lines.

You see that here one of the parts of the equal lever breaks the air only at a single point, which is .m.; the other breaks it at several points, namely at .f. .n. .s. .e. .r. .m. and therefore this side will be lighter than the other, because where there is more breaking of the air original: "rōsura d’aria", a characteristic Leonardesque term for air resistance or friction there is greater resistance original: "fatica", literally "toil" or "effort". Hence, if the said weights are hung from the aforementioned points of the same lever and at an equal distance from the center of that lever, the one hanging from multiple points will become lighter for the said reason.

A small diagram at the bottom right showing a lever arm with specific points marked. Next to it are handwritten notes and a series of mathematical-style symbols (+ and - signs).