Weights in the balance: friction and the impossibility of measure
Aphorisms and calculations on the friction of the fulcrum, continued from the recto
Continuing the study of the balance from the recto, four aphorisms repeat that it is impossible to name the excess or difference by which the heavier weight in the balance overcomes the one that rises. Diagrams labelled with numbers and letters (4–f–12; d, n, b) reason that one unit of friction at the pole plus three of attached weight together resist, so that a single opposite weight will never overcome them unless placed three times farther out on its arm. A rule instructs dividing the balance arms into as many parts as the fractions of the weights require. Among the balance sketches a bladed rotor-like mechanism is also drawn.
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Four impossibilities of naming a weight difference
Leonardo states it is impossible to name the excess of the weight that overcomes its opposite in the balance; the difference between the descending weight and the rising one; the difference of the greater among weights tried in the balance; and the difference of greater to lesser at the moment of trial.
One against three: friction plus attached weight (4–f–12)
On a balance marked 4–f–12 he counts one unit of pole-friction (1/4) and three of attached weight (3/4). A single opposite of 1 must overcome a 3 made of 2 attached weight plus 1 friction, which it will never do unless it passes three times more distance out on the opposite arm at f.
Rule for dividing the arms by the fractions of the weights
Always divide the arms and the attached weight into as many parts as the fraction occurring in the weights requires; if the count of weight does not match that of the arms, use the rule of three. He works one unit of pole-friction (1/4) against four of attached weight standing for 1/4 in lever b.
A bladed rotor-like device among the balances
Set among the balance and lever sketches, a symmetrical mechanism with radiating arms ending in small discs is drawn, together with a spiral form. It is not addressed by the transcribed balance notes.