Collision of Discrete and Continuous Quantities
How struck bodies exchange their paths, and why a lighter mass rebounds farther from the median line f g
Leonardo sets out a small theory of impact: when two bodies strike one another, the lines of their motion transmute into one another after the blow, whether the quantity is continuous or discrete. He reasons that a body one-sixth as heavy rebounds six times farther from the middle line f g than its heavy counterpart, and that in continuous (water) impacts the blows are always equal even when the colliding masses are unequal — unless their speeds differ. The recto illustrates this with an X of crossing trajectories and rows of unequal circles keyed by numbers.
On this page
Colliding bodies exchange their lines of motion
The lines of motion made by bodies that strike one another transmute one into the other after the impact. This holds for continuous quantity with continuous impact as much as for discrete quantity with discrete impact.
A one-sixth mass rebounds six times farther from f g
If the discrete quantity is 6 times its counterpart, the rebound (balzo) of the one-sixth part is 6 times more remote from the middle line f g than that of the body 6 times as heavy. Leonardo ties rebound distance inversely to weight.
In continuous water-impacts the blows stay equal
In the continuous quantity of impact the blows are never other than equal, even though the bodies moved by the waters were very unequal. Inequality only arises if equal bodies meet with unequal velocity or motion before the impact.
As much strikes, so much springs off (6 f 1 - 1 6 - g)
Beneath a second figure keyed 6 f 1 - 1 6 - g Leonardo states the rule 'as much springs off as strikes.' The rebound is set equal in measure to the incoming blow.
Diagrams of crossing paths and unequal quantities
At the right an X of crossing lines shows the transmuted trajectories after impact, while below it rows of different-sized circles keyed with numbers represent the discrete quantities and their rebounds.