Notebook on Mechanics and Natural Philosophy

Why a cord, however it hangs

A geometric diagram in the upper right showing a trapezoid with internal lines connecting vertices (labeled 'a', 'b', 'c', 'd') and points on the sides, illustrating geometric relations of forces and gravity.

Every heavy body original: "graue"; referring to an object with mass/weight. that is suspended comes to rest above the center of the world Leonardo’s term for the center of gravity or the center of the Earth.. And that which is suspended by two ends will have so much less weight at one end than the other, as the one is shorter than the other. This occurs if the cord is of negligible weight. Because if it is of a weight that must be considered relative to the weight suspended upon it, the weight of the cord itself will be added to the weight suspended from it, and then the proportions vary, because the cord will be as much heavier as it is longer. And in whatever way a cord hangs, its weight will be above that center.

A perspective drawing of a truncated pyramid or a geometric solid with horizontal segments, marked with a central vertical line and letters, likely exploring the center of gravity in 3D shapes.

The weight that hangs suspended between the center of the world and its pole of suspension is always proportional to the cord from which it hangs, which is between the pole and the said weight. If one wishes to measure it, it must fall toward the center of the world. And if the cord is longer at one end than the other, the weight will create the same proportion from the pole to the cord as that of the cord from the pole to the center of the world. And if the cord is divided into two proportional parts, the center will be between those parts.

A diagram showing a horizontal beam from which several curved cords hang, all converging on a single central weight. Numerical values like 4, 8, and 10 are annotated along the cords and beam to show how weight is distributed.

A diagram of a simple lever or balance beam 'a-b' with a central support 'n' and a hanging weight '+' at point 'o'.

If you wish to see which part of the cord willingly Leonardo often personifies physical forces, using "willingly" (uolentieri) to describe the natural path or tendency of an object. supports the weight and which does not, place the cord upon a fixed straight line and place the weight in the middle of that cord. You will see that one end pulls more than the other, and you will arrive at the knowledge of the truth. This is because the strain on such cords changes from point to point, so that one is more strained than the other. And if you wish to see if this cord is more strained here than there, you will see by the angles of the cords which are more acute than others.

A composite diagram: On the left, a balance beam with multiple hanging cords forming a parabolic shape under a weight. On the right, a vertical diagram of a plumb line with a weight, labeled with points 'a', 'd', and 'n'.

• If you wish to find the length of a cord by weighing it, find the weight of 10 or more braccia A 'braccio' (plural 'braccia') was a Florentine unit of measurement, literally meaning 'arm,' approximately 23 inches or 58 centimeters. of that cord. Then, by weighing the entire cord, you will know its length.
• If 10 braccia weigh 1 pound original: "libra" and the whole cord weighs 10 pounds, then the cord is 100 braccia. And if it weighed 2 pounds, it would be 20 braccia. And if it weighed half a pound, it would be 5 braccia; and thus you will arrive at its full length. You shall do the same to find the weight of 10 braccia of a wall, to see how high the wall is. And likewise, you will see by weighing lead or another metal, of which you weigh a piece one finger in thickness; then by weighing a heavy body of the same metal, you would know its thickness. And if you weighed a piece of tin one square braccio in size, and then weighed another piece of one square braccio that weighed twice as much, you would say this one is double the thickness. And if it weighed triple, it would be of triple thickness. And if it weighed half, it would be of half thickness.