The Reasons of Motive Forces

Of motive forces.

of 6 pounds is hung at point E, it will be equally balanced by the said weight of 12 pounds hung at point I; and if a weight of 4 pounds is hung at point F, it will still be equally balanced with the said 12 pounds; and if one of 3 pounds is hung at point B, it will still be equal to the said 12 pounds, so that this progression will always occur by decreasing the heaviness of the weight as it moves further from the point of gravity In this context, the "point of gravity" refers to the fulcrum or the central pivot point of the scale..

A horizontal balance beam is shown with points labeled B, F, E, D, C, I, A. A hand emerging from a cloud—representing a divine or natural force—holds the beam at its central pivot point C. Numerical values are written below the beam: 3 under B, 4 under F, 6 under E, and 12 under D. A weight labeled 12 is suspended from the beam at the opposite side at point I, illustrating the law of the lever where distance multiplied by weight creates equilibrium.

THEOREM XI.

If one of the ends of the aforementioned Balance, or Beam, is lowered, the other will rise,
and all the aforementioned parts will move in proportion to their distance

To demonstrate the reason for these proportions here, let a straight line B. A. be drawn as long as the beam of the aforementioned balance B. A., and let the middle of the said line be the point of gravity marked C. The original French text repeats the phrase "& soit le milieu de ladite ligne le point de gravité marqué C." likely due to a printing error; it has been consolidated here for clarity. And let the said line also be graduated in similar portions as the previous one; afterward, another line must be drawn at will crossing through point C, which will pass through the point of gravity and will also be graduated in similar portions to the other. Then, one must place one of the feet of the compass at point C, and with the other, draw the arcs of circles as can be seen in the figure. Thus, the arc original: "portion de cercle" N. D. will be equal to Q. I., and O. E. will be double the said Q. I., and P. F. will be triple the said Q. I., and M. B. will be quadruple. Thus, it can be seen that the proportion of the weight corresponds to the proportion of the distance along the circles formed between the said lines; and by multiplying the units of the arcs of the circles between the said lines by the number of the weight attached there, one will have the quantity of the first. As for example, multiplying four parts of the arc M. B. by three pounds of weight, one will have 12, a number equal to the weight of the first point, and so it will be for the others.

A geometric diagram illustrates the mathematical proof of the lever. It shows a horizontal line (B-A) and a slanted line (M-A) intersecting at the pivot C. Concentric arcs, centered at C, connect points on the horizontal beam to the slanted line, demonstrating that the distance traveled by a point on the beam is proportional to its distance from the fulcrum. A hand holding the pivot at C emerges from a cloud. Numerical labels 4, 3, 2, 1 are placed along the arcs on the left side to indicate these proportional distances.