The Motor of Diminishing Force: Crossbow, Pulley and Weight
A 400-pound draw and force falling off like a pyramid to its middle
Under the heading 'On the motor of diminishing power,' Leonardo draws a crossbow with a nocked arrow whose cord runs over a pulley to a suspended weight marked 400. He reasons that if four hundred pounds draw the cord over the catch, the force present dwindles to nothing as the cord unwinds, diminishing in equal degrees like a pyramid, and that the middle of that pyramid is the 'middle of the force.' He compares this to a simple weighted staff, whose whole weight is found by taking its midpoint; the passage breaks off mid-sentence.
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Force decays like a pyramid to a 'middle of the force'
If four hundred pounds draw the crossbow's cord over the catch, that force abides while the cord is spanned and dwindles to nothing as it undoes itself, diminishing in equal degrees like a pyramid. Leonardo calls the middle of that pyramid the 'middle of the force,' comparing it to a simple weighted staff, whose whole weight is found by taking its midpoint.
Diagram: crossbow, pulley and a 400-pound weight
A crossbow with a nocked arrow is drawn horizontally; its cord is carried over a pulley at the right and tensioned by a weight hung on a cord, labelled 400. The arrangement measures the pull of the bow against a known weight.