Percussion Growing with the Distance Fallen
Sixteen graded points a-q show impact rising in fixed fractions with the fall
Two ruled propositions extend Leonardo's law of percussion for equal bodies falling one after another: the power of each blow stands to the other as the interval between them stands to the whole motion of the lower body. A column of sixteen equally spaced circles, lettered a through q, serves as a graduated scale of descent along the inner margin. Working through it, Leonardo reckons that because cb goes twice into ca, ball c strikes twice as hard as b, and so on by successive fractions up to q, whose blow exceeds p's by one-fifteenth.
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Blow proportional to the interval of the fall
When two equal bodies fall one after the other from a given height, the motion and power of the one stands to that of the other as their interval stands to the entire motion of the lower body. The greater the gap opened between them, the greater the disparity of their blows.
Impacts in the ratios cb, dc, ed ... qp
Because cb enters twice into ca, ball c gives twice the percussion of ball b; because dc is one-third of da, ball d strikes one-third harder than c; because ed is one-fourth of ea, e strikes one-fourth harder than d. The rule runs on to infinity, so that if qp goes fifteen times into qa, ball q exceeds ball p's blow by one-fifteenth.
Column of sixteen descent points a-q
Along the inner margin sixteen equally spaced circles are lettered a, b, c, d, e, f, g, h, i, K, l, m, n, o, p, q, each standing for one degree of descent. They give a scale against which the growing force of the falling ball can be reckoned.