Rod on two cords: weight change with unequal spacing
Diagrams labelled a m b c and d e f for a suspended rod
Continuing the suspended-rod investigation, Leonardo again states that a rod hung by cords at its two ends shares its weight equally, then studies the case where one cord moves toward the other so that each degree of motion produces a change of weight. Two lettered diagrams — one marked a m b c, the other d e f — treat the rod divided into unequal parts between the cords. He gives the governing rule as a set of proportions: the shifting weight relates to the original weights as the cord's motion relates to the rest of the rod, and the remaining weights relate as the opposite spaces between the cords and the rod's centre.
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Each degree of a cord's motion changes the weight it bears
A rod suspended by two cords at its ends shares its weight equally between them. But if one cord moves toward the other, every degree of that motion produces a variation of weight in it. The diagram is marked 2 2 with a 4.
Shifting weight as a sub-triple, in proportion to the motion
In the rod divided into unequal parts, the weight that moves is a sub-triple of the original weights. The weight moving between the cords stands in the same proportion to the first weights as the motion made by the cord bears to the remainder of the rod. This diagram carries the letters a m b c.
Remaining weights follow the opposite spaces on the rod
The weights left on the two cords will have together the same proportion as the opposite spaces enclosed between the two cords and the centre of the rod. The accompanying figure is labelled d e f.