The Manuscripts of Leonardo da Vinci, Vol. 4

Folio 3 (recto) contains a study on the physics of rebound (percussionthe striking of one body against another) and geometric diagrams.

Sketch of a vaulted or ribbed structure, possibly a bridge segment or architectural vaulting study.

Geometric diagram consisting of a circle with a vertical diameter and intersecting lines, likely related to optics or projection.

If an artillery ball strikes a wall of equal hardness, it will rebound from it with angles equal to its angles of incidencethe angle at which an object hits a surface, and this rebound will move as far beyond the angle of rebound as the impact of the ball was into the wall, or into the mud, or into the water. Leonardo is observing that the "law of reflection"—where the angle of approach equals the angle of departure—applies to physical objects like cannonballs just as it does to light.

Any ball that rebounds from any solid surface will rebound at angles equal to one another; that is, the angle of percussion shall be equal to the angle of rebound. This occurs if the rebound is from a single body without any yieldingoriginal: "cedimento" — the compression or deformation of a surface upon impact. But if it rebounds from a body that possesses some yielding, it will not rebound at equal angles, but will draw closer to the line of rebound than to the line of percussion; and this difference will be greater as the yielding of the struck body is greater. Here, Leonardo correctly identifies that if a surface is soft (like mud or water), it absorbs some of the energy and changes the trajectory, a sophisticated early observation of inelastic collisions.

Folio 3 (verso) contains studies on mechanics, specifically the equilibrium of a balance scale.

Diagram of a balance beam (lever) with weights suspended at various points.

If the balance scaleoriginal: "bilancia" has equal arms, and two equal weights hang from them at equal distances from the center of said balance, they will remain in equilibrium.

if one of said weights is moved further from the center of the balance? it will weigh more than the other? Leonardo is describing the principle of the lever: a weight placed further from the fulcrum exerts more "force" or "gravity" than an equal weight placed closer to the center.

The remaining text on Folio 3v is highly compressed and difficult to transcribe accurately due to the scale and reproduction quality, continuing the exploration of mechanical moments and centers of gravity.