Notebook on Mechanics and Natural Philosophy

The endpoints a [and] b, because they move toward b, and c [and] d, because they move toward d, so e.
Furthermore, even as the endpoints of such a line move along the arcs of the circles of d and of b, nevertheless a-d in b shall be displaced by its motor motor original: "motore"; the source or cause of motion, such as a weight or a hand. through the middle of the motion produced by the movement of the motor; nevertheless, by the endpoints of a-d, it shall be displaced through the middle of the motion, and also b-f for the same reason.

The endpoints a [and] b, because they move between the endpoints of a continuous line a-b, even though the endpoints of that line move along circular arcs b-d of various curvatures, nevertheless the endpoints of that [line] a-b shall, at the end of the motion, be the same.

A geometric diagram consisting of a horizontal top line with points marked by dots, and a central vertical line descending to a point 'f'. Arcs and diagonal lines connect the points on the top line to 'f' and other parts of the construction, illustrating trajectories or geometric proportions.

[If] the motor c-d is displaced,
the endpoints of a-b and a-d shall be
displaced just as much [at] b; nevertheless, c-d
shall be displaced as much as
the endpoints of the line a-b are displaced,
even if they describe the said arcs.

It is nothing other than the extension of
any line a-d, while the
endpoints a-d move along the arcs f-b of
various curvatures; nevertheless, the centers
of such arcs shall be on the same
straight line o-e, even though such
arcs are not of equal curvature;
nevertheless, the endpoints of the line a-b
move upon them.

Furthermore, even if the endpoints a-b move upon
arcs of various circles, nevertheless the endpoints
of the line a-b are displaced.

If f, the shaft shaft original: "albero"; the central rotating axis or axle of a machine. of a mill, were moved by a constant weight of such power power original: "virtù"; in this context, Leonardo uses it to mean the force or energy that creates movement. that it made the mill perform l revolutions Leonardo uses the letter "l" as a variable for an unspecified number of turns. in one minute of time, then the motion of this shaft would have t power original: "virtù"; here referring to momentum or impetus. that would keep it moving for 30 minutes of time. During this time t, if the power that moved it constantly were removed, and there remained only the natural power This "natural power" refers to what we now call "momentum" or "inertia"—the energy stored in a moving body. acquired by the shaft, it would turn with as much power as was imparted to it by its motor.

A small technical sketch of a vertical axle or screw mechanism on a horizontal base 'd'. The top of the axle is surmounted by a rectangular box marked with the letter 'a'.