The Perfection of the Cube; Friction of Pulleys on Their Axles
Solid geometry of the cube and the mechanics of friction in a block of pulleys.
The page opens with a note praising the cube as the first among bounded solids because it alone divides to infinity into parts like its whole, its centre sitting amid 24 right angles. Leonardo then turns to the friction that pulleys make upon their axles, arguing that smaller-diameter pulleys move less freely and that a thicker cord runs more easily than a thin one because its centre lies farther from the point of friction. A vertical block of stacked pulleys with a hook is drawn in the right margin to illustrate the tackle discussed.
On this page
Friction of pulleys of unequal diameter turning on their axles
Pulleys of smaller diameter turning about axles of equal thickness move with greater difficulty. A thicker cord gives easier motion to the pulleys of a tackle than a thin cord, because the centre of the thick cord is more remote from the friction made by the pulley's revolution upon its axle.
Block of stacked pulleys (tackle) with hook
A vertical block-and-tackle is drawn in the right margin: a case enclosing several sheaves in a column with a suspension eye above and a load hook below. It illustrates the tackle whose cord and sheaves are analysed in the adjacent text on friction.
The perfection of the cube
Among the solids bounded by faces the cube holds first place, since no other body divides to infinity into parts like its whole. Its centre lies amid 24 right angles that touch it, and its cubic division proceeds into 8, 64, 512 and beyond, always multiplying by 8.