Levers, counterweights and a self-closing door
Devices in which resistance changes at every degree of motion
The right column shows a triangular lever with a counterweight, a semicircular hinged mechanism carrying a weight, a ring-and-arm device, and a fan of lever lines radiating from a pivot. Leonardo analyses how a counterweight raised through a fraction of a height sheds part of its load onto the pivot, so that a 4-pound weight leaves 3 at a and 1 at n. He describes a door that shuts by a counterweight and offers a graded resistance at every degree of motion, and sets out how to make the differences between successive lever lines equal so that no degree of motion ever changes the weight felt.
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A counterweight shedding load onto the pivot
As the weight n is raised through a quarter of the height a b (to c b), it lifts a quarter of the load it had given to a. With an attached weight of 4 pounds, 3 pounds remain at a and one comes to rest at n, showing how the share carried shifts as the arm turns.
A door that shuts by a counterweight
This, Leonardo notes, is the nature of a door that closes by a counterweight, which likewise offers degrees of resistance at every degree of its motion. He remarks that he draws only the thickness of the door.
A weight that grows lighter as it rises
This arrangement keeps the same nature of weight at every degree of motion: the more the heaviness a b is raised toward b, the lighter it becomes, while the lever that moves it grows more difficult. Leonardo cites the 8th proposition of his ninth book.
Equal steps between lever lines keep the weight constant
Considering all the lines of the levers, a o, b o, c o and so on, Leonardo instructs that the excesses, the differences of their lengths, be made equal. Then, he finds, no degree of motion will ever change the weight.