Notebook on Mechanics and Natural Philosophy (1478-1518) - Page 19

⚠Page contains a library stamp "B.M." in red ink. Text is written in Renaissance Italian mirror script.

Whatever motion the counterweight makes that pulls the weight, that same motion, point by point, the weight will have; even though both descend along lines unequally distant from the center of the earth Leonardo is considering the weights relative to the Earth's center to account for gravitational pull, though in practical terms he is discussing linear motion. because what one loses in velocity in that same time, the other acquires. a d shall be the motion of the weight; b e shall be the motion of the counterweight; o e shall be of 1 finger original: "ditta"; a Renaissance unit of measurement approximately equal to the width of a finger.; f e shall be of 2 fingers; h e shall be of one finger.

![A technical drawing illustrating a pulley system. A rope passes over a horizontal bar and a pulley. A weight labeled '4' hangs from one end, and another weight labeled '2' hangs from a pulley connected to the same rope. A third vertical line shows a weight labeled '4'. Points are labeled with letters a, b, c, d, g, h, e.]

The weight d shall be of 2 pounds original: "libbre"; the Italian pound varied by city, but Leonardo uses it here as a general unit of mass. and the counterweight f shall be one pound. d descends through a space double that of weight f, because d is to send up a weight of 2 pounds with a counterweight of one. b d is the one, b e the other.

![A diagram of a lever or balance beam. A horizontal line has two vertical lines extending downwards, each ending in a circular weight. One weight is labeled '1' and the other '2'.]

Whatever weight is attached to two cords, [moving] between one and the other of these cords, shall be the same as if it were attached to a single one of such cords; because the weight is divided into two parts by the two cords.

![A drawing of a weight suspended from a central point where two ropes meet, forming an inverted triangle. Labels A, B, G, and weights are noted.]

The entire counterweight

is not

attached to the cord that pulls the weight, but is divided into as many parts as there are cords that support it; because each cord pulls its part, and from each cord they go to gather until a single end, and there the entire weight is united, because in such a place a single cord supports the weight, which had been divided among many cords Leonardo is describing the mechanical advantage gained by using multiple cords or pulleys to distribute weight..

![A simple diagram showing a weight suspended from a V-shaped rope arrangement.]

![A red circular stamp featuring a crown at the top and the initials "B.M." below, indicating the British Museum collection.]

Whatever weight is supported by two cords unequally distant from the center of its gravity, it weighs more upon that cord which is closer to it; and for this reason, weights do not weigh among themselves, but upon the line of their gravity. Hence, if you weigh unequal weights in equal scales, you will never be able to make them weigh equally, unless you distance them from the pole original: "polo"; the fulcrum or pivot point of the scale. of the balance in such a way that the one, with its motion, makes itself equal to the other. p d f s are one cord and the other.

![A complex geometric diagram showing a weight labeled '4' at point 'p' suspended from two ropes (m-p and n-p). Various auxiliary lines and arcs demonstrate the angles of force and the geometry of the motion. A smaller weight labeled '1' hangs from a pulley on the right side of the diagram. Points are labeled m, d, n, a, f, s, p, b.]

If you pull a weight toward you by a cord that does not pass through the center of its gravity, that weight will never rise [straight]; but it will always turn around a pole the point of rotation. that will rise with the weight, as appears in a m s and d f; for the weight always rises and never stops turning. And all this arises because the force that pulls the weight is not directed through the center of gravity; hence the weight always rises by the cord and never ceases turning until the center of its gravity aligns itself with the line of the cord that pulls it.

[Regarding] c v d f and this cord f s, I say that if it came straight up along the line d s, without doubt, it would support the weight of 4 pounds. But because it rises along the line d f, it will support only half of the weight, that is, 2 pounds; because the weight is then divided between d s and the line d f which pulls.

If the cord a b is pulled from below the pole of the motion of the weight d, I say that such a cord will not always have the same resistance, but will keep changing through the degrees of a proportion Leonardo is observing that as the angle of the cord changes, the effective force or resistance changes proportionally. that f s [shows]. And if it were at the pole a, the cord r s going to send along the line d b, without doubt it would not feel any resistance; because the cord will not be pulled by d of any weight. m s shall be the heights of the motion of weight d, and b shall be the depth of the same weight.