On Retrograde Motion: Gauging the Velocity of a Cord
A cord driven eastward at its top swings its lower part west; a weight at p lets its velocity be measured
All the writing sits on folio 242v (the facing 237r is left blank), where Leonardo takes up 'retrograde motion': the faster the top of a taut cord is driven toward the east, the more its lower part swings toward the west. He argues that although velocity can increase without limit, this rule cannot be demonstrated to infinity, since once the cord a b lies straight along the line of motion it will rise no higher; hanging a small weight at the end p lets one measure further degrees of velocity, in proportion to the spaces swept. The leaf carries several diagrams, including a spoked circle, a tall framed device holding three circles, and a graduated quarter-circle.
On this page
The retrograde swing of the cord
On retrograde motion: the faster the mover of the upper part of the cord toward the east, the more the lower part of that cord moves toward the west. The two ends thus travel in opposite senses.
Limit of the rule, and measuring velocity by a weight at p
Although velocity can extend to infinity, the rule cannot follow it infinitely: once the front b makes cord a b straight with the line of motion from end a, doubling its speed will not raise it further. But a small weight hung at end p of cord b p lets one measure the degrees of velocity of b over the space a b, since the velocity of cord m b is to that of o b as space t b is to space r b.
The vane 'n' shielded from the wind
A short caption at the centre of the sheet, beside a figure, warns that the point n must not be touched by the wind, so that the tested motion is not disturbed by air currents.
Continuous versus discontinuous quantity
Beneath the figure Leonardo notes that between the motion of continuous quantity and the motion of discontinuous quantity there is a great difference, distinguishing smooth motion from motion by discrete steps.