Beam balanced on a box: press end a or lift end d?
Comparing the effort to lighten corner m by pushing down at a or raising the opposite end d.
A long graduated beam rests symmetrically across the top of a small rectangular box, its length marked at points a, r, b, c and d, with the box's upper corners labeled n and m. Leonardo asks whether it takes less effort to lighten the loaded corner m by pushing down on end a or by lifting up the opposite end d. Weighing the counterbalancing segments of the beam, he concludes that the two methods require equal force.
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Lightening corner m: pushing at a versus lifting at d
Leonardo asks which costs the operator less: pushing down on end a or lifting the opposite end d to relieve the loaded corner m. He argues that lifting at a makes the segment c-d act as a counterweight equal to its own length from r to c, so the operator overcomes part c-d; pushing down at d beyond the two segments a-r does the same. He concludes that the two methods are equal.