Geometry of the Triangle; Ropes in Pulley-Blocks
A circle inscribed in an equilateral triangle, and why tackle ropes break and strain as they descend
The upper diagram sets an equilateral triangle between two concentric circles, and Leonardo records ratios: the circle touching the triangle's three angles compared with the one touching its three sides, and the greatest inscribed circle whose diameter equals two-thirds of the triangle's axis. Most of the page turns to the mechanics of ropes in pulley-blocks (tackle): the rope breaks where the mover's rope meets the first pulley, descending ropes always strain more than rising ones, and the swifter a rope the more weight it feels, the last rope being the swiftest. A balance sketch loaded with weights poses the further question of whether weights descending through the pulleys press more or less on the axles than when they stand still.
On this page
Circle and equilateral triangle: circumscribed vs inscribed
The circle touching the triangle's three angles is compared with the figure touching its three sides, and the greatest circle drawn within the triangle has a diameter equal to two-thirds of the triangle's axis (height). The marginal figure shows the triangle inscribed between two concentric circles.
Where a tackle rope breaks, and why descending ropes strain most
The rope of a tackle breaks where the mover's rope meets the first pulley. Ropes that descend always feel more strain than those that rise, and among the descending ropes the last feels less of the mover's power than the first.
Pulley-blocks and the swiftness of the last rope
The ropes of a tackle feel the more weight the swifter they are, and among the ropes moving within the blocks the last is swifter than any of the others. This links the speed of each rope in the system of pulleys to the load it must bear.
Do descending weights press more on the axles?
A balance drawn with weights (marked 1, 2, 3) frames an experiment: whether weights descending among the pulleys give more or less weight to the axles of the blocks in descending than in standing still. Leonardo poses it as an open question to be tested.