Crossbows, the shoulder's load, and falling hammers
Larger instruments do not shoot proportionally farther; violent motion follows its nature to mid-course
Folio 189r is a page of reasoning on motion, almost without diagrams. Leonardo argues that a crossbow ten times as powerful will not shoot its arrow ten times as far, a rule he says holds for all instruments whose motions beget other motions, and asks how much weight a shoulder truly bears when a 100-pound load is carried out on a stick a braccio in front. Two further notes state that every violent motion follows the nature of its violence only to the mid-point of its course before falling to the level from which it set out, and that dividing one heavy arrow into four light ones will not carry them to the same mark. A closing question returns to the hammer: one falling eight braccia sinks a finger and a half where one falling four sinks a single finger.
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A stronger crossbow does not shoot proportionally farther
If a 1-pound crossbow shoots an arrow 100 braccia, a 10-pound crossbow in like proportion will not shoot a thousand. Leonardo says this rule applies to every instrument whose motions give rise to other motions.
How much load the shoulder actually bears
A man rests 100 pounds on his shoulder, then moves it a braccio back on a stick held a braccio out in front. Leonardo asks how much weight the shoulder then bears and presses down with.
Violent motion holds its nature only to mid-course
Every violent motion follows the nature of the violence that drives it only as far as the mid-point of its course. Thereafter it falls to the level of the plane from which it departed.
Falling twice as far sinks the hammer one and a half fingers
A hammer fallen four braccia sinks one finger into a lead rod; one fallen eight braccia sinks a finger and a half, not two. The depth grows less than in proportion to the height of the fall.