Bouncing Balls and Rebounding Water: Discrete vs Continuous
Why a continuous body of water must move with equal motion in every part
Leonardo contrasts the motion and leaps of a discontinuous quantity—bouncing balls, shown as a scattered row of small marks at the top—with those of a continuous quantity, water, shown as a band of waves. He argues that because water is all joined together, every part of a stream of equal width and depth must pull and be pulled, push and be pushed, with equal motion and power. If it were otherwise, the water would pile up where it slowed and be lacking where it sped up.
On this page
Motion and leaps of a discontinuous quantity
The scattered marks at the top of the page stand for bouncing balls—a discontinuous, or discrete, quantity—whose motion and leaps are treated as the counter-case to flowing water.
A continuous quantity moves with equal motion throughout
Because a stream of equal width and depth is all joined together, every part must pull and be pulled, push and be pushed, or drive and be driven, with equal motion and power. Otherwise the water would multiply where it delayed and be lacking where it moved faster. A band of waves illustrates the continuous case.