A Falling Body Gains Speed at Every Degree of Motion
Column of descent-degrees with a demonstration that velocity grows with the distance fallen
The outer margin carries a column of dots (o) numbered 1 to 16 and keyed to the letters a, c, n, f, g and, near the foot, r, b, m, the successive gaps again drawn slightly larger to picture accelerating fall. The notes state the governing law: a freely descending heavy body acquires one degree of velocity at each degree of motion, so the length covered in each equal interval of time is progressively longer than the one before. Leonardo demonstrates this with weights a and b, arguing that in the same time a descends to c, body b (fifteen times faster) travels fifteen times as far. A closing remark notes that distance cn is twice its antecedent ac.
On this page
Scale of degrees of descent (outer column)
The outer column represents the degrees of motion of a falling body as a file of dots labelled o and numbered 1 to 16, keyed to letters a, c, n, f, g at the top and r, b, m at the foot. Each successive separation is slightly greater than the one above it.
One degree of velocity per degree of motion
A freely descending heavy body acquires one degree of velocity at each degree of motion, and the part of the descent made in each equal interval of time is always progressively longer than its antecedent. This is the law the column of widening intervals is meant to picture.
Fifteen-fold speed and doubled intervals
In the same time that weight a descends to c, weight b, being fifteen times faster than a, will have gained a length of descent fifteen times greater. Leonardo adds that distance cn is twice its antecedent ac, and directs attention to the corresponding point at nf.