Percussion, rebound, and weights on pulley cords (ff. 92v-80r)
Definitions of the central lines of weight, motion, and blow, with pulley loading.
This opening develops Leonardo's science of the blow and the rebound (balzo). The left page (folio 92v) states that a more powerful blow yields a shorter rebound, and defines the height and length of a rebound together with the central lines of weight, motion, and the blow; a marginal note distinguishes three natures of motion - augmentative, natural, and violent. The right page (folio 80r) turns to cords over pulleys, arguing that a cord bent at a wider obtuse angle loads the pulley's pole (polo) less, and working out cases where the pole feels one and a half or two times the hung weight. Diagrams of circles, a rebound fan, quadrants, and pulleys carry the letters a, b, c, d, g, m, n, and r.
On this page
A stronger blow makes a shorter rebound
Impetuses and moving bodies with equal distances and objects can produce percussions varying to infinity. The more powerful the blow, the shorter the rebound; the weaker the blow, the longer the rebound. Height and length of the rebound thus vary inversely with the force of impact.
Central lines of weight, motion, and the blow
Leonardo defines the height of the rebound as the rise above the level of the struck site, and the length of the reflected motion as running from the point of percussion to the start of natural motion. The central line of weight passes from a body's center of gravity to the center of the world; the central line of the blow rises from the point of percussion through the middle of equal upper and lower weights. The center of gravity stays concentric with these central lines even in an irregular body.
The three natures of motion
A marginal note divides motions into three natures: augmentative; the natural-observing motion of animals; and diminutive, that is, violent motion. The natural transverse motion ends where natural motion begins. The classification frames the rebound as a transition between violent and natural motion.
Weight m burdens weight n struck at r
In this figure the weight m weighs more than the weight n, which strikes at r. Because m keeps n so burdened, n cannot rise in its reflected motion. The case shows how a heavier partner suppresses the rebound of a lighter one.
A cord bent over a pulley at an obtuse angle
The wider the obtuse angle at which a cord bends over a pulley, the less it loads the pulley's pole. A straight cord a b is the limit of the last obtuse angle and gives the pulley no weight; a g c loads less than a g d. All obtuse angles end at the right angle, and at acute angles the pole gains no more than double the suspended weight.
The pole feels one and a half times the weight
A cord, straight or bent, is always loaded with twice the weight it sustains. The weight m acts wholly at n, where it counts for half its heaviness (per the quadrant figure above), so a one-pound load plus the one-pound resistance b, halved at n, makes the pole c feel exactly one and a half pounds. The reasoning carries through further pulley cases keyed by the same letters.
