Levers and Counterlevers: Real and Potential Arms
Proportions between a weight and the arm of the balance that sustains it
This folio develops Leonardo's theory of the balance, distinguishing the 'real' arm (of solid material) from the 'potential' arm that acts where matter is lacking. Beams hung with cords and weights show how a cord takes a lever d b that resists the counterlever b m, and how arms of equal length give equal resistance to equal weights. The central figure argues that the proportion the lever S t bears to the arm a t is the same the weight x bears to the potentia a t that sustains it. A weight is treated as spread equally along the whole of a supporting line.
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Cord, lever d b and counterlever b m
The cord m d takes hold of the lever d b, which resists the counterlever b m, and the same arrangement is repeated on the opposite side of the beam. The construction sets up the balance of a lever against its counterlever.
Equal arms give equal resistance
Leonardo argues that the weight 2 at f gains no advantage from the long lever m b against the small counterlever b d, because the hanging weights are equal. The potential arm o b c and the real arm b d are of equal length and offer equal resistance to equal weights, and a companion figure repeats the point for arms a b and a c.
Weight x proportional to the arm that sustains it
Because lever S t is one-half of counterlever d t, one pound at d requires 2 at S for resistance, and the weight x, divided between its two supports, yields 4 of resistance against 2 of weight. Generalising, if the arm is 4 times smaller it demands 4 times the weight, so the proportion S t has to a t is the same the weight x has to the potentia a t that resists it.
The potential rectangle a d n
The semireal line m t takes the potential lever a m, which resists the potential counterlever a d. Where these meet, the potential rectangle a d n is generated.