On Natural Motions Depending on Gravity

Page 6

...horizontally positioned, suspended, and tied at center C, and the entire weight will be applied at center D, the end of the string or line CD. But the nature of a pendulum is such that it strives to be carried downward through the arc of a quadrant DE around its fixed center C until it reaches the lowest point E. This point is closer to the center of the earth than the horizontal position D. It is clear that this entire operation is necessary and natural, depending on the descent of the whole weight. It is impossible for the cord-pendulum CD to be brought to the lowest position CE without the rigid balance beam acquiring a position perpendicular to the horizon, such as GCF. This position, indeed, cannot be achieved unless the less heavy part of the balance, B, ascends upward through the arc BF. Therefore, the fall and descent of the entire heavy body AB from the elevated position D to the lowest position E is the true and legitimate cause of the ascent of the heavy body B through the arc BF, which was to be shown. original: "quod fuerat ostendendum," a phrase used by mathematicians at the end of a proof, often abbreviated as Q.E.D.

A technical diagram illustrates the motion of a weighted beam or pendulum. A vertical line is intersected by a horizontal line at point C. The vertical line is labeled F at the top, E in the lower middle, and G at the bottom. The horizontal line is labeled D on the left and B on the right. A circle labeled A represents a weight centered at point D. Dotted curved lines indicate arcs of motion: one arc descends from D toward point E, while another arc ascends from B toward point F.

It is clear, therefore, that the simple fall or descent of a heavy body is the true and legitimate cause of the motion and ascent of some part of it upward. This clearly happens whenever the whole weight is supported by some point of a real or imaginary balance, so that a motion of all its parts is produced. This motion does not happen along straight lines parallel to each other and perpendicular to the horizon, but in whirling and circular paths.