Balance and friction rules, and a design for a pleasure garden
Inverse weights on balance arms, a quarter-weight friction law, a mill-fed summer garden, and a note on muscles
The upper part of the leaf sets out a rule that the proportions of opposing weights on a balance are the inverse of the proportions of their arms, working a numerical example (arm 8 balancing weight 8 against a counterweight of 2), and states that every friction of a clean, dense surface resists by a quarter of the weight rubbed. A friction figure lettered a, e, c with the values 4, 1 1/3 and 4/3 accompanies this. The long central passage is a vivid design for a summer garden and hall reached by a 'kneed' double-return staircase, cooled by a mill that raises fresh spring water through channels of chilled wine, waters citrus trees, drives fountains and hidden water-jets, and turns a copper aviary net and musical instruments. A closing note observes that the thicknesses of animals' limbs change as their muscles extend or contract.
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Opposing weights are inverse to the balance arms that support them
Divide the arms of the balance by the number of the weight that keeps them level, and the proportions of the opposite weights equal those of the opposite arms, but inverse. Worked through the example of an arm 8 counterweight balancing an 8 weight with a counterweight of 2.
Every friction resists by a quarter of the weight rubbed
Every friction, straight or rotary, made in bodies of clean and dense surface, has the power to resist by a quarter of the weight rubbed. The figure lettered a, e (counterweight arm) and a, c (friction arm) applies the balance rule to find the counterweight of a friction.
A double-return staircase serving a summer hall
The 'kneed' staircase is one braccio and three-quarters wide, sixteen braccia in all, with thirty-two steps and a turning landing; Leonardo widens it to two braccia and sizes the hall at twenty-one by ten and a half braccia, eight high. He rejects a taller proportion as melancholy and dark, making the stairs too steep.
A mill that raises spring water for fountains, an aviary and music
A mill blows summer wind and raises cool spring water through divided channels of chilled wine, waters oranges and citrons, and drives fountains and hidden jets that leap upward. A fine copper net roofs the garden as an aviary, and the mill sounds various instruments as long as its motion lasts.
Limb thickness changes with muscular extension
On the changes of the muscles of animals through the extension or contraction of their limbs. The thicknesses of the limbs change by reason of the extension of their muscles.