Counterweights on a balance and the infinite
Weights hung by cords, a table of resistances (0,2,4,6,8), and the balance arm as infinitely divisible
The left-hand column argues that a suspended weight r stays in the air only if an equal weight or force is opposed to it along the perpendicular of its cord, and that any such opposing force always bears upon the fulcrum (pole) of the balance. A short table pairs a weight of 8 at the points r, s, t, v and x with the resistances 0, 2, 4, 6 and 8. Leonardo then reasons that, because every continuous quantity and each arm of the balance is infinitely divisible, one could imaginatively set 'infinite worlds' equal to a single ounce. The diagrams show a beam balance carrying a load marked 100, a rig of pulleys and cords with hanging weights, and a row of weights suspended from a bar.
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A hanging weight needs an equal opposing force
The weight r cannot, as the others do, remain suspended in the air unless an equal weight or force is set against it. If that counterweight is x and the cord r f b x is all one piece, r is held; and if you oppose the weights with force, that force always loads upon the pole of the balance.
Table of resistances against a weight of 8
A short list pairs the weight 8 at successive points with the resistance it meets: against 8 of r resists 0, of s resists 2, of t resists 4, of v resists 6, and of x resists 8. Drawing the weight up the line K a changes its effective weight at every degree of motion.
Infinite worlds balanced against one ounce
Leonardo claims that against a single ounce placed on the balance one could imaginatively set infinite worlds beyond the centre of the pole, and they would stand equal to that one ounce. The reason is that every continuous quantity, and each arm of the balance, is divisible to infinity.
Beam balance, pulleys and suspended weights
At the top a beam balance carries a bell-shaped load marked 100. Below, a rig of cords and small pulleys hangs a series of weights lettered and numbered (8-8, 8-2, 8-4, 8-6), and at the foot a horizontal bar suspends a further row of weights.