Notebook on Mechanics and Natural Philosophy (1478-1518) - Page 23

Experience shows that upon impact original: "percussione"; Leonardo refers to the force exerted when a falling object hits a surface., a descending weight exerts a force as much greater than its actual weight as its motion is greater in velocity.

It is impossible for the motion of an object to double simply by doubling the heaviness of its cause The "cause" refers to the force or weight driving the movement.. It is likewise impossible for the effective weight of an object to double simply by doubling the velocity of its motion.

If a slender object moves through the air among other objects of equal weight, it will move faster than the others in proportion to how much smaller its body is compared to its equals. This occurs because the weight of the air that the slender body must divide is less than that which a thick body must divide; therefore, it encounters less resistance. Furthermore, a slender object penetrating the air has to displace a smaller quantity of air than a thick one. For this reason, when moved by the same power motore: the "mover" or source of force, such as a falling weight or a spring, it will achieve a faster motion.

Every object weighs as much as it resists its mover, and the mover resists the moved object as much as that mover weighs—or we might say that the mover moves as much weight as its own power, and therefore by doubling the mover, you should double the motion.

If the mover were doubled, it would double the motion of the moved object, provided that the resistance of that object did not increase due to the doubled velocity. But because an object moved through the air encounters a fourfold Leonardo correctly observes that air resistance increases disproportionately (quadratically) as speed increases. resistance from the air when its velocity is doubled, it is impossible for a doubled mover to result in doubled motion.

motion and weight

By doubling the power of the mover, the motion of the moved object is not doubled.
If the mover is doubled, it will not double the motion.

In what way can one double the motion of a moved object?
The motion is doubled by doubling both the mover and its weight; that is, if the mover doubles its weight and its power, it will double the motion of the moved object.

Treatise on the balance original: "trattato della bilancia" Along the right margin is a vertical sequence of six mechanical diagrams: 1\. A horizontal line with points d, a, n, b, p. A weight (m) hangs from n. Above it is the title "Treatise on the balance." 2\. A weight (m) suspended from point a by two cords forming an angle. 3\. A weight (m) suspended by cords in a triangular arrangement. Cords are labeled a, b, c, d, p. Text inside reads "Along the line of the balance." 4\. A larger triangular suspension diagram with cords extending to points a, b, c, d, p. Labels indicate geometry of forces. Text inside reads "Along the line of the balance." A red library stamp with a crown and "B.M." is placed next to this diagram. 5\. A diagram with two lines converging at a steep angle from points marked with "+" and "-" to a weight (m) at the bottom. 6\. Two separate diagrams at the bottom right. The left shows a trapezoidal frame labeled f, g, h, k. The right shows two vertical parallel lines within a frame labeled f, g, h, k, m, n. Red circular ink stamp with a crown above the initials B.M. (British Museum).