Motion of a Ball Along the Chords of an Arc
A pulley-cord sketch, and speed along oblique paths limited only by air resistance
The upper diagram shows a cord led over two pulleys with hanging weights, labelled only with the numbers 4, 32 and 32. Below, an arc with centre S and radii drawn to its rim illustrates a ball descending along paths of different obliquity. Leonardo argues that if speed grew simply in proportion to the shortening base m n, then, since a continuous quantity divides to infinity, the speed would become infinite, were it not checked by the resistance of the air.
On this page
Speed of a ball along paths of different slope
If the ball S moved twice as fast along S m as along S d because m n goes into n d twice, then, since every continuous quantity divides to infinity, the base m n could be halved endlessly and the speed along S n would become infinite compared with the time along S d. Only the resistance of the air prevents this.
Cord over two pulleys with weights
A cord runs over two pulleys carrying suspended weights, marked with the numbers 4, 32 and 32. The sketch sits at the head of the page above the study of the descending ball.