The Manuscripts of Leonardo da Vinci, Vol. 4

FOLIO 5 (recto)

Geometric diagrams showing the paths of motion and circular projections, illustrating the trajectory of an object through space.

Of the ball
And if said ball is struck struck; original: "perchossa" — referring to percussion or impact in mechanics against the ground,
the ball will be moved by its own motion
through the air in the manner of a circle Leonardo is likely describing the spin or the arc of a rebounding ball.;
and this ball, within itself, will have—
having struck the ground within its own bounds—
from its center, a third of the motion
made within itself.

Of the ball
Many balls of impact, calculating
their principle principle; original: "ragione" — meaning the underlying physical law or mathematical ratio, whether it be straight or oblique Referring to the angle of impact: a "straight" impact is perpendicular to the surface, while "oblique" is at an angle.,
and how much its impact will be
from the center of that ball outwards;
and this will be the principle, if said ball
is struck in part or in whole,
whether it be straight or oblique, and how much its
impact will be from the center of that ball
outwards; and this will be the principle, if
said ball be straight or oblique, and how much
its impact will be from the center
of that ball outwards; and this will
be the principle, if said ball be straight
or oblique, and how much its impact
will be from the center of that ball outwards;
and this will be the principle, if said ball
be straight or oblique, and how much its
impact will be from the center of that ball
outwards; and this will be the principle, if
said ball be straight or oblique, and how much
its impact will be from the center.
The repetition in this passage is characteristic of Leonardo’s drafting process, as he often restated a proposition multiple times to refine its phrasing or logic.

FOLIO 5 (verso)

Sketch of a small gabled building or shed, perhaps used to study the perspective of shadows cast by a solid structure.

Why the ball will be moved
If said ball is struck
within itself;
and if said ball is struck
within itself, it will have
its principle moved through the air
in the manner of a straight line
and of an oblique line.

Many balls of impact
calculating the principle original: "ragione" whether it
be straight or oblique, and how much
its impact will be
from the center of that ball
outwards; and how much it will be
from the impact of a single
body struck on the ground
in the manner of right angles
or oblique angles;
and this will be the principle
why the ball will have within
itself a finite original: "terminato" — limited or defined motion;
and this will be its principle.