Mechanical elements: beams, wheels and the pull of gravity
Descent of an obliquely raised beam and weights borne on two touching wheels
Under the heading 'Mechanical elements,' Leonardo studies how a beam raised obliquely by one end descends, arguing it must move more along an arc than a chord, and then treats the beam as the hypotenuse of a right triangle whose unequal sides govern the force at each end (texts 3, 5, 7, 9). He turns to two wheels touching at their rims, showing how a weight set on the point of contact discharges onto their poles, the smaller wheel bearing the larger share (texts 10, 11). A recurring principle is that every heavy body directs its force straight to the center of the world, so a load pressing perpendicularly toward a wheel's center can never turn it (texts 15, 16). Beams, pulleys and paired wheels are drawn throughout both folios.
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Descent of an obliquely raised beam: arc versus chord
A beam raised obliquely by one of its ends is forced to descend more along an arc than along a chord. If instead the descent is constrained to the chord, the beam behaves as the hypotenuse of a right angle and is more powerful at one end than the other in proportion to the unequal sides of its rectangle.
The beam as hypotenuse of a right triangle
Treating the beam as the hypotenuse of a right angle, Leonardo relates the force available at each end to the lengths of the two legs. When the two legs are equal, equal weights at the ends resist one another equally; when unequal, the smaller weight on the shorter leg can move the greater on the longer leg.
Equal and unequal weights on the hypotenuse
If the legs of the right angle are unequal, equal weights set at the opposite ends of the hypotenuse give it motion. When the weights themselves differ, the lesser weight placed on the shorter leg moves the greater weight placed on the longer leg.
A weight discharged over the poles of two touching wheels
A heavy body placed on the point where the circles of two wheels touch does not stay there but discharges onto their poles, passing along the lines drawn from each pole to the point of contact. Of two wheels that touch at their rims, the one of smaller circle takes the greater share of the load.
The line of force runs straight to the center of the world
The central line of a heavy body resting on a wheel's rim points straight to the center of the world, and equal weights at equal distances from the wheel's center resist equally. It is impossible for a power pressing perpendicularly from the rim toward the wheel's center ever to make the wheel turn.
