Acceleration of falling bodies: velocity gained, time lost
Natural descent doubles velocity as motion doubles: 1-2-4-8-16-32-64-128-256
This folio states Leonardo's law of natural 'local' motion: a weight descending by natural motion gains a degree of velocity at every degree of motion, so that when the motion is doubled the velocity is doubled, and so on down toward the centre of the world, following the series 1-2-4-8-16-32-64-128-256. He couples the velocity gained with time lost, each degree of motion adding a degree of velocity and subtracting a degree from the time in which the first degree was made, so that a degree made in less time is made with more speed. A vertical scale in the right margin, its units marked to show that 'the excesses of the degrees are equal', represents the equal spaces (each a braccio) traversed in ever-shorter times.
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Velocity gained and time lost in free descent
A weight descending by natural motion acquires a degree of velocity at every degree of motion; when the motion is doubled the velocity is doubled, continuing down toward the centre of the world. Each degree of motion adds a degree of velocity and takes away a degree of the time in which the first degree was made, so the descent covers equal spaces of one braccio each but measures them in steadily less time.
The doubling series and equal excesses of degrees
The doubling of velocity is set out as the series 1, 2, 4, 8, 16, 32, 64, 128, 256. A column of units marked along the right margin (1 1, 1 2 ... 1 16) is drawn to show that the excesses of the degrees are equal.
