Load carried by pulleys and little wheels on a shared cord
What the abacus letters record; two weights over wheels n f and m f; an odd-number aside
Folio 171v studies how weights hung on cords load the pulleys (girelle) and little wheels (rotelle) that carry them. A 'general rule' notes that the abacus letters set above the weights record not the pull on the cords but what is discharged onto the pulleys; two weights suspended at a and b resist one another over the wheels n f just as they would over pulleys m f. In one case the upper wheel bears 6 and the lower 2 of the eight pounds of two weights hung on a single cord. A separate arithmetical note observes that every odd number multiplied by itself makes another odd number, and rows of weights, pulleys and a wheel are drawn at the right.
On this page
What the abacus letters record about the pulleys
The letters of the abacus, taken from the weights upward, do not speak of the weight that pulls the cords but of that which is discharged onto the pulleys — a general rule distinguishing pull from load.
Two weights over little wheels versus pulleys
The two weights suspended at a and b make the same resistance to one another resting on the little wheels n f as they would on the pulleys m f, showing the equivalence of the two supports.
Six and two of eight pounds on one cord
Here the upper little wheel feels 6 and the lower suffers 2 of the eight pounds of the two weights attached to one and the same cord, quantifying how the load divides between the wheels.
Every odd number squared is odd
A short arithmetical note declares this a general rule: every odd number multiplied by itself composes another odd number.