The science of the cord: how a rope bears weight and where it breaks
Pyramidal load, rupture under a rope's own weight, and breaking at the diameter
This folio (100r) sets out Leonardo's science of the cord (corda) as the link that transmits force in a straight line between a mover and a load, resisting all powers lesser than or equal to its own. He argues that a vertically hung rope carries its weight unevenly, 'pyramidally', bearing most where it meets its upper fastening, so that it can break under its own weight, and that the cord joined to the mover is more strained than the one joined to the load. A celebrated demonstration holds that a rope able to sustain 100 pounds is snapped by adding a single grain, and that rupture occurs across the shortest section, the diameter. Diagrams of pulleys with hanging weights (top right) and a lettered figure (bottom left) accompany the reasoning.
On this page
The cord as the link that transmits force between mover and load
The cord is a single connection extending in a straight line between the mover and the moved, resisting all powers lesser than or equal to its own. If its extension is straight, its power is 'pyramidal': at every degree of its height it acquires degrees of weakness, so that over a length of 4 degrees it suffers as 4 at the top, 3 at the second, 2 at the third, and nothing at the fourth.
A hanging cord breaks under its own weight at its highest point
A perpendicularly hung cord can break by the weight of itself, and the break occurs where it feels most weight, at the contact with its upper fastening. Two ends of equal length over a pulley are wearied equally, but once in motion the cord joined to the mover suffers a greater power than the one joined to the load. A loaded cord never feels its fatigue uniformly along its length, since the middle bears the weight of its lower half and the whole bears the weight of the whole.
A single grain breaks a cord loaded to its limit
Every thickest cord will be broken by a minimum added weight. If a cord can just sustain 100 pounds, those 100 pounds do not break it, but adding one grain will, for the excess of a single grain over the limit is what breaks it. The rupture is made at the shortest section found in the cord, that is, at its diameter.
Pulleys with hanging weights and lettered rupture figure
The page is illustrated with pulley figures from which weights hang, keyed by letters and numbers, and a small figure at the lower left labelled b, d, c, a. The accompanying note reasons that the rope will break at c d and not at b a, because b a would be a much greater rupture than c d.