Notebook on Mechanics and Natural Philosophy (1478-1518) - Page 22

Every weight desires to descend by the shortest path, and counterweights raised out of the water vary their positions somewhat.

A geometric diagram of a quadrant of a circle. From the center (top left), a line drops vertically to a weight marked with a cross. Another line extends horizontally to the right. An arc connects the two points. A diagonal radius line extends from the center to a pulley on the arc, with a cord and a weight 'n' hanging from it. Another weight 'm' hangs from the horizontal line's end point via a pulley.

Regarding counterweights raised out of the water, their positions vary somewhat because those that are further from the center of the world original: "centro del mondo"; in the science of Leonardo's time, the center of the Earth was considered the universal center toward which all heavy things tend to fall. possess more heaviness than those that are closer. Therefore, that counterweight which descends is always drawing closer to the center of the world and becomes lighter original: "s'alegieriscie"; Leonardo suggests here that as an object nears the Earth's center, its effective "heaviness" changes relative to a counterweight., and that which rises is always moving further from that same center and becomes heavier. Thus, through this variation of weight, the motion is either accelerated or delayed.

A diagram showing a horizontal lever arm with a weight hanging from the end. To its right, a cord passes over a pulley to another hanging weight, illustrating a mechanical balance system.

One weight compared against another does not move except by the shortest path. That path is shortest which departs from the center of the world along the smallest line. Therefore, between two weights that counterbalance each other, the one that is further from the center has more heaviness original: "grauezza"; the physical quality of being heavy or the force exerted by a weight..

A small diagram of a horizontal line with regular markings (a scale) and a weight hanging from a central point.

One weight against another does not move except by the shortest path. Among all the lines that depart from the center of the world, the shortest is that which is closest to the perpendicular; and the perpendicular is the shortest of all paths by which weights can descend.

A sector of a circle representing a swing or arc. Multiple radii are drawn from the center at the top left. The word "opposition" is written inside the arc. A weight hangs vertically from the center point.

If one of the counterweights moves only by a short path, it is because the counterweights act as a single weight in motion. The counterweight moves only as much as it descends. The descent of the weight is that portion of the motion which approaches the center of the world. Therefore, the more one weight is heavier than the other due to its distance from the center, the lighter it becomes through the short path of the descent.

If one of the weights descends by a line of less obliquity original: "obbliquità"; refers to the slant or angle of the path of descent compared to a vertical line. than the other, it is heavier than the one descending by a path of greater obliquity. The portion of the motion of the weight that approaches the center of the world is the true descent of that weight.

A narrow triangular diagram representing a vertical centerline and two slightly diverging lines, possibly indicating the swing of a pendulum or the resolution of forces. A weight hangs at the bottom vertex. Letters 'm' and 'n' are at the top endpoints.