Friction on the Balance: No Weight Can Exactly Match Another
Fraction reckonings of friction, with balance diagrams and two suspended rings
Calculations and small balance diagrams explore how friction ('confregazione') changes the weights needed to bring a lever into equilibrium. Working through fractions — a fourth part, then 1/16, 1/32 — Leonardo argues that because one is a continuous quantity divisible to infinity, no fixed weight can ever be matched by another of precisely equal power in an equal position. At the foot, drawn upside down, are two suspended rings labelled 'this one sounds and this one does not.' Much of the writing is faint and stained.
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Friction alters the balancing weight
Taking weight 3 from a and weight 1 from c makes 4, whose fourth part (1) is lost to friction and placed at b. To equalize from the opposite balance he seeks a number whose friction equals the opposite friction, tracking how each added unit grows the friction by a further fourth.
Impossibility of an exactly equal weight
A margin note states the proof: it is impossible to give a fixed weight another weight, in an equal position, with precision of equal power.
Continuous quantity divisible to infinity
Below the halving series (1/4, 1/8, 1/32, 1/128 …) he concludes that because one is a continuous quantity, and every continuous quantity is divisible to infinity, this precision of giving such a weight is impossible.
Two suspended rings: one sounds, one does not
Drawn upside down at the lower margin are two hanging rings with the note that one of them sounds while the other does not.