The pyramidal power of the balance arms
A bent arm loses force by infinite degrees; a cord-and-bow problem
Leonardo poses a problem about a cord a b two braccia long: extended to four (c d) it retains a power of two libbre at each of its ends, and he asks with what power a single end would end its motion. A long demonstration then argues that the power of the balance arms is 'pyramidal': the straight arm r h resists its opposite h S precisely, but bending it by ever smaller equal degrees gains degrees of weakness, and because a continuous quantity is divisible to infinity, the acquired power grows infinitely. He concludes that all powers may be imagined as capable of infinite increase or decrease, growing from nothing to infinity and descending again to nothing, so that 'nothing borders upon the infinite'.
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Cord and bow: power retained at the ends of an arc
The cord a b is two braccia; made four, as shown in c d, it stays with a power of two libbre, having moved two braccia with its two ends. Leonardo asks what power remains if that motion is made by only one end of the bow, and answers that two remains at each end as before, the time dividing the two ends being equal for either arc.
Straight arm resists precisely; bending brings weakness
The power of the balance arms is shown to be pyramidal: the arm r h when straight resists the arm h S precisely, but bent by the smallest part, coming by minimal equal degrees to full flexure, it gains at every degree of motion a degree of weakness against the weight of its opposite arm h S. The power that h S acquires grows in proportion to the shortening of its opposite arm.
Powers as infinitely divisible, ending in nothing
Because every continuous quantity is divisible to infinity, Leonardo argues that all powers may be imagined capable of infinite augmentation or diminution, and are therefore pyramidal: from nothing they grow by equal degrees to infinity in magnitude, and by the same degrees descend to infinity by diminution, ending in nothing. Hence, he concludes, nothing borders upon the infinite.