The Simple Beam of a Balance and Where Its Weight Lies
Center of gravity at mid-length; a belt where one support bears all 4 pounds
Folio 165v distinguishes the "simple rod" (aste semplice) from the "compound rod" of a balance and argues that the parts of a simple beam grow heavier the farther they lie from the pole, while its true center of gravity falls at the middle of its length. Leonardo likens the rod's increase from end to end to the growth in weight and breadth of a pyramid from apex to base. Belt diagrams (cinglia) show cases in which one support carries the whole 4-pound load and the other nothing, because the line of the weight's center passes through the support. Tapering balance-beams and hatched blocks illustrate the reasoning.
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Parts of a simple beam grow heavier from the pole
The parts of the simple beam of a balance show themselves of greater heaviness the farther they are from their pole. The true gravity of the simple rod, however, is found at the middle of its length.
Center of gravity at the middle of the rod's length
The true gravity of the simple rod lies at the middle of its length. If you compute the greater weight against the lesser that the rod makes from its beginning to its end, the midpoint proves to be the point of equality.
Belt (cinglia): support c bears all 4 pounds
The central and right belt figures show that a b has nothing while c has all, that is 4 pounds; a companion note adds that the line 4 and 4 receives all the weight. Because the center of the weight passes through every part of the support, that support sustains nothing.
The rod's increase as a pyramid's growth
The proportion in the increase a simple rod makes from its beginning to its end is the same as the increase in weight and breadth of pyramids between the apex and their base.