Degrees of Motion in a Falling Body
A column of widening intervals with a proportional analysis of accelerated descent
A column running down the inner margin plots the degrees of motion of a falling body as a stack of dots (o) tied to letters a, n, m, S, c, f, g, l, h, K, b, v, x and the numbers 1 to 13, each successive gap slightly larger than the one above it. The accompanying note works out the proportions between these intervals: mn is twice na, mn is two-thirds of mS, mS three-fourths of Sc, and so on in succession. Leonardo observes that as the number of spaces grows, the difference between each interval and its antecedent shrinks while the denominator of the ratio increases. The sheet belongs to a run of studies on the accelerating fall of heavy bodies.
On this page
Scale of accelerating descent
The inner column represents the degrees of motion of a falling body as a vertical file of dots labelled o, each attached to a letter and a number from 1 to 13. Each successive separation between the marks is drawn slightly greater than the preceding one, picturing the growing steps of an accelerating fall.
Proportions between successive intervals
Distance mn is twice distance na, and mn is two-thirds of mS; mS is three-fourths of Sc, Sc is four-fifths of cf, and so it continues. As the number of the spaces increases the difference between an interval and its antecedent diminishes, and the more that difference diminishes the more the denominator of the proportion increases.