A Balance Multiplied by Pulleys: Proportion of Powers
How arms n m and m 8 set opposite powers, minus what the pivot absorbs
A balance pivoted at m carries a weight (labeled 2) at end n, while from the opposite arm a cord threads back and forth over two vertical banks of three pulleys each to hold a weight labeled 8. A semicircle drawn about m, and the perpendicular dropped from the pivot to the cord, locate the effective counterweight. Leonardo states that the powers of the two sides stand in inverse proportion to the arm-lengths n m and m 8, that whatever weight n lacks against 8 is discharged onto the pivot, and he adds that the pivots and the friction of the pulleys must also be reckoned with.
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Powers inversely proportional to arms nm and m8
Leonardo states that the proportion arm n m bears to arm m 8 is the same their powers bear to one another, but contrarily. Whatever is lacking in weight for n against the weight of 8 is discharged over the pivot of the balance.
Cord threaded over two banks of three pulleys
From one arm of the balance a cord alternates back and forth over two vertical series of three pulleys each, from whose end the weight labeled 8 is suspended. A semicircle about the pivot m and the perpendicular from m to the cord mark the counterweight.
Losses to the pivot and to pulley friction
Beyond the discharge of surplus weight onto the pivot, Leonardo notes a further caution. One must also reckon with the pivots and the friction of the pulleys.