The Reasons of Motive Forces

Book one,

THEOREM XII.

The time of motion accords with the movement of the counterweight.

What is here called time is the interval from the beginning of the machine's movement until the end of said movement; and if this demonstration were well-considered, many men would not be deceived in the construction of various machines by which they think to raise a great burden with a small force. This is indeed possible, as will be demonstrated, but it is also necessary that the small force travel a greater distance, as was demonstrated by the preceding [theorem]; and by the present one, I shall demonstrate that this path must be traveled in the same amount of time. Imagine a figure similar to the previous one, in which a weight of 12 pounds is placed at point Q, which will cause the beam original: "fleau" — the horizontal arm of a balance scale. to lower to point I. It is certain that if there is a weight of three pounds at point B, it will rise at the same time to point M; and just as the distance C-B is four times as long as Q-C, so B-M will be four times as long as Q-I. Thus, it can be seen that these two weights being in equilibrium with one another, if one is lowered, the other will rise proportionally according to the distance from the point of gravity The pivot point or fulcrum., so much so that three pounds may well lift twelve pounds one foot in height, but it will be necessary for the three pounds to descend at least four feet.

A technical diagram shows a lever system in action. A horizontal balance beam is pivoted at a central point C. On the right side, a hand pulls a weight marked '12' at point Q down to a lower point I. On the left side, point B moves upward along a curved arc to point M. To illustrate the ratio, the left arm of the lever (C-B) is divided into four equal segments marked 1, 2, 3, and 4, showing it is four times the length of the right arm (C-Q). This visually demonstrates that the longer arm must travel a much larger arc to move the shorter arm a small distance.

THEOREM XIII.

The movement of the Lever accords with that of the Balance.

The principle of the force of the Lever—otherwise called a "goat's foot" original: "pied de Chevre" — a historical term for a crowbar or pry bar, named for its forked end.—is demonstrated to be the same as the preceding ones. For example: let there be a large square stone marked R, and the Lever N-O, of which the tip O touches the ground and supports the stone at point P. Thus, if the force of a man lifts point C with a force equivalent to fifty pounds of weight, point P will by proportion lift 200 pounds; this is because point C will travel four times as much distance in the same time as point P, and therefore, it becomes equal to four times the weight.

An illustration depicts a man dressed in early 17th-century attire using a long wooden lever to lift a heavy, square stone block labeled 'R'. The tip of the lever, marked 'O', rests on the ground to act as a pivot point (fulcrum), while the lever catches the underside of the stone at point 'P'. The man stands at the far end, lifting the lever at point 'C'. The diagram illustrates how mechanical advantage allows a single person to lift a weight far beyond their natural strength by increasing the length of the lever arm.